Finite Group Databasebeta

← #14738860

Subgroups — #14738860

Order 2816.

572 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079989C211yesmaximal, characteristic
2#13079834C211yesmaximal, characteristic
3#13079162C211yesmaximal, characteristic, complemented
4#13068144C211yesmaximal, characteristic, complemented
5#13068139C211yesmaximal, characteristic, complemented
6#13068122C211yesmaximal, characteristic, complemented
7#13068115C211yesmaximal, characteristic, complemented
8#13068020C211yesmaximal, characteristic, complemented
9#13068015C211yesmaximal, characteristic, complemented
10#13067998C211yesmaximal, characteristic, complemented
11#13067991C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067324C211yesmaximal, characteristic, complemented
14#13067296C211yesmaximal, characteristic, complemented
15C11×#2969C211yesmaximal, characteristic
16C11×#529C2211yescharacteristic
17#10623001C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C11×#446C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C11×#436—21no—
22C11×#436C2211yescharacteristic
23C11×#435—21no—
24C8×D4×C11C2211yescharacteristic
25C11×#433—21no—
26C11×#431C2211yescharacteristic
27C11×#405—21no—
28C4×C11×M16C2211yescharacteristic
29#10622734—21no—
30#10622734—21no—
31#10622678—21no—
32#10622676—21no—
33#10622668—21no—
34#10622667—21no—
35#10622665—21no—
36#10622656—21no—
37#10622655—21no—
38#10622646—21no—
39#10622644C2211yescharacteristic
40#10622634C2211yescharacteristic
41#10622634C2211yescharacteristic
42#10622634C2211yescharacteristic
43#10622632C2211yescharacteristic
44#10622621C2211yescharacteristic
45#10622621C2211yescharacteristic
46#10622621C2211yescharacteristic
47#10622539C2211yescharacteristic
48#10622537C2211yescharacteristic
49#10622315—21no—
50#10622315—21no—
51#10622295C2211yescharacteristic
52#10622295C2211yescharacteristic
53#10622293C2211yescharacteristic
54#10622293C2211yescharacteristic
55#10622124C2211yescharacteristic
56#10622124C2211yescharacteristic
57#10622119C2211yescharacteristic
58#10622119C2211yescharacteristic
59#10622119C2211yescharacteristic
60#10622119C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C22×Dic22—21no—
68C2×C11×M16—21no—
69C2×C11×M16D411yescharacteristic
70C2×C11×M16D411yescharacteristic
71C22×C8×C11—21no—
72C11×#126—21no—
73C11×#125D411yescharacteristic
74C11×#124D411yescharacteristic
75C11×#123—21no—
76C11×C22⋊Q8D411yescharacteristic
77C11×#121D411yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11C2311yescharacteristic
81C11×#117—21no—
82C2×C42×C11C2311yescharacteristic
83C2×#4326—21no—
84C2×#4324—21no—
85#66979—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88#66977—21no—
89#66977—21no—
90C2×#4318—21no—
91#66923—21no—
92#66922—21no—
93#66922—21no—
94#66922—21no—
95#66922C2311yescharacteristic
96#66922C2311yescharacteristic
97#66922C2311yescharacteristic
98#66922C2311yescharacteristic
99C4×Dic22—21no—
100C4×Dic22—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C22⋊C8—21no—
106C11×C22⋊C8—21no—
107C11×C22⋊C8—21no—
108C11×#97—21no—
109C11×#97D411yescharacteristic
110C11×#97D411yescharacteristic
111C4×C8×C11—21no—
112C4×C8×C11—21no—
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115#66899—21no—
116#66899—21no—
117#66899—21no—
118#66896—21no—
119#66896—21no—
120#66896—21no—
121C22⋊(C11⋊C8)—21no—
122#66882—21no—
123#66882—21no—
124#66882—21no—
125#66882—21no—
126#66881—21no—
127#66881—21no—
128#66881—21no—
129#66881—21no—
130#66874—21no—
131#66874—21no—
132#66872—21no—
133#66872—21no—
134#66872—21no—
135#66871—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#19379—111nomaximal, Sylow
145C2×Q8×C11C2×D411yescharacteristic
146C2×D4×C11—21no—
147C2×D4×C11C2×D411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C22×Dic11—41no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—41no—
158C2×Dic22—82no—
159C11×M16—22no—
160C11×M16—22no—
161C11×M16—42no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—42no—
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4C2×D411yescharacteristic
174C11×C4⋊C4C2×D411yescharacteristic
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C42×C11—21no—
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11#4111yescharacteristic
184C42×C11C2411yescharacteristic
185C22⋊Dic11—41no—
186#4326—81no—
187#4324—81no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—41no—
197C4⋊Dic11—41no—
198Dic11⋊C4—41no—
199Dic11⋊C4—41no—
200C4×Dic11—41no—
201#4318—81no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206#3252—111no—
207#3238—111no—
208#3165—111no—
209#2969D1111yescharacteristic
210#1696—111no—
211#1695—111no—
212#1692—111no—
213#1691—111no—
214#1676—111no—
215#1675—111no—
216#1672—111no—
217#1671—111no—
218#1569—111no—
219#1554—111no—
220#1548—111no—
221C23×C11—21no—
222C23×C11#12111yescharacteristic
223Q8×C11—21no—
224Q8×C11—21no—
225D4×C11—21no—
226D4×C11—21no—
227D4×C11—81no—
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—41no—
237C2×C4×C11—41no—
238C2×C4×C11#12111yescharacteristic
239C2×C4×C11#12111yescharacteristic
240C2×C4×C11#12111yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—82no—
249Dic22—41no—
250Dic22—41no—
251Dic22—82no—
252Dic22—81no—
253Dic22—81no—
254Dic22—81no—
255C8×C11—21no—
256C8×C11—21no—
257C8×C11—41no—
258C8×C11—41no—
259C8×C11#13712yes—
260C8×C11#13712yes—
261C11⋊C8—41no—
262C11⋊C8—41no—
263C11⋊C8—41no—
264C11⋊C8—41no—
265#533—111no—
266C2×C4⋊Q8—111no—
267#529C2×D1111yescharacteristic
268#501—221no—
269#501—221no—
270#501—221no—
271#500—111no—
272#500—111no—
273#498—111no—
274#498—111no—
275#489—221no—
276#483—221no—
277#480—221no—
278#479—221no—
279#477—111no—
280#477—111no—
281#477—111no—
282#476—111no—
283#476—111no—
284#476—111no—
285#470—221no—
286#468—221no—
287#464—221no—
288#462—111no—
289#461—111no—
290#446C2×D1111yescharacteristic
291C8×Q8C2×D1111yescharacteristic
292#436—21no—
293#436C2×D1111yescharacteristic
294#435—21no—
295C8×D4C2×D1111yescharacteristic
296#433—21no—
297#432—111no—
298#431C2×D1111yescharacteristic
299#428—221no—
300#428—221no—
301#423—111no—
302#405—21no—
303C4×M16C2×D1111yescharacteristic
304#335—111no—
305#335—111no—
306#334—111no—
307#334—111no—
308#333—111no—
309#333—111no—
310#333—111no—
311#333—111no—
312#333—111no—
313#333—111no—
314#332—111no—
315#332—111no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11C2×#12111yescharacteristic
323C4×C11—21no—
324C4×C11—21no—
325C4×C11—21no—
326C4×C11—21no—
327C4×C11—41no—
328C4×C11—41no—
329C4×C11—41no—
330C4×C11C2×#13711yescharacteristic
331C4×C11C2×#13711yescharacteristic
332C4×C11#57711yescharacteristic
333C4×C11#57811yescharacteristic
334Dic11—81no—
335Dic11—81no—
336Dic11—81no—
337Dic11—81no—
338C22×Q8—221no—
339C2×Q16—221no—
340C2×SD16—221no—
341C2×M16—21no—
342C2×M16—221no—
343C2×M16C22⋊D1111yescharacteristic
344C2×M16C22⋊D1111yescharacteristic
345C22×C8—21no—
346C4⋊Q8—111no—
347C4⋊Q8—111no—
348C4⋊Q8—111no—
349C4⋊Q8—111no—
350C4⋊Q8—221no—
351C4⋊Q8—221no—
352C4⋊Q8—221no—
353#126—21no—
354#125—221no—
355#125D4411yescharacteristic
356#124D4411yescharacteristic
357#123—21no—
358C22⋊Q8—221no—
359C22⋊Q8—221no—
360C22⋊Q8D4411yescharacteristic
361#121D4411yescharacteristic
362C4×Q8—221no—
363C4×Q8—221no—
364C4×Q8C22×D1111yescharacteristic
365C4×D4—21no—
366C4×D4C22×D1111yescharacteristic
367#117—21no—
368#117—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C42C22×D1111yescharacteristic
372#107—221no—
373#107—221no—
374#107—221no—
375#107—221no—
376#107—221no—
377#107—221no—
378#107—221no—
379#106—221no—
380#106—221no—
381#106—221no—
382#106—221no—
383#106—221no—
384#106—221no—
385#106—221no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—221no—
393C4⋊C8C22×D1111yescharacteristic
394C4⋊C8C22×D1111yescharacteristic
395#103—221no—
396#103—221no—
397#103—221no—
398#103—221no—
399#103—221no—
400#102—221no—
401#102—221no—
402#102—221no—
403C22⋊C8—21no—
404C22⋊C8—21no—
405C22⋊C8—21no—
406C22⋊C8—221no—
407#97—21no—
408#97—221no—
409#97C22⋊D1111yescharacteristic
410#97C22⋊D1111yescharacteristic
411C4×C8—21no—
412C4×C8—21no—
413C4×C8C22×D1111yescharacteristic
414C4×C8C22×D1111yescharacteristic
415C2×C11—41no—
416C2×C11—81no—
417C2×C11#303911yescharacteristic
418C2×C11#306311yescharacteristic
419C2×C11#306811yescharacteristic
420C2×Q8—221no—
421C2×Q8—221no—
422C2×Q8—221no—
423C2×Q8—221no—
424C2×Q8—441no—
425C2×Q8—882no—
426C2×Q8C2×D4411yescharacteristic
427C2×D4—21no—
428C2×D4C2×D4411yescharacteristic
429C22×C4—21no—
430C22×C4—441no—
431C22×C4C2×D4411yescharacteristic
432C22×C4#433911yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434Q16—881no—
435SD16—881no—
436M16—22no—
437M16—22no—
438M16—42no—
439M16—881no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—42no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8C2×C22⋊D1111yescharacteristic
448C2×C8C2×C22⋊D1111yescharacteristic
449C2×C8C2×C22⋊D1111yescharacteristic
450C2×C8C2×C22⋊D1111yescharacteristic
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—441no—
464C4⋊C4—441no—
465C4⋊C4—441no—
466C4⋊C4—441no—
467C4⋊C4C2×D4411yescharacteristic
468C4⋊C4C2×D4411yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—441no—
475C42—21no—
476C42—441no—
477C42C2×D4411yescharacteristic
478C42#433911yescharacteristic
479C42C2×C22⋊D1111yescharacteristic
480C42C23×D1111yescharacteristic
481C11#1937911yescharacteristic, complemented, Sylow
482C23—21no—
483C23#6698311yescharacteristic
484Q8—21no—
485Q8—21no—
486Q8—441no—
487Q8—441no—
488Q8—881no—
489Q8—881no—
490Q8—881no—
491Q8—882no—
492D4—21no—
493D4—21no—
494D4—81no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—441no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—882no—
510C2×C4#6698311yescharacteristic
511C2×C4#6698311yescharacteristic
512C2×C4#6698311yescharacteristic
513C2×C4C22×D4411yescharacteristic
514C2×C4C2×#433911yescharacteristic
515C2×C4C22×C22⋊D1111yescharacteristic
516C8—21no—
517C8—21no—
518C8—41no—
519C8—41no—
520C8—441no—
521C8—441no—
522C8—441no—
523C8—441no—
524C8#6700412yes—
525C8#6700412yes—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22C2×#6698311yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—881no—
541C4—881no—
542C4—881no—
543C4—881no—
544C4#1062328211yescharacteristic
545C4#1062328411yescharacteristic
546C4C2×#6700411yescharacteristic
547C4C2×#6700411yescharacteristic
548C2—41no—
549C2—81no—
550C2#1307810311yescharacteristic
551C2#1307830711yescharacteristic
552C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2969C2
socleC22×C11C2×#121
prime radicalC11×#121D4
hypercenter#2969D11
hypocenterC11#19379
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2969

Complements

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

NH ≅ G/Ntype
3. #13079162C2semidirect
4. #13068144C2semidirect
5. #13068139C2semidirect
6. #13068122C2semidirect
7. #13068115C2semidirect
8. #13068020C2semidirect
9. #13068015C2semidirect
10. #13067998C2semidirect
11. #13067991C2semidirect
12. #13067383C2semidirect
13. #13067324C2semidirect
14. #13067296C2semidirect
481. C11#19379semidirect

Maximal subgroups

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

subgroupindex
#130799892
#130798342
#130791622
#130681442
#130681392
#130681222
#130681152
#130680202
#130680152
#130679982
#130679912
#130673832
#130673242
#130672962
C11×#29692
#1937911