Finite Group Databasebeta

← #14737472

Subgroups — #14737472

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079947C211yesmaximal, characteristic
2#13079795C211yesmaximal, characteristic
3#13077620C211yesmaximal, characteristic
4#13068188C211yesmaximal, characteristic, complemented
5#13068160C211yesmaximal, characteristic, complemented
6#13068119C211yesmaximal, characteristic, complemented
7#13068107C211yesmaximal, characteristic, complemented
8#13068071C211yesmaximal, characteristic, complemented
9#13068043C211yesmaximal, characteristic, complemented
10#13067988C211yesmaximal, characteristic, complemented
11#13067978C211yesmaximal, characteristic, complemented
12#13067368C211yesmaximal, characteristic, complemented
13#13067281C211yesmaximal, characteristic, complemented
14#13067273C211yesmaximal, characteristic, complemented
15C11×#3185C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#533C2211yescharacteristic
18#10623010C2211yescharacteristic
19C11×#498C2211yescharacteristic
20C11×#494C2211yescharacteristic
21C11×#487C2211yescharacteristic
22C11×#487C2211yescharacteristic
23C11×#470—21no—
24C11×#470—21no—
25C11×#441—21no—
26C11×#441—21no—
27C4×C11×M16C2211yescharacteristic
28#10622741—21no—
29#10622740—21no—
30#10622707C2211yescharacteristic
31#10622707C2211yescharacteristic
32#10622704C2211yescharacteristic
33#10622703C2211yescharacteristic
34#10622700C2211yescharacteristic
35#10622700C2211yescharacteristic
36#10622697C2211yescharacteristic
37#10622696C2211yescharacteristic
38#10622681—21no—
39#10622677—21no—
40#10622664—21no—
41#10622661—21no—
42#10622641—21no—
43#10622635—21no—
44#10622616—21no—
45#10622609—21no—
46#10622538C2211yescharacteristic
47#10622538C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622322—21no—
50#10622321—21no—
51#10622301C2211yescharacteristic
52C8×D44C2211yescharacteristic
53#10622292C2211yescharacteristic
54C8×Dic22C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622185C2211yescharacteristic
60#10622185C2211yescharacteristic
61#10622184C2211yescharacteristic
62#10622184C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×Q16—21no—
68C2×C11×Q16—21no—
69C2×C11×M16D411yescharacteristic
70C2×C11×M16D411yescharacteristic
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×#125—21no—
76C11×#125—21no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C4×Q8×C11—21no—
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11—21no—
85C11×#117—21no—
86C11×#117—21no—
87C2×C42×C11C2311yescharacteristic
88C2×#4326—21no—
89C2×#4325—21no—
90#66983D411yescharacteristic
91#66982—21no—
92C4×C22⋊D11—21no—
93#66977D411yescharacteristic
94C22×C11⋊C8—21no—
95C2×#4313—21no—
96C2×C8×D11—21no—
97#66929—21no—
98#66928D411yescharacteristic
99C4×D44C2311yescharacteristic
100#66925—21no—
101#66923D411yescharacteristic
102C4×Dic22C2311yescharacteristic
103C11×#106—21no—
104C11×#106—21no—
105C11×#103—21no—
106C11×#103—21no—
107C11×#103—21no—
108C11×#103—21no—
109C11×#97D411yescharacteristic
110C11×#97D411yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113#66899—21no—
114#66899—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119#66879—21no—
120Dic11⋊C8—21no—
121Dic11⋊C8—21no—
122C8×Dic11—21no—
123#66874—21no—
124#66874—21no—
125#66874—21no—
126#66873—21no—
127#66873—21no—
128#66873—21no—
129#66872—21no—
130#66872—21no—
131#66872—21no—
132#66871—21no—
133#66871—21no—
134#66871—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8—21no—
143C4×C11⋊C8—21no—
144#19249—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C2×C22⋊D11—21no—
153C2×D44C2×D411yescharacteristic
154C2×C4×D11—21no—
155C2×Dic22C2×D411yescharacteristic
156C11×Q16—42no—
157C11×Q16—42no—
158C11×M16—22no—
159C11×M16—41no—
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⋊C4—21no—
172C11×C4⋊C4—41no—
173C11×C4⋊C4—41no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—41no—
176C11×C22⋊C4—41no—
177C11×C22⋊C4—41no—
178C42×C11—41no—
179C42×C11—41no—
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11#4111yescharacteristic
183C42×C11C2411yescharacteristic
184C22⋊Dic11—21no—
185#4326—81no—
186#4325—81no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191C4⋊Dic11C2×D411yescharacteristic
192C4⋊Dic11C2×D411yescharacteristic
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197C4×Dic11—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—81no—
205#4313—42no—
206C8×D11—42no—
207#3248—111no—
208#3233—111no—
209#3185D1111yescharacteristic, complemented
210#2969—111no—
211#1703—111no—
212#1699—111no—
213#1692—111no—
214#1690—111no—
215#1684—111no—
216#1680—111no—
217#1671—111no—
218#1669—111no—
219#1565—111no—
220#1544—111no—
221#1542—111no—
222C23×C11#12111yescharacteristic
223C22×D11—21no—
224Q8×C11—41no—
225Q8×C11—41no—
226Q8×C11—41no—
227Q8×C11—41no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—81no—
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—41no—
239C2×C4×C11—41no—
240C2×C4×C11#12111yescharacteristic
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C22⋊D11—81no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250D44—21no—
251D44—21no—
252C4×D11—41no—
253C4×D11—41no—
254Dic22—21no—
255Dic22—21no—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11#13512yes—
260C11⋊C8—41no—
261C11⋊C8—41no—
262C11⋊C8—41no—
263C11⋊C8—41no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266#533C2×D1111yescharacteristic
267#533C2×D1111yescharacteristic
268#529—111no—
269#499—221no—
270#498C2×D1111yescharacteristic
271#494C2×D1111yescharacteristic
272#488—221no—
273#487C2×D1111yescharacteristic
274#487C2×D1111yescharacteristic
275#485—221no—
276#482—221no—
277#479—221no—
278#477—111no—
279#476—111no—
280#475—111no—
281#475—111no—
282#474—111no—
283#474—111no—
284#470—21no—
285#470—21no—
286#467—221no—
287#465—221no—
288#464—221no—
289#462—111no—
290#461—111no—
291#446—111no—
292C8×Q8—111no—
293#441—21no—
294#441—21no—
295#436—111no—
296#436—221no—
297#435—221no—
298C8×D4—111no—
299#433—221no—
300#431—111no—
301#431—111no—
302C2×C4⋊C8—111no—
303#405—221no—
304C4×M16C2×D1111yescharacteristic
305#335—111no—
306#335—111no—
307#334—111no—
308#334—111no—
309#333—111no—
310#333—111no—
311#332—111no—
312#332—111no—
313#332—111no—
314#332—111no—
315#332—111no—
316#332—111no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11C2×#12111yescharacteristic
321C2×D11—41no—
322C2×D11—41no—
323C2×D11—41no—
324C4×C11—21no—
325C4×C11—21no—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—81no—
329C4×C11—81no—
330C4×C11—81no—
331C4×C11—81no—
332C4×C11C2×#13511yescharacteristic
333C4×C11#57511yescharacteristic
334C4×C11#57711yescharacteristic
335C4×C11#57811yescharacteristic
336Dic11—41no—
337Dic11—41no—
338Dic11—41no—
339C2×Q16—21no—
340C2×Q16—21no—
341C2×Q16—221no—
342C2×SD16—221no—
343C2×M16—221no—
344C2×M16C22⋊D1111yescharacteristic
345C2×M16C22⋊D1111yescharacteristic
346C22×C8—221no—
347C22×C8—221no—
348C4⋊Q8C22×D1111yescharacteristic
349C4⋊Q8C22×D1111yescharacteristic
350C4⋊Q8C22×D1111yescharacteristic
351C4⋊Q8C22×D1111yescharacteristic
352#126—221no—
353#125—21no—
354#125—21no—
355#125—111no—
356#124—111no—
357#123—221no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C22⋊Q8—111no—
363#121—111no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—111no—
369C4×D4—111no—
370C4×D4—221no—
371#117—21no—
372#117—21no—
373#117—221no—
374C2×C42C22×D1111yescharacteristic
375#107—221no—
376#107—221no—
377#107—221no—
378#106—21no—
379#106—21no—
380#106—221no—
381#106—221no—
382#106—221no—
383C4⋊C8—111no—
384C4⋊C8—111no—
385C4⋊C8—111no—
386C4⋊C8—111no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—221no—
390C4⋊C8—221no—
391C4⋊C8—221no—
392#103—21no—
393#103—21no—
394#103—21no—
395#103—21no—
396#103—221no—
397#103—221no—
398#103—221no—
399#103—221no—
400#103—221no—
401#102—221no—
402#102—221no—
403#102—221no—
404C22⋊C8—221no—
405C22⋊C8—221no—
406C22⋊C8—221no—
407C22⋊C8—221no—
408#97—221no—
409#97C22⋊D1111yescharacteristic
410#97C22⋊D1111yescharacteristic
411C4×C8—221no—
412C4×C8—221no—
413C4×C8—221no—
414C4×C8C22×D1111yescharacteristic
415C4×C8C22×D1111yescharacteristic
416C2×C11—41no—
417C2×C11#303511yescharacteristic
418C2×C11#306311yescharacteristic
419C2×C11#306911yescharacteristic
420D11—81no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—111no—
426C2×D4—111no—
427C2×D4—221no—
428C22×C4—221no—
429C22×C4D4×D1111yescharacteristic
430C22×C4#434111yescharacteristic
431C22×C4C2×C22⋊D1111yescharacteristic
432Q16—42no—
433Q16—42no—
434Q16—881no—
435SD16—881no—
436M16—22no—
437M16—41no—
438M16—442no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—442no—
446C2×C8—881no—
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—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—111no—
464C4⋊C4—111no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C22⋊C4—221no—
472C22⋊C4—221no—
473C22⋊C4—221no—
474C22⋊C4—221no—
475C22⋊C4—221no—
476C42—41no—
477C42—41no—
478C42—221no—
479C42D4×D1111yescharacteristic
480C42#434111yescharacteristic
481C42C2×C22⋊D1111yescharacteristic
482C42C23×D1111yescharacteristic
483C11#1924911yescharacteristic, complemented, Sylow
484C23—221no—
485C23#6699111yescharacteristic
486Q8—41no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—81no—
493Q8—221no—
494Q8—221no—
495D4—221no—
496D4—221no—
497D4—881no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4#6699111yescharacteristic
513C2×C4#6699111yescharacteristic
514C2×C4#6699111yescharacteristic
515C2×C4C2×D4×D1111yescharacteristic
516C2×C4C2×#434111yescharacteristic
517C2×C4C22×C22⋊D1111yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—441no—
522C8—441no—
523C8—441no—
524C8—441no—
525C8—441no—
526C8—441no—
527C8#6700312yes—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—441no—
532C22—441no—
533C22—441no—
534C22C2×#6699111yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—81no—
540C4—81no—
541C4—81no—
542C4—81no—
543C4—441no—
544C4—441no—
545C4—441no—
546C4#1062330911yescharacteristic
547C4#1062331011yescharacteristic
548C4C2×#6700311yescharacteristic
549C4#1062335311yescharacteristic
550C2—41no—
551C2—881no—
552C2#1307806511yescharacteristic
553C2#1307830111yescharacteristic
554C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3185C2
socleC22×C11C2×#121
prime radical#66983D4
hypercenter#3185D11
hypocenterC11#19249
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3185

Complements

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

NH ≅ G/Ntype
4. #13068188C2semidirect
5. #13068160C2semidirect
6. #13068119C2semidirect
7. #13068107C2semidirect
8. #13068071C2semidirect
9. #13068043C2semidirect
10. #13067988C2semidirect
11. #13067978C2semidirect
12. #13067368C2semidirect
13. #13067281C2semidirect
14. #13067273C2semidirect
15. C11×#3185C2semidirect
209. #3185D11semidirect
483. C11#19249semidirect

Maximal subgroups

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

subgroupindex
#130799472
#130797952
#130776202
#130681882
#130681602
#130681192
#130681072
#130680712
#130680432
#130679882
#130679782
#130673682
#130672812
#130672732
C11×#31852
#1924911