Finite Group Databasebeta

← #14737714

Subgroups — #14737714

Order 2816.

608 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#13079126C211yesmaximal, characteristic, complemented
2#13078778C211yesmaximal, characteristic
3#41×C11⋊C8C211yesmaximal, characteristic
4#13068018C211yesmaximal, characteristic, complemented
5#13068013C211yesmaximal, characteristic, complemented
6#13068008C211yesmaximal, characteristic, complemented
7#13068003C211yesmaximal, characteristic, complemented
8#13068000C211yesmaximal, characteristic, complemented
9#13067996C211yesmaximal, characteristic, complemented
10#13067993C211yesmaximal, characteristic, complemented
11#13067989C211yesmaximal, characteristic, complemented
12#13067377C211yesmaximal, characteristic, complemented
13#13067327C211yesmaximal, characteristic, complemented
14#13067326C211yesmaximal, characteristic, complemented
15C11×#3116C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#485—21no—
20C11×#477C2211yescharacteristic
21C11×#476C2211yescharacteristic
22C11×#462C2211yescharacteristic
23C11×#461C2211yescharacteristic
24C11×#452—21no—
25C11×#441—21no—
26C11×#440—21no—
27C11×#432C2211yescharacteristic
28#10622852—21no—
29#10622692C2211yescharacteristic
30#10622692C2211yescharacteristic
31#10622691C2211yescharacteristic
32#10622691C2211yescharacteristic
33#10622677—21no—
34#10622677—21no—
35#10622644C2211yescharacteristic
36#10622643—21no—
37Q8×C11⋊C8C2211yescharacteristic
38Q8×C11⋊C8C2211yescharacteristic
39#10622634C2211yescharacteristic
40#10622632C2211yescharacteristic
41#10622631—21no—
42D4×C11⋊C8—21no—
43D4×C11⋊C8—21no—
44D4×C11⋊C8C2211yescharacteristic
45D4×C11⋊C8C2211yescharacteristic
46#10622621C2211yescharacteristic
47#10622611—21no—
48#10622611—21no—
49#10622609—21no—
50#10622539C2211yescharacteristic
51#10622538—21no—
52#10622538C2211yescharacteristic
53C2×C4×C11⋊C8—21no—
54C2×C4×C11⋊C8C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58#10622184C2211yescharacteristic
59#10622120C2211yescharacteristic
60#10622120C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41D411yescharacteristic
68C2×C11×Q16—21no—
69C2×C11×SD16—21no—
70C11×C4⋊Q8C2311yescharacteristic
71C11×C4⋊Q8C2311yescharacteristic
72C11×#125—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—21no—
75C4×Q8×C11—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11D411yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11D411yescharacteristic
82C4×D4×C11C2311yescharacteristic
83C11×#117—21no—
84C11×#117—21no—
85C11×#117D411yescharacteristic
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×#4326—21no—
89C2×#4324—21no—
90#66979—21no—
91#66977—21no—
92#66977—21no—
93C22×C11⋊C8—21no—
94C22×C11⋊C8—21no—
95C22×C11⋊C8D411yescharacteristic
96C22×C11⋊C8D411yescharacteristic
97#66923—21no—
98#66922C2311yescharacteristic
99#66922C2311yescharacteristic
100C4×Dic22—21no—
101C4×Dic22—21no—
102C11×#107—21no—
103C11×#106—21no—
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×#103—21no—
107C11×#103—21no—
108C11×#103—21no—
109C11×#102—21no—
110C11×C22⋊C8—21no—
111C11×#97—21no—
112#66899—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#66872—21no—
121#66872—21no—
122#66872—21no—
123#66872—21no—
124#66872—21no—
125#66871—21no—
126#66871—21no—
127#66871—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—
137C4×C11⋊C8—21no—
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8D411yescharacteristic
141C4×C11⋊C8D411yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19273—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—22no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11C2×D411yescharacteristic
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C2×Dic22—21no—
159C2×Dic22—21no—
160C11×Q16—42no—
161C11×SD16—42no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
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—41no—
171C11×C4⋊C4—41no—
172C11×C4⋊C4C2×D411yescharacteristic
173C11×C4⋊C4C2×D411yescharacteristic
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—41no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—41no—
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11#4111yescharacteristic
185C42×C11C2411yescharacteristic
186C22⋊Dic11—41no—
187#4326—42no—
188#4324—42no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193Dic11⋊C4—41no—
194Dic11⋊C4—41no—
195C4×Dic11—41no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—42no—
203C2×C11⋊C8—42no—
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208#3160—111no—
209#3116—111no—
210#3116D1111yescharacteristic
211C8×#41—111no—
212#1676—111no—
213#1675—111no—
214#1674—111no—
215#1673—111no—
216#1672—111no—
217#1672—111no—
218#1671—111no—
219#1671—111no—
220#1568—111no—
221#1554—111no—
222#1554—111no—
223C23×C11—21no—
224C23×C11#12111yescharacteristic
225Q8×C11—21no—
226Q8×C11—41no—
227Q8×C11—41no—
228Q8×C11—81no—
229Q8×C11#13512yes—
230D4×C11—24no—
231D4×C11—21no—
232D4×C11#13512yes—
233C2×C4×C11—24no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×Dic11—41no—
254C2×Dic11—41no—
255Dic22—41no—
256Dic22—41no—
257Dic22—81no—
258C8×C11—41no—
259C8×C11—41no—
260C11⋊C8—21no—
261C11⋊C8—21no—
262C11⋊C8—41no—
263C11⋊C8—41no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C11⋊C8#13712yes—
267C11⋊C8#13712yes—
268#533—111no—
269#533C2×D1111yescharacteristic
270C4×#41C2×D1111yescharacteristic
271#500—111no—
272#500—111no—
273#499—221no—
274#499—221no—
275#498—111no—
276#498—111no—
277#485—21no—
278#485—221no—
279#477—111no—
280#477C2×D1111yescharacteristic
281#476—111no—
282#476C2×D1111yescharacteristic
283#462—111no—
284#462C2×D1111yescharacteristic
285#461—111no—
286#461C2×D1111yescharacteristic
287#452—21no—
288#452—221no—
289C8×Q8—111no—
290C8×Q8—111no—
291#441—21no—
292#441—221no—
293#440—21no—
294#440—221no—
295C8×D4—111no—
296C8×D4—111no—
297C8×D4—221no—
298C8×D4—221no—
299#432—111no—
300#432C2×D1111yescharacteristic
301#431—111no—
302#431—221no—
303#427—221no—
304#427—221no—
305C2×C4×C8—111no—
306C2×C4×C8—221no—
307#335—111no—
308#335—111no—
309#334—111no—
310#334—111no—
311#333—111no—
312#333—111no—
313#333—111no—
314#333—111no—
315#332—111no—
316#332—111no—
317#332—111no—
318#332—111no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—22no—
322C22×C11—21no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11C2×#12111yescharacteristic
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—22no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11C2×#13511yescharacteristic
336C4×C11C2×#13511yescharacteristic
337C4×C11C2×#13711yescharacteristic
338C4×C11C2×#13711yescharacteristic
339Dic11—81no—
340Dic11—81no—
341C2×#41C22⋊D1111yescharacteristic
342C2×Q16—21no—
343C2×Q16—221no—
344C2×SD16—21no—
345C2×SD16—221no—
346C22×C8—111no—
347C22×C8—111no—
348C22×C8—221no—
349C22×C8—221no—
350C4⋊Q8—111no—
351C4⋊Q8—111no—
352C4⋊Q8C22×D1111yescharacteristic
353C4⋊Q8C22×D1111yescharacteristic
354#125—21no—
355#125—221no—
356C22⋊Q8—21no—
357C22⋊Q8—21no—
358C22⋊Q8—221no—
359C22⋊Q8—221no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—221no—
363C4×Q8—221no—
364C4×Q8C22⋊D1111yescharacteristic
365C4×Q8C22×D1111yescharacteristic
366C4×D4—21no—
367C4×D4—21no—
368C4×D4C22⋊D1111yescharacteristic
369C4×D4C22×D1111yescharacteristic
370#117—21no—
371#117—21no—
372#117—221no—
373#117C22⋊D1111yescharacteristic
374C2×C42—21no—
375C2×C42C22×D1111yescharacteristic
376#107—21no—
377#107—221no—
378#107—221no—
379#107—221no—
380#107—221no—
381#107—221no—
382#106—21no—
383#106—221no—
384#106—221no—
385#106—221no—
386#106—221no—
387#106—221no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8C22×D1111yescharacteristic
395C4⋊C8C22×D1111yescharacteristic
396#103—21no—
397#103—21no—
398#103—21no—
399#103—221no—
400#103—221no—
401#103—221no—
402#102—21no—
403#102—221no—
404C22⋊C8—21no—
405C22⋊C8—221no—
406C22⋊C8—221no—
407C22⋊C8—221no—
408C22⋊C8—221no—
409#97—21no—
410#97—221no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—221no—
416C4×C8—221no—
417C4×C8—221no—
418C2×C11—41no—
419C2×C11—42no—
420C2×C11#303911yescharacteristic
421C2×C11#305011yescharacteristic
422C2×C11#306711yescharacteristic
423#41—22no—
424#41—22no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—221no—
428C2×Q8—221no—
429C2×Q8C2×C22⋊D1111yescharacteristic
430C2×D4—21no—
431C2×D4C2×C22⋊D1111yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4D4×D1111yescharacteristic
436C22×C4#434111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438Q16—42no—
439Q16—442no—
440SD16—42no—
441SD16—442no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—111no—
445C2×C8—111no—
446C2×C8—111no—
447C2×C8—111no—
448C2×C8—222no—
449C2×C8—222no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—442no—
455C2×C8—442no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—441no—
469C4⋊C4—441no—
470C4⋊C4C2×C22⋊D1111yescharacteristic
471C4⋊C4C2×C22⋊D1111yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—41no—
476C22⋊C4—441no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—41no—
481C42—441no—
482C42D4×D1111yescharacteristic
483C42#434111yescharacteristic
484C42C2×C22⋊D1111yescharacteristic
485C42C23×D1111yescharacteristic
486C11#1927311yescharacteristic, complemented, Sylow
487C23—21no—
488C23#6699211yescharacteristic
489Q8—21no—
490Q8—41no—
491Q8—41no—
492Q8—81no—
493Q8—441no—
494Q8—441no—
495Q8—881no—
496Q8#6700312yes—
497D4—24no—
498D4—21no—
499D4#6700312yes—
500C2×C4—24no—
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—42no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—441no—
515C2×C4—441no—
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—112no—
525C8—112no—
526C8—221no—
527C8—221no—
528C8—441no—
529C8—441no—
530C8—441no—
531C8—441no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—22no—
536C22—41no—
537C22—41no—
538C22C2×#6699211yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—22no—
544C4—41no—
545C4—41no—
546C4—81no—
547C4—81no—
548C4—881no—
549C4—881no—
550C4D11×#13711yescharacteristic
551C4D11×#13711yescharacteristic
552C4C2×#6700311yescharacteristic
553C4C2×#6700311yescharacteristic
554C2—41no—
555C2—42no—
556C2#1307810111yescharacteristic
557C2#1307819411yescharacteristic
558C2#1307833311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3116C2
socleC22×C11C2×#121
prime radicalC2×C11×#41D4
hypercenter#3116D11
hypocenterC11#19273
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3116

Complements

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

NH ≅ G/Ntype
1. #13079126C2semidirect
4. #13068018C2semidirect
5. #13068013C2semidirect
6. #13068008C2semidirect
7. #13068003C2semidirect
8. #13068000C2semidirect
9. #13067996C2semidirect
10. #13067993C2semidirect
11. #13067989C2semidirect
12. #13067377C2semidirect
13. #13067327C2semidirect
14. #13067326C2semidirect
486. C11#19273semidirect

Maximal subgroups

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

subgroupindex
#130791262
#130787782
#41×C11⋊C82
#130680182
#130680132
#130680082
#130680032
#130680002
#130679962
#130679932
#130679892
#130673772
#130673272
#130673262
C11×#31162
#1927311