Finite Group Databasebeta

← #14736822

Subgroups — #14736822

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079361C211yesmaximal, characteristic, complemented
2#13078687C211yesmaximal, characteristic
3#13078404C211yesmaximal, characteristic
4#13068191C211yesmaximal, characteristic, complemented
5#13068163C211yesmaximal, characteristic, complemented
6#13068115C211yesmaximal, characteristic, complemented
7#13068105C211yesmaximal, characteristic, complemented
8#13068074C211yesmaximal, characteristic, complemented
9#13068046C211yesmaximal, characteristic, complemented
10#13067998C211yesmaximal, characteristic, complemented
11#13067986C211yesmaximal, characteristic, complemented
12#13067368C211yesmaximal, characteristic, complemented
13#13067327C211yesmaximal, characteristic, complemented
14#13067317C211yesmaximal, characteristic, complemented
15C11×#2971C211yesmaximal, characteristic
16C4×C11×#41C2211yescharacteristic
17#10623001C2211yescharacteristic
18#10623001C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C11×#436—21no—
22C11×#436—21no—
23C11×#436C2211yescharacteristic
24C11×#436C2211yescharacteristic
25C11×#432—21no—
26C11×#432C2211yescharacteristic
27C4×C11×M16—21no—
28C4×C11×M16C2211yescharacteristic
29#10622852—21no—
30#10622846—21no—
31#10622750—21no—
32#10622750—21no—
33#10622644C2211yescharacteristic
34C4×#4326—21no—
35#10622635—21no—
36#10622634C2211yescharacteristic
37#10622633C2211yescharacteristic
38#10622633C2211yescharacteristic
39#10622632C2211yescharacteristic
40C4×#4324—21no—
41#10622622—21no—
42#10622621C2211yescharacteristic
43#10622620C2211yescharacteristic
44#10622620C2211yescharacteristic
45#10622611—21no—
46#10622609—21no—
47#10622538C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622329—21no—
50#10622329—21no—
51#10622312C2211yescharacteristic
52#10622294C2211yescharacteristic
53#10622294C2211yescharacteristic
54#10622293C2211yescharacteristic
55#10622124C2211yescharacteristic
56#10622124C2211yescharacteristic
57#10622120C2211yescharacteristic
58#10622120C2211yescharacteristic
59#10622120C2211yescharacteristic
60#10622120C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×#41D411yescharacteristic
68C2×C11×M16—21no—
69C2×C11×M16—21no—
70C2×C11×M16D411yescharacteristic
71C2×C11×M16D411yescharacteristic
72C4×Q8×C11D411yescharacteristic
73C4×Q8×C11C2311yescharacteristic
74C4×D4×C11—21no—
75C4×D4×C11—21no—
76C4×D4×C11D411yescharacteristic
77C4×D4×C11C2311yescharacteristic
78C11×#117—21no—
79C11×#117D411yescharacteristic
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4326—21no—
83C2×#4324—21no—
84#66979—21no—
85#66979—21no—
86#66977—21no—
87#66977—21no—
88#66977—21no—
89#66977—21no—
90C22×C11⋊C8—21no—
91C2×Dic44—21no—
92C2×Dic44—21no—
93#66923—21no—
94#66923—21no—
95#66922C2311yescharacteristic
96#66922C2311yescharacteristic
97#66922C2311yescharacteristic
98#66922C2311yescharacteristic
99C4×Dic22—21no—
100C4×Dic22—21no—
101C4×Dic22—21no—
102C4×Dic22—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8—21no—
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C11×C22⋊C8—21no—
110C11×#97—21no—
111C11×#97D411yescharacteristic
112C11×#97D411yescharacteristic
113C4×C8×C11—21no—
114C4×C8×C11—21no—
115C4×C8×C11C2311yescharacteristic
116C4×C8×C11C2311yescharacteristic
117#66899—21no—
118#66899—21no—
119#66899—21no—
120#66896—21no—
121#66896—21no—
122#66896—21no—
123C22⋊(C11⋊C8)—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#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
143C4×C11⋊C8—21no—
144#19185—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—41no—
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—
160C11×M16—22no—
161C11×M16—41no—
162C11×M16—42no—
163C11×M16—42no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4C2×D411yescharacteristic
173C11×C4⋊C4C2×D411yescharacteristic
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11#4111yescharacteristic
183C42×C11C2411yescharacteristic
184C22⋊Dic11—41no—
185C22⋊Dic11—41no—
186#4326—42no—
187#4324—42no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196Dic11⋊C4—41no—
197Dic11⋊C4—41no—
198Dic11⋊C4—41no—
199Dic11⋊C4—41no—
200C4×Dic11—41no—
201C4×Dic11—41no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—42no—
207Dic44—42no—
208Dic44—42no—
209#3185—111no—
210#3107—111no—
211#3076—111no—
212#2971D1111yescharacteristic
213#1703—111no—
214#1699—111no—
215#1691—111no—
216#1689—111no—
217#1684—111no—
218#1680—111no—
219#1672—111no—
220#1670—111no—
221#1565—111no—
222#1554—111no—
223#1552—111no—
224C23×C11—21no—
225C23×C11#12111yescharacteristic
226Q8×C11—21no—
227Q8×C11#13712yes—
228D4×C11—21no—
229D4×C11—21no—
230D4×C11—42no—
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—21no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—81no—
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253Dic22—41no—
254Dic22—41no—
255Dic22—41no—
256Dic22—41no—
257Dic22—41no—
258Dic22—41no—
259Dic22—81no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—41no—
264C8×C11—41no—
265C8×C11#13512yes—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270#533—111no—
271#533—111no—
272C4×#41C2×D1111yescharacteristic
273#498—111no—
274#494—111no—
275#487—111no—
276#487—111no—
277#485—221no—
278#479—221no—
279#478—221no—
280#477—111no—
281#476—111no—
282#475—111no—
283#475—111no—
284#474—111no—
285#474—111no—
286#470—221no—
287#470—221no—
288#462—111no—
289#461—111no—
290#452—221no—
291C8×Q8C2×D1111yescharacteristic
292C8×Q8C2×D1111yescharacteristic
293#441—221no—
294#441—221no—
295C4×Q16—221no—
296C4×SD16—221no—
297#436—21no—
298#436—21no—
299#436C2×D1111yescharacteristic
300#436C2×D1111yescharacteristic
301#432—21no—
302#432C2×D1111yescharacteristic
303#431—111no—
304#427—221no—
305C2×C4⋊C8—111no—
306#416—221no—
307C4×M16—21no—
308C4×M16C2×D1111yescharacteristic
309#335—111no—
310#335—111no—
311#334—111no—
312#334—111no—
313#333—111no—
314#333—111no—
315#332—111no—
316#332—111no—
317#332—111no—
318#332—111no—
319#332—111no—
320#332—111no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11C2×#12111yescharacteristic
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—22no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11C2×#13511yescharacteristic
336C4×C11C2×#13711yescharacteristic
337C4×C11#57511yescharacteristic
338C4×C11#57511yescharacteristic
339Dic11—81no—
340Dic11—81no—
341Dic11—81no—
342Dic11—81no—
343C2×#41D4411yescharacteristic
344C2×Q16—221no—
345C2×Q16—221no—
346C2×Q16—221no—
347C2×SD16—221no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16C22⋊D1111yescharacteristic
351C2×M16C22⋊D1111yescharacteristic
352C22×C8—221no—
353C4⋊Q8—111no—
354C4⋊Q8—111no—
355C4⋊Q8—111no—
356C4⋊Q8—111no—
357#125—221no—
358#125—221no—
359C22⋊Q8—221no—
360C22⋊Q8—221no—
361C22⋊Q8—221no—
362C22⋊Q8—221no—
363C4×Q8—221no—
364C4×Q8—221no—
365C4×Q8—221no—
366C4×Q8—221no—
367C4×Q8D4411yescharacteristic
368C4×Q8C22×D1111yescharacteristic
369C4×D4—21no—
370C4×D4—21no—
371C4×D4D4411yescharacteristic
372C4×D4C22×D1111yescharacteristic
373#117—21no—
374#117—221no—
375#117—221no—
376#117D4411yescharacteristic
377C2×C42—21no—
378C2×C42C22×D1111yescharacteristic
379#107—221no—
380#107—221no—
381#107—221no—
382#106—221no—
383#106—221no—
384#106—221no—
385#106—221no—
386#106—221no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—221no—
394C4⋊C8C22×D1111yescharacteristic
395C4⋊C8C22×D1111yescharacteristic
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#103—221no—
405#102—221no—
406#102—221no—
407#102—221no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—221no—
412#97—21no—
413#97C22⋊D1111yescharacteristic
414#97C22⋊D1111yescharacteristic
415C4×C8—21no—
416C4×C8—21no—
417C4×C8—221no—
418C4×C8C22×D1111yescharacteristic
419C4×C8C22×D1111yescharacteristic
420C2×C11—41no—
421C2×C11—81no—
422C2×C11#303511yescharacteristic
423C2×C11#305611yescharacteristic
424C2×C11#306911yescharacteristic
425#41—22no—
426#41—41no—
427C2×Q8—221no—
428C2×Q8—221no—
429C2×Q8—221no—
430C2×Q8—221no—
431C2×Q8C2×D4411yescharacteristic
432C2×D4—21no—
433C2×D4C2×D4411yescharacteristic
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4C2×D4411yescharacteristic
438C22×C4#433911yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440Q16—442no—
441Q16—442no—
442Q16—442no—
443SD16—442no—
444M16—22no—
445M16—41no—
446M16—42no—
447M16—42no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—442no—
455C2×C8C2×C22⋊D1111yescharacteristic
456C2×C8C2×C22⋊D1111yescharacteristic
457C2×C8C2×C22⋊D1111yescharacteristic
458C2×C8C2×C22⋊D1111yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—441no—
470C4⋊C4—441no—
471C4⋊C4—441no—
472C4⋊C4—441no—
473C4⋊C4C2×D4411yescharacteristic
474C4⋊C4C2×D4411yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—441no—
479C22⋊C4—441no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—441no—
484C42—441no—
485C42C2×D4411yescharacteristic
486C42#433911yescharacteristic
487C42C2×C22⋊D1111yescharacteristic
488C42C23×D1111yescharacteristic
489C11#1918511yescharacteristic, complemented, Sylow
490C23—21no—
491C23#6698311yescharacteristic
492Q8—21no—
493Q8—441no—
494Q8—441no—
495Q8—441no—
496Q8—441no—
497Q8—441no—
498Q8—441no—
499Q8—881no—
500Q8#6696212yes—
501D4—21no—
502D4—21no—
503D4—42no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—81no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—441no—
520C2×C4#6698311yescharacteristic
521C2×C4#6698311yescharacteristic
522C2×C4#6698311yescharacteristic
523C2×C4C22×D4411yescharacteristic
524C2×C4C2×#433911yescharacteristic
525C2×C4C22×C22⋊D1111yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—441no—
532C8—441no—
533C8—441no—
534C8—441no—
535C8#6700312yes—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22C2×#6698311yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—22no—
548C4—41no—
549C4—41no—
550C4—881no—
551C4—881no—
552C4—881no—
553C4—881no—
554C4C2×#6696211yescharacteristic
555C4#1062327911yescharacteristic
556C4C2×#6700311yescharacteristic
557C4#1062335311yescharacteristic
558C2—41no—
559C2—81no—
560C2#1307807111yescharacteristic
561C2#1307824611yescharacteristic
562C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2971C2
socleC22×C11C2×#121
prime radicalC2×C11×#41D4
hypercenter#2971D11
hypocenterC11#19185
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2971

Complements

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

NH ≅ G/Ntype
1. #13079361C2semidirect
4. #13068191C2semidirect
5. #13068163C2semidirect
6. #13068115C2semidirect
7. #13068105C2semidirect
8. #13068074C2semidirect
9. #13068046C2semidirect
10. #13067998C2semidirect
11. #13067986C2semidirect
12. #13067368C2semidirect
13. #13067327C2semidirect
14. #13067317C2semidirect
489. C11#19185semidirect

Maximal subgroups

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

subgroupindex
#130793612
#130786872
#130784042
#130681912
#130681632
#130681152
#130681052
#130680742
#130680462
#130679982
#130679862
#130673682
#130673272
#130673172
C11×#29712
#1918511