Finite Group Databasebeta

← #14738800

Subgroups — #14738800

Order 2816.

554 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080007C211yesmaximal, characteristic
2#13079826C211yesmaximal, characteristic
3#13079361C211yesmaximal, characteristic
4#13068198C211yesmaximal, characteristic, complemented
5#13068170C211yesmaximal, characteristic, complemented
6#13068122C211yesmaximal, characteristic, complemented
7#13068110C211yesmaximal, characteristic, complemented
8#13068074C211yesmaximal, characteristic, complemented
9#13068046C211yesmaximal, characteristic, complemented
10#13067998C211yesmaximal, characteristic, complemented
11#13067986C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic
13#13067314C211yesmaximal, characteristic
14#13067304C211yesmaximal, characteristic
15C11×#2962C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17#10623001C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#446—21no—
20C11×#446—21no—
21C11×#446C2211yescharacteristic
22C11×#446C2211yescharacteristic
23C8×Q8×C11C2211yescharacteristic
24C8×Q8×C11C2211yescharacteristic
25C11×#424—21no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C11×#405—21no—
28C4×C11×M16C2211yescharacteristic
29#10622750—21no—
30#10622750—21no—
31#10622707—21no—
32#10622703—21no—
33#10622695—21no—
34#10622693—21no—
35#10622665—21no—
36#10622665—21no—
37#10622658—21no—
38#10622658—21no—
39#10622644C2211yescharacteristic
40#10622644C2211yescharacteristic
41#10622634C2211yescharacteristic
42#10622634C2211yescharacteristic
43#10622633C2211yescharacteristic
44#10622633C2211yescharacteristic
45#10622633C2211yescharacteristic
46#10622633C2211yescharacteristic
47#10622539C2211yescharacteristic
48#10622537C2211yescharacteristic
49#10622329—21no—
50#10622329—21no—
51#10622312C2211yescharacteristic
52#10622294C2211yescharacteristic
53#10622294C2211yescharacteristic
54#10622293C2211yescharacteristic
55#10622124C2211yescharacteristic
56#10622124C2211yescharacteristic
57#10622120C2211yescharacteristic
58#10622120C2211yescharacteristic
59#10622120C2211yescharacteristic
60#10622120C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×M16D411yescharacteristic
68C2×C11×M16D411yescharacteristic
69C22×C8×C11—21no—
70C11×C4⋊Q8D411yescharacteristic
71C11×C4⋊Q8D411yescharacteristic
72C11×#125—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8D411yescharacteristic
75C11×C22⋊Q8D411yescharacteristic
76C4×Q8×C11—21no—
77C4×Q8×C11C2311yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C11×#117—21no—
80C2×C42×C11C2311yescharacteristic
81C2×#4326—21no—
82C2×#4326—21no—
83#66979—21no—
84#66979—21no—
85#66977—21no—
86#66977—21no—
87#66977—21no—
88#66977—21no—
89C2×#4318—21no—
90C2×Dic44—21no—
91C2×Dic44—21no—
92#66923—21no—
93#66923—21no—
94#66922C2311yescharacteristic
95#66922C2311yescharacteristic
96#66922C2311yescharacteristic
97#66922C2311yescharacteristic
98C4×Dic22—21no—
99C4×Dic22—21no—
100C4×Dic22—21no—
101C4×Dic22—21no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8—21no—
105C11×C4⋊C8—21no—
106C11×C4⋊C8—21no—
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×#97—21no—
110C11×#97—21no—
111C11×#97D411yescharacteristic
112C11×#97D411yescharacteristic
113C4×C8×C11—21no—
114C4×C8×C11—21no—
115C4×C8×C11C2311yescharacteristic
116C4×C8×C11C2311yescharacteristic
117#66899—21no—
118#66899—21no—
119#66899—21no—
120#66899—21no—
121#66899—21no—
122#66899—21no—
123C22⋊(C11⋊C8)—21no—
124#66881—21no—
125#66881—21no—
126#66880—21no—
127#66880—21no—
128#66880—21no—
129#66880—21no—
130#66874—21no—
131#66874—21no—
132#66872—21no—
133#66872—21no—
134#66872—21no—
135#66872—21no—
136#66871—21no—
137#66871—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143#66867—21no—
144#19375—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11C2×D411yescharacteristic
147C2×Q8×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4111yescharacteristic
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C11×M16—22no—
156C11×M16—41no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—42no—
160C2×C8×C11C2×D411yescharacteristic
161C2×C8×C11C2×D411yescharacteristic
162C2×C8×C11C2×D411yescharacteristic
163C2×C8×C11C2×D411yescharacteristic
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4C2×D411yescharacteristic
172C11×C4⋊C4C2×D411yescharacteristic
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11C2×D411yescharacteristic
178C42×C11C2×D411yescharacteristic
179C42×C11#4111yescharacteristic
180C42×C11C2411yescharacteristic
181C22⋊Dic11—41no—
182C22⋊Dic11—41no—
183#4326—81no—
184#4326—81no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193Dic11⋊C4—41no—
194Dic11⋊C4—41no—
195Dic11⋊C4—41no—
196Dic11⋊C4—41no—
197C4×Dic11—41no—
198C4×Dic11—41no—
199#4318—81no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204Dic44—42no—
205Dic44—42no—
206#3255—111no—
207#3237—111no—
208#3185—111no—
209#2962D1111yescharacteristic
210#1704—111no—
211#1700—111no—
212#1692—111no—
213#1690—111no—
214#1684—111no—
215#1680—111no—
216#1672—111no—
217#1670—111no—
218#1569—111no—
219#1552—111no—
220#1550—111no—
221C23×C11#12111yescharacteristic
222Q8×C11—21no—
223Q8×C11—21no—
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—81no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—41no—
236C2×C4×C11#12111yescharacteristic
237C2×C4×C11#12111yescharacteristic
238C2×C4×C11#12111yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246Dic22—41no—
247Dic22—41no—
248Dic22—41no—
249Dic22—41no—
250Dic22—41no—
251Dic22—41no—
252Dic22—81no—
253C8×C11—21no—
254C8×C11—21no—
255C8×C11—21no—
256C8×C11—41no—
257C8×C11—41no—
258C8×C11#13712yes—
259C11⋊C8—41no—
260C11⋊C8—41no—
261C11⋊C8—41no—
262C11⋊C8—41no—
263#533—111no—
264#533—111no—
265#533C2×D1111yescharacteristic
266#501—221no—
267#498—111no—
268#494—111no—
269#491—221no—
270#487—111no—
271#487—111no—
272#485—221no—
273#485—221no—
274#477—111no—
275#477—111no—
276#475—111no—
277#475—111no—
278#475—111no—
279#475—111no—
280#475—221no—
281#470—221no—
282#470—221no—
283#470—221no—
284#470—221no—
285#462—111no—
286#462—111no—
287#462—221no—
288#446—21no—
289#446—21no—
290#446C2×D1111yescharacteristic
291#446C2×D1111yescharacteristic
292C8×Q8C2×D1111yescharacteristic
293C8×Q8C2×D1111yescharacteristic
294#441—221no—
295#441—221no—
296#432—111no—
297#424—21no—
298#423—111no—
299C2×C4⋊C8C2×D1111yescharacteristic
300#405—21no—
301C4×M16C2×D1111yescharacteristic
302#335—111no—
303#335—111no—
304#334—111no—
305#334—111no—
306#333—111no—
307#333—111no—
308#332—111no—
309#332—111no—
310#332—111no—
311#332—111no—
312#332—111no—
313#332—111no—
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—21no—
317C22×C11C2×#12111yescharacteristic
318C4×C11—21no—
319C4×C11—21no—
320C4×C11—21no—
321C4×C11—21no—
322C4×C11—41no—
323C4×C11—41no—
324C4×C11—41no—
325C4×C11—41no—
326C4×C11C2×#13711yescharacteristic
327C4×C11#57511yescharacteristic
328C4×C11#57711yescharacteristic
329C4×C11#57811yescharacteristic
330Dic11—81no—
331Dic11—81no—
332Dic11—81no—
333Dic11—81no—
334C2×Q16—221no—
335C2×Q16—221no—
336C2×Q16—221no—
337C2×Q16—221no—
338C2×M16—221no—
339C2×M16C22⋊D1111yescharacteristic
340C2×M16C22⋊D1111yescharacteristic
341C22×C8—21no—
342C4⋊Q8—111no—
343C4⋊Q8—111no—
344C4⋊Q8—111no—
345C4⋊Q8—111no—
346C4⋊Q8D4411yescharacteristic
347C4⋊Q8D4411yescharacteristic
348#125—21no—
349#125—221no—
350#125—221no—
351C22⋊Q8—21no—
352C22⋊Q8—221no—
353C22⋊Q8—221no—
354C22⋊Q8—221no—
355C22⋊Q8—221no—
356C22⋊Q8D4411yescharacteristic
357C22⋊Q8D4411yescharacteristic
358C4×Q8—21no—
359C4×Q8—221no—
360C4×Q8—221no—
361C4×Q8—221no—
362C4×Q8—221no—
363C4×Q8C22×D1111yescharacteristic
364C4×Q8C22×D1111yescharacteristic
365#117—21no—
366#117—221no—
367#117—221no—
368C2×C42C22×D1111yescharacteristic
369#107—221no—
370#107—221no—
371#106—221no—
372#106—221no—
373#106—221no—
374#106—221no—
375#106—221no—
376#106—221no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8—111no—
383C4⋊C8—111no—
384C4⋊C8—111no—
385C4⋊C8—111no—
386C4⋊C8—221no—
387C4⋊C8C22×D1111yescharacteristic
388C4⋊C8C22×D1111yescharacteristic
389#103—221no—
390#103—221no—
391#103—221no—
392#103—221no—
393#103—221no—
394#103—221no—
395#103—221no—
396#103—221no—
397#103—221no—
398#103—221no—
399#103—221no—
400#103—221no—
401C22⋊C8—221no—
402#97—21no—
403#97—21no—
404#97—221no—
405#97C22⋊D1111yescharacteristic
406#97C22⋊D1111yescharacteristic
407C4×C8—21no—
408C4×C8—21no—
409C4×C8C22×D1111yescharacteristic
410C4×C8C22×D1111yescharacteristic
411C2×C11—41no—
412C2×C11#303711yescharacteristic
413C2×C11#306311yescharacteristic
414C2×C11#306911yescharacteristic
415C2×Q8—21no—
416C2×Q8—221no—
417C2×Q8—221no—
418C2×Q8—221no—
419C2×Q8—221no—
420C2×Q8C2×D4411yescharacteristic
421C2×Q8C2×D4411yescharacteristic
422C22×C4C2×D4411yescharacteristic
423C22×C4#433911yescharacteristic
424C22×C4C2×C22⋊D1111yescharacteristic
425Q16—442no—
426Q16—442no—
427Q16—881no—
428Q16—881no—
429M16—22no—
430M16—41no—
431M16—881no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—42no—
435C2×C8—221no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8C2×C22⋊D1111yescharacteristic
440C2×C8C2×C22⋊D1111yescharacteristic
441C2×C8C2×C22⋊D1111yescharacteristic
442C2×C8C2×C22⋊D1111yescharacteristic
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—221no—
451C4⋊C4—221no—
452C4⋊C4—221no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—441no—
459C4⋊C4—441no—
460C4⋊C4—441no—
461C4⋊C4—441no—
462C4⋊C4C2×D4411yescharacteristic
463C4⋊C4C2×D4411yescharacteristic
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—441no—
467C22⋊C4—441no—
468C42—21no—
469C42—21no—
470C42—441no—
471C42—441no—
472C42C2×D4411yescharacteristic
473C42#433911yescharacteristic
474C42C2×C22⋊D1111yescharacteristic
475C42C23×D1111yescharacteristic
476C11#1937511yescharacteristic, complemented, Sylow
477C23#6698311yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—81no—
483Q8—441no—
484Q8—441no—
485Q8—441no—
486Q8—441no—
487Q8—441no—
488Q8—441no—
489Q8—881no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—41no—
499C2×C4—441no—
500C2×C4—441no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4#6698311yescharacteristic
504C2×C4#6698311yescharacteristic
505C2×C4#6698311yescharacteristic
506C2×C4C22×D4411yescharacteristic
507C2×C4C2×#433911yescharacteristic
508C2×C4C22×C22⋊D1111yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—41no—
513C8—41no—
514C8—441no—
515C8—441no—
516C8—441no—
517C8—441no—
518C8#6699512yes—
519C22—21no—
520C22—21no—
521C22—21no—
522C22C2×#6698311yescharacteristic
523C4—21no—
524C4—21no—
525C4—21no—
526C4—21no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—881no—
532C4—881no—
533C4—881no—
534C4—881no—
535C4#1062328211yescharacteristic
536C4#1062328411yescharacteristic
537C4C2×#6699511yescharacteristic
538C4#1062335311yescharacteristic
539C2—41no—
540C2#1307808811yescharacteristic
541C2#1307830711yescharacteristic
542C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2962C2
socleC22×C11C2×#121
prime radicalC23×C11#121
hypercenter#2962D11
hypocenterC11#19375
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
4. #13068198C2semidirect
5. #13068170C2semidirect
6. #13068122C2semidirect
7. #13068110C2semidirect
8. #13068074C2semidirect
9. #13068046C2semidirect
10. #13067998C2semidirect
11. #13067986C2semidirect
476. C11#19375semidirect

Maximal subgroups

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

subgroupindex
#130800072
#130798262
#130793612
#130681982
#130681702
#130681222
#130681102
#130680742
#130680462
#130679982
#130679862
#130673832
#130673142
#130673042
C11×#29622
#1937511