Finite Group Databasebeta

← #17204503

Subgroups — #17204503

Order 4352.

2804 conjugacy classes of subgroups.

The subgroup lattice has 1708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763342C211yesmaximal, characteristic, complemented
2C2×#11763317C211yesmaximal, characteristic, complemented
3#14533926C211yesmaximal, characteristic, complemented
4#14533919C211yesmaximal, characteristic, complemented
5#14533894C211yesmaximal, characteristic, complemented
6#14533887C211yesmaximal, characteristic, complemented
7#14533862C211yesmaximal, characteristic, complemented
8#14533858C211yesmaximal, characteristic, complemented
9#14533829C211yesmaximal, characteristic, complemented
10#14533791C211yesmaximal, characteristic, complemented
11#14533747C211yesmaximal, characteristic, complemented
12#14533709C211yesmaximal, characteristic, complemented
13#14533675C211yesmaximal, characteristic, complemented
14#14533115C211yesmaximal, characteristic, complemented
15#14532916C211yesmaximal, characteristic, complemented
16#14532340C211yesmaximal, characteristic, complemented
17#14532327C211yesmaximal, characteristic, complemented
18#14532059C211yesmaximal, characteristic, complemented
19#14532048C211yesmaximal, characteristic, complemented
20#14532027C211yesmaximal, characteristic, complemented
21#14531996C211yesmaximal, characteristic, complemented
22#14531325C211yesmaximal, characteristic, complemented
23#14531311C211yesmaximal, characteristic, complemented
24#14531300C211yesmaximal, characteristic, complemented
25#14531296C211yesmaximal, characteristic, complemented
26#14531289C211yesmaximal, characteristic, complemented
27#14531271C211yesmaximal, characteristic, complemented
28#14531246C211yesmaximal, characteristic, complemented
29C4×#10587579C211yesmaximal, characteristic, complemented
30C4×C22⋊C4×D17C211yesmaximal, characteristic, complemented
31C17×#2554C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34#11763342—28no—
35C2×#10587562C2211yescharacteristic, complemented
36C2×#10587575C2211yescharacteristic, complemented
37C2×#10587571C2211yescharacteristic
38C2×#10587571C2211yescharacteristic, complemented
39#11763317—28no—
40C2×#10587580C2211yescharacteristic
41C2×#10587615C2211yescharacteristic
42C2×#10587569C2211yescharacteristic
43C2×#10587569C2211yescharacteristic
44C2×#10587582C2211yescharacteristic
45C2×#10587582C2211yescharacteristic
46C2×#10587582C2211yescharacteristic
47C2×#10587570C2211yescharacteristic
48C2×#10587570C2211yescharacteristic
49C2×#10587570C2211yescharacteristic
50C2×#10587570C2211yescharacteristic
51C2×#10587624C2211yescharacteristic
52C2×#10587568C2211yescharacteristic
53C2×#10587623C2211yescharacteristic
54C2×#10587623C2211yescharacteristic
55C2×#10587573C2211yescharacteristic, complemented
56C2×C4×D68C2211yescharacteristic
57C2×D4×Dic17C2211yescharacteristic
58C2×D4×Dic17C2211yescharacteristic, complemented
59C2×#10587579C2211yescharacteristic
60C2×#10587579C2211yescharacteristic
61C2×#10587579C2211yescharacteristic
62C2×#10587567C2211yescharacteristic
63C2×#10587567C2211yescharacteristic
64C2×#10587567C2211yescharacteristic
65C2×#10587567C2211yescharacteristic
66C2×#10587567C2211yescharacteristic, complemented
67C2×#10587578C2211yescharacteristic, complemented
68C2×#10587563C2211yescharacteristic
69C2×#10587563C2211yescharacteristic, complemented
70C2×C22⋊C4×D17C2211yescharacteristic
71C2×C22⋊C4×D17C2211yescharacteristic
72C2×C42×D17C2211yescharacteristic
73C2×C42×D17C2211yescharacteristic
74C2×C42×D17C2211yescharacteristic, complemented
75#11762750C2211yescharacteristic, complemented
76#11762748C2211yescharacteristic, complemented
77#11762746C2211yescharacteristic
78#11762745C2211yescharacteristic
79#11762743C2211yescharacteristic, complemented
80#11762742C2211yescharacteristic, complemented
81#11762739C2211yescharacteristic, complemented
82#11762737C2211yescharacteristic, complemented
83#11762736C2211yescharacteristic, complemented
84#11762736C2211yescharacteristic, complemented
85#11762735C2211yescharacteristic
86#11762732C2211yescharacteristic
87#11762732C2211yescharacteristic, complemented
88#11762731C2211yescharacteristic
89#11762730C2211yescharacteristic, complemented
90#11762729C2211yescharacteristic, complemented
91#11762726C2211yescharacteristic
92#11762726C2211yescharacteristic
93#11762725C2211yescharacteristic
94#11762725C2211yescharacteristic
95#11762725C2211yescharacteristic, complemented
96#11762724C2211yescharacteristic
97#11762723C2211yescharacteristic
98#11762721C2211yescharacteristic
99#11762721C2211yescharacteristic, complemented
100#11762717C2211yescharacteristic
101#11762717C2211yescharacteristic
102#11762717C2211yescharacteristic, complemented
103#11762715C2211yescharacteristic, complemented
104#11762714C2211yescharacteristic, complemented
105#11762713C2211yescharacteristic, complemented
106#11762712C2211yescharacteristic
107#11762712C2211yescharacteristic
108#11762709C2211yescharacteristic
109#11762709C2211yescharacteristic
110#11762707C2211yescharacteristic, complemented
111#11762707C2211yescharacteristic, complemented
112#11762705C2211yescharacteristic, complemented
113#11762704C2211yescharacteristic, complemented
114#11762703C2211yescharacteristic
115#11762703C2211yescharacteristic, complemented
116#11762703C2211yescharacteristic, complemented
117#11762703C2211yescharacteristic, complemented
118#11762703C2211yescharacteristic, complemented
119#11762700C2211yescharacteristic
120#11762700C2211yescharacteristic
121#11762699C2211yescharacteristic
122#11762697C2211yescharacteristic
123#11762697C2211yescharacteristic, complemented
124#11762697C2211yescharacteristic, complemented
125#11762694C2211yescharacteristic, complemented
126#11762693C2211yescharacteristic, complemented
127#11762687C2211yescharacteristic
128#11762685C2211yescharacteristic
129#11762685C2211yescharacteristic
130#11762685C2211yescharacteristic
131#11762685C2211yescharacteristic
132#11762685C2211yescharacteristic
133#11762685C2211yescharacteristic
134#11762685C2211yescharacteristic
135#11762685C2211yescharacteristic, complemented
136#11762685C2211yescharacteristic, complemented
137#11762685C2211yescharacteristic, complemented
138#11762683C2211yescharacteristic
139#11762683C2211yescharacteristic
140#11762682C2211yescharacteristic
141#11762680C2211yescharacteristic
142#11762673C2211yescharacteristic, complemented
143#11762671C2211yescharacteristic
144#11762668C2211yescharacteristic, complemented
145#11762666C2211yescharacteristic
146#11762664C2211yescharacteristic
147C4⋊C4×Dic17C2211yescharacteristic, complemented
148C4⋊C4×Dic17C2211yescharacteristic, complemented
149C4⋊C4×Dic17C2211yescharacteristic, complemented
150C4⋊C4×Dic17C2211yescharacteristic, complemented
151#11762660C2211yescharacteristic, complemented
152C22⋊C4×Dic17C2211yescharacteristic
153C22⋊C4×Dic17C2211yescharacteristic
154C22⋊C4×Dic17C2211yescharacteristic
155C22⋊C4×Dic17C2211yescharacteristic, complemented
156C22⋊C4×Dic17C2211yescharacteristic, complemented
157C22⋊C4×Dic17C2211yescharacteristic, complemented
158C22⋊C4×Dic17C2211yescharacteristic, complemented
159C4×#63227C2211yescharacteristic
160C4×#63227C2211yescharacteristic
161C4×#63227C2211yescharacteristic
162C4×#63227C2211yescharacteristic, complemented
163C4×C22⋊Dic17C2211yescharacteristic
164#11762656C2211yescharacteristic
165#11762656C2211yescharacteristic
166#11762656C2211yescharacteristic
167#11762656C2211yescharacteristic
168#11762656C2211yescharacteristic
169#11762656C2211yescharacteristic, complemented
170#11762656C2211yescharacteristic, complemented
171#95×D17C2211yescharacteristic
172#95×D17C2211yescharacteristic
173C42×Dic17C2211yescharacteristic, complemented
174C2×C17×#126C2211yescharacteristic, complemented
175C2×C17×#123C2211yescharacteristic
176C17×#398C2211yescharacteristic, complemented
177C17×#396C2211yescharacteristic
178C17×#394C2211yescharacteristic, complemented
179C17×#392C2211yescharacteristic
180C17×#390C2211yescharacteristic
181C17×#390C2211yescharacteristic
182C17×#390C2211yescharacteristic, complemented
183C17×#388C2211yescharacteristic, complemented
184C17×#388C2211yescharacteristic, complemented
185C17×#388C2211yescharacteristic, complemented
186C17×#386C2211yescharacteristic
187C4×C4⋊C4×C17C2211yescharacteristic, complemented
188C4×C22⋊C4×C17C2211yescharacteristic
189C24×D17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C23×Dic17C2311yescharacteristic
202C23×Dic17C2311yescharacteristic
203C23×Dic17C2311yescharacteristic
204C2×#63254—24no—
205C2×#63254—24no—
206C2×#63254—42no—
207C22×D68C2311yescharacteristic
208C22×D68C2311yescharacteristic
209C22×C4×D17—24no—
210C22×C4×D17—24no—
211C22×C4×D17—42no—
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C22×C4×D17C2311yescharacteristic
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×C4×D17C2311yescharacteristic
222C22×C4×D17C2311yescharacteristic
223C22×Dic34C2311yescharacteristic
224C22×Dic34C2311yescharacteristic
225C17×#126—24no—
226C17×#123—24no—
227C2×C4⋊C4×C17C2311yescharacteristic
228C2×C4⋊C4×C17C2311yescharacteristic
229C2×C4⋊C4×C17C2311yescharacteristic
230C2×C4⋊C4×C17C2311yescharacteristic
231C2×C4⋊C4×C17C2311yescharacteristic
232C2×C4⋊C4×C17C2311yescharacteristic
233C2×C4⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
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×C42×C17C2311yescharacteristic
249C2×C42×C17C2311yescharacteristic
250C2×C42×C17C2311yescharacteristic
251C2×C42×C17C2311yescharacteristic
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
265#10587624—24no—
266#10587623—24no—
267#10587623—24no—
268D4×Dic17—24no—
269D4×Dic17—42no—
270#10587615—24no—
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
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×C4⋊Dic17C2311yescharacteristic
293C2×C4⋊Dic17C2311yescharacteristic
294C2×C4⋊Dic17C2311yescharacteristic
295C2×C4⋊Dic17C2311yescharacteristic
296C2×C4⋊Dic17C2311yescharacteristic
297C2×C4⋊Dic17C2311yescharacteristic
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314C2×C4×Dic17C2311yescharacteristic
315C2×C4×Dic17C2311yescharacteristic
316C2×C4×Dic17C2311yescharacteristic
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
321C2×C4×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323C2×C4×Dic17C2311yescharacteristic
324C2×C4×Dic17C2311yescharacteristic
325C2×C4×Dic17C2311yescharacteristic
326#10587582—24no—
327#10587582—24no—
328#10587582—24no—
329#10587580—24no—
330#10587579—24no—
331#10587579—24no—
332#10587579D418yescomplemented
333#10587578—24no—
334#10587575—24no—
335#10587573—24no—
336#10587571—24no—
337#10587571—24no—
338#10587570—24no—
339#10587570—24no—
340#10587570—24no—
341#10587570—24no—
342#10587569—24no—
343#10587569—24no—
344#10587568—24no—
345#10587567—24no—
346#10587567—24no—
347#10587567—24no—
348#10587567—24no—
349#10587567—42no—
350C22⋊C4×D17—24no—
351C22⋊C4×D17—24no—
352#10587563—24no—
353#10587563—24no—
354#10587562—24no—
355C4×D68—24no—
356C42×D17—24no—
357C42×D17—42no—
358C42×D17—42no—
359C17×#95C2311yescharacteristic
360C17×#95C2311yescharacteristic
361C17×#95C2311yescharacteristic
362C17×#95C2311yescharacteristic
363C17×#95C2311yescharacteristic
364C17×#95C2311yescharacteristic
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×C17C2411yescharacteristic
392C24×C17C2411yescharacteristic
393C24×C17C2411yescharacteristic
394C23×D17—22no—
395C23×D17—22no—
396C23×D17—22no—
397C23×D17—22no—
398C23×D17—22no—
399C23×D17—41no—
400C23×D17—41no—
401C23×D17C2411yescharacteristic
402C23×D17C2411yescharacteristic
403C23×D17C2411yescharacteristic
404C2×D4×C17—22no—
405C2×D4×C17—22no—
406C2×D4×C17—22no—
407C2×D4×C17—22no—
408C2×D4×C17—22no—
409C2×D4×C17—41no—
410C2×D4×C17—41no—
411C2×D4×C17—41no—
412C2×D4×C17—41no—
413C22×C4×C17—22no—
414C22×C4×C17—22no—
415C22×C4×C17—41no—
416C22×C4×C17C2411yescharacteristic
417C22×C4×C17C2411yescharacteristic
418C22×C4×C17C2411yescharacteristic
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C22×C4×C17C2411yescharacteristic
424C22×C4×C17C2411yescharacteristic
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C22×C4×C17C2411yescharacteristic
428C2×C22⋊D17—22no—
429C2×C22⋊D17—22no—
430C2×C22⋊D17—22no—
431C2×C22⋊D17—22no—
432C2×C22⋊D17—22no—
433C2×C22⋊D17—22no—
434C2×C22⋊D17—22no—
435C2×C22⋊D17—22no—
436C2×C22⋊D17—22no—
437C2×C22⋊D17—22no—
438C2×C22⋊D17—22no—
439C2×C22⋊D17—22no—
440C2×C22⋊D17—22no—
441C2×C22⋊D17—22no—
442C2×C22⋊D17—22no—
443C2×C22⋊D17—22no—
444C2×C22⋊D17—41no—
445C2×C22⋊D17—41no—
446C2×C22⋊D17—41no—
447C2×C22⋊D17—41no—
448C2×C22⋊D17—41no—
449C22×Dic17—22no—
450C22×Dic17—22no—
451C22×Dic17—22no—
452C22×Dic17—22no—
453C22×Dic17—22no—
454C22×Dic17—22no—
455C22×Dic17—22no—
456C22×Dic17—22no—
457C22×Dic17#4114yes—
458C22×Dic17C2411yescharacteristic
459C22×Dic17C2411yescharacteristic
460C22×Dic17C2411yescharacteristic
461C22×Dic17C2411yescharacteristic
462C22×Dic17C2411yescharacteristic
463C22×Dic17C2411yescharacteristic
464C22×Dic17C2411yescharacteristic
465C22×Dic17C2411yescharacteristic
466C22×Dic17C2411yescharacteristic
467C22×Dic17C2411yescharacteristic
468C22×Dic17C2411yescharacteristic
469C22×Dic17C2411yescharacteristic
470C22×Dic17C2411yescharacteristic
471#63254—416no—
472C2×D68—22no—
473C2×D68—22no—
474C2×D68—22no—
475C2×D68—22no—
476C2×D68—41no—
477C2×D68C2×D414yes—
478C2×C4×D17—22no—
479C2×C4×D17—22no—
480C2×C4×D17—22no—
481C2×C4×D17—22no—
482C2×C4×D17—22no—
483C2×C4×D17—22no—
484C2×C4×D17—22no—
485C2×C4×D17—22no—
486C2×C4×D17—22no—
487C2×C4×D17—22no—
488C2×C4×D17—22no—
489C2×C4×D17—22no—
490C2×C4×D17—22no—
491C2×C4×D17—22no—
492C2×C4×D17—22no—
493C2×C4×D17—22no—
494C2×C4×D17—22no—
495C2×C4×D17—22no—
496C2×C4×D17—22no—
497C2×C4×D17—22no—
498C2×C4×D17—22no—
499C2×C4×D17—416no—
500C2×C4×D17—41no—
501C2×C4×D17—41no—
502C2×C4×D17—41no—
503C2×C4×D17—41no—
504C2×C4×D17—41no—
505C2×C4×D17—41no—
506C2×C4×D17—41no—
507C2×C4×D17—41no—
508C2×C4×D17—41no—
509C2×C4×D17C2×D414yes—
510C2×C4×D17C2×D414yes—
511C2×C4×D17#4114yescomplemented
512C2×Dic34—22no—
513C2×Dic34—22no—
514C2×Dic34—22no—
515C2×Dic34—22no—
516C2×Dic34—41no—
517C2×Dic34—41no—
518C4⋊C4×C17—22no—
519C4⋊C4×C17—22no—
520C4⋊C4×C17—22no—
521C4⋊C4×C17—22no—
522C4⋊C4×C17—41no—
523C4⋊C4×C17—41no—
524C4⋊C4×C17C2×D414yes—
525C22⋊C4×C17—22no—
526C22⋊C4×C17—22no—
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—41no—
537C22⋊C4×C17—41no—
538C22⋊C4×C17—41no—
539C42×C17—22no—
540C42×C17—22no—
541C42×C17—41no—
542C42×C17—41no—
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—22no—
554C22⋊Dic17—41no—
555C22⋊Dic17—41no—
556#63227—22no—
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—22no—
569#63227—22no—
570#63227—22no—
571#63227—22no—
572#63227—41no—
573#63227C2×D414yes—
574#63227C2×D414yes—
575#63227#4114yescomplemented
576#63227#4114yescomplemented
577C4⋊Dic17—22no—
578C4⋊Dic17—22no—
579C4⋊Dic17—22no—
580C4⋊Dic17—22no—
581C4⋊Dic17—22no—
582C4⋊Dic17—41no—
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—22no—
595#63225—41no—
596C4×Dic17—22no—
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—41no—
608C4×Dic17—41no—
609C4×Dic17—41no—
610C4×Dic17C2×D414yes—
611#34829—171nomaximal, Sylow
612C23×C17—21no—
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—21no—
622C23×C17—21no—
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×C17C2×#4112yes—
633C23×C17C2511yescharacteristic
634C22×D17—21no—
635C22×D17—21no—
636C22×D17—21no—
637C22×D17—21no—
638C22×D17—28no—
639C22×D17—21no—
640C22×D17—21no—
641C22×D17—21no—
642C22×D17—21no—
643C22×D17—21no—
644C22×D17—21no—
645C22×D17—21no—
646C22×D17—21no—
647C22×D17—21no—
648C22×D17—21no—
649C22×D17—21no—
650C22×D17—21no—
651C22×D17—44no—
652C22×D17—44no—
653C22×D17—44no—
654C22×D17—44no—
655C22×D17—44no—
656C22×D17—44no—
657C22×D17C22×D412yes—
658C22×D17C22×D412yes—
659C22×D17C2×#4112yes—
660C22×D17C2×#4112yes—
661C22×D17C2×#4112yes—
662D4×C17—44no—
663D4×C17—44no—
664D4×C17—44no—
665C2×C4×C17—21no—
666C2×C4×C17—21no—
667C2×C4×C17—21no—
668C2×C4×C17—21no—
669C2×C4×C17—21no—
670C2×C4×C17—21no—
671C2×C4×C17—21no—
672C2×C4×C17—21no—
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—44no—
696C2×C4×C17C22×D412yes—
697C2×C4×C17C22×D412yes—
698C2×C4×C17C22×D412yes—
699C2×C4×C17C2×#4112yes—
700C2×C4×C17C2×#4112yes—
701C2×C4×C17C2×#4112yes—
702C22⋊D17—44no—
703C22⋊D17—44no—
704C22⋊D17—44no—
705C22⋊D17—44no—
706C22⋊D17—44no—
707C22⋊D17—44no—
708C22⋊D17—44no—
709C2×Dic17—21no—
710C2×Dic17—21no—
711C2×Dic17—21no—
712C2×Dic17—21no—
713C2×Dic17—21no—
714C2×Dic17—21no—
715C2×Dic17—21no—
716C2×Dic17—21no—
717C2×Dic17—21no—
718C2×Dic17—21no—
719C2×Dic17—28no—
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—21no—
730C2×Dic17—21no—
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—44no—
742C2×Dic17—44no—
743C2×Dic17C22×D412yes—
744C2×Dic17C22×D412yes—
745C2×Dic17C2×#4112yes—
746C2×Dic17C2×#4112yes—
747C2×Dic17C2×#4112yes—
748C2×Dic17C2×#4112yes—
749C2×Dic17C2×#4112yes—
750C2×Dic17H(5,𝔽2)12yes—
751D68—28no—
752D68—44no—
753C4×D17—28no—
754C4×D17—28no—
755C4×D17—44no—
756C4×D17—44no—
757C4×D17—44no—
758C4×D17—44no—
759C4×D17—44no—
760C4×D17—44no—
761C4×D17—44no—
762C4×D17—44no—
763C4×D17—44no—
764Dic34—44no—
765Dic34—44no—
766C2×#529—171no—
767C2×#525—171no—
768#2560—171no—
769#2559—171no—
770#2558—171no—
771#2557—171no—
772#2556—171no—
773#2555—171no—
774#2554D1711yescharacteristic, complemented
775#2553—171no—
776#2549—171no—
777#2543—171no—
778#2539—171no—
779#2534—171no—
780#2488—171no—
781#2472—171no—
782#2425—171no—
783#2424—171no—
784#2396—171no—
785#2395—171no—
786#2392—171no—
787#2388—171no—
788C4×#124—171no—
789C4×#123—171no—
790C4×#121—171no—
791C4×#121—171no—
792C4×#120—171no—
793#2297—171no—
794#2293—171no—
795C42×D4—171no—
796C2×C4×C22⋊C4—171no—
797C22×C17—22no—
798C22×C17—22no—
799C22×C17—22no—
800C22×C17—41no—
801C22×C17—41no—
802C22×C17—41no—
803C22×C17—41no—
804C22×C17—41no—
805C22×C17—41no—
806C22×C17—41no—
807C22×C17—41no—
808C22×C17—41no—
809C22×C17—41no—
810C22×C17—41no—
811C22×C17—41no—
812C22×C17—41no—
813C22×C17—41no—
814C22×C17—41no—
815C22×C17—41no—
816C22×C17—41no—
817C22×C17—41no—
818C22×C17C23×D411yescharacteristic
819C22×C17C22×#4111yescharacteristic
820C22×C17C22×#4111yescharacteristic
821C22×C17C22×#4111yescharacteristic
822C22×C17C22×#4111yescharacteristic
823C22×C17C2×H(5,𝔽2)11yescharacteristic
824C22×C17#58511yescharacteristic
825C2×D17—22no—
826C2×D17—22no—
827C2×D17—22no—
828C2×D17—22no—
829C2×D17—22no—
830C2×D17—22no—
831C2×D17—22no—
832C2×D17—22no—
833C2×D17—22no—
834C2×D17—22no—
835C2×D17—22no—
836C2×D17—22no—
837C2×D17—416no—
838C2×D17—41no—
839C2×D17—41no—
840C2×D17—41no—
841C2×D17—41no—
842C2×D17—41no—
843C2×D17—41no—
844C2×D17—41no—
845C2×D17—41no—
846C2×D17#53214yes—
847C4×C17—22no—
848C4×C17—22no—
849C4×C17—22no—
850C4×C17—22no—
851C4×C17—22no—
852C4×C17—22no—
853C4×C17—41no—
854C4×C17—41no—
855C4×C17—41no—
856C4×C17—41no—
857C4×C17—41no—
858C4×C17—41no—
859Dic17—22no—
860Dic17—22no—
861Dic17—22no—
862Dic17—22no—
863Dic17—22no—
864Dic17—41no—
865Dic17—41no—
866Dic17—41no—
867Dic17—41no—
868Dic17—41no—
869Dic17—41no—
870Dic17—41no—
871Dic17#54614yes—
872C22×#41—171no—
873C24×C4—171no—
874#529—348no—
875C2×#126—171no—
876C2×#126C2×D1711yescharacteristic, complemented
877C2×#125—171no—
878C2×#124—171no—
879C2×#124—171no—
880#525—348no—
881C2×#123—171no—
882C2×#123—171no—
883C2×#123—171no—
884C2×#123—171no—
885C2×#123C2×D1711yescharacteristic
886C2×C22⋊Q8—171no—
887C2×C22⋊Q8—171no—
888C2×C22⋊Q8—171no—
889C2×#121—171no—
890C2×#121—171no—
891C2×#121—171no—
892C2×#121—171no—
893C2×#121—171no—
894C2×#120—171no—
895C2×#120—171no—
896C2×#120—171no—
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×#117—171no—
910C2×#117—171no—
911C2×#117—171no—
912C22×C22⋊C4—171no—
913C22×C22⋊C4—171no—
914C22×C42—171no—
915C22×C42—171no—
916C22×C42—171no—
917#400—171no—
918#400—171no—
919#399—171no—
920#399—171no—
921#398—171no—
922#398—171no—
923#398—171no—
924#398C2×D1711yescharacteristic, complemented
925#397—171no—
926#397—171no—
927#397—171no—
928#397—171no—
929#396—171no—
930#396—171no—
931#396—171no—
932#396C2×D1711yescharacteristic
933#395—171no—
934#395—171no—
935#394—171no—
936#394—171no—
937#394—171no—
938#394—171no—
939#394—171no—
940#394—171no—
941#394—171no—
942#394C2×D1711yescharacteristic, complemented
943#393—171no—
944#393—171no—
945#392—171no—
946#392—171no—
947#392—171no—
948#392C2×D1711yescharacteristic
949#391—171no—
950#391—171no—
951#391—171no—
952#390—171no—
953#390—171no—
954#390—171no—
955#390—171no—
956#390C2×D1711yescharacteristic
957#390C2×D1711yescharacteristic
958#390C2×D1711yescharacteristic, complemented
959#389—171no—
960#389—171no—
961#389—171no—
962#389—171no—
963#388—171no—
964#388—171no—
965#388—171no—
966#388—171no—
967#388—171no—
968#388—171no—
969#388—171no—
970#388—171no—
971#388—171no—
972#388—171no—
973#388—171no—
974#388C2×D1711yescharacteristic, complemented
975#388C2×D1711yescharacteristic, complemented
976#388C2×D1711yescharacteristic, complemented
977#387—171no—
978#387—171no—
979#386—171no—
980#386—171no—
981#386—171no—
982#386—171no—
983#386—171no—
984#386—171no—
985#386—171no—
986#386—171no—
987#386—171no—
988#386—171no—
989#386—171no—
990#386C2×D1711yescharacteristic
991#385—171no—
992#385—171no—
993#385—171no—
994#385—171no—
995#382—171no—
996#381—171no—
997#380—171no—
998#380—171no—
999#379—171no—
1000C4×C4⋊C4—171no—
1001C4×C4⋊C4—171no—
1002C4×C4⋊C4—171no—
1003C4×C4⋊C4—171no—
1004C4×C4⋊C4—171no—
1005C4×C4⋊C4C2×D1711yescharacteristic, complemented
1006C4×C22⋊C4—171no—
1007C4×C22⋊C4—171no—
1008C4×C22⋊C4—171no—
1009C4×C22⋊C4—171no—
1010C4×C22⋊C4—171no—
1011C4×C22⋊C4—171no—
1012C4×C22⋊C4—171no—
1013C4×C22⋊C4—171no—
1014C4×C22⋊C4—171no—
1015C4×C22⋊C4—171no—
1016C4×C22⋊C4—171no—
1017C4×C22⋊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⋊C4C2×D1711yescharacteristic
1026C2×#95—171no—
1027C2×#95—171no—
1028C43—171no—
1029C2×C17—42no—
1030C2×C17—81no—
1031C2×C17—81no—
1032C2×C17C2×#53211yescharacteristic
1033C2×C17#344411yescharacteristic
1034C2×C17#345911yescharacteristic
1035C2×C17C2×#54611yescharacteristic
1036C2×C17D4×#4111yescharacteristic
1037C2×C17#347511yescharacteristic
1038C2×C17#348111yescharacteristic
1039D17—24no—
1040D17—42no—
1041D17—42no—
1042C25—171no—
1043C2×#41—344no—
1044C2×#41—344no—
1045C2×#41—682no—
1046C22×Q8—171no—
1047C22×Q8—171no—
1048C22×D4—171no—
1049C22×D4—171no—
1050C22×D4—171no—
1051C22×D4—171no—
1052C22×D4—171no—
1053C22×D4—171no—
1054C22×D4—171no—
1055C22×D4—171no—
1056C22×D4—171no—
1057C22×D4C22×D1711yescharacteristic
1058C22×D4C22×D1711yescharacteristic
1059C22×D4C22×D1711yescharacteristic
1060C23×C4—171no—
1061C23×C4—171no—
1062C23×C4—171no—
1063C23×C4—171no—
1064C23×C4—171no—
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—344no—
1075C23×C4—344no—
1076C23×C4—682no—
1077C23×C4C22×D1711yescharacteristic
1078#126—24no—
1079#126—344no—
1080#125—344no—
1081#124—344no—
1082#124—344no—
1083#123—24no—
1084#123—344no—
1085#123—344no—
1086#123—344no—
1087#123—344no—
1088C22⋊Q8—344no—
1089C22⋊Q8—344no—
1090C22⋊Q8—344no—
1091#121—344no—
1092#121—344no—
1093#121—344no—
1094#121—344no—
1095#121—344no—
1096#120—344no—
1097#120—344no—
1098#120—344no—
1099C4×Q8—344no—
1100C4×D4—178no—
1101C4×D4—344no—
1102C4×D4—344no—
1103C4×D4—344no—
1104C4×D4—344no—
1105C4×D4—344no—
1106C4×D4—344no—
1107C4×D4—344no—
1108C4×D4—344no—
1109C4×D4—682no—
1110C4×D4—682no—
1111#117—344no—
1112#117—344no—
1113#117—344no—
1114C2×C4⋊C4—171no—
1115C2×C4⋊C4—171no—
1116C2×C4⋊C4—171no—
1117C2×C4⋊C4—171no—
1118C2×C4⋊C4—171no—
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⋊C4C22×D1711yescharacteristic
1134C2×C4⋊C4C22×D1711yescharacteristic
1135C2×C4⋊C4C22×D1711yescharacteristic
1136C2×C4⋊C4C22×D1711yescharacteristic
1137C2×C4⋊C4C22×D1711yescharacteristic
1138C2×C4⋊C4C22×D1711yescharacteristic
1139C2×C4⋊C4C22×D1711yescharacteristic
1140C2×C22⋊C4—171no—
1141C2×C22⋊C4—171no—
1142C2×C22⋊C4—171no—
1143C2×C22⋊C4—171no—
1144C2×C22⋊C4—171no—
1145C2×C22⋊C4—171no—
1146C2×C22⋊C4—171no—
1147C2×C22⋊C4—171no—
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—344no—
1175C2×C22⋊C4—344no—
1176C2×C22⋊C4C22×D1711yescharacteristic
1177C2×C22⋊C4C22×D1711yescharacteristic
1178C2×C22⋊C4C22×D1711yescharacteristic
1179C2×C22⋊C4C22×D1711yescharacteristic
1180C2×C22⋊C4C22×D1711yescharacteristic
1181C2×C22⋊C4C22×D1711yescharacteristic
1182C2×C22⋊C4C22×D1711yescharacteristic
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×C42—171no—
1191C2×C42—171no—
1192C2×C42—171no—
1193C2×C42—171no—
1194C2×C42—171no—
1195C2×C42—171no—
1196C2×C42—171no—
1197C2×C42—171no—
1198C2×C42—171no—
1199C2×C42—171no—
1200C2×C42—171no—
1201C2×C42—171no—
1202C2×C42—171no—
1203C2×C42—171no—
1204C2×C42—171no—
1205C2×C42—344no—
1206C2×C42—682no—
1207C2×C42—682no—
1208C2×C42C22×D1711yescharacteristic
1209C2×C42C22×D1711yescharacteristic
1210C2×C42C22×D1711yescharacteristic
1211C2×C42C22×D1711yescharacteristic
1212#95—171no—
1213#95—171no—
1214#95—171no—
1215#95—171no—
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#95C22×D1711yescharacteristic
1239#95C22×D1711yescharacteristic
1240#95C22×D1711yescharacteristic
1241#95C22×D1711yescharacteristic
1242#95C22×D1711yescharacteristic
1243#95C22×D1711yescharacteristic
1244C17#3482911yescharacteristic, complemented, Sylow
1245C24—171no—
1246C24—171no—
1247C24—171no—
1248C24—342no—
1249C24—342no—
1250C24—342no—
1251C24—342no—
1252C24—342no—
1253C24—681no—
1254C24—681no—
1255C24C23×D1711yescharacteristic
1256C24C23×D1711yescharacteristic
1257C24C23×D1711yescharacteristic
1258#41—6816no—
1259C2×Q8—342no—
1260C2×Q8—342no—
1261C2×Q8—342no—
1262C2×Q8—342no—
1263C2×Q8—681no—
1264C2×Q8—681no—
1265C2×D4—22no—
1266C2×D4—22no—
1267C2×D4—22no—
1268C2×D4—22no—
1269C2×D4—22no—
1270C2×D4—41no—
1271C2×D4—41no—
1272C2×D4—41no—
1273C2×D4—41no—
1274C2×D4—174no—
1275C2×D4—342no—
1276C2×D4—342no—
1277C2×D4—342no—
1278C2×D4—342no—
1279C2×D4—342no—
1280C2×D4—342no—
1281C2×D4—342no—
1282C2×D4—342no—
1283C2×D4—342no—
1284C2×D4—342no—
1285C2×D4—342no—
1286C2×D4—342no—
1287C2×D4—342no—
1288C2×D4—342no—
1289C2×D4—342no—
1290C2×D4—342no—
1291C2×D4—342no—
1292C2×D4—342no—
1293C2×D4—342no—
1294C2×D4—342no—
1295C2×D4—681no—
1296C2×D4—681no—
1297C2×D4—681no—
1298C2×D4—681no—
1299C2×D4—681no—
1300C2×D4—681no—
1301C22×C4—22no—
1302C22×C4—22no—
1303C22×C4—41no—
1304C22×C4—171no—
1305C22×C4—174no—
1306C22×C4—171no—
1307C22×C4—171no—
1308C22×C4—171no—
1309C22×C4—171no—
1310C22×C4—171no—
1311C22×C4—174no—
1312C22×C4—174no—
1313C22×C4—174no—
1314C22×C4—171no—
1315C22×C4—171no—
1316C22×C4—171no—
1317C22×C4—171no—
1318C22×C4—171no—
1319C22×C4—171no—
1320C22×C4—171no—
1321C22×C4—342no—
1322C22×C4—342no—
1323C22×C4—342no—
1324C22×C4—342no—
1325C22×C4—342no—
1326C22×C4—342no—
1327C22×C4—342no—
1328C22×C4—342no—
1329C22×C4—342no—
1330C22×C4—342no—
1331C22×C4—342no—
1332C22×C4—342no—
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—681no—
1351C22×C4—681no—
1352C22×C4—681no—
1353C22×C4—681no—
1354C22×C4—681no—
1355C22×C4—681no—
1356C22×C4—681no—
1357C22×C4—681no—
1358C22×C4—681no—
1359C22×C4—6816no—
1360C22×C4C23×D1711yescharacteristic
1361C22×C4C23×D1711yescharacteristic
1362C22×C4C23×D1711yescharacteristic
1363C22×C4C23×D1711yescharacteristic
1364C22×C4C23×D1711yescharacteristic
1365C22×C4C23×D1711yescharacteristic
1366C22×C4C23×D1711yescharacteristic
1367C22×C4C23×D1711yescharacteristic
1368C22×C4C23×D1711yescharacteristic
1369C22×C4C23×D1711yescharacteristic
1370C22×C4C23×D1711yescharacteristic
1371C22×C4C23×D1711yescharacteristic
1372C4⋊C4—22no—
1373C4⋊C4—22no—
1374C4⋊C4—22no—
1375C4⋊C4—22no—
1376C4⋊C4—41no—
1377C4⋊C4—41no—
1378C4⋊C4—342no—
1379C4⋊C4—342no—
1380C4⋊C4—342no—
1381C4⋊C4—342no—
1382C4⋊C4—342no—
1383C4⋊C4—342no—
1384C4⋊C4—342no—
1385C4⋊C4—342no—
1386C4⋊C4—342no—
1387C4⋊C4—342no—
1388C4⋊C4—342no—
1389C4⋊C4—342no—
1390C4⋊C4—342no—
1391C4⋊C4—342no—
1392C4⋊C4—342no—
1393C4⋊C4—342no—
1394C4⋊C4—342no—
1395C4⋊C4—681no—
1396C4⋊C4—681no—
1397C4⋊C4D4×D1714yes—
1398C22⋊C4—22no—
1399C22⋊C4—22no—
1400C22⋊C4—22no—
1401C22⋊C4—22no—
1402C22⋊C4—22no—
1403C22⋊C4—22no—
1404C22⋊C4—22no—
1405C22⋊C4—22no—
1406C22⋊C4—22no—
1407C22⋊C4—22no—
1408C22⋊C4—22no—
1409C22⋊C4—41no—
1410C22⋊C4—41no—
1411C22⋊C4—41no—
1412C22⋊C4—174no—
1413C22⋊C4—174no—
1414C22⋊C4—174no—
1415C22⋊C4—174no—
1416C22⋊C4—342no—
1417C22⋊C4—342no—
1418C22⋊C4—342no—
1419C22⋊C4—342no—
1420C22⋊C4—342no—
1421C22⋊C4—342no—
1422C22⋊C4—342no—
1423C22⋊C4—342no—
1424C22⋊C4—342no—
1425C22⋊C4—342no—
1426C22⋊C4—342no—
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—681no—
1444C22⋊C4—681no—
1445C22⋊C4—681no—
1446C42—22no—
1447C42—22no—
1448C42—41no—
1449C42—41no—
1450C42—174no—
1451C42—342no—
1452C42—342no—
1453C42—342no—
1454C42—342no—
1455C42—342no—
1456C42—342no—
1457C42—342no—
1458C42—342no—
1459C42—342no—
1460C42—342no—
1461C42—342no—
1462C42—681no—
1463C42—681no—
1464C42—681no—
1465C23—21no—
1466C23—21no—
1467C23—21no—
1468C23—21no—
1469C23—21no—
1470C23—21no—
1471C23—21no—
1472C23—21no—
1473C23—21no—
1474C23—21no—
1475C23—21no—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—21no—
1480C23—21no—
1481C23—21no—
1482C23—21no—
1483C23—21no—
1484C23—21no—
1485C23—172no—
1486C23—172no—
1487C23—172no—
1488C23—172no—
1489C23—172no—
1490C23—348no—
1491C23—341no—
1492C23—341no—
1493C23—341no—
1494C23—341no—
1495C23—341no—
1496C23—341no—
1497C23—341no—
1498C23—341no—
1499C23—341no—
1500C23—341no—
1501C23—341no—
1502C23—341no—
1503C23—341no—
1504C23—341no—
1505C23—341no—
1506C23—341no—
1507C23—684no—
1508C23—684no—
1509C23—684no—
1510C23—684no—
1511C23—684no—
1512C23—684no—
1513C23#41×D1712yes—
1514C23C24×D1711yescharacteristic
1515Q8—684no—
1516Q8—684no—
1517D4—44no—
1518D4—44no—
1519D4—44no—
1520D4—348no—
1521D4—684no—
1522D4—684no—
1523D4—684no—
1524D4—684no—
1525D4—684no—
1526D4—684no—
1527D4—684no—
1528D4—684no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
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—44no—
1560C2×C4—172no—
1561C2×C4—172no—
1562C2×C4—172no—
1563C2×C4—172no—
1564C2×C4—172no—
1565C2×C4—172no—
1566C2×C4—172no—
1567C2×C4—172no—
1568C2×C4—348no—
1569C2×C4—348no—
1570C2×C4—348no—
1571C2×C4—341no—
1572C2×C4—341no—
1573C2×C4—341no—
1574C2×C4—341no—
1575C2×C4—341no—
1576C2×C4—341no—
1577C2×C4—341no—
1578C2×C4—341no—
1579C2×C4—341no—
1580C2×C4—341no—
1581C2×C4—341no—
1582C2×C4—341no—
1583C2×C4—341no—
1584C2×C4—341no—
1585C2×C4—341no—
1586C2×C4—341no—
1587C2×C4—341no—
1588C2×C4—341no—
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—684no—
1603C2×C4—684no—
1604C2×C4—684no—
1605C2×C4—684no—
1606C2×C4—684no—
1607C2×C4—684no—
1608C2×C4—684no—
1609C2×C4—684no—
1610C2×C4—684no—
1611C2×C4—684no—
1612C2×C4—684no—
1613C2×C4C2×D4×D1712yes—
1614C2×C4C2×D4×D1712yes—
1615C2×C4C2×D4×D1712yes—
1616C2×C4#41×D1712yes—
1617C2×C4#41×D1712yes—
1618C2×C4#41×D1712yes—
1619C22—22no—
1620C22—22no—
1621C22—22no—
1622C22—41no—
1623C22—41no—
1624C22—41no—
1625C22—41no—
1626C22—41no—
1627C22—41no—
1628C22—41no—
1629C22—41no—
1630C22—41no—
1631C22—41no—
1632C22—41no—
1633C22—41no—
1634C22—41no—
1635C22—41no—
1636C22—41no—
1637C22—41no—
1638C22—41no—
1639C22—41no—
1640C22—174no—
1641C22—342no—
1642C22—342no—
1643C22—342no—
1644C22—342no—
1645C22—342no—
1646C22—342no—
1647C22—342no—
1648C22—342no—
1649C22—342no—
1650C22—342no—
1651C22—342no—
1652C22—342no—
1653C22—6816no—
1654C22—681no—
1655C22—681no—
1656C22—681no—
1657C22—681no—
1658C22—681no—
1659C22—681no—
1660C22—681no—
1661C22—681no—
1662C22C22×D4×D1711yescharacteristic
1663C22C2×#41×D1711yescharacteristic
1664C22C2×#41×D1711yescharacteristic
1665C22C2×#41×D1711yescharacteristic
1666C22C2×#41×D1711yescharacteristic
1667C22H(5,𝔽2)×D1711yescharacteristic
1668C22#1176364411yescharacteristic
1669C4—22no—
1670C4—22no—
1671C4—22no—
1672C4—22no—
1673C4—22no—
1674C4—22no—
1675C4—41no—
1676C4—41no—
1677C4—41no—
1678C4—41no—
1679C4—41no—
1680C4—41no—
1681C4—174no—
1682C4—342no—
1683C4—342no—
1684C4—342no—
1685C4—342no—
1686C4—342no—
1687C4—681no—
1688C4—681no—
1689C4—681no—
1690C4—681no—
1691C4—681no—
1692C4—681no—
1693C4—681no—
1694C2—42no—
1695C2—81no—
1696C2—81no—
1697C2—344no—
1698C2—682no—
1699C2—682no—
1700C2D17×#53211yescharacteristic
1701C2#1454207811yescharacteristic
1702C2#1454219511yescharacteristic
1703C2D17×#54611yescharacteristic
1704C2#1454227411yescharacteristic
1705C2#1454233911yescharacteristic
1706C2#1454239111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2554C2
hypercenter#2554D17
hypocenterC17#34829
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2554

Complements

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

NH ≅ G/Ntype
1. C2×#11763342C2semidirect
2. C2×#11763317C2semidirect
3. #14533926C2semidirect
4. #14533919C2semidirect
5. #14533894C2semidirect
6. #14533887C2semidirect
7. #14533862C2semidirect
8. #14533858C2semidirect
9. #14533829C2semidirect
10. #14533791C2semidirect
11. #14533747C2semidirect
12. #14533709C2semidirect
13. #14533675C2semidirect
14. #14533115C2semidirect
15. #14532916C2semidirect
16. #14532340C2semidirect
17. #14532327C2semidirect
18. #14532059C2semidirect
19. #14532048C2semidirect
20. #14532027C2semidirect
21. #14531996C2semidirect
22. #14531325C2semidirect
23. #14531311C2semidirect
24. #14531300C2semidirect
25. #14531296C2semidirect
26. #14531289C2semidirect
27. #14531271C2semidirect
28. #14531246C2semidirect
29. C4×#10587579C2semidirect
30. C4×C22⋊C4×D17C2semidirect
31. C17×#2554C2semidirect
35. C2×#10587562C22semidirect
36. C2×#10587575C22semidirect
38. C2×#10587571C22semidirect
55. C2×#10587573C22semidirect
58. C2×D4×Dic17C22semidirect
66. C2×#10587567C22semidirect
67. C2×#10587578C22semidirect
69. C2×#10587563C22semidirect
74. C2×C42×D17C22semidirect
75. #11762750C22semidirect
76. #11762748C22semidirect
79. #11762743C22semidirect
80. #11762742C22semidirect
81. #11762739C22semidirect
82. #11762737C22semidirect
83. #11762736C22semidirect
84. #11762736C22semidirect
87. #11762732C22semidirect
89. #11762730C22semidirect
90. #11762729C22semidirect
95. #11762725C22semidirect
99. #11762721C22semidirect
102. #11762717C22semidirect
103. #11762715C22semidirect
104. #11762714C22semidirect
105. #11762713C22semidirect
110. #11762707C22semidirect
111. #11762707C22semidirect
112. #11762705C22semidirect
113. #11762704C22semidirect
115. #11762703C22semidirect
116. #11762703C22semidirect
117. #11762703C22semidirect
118. #11762703C22semidirect
123. #11762697C22semidirect
124. #11762697C22semidirect
125. #11762694C22semidirect
126. #11762693C22semidirect
135. #11762685C22semidirect
136. #11762685C22semidirect
137. #11762685C22semidirect
142. #11762673C22semidirect
144. #11762668C22semidirect
147. C4⋊C4×Dic17C22semidirect
148. C4⋊C4×Dic17C22semidirect
149. C4⋊C4×Dic17C22semidirect
150. C4⋊C4×Dic17C22semidirect
151. #11762660C22semidirect
155. C22⋊C4×Dic17C22semidirect
156. C22⋊C4×Dic17C22semidirect
157. C22⋊C4×Dic17C22semidirect
158. C22⋊C4×Dic17C22semidirect
162. C4×#63227C22semidirect
169. #11762656C22semidirect
170. #11762656C22semidirect
173. C42×Dic17C22semidirect
174. C2×C17×#126C22semidirect
176. C17×#398C22semidirect
178. C17×#394C22semidirect
182. C17×#390C22semidirect
183. C17×#388C22semidirect
184. C17×#388C22semidirect
185. C17×#388C22semidirect
187. C4×C4⋊C4×C17C22semidirect
332. #10587579D4semidirect
511. C2×C4×D17#41semidirect
575. #63227#41semidirect
576. #63227#41semidirect
774. #2554D17semidirect
876. C2×#126C2×D17semidirect
924. #398C2×D17semidirect
942. #394C2×D17semidirect
958. #390C2×D17semidirect
974. #388C2×D17semidirect
975. #388C2×D17semidirect
976. #388C2×D17semidirect
1005. C4×C4⋊C4C2×D17semidirect
1244. C17#34829semidirect

Maximal subgroups

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

subgroupindex
C2×#117633422
C2×#117633172
#145339262
#145339192
#145338942
#145338872
#145338622
#145338582
#145338292
#145337912
#145337472
#145337092
#145336752
#145331152
#145329162
#145323402
#145323272
#145320592
#145320482
#145320272
#145319962
#145313252
#145313112
#145313002
#145312962
#145312892
#145312712
#145312462
C4×#105875792
C4×C22⋊C4×D172
C17×#25542
#3482917