Finite Group Databasebeta

← #34018604

Subgroups — #34018604

Order 18688.

626 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626744C211yesmaximal, characteristic, complemented
2#41×#10596833C211yesmaximal, characteristic, complemented
3#22625560C211yesmaximal, characteristic, complemented
4#22625554C211yesmaximal, characteristic, complemented
5#22625552C211yesmaximal, characteristic, complemented
6#22625546C211yesmaximal, characteristic, complemented
7#22625527C211yesmaximal, characteristic, complemented
8#22625525C211yesmaximal, characteristic, complemented
9#22625522C211yesmaximal, characteristic, complemented
10SD16⋊#10596833C211yesmaximal, characteristic, complemented
11#22625502C211yesmaximal, characteristic, complemented
12#22625262C211yesmaximal, characteristic, complemented
13#22625242C211yesmaximal, characteristic, complemented
14#22625146C211yesmaximal, characteristic, complemented
15#22619942C211yesmaximal, characteristic
16#17989637C2211yescharacteristic
17#17989636C2211yescharacteristic
18Q8×#10596833C2211yescharacteristic
19Q8×#10596833C2211yescharacteristic
20#17989622C2211yescharacteristic
21#17989618—21no—
22D4×#10596833—21no—
23D4×#10596833—21no—
24D4×#10596833—21no—
25D4×#10596833C2211yescharacteristic
26D4×#10596833C2211yescharacteristic
27D4×#10596833C2211yescharacteristic
28#17989611—21no—
29#17989608C2211yescharacteristic
30#17989604C2211yescharacteristic
31#17989603—21no—
32#17989603C2211yescharacteristic
33#17989551—21no—
34C2×C4×#10596833—21no—
35C2×C4×#10596833C2211yescharacteristic
36#17989451C2211yescharacteristic
37#17989450C2211yescharacteristic
38#17989449C2211yescharacteristic
39#17989448C2211yescharacteristic
40#17989437C2211yescharacteristic
41#17989437C2211yescharacteristic
42Q8⋊#10596833C2211yescharacteristic
43Q8⋊#10596833C2211yescharacteristic
44D4⋊#10596833C2211yescharacteristic
45D4⋊#10596833C2211yescharacteristic
46D4⋊#10596833C2211yescharacteristic
47D4⋊#10596833C2211yescharacteristic
48#17989429C2211yescharacteristic
49#17989429C2211yescharacteristic
50#17989428C2211yescharacteristic
51#17989428C2211yescharacteristic
52#17989118C2211yescharacteristic
53#41×Dic73C2211yescharacteristic
54#17988929C411yescharacteristic
55#17988908C411yescharacteristic
56#17988896C411yescharacteristic
57#17988889C411yescharacteristic
58#17988807C411yescharacteristic
59#17988800C411yescharacteristic
60#17988749C411yescharacteristic
61#17988679C2211yescharacteristic
62#17988678C2211yescharacteristic
63SD16×Dic73C2211yescharacteristic
64D8×Dic73C2211yescharacteristic
65#17988637C2211yescharacteristic
66#449×C73C411yescharacteristic
67C2×#11924037—21no—
68C22×#10596833—21no—
69C22×#10596833—21no—
70C22×#10596833—21no—
71C22×#10596833D411yescharacteristic
72C22×#10596833D411yescharacteristic
73#14556658—21no—
74#14556658—21no—
75C4⋊#10596833—21no—
76C4⋊#10596833—21no—
77C4⋊#10596833—21no—
78C4⋊#10596833C2311yescharacteristic
79C4⋊#10596833C2311yescharacteristic
80C4⋊#10596833C2311yescharacteristic
81C4⋊#10596833C2311yescharacteristic
82C22⋊#10596833—21no—
83C22⋊#10596833—21no—
84C22⋊#10596833—21no—
85C22⋊#10596833—21no—
86C22⋊#10596833—21no—
87C22⋊#10596833—21no—
88C22⋊#10596833—21no—
89#14556646—21no—
90#14556646—21no—
91C4×#10596833—21no—
92C4×#10596833—21no—
93C4×#10596833—21no—
94C4×#10596833—21no—
95C4×#10596833D411yescharacteristic
96C4×#10596833D411yescharacteristic
97C4×#10596833C2311yescharacteristic
98C4×#10596833C2311yescharacteristic
99C4×#10596833C2311yescharacteristic
100C4×#10596833C2311yescharacteristic
101C2×#11924018C2×C411yescharacteristic
102C2×#11924016C2×C411yescharacteristic
103#14556584—21no—
104#14556582C2×C411yescharacteristic
105#14556578C2×C411yescharacteristic
106#14556572—21no—
107#14556570C2×C411yescharacteristic
108Q8×Dic73C2×C411yescharacteristic
109Q8×Dic73C2311yescharacteristic
110#14556556C2311yescharacteristic
111D4×Dic73—21no—
112D4×Dic73—21no—
113D4×Dic73—21no—
114D4×Dic73C2×C411yescharacteristic
115D4×Dic73C2311yescharacteristic
116D4×Dic73C2311yescharacteristic
117#14556550—21no—
118#14556550C2×C411yescharacteristic
119#14556547—21no—
120C2×C4×Dic73—21no—
121C2×C4×Dic73C2311yescharacteristic
122#14556525C2×C411yescharacteristic
123#14556524C2×C411yescharacteristic
124#14556523C2×C411yescharacteristic
125#14556522C2×C411yescharacteristic
126#14556520C2×C411yescharacteristic
127#14556520C2×C411yescharacteristic
128#14556516C2×C411yescharacteristic
129#14556516C2×C411yescharacteristic
130#14556515C2×C411yescharacteristic
131#14556512C2×C411yescharacteristic
132#14556512C2×C411yescharacteristic
133#14556512C2×C411yescharacteristic
134C22⋊#10596831C2×C411yescharacteristic
135C8×Dic73C2311yescharacteristic
136C8×Dic73C2311yescharacteristic
137C2×#41×C73C2×C411yescharacteristic
138C2×SD16×C73C2×C411yescharacteristic
139C2×D8×C73C2×C411yescharacteristic
140#121×C73C2×C411yescharacteristic
141#103×C73C2×C411yescharacteristic
142#102×C73C2×C411yescharacteristic
143C22⋊C8×C73C2×C411yescharacteristic
144#11924037—42no—
145C2×#10596833—21no—
146C2×#10596833—21no—
147C2×#10596833—21no—
148C2×#10596833—21no—
149C2×#10596833—21no—
150C2×#10596833—21no—
151C2×#10596833—41no—
152C2×#10596833—41no—
153C2×#10596833—42no—
154C2×#10596833—42no—
155C2×#10596833—42no—
156C2×#10596833C2×D411yescharacteristic
157C2×#10596833C2×D411yescharacteristic
158C2×#10596833C2×D411yescharacteristic
159C2×#10596833C2×D411yescharacteristic
160C2×Dic146C22×C411yescharacteristic
161C22×Dic73—21no—
162C22×Dic73—21no—
163C22×Dic73—21no—
164C22×Dic73C2×D411yescharacteristic
165C22×Dic73#4111yescharacteristic
166#11924018—22no—
167#11924016—22no—
168C2×#10596831C22×C411yescharacteristic
169C2×#10596831C22×C411yescharacteristic
170C4⋊Dic73—21no—
171C4⋊Dic73—21no—
172C4⋊Dic73—21no—
173C4⋊Dic73C22×C411yescharacteristic
174C4⋊Dic73C22×C411yescharacteristic
175C4⋊Dic73C22×C411yescharacteristic
176#11924007—21no—
177#11924007—21no—
178#11924007—21no—
179C22⋊Dic73—21no—
180C22⋊Dic73—21no—
181C22⋊Dic73—21no—
182C22⋊Dic73—21no—
183C22⋊Dic73—21no—
184C22⋊Dic73—21no—
185C22⋊Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C4×Dic73C22×C411yescharacteristic
191C4×Dic73C2×D411yescharacteristic
192C4×Dic73#4111yescharacteristic
193C4×Dic73C2411yescharacteristic
194#41×C73—22no—
195#41×C73—22no—
196C2×Q8×C73C22×C411yescharacteristic
197C2×D4×C73—21no—
198C2×D4×C73—21no—
199C2×D4×C73C22×C411yescharacteristic
200C2×D4×C73C22×C411yescharacteristic
201C22×C4×C73—21no—
202C22×C4×C73C22×C411yescharacteristic
203SD16×C73—22no—
204D8×C73—22no—
205C2×C8×C73C22×C411yescharacteristic
206C2×C8×C73C22×C411yescharacteristic
207C4⋊C4×C73C22×C411yescharacteristic
208C22⋊C4×C73—21no—
209C23×C73—21no—
210C23×C73—21no—
211C23×C73C4×D411yescharacteristic
212Q8×C73—21no—
213Q8×C73#13112yes—
214D4×C73—24no—
215D4×C73—21no—
216D4×C73—21no—
217D4×C73—21no—
218D4×C73—42no—
219D4×C73#13112yes—
220C2×C4×C73—24no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73C4×D411yescharacteristic
226C2×C4×C73C23×C411yescharacteristic
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—41no—
234C2×Dic73—42no—
235C2×Dic73—41no—
236C2×Dic73—41no—
237C2×Dic73—41no—
238C2×Dic73—41no—
239C2×Dic73C4×D411yescharacteristic
240C2×Dic73C4×D411yescharacteristic
241C2×Dic73C22×D411yescharacteristic
242C2×Dic73C2×#4111yescharacteristic
243Dic146—21no—
244Dic146—21no—
245#10596833—21no—
246#10596833—21no—
247#10596833—21no—
248#10596833—21no—
249#10596833—41no—
250#10596833—41no—
251#10596833—41no—
252#10596833—41no—
253#10596833—41no—
254#10596833—41no—
255C8×C73—21no—
256C8×C73—21no—
257#10596831—21no—
258#10596831—21no—
259C22×C73—21no—
260C22×C73—22no—
261C22×C73—21no—
262C22×C73—21no—
263C22×C73—41no—
264C22×C73—41no—
265C22×C73—41no—
266C22×C73—41no—
267C22×C73—41no—
268C22×C73C2×C4×D411yescharacteristic
269C4×C73—21no—
270C4×C73—22no—
271C4×C73—41no—
272C4×C73C2×#13111yescharacteristic
273C4×C73C2×#13111yescharacteristic
274Dic73—21no—
275Dic73—21no—
276Dic73—21no—
277Dic73—41no—
278Dic73—41no—
279Dic73—41no—
280Dic73—41no—
281Dic73#57511yescharacteristic
282Dic73#57511yescharacteristic
283#17909—731nomaximal, Sylow
284C2×C73—41no—
285C2×C73—42no—
286C2×C73—81no—
287C2×C73#292911yescharacteristic
288C2×C73#294311yescharacteristic
289C2×C73#295511yescharacteristic
290#3102—731no—
291#2966—731no—
292C8×#41—731no—
293#1588—731no—
294#1587—731no—
295#1586—731no—
296#1585—731no—
297#1580—731no—
298#1579—731no—
299SD16⋊C8—731no—
300SD16⋊C8—731no—
301#1572—731no—
302#1488—731no—
303#1482—731no—
304#1452—731no—
305C73#1790911yescharacteristic, complemented, Sylow
306#529—731no—
307C4×#41—731no—
308#485—731no—
309#482—731no—
310#479—731no—
311#478—731no—
312#464—731no—
313#463—731no—
314#452—731no—
315#449#6440811yescharacteristic
316#446—731no—
317C8×Q8—731no—
318C8×Q8—731no—
319C8×Q8—731no—
320C4×Q16—731no—
321C4×SD16—731no—
322C4×SD16—731no—
323C4×D8—731no—
324#436—731no—
325#435—1461no—
326C8×D4—731no—
327C8×D4—731no—
328C8×D4—731no—
329C8×D4—1461no—
330C8×D4—1461no—
331C8×D4—1461no—
332#433—1461no—
333#432—731no—
334#431—731no—
335#431—731no—
336#431—731no—
337#431—1461no—
338#405—1461no—
339C2×C4×C8—731no—
340C2×C4×C8—1461no—
341#335—731no—
342#335—731no—
343#334—731no—
344#334—731no—
345Q8⋊C8—731no—
346Q8⋊C8—731no—
347Q8⋊C8—731no—
348Q8⋊C8—731no—
349D4⋊C8—731no—
350D4⋊C8—731no—
351D4⋊C8—731no—
352D4⋊C8—731no—
353#322—731no—
354#322—731no—
355#322—731no—
356#322—731no—
357C2×#41C2×#6440811yescharacteristic
358C2×Q16—731no—
359C2×SD16—731no—
360C2×SD16C2×#6440811yescharacteristic
361C2×D8C2×#6440811yescharacteristic
362C2×M16—1461no—
363C22×C8—731no—
364C22×C8—731no—
365C22×C8—1461no—
366C22×C8—1461no—
367C22×C8—1461no—
368#126—1461no—
369#125—731no—
370#124—731no—
371#123—1461no—
372C22⋊Q8—731no—
373#121C2×#6440811yescharacteristic
374C4×Q8—731no—
375C4×Q8—731no—
376C4×Q8—731no—
377C4×D4—731no—
378C4×D4—731no—
379C4×D4—731no—
380C4×D4—1461no—
381C4×D4—1461no—
382C4×D4—1461no—
383#117—731no—
384#117—1461no—
385#117—1461no—
386C2×C42—731no—
387C2×C42—1461no—
388#107—731no—
389#107—731no—
390#106—731no—
391#106—731no—
392C4⋊C8—731no—
393C4⋊C8—731no—
394C4⋊C8—731no—
395C4⋊C8—731no—
396C4⋊C8—731no—
397C4⋊C8—731no—
398C4⋊C8—1461no—
399C4⋊C8—1461no—
400C4⋊C8—1461no—
401C4⋊C8—1461no—
402C4⋊C8—1461no—
403#103—731no—
404#103—731no—
405#103—731no—
406#103C2×#6440811yescharacteristic
407#102—731no—
408#102—731no—
409#102—731no—
410#102C2×#6440811yescharacteristic
411C22⋊C8—731no—
412C22⋊C8—1461no—
413C22⋊C8—1461no—
414C22⋊C8—1461no—
415C22⋊C8—1461no—
416C22⋊C8—1461no—
417C22⋊C8—1461no—
418C22⋊C8—1461no—
419C22⋊C8C2×#6440811yescharacteristic
420#97—1461no—
421#97—1461no—
422C4×C8—731no—
423C4×C8—731no—
424C4×C8—731no—
425C4×C8—731no—
426C4×C8—731no—
427C4×C8—731no—
428C4×C8—731no—
429C4×C8—731no—
430C4×C8—1461no—
431C4×C8—1461no—
432C4×C8—1461no—
433C4×C8—1461no—
434#41—22no—
435#41—22no—
436C2×Q8—731no—
437C2×Q8C22×#6440811yescharacteristic
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C22×#6440811yescharacteristic
441C2×D4C22×#6440811yescharacteristic
442C22×C4—21no—
443C22×C4—731no—
444C22×C4—731no—
445C22×C4—1461no—
446C22×C4—1461no—
447C22×C4—1461no—
448C22×C4C22×#6440811yescharacteristic
449Q16—1462no—
450SD16—22no—
451SD16—1462no—
452D8—22no—
453M16—2922no—
454C2×C8—2922no—
455C2×C8—2922no—
456C2×C8—2922no—
457C2×C8—2921no—
458C2×C8—2921no—
459C2×C8—731no—
460C2×C8—731no—
461C2×C8—731no—
462C2×C8—731no—
463C2×C8—731no—
464C2×C8—731no—
465C2×C8—1461no—
466C2×C8—1461no—
467C2×C8—1461no—
468C2×C8—1461no—
469C2×C8—1461no—
470C2×C8—1461no—
471C2×C8C22×#6440811yescharacteristic
472C2×C8C22×#6440811yescharacteristic
473C4⋊C4—731no—
474C4⋊C4—731no—
475C4⋊C4—731no—
476C4⋊C4—1461no—
477C4⋊C4—1461no—
478C4⋊C4—1461no—
479C4⋊C4—1461no—
480C4⋊C4—1461no—
481C4⋊C4—1461no—
482C4⋊C4C22×#6440811yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—1461no—
485C22⋊C4—1461no—
486C22⋊C4—1461no—
487C22⋊C4—1461no—
488C22⋊C4—1461no—
489C22⋊C4—1461no—
490C22⋊C4—1461no—
491C42—731no—
492C42—731no—
493C42—731no—
494C42—731no—
495C42—1461no—
496C42—1461no—
497C42—1461no—
498C42—1461no—
499C23—21no—
500C23—21no—
501C23D4×#6440811yescharacteristic
502Q8—21no—
503Q8—1461no—
504Q8—1461no—
505Q8#1455667812yes—
506D4—24no—
507D4—21no—
508D4—21no—
509D4—21no—
510D4—42no—
511D4#1455667812yes—
512C2×C4—24no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—2921no—
518C2×C4—2921no—
519C2×C4—2921no—
520C2×C4—2921no—
521C2×C4—2922no—
522C2×C4—2921no—
523C2×C4—731no—
524C2×C4—731no—
525C2×C4—731no—
526C2×C4—731no—
527C2×C4—1461no—
528C2×C4—1461no—
529C2×C4—1461no—
530C2×C4—1461no—
531C2×C4—1461no—
532C2×C4—1461no—
533C2×C4D4×#6440811yescharacteristic
534C2×C4C23×#6440811yescharacteristic
535C8—21no—
536C8—21no—
537C8—2921no—
538C8—2921no—
539C8—2921no—
540C8—2921no—
541C8—2921no—
542C8—2921no—
543C8—1461no—
544C8—1461no—
545C8—1461no—
546C8—1461no—
547C8—1461no—
548C8—1461no—
549C22—21no—
550C22—22no—
551C22—21no—
552C22—21no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22C2×D4×#6440811yescharacteristic
559C4—21no—
560C4—22no—
561C4—41no—
562C4—2921no—
563C4—2921no—
564C4—2921no—
565C4—2921no—
566C4—731no—
567C4—731no—
568C4—1461no—
569C4—1461no—
570C4—1461no—
571C4C2×#1455667811yescharacteristic
572C4C2×#1455667811yescharacteristic
573C2—41no—
574C2—42no—
575C2—81no—
576C2#2262664611yescharacteristic
577C2#2262668511yescharacteristic
578C2#2262670311yescharacteristic
subgroupG/H
centerC22C2×D4×#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
Fitting, prime radical#449×C73C4
socleC22×C73C2×C4×D4
cosocleC4×Dic73C24
hypercenter#449#64408
hypocenterC73#17909
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #22626744C2semidirect
2. #41×#10596833C2semidirect
3. #22625560C2semidirect
4. #22625554C2semidirect
5. #22625552C2semidirect
6. #22625546C2semidirect
7. #22625527C2semidirect
8. #22625525C2semidirect
9. #22625522C2semidirect
10. SD16⋊#10596833C2semidirect
11. #22625502C2semidirect
12. #22625262C2semidirect
13. #22625242C2semidirect
14. #22625146C2semidirect
305. C73#17909semidirect

Maximal subgroups

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

subgroupindex
#226267442
#41×#105968332
#226255602
#226255542
#226255522
#226255462
#226255272
#226255252
#226255222
SD16⋊#105968332
#226255022
#226252622
#226252422
#226251462
#226199422
#1790973