Finite Group Databasebeta

← #14739285

Subgroups — #14739285

Order 2816.

594 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#13079777C211yesmaximal, characteristic, complemented
2#13078778C211yesmaximal, characteristic
3#13078687C211yesmaximal, characteristic
4#13068074C211yesmaximal, characteristic, complemented
5#13068067C211yesmaximal, characteristic, complemented
6#13068046C211yesmaximal, characteristic, complemented
7#13068039C211yesmaximal, characteristic, complemented
8#13068010C211yesmaximal, characteristic, complemented
9#13068005C211yesmaximal, characteristic, complemented
10#13067998C211yesmaximal, characteristic, complemented
11#13067991C211yesmaximal, characteristic, complemented
12#13067396C211yesmaximal, characteristic, complemented
13#13067314C211yesmaximal, characteristic, complemented
14#13067274C211yesmaximal, characteristic, complemented
15C11×#2988C211yesmaximal, characteristic
16C4×C11×#41C2211yescharacteristic
17#10623001C2211yescharacteristic
18#10623001C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C8×D4×C11—21no—
22C8×D4×C11—21no—
23C8×D4×C11C2211yescharacteristic
24C8×D4×C11C2211yescharacteristic
25C11×#431—21no—
26C11×#431C2211yescharacteristic
27C2×C11×C4⋊C8—21no—
28C2×C11×C4⋊C8C2211yescharacteristic
29#10622852—21no—
30#10622852—21no—
31#10622644C2211yescharacteristic
32#10622644C2211yescharacteristic
33#10622643—21no—
34C4×#4326—21no—
35#10622634C2211yescharacteristic
36#10622633C2211yescharacteristic
37#10622632C2211yescharacteristic
38#10622632C2211yescharacteristic
39#10622631—21no—
40C4×#4324—21no—
41#10622621C2211yescharacteristic
42#10622620C2211yescharacteristic
43#10622609—21no—
44#10622609—21no—
45#10622539C2211yescharacteristic
46#10622538C2211yescharacteristic
47#10622442—21no—
48#10622442—21no—
49#10622336—21no—
50#10622336—21no—
51#10622295C2211yescharacteristic
52#10622294C2211yescharacteristic
53#10622294C2211yescharacteristic
54#10622293C2211yescharacteristic
55#10622124C2211yescharacteristic
56#10622124C2211yescharacteristic
57#10622124C2211yescharacteristic
58#10622124C2211yescharacteristic
59#10622120C2211yescharacteristic
60#10622120C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×#41D411yescharacteristic
68C22×C8×C11—21no—
69C22×C8×C11—21no—
70C22×C8×C11—21no—
71C4×Q8×C11D411yescharacteristic
72C4×Q8×C11C2311yescharacteristic
73C4×D4×C11—21no—
74C4×D4×C11—21no—
75C4×D4×C11D411yescharacteristic
76C4×D4×C11C2311yescharacteristic
77C11×#117—21no—
78C11×#117D411yescharacteristic
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×#4326—21no—
82C2×#4326—21no—
83C2×#4324—21no—
84C2×#4324—21no—
85#66979—21no—
86#66979—21no—
87#66977—21no—
88#66977—21no—
89#66977—21no—
90#66977—21no—
91#66923—21no—
92#66923—21no—
93#66922C2311yescharacteristic
94#66922C2311yescharacteristic
95#66922C2311yescharacteristic
96#66922C2311yescharacteristic
97C4×Dic22—21no—
98C4×Dic22—21no—
99C4×Dic22—21no—
100C4×Dic22—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8D411yescharacteristic
105C11×C4⋊C8D411yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×C22⋊C8—21no—
109C11×C22⋊C8—21no—
110C11×C22⋊C8D411yescharacteristic
111C11×C22⋊C8D411yescharacteristic
112C4×C8×C11—21no—
113C4×C8×C11—21no—
114C4×C8×C11C2311yescharacteristic
115C4×C8×C11C2311yescharacteristic
116#66899—21no—
117#66899—21no—
118#66896—21no—
119#66896—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122#66882—21no—
123#66882—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#66874—21no—
133#66874—21no—
134#66872—21no—
135#66872—21no—
136#66871—21no—
137#66871—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142#66867—21no—
143C4×C11⋊C8—21no—
144#19418—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—22no—
147C2×Q8×C11C2×D411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11C2×D411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—81no—
163C2×C8×C11—81no—
164C2×C8×C11—81no—
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⋊C4C2×D411yescharacteristic
172C11×C4⋊C4C2×D411yescharacteristic
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11#4111yescharacteristic
182C42×C11C2411yescharacteristic
183C22⋊Dic11—41no—
184C22⋊Dic11—41no—
185#4326—42no—
186#4326—42no—
187#4324—42no—
188#4324—42no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197Dic11⋊C4—41no—
198Dic11⋊C4—41no—
199Dic11⋊C4—41no—
200Dic11⋊C4—41no—
201C4×Dic11—41no—
202C4×Dic11—41no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207#3231—111no—
208#3116—111no—
209#3107—111no—
210#2988D1111yescharacteristic
211#1684—111no—
212#1683—111no—
213#1680—111no—
214#1679—111no—
215#1674—111no—
216#1673—111no—
217#1672—111no—
218#1671—111no—
219#1572—111no—
220#1552—111no—
221#1542—111no—
222C23×C11—21no—
223C23×C11#12111yescharacteristic
224Q8×C11—21no—
225Q8×C11#13512yes—
226D4×C11—24no—
227D4×C11—21no—
228D4×C11#13512yes—
229C2×C4×C11—24no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—81no—
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251Dic22—41no—
252Dic22—41no—
253Dic22—41no—
254Dic22—41no—
255Dic22—41no—
256Dic22—41no—
257Dic22—81no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—41no—
263C8×C11—41no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268#533—111no—
269#533—111no—
270C4×#41C2×D1111yescharacteristic
271#500—111no—
272#498—111no—
273#487—111no—
274#487—111no—
275#485—221no—
276#485—221no—
277#485—221no—
278#485—221no—
279#479—221no—
280#479—221no—
281#477—111no—
282#476—111no—
283#475—111no—
284#474—111no—
285#462—111no—
286#462—111no—
287#461—111no—
288#461—111no—
289#452—221no—
290#452—221no—
291C8×Q8C2×D1111yescharacteristic
292C8×Q8C2×D1111yescharacteristic
293#441—221no—
294#440—221no—
295C4×Q16—221no—
296C4×SD16—221no—
297C8×D4—21no—
298C8×D4—21no—
299C8×D4C2×D1111yescharacteristic
300C8×D4C2×D1111yescharacteristic
301#432—111no—
302#431—21no—
303#431—111no—
304#431C2×D1111yescharacteristic
305C2×C4⋊C8—21no—
306C2×C4⋊C8C2×D1111yescharacteristic
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—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×C11C2×#13511yescharacteristic
334C4×C11C2×#13511yescharacteristic
335C4×C11#57711yescharacteristic
336C4×C11#57811yescharacteristic
337Dic11—81no—
338Dic11—81no—
339Dic11—81no—
340Dic11—81no—
341C2×#41D4411yescharacteristic
342C2×Q16—221no—
343C2×Q16—221no—
344C2×SD16—221no—
345C2×SD16—221no—
346C22×C8—21no—
347C22×C8—21no—
348C22×C8—21no—
349C4⋊Q8—111no—
350C4⋊Q8—111no—
351C4⋊Q8—111no—
352C4⋊Q8—111no—
353#125—221no—
354#125—221no—
355C22⋊Q8—221no—
356C22⋊Q8—221no—
357C22⋊Q8—221no—
358C22⋊Q8—221no—
359C4×Q8—221no—
360C4×Q8—221no—
361C4×Q8—221no—
362C4×Q8—221no—
363C4×Q8D4411yescharacteristic
364C4×Q8C22×D1111yescharacteristic
365C4×D4—21no—
366C4×D4—21no—
367C4×D4D4411yescharacteristic
368C4×D4C22×D1111yescharacteristic
369#117—21no—
370#117—221no—
371#117—221no—
372#117D4411yescharacteristic
373C2×C42—21no—
374C2×C42C22×D1111yescharacteristic
375#107—221no—
376#107—221no—
377#107—221no—
378#107—221no—
379#106—221no—
380#106—221no—
381#106—221no—
382#106—221no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—111no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8C22⋊D1111yescharacteristic
391C4⋊C8C22⋊D1111yescharacteristic
392C4⋊C8C22×D1111yescharacteristic
393C4⋊C8C22×D1111yescharacteristic
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#103—221no—
404#102—221no—
405#102—221no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—221no—
409C22⋊C8—221no—
410C22⋊C8C22⋊D1111yescharacteristic
411C22⋊C8C22⋊D1111yescharacteristic
412#97—221no—
413C4×C8—21no—
414C4×C8—21no—
415C4×C8—221no—
416C4×C8C22×D1111yescharacteristic
417C4×C8C22×D1111yescharacteristic
418C2×C11—41no—
419C2×C11—42no—
420C2×C11#304611yescharacteristic
421C2×C11#305011yescharacteristic
422C2×C11#306911yescharacteristic
423#41—22no—
424#41—22no—
425C2×Q8—221no—
426C2×Q8—221no—
427C2×Q8—221no—
428C2×Q8—221no—
429C2×Q8C2×D4411yescharacteristic
430C2×D4—21no—
431C2×D4C2×D4411yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4C2×D4411yescharacteristic
436C22×C4#433911yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438Q16—442no—
439Q16—442no—
440SD16—442no—
441SD16—442no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—81no—
445C2×C8—81no—
446C2×C8—81no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8C2×C22⋊D1111yescharacteristic
452C2×C8C2×C22⋊D1111yescharacteristic
453C2×C8C2×C22⋊D1111yescharacteristic
454C2×C8C2×C22⋊D1111yescharacteristic
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—441no—
466C4⋊C4—441no—
467C4⋊C4—441no—
468C4⋊C4—441no—
469C4⋊C4C2×D4411yescharacteristic
470C4⋊C4C2×D4411yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—441no—
475C22⋊C4—441no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—441no—
480C42—441no—
481C42C2×D4411yescharacteristic
482C42#433911yescharacteristic
483C42C2×C22⋊D1111yescharacteristic
484C42C23×D1111yescharacteristic
485C11#1941811yescharacteristic, complemented, Sylow
486C23—21no—
487C23#6698311yescharacteristic
488Q8—21no—
489Q8—441no—
490Q8—441no—
491Q8—441no—
492Q8—441no—
493Q8—441no—
494Q8—441no—
495Q8—881no—
496Q8#6695712yes—
497D4—24no—
498D4—21no—
499D4#6695712yes—
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—41no—
510C2×C4—41no—
511C2×C4—81no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4#6698311yescharacteristic
517C2×C4#6698311yescharacteristic
518C2×C4#6698311yescharacteristic
519C2×C4C22×D4411yescharacteristic
520C2×C4C2×#433911yescharacteristic
521C2×C4C22×C22⋊D1111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—441no—
529C8—441no—
530C8—441no—
531C8—441no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—22no—
536C22—41no—
537C22—41no—
538C22C2×#6698311yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—22no—
544C4—41no—
545C4—41no—
546C4—881no—
547C4—881no—
548C4—881no—
549C4—881no—
550C4C2×#6695711yescharacteristic
551C4C2×#6695711yescharacteristic
552C4#1062336711yescharacteristic
553C4#1062336911yescharacteristic
554C2—41no—
555C2—42no—
556C2#1307816611yescharacteristic
557C2#1307819711yescharacteristic
558C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2988C2
socleC22×C11C2×#121
prime radicalC2×C11×#41D4
hypercenter#2988D11
hypocenterC11#19418
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #13079777C2semidirect
4. #13068074C2semidirect
5. #13068067C2semidirect
6. #13068046C2semidirect
7. #13068039C2semidirect
8. #13068010C2semidirect
9. #13068005C2semidirect
10. #13067998C2semidirect
11. #13067991C2semidirect
12. #13067396C2semidirect
13. #13067314C2semidirect
14. #13067274C2semidirect
485. C11#19418semidirect

Maximal subgroups

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

subgroupindex
#130797772
#130787782
#130786872
#130680742
#130680672
#130680462
#130680392
#130680102
#130680052
#130679982
#130679912
#130673962
#130673142
#130672742
C11×#29882
#1941811