Finite Group Databasebeta

← #14745619

Subgroups — #14745619

Order 2816.

626 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081513C211yesmaximal, characteristic
2#13081004C211yesmaximal, characteristic, complemented
3D4×#4326C211yesmaximal, characteristic, complemented
4#13068211C211yesmaximal, characteristic, complemented
5#13068122C211yesmaximal, characteristic, complemented
6#13068119C211yesmaximal, characteristic, complemented
7#13068013C211yesmaximal, characteristic, complemented
8#13067979C211yesmaximal, characteristic, complemented
9#13067830C211yesmaximal, characteristic, complemented
10#13067829C211yesmaximal, characteristic, complemented
11#13067781C211yesmaximal, characteristic, complemented
12#13067780C211yesmaximal, characteristic, complemented
13#13067511C211yesmaximal, characteristic, complemented
14D8×C11⋊C8C211yesmaximal, characteristic
15C11×#3384C211yesmaximal, characteristic
16C11×#554C2211yescharacteristic
17D4×Q8×C11C2211yescharacteristic
18C22×#4326—21no—
19#10623074C2211yescharacteristic
20D4×Dic22C2211yescharacteristic
21C11×#501—21no—
22C11×#498C2211yescharacteristic
23C11×#478—21no—
24C11×#476—21no—
25C11×#476C2211yescharacteristic
26C11×#474C2211yescharacteristic
27C11×#446C2211yescharacteristic
28C11×#442—21no—
29C4×C11×D8C2211yescharacteristic
30#10622841—21no—
31#10622765—21no—
32#10622706C2211yescharacteristic
33#10622705C2211yescharacteristic
34#10622704C2211yescharacteristic
35#10622703C2211yescharacteristic
36#10622694C2211yescharacteristic
37#10622691C2211yescharacteristic
38#10622664—21no—
39#10622664—21no—
40#10622663—21no—
41#10622657—21no—
42#10622644C2211yescharacteristic
43C4×#4326C2211yescharacteristic
44#10622634C2211yescharacteristic
45D4×C11⋊C8C2211yescharacteristic
46D4×C11⋊C8C2211yescharacteristic
47#10622621C2211yescharacteristic
48#10622620C2211yescharacteristic
49#10622583—21no—
50C2×#66871—21no—
51#10622489—21no—
52#10622376—21no—
53#10622374—21no—
54#10622293C2211yescharacteristic
55#10622292C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58Q8⋊(C11⋊C8)C2211yescharacteristic
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622124C2211yescharacteristic
62#10622122C2211yescharacteristic
63#10622119C2211yescharacteristic
64#10622117C2211yescharacteristic
65#10622096C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C22×Q8×C11—21no—
68C22×Dic22—21no—
69C2×C11×D8D411yescharacteristic
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×#125—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—41no—
77C11×C22⋊Q8—41no—
78C4×Q8×C11C2311yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11C2311yescharacteristic
82C4×D4×C11C2311yescharacteristic
83C2×C11×C4⋊C4—21no—
84C2×#4326—21no—
85C2×#4326—21no—
86C2×#4326—21no—
87C2×#4326—21no—
88C2×#4326—44no—
89C2×#4326D411yescharacteristic
90D4×Dic11—21no—
91D4×Dic11—21no—
92C2×C4⋊Dic11—21no—
93#66977—21no—
94#66977—21no—
95C22×C11⋊C8—21no—
96C22×C11⋊C8—21no—
97#66943—21no—
98#66941—21no—
99#66931—41no—
100#66931—41no—
101#66922C2311yescharacteristic
102#66922C2311yescharacteristic
103C4×Dic22C2311yescharacteristic
104C11×#107—21no—
105C11×#107D411yescharacteristic
106C11×#106—21no—
107C11×#106—21no—
108C11×#106—21no—
109C11×C4⋊C8—21no—
110C11×C4⋊C8C2311yescharacteristic
111C11×#102—21no—
112C11×#102—21no—
113C11×#102D411yescharacteristic
114C11×#102D411yescharacteristic
115C11×#97—21no—
116C4×C8×C11C2311yescharacteristic
117#66899—21no—
118#66899—21no—
119#66899—41no—
120#66899D411yescharacteristic
121#66896—21no—
122#66896—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125#66881—21no—
126#66881—21no—
127#66879—21no—
128Dic11⋊C8—21no—
129#66874—21no—
130#66874—21no—
131#66874—41no—
132#66874D411yescharacteristic
133#66872—21no—
134#66871—21no—
135#66871—21no—
136#66871—21no—
137#66871—21no—
138#66871—21no—
139#66871D411yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19926—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×D4×C11C2×D411yescharacteristic
153C2×D4×C11C2×D411yescharacteristic
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—41no—
157C22×C4×C11—41no—
158C22×Dic11—41no—
159C22×Dic11—41no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—41no—
163C2×Dic22—42no—
164C2×Dic22—81no—
165C2×Dic22C2×D411yescharacteristic
166C11×D8Q1614yescomplemented
167C2×C8×C11—21no—
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C4⋊C4C2×D411yescharacteristic
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—41no—
184C11×C22⋊C4—41no—
185C42×C11—21no—
186C42×C11C2411yescharacteristic
187C22⋊Dic11—41no—
188C22⋊Dic11—41no—
189#4326—22no—
190#4326—42no—
191#4326—42no—
192#4326—42no—
193#4326—81no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—41no—
199C4⋊Dic11C2×D411yescharacteristic
200Dic11⋊C4—21no—
201Dic11⋊C4—41no—
202Dic11⋊C4—41no—
203C4×Dic11—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—42no—
209C2×C11⋊C8—42no—
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212#3384—111no—
213#3384D1111yescharacteristic
214#3338—111no—
215D4×Q16—111no—
216#1707—111no—
217#1692—111no—
218#1692—111no—
219#1675—111no—
220#1669—111no—
221#1644—111no—
222#1644—111no—
223#1637—111no—
224#1637—111no—
225#1591—111no—
226C8×D8—111no—
227C23×C11—21no—
228C23×C11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—81no—
234Q8×C11—82no—
235D4×C11—21no—
236D4×C11—21no—
237D4×C11C2×Q1612yes—
238D4×C11C2×Q1612yescomplemented
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—82no—
250C2×C4×C11—161no—
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—82no—
259C2×Dic11—161no—
260Dic22—21no—
261Dic22—21no—
262Dic22—41no—
263Dic22—41no—
264Dic22—82no—
265Dic22—81no—
266C8×C11—21no—
267C8×C11—41no—
268C8×C11C2×Q1612yescomplemented
269C11⋊C8—21no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8AGL(1,ℤ/8)12yes—
275C22×Q16—221no—
276#554—111no—
277#554C2×D1111yescharacteristic
278D4×Q8—111no—
279D4×Q8C2×D1111yescharacteristic
280#501—21no—
281#501—221no—
282#500—111no—
283#498—111no—
284#498C2×D1111yescharacteristic
285#494—111no—
286#487—111no—
287#487—111no—
288#484—221no—
289#484—221no—
290#478—21no—
291#478—221no—
292#477—111no—
293#477—111no—
294#476—21no—
295#476—111no—
296#476—221no—
297#476C2×D1111yescharacteristic
298#474—111no—
299#474C2×D1111yescharacteristic
300#467—221no—
301#467—221no—
302#462—111no—
303#462—111no—
304#451—221no—
305#451—221no—
306#446—111no—
307#446C2×D1111yescharacteristic
308#442—21no—
309#442—221no—
310C4×Q16—111no—
311C4×D8C2×D1111yescharacteristic
312C8×D4—111no—
313C8×D4—111no—
314C2×#107—221no—
315#335—111no—
316#335—111no—
317#333—111no—
318#333—111no—
319#332—111no—
320#332—111no—
321Q8⋊C8—111no—
322Q8⋊C8—111no—
323D4⋊C8—111no—
324D4⋊C8—111no—
325C82—111no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11D4211yescharacteristic
333C4×C11—21no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11C22×Q1611yescharacteristic
341C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
342C4×C11#57711yescharacteristic
343C4×C11#57811yescharacteristic
344Dic11—41no—
345Dic11—41no—
346Dic11—81no—
347Dic11—81no—
348C22×Q8—21no—
349C22×Q8—221no—
350C2×Q16—111no—
351C2×Q16—221no—
352C2×Q16—221no—
353C2×Q16—221no—
354C2×Q16—221no—
355C2×Q16—444no—
356C2×D8C22⋊D1111yescharacteristic
357C22×C8—221no—
358C22×C8—221no—
359C4⋊Q8—21no—
360C4⋊Q8—111no—
361C4⋊Q8—111no—
362C4⋊Q8—221no—
363C4⋊Q8C22×D1111yescharacteristic
364C4⋊Q8C22×D1111yescharacteristic
365#125—21no—
366#125—221no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—41no—
370C22⋊Q8—41no—
371C22⋊Q8—221no—
372C22⋊Q8—221no—
373C22⋊Q8—441no—
374C22⋊Q8—441no—
375C4×Q8—111no—
376C4×Q8C22×D1111yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—221no—
380C4×D4—221no—
381C4×D4C22×D1111yescharacteristic
382C4×D4C22×D1111yescharacteristic
383C2×C4⋊C4—21no—
384C2×C4⋊C4—221no—
385#107—21no—
386#107—111no—
387#107—221no—
388#107—221no—
389#107—221no—
390#107—221no—
391#107—221no—
392#107C22⋊D1111yescharacteristic
393#106—21no—
394#106—21no—
395#106—21no—
396#106—221no—
397#106—221no—
398#106—221no—
399C4⋊C8—21no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—221no—
404C4⋊C8C22×D1111yescharacteristic
405#103—111no—
406#103—111no—
407#103—221no—
408#103—221no—
409#103—221no—
410#103—221no—
411#103—441no—
412#103—441no—
413#102—21no—
414#102—21no—
415#102—221no—
416#102—221no—
417#102C22⋊D1111yescharacteristic
418#102C22⋊D1111yescharacteristic
419C22⋊C8—221no—
420C22⋊C8—221no—
421#97—21no—
422#97—221no—
423C4×C8—111no—
424C4×C8—111no—
425C4×C8C22×D1111yescharacteristic
426C2×C11—42no—
427C2×C11—42no—
428C2×C11#327211yescharacteristic
429C2×C11D4×Q1611yescharacteristic
430C2×C11#329011yescharacteristic
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—41no—
434C2×Q8—42no—
435C2×Q8—81no—
436C2×Q8—111no—
437C2×Q8—221no—
438C2×Q8—221no—
439C2×Q8—441no—
440C2×Q8—442no—
441C2×Q8—881no—
442C2×Q8D4×D1111yescharacteristic
443C2×D4C2×C22⋊D1111yescharacteristic
444C2×D4C2×C22⋊D1111yescharacteristic
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—441no—
450C22×C4—441no—
451Q16—222no—
452Q16—442no—
453Q16—442no—
454Q16—442no—
455Q16—881no—
456D8#432614yescomplemented
457C2×C8—21no—
458C2×C8—111no—
459C2×C8—111no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—442no—
465C2×C8—442no—
466C2×C8C2×C22⋊D1111yescharacteristic
467C2×C8C2×C22⋊D1111yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
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⋊C4D4×D1111yescharacteristic
486C4⋊C4C2×C22⋊D1111yescharacteristic
487C4⋊C4C2×C22⋊D1111yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—441no—
493C22⋊C4—441no—
494C42—21no—
495C42—221no—
496C42C23×D1111yescharacteristic
497C11#1992611yescharacteristic, complemented, Sylow
498C23—21no—
499C23—21no—
500Q8—21no—
501Q8—21no—
502Q8—41no—
503Q8—41no—
504Q8—81no—
505Q8—82no—
506Q8—221no—
507Q8—221no—
508Q8—441no—
509Q8—441no—
510Q8—881no—
511Q8—882no—
512D4—21no—
513D4—21no—
514D4C2×#432612yes—
515D4C2×#432612yescomplemented
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—82no—
527C2×C4—161no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—882no—
533C2×C4—1761no—
534C2×C4C2×D4×D1111yescharacteristic
535C2×C4#6703711yescharacteristic
536C2×C4C22×C22⋊D1111yescharacteristic
537C8—21no—
538C8—41no—
539C8—112no—
540C8—221no—
541C8—441no—
542C8—441no—
543C8—441no—
544C8—441no—
545C8C2×#432612yescomplemented
546C22—22no—
547C22—22no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22D4×C22⋊D1111yescharacteristic
553C4—21no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—81no—
559C4—81no—
560C4—441no—
561C4—441no—
562C4—881no—
563C4—881no—
564C4D11×AGL(1,ℤ/8)11yescharacteristic
565C4#1062330611yescharacteristic
566C4C22×#432611yescharacteristic
567C4#1062336911yescharacteristic
568C2—42no—
569C2—42no—
570C2#1308021011yescharacteristic
571C2D4×#432611yescharacteristic
572C2#1308039611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3384C2
socleC22×C11D42
prime radicalC2×C11×D8D4
hypercenter#3384D11
hypocenterC11#19926
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3384

Complements

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

NH ≅ G/Ntype
2. #13081004C2semidirect
3. D4×#4326C2semidirect
4. #13068211C2semidirect
5. #13068122C2semidirect
6. #13068119C2semidirect
7. #13068013C2semidirect
8. #13067979C2semidirect
9. #13067830C2semidirect
10. #13067829C2semidirect
11. #13067781C2semidirect
12. #13067780C2semidirect
13. #13067511C2semidirect
166. C11×D8Q16semidirect
238. D4×C11C2×Q16semidirect
268. C8×C11C2×Q16semidirect
456. D8#4326semidirect
497. C11#19926semidirect
515. D4C2×#4326semidirect
545. C8C2×#4326semidirect

Maximal subgroups

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

subgroupindex
#130815132
#130810042
D4×#43262
#130682112
#130681222
#130681192
#130680132
#130679792
#130678302
#130678292
#130677812
#130677802
#130675112
D8×C11⋊C82
C11×#33842
#1992611