Finite Group Databasebeta

← #17207009

Subgroups — #17207009

Order 4352.

2878 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×#11763404C211yesmaximal, characteristic, complemented
2C22×D4×Dic17C211yesmaximal, characteristic, complemented
3#14537097C211yesmaximal, characteristic, complemented
4#14537090C211yesmaximal, characteristic, complemented
5#14537074C211yesmaximal, characteristic, complemented
6#14537069C211yesmaximal, characteristic, complemented
7#14534700C211yesmaximal, characteristic, complemented
8#14534678C211yesmaximal, characteristic, complemented
9#14534651C211yesmaximal, characteristic, complemented
10#14534620C211yesmaximal, characteristic, complemented
11#14533027C211yesmaximal, characteristic, complemented
12#14532922C211yesmaximal, characteristic, complemented
13#14532813C211yesmaximal, characteristic, complemented
14#14532774C211yesmaximal, characteristic, complemented
15#14532729C211yesmaximal, characteristic, complemented
16#14532660C211yesmaximal, characteristic, complemented
17#14532599C211yesmaximal, characteristic, complemented
18#14532597C211yesmaximal, characteristic, complemented
19#14532515C211yesmaximal, characteristic, complemented
20#14532445C211yesmaximal, characteristic, complemented
21#14532341C211yesmaximal, characteristic, complemented
22#14532259C211yesmaximal, characteristic, complemented
23#14532242C211yesmaximal, characteristic, complemented
24#14532181C211yesmaximal, characteristic, complemented
25#14532107C211yesmaximal, characteristic, complemented
26#14531489C211yesmaximal, characteristic, complemented
27#14531458C211yesmaximal, characteristic, complemented
28#14531410C211yesmaximal, characteristic, complemented
29#120×Dic17C211yesmaximal, characteristic, complemented
30C2×#11762681C211yesmaximal, characteristic, complemented
31C17×#2410C211yesmaximal, characteristic
32C24×Dic17C2211yescharacteristic
33C24×Dic17C2211yescharacteristic
34#11763404—28no—
35C2×#10587565C2211yescharacteristic, complemented
36C2×#10587565C2211yescharacteristic, complemented
37C2×#10587575C2211yescharacteristic, complemented
38C2×#10587575C2211yescharacteristic, complemented
39C2×#10587621C2211yescharacteristic
40C2×#10587621C2211yescharacteristic
41C2×#10587621C2211yescharacteristic, complemented
42C2×#10587621C2211yescharacteristic, complemented
43C2×#10587621C2211yescharacteristic, complemented
44C2×#10587621C2211yescharacteristic, complemented
45C2×#10587610C2211yescharacteristic, complemented
46C2×#10587564C2211yescharacteristic
47C2×#10587564C2211yescharacteristic, complemented
48C2×#10587564C2211yescharacteristic, complemented
49C2×#10587564C2211yescharacteristic, complemented
50C2×D4×Dic17—28no—
51C2×D4×Dic17C2211yescharacteristic
52C2×D4×Dic17C2211yescharacteristic
53C2×D4×Dic17C2211yescharacteristic
54C2×D4×Dic17C2211yescharacteristic
55C2×D4×Dic17C2211yescharacteristic
56C2×D4×Dic17C2211yescharacteristic
57C2×D4×Dic17C2211yescharacteristic
58C2×D4×Dic17C2211yescharacteristic
59C2×D4×Dic17C2211yescharacteristic
60C2×D4×Dic17C2211yescharacteristic, complemented
61C2×D4×Dic17C2211yescharacteristic, complemented
62C22×C4⋊Dic17C2211yescharacteristic
63C22×#63225C2211yescharacteristic, complemented
64C22×#63225C2211yescharacteristic, complemented
65C22×C22⋊Dic17C2211yescharacteristic
66C22×C22⋊Dic17C2211yescharacteristic
67C22×C22⋊Dic17C2211yescharacteristic
68C22×C4×Dic17C2211yescharacteristic
69#11762749C2211yescharacteristic, complemented
70#11762745C2211yescharacteristic, complemented
71#11762745C2211yescharacteristic, complemented
72#11762745C2211yescharacteristic, complemented
73#11762743C2211yescharacteristic, complemented
74#11762742C2211yescharacteristic, complemented
75#11762741C2211yescharacteristic, complemented
76#11762739C2211yescharacteristic, complemented
77#11762737C2211yescharacteristic, complemented
78#11762737C2211yescharacteristic, complemented
79#11762737C2211yescharacteristic, complemented
80#11762737C2211yescharacteristic, complemented
81#11762734C2211yescharacteristic, complemented
82#11762734C2211yescharacteristic, complemented
83#11762732C2211yescharacteristic, complemented
84#11762732C2211yescharacteristic, complemented
85#11762732C2211yescharacteristic, complemented
86#11762732C2211yescharacteristic, complemented
87#11762730C2211yescharacteristic, complemented
88#11762723C2211yescharacteristic
89#11762723C2211yescharacteristic
90#11762723C2211yescharacteristic
91#11762723C2211yescharacteristic
92#11762723C2211yescharacteristic, complemented
93#11762723C2211yescharacteristic, complemented
94#11762723C2211yescharacteristic, complemented
95#11762723C2211yescharacteristic, complemented
96#11762721C2211yescharacteristic, complemented
97#11762706C2211yescharacteristic, complemented
98#11762706C2211yescharacteristic, complemented
99#11762706C2211yescharacteristic, complemented
100#11762704C2211yescharacteristic, complemented
101#11762703C2211yescharacteristic, complemented
102#11762703C2211yescharacteristic, complemented
103#11762702C2211yescharacteristic, complemented
104#11762702C2211yescharacteristic, complemented
105#11762697C2211yescharacteristic, complemented
106#11762697C2211yescharacteristic, complemented
107#11762697C2211yescharacteristic, complemented
108#11762697C2211yescharacteristic, complemented
109#11762696C2211yescharacteristic, complemented
110#11762695C2211yescharacteristic, complemented
111#11762695C2211yescharacteristic, complemented
112#11762694C2211yescharacteristic, complemented
113#11762694C2211yescharacteristic, complemented
114#11762694C2211yescharacteristic, complemented
115#11762692C2211yescharacteristic, complemented
116#11762691C2211yescharacteristic, complemented
117#11762691C2211yescharacteristic, complemented
118#11762690C2211yescharacteristic, complemented
119#11762689C2211yescharacteristic
120#11762689C2211yescharacteristic
121#11762689C2211yescharacteristic
122#11762689C2211yescharacteristic
123#11762689C2211yescharacteristic
124#11762689C2211yescharacteristic, complemented
125#11762689C2211yescharacteristic, complemented
126#11762689C2211yescharacteristic, complemented
127#11762689C2211yescharacteristic, complemented
128#11762689C2211yescharacteristic, complemented
129#11762689C2211yescharacteristic, complemented
130#11762684C2211yescharacteristic
131#11762684C2211yescharacteristic
132#11762684C2211yescharacteristic, complemented
133#11762684C2211yescharacteristic, complemented
134#11762684C2211yescharacteristic, complemented
135#11762684C2211yescharacteristic, complemented
136#11762684C2211yescharacteristic, complemented
137#11762682C2211yescharacteristic
138#11762682C2211yescharacteristic
139#11762682C2211yescharacteristic, complemented
140#11762682C2211yescharacteristic, complemented
141#11762681C2211yescharacteristic
142#11762681C2211yescharacteristic
143#11762681C2211yescharacteristic
144#11762681C2211yescharacteristic
145#11762681C2211yescharacteristic
146#11762681C2211yescharacteristic, complemented
147#11762681C2211yescharacteristic, complemented
148#11762681C2211yescharacteristic, complemented
149#11762681C2211yescharacteristic, complemented
150#11762681C2211yescharacteristic, complemented
151#11762681C2211yescharacteristic, complemented
152#11762681C2211yescharacteristic, complemented
153#11762681C2211yescharacteristic, complemented
154#11762681C2211yescharacteristic, complemented
155#11762676C2211yescharacteristic, complemented
156#11762673C2211yescharacteristic, complemented
157#11762670C2211yescharacteristic, complemented
158#11762670C2211yescharacteristic, complemented
159#11762670C2211yescharacteristic, complemented
160#11762669C2211yescharacteristic, complemented
161#11762667C2211yescharacteristic
162#11762667C2211yescharacteristic
163#11762667C2211yescharacteristic
164#11762667C2211yescharacteristic, complemented
165#11762667C2211yescharacteristic, complemented
166#11762665C2211yescharacteristic
167#11762665C2211yescharacteristic
168#11762665C2211yescharacteristic
169C22⋊C4×Dic17C2211yescharacteristic
170C22⋊C4×Dic17C2211yescharacteristic, complemented
171C22⋊C4×Dic17C2211yescharacteristic, complemented
172C2×#10587502C2211yescharacteristic, complemented
173C2×#10587502C2211yescharacteristic, complemented
174C23×D4×C17C2211yescharacteristic
175C2×C17×#121C2211yescharacteristic
176C2×C17×#121C2211yescharacteristic
177C2×C17×#120C2211yescharacteristic
178C2×C17×#120C2211yescharacteristic
179C22×C22⋊C4×C17C2211yescharacteristic
180C17×#394C2211yescharacteristic
181C17×#394C2211yescharacteristic
182C17×#392C2211yescharacteristic
183C17×#392C2211yescharacteristic
184C17×#386C2211yescharacteristic
185C17×#386C2211yescharacteristic
186C17×#386C2211yescharacteristic
187C17×#385C2211yescharacteristic
188C17×#379C2211yescharacteristic
189C25×C17C2311yescharacteristic
190C25×C17C2311yescharacteristic
191C22×D4×C17—24no—
192C22×D4×C17—24no—
193C22×D4×C17—24no—
194C22×D4×C17C2311yescharacteristic
195C22×D4×C17C2311yescharacteristic
196C22×D4×C17C2311yescharacteristic
197C22×D4×C17C2311yescharacteristic
198C22×D4×C17C2311yescharacteristic
199C22×D4×C17C2311yescharacteristic
200C22×D4×C17C2311yescharacteristic
201C22×D4×C17C2311yescharacteristic
202C22×D4×C17C2311yescharacteristic
203C23×C4×C17C2311yescharacteristic
204C23×C4×C17C2311yescharacteristic
205C23×C4×C17C2311yescharacteristic
206C23×Dic17—24no—
207C23×Dic17—24no—
208C23×Dic17—42no—
209C23×Dic17—42no—
210C23×Dic17—42no—
211C23×Dic17—42no—
212C23×Dic17C2311yescharacteristic
213C23×Dic17C2311yescharacteristic
214C23×Dic17C2311yescharacteristic
215C23×Dic17C2311yescharacteristic
216C23×Dic17C2311yescharacteristic
217C23×Dic17C2311yescharacteristic
218C23×Dic17C2311yescharacteristic
219C23×Dic17C2311yescharacteristic
220C23×Dic17C2311yescharacteristic
221C23×Dic17C2311yescharacteristic
222C23×Dic17C2311yescharacteristic
223C23×Dic17C2311yescharacteristic
224C23×Dic17C2311yescharacteristic
225C23×Dic17C2311yescharacteristic
226C23×Dic17C2311yescharacteristic
227C22×Dic34C2311yescharacteristic
228C17×#121—24no—
229C17×#121—24no—
230C17×#120—24no—
231C17×#120—42no—
232C2×C4⋊C4×C17C2311yescharacteristic
233C2×C4⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17—42no—
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×C22⋊C4×C17C2311yescharacteristic
249C2×C22⋊C4×C17C2311yescharacteristic
250C2×C22⋊Dic17—24no—
251C2×C22⋊Dic17—24no—
252C2×C22⋊Dic17—24no—
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
267C2×C22⋊Dic17C2311yescharacteristic
268C2×C22⋊Dic17C2311yescharacteristic
269C2×C22⋊Dic17C2311yescharacteristic
270C2×C22⋊Dic17C2311yescharacteristic
271C2×C22⋊Dic17C2311yescharacteristic
272C2×C22⋊Dic17C2311yescharacteristic
273C2×C22⋊Dic17C2311yescharacteristic
274C2×C22⋊Dic17C2311yescharacteristic
275C2×C22⋊Dic17C2311yescharacteristic
276C2×C22⋊Dic17C2311yescharacteristic
277C2×C22⋊Dic17C2311yescharacteristic
278C2×C22⋊Dic17C2311yescharacteristic
279C2×C22⋊Dic17C2311yescharacteristic
280C2×C22⋊Dic17C2311yescharacteristic
281C2×C22⋊Dic17C2311yescharacteristic
282C2×C22⋊Dic17C2311yescharacteristic
283C2×C22⋊Dic17C2311yescharacteristic
284C2×C22⋊Dic17C2311yescharacteristic
285C2×C22⋊Dic17C2311yescharacteristic
286#10587621—24no—
287#10587621—24no—
288#10587621—24no—
289#10587621—24no—
290#10587621—24no—
291#10587621—42no—
292D4×Dic17—24no—
293D4×Dic17—24no—
294D4×Dic17—24no—
295D4×Dic17—24no—
296D4×Dic17—24no—
297D4×Dic17—24no—
298D4×Dic17—24no—
299D4×Dic17—24no—
300D4×Dic17—42no—
301D4×Dic17—42no—
302D4×Dic17D418yescomplemented
303C2×C4⋊Dic17—24no—
304C2×C4⋊Dic17C2311yescharacteristic
305C2×C4⋊Dic17C2311yescharacteristic
306C2×C4⋊Dic17C2311yescharacteristic
307C2×C4⋊Dic17C2311yescharacteristic
308C2×C4⋊Dic17C2311yescharacteristic
309C2×C4⋊Dic17C2311yescharacteristic
310C2×C4⋊Dic17C2311yescharacteristic
311C2×C4⋊Dic17C2311yescharacteristic
312C2×C4⋊Dic17C2311yescharacteristic
313C2×C4⋊Dic17C2311yescharacteristic
314#10587610—24no—
315C2×#63225—24no—
316C2×#63225—42no—
317C2×#63225C2311yescharacteristic
318C2×#63225C2311yescharacteristic
319C2×#63225C2311yescharacteristic
320C2×#63225C2311yescharacteristic
321C2×#63225C2311yescharacteristic
322C2×#63225C2311yescharacteristic
323C2×#63225C2311yescharacteristic
324C2×#63225C2311yescharacteristic
325C2×#63225C2311yescharacteristic
326C2×#63225C2311yescharacteristic
327C2×#63225C2311yescharacteristic
328C2×#63225C2311yescharacteristic
329C2×#63225C2311yescharacteristic
330C2×#63225C2311yescharacteristic
331C2×#63225C2311yescharacteristic
332C2×#63225C2311yescharacteristic
333C2×#63225C2311yescharacteristic
334C2×#63225C2311yescharacteristic
335C2×#63225C2311yescharacteristic
336C2×#63225C2311yescharacteristic
337C2×#63225C2311yescharacteristic
338C2×#63225C2311yescharacteristic
339C2×C4×Dic17—24no—
340C2×C4×Dic17C2311yescharacteristic
341C2×C4×Dic17C2311yescharacteristic
342C2×C4×Dic17C2311yescharacteristic
343C2×C4×Dic17C2311yescharacteristic
344C2×C4×Dic17C2311yescharacteristic
345C2×C4×Dic17C2311yescharacteristic
346C2×C4×Dic17C2311yescharacteristic
347#10587575—24no—
348#10587575—24no—
349#10587565—24no—
350#10587565—24no—
351#10587564—24no—
352#10587564—24no—
353#10587564—42no—
354#10587564—42no—
355C17×#95C2311yescharacteristic
356C17×#95C2311yescharacteristic
357C17×#95C2311yescharacteristic
358C17×#95C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
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—22no—
396C24×C17—22no—
397C24×C17—22no—
398C24×C17—22no—
399C24×C17—22no—
400C24×C17—41no—
401C24×C17—41no—
402C24×C17—41no—
403C24×C17—41no—
404C24×C17#4114yes—
405C24×C17C2411yescharacteristic
406C24×C17C2411yescharacteristic
407C24×C17C2411yescharacteristic
408C24×C17C2411yescharacteristic
409C24×C17C2411yescharacteristic
410C24×C17C2411yescharacteristic
411C2×D4×C17—232no—
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—22no—
419C2×D4×C17—22no—
420C2×D4×C17—22no—
421C2×D4×C17—22no—
422C2×D4×C17—22no—
423C2×D4×C17—22no—
424C2×D4×C17—22no—
425C2×D4×C17—22no—
426C2×D4×C17—22no—
427C2×D4×C17—22no—
428C2×D4×C17—22no—
429C2×D4×C17—22no—
430C2×D4×C17—22no—
431C2×D4×C17—41no—
432C2×D4×C17—41no—
433C2×D4×C17—41no—
434C2×D4×C17—41no—
435C2×D4×C17—41no—
436C2×D4×C17—41no—
437C2×D4×C17C2×D414yes—
438C2×D4×C17#4114yes—
439C22×C4×C17—22no—
440C22×C4×C17—22no—
441C22×C4×C17—22no—
442C22×C4×C17—22no—
443C22×C4×C17—22no—
444C22×C4×C17—41no—
445C22×C4×C17—41no—
446C22×C4×C17—41no—
447C22×C4×C17—41no—
448C22×C4×C17C2411yescharacteristic
449C22×C4×C17C2411yescharacteristic
450C22×C4×C17C2411yescharacteristic
451C22×C4×C17C2411yescharacteristic
452C22×C4×C17C2411yescharacteristic
453C22×C4×C17C2411yescharacteristic
454C22×C4×C17C2411yescharacteristic
455C22×C4×C17C2411yescharacteristic
456C22×C4×C17C2411yescharacteristic
457C22×Dic17—22no—
458C22×Dic17—22no—
459C22×Dic17—22no—
460C22×Dic17—22no—
461C22×Dic17—22no—
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—41no—
482C22×Dic17—41no—
483C22×Dic17—41no—
484C22×Dic17—41no—
485C22×Dic17—41no—
486C22×Dic17—41no—
487C22×Dic17—41no—
488C22×Dic17—41no—
489C22×Dic17—41no—
490C22×Dic17—41no—
491C22×Dic17—41no—
492C22×Dic17—41no—
493C22×Dic17—41no—
494C22×Dic17—41no—
495C22×Dic17—41no—
496C22×Dic17—41no—
497C22×Dic17—41no—
498C22×Dic17—41no—
499C22×Dic17—41no—
500C22×Dic17—416no—
501C22×Dic17—416no—
502C22×Dic17C2×D414yes—
503C22×Dic17C2×D414yes—
504C22×Dic17C2411yescharacteristic
505C22×Dic17C2411yescharacteristic
506C22×Dic17C2411yescharacteristic
507C22×Dic17C2411yescharacteristic
508C22×Dic17C2411yescharacteristic
509C22×Dic17C2411yescharacteristic
510C22×Dic17C2411yescharacteristic
511C22×Dic17C2411yescharacteristic
512C22×Dic17C2411yescharacteristic
513C22×Dic17C2411yescharacteristic
514C22×Dic17C2411yescharacteristic
515C22×Dic17C2411yescharacteristic
516C22×Dic17C2411yescharacteristic
517C22×Dic17C2411yescharacteristic
518C22×Dic17C2411yescharacteristic
519C22×Dic17C2411yescharacteristic
520C2×Dic34—22no—
521C2×Dic34—41no—
522C2×Dic34—41no—
523C4⋊C4×C17—22no—
524C4⋊C4×C17—22no—
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—41no—
535C22⋊C4×C17—41no—
536C22⋊C4×C17—41no—
537C22⋊C4×C17—41no—
538C22⋊C4×C17—41no—
539C22⋊C4×C17—41no—
540C22⋊Dic17—22no—
541C22⋊Dic17—22no—
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—22no—
554C22⋊Dic17—22no—
555C22⋊Dic17—22no—
556C22⋊Dic17—22no—
557C22⋊Dic17—22no—
558C22⋊Dic17—22no—
559C22⋊Dic17—22no—
560C22⋊Dic17—22no—
561C22⋊Dic17—22no—
562C22⋊Dic17—41no—
563C22⋊Dic17—41no—
564C22⋊Dic17—41no—
565C22⋊Dic17—41no—
566C22⋊Dic17—41no—
567C22⋊Dic17—41no—
568C22⋊Dic17—41no—
569C22⋊Dic17—41no—
570C22⋊Dic17—41no—
571C22⋊Dic17C2×D414yes—
572C22⋊Dic17C2×D414yes—
573C4⋊Dic17—22no—
574C4⋊Dic17—22no—
575C4⋊Dic17—22no—
576C4⋊Dic17—22no—
577C4⋊Dic17—22no—
578C4⋊Dic17—22no—
579C4⋊Dic17—41no—
580C4⋊Dic17—41no—
581C4⋊Dic17—41no—
582C4⋊Dic17C2×D414yes—
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—22no—
596#63225—22no—
597#63225—41no—
598#63225—41no—
599#63225—41no—
600#63225—41no—
601#63225—41no—
602#63225—41no—
603#63225—41no—
604#63225—41no—
605C4×Dic17—22no—
606C4×Dic17—22no—
607C4×Dic17—22no—
608C4×Dic17—22no—
609C4×Dic17—41no—
610C4×Dic17—41no—
611C4×Dic17C2×D414yes—
612#34991—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—28no—
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—21no—
637C23×C17—21no—
638C23×C17—21no—
639C23×C17—21no—
640C23×C17—21no—
641C23×C17—21no—
642C23×C17—21no—
643C23×C17—21no—
644C23×C17—21no—
645C23×C17—21no—
646C23×C17—21no—
647C23×C17—21no—
648C23×C17—21no—
649C23×C17—44no—
650C23×C17—44no—
651C23×C17—44no—
652C23×C17—44no—
653C23×C17—44no—
654C23×C17—44no—
655C23×C17—44no—
656C23×C17—44no—
657C23×C17—44no—
658C23×C17—44no—
659C23×C17—44no—
660C23×C17C22×D412yes—
661C23×C17C22×D412yes—
662C23×C17C2×#4112yes—
663C23×C17C2×#4112yes—
664C23×C17C2×#4112yes—
665C23×C17C2×#4112yes—
666C23×C17C2×#4112yes—
667C23×C17H(5,𝔽2)12yes—
668C23×C172−1+412yes—
669C23×C17C2511yescharacteristic
670D4×C17—28no—
671D4×C17—28no—
672D4×C17—28no—
673D4×C17—28no—
674D4×C17—44no—
675D4×C17—44no—
676D4×C17—44no—
677D4×C17—82no—
678D4×C17—82no—
679C2×C4×C17—28no—
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—21no—
705C2×C4×C17—82no—
706C2×C4×C17—82no—
707C2×C4×C17C22×D412yes—
708C2×C4×C17C2×#4112yes—
709C2×Dic17—28no—
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—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—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—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—21no—
753C2×Dic17—44no—
754C2×Dic17—44no—
755C2×Dic17—44no—
756C2×Dic17—44no—
757C2×Dic17—44no—
758C2×Dic17—44no—
759C2×Dic17—44no—
760C2×Dic17—44no—
761C2×Dic17—44no—
762C2×Dic17—44no—
763C2×Dic17—44no—
764C2×Dic17—44no—
765C2×Dic17—44no—
766C2×Dic17—82no—
767C2×Dic17C22×D412yes—
768C2×Dic17C22×D412yes—
769C2×Dic17C22×D412yes—
770C2×Dic17C22×D412yes—
771C2×Dic17H(5,𝔽2)12yes—
772Dic34—82no—
773C2×#539—171no—
774C22×C4×D4—171no—
775#2852—171no—
776#2851—171no—
777#2849—171no—
778#2848—171no—
779#2638—171no—
780#2636—171no—
781#2633—171no—
782#2630—171no—
783#2480—171no—
784#2473—171no—
785#2466—171no—
786#2463—171no—
787#2460—171no—
788#2455—171no—
789#2449—171no—
790#2449—171no—
791#2443—171no—
792#2437—171no—
793#2425—171no—
794#2419—171no—
795#2418—171no—
796#2412—171no—
797#2410D1711yescharacteristic
798#2405—171no—
799#2325—171no—
800#2322—171no—
801#2318—171no—
802C4×#120—171no—
803C2×#385—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—22no—
820C22×C17—22no—
821C22×C17—22no—
822C22×C17—22no—
823C22×C17—22no—
824C22×C17—22no—
825C22×C17—416no—
826C22×C17—416no—
827C22×C17—41no—
828C22×C17—41no—
829C22×C17—41no—
830C22×C17—41no—
831C22×C17—41no—
832C22×C17—41no—
833C22×C17—41no—
834C22×C17—41no—
835C22×C17—41no—
836C22×C17—41no—
837C22×C17—41no—
838C22×C17—41no—
839C22×C17—41no—
840C22×C17—41no—
841C22×C17—41no—
842C22×C17—41no—
843C22×C17—41no—
844C22×C17—41no—
845C22×C17—41no—
846C22×C17#52514yes—
847C22×C17#53914yescomplemented
848C22×C17C23×D411yescharacteristic
849C22×C17C22×#4111yescharacteristic
850C22×C17C22×#4111yescharacteristic
851C22×C17C2×H(5,𝔽2)11yescharacteristic
852C22×C17C2×H(5,𝔽2)11yescharacteristic
853C22×C17C2×2−1+411yescharacteristic
854C22×C17#58511yescharacteristic
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—
864Dic17—22no—
865Dic17—22no—
866Dic17—22no—
867Dic17—22no—
868Dic17—22no—
869Dic17—41no—
870Dic17—41no—
871Dic17—41no—
872Dic17—41no—
873Dic17—41no—
874Dic17—41no—
875Dic17—41no—
876Dic17—41no—
877Dic17—41no—
878Dic17—41no—
879Dic17—41no—
880C23×D4C2×D1711yescharacteristic
881C24×C4—171no—
882C24×C4—171no—
883#539—348no—
884C2×#126—171no—
885C2×#126—171no—
886C2×#125—171no—
887C2×#125—171no—
888C2×#123—171no—
889C2×#123—171no—
890C2×#123—171no—
891C2×#123—171no—
892C2×#123—171no—
893C2×#123—171no—
894C2×C22⋊Q8—171no—
895C2×C22⋊Q8—171no—
896C2×C22⋊Q8—171no—
897C2×C22⋊Q8—171no—
898C2×C22⋊Q8—171no—
899C2×#121C2×D1711yescharacteristic
900C2×#121C2×D1711yescharacteristic
901C2×#120C2×D1711yescharacteristic
902C2×#120C2×D1711yescharacteristic
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—171no—
912C2×C4×D4—171no—
913C2×C4×D4—171no—
914C2×C4×D4—348no—
915C22×C4⋊C4—171no—
916C22×C4⋊C4—171no—
917C22×C4⋊C4—171no—
918C22×C22⋊C4—171no—
919C22×C22⋊C4—171no—
920C22×C22⋊C4—171no—
921C22×C22⋊C4C2×D1711yescharacteristic
922C22×C42—171no—
923#400—171no—
924#399—171no—
925#399—171no—
926#399—171no—
927#398—171no—
928#398—171no—
929#398—171no—
930#398—171no—
931#397—171no—
932#397—171no—
933#397—171no—
934#397—171no—
935#397—171no—
936#397—171no—
937#396—171no—
938#396—171no—
939#396—171no—
940#396—171no—
941#395—171no—
942#394—171no—
943#394—171no—
944#394—171no—
945#394—171no—
946#394—171no—
947#394—171no—
948#394—171no—
949#394—171no—
950#394C2×D1711yescharacteristic
951#394C2×D1711yescharacteristic
952#393—171no—
953#392C2×D1711yescharacteristic
954#392C2×D1711yescharacteristic
955#389—171no—
956#389—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#387—171no—
976#387—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#386—171no—
986#386—171no—
987#386—171no—
988#386C2×D1711yescharacteristic
989#386C2×D1711yescharacteristic
990#386C2×D1711yescharacteristic
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#385—171no—
1001#385—171no—
1002#385—171no—
1003#385—171no—
1004#385—171no—
1005#385—171no—
1006#385—171no—
1007#385—171no—
1008#385—171no—
1009#385—171no—
1010#385—171no—
1011#385—171no—
1012#385—171no—
1013#385—171no—
1014#385—171no—
1015#385—171no—
1016#385C2×D1711yescharacteristic
1017#383—171no—
1018#382—171no—
1019#381—171no—
1020#381—171no—
1021#381—171no—
1022#380—171no—
1023#380—171no—
1024#380—171no—
1025#380—171no—
1026#380—171no—
1027#380—171no—
1028#379—171no—
1029#379—171no—
1030#379—171no—
1031#379C2×D1711yescharacteristic
1032C4×C22⋊C4—171no—
1033C4×C22⋊C4—171no—
1034C4×C22⋊C4—171no—
1035C2×#95—171no—
1036C2×#95—171no—
1037C2×C17—24no—
1038C2×C17—24no—
1039C2×C17—42no—
1040C2×C17—42no—
1041C2×C17—42no—
1042C2×C17—81no—
1043C2×C17C2×#52511yescharacteristic
1044C2×C17C2×#53911yescharacteristic
1045C2×C17#345911yescharacteristic
1046C2×C17#348411yescharacteristic
1047C2×C17#348911yescharacteristic
1048C2×C17#351311yescharacteristic
1049C2×C17#352011yescharacteristic
1050C25C22×D1711yescharacteristic
1051C25C22×D1711yescharacteristic
1052C22×Q8—171no—
1053C22×D4—24no—
1054C22×D4—24no—
1055C22×D4—24no—
1056C22×D4C22×D1711yescharacteristic
1057C22×D4C22×D1711yescharacteristic
1058C22×D4C22×D1711yescharacteristic
1059C22×D4C22×D1711yescharacteristic
1060C22×D4C22×D1711yescharacteristic
1061C22×D4C22×D1711yescharacteristic
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—171no—
1080C23×C4—344no—
1081C23×C4—344no—
1082C23×C4—682no—
1083C23×C4—682no—
1084C23×C4—682no—
1085C23×C4—682no—
1086C23×C4C22×D1711yescharacteristic
1087C23×C4C22×D1711yescharacteristic
1088C23×C4C22×D1711yescharacteristic
1089#126—344no—
1090#126—344no—
1091#125—344no—
1092#125—344no—
1093#123—344no—
1094#123—344no—
1095#123—344no—
1096#123—344no—
1097#123—344no—
1098#123—682no—
1099C22⋊Q8—344no—
1100C22⋊Q8—344no—
1101C22⋊Q8—344no—
1102C22⋊Q8—682no—
1103C22⋊Q8—682no—
1104#121—24no—
1105#121—24no—
1106#120—24no—
1107#120—42no—
1108C4×D4—178no—
1109C4×D4—344no—
1110C4×D4—344no—
1111C4×D4—344no—
1112C4×D4—344no—
1113C4×D4—344no—
1114C4×D4—344no—
1115C4×D4—344no—
1116C4×D4—344no—
1117C4×D4—682no—
1118C4×D4—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—171no—
1142C2×C4⋊C4—171no—
1143C2×C4⋊C4—171no—
1144C2×C4⋊C4—171no—
1145C2×C4⋊C4—171no—
1146C2×C4⋊C4—171no—
1147C2×C4⋊C4—171no—
1148C2×C4⋊C4—171no—
1149C2×C4⋊C4—171no—
1150C2×C4⋊C4—171no—
1151C2×C4⋊C4—344no—
1152C2×C4⋊C4—344no—
1153C2×C4⋊C4—682no—
1154C2×C4⋊C4C22×D1711yescharacteristic
1155C2×C4⋊C4C22×D1711yescharacteristic
1156C2×C22⋊C4—42no—
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—171no—
1182C2×C22⋊C4—171no—
1183C2×C22⋊C4—171no—
1184C2×C22⋊C4—171no—
1185C2×C22⋊C4—171no—
1186C2×C22⋊C4—171no—
1187C2×C22⋊C4—171no—
1188C2×C22⋊C4—171no—
1189C2×C22⋊C4—171no—
1190C2×C22⋊C4—344no—
1191C2×C22⋊C4—344no—
1192C2×C22⋊C4—344no—
1193C2×C22⋊C4C22×D1711yescharacteristic
1194C2×C22⋊C4C22×D1711yescharacteristic
1195C2×C22⋊C4C22×D1711yescharacteristic
1196C2×C22⋊C4C22×D1711yescharacteristic
1197C2×C22⋊C4C22×D1711yescharacteristic
1198C2×C22⋊C4C22×D1711yescharacteristic
1199C2×C22⋊C4C22×D1711yescharacteristic
1200C2×C22⋊C4C22×D1711yescharacteristic
1201C2×C22⋊C4C22×D1711yescharacteristic
1202C2×C22⋊C4C22×D1711yescharacteristic
1203C2×C22⋊C4C22×D1711yescharacteristic
1204C2×C22⋊C4C22×D1711yescharacteristic
1205C2×C22⋊C4C22×D1711yescharacteristic
1206C2×C22⋊C4C22×D1711yescharacteristic
1207C2×C22⋊C4C22×D1711yescharacteristic
1208C2×C42—171no—
1209C2×C42—171no—
1210C2×C42—171no—
1211C2×C42—171no—
1212C2×C42—171no—
1213C2×C42—171no—
1214C2×C42—171no—
1215C2×C42—344no—
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#95—171no—
1245#95—171no—
1246#95—171no—
1247#95—171no—
1248#95C22×D1711yescharacteristic
1249#95C22×D1711yescharacteristic
1250#95C22×D1711yescharacteristic
1251#95C22×D1711yescharacteristic
1252C17#3499111yescharacteristic, complemented, Sylow
1253C24—22no—
1254C24—22no—
1255C24—22no—
1256C24—22no—
1257C24—22no—
1258C24—22no—
1259C24—22no—
1260C24—22no—
1261C24—22no—
1262C24—41no—
1263C24—41no—
1264C24—41no—
1265C24—41no—
1266C24#6325414yes—
1267C24C23×D1711yescharacteristic
1268C24C23×D1711yescharacteristic
1269C24C23×D1711yescharacteristic
1270C24C23×D1711yescharacteristic
1271C24C23×D1711yescharacteristic
1272C24C23×D1711yescharacteristic
1273C2×Q8—342no—
1274C2×Q8—681no—
1275C2×Q8—681no—
1276C2×D4—232no—
1277C2×D4—22no—
1278C2×D4—22no—
1279C2×D4—22no—
1280C2×D4—22no—
1281C2×D4—22no—
1282C2×D4—22no—
1283C2×D4—22no—
1284C2×D4—22no—
1285C2×D4—22no—
1286C2×D4—22no—
1287C2×D4—22no—
1288C2×D4—22no—
1289C2×D4—22no—
1290C2×D4—22no—
1291C2×D4—22no—
1292C2×D4—22no—
1293C2×D4—22no—
1294C2×D4—22no—
1295C2×D4—22no—
1296C2×D4—41no—
1297C2×D4—41no—
1298C2×D4—41no—
1299C2×D4—41no—
1300C2×D4—41no—
1301C2×D4—41no—
1302C2×D4D4×D1714yes—
1303C2×D4#6325414yes—
1304C22×C4—22no—
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—41no—
1310C22×C4—41no—
1311C22×C4—41no—
1312C22×C4—41no—
1313C22×C4—171no—
1314C22×C4—171no—
1315C22×C4—171no—
1316C22×C4—171no—
1317C22×C4—171no—
1318C22×C4—174no—
1319C22×C4—174no—
1320C22×C4—171no—
1321C22×C4—171no—
1322C22×C4—171no—
1323C22×C4—171no—
1324C22×C4—171no—
1325C22×C4—171no—
1326C22×C4—171no—
1327C22×C4—171no—
1328C22×C4—171no—
1329C22×C4—171no—
1330C22×C4—171no—
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—342no—
1351C22×C4—342no—
1352C22×C4—342no—
1353C22×C4—342no—
1354C22×C4—342no—
1355C22×C4—681no—
1356C22×C4—681no—
1357C22×C4—681no—
1358C22×C4—681no—
1359C22×C4—681no—
1360C22×C4—681no—
1361C22×C4—681no—
1362C22×C4—681no—
1363C22×C4—681no—
1364C22×C4—681no—
1365C22×C4—681no—
1366C22×C4—681no—
1367C22×C4—681no—
1368C22×C4—681no—
1369C22×C4—681no—
1370C22×C4—681no—
1371C22×C4—681no—
1372C22×C4—681no—
1373C22×C4—681no—
1374C22×C4—6816no—
1375C22×C4—6816no—
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—174no—
1388C4⋊C4—342no—
1389C4⋊C4—342no—
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—342no—
1408C4⋊C4—681no—
1409C4⋊C4—681no—
1410C4⋊C4—681no—
1411C4⋊C4—681no—
1412C4⋊C4—681no—
1413C4⋊C4—681no—
1414C4⋊C4—681no—
1415C4⋊C4—681no—
1416C4⋊C4—681no—
1417C4⋊C4—681no—
1418C4⋊C4—681no—
1419C22⋊C4—22no—
1420C22⋊C4—22no—
1421C22⋊C4—22no—
1422C22⋊C4—22no—
1423C22⋊C4—22no—
1424C22⋊C4—22no—
1425C22⋊C4—22no—
1426C22⋊C4—22no—
1427C22⋊C4—22no—
1428C22⋊C4—41no—
1429C22⋊C4—41no—
1430C22⋊C4—41no—
1431C22⋊C4—41no—
1432C22⋊C4—41no—
1433C22⋊C4—41no—
1434C22⋊C4—174no—
1435C22⋊C4—174no—
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—342no—
1450C22⋊C4—342no—
1451C22⋊C4—342no—
1452C22⋊C4—342no—
1453C22⋊C4—342no—
1454C22⋊C4—342no—
1455C22⋊C4—342no—
1456C22⋊C4—342no—
1457C22⋊C4—342no—
1458C22⋊C4—681no—
1459C22⋊C4—681no—
1460C22⋊C4—681no—
1461C22⋊C4—681no—
1462C22⋊C4—681no—
1463C22⋊C4—681no—
1464C22⋊C4—681no—
1465C22⋊C4—681no—
1466C22⋊C4—681no—
1467C42—174no—
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—21no—
1498C23—21no—
1499C23—21no—
1500C23—21no—
1501C23—21no—
1502C23—28no—
1503C23—21no—
1504C23—21no—
1505C23—21no—
1506C23—21no—
1507C23—21no—
1508C23—21no—
1509C23—21no—
1510C23—44no—
1511C23—44no—
1512C23—44no—
1513C23—44no—
1514C23—44no—
1515C23—44no—
1516C23—44no—
1517C23—44no—
1518C23—44no—
1519C23—44no—
1520C23—44no—
1521C23C2×D4×D1712yes—
1522C23C2×D4×D1712yes—
1523C23C2×#6325412yes—
1524C23C2×#6325412yes—
1525C23C2×#6325412yes—
1526C23C2×#6325412yes—
1527C23C2×#6325412yes—
1528C23#1058769112yes—
1529C23#1058769712yes—
1530C23C24×D1711yescharacteristic
1531Q8—1362no—
1532D4—28no—
1533D4—28no—
1534D4—28no—
1535D4—28no—
1536D4—44no—
1537D4—44no—
1538D4—44no—
1539D4—82no—
1540D4—82no—
1541C2×C4—28no—
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—82no—
1568C2×C4—82no—
1569C2×C4—172no—
1570C2×C4—172no—
1571C2×C4—172no—
1572C2×C4—172no—
1573C2×C4—172no—
1574C2×C4—348no—
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—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—684no—
1619C2×C4—684no—
1620C2×C4—684no—
1621C2×C4—684no—
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—1362no—
1632C2×C4C2×D4×D1712yes—
1633C2×C4C2×#6325412yes—
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—22no—
1650C22—22no—
1651C22—22no—
1652C22—22no—
1653C22—22no—
1654C22—22no—
1655C22—416no—
1656C22—416no—
1657C22—41no—
1658C22—41no—
1659C22—41no—
1660C22—41no—
1661C22—41no—
1662C22—41no—
1663C22—41no—
1664C22—41no—
1665C22—41no—
1666C22—41no—
1667C22—41no—
1668C22—41no—
1669C22—41no—
1670C22—41no—
1671C22—41no—
1672C22—41no—
1673C22—41no—
1674C22—41no—
1675C22—41no—
1676C22#1176331514yes—
1677C22#1176340414yescomplemented
1678C22C22×D4×D1711yescharacteristic
1679C22C22×#6325411yescharacteristic
1680C22C22×#6325411yescharacteristic
1681C22H(5,𝔽2)×D1711yescharacteristic
1682C22C2×#1058769111yescharacteristic
1683C22C2×#1058769711yescharacteristic
1684C22#1176364411yescharacteristic
1685C4—22no—
1686C4—22no—
1687C4—41no—
1688C4—41no—
1689C4—41no—
1690C4—41no—
1691C4—41no—
1692C4—41no—
1693C4—41no—
1694C4—342no—
1695C4—342no—
1696C4—342no—
1697C4—342no—
1698C4—342no—
1699C4—681no—
1700C4—681no—
1701C4—681no—
1702C4—681no—
1703C4—681no—
1704C4—681no—
1705C4—681no—
1706C4—681no—
1707C4—681no—
1708C4—681no—
1709C4—681no—
1710C2—24no—
1711C2—24no—
1712C2—42no—
1713C2—42no—
1714C2—42no—
1715C2—81no—
1716C2C2×#1176331511yescharacteristic
1717C2C2×#1176340411yescharacteristic
1718C2#1454219011yescharacteristic
1719C2#1454241211yescharacteristic
1720C2#1454245511yescharacteristic
1721C2#1454270911yescharacteristic
1722C2#1454282011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
Fitting, prime radicalC17×#2410C2
hypercenter#2410D17
hypocenterC17#34991
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2410

Complements

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

NH ≅ G/Ntype
1. C2×#11763404C2semidirect
2. C22×D4×Dic17C2semidirect
3. #14537097C2semidirect
4. #14537090C2semidirect
5. #14537074C2semidirect
6. #14537069C2semidirect
7. #14534700C2semidirect
8. #14534678C2semidirect
9. #14534651C2semidirect
10. #14534620C2semidirect
11. #14533027C2semidirect
12. #14532922C2semidirect
13. #14532813C2semidirect
14. #14532774C2semidirect
15. #14532729C2semidirect
16. #14532660C2semidirect
17. #14532599C2semidirect
18. #14532597C2semidirect
19. #14532515C2semidirect
20. #14532445C2semidirect
21. #14532341C2semidirect
22. #14532259C2semidirect
23. #14532242C2semidirect
24. #14532181C2semidirect
25. #14532107C2semidirect
26. #14531489C2semidirect
27. #14531458C2semidirect
28. #14531410C2semidirect
29. #120×Dic17C2semidirect
30. C2×#11762681C2semidirect
35. C2×#10587565C22semidirect
36. C2×#10587565C22semidirect
37. C2×#10587575C22semidirect
38. C2×#10587575C22semidirect
41. C2×#10587621C22semidirect
42. C2×#10587621C22semidirect
43. C2×#10587621C22semidirect
44. C2×#10587621C22semidirect
45. C2×#10587610C22semidirect
47. C2×#10587564C22semidirect
48. C2×#10587564C22semidirect
49. C2×#10587564C22semidirect
60. C2×D4×Dic17C22semidirect
61. C2×D4×Dic17C22semidirect
63. C22×#63225C22semidirect
64. C22×#63225C22semidirect
69. #11762749C22semidirect
70. #11762745C22semidirect
71. #11762745C22semidirect
72. #11762745C22semidirect
73. #11762743C22semidirect
74. #11762742C22semidirect
75. #11762741C22semidirect
76. #11762739C22semidirect
77. #11762737C22semidirect
78. #11762737C22semidirect
79. #11762737C22semidirect
80. #11762737C22semidirect
81. #11762734C22semidirect
82. #11762734C22semidirect
83. #11762732C22semidirect
84. #11762732C22semidirect
85. #11762732C22semidirect
86. #11762732C22semidirect
87. #11762730C22semidirect
92. #11762723C22semidirect
93. #11762723C22semidirect
94. #11762723C22semidirect
95. #11762723C22semidirect
96. #11762721C22semidirect
97. #11762706C22semidirect
98. #11762706C22semidirect
99. #11762706C22semidirect
100. #11762704C22semidirect
101. #11762703C22semidirect
102. #11762703C22semidirect
103. #11762702C22semidirect
104. #11762702C22semidirect
105. #11762697C22semidirect
106. #11762697C22semidirect
107. #11762697C22semidirect
108. #11762697C22semidirect
109. #11762696C22semidirect
110. #11762695C22semidirect
111. #11762695C22semidirect
112. #11762694C22semidirect
113. #11762694C22semidirect
114. #11762694C22semidirect
115. #11762692C22semidirect
116. #11762691C22semidirect
117. #11762691C22semidirect
118. #11762690C22semidirect
124. #11762689C22semidirect
125. #11762689C22semidirect
126. #11762689C22semidirect
127. #11762689C22semidirect
128. #11762689C22semidirect
129. #11762689C22semidirect
132. #11762684C22semidirect
133. #11762684C22semidirect
134. #11762684C22semidirect
135. #11762684C22semidirect
136. #11762684C22semidirect
139. #11762682C22semidirect
140. #11762682C22semidirect
146. #11762681C22semidirect
147. #11762681C22semidirect
148. #11762681C22semidirect
149. #11762681C22semidirect
150. #11762681C22semidirect
151. #11762681C22semidirect
152. #11762681C22semidirect
153. #11762681C22semidirect
154. #11762681C22semidirect
155. #11762676C22semidirect
156. #11762673C22semidirect
157. #11762670C22semidirect
158. #11762670C22semidirect
159. #11762670C22semidirect
160. #11762669C22semidirect
164. #11762667C22semidirect
165. #11762667C22semidirect
170. C22⋊C4×Dic17C22semidirect
171. C22⋊C4×Dic17C22semidirect
172. C2×#10587502C22semidirect
173. C2×#10587502C22semidirect
302. D4×Dic17D4semidirect
847. C22×C17#539semidirect
1252. C17#34991semidirect
1677. C22#11763404semidirect

Maximal subgroups

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

subgroupindex
C2×#117634042
C22×D4×Dic172
#145370972
#145370902
#145370742
#145370692
#145347002
#145346782
#145346512
#145346202
#145330272
#145329222
#145328132
#145327742
#145327292
#145326602
#145325992
#145325972
#145325152
#145324452
#145323412
#145322592
#145322422
#145321812
#145321072
#145314892
#145314582
#145314102
#120×Dic172
C2×#117626812
C17×#24102
#3499117