Finite Group Databasebeta

← #17202102

Subgroups — #17202102

Order 4352.

3014 conjugacy classes of subgroups.

The subgroup lattice has 1724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763336C211yesmaximal, characteristic, complemented
2C22×#10587567C211yesmaximal, characteristic, complemented
3#14533050C211yesmaximal, characteristic, complemented
4#14533035C211yesmaximal, characteristic, complemented
5#14532930C211yesmaximal, characteristic, complemented
6#14532915C211yesmaximal, characteristic, complemented
7#14532836C211yesmaximal, characteristic, complemented
8#14532821C211yesmaximal, characteristic, complemented
9#14532737C211yesmaximal, characteristic, complemented
10#14532722C211yesmaximal, characteristic, complemented
11#14532606C211yesmaximal, characteristic, complemented
12#14532540C211yesmaximal, characteristic, complemented
13#14532445C211yesmaximal, characteristic, complemented
14#14532331C211yesmaximal, characteristic, complemented
15#14532265C211yesmaximal, characteristic, complemented
16#14532159C211yesmaximal, characteristic
17#14532111C211yesmaximal, characteristic, complemented
18#14532069C211yesmaximal, characteristic, complemented
19#14532046C211yesmaximal, characteristic, complemented
20#14532027C211yesmaximal, characteristic, complemented
21#14532023C211yesmaximal, characteristic, complemented
22#14531312C211yesmaximal, characteristic, complemented
23#14531301C211yesmaximal, characteristic, complemented
24#14531294C211yesmaximal, characteristic, complemented
25#14531289C211yesmaximal, characteristic, complemented
26#120×Dic17C211yesmaximal, characteristic, complemented
27#14531224C211yesmaximal, characteristic, complemented
28#14531220C211yesmaximal, characteristic, complemented
29#14531166C211yesmaximal, characteristic, complemented
30C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
31C17×#2412C211yesmaximal, characteristic, complemented
32C23×C22⋊D17C2211yescharacteristic
33C24×Dic17C2211yescharacteristic
34C23×C4×D17C2211yescharacteristic
35#11763336—28no—
36C2×#10587584C2211yescharacteristic, complemented
37C2×#10587565C2211yescharacteristic, complemented
38C2×#10587575C2211yescharacteristic, complemented
39C2×#10587571C2211yescharacteristic, complemented
40C2×#10587615C2211yescharacteristic
41C2×#10587615C2211yescharacteristic
42C2×#10587610C2211yescharacteristic
43C2×#10587564C2211yescharacteristic, complemented
44C2×#10587625C2211yescharacteristic
45C2×#10587625C2211yescharacteristic
46C2×#10587623C2211yescharacteristic
47C2×#10587573C2211yescharacteristic, complemented
48C2×D4×Dic17C2211yescharacteristic
49C2×D4×Dic17C2211yescharacteristic, complemented
50C2×D4×Dic17C2211yescharacteristic, complemented
51C2×#10587567—28no—
52C2×#10587567C2211yescharacteristic
53C2×#10587567C2211yescharacteristic
54C2×#10587567C2211yescharacteristic
55C2×#10587567C2211yescharacteristic
56C2×#10587567C2211yescharacteristic
57C2×#10587567C2211yescharacteristic
58C2×#10587567C2211yescharacteristic
59C2×#10587567C2211yescharacteristic
60C2×#10587567C2211yescharacteristic, complemented
61C2×#10587567C2211yescharacteristic, complemented
62C2×#10587578C2211yescharacteristic, complemented
63C2×#10587578C2211yescharacteristic, complemented
64C2×#10587563C2211yescharacteristic, complemented
65C22×#63225C2211yescharacteristic
66C22×C22⋊Dic17C2211yescharacteristic
67C22×#63227C2211yescharacteristic
68C22×C4×Dic17C2211yescharacteristic
69C22×C4×Dic17C2211yescharacteristic, complemented
70C22×C4×Dic17C2211yescharacteristic, complemented
71#11762750C2211yescharacteristic, complemented
72#11762750C2211yescharacteristic, complemented
73#11762749C2211yescharacteristic, complemented
74#11762745C2211yescharacteristic, complemented
75#11762743C2211yescharacteristic, complemented
76#11762740C2211yescharacteristic, complemented
77#11762739C2211yescharacteristic, complemented
78#11762738C2211yescharacteristic, complemented
79#11762738C2211yescharacteristic, complemented
80#11762737C2211yescharacteristic, complemented
81#11762736C2211yescharacteristic, complemented
82#11762735C2211yescharacteristic, complemented
83#11762732C2211yescharacteristic, complemented
84#11762732C2211yescharacteristic, complemented
85#11762732C2211yescharacteristic, complemented
86#11762731C2211yescharacteristic, complemented
87#11762725C2211yescharacteristic, complemented
88#11762724C2211yescharacteristic
89#11762724C2211yescharacteristic
90#11762724C2211yescharacteristic
91#11762724C2211yescharacteristic
92#11762724C2211yescharacteristic
93#11762724C2211yescharacteristic
94#11762724C2211yescharacteristic, complemented
95#11762722C2211yescharacteristic, complemented
96#11762721C2211yescharacteristic, complemented
97#11762717C2211yescharacteristic
98#11762717C2211yescharacteristic
99#11762714C2211yescharacteristic, complemented
100#11762709C2211yescharacteristic, complemented
101#11762706C2211yescharacteristic, complemented
102#11762705C2211yescharacteristic, complemented
103#11762703C2211yescharacteristic, complemented
104#11762701C2211yescharacteristic, complemented
105#11762701C2211yescharacteristic, complemented
106#11762699C2211yescharacteristic, complemented
107#11762698C2211yescharacteristic, complemented
108#11762698C2211yescharacteristic, complemented
109#11762697C2211yescharacteristic, complemented
110#11762697C2211yescharacteristic, complemented
111#11762696C2211yescharacteristic, complemented
112#11762694C2211yescharacteristic, complemented
113#11762692C2211yescharacteristic, complemented
114#11762691C2211yescharacteristic, complemented
115#11762691C2211yescharacteristic, complemented
116#11762691C2211yescharacteristic, complemented
117#11762691C2211yescharacteristic, complemented
118#11762690C2211yescharacteristic, complemented
119#11762689C2211yescharacteristic
120#11762689C2211yescharacteristic
121#11762689C2211yescharacteristic, complemented
122#11762689C2211yescharacteristic, complemented
123#11762688C2211yescharacteristic
124#11762688C2211yescharacteristic
125#11762686C2211yescharacteristic
126#11762686C2211yescharacteristic
127#11762685C2211yescharacteristic, complemented
128#11762685C2211yescharacteristic, complemented
129#11762684C2211yescharacteristic
130#11762684C2211yescharacteristic, complemented
131#11762684C2211yescharacteristic, complemented
132#11762684C2211yescharacteristic, complemented
133#11762683C2211yescharacteristic, complemented
134#11762683C2211yescharacteristic, complemented
135#11762682C2211yescharacteristic
136#11762682C2211yescharacteristic
137#11762681C2211yescharacteristic
138#11762681C2211yescharacteristic
139#11762681C2211yescharacteristic
140#11762681C2211yescharacteristic, complemented
141#11762671C2211yescharacteristic, complemented
142#11762671C2211yescharacteristic, complemented
143#11762669C2211yescharacteristic
144#11762667C2211yescharacteristic, complemented
145#11762666C2211yescharacteristic, complemented
146#11762666C2211yescharacteristic, complemented
147#11762665C2211yescharacteristic
148#11762664C2211yescharacteristic
149#11762664C2211yescharacteristic
150#11762664C2211yescharacteristic
151C4⋊C4×Dic17C2211yescharacteristic, complemented
152#11762660C2211yescharacteristic, complemented
153#11762660C2211yescharacteristic, complemented
154#11762660C2211yescharacteristic, complemented
155C22⋊C4×Dic17C2211yescharacteristic
156C22⋊C4×Dic17C2211yescharacteristic
157C22⋊C4×Dic17C2211yescharacteristic
158C22⋊C4×Dic17C2211yescharacteristic
159C22⋊C4×Dic17C2211yescharacteristic
160C22⋊C4×Dic17C2211yescharacteristic, complemented
161C22⋊C4×Dic17C2211yescharacteristic, complemented
162C22⋊C4×Dic17C2211yescharacteristic, complemented
163C22⋊C4×Dic17C2211yescharacteristic, complemented
164C22⋊C4×Dic17C2211yescharacteristic, complemented
165C22⋊C4×Dic17C2211yescharacteristic, complemented
166C22⋊C4×Dic17C2211yescharacteristic, complemented
167#11762656C2211yescharacteristic, complemented
168#11762656C2211yescharacteristic, complemented
169#11762656C2211yescharacteristic, complemented
170#11762656C2211yescharacteristic, complemented
171#11762654C2211yescharacteristic, complemented
172C2×#10587502C2211yescharacteristic, complemented
173C2×#10587502C2211yescharacteristic, complemented
174C2×C17×#123C2211yescharacteristic, complemented
175C2×C17×#120C2211yescharacteristic
176C22×C22⋊C4×C17C2211yescharacteristic
177C22×C22⋊C4×C17C2211yescharacteristic
178C17×#397C2211yescharacteristic, complemented
179C17×#397C2211yescharacteristic, complemented
180C17×#394C2211yescharacteristic, complemented
181C17×#394C2211yescharacteristic, complemented
182C17×#386C2211yescharacteristic
183C17×#386C2211yescharacteristic
184C17×#386C2211yescharacteristic, complemented
185C17×#385C2211yescharacteristic, complemented
186C17×#381C2211yescharacteristic, complemented
187C17×#380C2211yescharacteristic
188C17×#380C2211yescharacteristic
189C25×C17C2311yescharacteristic
190C24×D17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C23×C4×C17C2311yescharacteristic
197C23×C4×C17C2311yescharacteristic
198C22×C22⋊D17—24no—
199C22×C22⋊D17—24no—
200C22×C22⋊D17—24no—
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C22×C22⋊D17C2311yescharacteristic
205C22×C22⋊D17C2311yescharacteristic
206C22×C22⋊D17C2311yescharacteristic
207C23×Dic17—24no—
208C23×Dic17—24no—
209C23×Dic17—42no—
210C23×Dic17C2311yescharacteristic
211C23×Dic17C2311yescharacteristic
212C23×Dic17C2311yescharacteristic
213C23×Dic17C2311yescharacteristic
214C23×Dic17C2311yescharacteristic
215C23×Dic17C2311yescharacteristic
216C23×Dic17C2311yescharacteristic
217C23×Dic17C2311yescharacteristic
218C23×Dic17C2311yescharacteristic
219C23×Dic17C2311yescharacteristic
220C22×C4×D17—24no—
221C22×C4×D17—24no—
222C22×C4×D17—42no—
223C22×C4×D17C2311yescharacteristic
224C22×C4×D17C2311yescharacteristic
225C22×C4×D17C2311yescharacteristic
226C22×C4×D17C2311yescharacteristic
227C22×Dic34C2311yescharacteristic
228C17×#123—24no—
229C17×#120—24no—
230C2×C4⋊C4×C17C2311yescharacteristic
231C2×C4⋊C4×C17C2311yescharacteristic
232C2×C4⋊C4×C17C2311yescharacteristic
233C2×C4⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17—24no—
235C2×C22⋊C4×C17—24no—
236C2×C22⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239C2×C22⋊C4×C17C2311yescharacteristic
240C2×C22⋊C4×C17C2311yescharacteristic
241C2×C22⋊C4×C17C2311yescharacteristic
242C2×C22⋊C4×C17C2311yescharacteristic
243C2×C22⋊C4×C17C2311yescharacteristic
244C2×C22⋊C4×C17C2311yescharacteristic
245C2×C22⋊C4×C17C2311yescharacteristic
246C2×C22⋊C4×C17C2311yescharacteristic
247C2×C22⋊C4×C17C2311yescharacteristic
248C2×C22⋊C4×C17C2311yescharacteristic
249C2×C22⋊C4×C17C2311yescharacteristic
250C2×C22⋊C4×C17C2311yescharacteristic
251C2×C22⋊Dic17—24no—
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261C2×C22⋊Dic17C2311yescharacteristic
262C2×C22⋊Dic17C2311yescharacteristic
263C2×C22⋊Dic17C2311yescharacteristic
264C2×C22⋊Dic17C2311yescharacteristic
265C2×C22⋊Dic17C2311yescharacteristic
266C2×C22⋊Dic17C2311yescharacteristic
267#10587625—24no—
268#10587625—24no—
269#10587623—24no—
270D4×Dic17—24no—
271D4×Dic17—24no—
272D4×Dic17—42no—
273#10587615—24no—
274#10587615—24no—
275C2×#63227—24no—
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×#63227C2311yescharacteristic
292C2×#63227C2311yescharacteristic
293C2×#63227C2311yescharacteristic
294C2×C4⋊Dic17C2311yescharacteristic
295C2×C4⋊Dic17C2311yescharacteristic
296C2×C4⋊Dic17C2311yescharacteristic
297C2×C4⋊Dic17C2311yescharacteristic
298C2×C4⋊Dic17C2311yescharacteristic
299C2×C4⋊Dic17C2311yescharacteristic
300#10587610—24no—
301C2×#63225—24no—
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×#63225C2311yescharacteristic
317C2×#63225C2311yescharacteristic
318C2×C4×Dic17—24no—
319C2×C4×Dic17—24no—
320C2×C4×Dic17—42no—
321C2×C4×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323C2×C4×Dic17C2311yescharacteristic
324C2×C4×Dic17C2311yescharacteristic
325C2×C4×Dic17C2311yescharacteristic
326C2×C4×Dic17C2311yescharacteristic
327C2×C4×Dic17C2311yescharacteristic
328C2×C4×Dic17C2311yescharacteristic
329C2×C4×Dic17C2311yescharacteristic
330C2×C4×Dic17C2311yescharacteristic
331C2×C4×Dic17C2311yescharacteristic
332C2×C4×Dic17C2311yescharacteristic
333C2×C4×Dic17C2311yescharacteristic
334C2×C4×Dic17C2311yescharacteristic
335C2×C4×Dic17C2311yescharacteristic
336#10587584—24no—
337#10587578—24no—
338#10587578—42no—
339#10587575—24no—
340#10587573—24no—
341#10587571—24no—
342#10587567—24no—
343#10587567—24no—
344#10587567—24no—
345#10587567—24no—
346#10587567—24no—
347#10587567—24no—
348#10587567—24no—
349#10587567—24no—
350#10587567—42no—
351#10587567D418yescomplemented
352#10587565—24no—
353#10587564—24no—
354#10587563—24no—
355C17×#95C2311yescharacteristic
356C17×#95C2311yescharacteristic
357C17×#95C2311yescharacteristic
358C17×#95C2311yescharacteristic
359C17×#95C2311yescharacteristic
360C17×#95C2311yescharacteristic
361C17×#95C2311yescharacteristic
362C17×#95C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376#10587502C2311yescharacteristic
377#10587502C2311yescharacteristic
378#10587502C2311yescharacteristic
379#10587502C2311yescharacteristic
380#10587502C2311yescharacteristic
381#10587502C2311yescharacteristic
382#10587502C2311yescharacteristic
383#10587502C2311yescharacteristic
384#10587502C2311yescharacteristic
385#10587502C2311yescharacteristic
386#10587502C2311yescharacteristic
387#10587502C2311yescharacteristic
388#10587502C2311yescharacteristic
389#10587502C2311yescharacteristic
390#10587502C2311yescharacteristic
391C24×C17—22no—
392C24×C17—22no—
393C24×C17—22no—
394C24×C17—22no—
395C24×C17—41no—
396C24×C17—41no—
397C24×C17#4114yes—
398C24×C17C2411yescharacteristic
399C24×C17C2411yescharacteristic
400C24×C17C2411yescharacteristic
401C24×C17C2411yescharacteristic
402C23×D17—22no—
403C23×D17—22no—
404C23×D17—22no—
405C23×D17—22no—
406C23×D17—22no—
407C23×D17—41no—
408C23×D17—41no—
409C23×D17C2411yescharacteristic
410C23×D17C2411yescharacteristic
411C2×D4×C17—22no—
412C2×D4×C17—22no—
413C2×D4×C17—22no—
414C2×D4×C17—22no—
415C2×D4×C17—22no—
416C2×D4×C17—22no—
417C2×D4×C17—22no—
418C2×D4×C17—41no—
419C2×D4×C17—41no—
420C22×C4×C17—22no—
421C22×C4×C17—22no—
422C22×C4×C17—22no—
423C22×C4×C17—22no—
424C22×C4×C17—22no—
425C22×C4×C17—22no—
426C22×C4×C17—22no—
427C22×C4×C17—22no—
428C22×C4×C17—41no—
429C22×C4×C17—41no—
430C22×C4×C17—41no—
431C22×C4×C17—41no—
432C22×C4×C17C2411yescharacteristic
433C22×C4×C17C2411yescharacteristic
434C22×C4×C17C2411yescharacteristic
435C22×C4×C17C2411yescharacteristic
436C22×C4×C17C2411yescharacteristic
437C22×C4×C17C2411yescharacteristic
438C22×C4×C17C2411yescharacteristic
439C22×C4×C17C2411yescharacteristic
440C22×C4×C17C2411yescharacteristic
441C22×C4×C17C2411yescharacteristic
442C22×C4×C17C2411yescharacteristic
443C2×C22⋊D17—232no—
444C2×C22⋊D17—22no—
445C2×C22⋊D17—22no—
446C2×C22⋊D17—22no—
447C2×C22⋊D17—22no—
448C2×C22⋊D17—22no—
449C2×C22⋊D17—22no—
450C2×C22⋊D17—22no—
451C2×C22⋊D17—22no—
452C2×C22⋊D17—22no—
453C2×C22⋊D17—22no—
454C2×C22⋊D17—22no—
455C2×C22⋊D17—22no—
456C2×C22⋊D17—22no—
457C2×C22⋊D17—22no—
458C2×C22⋊D17—41no—
459C2×C22⋊D17—41no—
460C2×C22⋊D17C2×D414yes—
461C2×C22⋊D17#4114yes—
462C22×Dic17—22no—
463C22×Dic17—22no—
464C22×Dic17—22no—
465C22×Dic17—22no—
466C22×Dic17—22no—
467C22×Dic17—22no—
468C22×Dic17—22no—
469C22×Dic17—22no—
470C22×Dic17—22no—
471C22×Dic17—22no—
472C22×Dic17—22no—
473C22×Dic17—22no—
474C22×Dic17—22no—
475C22×Dic17—22no—
476C22×Dic17—22no—
477C22×Dic17—22no—
478C22×Dic17—22no—
479C22×Dic17—22no—
480C22×Dic17—22no—
481C22×Dic17—22no—
482C22×Dic17—22no—
483C22×Dic17—22no—
484C22×Dic17—22no—
485C22×Dic17—41no—
486C22×Dic17—41no—
487C22×Dic17—41no—
488C22×Dic17—41no—
489C22×Dic17—41no—
490C22×Dic17—416no—
491C22×Dic17C2×D414yes—
492C22×Dic17#4114yes—
493C22×Dic17C2411yescharacteristic
494C22×Dic17C2411yescharacteristic
495C22×Dic17C2411yescharacteristic
496C22×Dic17C2411yescharacteristic
497C22×Dic17C2411yescharacteristic
498C22×Dic17C2411yescharacteristic
499C22×Dic17C2411yescharacteristic
500C22×Dic17C2411yescharacteristic
501C22×Dic17C2411yescharacteristic
502C22×Dic17C2411yescharacteristic
503C22×Dic17C2411yescharacteristic
504C22×Dic17C2411yescharacteristic
505C22×Dic17C2411yescharacteristic
506C22×Dic17C2411yescharacteristic
507C2×C4×D17—22no—
508C2×C4×D17—22no—
509C2×C4×D17—22no—
510C2×C4×D17—22no—
511C2×C4×D17—22no—
512C2×C4×D17—22no—
513C2×C4×D17—22no—
514C2×C4×D17—22no—
515C2×C4×D17—22no—
516C2×C4×D17—416no—
517C2×C4×D17—41no—
518C2×C4×D17—41no—
519C2×C4×D17C2×D414yes—
520C2×Dic34—22no—
521C2×Dic34—22no—
522C2×Dic34—41no—
523C4⋊C4×C17—22no—
524C4⋊C4×C17—22no—
525C4⋊C4×C17—41no—
526C4⋊C4×C17—41no—
527C22⋊C4×C17—22no—
528C22⋊C4×C17—22no—
529C22⋊C4×C17—22no—
530C22⋊C4×C17—22no—
531C22⋊C4×C17—22no—
532C22⋊C4×C17—22no—
533C22⋊C4×C17—22no—
534C22⋊C4×C17—22no—
535C22⋊C4×C17—22no—
536C22⋊C4×C17—22no—
537C22⋊C4×C17—22no—
538C22⋊C4×C17—22no—
539C22⋊C4×C17—41no—
540C22⋊C4×C17—41no—
541C22⋊C4×C17C2×D414yes—
542C22⋊Dic17—22no—
543C22⋊Dic17—22no—
544C22⋊Dic17—22no—
545C22⋊Dic17—22no—
546C22⋊Dic17—22no—
547C22⋊Dic17—22no—
548C22⋊Dic17—22no—
549C22⋊Dic17—22no—
550C22⋊Dic17—22no—
551C22⋊Dic17—22no—
552C22⋊Dic17—22no—
553C22⋊Dic17—41no—
554C22⋊Dic17—41no—
555C22⋊Dic17—41no—
556C22⋊Dic17#4114yes—
557#63227—22no—
558#63227—22no—
559#63227—22no—
560#63227—22no—
561#63227—22no—
562#63227—22no—
563#63227—22no—
564#63227—22no—
565#63227—22no—
566#63227—22no—
567#63227—22no—
568#63227—41no—
569#63227—41no—
570#63227—41no—
571#63227—41no—
572#63227—41no—
573#63227—41no—
574#63227C2×D414yes—
575C4⋊Dic17—22no—
576C4⋊Dic17—22no—
577C4⋊Dic17—22no—
578C4⋊Dic17—22no—
579C4⋊Dic17—41no—
580C4⋊Dic17—41no—
581#63225—22no—
582#63225—22no—
583#63225—22no—
584#63225—22no—
585#63225—22no—
586#63225—22no—
587#63225—22no—
588#63225—22no—
589#63225—22no—
590#63225—22no—
591#63225—22no—
592#63225—22no—
593#63225—22no—
594#63225—41no—
595#63225—41no—
596#63225C2×D414yes—
597C4×Dic17—22no—
598C4×Dic17—22no—
599C4×Dic17—22no—
600C4×Dic17—22no—
601C4×Dic17—22no—
602C4×Dic17—22no—
603C4×Dic17—22no—
604C4×Dic17—22no—
605C4×Dic17—22no—
606C4×Dic17—22no—
607C4×Dic17—22no—
608C4×Dic17—22no—
609C4×Dic17—41no—
610C4×Dic17—41no—
611C4×Dic17C2×D414yes—
612#34670—171nomaximal, Sylow
613C23×C17—21no—
614C23×C17—21no—
615C23×C17—21no—
616C23×C17—21no—
617C23×C17—21no—
618C23×C17—21no—
619C23×C17—21no—
620C23×C17—21no—
621C23×C17—28no—
622C23×C17—28no—
623C23×C17—21no—
624C23×C17—21no—
625C23×C17—21no—
626C23×C17—21no—
627C23×C17—21no—
628C23×C17—21no—
629C23×C17—21no—
630C23×C17—21no—
631C23×C17—21no—
632C23×C17—21no—
633C23×C17—21no—
634C23×C17—21no—
635C23×C17—21no—
636C23×C17—44no—
637C23×C17—44no—
638C23×C17—44no—
639C23×C17—44no—
640C23×C17—44no—
641C23×C17C22×D412yes—
642C23×C17C2×#4112yes—
643C23×C17C2×#4112yes—
644C23×C17C2×#4112yes—
645C23×C17C2×#4112yes—
646C23×C17C2×#4112yes—
647C23×C17C2×#4112yes—
648C23×C17C2511yescharacteristic
649C22×D17—28no—
650C22×D17—21no—
651C22×D17—21no—
652C22×D17—21no—
653C22×D17—21no—
654C22×D17—21no—
655C22×D17—21no—
656C22×D17—21no—
657C22×D17—21no—
658C22×D17—21no—
659C22×D17—21no—
660C22×D17—21no—
661C22×D17—21no—
662C22×D17—44no—
663C22×D17—44no—
664C22×D17—44no—
665C22×D17—44no—
666C22×D17—44no—
667C22×D17—44no—
668C22×D17C22×D412yes—
669C22×D17C2×#4112yes—
670D4×C17—44no—
671D4×C17—44no—
672D4×C17—44no—
673C2×C4×C17—21no—
674C2×C4×C17—21no—
675C2×C4×C17—21no—
676C2×C4×C17—21no—
677C2×C4×C17—21no—
678C2×C4×C17—21no—
679C2×C4×C17—21no—
680C2×C4×C17—21no—
681C2×C4×C17—21no—
682C2×C4×C17—21no—
683C2×C4×C17—21no—
684C2×C4×C17—21no—
685C2×C4×C17—21no—
686C2×C4×C17—21no—
687C2×C4×C17—21no—
688C2×C4×C17—21no—
689C2×C4×C17—21no—
690C2×C4×C17—21no—
691C2×C4×C17—21no—
692C2×C4×C17—21no—
693C2×C4×C17—21no—
694C2×C4×C17—21no—
695C2×C4×C17—21no—
696C2×C4×C17—21no—
697C2×C4×C17—21no—
698C2×C4×C17—21no—
699C2×C4×C17—21no—
700C2×C4×C17—21no—
701C2×C4×C17—21no—
702C2×C4×C17—21no—
703C2×C4×C17—21no—
704C2×C4×C17—44no—
705C2×C4×C17—44no—
706C2×C4×C17—44no—
707C2×C4×C17—44no—
708C2×C4×C17C22×D412yes—
709C2×C4×C17C22×D412yes—
710C22⋊D17—28no—
711C22⋊D17—28no—
712C22⋊D17—28no—
713C22⋊D17—28no—
714C22⋊D17—44no—
715C22⋊D17—44no—
716C2×Dic17—28no—
717C2×Dic17—21no—
718C2×Dic17—21no—
719C2×Dic17—21no—
720C2×Dic17—21no—
721C2×Dic17—21no—
722C2×Dic17—21no—
723C2×Dic17—21no—
724C2×Dic17—21no—
725C2×Dic17—21no—
726C2×Dic17—21no—
727C2×Dic17—21no—
728C2×Dic17—21no—
729C2×Dic17—28no—
730C2×Dic17—28no—
731C2×Dic17—21no—
732C2×Dic17—21no—
733C2×Dic17—21no—
734C2×Dic17—21no—
735C2×Dic17—21no—
736C2×Dic17—21no—
737C2×Dic17—21no—
738C2×Dic17—21no—
739C2×Dic17—21no—
740C2×Dic17—21no—
741C2×Dic17—21no—
742C2×Dic17—21no—
743C2×Dic17—21no—
744C2×Dic17—21no—
745C2×Dic17—21no—
746C2×Dic17—21no—
747C2×Dic17—21no—
748C2×Dic17—21no—
749C2×Dic17—21no—
750C2×Dic17—21no—
751C2×Dic17—21no—
752C2×Dic17—44no—
753C2×Dic17—44no—
754C2×Dic17—44no—
755C2×Dic17—44no—
756C2×Dic17—44no—
757C2×Dic17—44no—
758C2×Dic17—44no—
759C2×Dic17C22×D412yes—
760C2×Dic17C22×D412yes—
761C2×Dic17C22×D412yes—
762C2×Dic17C2×#4112yes—
763C2×Dic17C2×#4112yes—
764C2×Dic17C2×#4112yes—
765C2×Dic17C2×#4112yes—
766C2×Dic17C2×#4112yes—
767C2×Dic17H(5,𝔽2)12yes—
768C4×D17—28no—
769C4×D17—44no—
770C4×D17—44no—
771C4×D17—44no—
772Dic34—44no—
773C2×#529—171no—
774C22×C4×D4—171no—
775#2481—171no—
776#2480—171no—
777#2473—171no—
778#2472—171no—
779#2467—171no—
780#2466—171no—
781#2460—171no—
782#2459—171no—
783#2450—171no—
784#2444—171no—
785#2437—171no—
786#2425—171no—
787#2419—171no—
788#2412D1711yescharacteristic, complemented
789#2410—171no—
790#2405—171no—
791#2398—171no—
792#2395—171no—
793#2392—171no—
794#2392—171no—
795C4×C22⋊Q8—171no—
796C4×#123—171no—
797C4×#121—171no—
798C4×#120—171no—
799C4×#120—171no—
800#2290—171no—
801#2290—171no—
802#2280—171no—
803C2×C4×C22⋊C4—171no—
804C22×C17—22no—
805C22×C17—22no—
806C22×C17—22no—
807C22×C17—22no—
808C22×C17—22no—
809C22×C17—22no—
810C22×C17—22no—
811C22×C17—22no—
812C22×C17—22no—
813C22×C17—22no—
814C22×C17—22no—
815C22×C17—22no—
816C22×C17—22no—
817C22×C17—22no—
818C22×C17—22no—
819C22×C17—416no—
820C22×C17—41no—
821C22×C17—41no—
822C22×C17—41no—
823C22×C17—41no—
824C22×C17—41no—
825C22×C17—41no—
826C22×C17—41no—
827C22×C17—41no—
828C22×C17—41no—
829C22×C17—41no—
830C22×C17—41no—
831C22×C17#52514yes—
832C22×C17#52914yescomplemented
833C22×C17C23×D411yescharacteristic
834C22×C17C22×#4111yescharacteristic
835C22×C17C22×#4111yescharacteristic
836C22×C17C22×#4111yescharacteristic
837C22×C17C22×#4111yescharacteristic
838C22×C17C2×H(5,𝔽2)11yescharacteristic
839C22×C17#58511yescharacteristic
840C2×D17—22no—
841C2×D17—22no—
842C2×D17—22no—
843C2×D17—22no—
844C2×D17—22no—
845C2×D17—22no—
846C2×D17—416no—
847C2×D17—41no—
848C2×D17—41no—
849C2×D17—41no—
850C2×D17—41no—
851C2×D17—41no—
852C2×D17—41no—
853C2×D17—41no—
854C2×D17—41no—
855C4×C17—22no—
856C4×C17—22no—
857C4×C17—41no—
858C4×C17—41no—
859C4×C17—41no—
860C4×C17—41no—
861C4×C17—41no—
862C4×C17—41no—
863C4×C17—41no—
864C4×C17—41no—
865C4×C17—41no—
866Dic17—22no—
867Dic17—22no—
868Dic17—22no—
869Dic17—22no—
870Dic17—22no—
871Dic17—22no—
872Dic17—41no—
873Dic17—41no—
874Dic17—41no—
875Dic17—41no—
876Dic17—41no—
877Dic17—41no—
878Dic17—41no—
879Dic17#54614yes—
880C23×D4—171no—
881C24×C4—171no—
882C24×C4—171no—
883#529—348no—
884C2×#126—171no—
885C2×#126—171no—
886C2×#125—171no—
887C2×#124—171no—
888C2×#123—171no—
889C2×#123—171no—
890C2×#123C2×D1711yescharacteristic, complemented
891C2×C22⋊Q8—171no—
892C2×C22⋊Q8—171no—
893C2×#121—171no—
894C2×#121—171no—
895C2×#120—171no—
896C2×#120C2×D1711yescharacteristic
897C2×C4×Q8—171no—
898C2×C4×D4—171no—
899C2×C4×D4—171no—
900C2×C4×D4—171no—
901C2×C4×D4—171no—
902C2×C4×D4—171no—
903C2×C4×D4—171no—
904C2×C4×D4—171no—
905C2×C4×D4—171no—
906C2×C4×D4—171no—
907C2×C4×D4—171no—
908C2×C4×D4—171no—
909C2×C4×D4—171no—
910C2×C4×D4—171no—
911C2×C4×D4—348no—
912C2×#117—171no—
913C2×#117—171no—
914C2×#117—171no—
915C22×C4⋊C4—171no—
916C22×C22⋊C4—171no—
917C22×C22⋊C4—171no—
918C22×C22⋊C4C2×D1711yescharacteristic
919C22×C22⋊C4C2×D1711yescharacteristic
920C22×C42—171no—
921C22×C42—171no—
922C22×C42—171no—
923#400—171no—
924#400—171no—
925#400—171no—
926#399—171no—
927#398—171no—
928#398—171no—
929#398—171no—
930#397—171no—
931#397—171no—
932#397—171no—
933#397—171no—
934#397—171no—
935#397C2×D1711yescharacteristic, complemented
936#397C2×D1711yescharacteristic, complemented
937#396—171no—
938#396—171no—
939#396—171no—
940#396—171no—
941#394—171no—
942#394—171no—
943#394—171no—
944#394—171no—
945#394—171no—
946#394—171no—
947#394—171no—
948#394—171no—
949#394C2×D1711yescharacteristic, complemented
950#394C2×D1711yescharacteristic, complemented
951#393—171no—
952#393—171no—
953#392—171no—
954#392—171no—
955#391—171no—
956#390—171no—
957#389—171no—
958#389—171no—
959#388—171no—
960#388—171no—
961#388—171no—
962#388—171no—
963#388—171no—
964#388—171no—
965#388—171no—
966#388—171no—
967#387—171no—
968#387—171no—
969#387—171no—
970#387—171no—
971#387—171no—
972#387—171no—
973#387—171no—
974#387—171no—
975#386—171no—
976#386—171no—
977#386—171no—
978#386—171no—
979#386—171no—
980#386—171no—
981#386—171no—
982#386—171no—
983#386—171no—
984#386—171no—
985#386C2×D1711yescharacteristic
986#386C2×D1711yescharacteristic
987#386C2×D1711yescharacteristic, complemented
988#385—171no—
989#385—171no—
990#385—171no—
991#385—171no—
992#385—171no—
993#385—171no—
994#385—171no—
995#385—171no—
996#385—171no—
997#385—171no—
998#385—171no—
999#385—171no—
1000#385C2×D1711yescharacteristic, complemented
1001#381—171no—
1002#381—171no—
1003#381C2×D1711yescharacteristic, complemented
1004#380—171no—
1005#380—171no—
1006#380—171no—
1007#380—171no—
1008#380C2×D1711yescharacteristic
1009#380C2×D1711yescharacteristic
1010#379—171no—
1011#379—171no—
1012#379—171no—
1013#379—171no—
1014C4×C4⋊C4—171no—
1015C4×C4⋊C4—171no—
1016C4×C4⋊C4—171no—
1017C4×C4⋊C4—171no—
1018C4×C22⋊C4—171no—
1019C4×C22⋊C4—171no—
1020C4×C22⋊C4—171no—
1021C4×C22⋊C4—171no—
1022C4×C22⋊C4—171no—
1023C4×C22⋊C4—171no—
1024C4×C22⋊C4—171no—
1025C4×C22⋊C4—171no—
1026C4×C22⋊C4—171no—
1027C4×C22⋊C4—171no—
1028C4×C22⋊C4—171no—
1029C4×C22⋊C4—171no—
1030C4×C22⋊C4—171no—
1031C4×C22⋊C4—171no—
1032C4×C22⋊C4—171no—
1033C4×C22⋊C4—171no—
1034#376—171no—
1035C2×#95—171no—
1036C2×#95—171no—
1037C2×C17—24no—
1038C2×C17—24no—
1039C2×C17—42no—
1040C2×C17—81no—
1041C2×C17C2×#52511yescharacteristic
1042C2×C17C2×#52911yescharacteristic
1043C2×C17#345911yescharacteristic
1044C2×C17C2×#54611yescharacteristic
1045C2×C17D4×#4111yescharacteristic
1046C2×C17#347511yescharacteristic
1047C2×C17#348111yescharacteristic
1048D17—42no—
1049D17—42no—
1050C25—171no—
1051C25C22×D1711yescharacteristic
1052C22×Q8—171no—
1053C22×D4—171no—
1054C22×D4—171no—
1055C22×D4—171no—
1056C22×D4—171no—
1057C22×D4—171no—
1058C22×D4—171no—
1059C22×D4—344no—
1060C22×D4—344no—
1061C22×D4—344no—
1062C22×D4C22×D1711yescharacteristic
1063C22×D4C22×D1711yescharacteristic
1064C22×D4C22×D1711yescharacteristic
1065C23×C4—171no—
1066C23×C4—171no—
1067C23×C4—171no—
1068C23×C4—171no—
1069C23×C4—171no—
1070C23×C4—171no—
1071C23×C4—171no—
1072C23×C4—171no—
1073C23×C4—171no—
1074C23×C4—171no—
1075C23×C4—171no—
1076C23×C4—171no—
1077C23×C4—171no—
1078C23×C4—171no—
1079C23×C4—344no—
1080C23×C4—344no—
1081C23×C4—344no—
1082C23×C4—344no—
1083C23×C4—682no—
1084C23×C4—682no—
1085C23×C4C22×D1711yescharacteristic
1086C23×C4C22×D1711yescharacteristic
1087C23×C4C22×D1711yescharacteristic
1088C23×C4C22×D1711yescharacteristic
1089#126—344no—
1090#126—344no—
1091#125—344no—
1092#124—344no—
1093#123—24no—
1094#123—344no—
1095#123—344no—
1096C22⋊Q8—344no—
1097C22⋊Q8—344no—
1098#121—344no—
1099#121—344no—
1100#120—24no—
1101#120—344no—
1102C4×Q8—344no—
1103C4×D4—178no—
1104C4×D4—344no—
1105C4×D4—344no—
1106C4×D4—344no—
1107C4×D4—344no—
1108C4×D4—344no—
1109C4×D4—344no—
1110C4×D4—344no—
1111C4×D4—344no—
1112C4×D4—344no—
1113C4×D4—344no—
1114C4×D4—682no—
1115C4×D4—682no—
1116#117—344no—
1117#117—344no—
1118#117—682no—
1119C2×C4⋊C4—171no—
1120C2×C4⋊C4—171no—
1121C2×C4⋊C4—171no—
1122C2×C4⋊C4—171no—
1123C2×C4⋊C4—171no—
1124C2×C4⋊C4—171no—
1125C2×C4⋊C4—171no—
1126C2×C4⋊C4—171no—
1127C2×C4⋊C4—171no—
1128C2×C4⋊C4—171no—
1129C2×C4⋊C4—171no—
1130C2×C4⋊C4—171no—
1131C2×C4⋊C4—171no—
1132C2×C4⋊C4—171no—
1133C2×C4⋊C4—171no—
1134C2×C4⋊C4—171no—
1135C2×C4⋊C4—171no—
1136C2×C4⋊C4—171no—
1137C2×C4⋊C4—171no—
1138C2×C4⋊C4—171no—
1139C2×C4⋊C4—171no—
1140C2×C4⋊C4—171no—
1141C2×C4⋊C4—344no—
1142C2×C4⋊C4C22×D1711yescharacteristic
1143C2×C4⋊C4C22×D1711yescharacteristic
1144C2×C4⋊C4C22×D1711yescharacteristic
1145C2×C4⋊C4C22×D1711yescharacteristic
1146C2×C22⋊C4—24no—
1147C2×C22⋊C4—24no—
1148C2×C22⋊C4—171no—
1149C2×C22⋊C4—171no—
1150C2×C22⋊C4—171no—
1151C2×C22⋊C4—171no—
1152C2×C22⋊C4—171no—
1153C2×C22⋊C4—171no—
1154C2×C22⋊C4—171no—
1155C2×C22⋊C4—171no—
1156C2×C22⋊C4—171no—
1157C2×C22⋊C4—171no—
1158C2×C22⋊C4—171no—
1159C2×C22⋊C4—171no—
1160C2×C22⋊C4—171no—
1161C2×C22⋊C4—171no—
1162C2×C22⋊C4—171no—
1163C2×C22⋊C4—171no—
1164C2×C22⋊C4—171no—
1165C2×C22⋊C4—171no—
1166C2×C22⋊C4—171no—
1167C2×C22⋊C4—171no—
1168C2×C22⋊C4—171no—
1169C2×C22⋊C4—171no—
1170C2×C22⋊C4—171no—
1171C2×C22⋊C4—171no—
1172C2×C22⋊C4—171no—
1173C2×C22⋊C4—171no—
1174C2×C22⋊C4—171no—
1175C2×C22⋊C4—171no—
1176C2×C22⋊C4—171no—
1177C2×C22⋊C4—171no—
1178C2×C22⋊C4—171no—
1179C2×C22⋊C4—171no—
1180C2×C22⋊C4—171no—
1181C2×C22⋊C4—344no—
1182C2×C22⋊C4—344no—
1183C2×C22⋊C4C22×D1711yescharacteristic
1184C2×C22⋊C4C22×D1711yescharacteristic
1185C2×C22⋊C4C22×D1711yescharacteristic
1186C2×C22⋊C4C22×D1711yescharacteristic
1187C2×C22⋊C4C22×D1711yescharacteristic
1188C2×C22⋊C4C22×D1711yescharacteristic
1189C2×C22⋊C4C22×D1711yescharacteristic
1190C2×C22⋊C4C22×D1711yescharacteristic
1191C2×C22⋊C4C22×D1711yescharacteristic
1192C2×C22⋊C4C22×D1711yescharacteristic
1193C2×C22⋊C4C22×D1711yescharacteristic
1194C2×C22⋊C4C22×D1711yescharacteristic
1195C2×C22⋊C4C22×D1711yescharacteristic
1196C2×C22⋊C4C22×D1711yescharacteristic
1197C2×C22⋊C4C22×D1711yescharacteristic
1198C2×C42—171no—
1199C2×C42—171no—
1200C2×C42—171no—
1201C2×C42—171no—
1202C2×C42—171no—
1203C2×C42—171no—
1204C2×C42—171no—
1205C2×C42—171no—
1206C2×C42—171no—
1207C2×C42—171no—
1208C2×C42—171no—
1209C2×C42—171no—
1210C2×C42—171no—
1211C2×C42—171no—
1212C2×C42—171no—
1213C2×C42—344no—
1214C2×C42—344no—
1215C2×C42—682no—
1216#95—171no—
1217#95—171no—
1218#95—171no—
1219#95—171no—
1220#95—171no—
1221#95—171no—
1222#95—171no—
1223#95—171no—
1224#95—171no—
1225#95—171no—
1226#95—171no—
1227#95—171no—
1228#95—171no—
1229#95—171no—
1230#95—171no—
1231#95—171no—
1232#95—171no—
1233#95—171no—
1234#95—171no—
1235#95—171no—
1236#95—171no—
1237#95—171no—
1238#95—171no—
1239#95—171no—
1240#95—171no—
1241#95—171no—
1242#95—171no—
1243#95—171no—
1244#95C22×D1711yescharacteristic
1245#95C22×D1711yescharacteristic
1246#95C22×D1711yescharacteristic
1247#95C22×D1711yescharacteristic
1248#95C22×D1711yescharacteristic
1249#95C22×D1711yescharacteristic
1250#95C22×D1711yescharacteristic
1251#95C22×D1711yescharacteristic
1252C17#3467011yescharacteristic, complemented, Sylow
1253C24—22no—
1254C24—22no—
1255C24—22no—
1256C24—22no—
1257C24—41no—
1258C24—41no—
1259C24—171no—
1260C24—171no—
1261C24—342no—
1262C24—342no—
1263C24—342no—
1264C24—342no—
1265C24—342no—
1266C24—681no—
1267C24—681no—
1268C24#6325414yes—
1269C24C23×D1711yescharacteristic
1270C24C23×D1711yescharacteristic
1271C24C23×D1711yescharacteristic
1272C24C23×D1711yescharacteristic
1273C2×Q8—342no—
1274C2×Q8—342no—
1275C2×Q8—681no—
1276C2×D4—22no—
1277C2×D4—22no—
1278C2×D4—22no—
1279C2×D4—22no—
1280C2×D4—22no—
1281C2×D4—22no—
1282C2×D4—22no—
1283C2×D4—41no—
1284C2×D4—41no—
1285C2×D4—174no—
1286C2×D4—174no—
1287C2×D4—342no—
1288C2×D4—342no—
1289C2×D4—342no—
1290C2×D4—342no—
1291C2×D4—342no—
1292C2×D4—342no—
1293C2×D4—3432no—
1294C2×D4—342no—
1295C2×D4—342no—
1296C2×D4—342no—
1297C2×D4—342no—
1298C2×D4—342no—
1299C2×D4—342no—
1300C2×D4—342no—
1301C2×D4—342no—
1302C2×D4—681no—
1303C2×D4—681no—
1304C22×C4—22no—
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—22no—
1311C22×C4—22no—
1312C22×C4—41no—
1313C22×C4—41no—
1314C22×C4—41no—
1315C22×C4—41no—
1316C22×C4—171no—
1317C22×C4—174no—
1318C22×C4—174no—
1319C22×C4—171no—
1320C22×C4—171no—
1321C22×C4—171no—
1322C22×C4—171no—
1323C22×C4—171no—
1324C22×C4—171no—
1325C22×C4—174no—
1326C22×C4—171no—
1327C22×C4—171no—
1328C22×C4—171no—
1329C22×C4—171no—
1330C22×C4—171no—
1331C22×C4—171no—
1332C22×C4—171no—
1333C22×C4—342no—
1334C22×C4—342no—
1335C22×C4—342no—
1336C22×C4—342no—
1337C22×C4—342no—
1338C22×C4—342no—
1339C22×C4—342no—
1340C22×C4—342no—
1341C22×C4—342no—
1342C22×C4—342no—
1343C22×C4—342no—
1344C22×C4—342no—
1345C22×C4—342no—
1346C22×C4—342no—
1347C22×C4—342no—
1348C22×C4—342no—
1349C22×C4—342no—
1350C22×C4—342no—
1351C22×C4—342no—
1352C22×C4—342no—
1353C22×C4—342no—
1354C22×C4—342no—
1355C22×C4—342no—
1356C22×C4—342no—
1357C22×C4—342no—
1358C22×C4—342no—
1359C22×C4—342no—
1360C22×C4—342no—
1361C22×C4—342no—
1362C22×C4—342no—
1363C22×C4—342no—
1364C22×C4—342no—
1365C22×C4—681no—
1366C22×C4—681no—
1367C22×C4—6816no—
1368C22×C4—681no—
1369C22×C4—681no—
1370C22×C4—681no—
1371C22×C4—681no—
1372C22×C4—681no—
1373C22×C4—6816no—
1374C22×C4C23×D1711yescharacteristic
1375C22×C4C23×D1711yescharacteristic
1376C22×C4C23×D1711yescharacteristic
1377C22×C4C23×D1711yescharacteristic
1378C22×C4C23×D1711yescharacteristic
1379C22×C4C23×D1711yescharacteristic
1380C22×C4C23×D1711yescharacteristic
1381C22×C4C23×D1711yescharacteristic
1382C22×C4C23×D1711yescharacteristic
1383C22×C4C23×D1711yescharacteristic
1384C22×C4C23×D1711yescharacteristic
1385C4⋊C4—22no—
1386C4⋊C4—22no—
1387C4⋊C4—41no—
1388C4⋊C4—41no—
1389C4⋊C4—174no—
1390C4⋊C4—342no—
1391C4⋊C4—342no—
1392C4⋊C4—342no—
1393C4⋊C4—342no—
1394C4⋊C4—342no—
1395C4⋊C4—342no—
1396C4⋊C4—342no—
1397C4⋊C4—342no—
1398C4⋊C4—342no—
1399C4⋊C4—342no—
1400C4⋊C4—342no—
1401C4⋊C4—342no—
1402C4⋊C4—342no—
1403C4⋊C4—342no—
1404C4⋊C4—342no—
1405C4⋊C4—342no—
1406C4⋊C4—342no—
1407C4⋊C4—681no—
1408C4⋊C4—681no—
1409C4⋊C4—681no—
1410C4⋊C4—681no—
1411C22⋊C4—22no—
1412C22⋊C4—22no—
1413C22⋊C4—22no—
1414C22⋊C4—22no—
1415C22⋊C4—22no—
1416C22⋊C4—22no—
1417C22⋊C4—22no—
1418C22⋊C4—22no—
1419C22⋊C4—22no—
1420C22⋊C4—22no—
1421C22⋊C4—22no—
1422C22⋊C4—22no—
1423C22⋊C4—41no—
1424C22⋊C4—41no—
1425C22⋊C4—174no—
1426C22⋊C4—174no—
1427C22⋊C4—342no—
1428C22⋊C4—342no—
1429C22⋊C4—342no—
1430C22⋊C4—342no—
1431C22⋊C4—342no—
1432C22⋊C4—342no—
1433C22⋊C4—342no—
1434C22⋊C4—342no—
1435C22⋊C4—342no—
1436C22⋊C4—342no—
1437C22⋊C4—342no—
1438C22⋊C4—342no—
1439C22⋊C4—342no—
1440C22⋊C4—342no—
1441C22⋊C4—342no—
1442C22⋊C4—342no—
1443C22⋊C4—342no—
1444C22⋊C4—342no—
1445C22⋊C4—342no—
1446C22⋊C4—342no—
1447C22⋊C4—342no—
1448C22⋊C4—342no—
1449C22⋊C4—681no—
1450C22⋊C4—681no—
1451C22⋊C4—681no—
1452C22⋊C4—681no—
1453C22⋊C4—681no—
1454C22⋊C4—681no—
1455C22⋊C4—681no—
1456C22⋊C4—681no—
1457C22⋊C4—681no—
1458C22⋊C4D4×D1714yes—
1459C42—174no—
1460C42—342no—
1461C42—342no—
1462C42—342no—
1463C42—342no—
1464C42—342no—
1465C42—342no—
1466C42—342no—
1467C42—342no—
1468C42—342no—
1469C42—342no—
1470C42—342no—
1471C42—342no—
1472C42—681no—
1473C42—681no—
1474C23—21no—
1475C23—21no—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—21no—
1480C23—21no—
1481C23—21no—
1482C23—28no—
1483C23—28no—
1484C23—21no—
1485C23—21no—
1486C23—21no—
1487C23—21no—
1488C23—21no—
1489C23—21no—
1490C23—21no—
1491C23—21no—
1492C23—21no—
1493C23—21no—
1494C23—21no—
1495C23—21no—
1496C23—21no—
1497C23—44no—
1498C23—44no—
1499C23—44no—
1500C23—44no—
1501C23—44no—
1502C23—172no—
1503C23—172no—
1504C23—348no—
1505C23—341no—
1506C23—341no—
1507C23—341no—
1508C23—341no—
1509C23—341no—
1510C23—341no—
1511C23—341no—
1512C23—341no—
1513C23—341no—
1514C23—341no—
1515C23—341no—
1516C23—341no—
1517C23—684no—
1518C23—684no—
1519C23—684no—
1520C23—684no—
1521C23—684no—
1522C23—684no—
1523C23C2×D4×D1712yes—
1524C23C2×#6325412yes—
1525C23C2×#6325412yes—
1526C23C2×#6325412yes—
1527C23#41×D1712yes—
1528C23#41×D1712yes—
1529C23#41×D1712yes—
1530C23C24×D1711yescharacteristic
1531Q8—684no—
1532D4—44no—
1533D4—44no—
1534D4—44no—
1535D4—348no—
1536D4—348no—
1537D4—348no—
1538D4—348no—
1539D4—684no—
1540D4—684no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—21no—
1565C2×C4—21no—
1566C2×C4—21no—
1567C2×C4—21no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—44no—
1573C2×C4—44no—
1574C2×C4—44no—
1575C2×C4—44no—
1576C2×C4—172no—
1577C2×C4—172no—
1578C2×C4—172no—
1579C2×C4—172no—
1580C2×C4—172no—
1581C2×C4—172no—
1582C2×C4—172no—
1583C2×C4—172no—
1584C2×C4—172no—
1585C2×C4—348no—
1586C2×C4—348no—
1587C2×C4—348no—
1588C2×C4—348no—
1589C2×C4—341no—
1590C2×C4—341no—
1591C2×C4—341no—
1592C2×C4—341no—
1593C2×C4—341no—
1594C2×C4—341no—
1595C2×C4—341no—
1596C2×C4—341no—
1597C2×C4—341no—
1598C2×C4—341no—
1599C2×C4—341no—
1600C2×C4—341no—
1601C2×C4—341no—
1602C2×C4—341no—
1603C2×C4—341no—
1604C2×C4—341no—
1605C2×C4—341no—
1606C2×C4—341no—
1607C2×C4—341no—
1608C2×C4—341no—
1609C2×C4—341no—
1610C2×C4—341no—
1611C2×C4—341no—
1612C2×C4—341no—
1613C2×C4—341no—
1614C2×C4—341no—
1615C2×C4—341no—
1616C2×C4—341no—
1617C2×C4—341no—
1618C2×C4—341no—
1619C2×C4—341no—
1620C2×C4—341no—
1621C2×C4—341no—
1622C2×C4—684no—
1623C2×C4—684no—
1624C2×C4—684no—
1625C2×C4—684no—
1626C2×C4—684no—
1627C2×C4—684no—
1628C2×C4—684no—
1629C2×C4—684no—
1630C2×C4—684no—
1631C2×C4—684no—
1632C2×C4C2×D4×D1712yes—
1633C2×C4C2×D4×D1712yes—
1634C22—22no—
1635C22—22no—
1636C22—22no—
1637C22—22no—
1638C22—22no—
1639C22—22no—
1640C22—22no—
1641C22—22no—
1642C22—22no—
1643C22—22no—
1644C22—22no—
1645C22—22no—
1646C22—22no—
1647C22—22no—
1648C22—22no—
1649C22—416no—
1650C22—41no—
1651C22—41no—
1652C22—41no—
1653C22—41no—
1654C22—41no—
1655C22—41no—
1656C22—41no—
1657C22—41no—
1658C22—41no—
1659C22—41no—
1660C22—41no—
1661C22—342no—
1662C22—342no—
1663C22—342no—
1664C22—342no—
1665C22—342no—
1666C22—342no—
1667C22—6816no—
1668C22—681no—
1669C22—681no—
1670C22—681no—
1671C22—681no—
1672C22—681no—
1673C22—681no—
1674C22—681no—
1675C22—681no—
1676C22#1176331914yes—
1677C22#1176333614yescomplemented
1678C22C22×D4×D1711yescharacteristic
1679C22C2×#41×D1711yescharacteristic
1680C22C2×#41×D1711yescharacteristic
1681C22C2×#41×D1711yescharacteristic
1682C22C22×#6325411yescharacteristic
1683C22H(5,𝔽2)×D1711yescharacteristic
1684C22#1176364411yescharacteristic
1685C4—22no—
1686C4—22no—
1687C4—41no—
1688C4—41no—
1689C4—41no—
1690C4—41no—
1691C4—41no—
1692C4—41no—
1693C4—41no—
1694C4—41no—
1695C4—41no—
1696C4—174no—
1697C4—342no—
1698C4—342no—
1699C4—342no—
1700C4—342no—
1701C4—342no—
1702C4—342no—
1703C4—681no—
1704C4—681no—
1705C4—681no—
1706C4—681no—
1707C4—681no—
1708C4—681no—
1709C4—681no—
1710C2—24no—
1711C2—24no—
1712C2—42no—
1713C2—81no—
1714C2—682no—
1715C2—682no—
1716C2C2×#1176331911yescharacteristic
1717C2C2×#1176333611yescharacteristic
1718C2#1454219011yescharacteristic
1719C2D17×#54611yescharacteristic
1720C2#1454226811yescharacteristic
1721C2#1454233911yescharacteristic
1722C2#1454238711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2412C2
prime radical#14532159C2
hypercenter#2412D17
hypocenterC17#34670
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2412

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#11763336C2semidirect
2. C22×#10587567C2semidirect
3. #14533050C2semidirect
4. #14533035C2semidirect
5. #14532930C2semidirect
6. #14532915C2semidirect
7. #14532836C2semidirect
8. #14532821C2semidirect
9. #14532737C2semidirect
10. #14532722C2semidirect
11. #14532606C2semidirect
12. #14532540C2semidirect
13. #14532445C2semidirect
14. #14532331C2semidirect
15. #14532265C2semidirect
17. #14532111C2semidirect
18. #14532069C2semidirect
19. #14532046C2semidirect
20. #14532027C2semidirect
21. #14532023C2semidirect
22. #14531312C2semidirect
23. #14531301C2semidirect
24. #14531294C2semidirect
25. #14531289C2semidirect
26. #120×Dic17C2semidirect
27. #14531224C2semidirect
28. #14531220C2semidirect
29. #14531166C2semidirect
30. C2×C22⋊C4×Dic17C2semidirect
31. C17×#2412C2semidirect
36. C2×#10587584C22semidirect
37. C2×#10587565C22semidirect
38. C2×#10587575C22semidirect
39. C2×#10587571C22semidirect
43. C2×#10587564C22semidirect
47. C2×#10587573C22semidirect
49. C2×D4×Dic17C22semidirect
50. C2×D4×Dic17C22semidirect
60. C2×#10587567C22semidirect
61. C2×#10587567C22semidirect
62. C2×#10587578C22semidirect
63. C2×#10587578C22semidirect
64. C2×#10587563C22semidirect
69. C22×C4×Dic17C22semidirect
70. C22×C4×Dic17C22semidirect
71. #11762750C22semidirect
72. #11762750C22semidirect
73. #11762749C22semidirect
74. #11762745C22semidirect
75. #11762743C22semidirect
76. #11762740C22semidirect
77. #11762739C22semidirect
78. #11762738C22semidirect
79. #11762738C22semidirect
80. #11762737C22semidirect
81. #11762736C22semidirect
82. #11762735C22semidirect
83. #11762732C22semidirect
84. #11762732C22semidirect
85. #11762732C22semidirect
86. #11762731C22semidirect
87. #11762725C22semidirect
94. #11762724C22semidirect
95. #11762722C22semidirect
96. #11762721C22semidirect
99. #11762714C22semidirect
100. #11762709C22semidirect
101. #11762706C22semidirect
102. #11762705C22semidirect
103. #11762703C22semidirect
104. #11762701C22semidirect
105. #11762701C22semidirect
106. #11762699C22semidirect
107. #11762698C22semidirect
108. #11762698C22semidirect
109. #11762697C22semidirect
110. #11762697C22semidirect
111. #11762696C22semidirect
112. #11762694C22semidirect
113. #11762692C22semidirect
114. #11762691C22semidirect
115. #11762691C22semidirect
116. #11762691C22semidirect
117. #11762691C22semidirect
118. #11762690C22semidirect
121. #11762689C22semidirect
122. #11762689C22semidirect
127. #11762685C22semidirect
128. #11762685C22semidirect
130. #11762684C22semidirect
131. #11762684C22semidirect
132. #11762684C22semidirect
133. #11762683C22semidirect
134. #11762683C22semidirect
140. #11762681C22semidirect
141. #11762671C22semidirect
142. #11762671C22semidirect
144. #11762667C22semidirect
145. #11762666C22semidirect
146. #11762666C22semidirect
151. C4⋊C4×Dic17C22semidirect
152. #11762660C22semidirect
153. #11762660C22semidirect
154. #11762660C22semidirect
160. C22⋊C4×Dic17C22semidirect
161. C22⋊C4×Dic17C22semidirect
162. C22⋊C4×Dic17C22semidirect
163. C22⋊C4×Dic17C22semidirect
164. C22⋊C4×Dic17C22semidirect
165. C22⋊C4×Dic17C22semidirect
166. C22⋊C4×Dic17C22semidirect
167. #11762656C22semidirect
168. #11762656C22semidirect
169. #11762656C22semidirect
170. #11762656C22semidirect
171. #11762654C22semidirect
172. C2×#10587502C22semidirect
173. C2×#10587502C22semidirect
174. C2×C17×#123C22semidirect
178. C17×#397C22semidirect
179. C17×#397C22semidirect
180. C17×#394C22semidirect
181. C17×#394C22semidirect
184. C17×#386C22semidirect
185. C17×#385C22semidirect
186. C17×#381C22semidirect
351. #10587567D4semidirect
788. #2412D17semidirect
832. C22×C17#529semidirect
890. C2×#123C2×D17semidirect
935. #397C2×D17semidirect
936. #397C2×D17semidirect
949. #394C2×D17semidirect
950. #394C2×D17semidirect
987. #386C2×D17semidirect
1000. #385C2×D17semidirect
1003. #381C2×D17semidirect
1252. C17#34670semidirect
1677. C22#11763336semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117633362
C22×#105875672
#145330502
#145330352
#145329302
#145329152
#145328362
#145328212
#145327372
#145327222
#145326062
#145325402
#145324452
#145323312
#145322652
#145321592
#145321112
#145320692
#145320462
#145320272
#145320232
#145313122
#145313012
#145312942
#145312892
#120×Dic172
#145312242
#145312202
#145311662
C2×C22⋊C4×Dic172
C17×#24122
#3467017