Finite Group Databasebeta

← #17899170

Subgroups — #17899170

Order 4352.

2094 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542111C211yesmaximal, characteristic
2#14537862C212yesmaximal, complemented
3#14537857C212yesmaximal, complemented
4#14537853C211yesmaximal, characteristic, complemented
5#14537851C211yesmaximal, characteristic, complemented
6#14537848C211yesmaximal, characteristic, complemented
7#14537843C212yesmaximal, complemented
8#14537835C212yesmaximal, complemented
9#14537833C212yesmaximal, complemented
10#14537831C212yesmaximal, complemented
11#14537510C212yesmaximal, complemented
12#14537507C212yesmaximal, complemented
13#14537482C212yesmaximal, complemented
14#14537475C212yesmaximal, complemented
15#14537443C212yesmaximal, complemented
16#14537232C212yesmaximal, complemented
17#14537226C211yesmaximal, characteristic, complemented
18D17×#408C211yesmaximal, characteristic, complemented
19C17×#2980C211yesmaximal, characteristic, complemented
20C2×#41×D17C2211yescharacteristic
21C2×#41×D17C2211yescharacteristic
22C2×#10587593C2212yes—
23C2×#10587587C2212yes—
24C22×#63218C2211yescharacteristic, complemented
25C2×M16×D17C2211yescharacteristic, complemented
26C2×M16×D17C2211yescharacteristic, complemented
27C22×C8×D17C2211yescharacteristic, complemented
28#11763386C412yes—
29#11763386C412yes—
30#11763384C411yescharacteristic
31#11763384C411yescharacteristic
32#11763379C411yescharacteristic
33#11763379C411yescharacteristic
34#11763377C411yescharacteristic
35#11763377C411yescharacteristic
36#11763372C411yescharacteristic
37#11763372C411yescharacteristic
38#11763367C412yes—
39#11763367C412yes—
40#11763359C2211yescharacteristic
41#11763355C2211yescharacteristic
42#11763355C2211yescharacteristic
43#11763318C2212yes—
44#11763318C2212yes—
45#11763318C2212yes—
46#11763318C2212yes—
47C2×#10587558C2211yescharacteristic
48#11762887C2212yescomplemented
49#11762887C2212yescomplemented
50#11762886C2212yescomplemented
51#11762886C2212yescomplemented
52#11762885C2212yescomplemented
53#11762885C2212yescomplemented
54#11762884C2212yescomplemented
55#11762884C2212yescomplemented
56#11762883C2212yescomplemented
57#11762883C2212yescomplemented
58#11762882C2212yescomplemented
59#11762882C2212yescomplemented
60#11762882C2212yescomplemented
61#11762882C2212yescomplemented
62#11762880C2212yescomplemented
63#11762880C2212yescomplemented
64#11762878C2212yescomplemented
65#11762878C2212yescomplemented
66#11762877C2212yescomplemented
67#11762877C2212yescomplemented
68D4×#3622C2212yescomplemented
69D4×#3622C2212yescomplemented
70#11762874C2212yescomplemented
71#11762874C2212yescomplemented
72C8×C22⋊D17C2212yescomplemented
73C8×C22⋊D17C2212yescomplemented
74#11762872C2212yescomplemented
75#11762872C2212yescomplemented
76#11762871C2212yescomplemented
77#11762871C2212yescomplemented
78#11762869C2212yescomplemented
79#11762869C2212yescomplemented
80#11762863C2212yescomplemented
81#11762862C2212yescomplemented
82#11762859C2212yescomplemented
83#11762834C2212yescomplemented
84#11762834C2212yescomplemented
85#11762777C2211yescharacteristic
86#11762777C2211yescharacteristic
87#11762776C2211yescharacteristic, complemented
88#11762776C2211yescharacteristic, complemented
89#11762776C2212yescomplemented
90#11762775C2211yescharacteristic
91#11762775C2211yescharacteristic
92#11762774C2212yes—
93#11762774C2212yes—
94#11762774C2212yes—
95#11762774C2212yes—
96#11762774C2212yescomplemented
97#11762774C2212yescomplemented
98#11762774C2212yescomplemented
99#11762774C2212yescomplemented
100#11762772C2212yescomplemented
101#11762771C2212yes—
102#11762771C2212yescomplemented
103#11762771C2212yescomplemented
104C2×#10587491C2212yescomplemented
105C22⋊C8×D17C2212yes—
106C22⋊C8×D17C2212yescomplemented
107C22⋊C8×D17C2212yescomplemented
108#11762766C2212yescomplemented
109#11762766C2212yescomplemented
110C17×#532C2211yescharacteristic
111C17×#435C2212yescomplemented
112C17×#435C2212yescomplemented
113C17×#435C2212yescomplemented
114C17×#435C2212yescomplemented
115C17×#432C2212yescomplemented
116C17×#408C2211yescharacteristic, complemented
117C17×#408C2211yescharacteristic, complemented
118C17×#408C2212yescomplemented
119C2×#41×C17C2311yescharacteristic
120C2×#41×C17C2311yescharacteristic
121#41×D17—42no—
122#41×D17—42no—
123#41×D17—42no—
124#41×D17—42no—
125C2×#63256C2×C411yescharacteristic
126C2×#63256C2×C411yescharacteristic
127C2×Q8×D17C2×C411yescharacteristic
128C2×Q8×D17C2×C411yescharacteristic
129C2×#63254C2×C411yescharacteristic
130C2×#63254C2×C411yescharacteristic
131C2×#63254C2×C412yes—
132C2×#63254C2×C411yescharacteristic
133C2×#63254C2×C411yescharacteristic
134C2×D4×D17C2×C411yescharacteristic
135C2×D4×D17C2×C411yescharacteristic
136C2×D4×D17C2×C412yes—
137C2×D4×D17C2×C411yescharacteristic
138C2×D4×D17C2×C411yescharacteristic
139C2×#63252C2312yes—
140C2×#63252C2311yescharacteristic
141C2×#63252C2311yescharacteristic
142C2×#63252C2311yescharacteristic
143C2×#63252C2311yescharacteristic
144C22×C4×D17C2311yescharacteristic
145C22×C4×D17C2311yescharacteristic
146C22×C4×D17C2311yescharacteristic
147C22×C4×D17C2312yes—
148C2×M16×C17C2312yes—
149C2×M16×C17C2311yescharacteristic
150C2×M16×C17C2311yescharacteristic
151C22×C8×C17C2312yes—
152C22×C8×C17C2311yescharacteristic
153C22×C8×C17C2311yescharacteristic
154C17×C4⋊Q8C2×C411yescharacteristic
155C17×#127C2×C411yescharacteristic
156C17×#124C2×C411yescharacteristic
157C17×#124C2×C411yescharacteristic
158C17×#121C2×C412yes—
159C17×#121C2×C412yes—
160C4×D4×C17C2312yes—
161C4×D4×C17C2312yes—
162C2×C42×C17C2311yescharacteristic
163#10587633C2×C411yescharacteristic
164#10587633C2×C411yescharacteristic
165#10587630C2×C411yescharacteristic
166#10587630C2×C411yescharacteristic
167#10587626C2×C411yescharacteristic
168#10587626C2×C411yescharacteristic
169#10587625C2×C412yes—
170#10587625C2×C412yes—
171#10587625C2×C412yes—
172#10587625C2×C412yes—
173#10587625C2×C412yes—
174#10587625C2×C412yes—
175#10587625C2×C412yes—
176#10587625C2×C412yes—
177#10587623C2×C412yes—
178#10587623C2×C412yes—
179#10587623C2×C412yes—
180#10587623C2×C412yes—
181#10587622C2×C411yescharacteristic
182#10587622C2×C411yescharacteristic
183#10587616C2×C412yes—
184#10587616C2×C412yes—
185C4×C22⋊D17C2312yes—
186C4×C22⋊D17C2312yes—
187C4×C22⋊D17C2312yes—
188C4×C22⋊D17C2312yes—
189C2×#63227C2×C412yes—
190C2×#63225C2×C412yes—
191C2×C4×Dic17C2311yescharacteristic
192C2×#63223C2312yes—
193C2×#63223C2311yescharacteristic
194C2×#63223C2311yescharacteristic
195C22×#3622C2312yes—
196C22×#3622C2311yescharacteristic
197C22×#3622C2311yescharacteristic
198#10587593—44no—
199M16×D17—42no—
200M16×D17—42no—
201#10587587—44no—
202C2×#63218—42no—
203C2×#63218C2312yes—
204C2×#63218C2312yes—
205C2×#63218C2312yes—
206C2×#63218C2312yes—
207C2×#63218C2312yes—
208C2×#63218C2312yes—
209C2×C8×D17—42no—
210C2×C8×D17C2312yes—
211C2×C8×D17C2312yes—
212C2×C8×D17C2312yes—
213C2×C8×D17C2312yes—
214C2×C8×D17C2312yes—
215C2×C8×D17C2312yes—
216#10587582C2×C412yes—
217#10587582C2×C412yes—
218#10587582C2×C412yes—
219#10587582C2×C412yes—
220#10587580C2×C412yes—
221#10587580C2×C412yes—
222#10587580C2×C412yes—
223#10587580C2×C412yes—
224#10587570C2×C412yes—
225#10587570C2×C412yes—
226#10587570C2×C412yes—
227#10587570C2×C412yes—
228#10587569C2×C412yes—
229#10587569C2×C412yes—
230#10587569C2×C412yes—
231#10587569C2×C412yes—
232#10587568C2×C412yes—
233#10587568C2×C412yes—
234#10587568C2×C412yes—
235#10587568C2×C412yes—
236#10587564C2×C412yes—
237#10587564C2×C412yes—
238#10587564C2×C412yes—
239#10587564C2×C412yes—
240#10587561C2×C411yescharacteristic
241#10587561C2×C411yescharacteristic
242#10587560C2×C411yescharacteristic
243C4×D68C2312yes—
244C4×D68C2312yes—
245#10587558C2×C411yescharacteristic
246#10587558C2×C411yescharacteristic
247#10587558C2×C411yescharacteristic
248#10587558C2×C411yescharacteristic
249#10587558C2312yes—
250#10587558C2312yes—
251#10587555C2×C411yescharacteristic
252C17×C4⋊C8C2312yes—
253C17×C4⋊C8C2312yes—
254C17×C22⋊C8C2312yes—
255C17×C22⋊C8C2312yes—
256C17×C22⋊C8C2312yes—
257C17×C22⋊C8C2312yes—
258C17×C22⋊C8C2312yes—
259C17×C22⋊C8C2312yes—
260C17×#97C2312yes—
261C17×#97C2312yes—
262C22⋊#3622C2312yes—
263C22⋊#3622C2312yes—
264C22⋊#3622C2312yes—
265C22⋊#3622C2312yes—
266C22⋊#3622C2312yes—
267C22⋊#3622C2312yes—
268#10587491C2312yes—
269#10587491C2312yes—
270#10587491C2312yes—
271#10587491C2312yes—
272#10587491C2312yes—
273#10587491C2312yes—
274#10587491C2312yes—
275#10587491C2312yes—
276#10587491C2312yes—
277#10587491C2312yes—
278#10587491C2312yes—
279#10587491C2312yes—
280#10587486C2312yes—
281#10587486C2312yes—
282#10587485C2312yes—
283#10587485C2312yes—
284#10587485C2312yes—
285#10587485C2312yes—
286C8×Dic17C2312yes—
287C8×Dic17C2312yes—
288C4⋊#3622C2312yes—
289C4⋊#3622C2312yes—
290C4×#3622C2312yes—
291C4×#3622C2312yes—
292C23×D17C22×C411yescharacteristic
293C23×D17C22×C411yescharacteristic
294C23×D17C22×C411yescharacteristic
295C23×D17C22×C412yes—
296#41×C17—41no—
297#41×C17—41no—
298#41×C17—41no—
299#41×C17—41no—
300C2×Q8×C17C22×C411yescharacteristic
301C2×Q8×C17C22×C411yescharacteristic
302C2×D4×C17C22×C411yescharacteristic
303C2×D4×C17C22×C411yescharacteristic
304C2×D4×C17C22×C412yes—
305C2×D4×C17C22×C412yes—
306C2×D4×C17C22×C412yes—
307C2×D4×C17C22×C411yescharacteristic
308C2×D4×C17C22×C411yescharacteristic
309C22×C4×C17C22×C412yes—
310C22×C4×C17C2411yescharacteristic
311C22×C4×C17C2411yescharacteristic
312C22×C4×C17C2412yes—
313C22×C4×C17C2411yescharacteristic
314C2×C22⋊D17C22×C412yes—
315C2×C22⋊D17C22×C412yes—
316C2×C22⋊D17C22×C411yescharacteristic
317C2×C22⋊D17C22×C411yescharacteristic
318C2×C22⋊D17C22×C411yescharacteristic
319C2×C22⋊D17C22×C411yescharacteristic
320C2×C22⋊D17C22×C412yes—
321C2×C22⋊D17C22×C411yescharacteristic
322C2×C22⋊D17C22×C411yescharacteristic
323C2×C22⋊D17C22×C412yes—
324C2×C22⋊D17C22×C412yes—
325C2×C22⋊D17C22×C412yes—
326C2×C22⋊D17C22×C412yes—
327C22×Dic17C22×C411yescharacteristic
328C22×Dic17C22×C411yescharacteristic
329C22×Dic17C22×C411yescharacteristic
330C22×Dic17C22×C412yes—
331C22×Dic17C22×C412yes—
332#63256—42no—
333#63256—42no—
334Q8×D17—42no—
335Q8×D17—42no—
336#63254—44no—
337#63254—42no—
338#63254—42no—
339#63254—42no—
340#63254—42no—
341D4×D17—42no—
342D4×D17—42no—
343D4×D17—42no—
344D4×D17—42no—
345D4×D17—44no—
346#63252—24no—
347#63252—24no—
348#63252—41no—
349#63252—41no—
350#63252—41no—
351#63252—41no—
352#63252—41no—
353#63252—41no—
354#63252—41no—
355#63252—41no—
356C2×D68C22×C412yes—
357C2×D68C22×C411yescharacteristic
358C2×D68C22×C411yescharacteristic
359C2×D68C22×C411yescharacteristic
360C2×D68C22×C411yescharacteristic
361C2×D68C22×C412yes—
362C2×D68C22×C412yes—
363C2×C4×D17—22no—
364C2×C4×D17—22no—
365C2×C4×D17—22no—
366C2×C4×D17—22no—
367C2×C4×D17—22no—
368C2×C4×D17—22no—
369C2×C4×D17—42no—
370C2×C4×D17—42no—
371C2×C4×D17C22×C411yescharacteristic
372C2×C4×D17C22×C411yescharacteristic
373C2×C4×D17C22×C411yescharacteristic
374C2×C4×D17C22×C411yescharacteristic
375C2×C4×D17C22×C411yescharacteristic
376C2×C4×D17C22×C411yescharacteristic
377C2×C4×D17C22×C412yes—
378C2×C4×D17C22×C412yes—
379C2×C4×D17C2411yescharacteristic
380C2×C4×D17C2411yescharacteristic
381C2×C4×D17C2411yescharacteristic
382C2×C4×D17C2412yes—
383C2×C4×D17C2411yescharacteristic
384C2×Dic34C22×C412yes—
385C2×Dic34C22×C411yescharacteristic
386C2×Dic34C22×C411yescharacteristic
387C2×Dic34C22×C411yescharacteristic
388C2×Dic34C22×C411yescharacteristic
389M16×C17—41no—
390M16×C17—41no—
391M16×C17—42no—
392C2×C8×C17—41no—
393C2×C8×C17—41no—
394C2×C8×C17—42no—
395C2×C8×C17C2412yes—
396C2×C8×C17C2412yes—
397C2×C8×C17C2412yes—
398C2×C8×C17C2412yes—
399C4⋊C4×C17C22×C412yes—
400C4⋊C4×C17C22×C412yes—
401C22⋊C4×C17C22×C412yes—
402C22⋊C4×C17C22×C412yes—
403C22⋊C4×C17C22×C412yes—
404C22⋊C4×C17C22×C412yes—
405C42×C17C22×C411yescharacteristic
406C42×C17C22×C411yescharacteristic
407C42×C17C2412yes—
408C22⋊Dic17C22×C412yes—
409C22⋊Dic17C22×C412yes—
410C22⋊Dic17C22×C412yes—
411C22⋊Dic17C22×C412yes—
412#63227C22×C412yes—
413#63227C22×C412yes—
414#63227C22×C412yes—
415#63227C22×C412yes—
416#63227C22×C412yes—
417#63227C22×C412yes—
418#63227C22×C412yes—
419#63227C22×C412yes—
420#63227C22×C412yes—
421#63227C22×C412yes—
422#63227C22×C412yes—
423#63227C22×C412yes—
424C4⋊Dic17C22×C412yes—
425C4⋊Dic17C22×C412yes—
426#63225C22×C412yes—
427#63225C22×C412yes—
428#63225C22×C412yes—
429#63225C22×C412yes—
430#63225C22×C412yes—
431#63225C22×C412yes—
432#63225C22×C412yes—
433#63225C22×C412yes—
434C4×Dic17C22×C411yescharacteristic
435C4×Dic17C22×C411yescharacteristic
436C4×Dic17C2412yes—
437#63223—42no—
438#63223—41no—
439#63223—41no—
440C2×#3622—41no—
441C2×#3622—41no—
442C2×#3622—42no—
443C2×#3622C2412yes—
444C2×#3622C2412yes—
445C2×#3622C2412yes—
446C2×#3622C2412yes—
447#63218—24no—
448#63218—24no—
449#63218—42no—
450#63218—42no—
451#63218—42no—
452#63218—42no—
453C8×D17—24no—
454C8×D17—24no—
455C8×D17—42no—
456C8×D17—42no—
457C8×D17—42no—
458C8×D17—42no—
459#60235—171nomaximal, Sylow
460C23×C17C23×C411yescharacteristic
461C23×C17C23×C411yescharacteristic
462C23×C17C23×C412yes—
463C23×C17C23×C411yescharacteristic
464C22×D17—22no—
465C22×D17—22no—
466C22×D17—22no—
467C22×D17—42no—
468C22×D17—42no—
469C22×D17—42no—
470C22×D17—42no—
471C22×D17—42no—
472C22×D17—42no—
473C22×D17C23×C411yescharacteristic
474C22×D17C23×C411yescharacteristic
475C22×D17C23×C411yescharacteristic
476C22×D17C23×C412yes—
477C22×D17C23×C411yescharacteristic
478Q8×C17—41no—
479Q8×C17—41no—
480D4×C17—42no—
481D4×C17—41no—
482D4×C17—41no—
483D4×C17—41no—
484D4×C17—41no—
485D4×C17—42no—
486D4×C17—42no—
487C2×C4×C17—21no—
488C2×C4×C17—21no—
489C2×C4×C17—22no—
490C2×C4×C17—21no—
491C2×C4×C17—21no—
492C2×C4×C17—22no—
493C2×C4×C17—21no—
494C2×C4×C17—21no—
495C2×C4×C17—42no—
496C2×C4×C17C23×C411yescharacteristic
497C2×C4×C17C23×C412yes—
498C2×C4×C17C23×C412yes—
499C2×C4×C17C23×C412yes—
500C2×C4×C17C23×C411yescharacteristic
501C2×C4×C17C23×C411yescharacteristic
502C2×C4×C17C2511yescharacteristic
503C22⋊D17—24no—
504C22⋊D17—24no—
505C22⋊D17—42no—
506C22⋊D17—41no—
507C22⋊D17—41no—
508C22⋊D17—41no—
509C22⋊D17—41no—
510C22⋊D17—41no—
511C22⋊D17—41no—
512C22⋊D17—42no—
513C22⋊D17—42no—
514C22⋊D17—42no—
515C22⋊D17—42no—
516C2×Dic17—22no—
517C2×Dic17—22no—
518C2×Dic17—22no—
519C2×Dic17—42no—
520C2×Dic17—42no—
521C2×Dic17C23×C412yes—
522C2×Dic17C23×C411yescharacteristic
523C2×Dic17C23×C411yescharacteristic
524C2×Dic17C23×C412yes—
525C2×Dic17C23×C412yes—
526C2×Dic17C23×C411yescharacteristic
527C2×Dic17C23×C411yescharacteristic
528D68—24no—
529D68—42no—
530D68—42no—
531D68—41no—
532D68—41no—
533D68—41no—
534D68—41no—
535C4×D17—22no—
536C4×D17—22no—
537C4×D17—22no—
538C4×D17—21no—
539C4×D17—21no—
540C4×D17—21no—
541C4×D17—21no—
542C4×D17—21no—
543C4×D17—21no—
544C4×D17—22no—
545C4×D17—22no—
546C4×D17—22no—
547C4×D17—22no—
548C4×D17—22no—
549C4×D17—42no—
550C4×D17—42no—
551C4×D17H(5,𝔽2)12yes—
552C4×D17H(5,𝔽2)12yes—
553Dic34—24no—
554Dic34—41no—
555Dic34—41no—
556Dic34—41no—
557Dic34—41no—
558C8×C17—22no—
559C8×C17—22no—
560C8×C17—22no—
561C8×C17—22no—
562#3622—22no—
563#3622—22no—
564#3622—22no—
565#3622—22no—
566#3449—171no—
567#2981—172no—
568#2981—172no—
569#2980—171no—
570#2980D1711yescharacteristic, complemented
571#2979—171no—
572#2979—171no—
573#2978—172no—
574#2977—172no—
575#2976—172no—
576#2976—172no—
577#2933—172no—
578#2933—172no—
579#2930—172no—
580#2929—172no—
581#2924—172no—
582#2880—172no—
583#2879—171no—
584C2×#408—171no—
585C22×C17—21no—
586C22×C17—21no—
587C22×C17—21no—
588C22×C17—22no—
589C22×C17—22no—
590C22×C17—22no—
591C22×C17—22no—
592C22×C17—22no—
593C22×C17—22no—
594C22×C17C24×C411yescharacteristic
595C2×D17—22no—
596C2×D17—21no—
597C2×D17—21no—
598C2×D17—21no—
599C2×D17—22no—
600C2×D17—22no—
601C2×D17—22no—
602C2×D17—22no—
603C2×D17—22no—
604C2×D17—22no—
605C2×D17—44no—
606C2×D17—82no—
607C2×D17—82no—
608C2×D17—84no—
609C2×D17#51812yes—
610C4×C17—22no—
611C4×C17—21no—
612C4×C17—21no—
613C4×C17—21no—
614C4×C17—22no—
615C4×C17—22no—
616C4×C17C2×H(5,𝔽2)11yescharacteristic
617C4×C17C2×H(5,𝔽2)11yescharacteristic
618Dic17—22no—
619Dic17—21no—
620Dic17—21no—
621Dic17—21no—
622Dic17—22no—
623Dic17—22no—
624Dic17#51812yes—
625C22×#41—171no—
626C22×#41—171no—
627C2×#131—172no—
628C2×#131—172no—
629C22×M16—171no—
630C22×M16—171no—
631C22×M16—171no—
632C23×C8—171no—
633#537—172no—
634#537—172no—
635#536—171no—
636#536—171no—
637#536—171no—
638#536—171no—
639#535—171no—
640#535—171no—
641#535—171no—
642#535—171no—
643#534—172no—
644#534—172no—
645#532—171no—
646#532—171no—
647#532—171no—
648#532C2×D1711yescharacteristic
649#525—172no—
650#525—172no—
651#525—172no—
652#525—172no—
653C2×#117—171no—
654#436—172no—
655#436—172no—
656#436—172no—
657#436—172no—
658#436—172no—
659#436—172no—
660#436—172no—
661#436—172no—
662#435—172no—
663#435—172no—
664#435—172no—
665#435—172no—
666#435—172no—
667#435—172no—
668#435—172no—
669#435—172no—
670#435—172no—
671#435—172no—
672#435—172no—
673#435—172no—
674#435C2×D1712yescomplemented
675#435C2×D1712yescomplemented
676#435C2×D1712yescomplemented
677#435C2×D1712yescomplemented
678C8×D4—172no—
679C8×D4—172no—
680C8×D4—172no—
681C8×D4—172no—
682C8×D4—172no—
683C8×D4—172no—
684C8×D4—172no—
685C8×D4—172no—
686#433—172no—
687#433—172no—
688#433—172no—
689#433—172no—
690#432—172no—
691#432C2×D1712yescomplemented
692#431—172no—
693#431—172no—
694#424—172no—
695#424—172no—
696#408—171no—
697#408—171no—
698#408—172no—
699#408—171no—
700#408—171no—
701#408—171no—
702#408—171no—
703#408—172no—
704#408—172no—
705#408—172no—
706#408—172no—
707#408—172no—
708#408—172no—
709#408—172no—
710#408—172no—
711#408C2×D1711yescharacteristic, complemented
712#408C2×D1711yescharacteristic, complemented
713#408C2×D1712yescomplemented
714#407—172no—
715#407—172no—
716#407—172no—
717#407—172no—
718C2×C22⋊C8—172no—
719C2×C22⋊C8—172no—
720C2×C22⋊C8—172no—
721C2×C22⋊C8—172no—
722#405—172no—
723#405—172no—
724C2×C17—41no—
725C2×C17—41no—
726C2×C17—41no—
727C2×C17—42no—
728C2×C17C2×#51811yescharacteristic
729C2×C17#357312yes—
730D17—22no—
731D17—41no—
732D17—41no—
733D17—42no—
734D17—41no—
735C2×#41—171no—
736C2×#41—171no—
737C2×#41—171no—
738C2×#41—171no—
739C2×#41—171no—
740C2×#41—171no—
741C2×#41—172no—
742C2×#41—172no—
743C2×#41—171no—
744C2×#41—171no—
745C2×#41—171no—
746C2×#41—171no—
747C2×#41—682no—
748C2×#41—682no—
749C2×#41—682no—
750C2×#41—682no—
751C2×#41C22×D1711yescharacteristic
752C2×#41C22×D1711yescharacteristic
753C22×Q8—171no—
754C22×Q8—171no—
755C22×D4—171no—
756C22×D4—171no—
757C22×D4—172no—
758C22×D4—171no—
759C22×D4—171no—
760C23×C4—171no—
761C23×C4—171no—
762C23×C4—171no—
763C23×C4—172no—
764#131—684no—
765#131—684no—
766C2×M16—171no—
767C2×M16—171no—
768C2×M16—172no—
769C2×M16—172no—
770C2×M16—172no—
771C2×M16—172no—
772C2×M16—172no—
773C2×M16—172no—
774C2×M16—172no—
775C2×M16—682no—
776C2×M16—682no—
777C2×M16—682no—
778C2×M16C22×D1711yescharacteristic
779C2×M16C22×D1711yescharacteristic
780C2×M16C22×D1712yes—
781C22×C8—171no—
782C22×C8—171no—
783C22×C8—172no—
784C22×C8—172no—
785C22×C8—172no—
786C22×C8—172no—
787C22×C8—172no—
788C22×C8—172no—
789C22×C8—172no—
790C22×C8—682no—
791C22×C8C22×D1711yescharacteristic
792C22×C8C22×D1711yescharacteristic
793C22×C8C22×D1712yes—
794C4⋊Q8—171no—
795C4⋊Q8—171no—
796C4⋊Q8—171no—
797C4⋊Q8C4×D1711yescharacteristic
798#127—171no—
799#127—171no—
800#127—171no—
801#127C4×D1711yescharacteristic
802#124—171no—
803#124—171no—
804#124—171no—
805#124—171no—
806#124—171no—
807#124—171no—
808#124C4×D1711yescharacteristic
809#124C4×D1711yescharacteristic
810#123—172no—
811#123—172no—
812#123—172no—
813#123—172no—
814#123—172no—
815#123—172no—
816#123—172no—
817#123—172no—
818C22⋊Q8—172no—
819C22⋊Q8—172no—
820C22⋊Q8—172no—
821C22⋊Q8—172no—
822C22⋊Q8—172no—
823C22⋊Q8—172no—
824C22⋊Q8—172no—
825C22⋊Q8—172no—
826#121—172no—
827#121—172no—
828#121—172no—
829#121—172no—
830#121—172no—
831#121—172no—
832#121—172no—
833#121—172no—
834#121—172no—
835#121—172no—
836#121—172no—
837#121—172no—
838#121—172no—
839#121—172no—
840#121C4×D1712yes—
841#121C4×D1712yes—
842#120—172no—
843#120—172no—
844#120—172no—
845#120—172no—
846#120—172no—
847#120—172no—
848#120—172no—
849#120—172no—
850C4×D4—172no—
851C4×D4—172no—
852C4×D4—172no—
853C4×D4—172no—
854C4×D4—172no—
855C4×D4—172no—
856C4×D4C22×D1712yes—
857C4×D4C22×D1712yes—
858#117—171no—
859#117—171no—
860#117—171no—
861#117—171no—
862#117—172no—
863#117—172no—
864C2×C4⋊C4—172no—
865C2×C22⋊C4—172no—
866C2×C42—171no—
867C2×C42C22×D1711yescharacteristic
868C4⋊C8—172no—
869C4⋊C8—172no—
870C4⋊C8—172no—
871C4⋊C8—172no—
872C4⋊C8—172no—
873C4⋊C8—172no—
874C4⋊C8C22×D1712yes—
875C4⋊C8C22×D1712yes—
876C22⋊C8—172no—
877C22⋊C8—172no—
878C22⋊C8—172no—
879C22⋊C8—172no—
880C22⋊C8—172no—
881C22⋊C8—172no—
882C22⋊C8—172no—
883C22⋊C8—172no—
884C22⋊C8—172no—
885C22⋊C8—172no—
886C22⋊C8—172no—
887C22⋊C8—172no—
888C22⋊C8—172no—
889C22⋊C8—172no—
890C22⋊C8—172no—
891C22⋊C8—172no—
892C22⋊C8—172no—
893C22⋊C8—172no—
894C22⋊C8C22×D1712yes—
895C22⋊C8C22×D1712yes—
896C22⋊C8C22×D1712yes—
897C22⋊C8C22×D1712yes—
898C22⋊C8C22×D1712yes—
899C22⋊C8C22×D1712yes—
900#97—172no—
901#97—172no—
902#97C22×D1712yes—
903#97C22×D1712yes—
904C4×C8—172no—
905C4×C8—172no—
906C4×C8—172no—
907C4×C8—172no—
908C17#6023511yescharacteristic, complemented, Sylow
909C24—171no—
910C24—171no—
911C24—171no—
912C24—172no—
913#41—41no—
914#41—41no—
915#41—41no—
916#41—41no—
917#41—344no—
918#41—344no—
919#41—681no—
920#41—681no—
921#41—681no—
922#41—681no—
923#41—681no—
924#41—681no—
925#41—681no—
926#41—681no—
927#41—682no—
928#41—682no—
929#41—682no—
930#41—682no—
931#41—682no—
932#41—684no—
933#41—682no—
934C2×Q8—172no—
935C2×Q8—171no—
936C2×Q8—171no—
937C2×Q8—171no—
938C2×Q8—171no—
939C2×Q8—682no—
940C2×Q8—682no—
941C2×Q8C2×C4×D1711yescharacteristic
942C2×Q8C2×C4×D1711yescharacteristic
943C2×D4—172no—
944C2×D4—172no—
945C2×D4—172no—
946C2×D4—172no—
947C2×D4—172no—
948C2×D4—172no—
949C2×D4—171no—
950C2×D4—171no—
951C2×D4—171no—
952C2×D4—171no—
953C2×D4—172no—
954C2×D4—171no—
955C2×D4—171no—
956C2×D4—172no—
957C2×D4—172no—
958C2×D4—172no—
959C2×D4—171no—
960C2×D4—171no—
961C2×D4—171no—
962C2×D4—171no—
963C2×D4—682no—
964C2×D4—682no—
965C2×D4—682no—
966C2×D4—682no—
967C2×D4—684no—
968C2×D4C2×C4×D1712yes—
969C2×D4C2×C4×D1712yes—
970C2×D4C2×C4×D1711yescharacteristic
971C2×D4C2×C4×D1711yescharacteristic
972C2×D4C2×C4×D1712yes—
973C2×D4C2×C4×D1711yescharacteristic
974C2×D4C2×C4×D1711yescharacteristic
975C22×C4—171no—
976C22×C4—171no—
977C22×C4—171no—
978C22×C4—171no—
979C22×C4—172no—
980C22×C4—172no—
981C22×C4—171no—
982C22×C4—171no—
983C22×C4—171no—
984C22×C4—171no—
985C22×C4—171no—
986C22×C4—171no—
987C22×C4—171no—
988C22×C4—171no—
989C22×C4—171no—
990C22×C4—172no—
991C22×C4—172no—
992C22×C4—172no—
993C22×C4—342no—
994C22×C4—342no—
995C22×C4—342no—
996C22×C4—342no—
997C22×C4—342no—
998C22×C4—342no—
999C22×C4—682no—
1000C22×C4—682no—
1001C22×C4C2×C4×D1712yes—
1002C22×C4C23×D1711yescharacteristic
1003C22×C4C23×D1711yescharacteristic
1004C22×C4C23×D1711yescharacteristic
1005C22×C4C23×D1712yes—
1006M16—41no—
1007M16—41no—
1008M16—42no—
1009M16—344no—
1010M16—344no—
1011M16—682no—
1012M16—682no—
1013M16—682no—
1014M16—682no—
1015M16—681no—
1016M16—681no—
1017M16—682no—
1018C2×C8—41no—
1019C2×C8—41no—
1020C2×C8—42no—
1021C2×C8—172no—
1022C2×C8—172no—
1023C2×C8—172no—
1024C2×C8—172no—
1025C2×C8—344no—
1026C2×C8—344no—
1027C2×C8—682no—
1028C2×C8—682no—
1029C2×C8—682no—
1030C2×C8—682no—
1031C2×C8—681no—
1032C2×C8—681no—
1033C2×C8—682no—
1034C2×C8C23×D1712yes—
1035C2×C8C23×D1712yes—
1036C2×C8C23×D1712yes—
1037C2×C8C23×D1712yes—
1038C4⋊C4—172no—
1039C4⋊C4—172no—
1040C4⋊C4—172no—
1041C4⋊C4—172no—
1042C4⋊C4—172no—
1043C4⋊C4—172no—
1044C4⋊C4—172no—
1045C4⋊C4—172no—
1046C4⋊C4—172no—
1047C4⋊C4—172no—
1048C4⋊C4C2×C4×D1712yes—
1049C4⋊C4C2×C4×D1712yes—
1050C22⋊C4—172no—
1051C22⋊C4—172no—
1052C22⋊C4—172no—
1053C22⋊C4—172no—
1054C22⋊C4—172no—
1055C22⋊C4—172no—
1056C22⋊C4—172no—
1057C22⋊C4—172no—
1058C22⋊C4—172no—
1059C22⋊C4—172no—
1060C22⋊C4—172no—
1061C22⋊C4—172no—
1062C22⋊C4—172no—
1063C22⋊C4—172no—
1064C22⋊C4—172no—
1065C22⋊C4—172no—
1066C22⋊C4C2×C4×D1712yes—
1067C22⋊C4C2×C4×D1712yes—
1068C22⋊C4C2×C4×D1712yes—
1069C22⋊C4C2×C4×D1712yes—
1070C42—171no—
1071C42—171no—
1072C42—172no—
1073C42C2×C4×D1711yescharacteristic
1074C42C2×C4×D1711yescharacteristic
1075C42C23×D1712yes—
1076C23—171no—
1077C23—171no—
1078C23—171no—
1079C23—171no—
1080C23—172no—
1081C23—342no—
1082C23—342no—
1083C23—342no—
1084C23—682no—
1085C23—682no—
1086C23—682no—
1087C23—682no—
1088C23—682no—
1089C23—682no—
1090C23C22×C4×D1711yescharacteristic
1091C23C22×C4×D1711yescharacteristic
1092C23C22×C4×D1712yes—
1093C23C22×C4×D1711yescharacteristic
1094Q8—41no—
1095Q8—41no—
1096Q8—344no—
1097Q8—681no—
1098Q8—681no—
1099Q8—681no—
1100Q8—681no—
1101D4—41no—
1102D4—41no—
1103D4—41no—
1104D4—41no—
1105D4—42no—
1106D4—42no—
1107D4—42no—
1108D4—344no—
1109D4—344no—
1110D4—344no—
1111D4—681no—
1112D4—681no—
1113D4—681no—
1114D4—681no—
1115D4—682no—
1116D4—682no—
1117D4—681no—
1118D4—681no—
1119D4—681no—
1120D4—681no—
1121D4—681no—
1122D4—681no—
1123D4—682no—
1124D4—682no—
1125D4—682no—
1126D4—682no—
1127D4—682no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—42no—
1137C2×C4—171no—
1138C2×C4—172no—
1139C2×C4—172no—
1140C2×C4—172no—
1141C2×C4—172no—
1142C2×C4—171no—
1143C2×C4—171no—
1144C2×C4—172no—
1145C2×C4—171no—
1146C2×C4—342no—
1147C2×C4—342no—
1148C2×C4—342no—
1149C2×C4—342no—
1150C2×C4—342no—
1151C2×C4—342no—
1152C2×C4—342no—
1153C2×C4—342no—
1154C2×C4—342no—
1155C2×C4—341no—
1156C2×C4—341no—
1157C2×C4—342no—
1158C2×C4—342no—
1159C2×C4—341no—
1160C2×C4—341no—
1161C2×C4—341no—
1162C2×C4—341no—
1163C2×C4—682no—
1164C2×C4—682no—
1165C2×C4—682no—
1166C2×C4—682no—
1167C2×C4C22×C4×D1711yescharacteristic
1168C2×C4C22×C4×D1712yes—
1169C2×C4C22×C4×D1712yes—
1170C2×C4C22×C4×D1711yescharacteristic
1171C2×C4C22×C4×D1711yescharacteristic
1172C2×C4C22×C4×D1712yes—
1173C2×C4C24×D1711yescharacteristic
1174C8—22no—
1175C8—22no—
1176C8—22no—
1177C8—22no—
1178C8—342no—
1179C8—342no—
1180C8—342no—
1181C8—342no—
1182C22—22no—
1183C22—22no—
1184C22—22no—
1185C22—22no—
1186C22—22no—
1187C22—21no—
1188C22—21no—
1189C22—21no—
1190C22—22no—
1191C22—172no—
1192C22—342no—
1193C22—342no—
1194C22—342no—
1195C22—342no—
1196C22—342no—
1197C22—342no—
1198C22—341no—
1199C22—341no—
1200C22—341no—
1201C22—342no—
1202C22—684no—
1203C22—1362no—
1204C22—1362no—
1205C22—1364no—
1206C22C23×C4×D1711yescharacteristic
1207C4—22no—
1208C4—22no—
1209C4—21no—
1210C4—21no—
1211C4—21no—
1212C4—22no—
1213C4—172no—
1214C4—342no—
1215C4—342no—
1216C4—341no—
1217C4—341no—
1218C4—341no—
1219C4—342no—
1220C4H(5,𝔽2)×D1711yescharacteristic
1221C4H(5,𝔽2)×D1711yescharacteristic
1222C2—41no—
1223C2—41no—
1224C2—41no—
1225C2—42no—
1226C2—342no—
1227C2—681no—
1228C2—681no—
1229C2—681no—
1230C2—682no—
1231C2D17×#51811yescharacteristic
1232C2#1454349712yes—
subgroupG/H
center, FrattiniC2×C4C24×D17
commutator, socleC22×C17C24×C4
FittingC17×#2980C2
prime radical#14542111C2
cosocleC2×C4×C17C25
hypercenter#2980D17
hypocenterC17#60235
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #2980

Complements

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

NH ≅ G/Ntype
2. #14537862C2semidirect
3. #14537857C2semidirect
4. #14537853C2semidirect
5. #14537851C2semidirect
6. #14537848C2semidirect
7. #14537843C2semidirect
8. #14537835C2semidirect
9. #14537833C2semidirect
10. #14537831C2semidirect
11. #14537510C2semidirect
12. #14537507C2semidirect
13. #14537482C2semidirect
14. #14537475C2semidirect
15. #14537443C2semidirect
16. #14537232C2semidirect
17. #14537226C2semidirect
18. D17×#408C2semidirect
19. C17×#2980C2semidirect
24. C22×#63218C22semidirect
25. C2×M16×D17C22semidirect
26. C2×M16×D17C22semidirect
27. C22×C8×D17C22semidirect
48. #11762887C22semidirect
49. #11762887C22semidirect
50. #11762886C22semidirect
51. #11762886C22semidirect
52. #11762885C22semidirect
53. #11762885C22semidirect
54. #11762884C22semidirect
55. #11762884C22semidirect
56. #11762883C22semidirect
57. #11762883C22semidirect
58. #11762882C22semidirect
59. #11762882C22semidirect
60. #11762882C22semidirect
61. #11762882C22semidirect
62. #11762880C22semidirect
63. #11762880C22semidirect
64. #11762878C22semidirect
65. #11762878C22semidirect
66. #11762877C22semidirect
67. #11762877C22semidirect
68. D4×#3622C22semidirect
69. D4×#3622C22semidirect
70. #11762874C22semidirect
71. #11762874C22semidirect
72. C8×C22⋊D17C22semidirect
73. C8×C22⋊D17C22semidirect
74. #11762872C22semidirect
75. #11762872C22semidirect
76. #11762871C22semidirect
77. #11762871C22semidirect
78. #11762869C22semidirect
79. #11762869C22semidirect
80. #11762863C22semidirect
81. #11762862C22semidirect
82. #11762859C22semidirect
83. #11762834C22semidirect
84. #11762834C22semidirect
87. #11762776C22semidirect
88. #11762776C22semidirect
89. #11762776C22semidirect
96. #11762774C22semidirect
97. #11762774C22semidirect
98. #11762774C22semidirect
99. #11762774C22semidirect
100. #11762772C22semidirect
102. #11762771C22semidirect
103. #11762771C22semidirect
104. C2×#10587491C22semidirect
106. C22⋊C8×D17C22semidirect
107. C22⋊C8×D17C22semidirect
108. #11762766C22semidirect
109. #11762766C22semidirect
111. C17×#435C22semidirect
112. C17×#435C22semidirect
113. C17×#435C22semidirect
114. C17×#435C22semidirect
115. C17×#432C22semidirect
116. C17×#408C22semidirect
117. C17×#408C22semidirect
118. C17×#408C22semidirect
570. #2980D17semidirect
674. #435C2×D17semidirect
675. #435C2×D17semidirect
676. #435C2×D17semidirect
677. #435C2×D17semidirect
691. #432C2×D17semidirect
711. #408C2×D17semidirect
712. #408C2×D17semidirect
713. #408C2×D17semidirect
908. C17#60235semidirect

Maximal subgroups

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

subgroupindex
#145421112
#145378622
#145378572
#145378532
#145378512
#145378482
#145378432
#145378352
#145378332
#145378312
#145375102
#145375072
#145374822
#145374752
#145374432
#145372322
#145372262
D17×#4082
C17×#29802
#6023517