Finite Group Databasebeta

← #14745639

Subgroups — #14745639

Order 2816.

622 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081619C211yesmaximal, characteristic, complemented
2#13081535C211yesmaximal, characteristic
3D4×#4326C211yesmaximal, characteristic
4#13068233C211yesmaximal, characteristic, complemented
5#13068134C211yesmaximal, characteristic, complemented
6#13068131C211yesmaximal, characteristic, complemented
7#13067984C211yesmaximal, characteristic, complemented
8#13067979C211yesmaximal, characteristic
9#13067865C211yesmaximal, characteristic
10#13067864C211yesmaximal, characteristic
11#13067858C211yesmaximal, characteristic, complemented
12#13067857C211yesmaximal, characteristic, complemented
13#13067511C211yesmaximal, characteristic, complemented
14SD16×C11⋊C8C211yesmaximal, characteristic
15C11×#3386C211yesmaximal, characteristic
16C11×#557C2211yescharacteristic
17D4×Q8×C11C2211yescharacteristic
18C22×#4326—21no—
19#10623101C2211yescharacteristic
20D4×Dic22C2211yescharacteristic
21C11×#501—21no—
22C11×#500C2211yescharacteristic
23C11×#478—21no—
24C11×#477—21no—
25C11×#475C2211yescharacteristic
26C11×#474C2211yescharacteristic
27C11×#446C2211yescharacteristic
28C11×#440—21no—
29C4×C11×SD16C2211yescharacteristic
30#10622841—21no—
31#10622777—21no—
32#10622705—21no—
33#10622705C2211yescharacteristic
34#10622705C2211yescharacteristic
35#10622703—21no—
36#10622703C2211yescharacteristic
37#10622703C2211yescharacteristic
38#10622691C2211yescharacteristic
39#10622691C2211yescharacteristic
40#10622664—21no—
41#10622663—21no—
42#10622644—21no—
43#10622644C2211yescharacteristic
44#10622644C2211yescharacteristic
45C4×#4326—21no—
46C4×#4326C2211yescharacteristic
47Q8×C11⋊C8C2211yescharacteristic
48#10622633C2211yescharacteristic
49D4×C11⋊C8C2211yescharacteristic
50#10622620C2211yescharacteristic
51#10622469—21no—
52#10622407—21no—
53#10622379—21no—
54#10622295C2211yescharacteristic
55#10622292C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58Q8⋊(C11⋊C8)C2211yescharacteristic
59Q8⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622124C2211yescharacteristic
62#10622124C2211yescharacteristic
63#10622122C2211yescharacteristic
64#10622117C2211yescharacteristic
65#10622095C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C22×Q8×C11—21no—
68C22×Dic22—21no—
69C2×C11×SD16D411yescharacteristic
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8C2311yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×#125—21no—
75C11×#125—41no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—41no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11C2311yescharacteristic
81C4×Q8×C11C2311yescharacteristic
82C4×D4×C11—21no—
83C4×D4×C11C2311yescharacteristic
84Q8×Dic11—21no—
85C2×#4326—21no—
86C2×#4326—21no—
87C2×#4326—21no—
88C2×#4326—21no—
89C2×#4326—21no—
90C2×#4326—21no—
91C2×#4326—21no—
92C2×#4326—21no—
93C2×#4326—44no—
94C2×#4326D411yescharacteristic
95D4×Dic11—21no—
96#66977—21no—
97C22×C11⋊C8—21no—
98#66943—21no—
99#66943—41no—
100#66941—21no—
101#66931—41no—
102#66922—21no—
103#66922C2311yescharacteristic
104#66922C2311yescharacteristic
105C4×Dic22—21no—
106C4×Dic22C2311yescharacteristic
107C11×#107—21no—
108C11×#107—21no—
109C11×#107—21no—
110C11×#106—21no—
111C11×#106D411yescharacteristic
112C11×C4⋊C8—21no—
113C11×C4⋊C8C2311yescharacteristic
114C11×#103—21no—
115C11×#103D411yescharacteristic
116C11×#102—21no—
117C11×#102D411yescharacteristic
118C11×#97—21no—
119C4×C8×C11C2311yescharacteristic
120#66899—21no—
121#66899—21no—
122#66899—21no—
123#66899D411yescharacteristic
124#66896—21no—
125C22⋊(C11⋊C8)—21no—
126#66882—21no—
127#66882—21no—
128#66879—21no—
129Dic11⋊C8—21no—
130#66874—21no—
131#66874—21no—
132#66874D411yescharacteristic
133#66872—21no—
134#66871—21no—
135#66871—41no—
136#66871—41no—
137#66871D411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8—21no—
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19928—111nomaximal, Sylow
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—41no—
149C2×Q8×C11—42no—
150C2×Q8×C11—81no—
151C2×Q8×C11C2×D411yescharacteristic
152C2×Q8×C11C2×D411yescharacteristic
153C2×D4×C11C2×D411yescharacteristic
154C22×C4×C11—21no—
155C22×C4×C11—41no—
156C22×Dic11—41no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—41no—
160C2×Dic22—42no—
161C2×Dic22—81no—
162C2×Dic22C2×D411yescharacteristic
163C11×SD16Q1614yescomplemented
164C2×C8×C11—21no—
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
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⋊C4—41no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C22⋊C4—21no—
181C11×C22⋊C4—41no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—41no—
185C42×C11C2411yescharacteristic
186C22⋊Dic11—41no—
187#4326—22no—
188#4326—42no—
189#4326—42no—
190#4326—42no—
191#4326—42no—
192#4326—81no—
193#4326—81no—
194#4326—81no—
195#4326—81no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—41no—
201C4⋊Dic11—41no—
202C4⋊Dic11C2×D411yescharacteristic
203Dic11⋊C4—21no—
204Dic11⋊C4—41no—
205Dic11⋊C4—41no—
206C4×Dic11—21no—
207C4×Dic11—41no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—42no—
213C2×C11⋊C8C2×D411yescharacteristic
214C2×C11⋊C8C2×D411yescharacteristic
215#3395—111no—
216#3386—111no—
217#3386D1111yescharacteristic
218D4×Q16—111no—
219#1713—111no—
220#1694—111no—
221#1694—111no—
222#1670—111no—
223#1669—111no—
224#1649—111no—
225#1649—111no—
226#1648—111no—
227#1648—111no—
228#1591—111no—
229C8×SD16—111no—
230C23×C11—21no—
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11—21no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—41no—
238Q8×C11—82no—
239Q8×C11C2×Q1612yescomplemented
240D4×C11—21no—
241D4×C11C2×Q1612yes—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—82no—
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—82no—
260Dic22—21no—
261Dic22—21no—
262Dic22—41no—
263Dic22—41no—
264Dic22—41no—
265Dic22—41no—
266Dic22—82no—
267C8×C11—21no—
268C8×C11—41no—
269C8×C11C2×Q1612yescomplemented
270C11⋊C8—22no—
271C11⋊C8—21no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8AGL(1,ℤ/8)12yes—
276C22×Q16—221no—
277#557—111no—
278#557C2×D1111yescharacteristic
279D4×Q8—111no—
280D4×Q8C2×D1111yescharacteristic
281#501—21no—
282#501—221no—
283#500—111no—
284#500—111no—
285#500—111no—
286#500C2×D1111yescharacteristic
287#494—111no—
288#494—111no—
289#494—221no—
290#478—21no—
291#478—221no—
292#477—21no—
293#477—221no—
294#475—111no—
295#475C2×D1111yescharacteristic
296#474—111no—
297#474C2×D1111yescharacteristic
298#467—221no—
299#462—111no—
300#462—111no—
301#462—111no—
302#462—111no—
303#462—221no—
304#462—221no—
305#451—221no—
306#451—221no—
307#446—111no—
308#446C2×D1111yescharacteristic
309C8×Q8—111no—
310#440—21no—
311#440—221no—
312C4×Q16—111no—
313C4×Q16—221no—
314C4×SD16C2×D1111yescharacteristic
315C8×D4—111no—
316#335—111no—
317#334—111no—
318#332—111no—
319#332—111no—
320#332—111no—
321#332—111no—
322Q8⋊C8—111no—
323Q8⋊C8—111no—
324Q8⋊C8—111no—
325D4⋊C8—111no—
326C82—111no—
327C22×C11—22no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11D4211yescharacteristic
331C4×C11—22no—
332C4×C11—21no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11C22×Q1611yescharacteristic
340C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
341C4×C11#57611yescharacteristic
342C4×C11#57811yescharacteristic
343Dic11—41no—
344Dic11—41no—
345Dic11—81no—
346Dic11—81no—
347C22×Q8—21no—
348C22×Q8—221no—
349C2×Q16—111no—
350C2×Q16—221no—
351C2×Q16—221no—
352C2×Q16—221no—
353C2×Q16—221no—
354C2×Q16—221no—
355C2×Q16—221no—
356C2×Q16—221no—
357C2×Q16—221no—
358C2×Q16—444no—
359C2×SD16C22⋊D1111yescharacteristic
360C22×C8—221no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—111no—
364C4⋊Q8—111no—
365C4⋊Q8—221no—
366C4⋊Q8—221no—
367C4⋊Q8C22×D1111yescharacteristic
368C4⋊Q8C22×D1111yescharacteristic
369#125—21no—
370#125—41no—
371#125—221no—
372#125—441no—
373C22⋊Q8—21no—
374C22⋊Q8—41no—
375C22⋊Q8—221no—
376C22⋊Q8—441no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—111no—
380C4×Q8—221no—
381C4×Q8—221no—
382C4×Q8C22×D1111yescharacteristic
383C4×Q8C22×D1111yescharacteristic
384C4×D4—21no—
385C4×D4—221no—
386C4×D4C22×D1111yescharacteristic
387#107—21no—
388#107—21no—
389#107—21no—
390#107—111no—
391#107—221no—
392#107—221no—
393#107—221no—
394#107—441no—
395#107—441no—
396#106—21no—
397#106—221no—
398#106C22⋊D1111yescharacteristic
399C4⋊C8—21no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—221no—
404C4⋊C8—221no—
405C4⋊C8C22×D1111yescharacteristic
406#103—21no—
407#103—111no—
408#103—111no—
409#103—221no—
410#103—221no—
411#103—221no—
412#103—221no—
413#103—221no—
414#103C22⋊D1111yescharacteristic
415#102—21no—
416#102—221no—
417#102C22⋊D1111yescharacteristic
418C22⋊C8—221no—
419#97—21no—
420#97—221no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—221no—
424C4×C8C22×D1111yescharacteristic
425C2×C11—42no—
426C2×C11#327411yescharacteristic
427C2×C11D4×Q1611yescharacteristic
428C2×C11#329311yescharacteristic
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—41no—
432C2×Q8—42no—
433C2×Q8—81no—
434C2×Q8—111no—
435C2×Q8—221no—
436C2×Q8—221no—
437C2×Q8—441no—
438C2×Q8—442no—
439C2×Q8—881no—
440C2×Q8D4×D1111yescharacteristic
441C2×Q8C2×C22⋊D1111yescharacteristic
442C2×D4C2×C22⋊D1111yescharacteristic
443C22×C4—21no—
444C22×C4—41no—
445C22×C4—441no—
446Q16—222no—
447Q16—442no—
448Q16—442no—
449Q16—442no—
450Q16—442no—
451Q16—881no—
452Q16—881no—
453Q16—881no—
454Q16—881no—
455SD16#432614yescomplemented
456C2×C8—21no—
457C2×C8—111no—
458C2×C8—111no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—442no—
464C2×C8C2×C22⋊D1111yescharacteristic
465C2×C8C2×C22⋊D1111yescharacteristic
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—111no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—441no—
483C4⋊C4—441no—
484C4⋊C4—441no—
485C4⋊C4—441no—
486C4⋊C4D4×D1111yescharacteristic
487C4⋊C4C2×C22⋊D1111yescharacteristic
488C4⋊C4C2×C22⋊D1111yescharacteristic
489C22⋊C4—21no—
490C22⋊C4—41no—
491C22⋊C4—441no—
492C42—21no—
493C42—21no—
494C42—41no—
495C42—221no—
496C42—441no—
497C42C23×D1111yescharacteristic
498C11#1992811yescharacteristic, complemented, Sylow
499C23—21no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—82no—
508Q8—221no—
509Q8—221no—
510Q8—441no—
511Q8—441no—
512Q8—441no—
513Q8—441no—
514Q8—882no—
515Q8C2×#432612yescomplemented
516D4—21no—
517D4C2×#432612yes—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—882no—
533C2×C4C2×D4×D1111yescharacteristic
534C2×C4#6703711yescharacteristic
535C2×C4C22×C22⋊D1111yescharacteristic
536C8—21no—
537C8—41no—
538C8—112no—
539C8—222no—
540C8—221no—
541C8—441no—
542C8—441no—
543C8—441no—
544C8C2×#432612yescomplemented
545C22—22no—
546C22—41no—
547C22—41no—
548C22D4×C22⋊D1111yescharacteristic
549C4—22no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—81no—
556C4—81no—
557C4—441no—
558C4—441no—
559C4—881no—
560C4—881no—
561C4D11×AGL(1,ℤ/8)11yescharacteristic
562C4#1062330511yescharacteristic
563C4C22×#432611yescharacteristic
564C4#1062336911yescharacteristic
565C2—42no—
566C2#1308023011yescharacteristic
567C2D4×#432611yescharacteristic
568C2#1308041811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3386C2
socleC22×C11D42
prime radicalC2×D4×C11C2×D4
hypercenter#3386D11
hypocenterC11#19928
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3386

Complements

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

NH ≅ G/Ntype
1. #13081619C2semidirect
4. #13068233C2semidirect
5. #13068134C2semidirect
6. #13068131C2semidirect
7. #13067984C2semidirect
11. #13067858C2semidirect
12. #13067857C2semidirect
13. #13067511C2semidirect
163. C11×SD16Q16semidirect
239. Q8×C11C2×Q16semidirect
269. C8×C11C2×Q16semidirect
455. SD16#4326semidirect
498. C11#19928semidirect
515. Q8C2×#4326semidirect
544. C8C2×#4326semidirect

Maximal subgroups

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

subgroupindex
#130816192
#130815352
D4×#43262
#130682332
#130681342
#130681312
#130679842
#130679792
#130678652
#130678642
#130678582
#130678572
#130675112
SD16×C11⋊C82
C11×#33862
#1992811