Finite Group Databasebeta

← #14738894

Subgroups — #14738894

Order 2816.

572 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079843C211yesmaximal, characteristic
2#13078998C211yesmaximal, characteristic, complemented
3#13077621C211yesmaximal, characteristic
4#13068200C211yesmaximal, characteristic, complemented
5#13068193C211yesmaximal, characteristic, complemented
6#13068172C211yesmaximal, characteristic, complemented
7#13068165C211yesmaximal, characteristic, complemented
8#13068076C211yesmaximal, characteristic, complemented
9#13068069C211yesmaximal, characteristic, complemented
10#13068048C211yesmaximal, characteristic, complemented
11#13068041C211yesmaximal, characteristic, complemented
12#13067381C211yesmaximal, characteristic, complemented
13#13067326C211yesmaximal, characteristic, complemented
14#13067302C211yesmaximal, characteristic, complemented
15C11×#3252C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C11×#529C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C11×#479—21no—
20C11×#477C2211yescharacteristic
21C11×#476C2211yescharacteristic
22C11×#470—21no—
23C11×#468—21no—
24C11×#464—21no—
25C11×#462C2211yescharacteristic
26C11×#461C2211yescharacteristic
27C11×#423C2211yescharacteristic
28#10622706C2211yescharacteristic
29#10622706C2211yescharacteristic
30#10622706C2211yescharacteristic
31#10622706C2211yescharacteristic
32#10622682—21no—
33#10622682—21no—
34#10622678—21no—
35#10622668—21no—
36#10622657—21no—
37#10622647—21no—
38#10622637C2211yescharacteristic
39Q8×C11⋊C8C2211yescharacteristic
40#10622633C2211yescharacteristic
41#10622633C2211yescharacteristic
42#10622625—21no—
43#10622625C2211yescharacteristic
44#10622624—21no—
45D4×C11⋊C8C2211yescharacteristic
46#10622620C2211yescharacteristic
47#10622620C2211yescharacteristic
48#10622617—21no—
49#10622617—21no—
50#10622613—21no—
51#10622610—21no—
52#10622539C2211yescharacteristic
53#10622538C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58#10622184C2211yescharacteristic
59#10622124C2211yescharacteristic
60#10622124C2211yescharacteristic
61#10622124C2211yescharacteristic
62#10622124C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C22×Dic22—21no—
68C2×C11×Q16—21no—
69C2×C11×SD16—21no—
70C2×C11×M16—21no—
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×#126—21no—
74C11×#125—21no—
75C11×#125D411yescharacteristic
76C11×#124D411yescharacteristic
77C11×#123—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8D411yescharacteristic
81C11×#121D411yescharacteristic
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11C2311yescharacteristic
85C4×D4×C11—21no—
86C4×D4×C11C2311yescharacteristic
87C11×#117—21no—
88C11×#117—21no—
89C2×C42×C11C2311yescharacteristic
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×#4318—21no—
93C2×#4318D411yescharacteristic
94C2×#4318D411yescharacteristic
95C22×C11⋊C8—21no—
96#66922—21no—
97#66922—21no—
98#66922—21no—
99#66922C2311yescharacteristic
100#66922C2311yescharacteristic
101C11×#107—21no—
102C11×#106—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×#103—21no—
107C11×#103—21no—
108C11×#103—21no—
109C11×#102—21no—
110#66899—21no—
111#66899—21no—
112#66896—21no—
113#66896—21no—
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117C22⋊(C11⋊C8)—21no—
118#66874—21no—
119#66874—21no—
120#66874—21no—
121#66874—21no—
122#66874—21no—
123#66874—21no—
124#66874—21no—
125#66874—21no—
126#66872—21no—
127#66872—21no—
128#66871—21no—
129#66871—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136#66867—21no—
137#66867—21no—
138#66867D411yescharacteristic
139#66867D411yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19381—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11C2×D411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11C2×D411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C22×Dic11—41no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—42no—
158C2×Dic22—42no—
159C2×Dic22—41no—
160C11×Q16—81no—
161C11×SD16—81no—
162C11×M16—81no—
163C2×C8×C11—21no—
164C2×C8×C11—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—21no—
173C11×C4⋊C4—41no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4C2×D411yescharacteristic
176C11×C4⋊C4C2×D411yescharacteristic
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—41no—
183C42×C11—21no—
184C42×C11—41no—
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11#4111yescharacteristic
188C42×C11C2411yescharacteristic
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—41no—
194C4⋊Dic11—41no—
195#4318—41no—
196#4318—41no—
197#4318—42no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—42no—
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207#3252D1111yescharacteristic
208#3239—111no—
209#3139—111no—
210#2969—111no—
211#1704—111no—
212#1703—111no—
213#1700—111no—
214#1699—111no—
215#1684—111no—
216#1683—111no—
217#1680—111no—
218#1679—111no—
219#1569—111no—
220#1554—111no—
221#1549—111no—
222C23×C11—21no—
223C23×C11#12111yescharacteristic
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—41no—
227Q8×C11—41no—
228Q8×C11—81no—
229D4×C11—21no—
230D4×C11—21no—
231D4×C11—81no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—82no—
253Dic22—41no—
254Dic22—41no—
255Dic22—41no—
256Dic22—41no—
257Dic22—82no—
258C8×C11—41no—
259C8×C11—41no—
260C11⋊C8—21no—
261C11⋊C8—21no—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268#533C2×D1111yescharacteristic
269C2×C4⋊Q8—111no—
270#529C2×D1111yescharacteristic
271#501—221no—
272#491—221no—
273#491—221no—
274#489—221no—
275#487—111no—
276#487—111no—
277#487—111no—
278#487—111no—
279#484—221no—
280#481—221no—
281#479—21no—
282#477C2×D1111yescharacteristic
283#476C2×D1111yescharacteristic
284#475—111no—
285#475—111no—
286#474—111no—
287#474—111no—
288#470—21no—
289#468—21no—
290#464—21no—
291#462C2×D1111yescharacteristic
292#461C2×D1111yescharacteristic
293#446—111no—
294C8×Q8—111no—
295#436—111no—
296#436—221no—
297#435—221no—
298C8×D4—111no—
299#433—221no—
300#432—111no—
301#431—111no—
302#423C2×D1111yescharacteristic
303#419—221no—
304#419—221no—
305#405—221no—
306C4×M16—111no—
307#335—111no—
308#335—111no—
309#334—111no—
310#334—111no—
311#333—111no—
312#333—111no—
313#332—111no—
314#332—111no—
315#332—111no—
316#332—111no—
317#332—111no—
318#332—111no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11C2×#12111yescharacteristic
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11#57511yescharacteristic
336C4×C11#57511yescharacteristic
337C4×C11#57711yescharacteristic
338C4×C11#57811yescharacteristic
339Dic11—81no—
340Dic11—81no—
341C22×Q8—221no—
342C2×Q16—21no—
343C2×SD16—21no—
344C2×M16—21no—
345C2×M16—111no—
346C2×M16—111no—
347C2×M16—221no—
348C22×C8—221no—
349C4⋊Q8—111no—
350C4⋊Q8—111no—
351C4⋊Q8—221no—
352C4⋊Q8—221no—
353C4⋊Q8—221no—
354C4⋊Q8C22×D1111yescharacteristic
355C4⋊Q8C22×D1111yescharacteristic
356#126—21no—
357#125—21no—
358#125C22⋊D1111yescharacteristic
359#124C22⋊D1111yescharacteristic
360#123—21no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8C22⋊D1111yescharacteristic
364#121C22⋊D1111yescharacteristic
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8C22×D1111yescharacteristic
368C4×D4—21no—
369C4×D4C22×D1111yescharacteristic
370#117—21no—
371#117—21no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C42C22×D1111yescharacteristic
375#107—21no—
376#107—221no—
377#107—221no—
378#106—21no—
379#106—221no—
380#106—221no—
381C4⋊C8—21no—
382C4⋊C8—111no—
383C4⋊C8—111no—
384C4⋊C8—111no—
385C4⋊C8—111no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8C22×D1111yescharacteristic
389C4⋊C8C22×D1111yescharacteristic
390#103—21no—
391#103—21no—
392#103—21no—
393#103—221no—
394#103—221no—
395#103—221no—
396#103—221no—
397#103—221no—
398#103—221no—
399#103—221no—
400#103—221no—
401#103—221no—
402#103—221no—
403#102—21no—
404#102—221no—
405#102—221no—
406C22⋊C8—221no—
407C22⋊C8—221no—
408C22⋊C8—221no—
409C22⋊C8—221no—
410#97—111no—
411#97—111no—
412#97—221no—
413#97—221no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—221no—
417C4×C8—221no—
418C2×C11—41no—
419C2×C11—81no—
420C2×C11#304011yescharacteristic
421C2×C11#306311yescharacteristic
422C2×C11#306911yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—221no—
426C2×Q8—221no—
427C2×Q8—442no—
428C2×Q8—442no—
429C2×Q8—441no—
430C2×Q8C2×C22⋊D1111yescharacteristic
431C2×D4—21no—
432C2×D4C2×C22⋊D1111yescharacteristic
433C22×C4—21no—
434C22×C4—441no—
435C22×C4D4×D1111yescharacteristic
436C22×C4#434111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438Q16—81no—
439SD16—81no—
440M16—81no—
441M16—441no—
442M16—441no—
443M16—442no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—111no—
447C2×C8—111no—
448C2×C8—111no—
449C2×C8—111no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—442no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—441no—
470C4⋊C4—441no—
471C4⋊C4C2×C22⋊D1111yescharacteristic
472C4⋊C4C2×C22⋊D1111yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—41no—
479C42—21no—
480C42—41no—
481C42D4×D1111yescharacteristic
482C42#434111yescharacteristic
483C42C2×C22⋊D1111yescharacteristic
484C42C23×D1111yescharacteristic
485C11#1938111yescharacteristic, complemented, Sylow
486C23—21no—
487C23#6699211yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—41no—
491Q8—41no—
492Q8—81no—
493Q8—441no—
494Q8—441no—
495Q8—441no—
496Q8—441no—
497Q8—882no—
498D4—21no—
499D4—21no—
500D4—81no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—882no—
516C2×C4#6699211yescharacteristic
517C2×C4#6699211yescharacteristic
518C2×C4#6699211yescharacteristic
519C2×C4C2×D4×D1111yescharacteristic
520C2×C4C2×#434111yescharacteristic
521C2×C4C22×C22⋊D1111yescharacteristic
522C8—41no—
523C8—41no—
524C8—221no—
525C8—221no—
526C8—221no—
527C8—221no—
528C8—441no—
529C8—441no—
530C8—441no—
531C8—441no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22C2×#6699211yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—81no—
547C4—81no—
548C4—881no—
549C4—881no—
550C4#1062330811yescharacteristic
551C4#1062330811yescharacteristic
552C4#1062336711yescharacteristic
553C4#1062336911yescharacteristic
554C2—41no—
555C2—81no—
556C2#1307811211yescharacteristic
557C2#1307830911yescharacteristic
558C2#1307835511yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3252C2
socleC22×C11C2×#121
prime radicalC11×#121D4
hypercenter#3252D11
hypocenterC11#19381
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3252

Complements

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

NH ≅ G/Ntype
2. #13078998C2semidirect
4. #13068200C2semidirect
5. #13068193C2semidirect
6. #13068172C2semidirect
7. #13068165C2semidirect
8. #13068076C2semidirect
9. #13068069C2semidirect
10. #13068048C2semidirect
11. #13068041C2semidirect
12. #13067381C2semidirect
13. #13067326C2semidirect
14. #13067302C2semidirect
485. C11#19381semidirect

Maximal subgroups

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

subgroupindex
#130798432
#130789982
#130776212
#130682002
#130681932
#130681722
#130681652
#130680762
#130680692
#130680482
#130680412
#130673812
#130673262
#130673022
C11×#32522
#1938111