Finite Group Databasebeta

← #14745630

Subgroups — #14745630

Order 2816.

606 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#13081513C211yesmaximal, characteristic
2#13080492C211yesmaximal, characteristic, complemented
3#13080486C211yesmaximal, characteristic, complemented
4#13068211C211yesmaximal, characteristic, complemented
5#13068122C211yesmaximal, characteristic, complemented
6#13068119C211yesmaximal, characteristic, complemented
7#13068069C211yesmaximal, characteristic, complemented
8#13068065C211yesmaximal, characteristic, complemented
9#13067865C211yesmaximal, characteristic, complemented
10#13067864C211yesmaximal, characteristic, complemented
11#13067750C211yesmaximal, characteristic, complemented
12#13067748C211yesmaximal, characteristic, complemented
13#13067511C211yesmaximal, characteristic, complemented
14D8×C11⋊C8C211yesmaximal, characteristic
15C11×#3384C211yesmaximal, characteristic
16C11×#554C2211yescharacteristic
17D4×Q8×C11C2211yescharacteristic
18#10623074C2211yescharacteristic
19D4×Dic22C2211yescharacteristic
20C11×#501—21no—
21C11×#498C2211yescharacteristic
22C11×#478—21no—
23C11×#476—21no—
24C11×#476C2211yescharacteristic
25C11×#474C2211yescharacteristic
26C11×#446C2211yescharacteristic
27C11×#442—21no—
28C4×C11×D8C2211yescharacteristic
29#10622841—21no—
30C2×#66899—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×#66874—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—41no—
87C2×#4326D411yescharacteristic
88D4×Dic11—21no—
89D4×Dic11—21no—
90C2×C4⋊Dic11—21no—
91#66977—21no—
92#66977—21no—
93C22×C11⋊C8—21no—
94C22×C11⋊C8—21no—
95#66943—21no—
96#66941—21no—
97#66931—41no—
98#66931—41no—
99#66922C2311yescharacteristic
100#66922C2311yescharacteristic
101C4×Dic22C2311yescharacteristic
102C11×#107—21no—
103C11×#107D411yescharacteristic
104C11×#106—21no—
105C11×#106—21no—
106C11×#106—21no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8C2311yescharacteristic
109C11×#102—21no—
110C11×#102—21no—
111C11×#102D411yescharacteristic
112C11×#102D411yescharacteristic
113C11×#97—21no—
114C4×C8×C11C2311yescharacteristic
115#66899—21no—
116#66899—21no—
117#66899—21no—
118#66899—21no—
119#66899D411yescharacteristic
120#66896—21no—
121#66896—21no—
122C22⋊(C11⋊C8)—21no—
123C22⋊(C11⋊C8)—21no—
124#66881—21no—
125#66881—21no—
126#66879—21no—
127Dic11⋊C8—21no—
128#66874—21no—
129#66874—21no—
130#66874—21no—
131#66874—21no—
132#66874D411yescharacteristic
133#66872—21no—
134#66871—21no—
135#66871—21no—
136#66871—21no—
137#66871—41no—
138#66871D411yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19927—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—41no—
148C2×Q8×C11—42no—
149C2×Q8×C11—81no—
150C2×Q8×C11C2×D411yescharacteristic
151C2×D4×C11C2×D411yescharacteristic
152C2×D4×C11C2×D411yescharacteristic
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—41no—
156C22×C4×C11—41no—
157C22×Dic11—41no—
158C22×Dic11—41no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—41no—
162C2×Dic22—42no—
163C2×Dic22—81no—
164C2×Dic22C2×D411yescharacteristic
165C11×D8Q1614yescomplemented
166C2×C8×C11—21no—
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
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—21no—
182C11×C22⋊C4—41no—
183C11×C22⋊C4—41no—
184C42×C11—21no—
185C42×C11C2411yescharacteristic
186C22⋊Dic11—41no—
187C22⋊Dic11—41no—
188#4326—41no—
189#4326—81no—
190#4326—81no—
191#4326—82no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—41no—
197C4⋊Dic11C2×D411yescharacteristic
198Dic11⋊C4—21no—
199Dic11⋊C4—41no—
200Dic11⋊C4—41no—
201C4×Dic11—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—81no—
207C2×C11⋊C8—81no—
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210#3384—111no—
211#3384D1111yescharacteristic
212#3299—111no—
213#3299—111no—
214#1707—111no—
215#1692—111no—
216#1692—111no—
217#1683—111no—
218#1683—111no—
219#1649—111no—
220#1649—111no—
221#1632—111no—
222#1632—111no—
223#1591—111no—
224C8×D8—111no—
225C23×C11—21no—
226C23×C11—21no—
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—81no—
232Q8×C11—82no—
233D4×C11—21no—
234D4×C11—21no—
235D4×C11C2×Q1612yes—
236D4×C11C2×Q1612yes—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—82no—
248C2×C4×C11—161no—
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—82no—
257C2×Dic11—161no—
258Dic22—21no—
259Dic22—21no—
260Dic22—41no—
261Dic22—41no—
262Dic22—82no—
263Dic22—81no—
264C8×C11—21no—
265C8×C11—41no—
266C8×C11C2×Q1612yes—
267C11⋊C8—22no—
268C11⋊C8—21no—
269C11⋊C8—21no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273#554—111no—
274#554C2×D1111yescharacteristic
275D4×Q8—111no—
276D4×Q8C2×D1111yescharacteristic
277#501—21no—
278#501—221no—
279#500—111no—
280#498—111no—
281#498C2×D1111yescharacteristic
282#494—111no—
283#487—111no—
284#487—111no—
285#484—221no—
286#484—221no—
287#478—21no—
288#478—221no—
289#477—111no—
290#477—111no—
291#476—21no—
292#476—111no—
293#476—221no—
294#476C2×D1111yescharacteristic
295#474—111no—
296#474C2×D1111yescharacteristic
297#467—221no—
298#467—221no—
299#462—111no—
300#462—111no—
301#451—221no—
302#451—221no—
303#446—111no—
304#446C2×D1111yescharacteristic
305#442—21no—
306#442—221no—
307C4×Q16—111no—
308C4×D8C2×D1111yescharacteristic
309C8×D4—111no—
310C8×D4—111no—
311C2×#103—221no—
312C2×#103—221no—
313#335—111no—
314#335—111no—
315#333—111no—
316#333—111no—
317#332—111no—
318#332—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321D4⋊C8—111no—
322D4⋊C8—111no—
323C82—111no—
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11D4211yescharacteristic
331C4×C11—21no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11C22×Q1611yescharacteristic
339C4×C11#57511yescharacteristic
340C4×C11#57611yescharacteristic
341C4×C11#57811yescharacteristic
342Dic11—41no—
343Dic11—41no—
344Dic11—81no—
345Dic11—81no—
346C22×Q8—21no—
347C22×Q8—221no—
348C2×Q16—111no—
349C2×Q16—221no—
350C2×Q16—221no—
351C2×Q16—441no—
352C2×D8C22⋊D1111yescharacteristic
353C22×C8—221no—
354C22×C8—221no—
355C4⋊Q8—21no—
356C4⋊Q8—111no—
357C4⋊Q8—111no—
358C4⋊Q8—221no—
359C4⋊Q8C22×D1111yescharacteristic
360C4⋊Q8C22×D1111yescharacteristic
361#125—21no—
362#125—221no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—41no—
366C22⋊Q8—41no—
367C22⋊Q8—221no—
368C22⋊Q8—221no—
369C22⋊Q8—441no—
370C22⋊Q8—441no—
371C4×Q8—111no—
372C4×Q8C22×D1111yescharacteristic
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—221no—
376C4×D4—221no—
377C4×D4C22×D1111yescharacteristic
378C4×D4C22×D1111yescharacteristic
379C2×C4⋊C4—21no—
380C2×C4⋊C4—221no—
381#107—21no—
382#107—111no—
383#107—221no—
384#107—221no—
385#107—221no—
386#107—441no—
387#107C22⋊D1111yescharacteristic
388#106—21no—
389#106—21no—
390#106—21no—
391#106—221no—
392#106—221no—
393#106—221no—
394C4⋊C8—21no—
395C4⋊C8—111no—
396C4⋊C8—111no—
397C4⋊C8—111no—
398C4⋊C8—221no—
399C4⋊C8C22×D1111yescharacteristic
400#103—111no—
401#103—111no—
402#103—221no—
403#103—221no—
404#103—221no—
405#103—221no—
406#103—221no—
407#103—221no—
408#103—221no—
409#103—221no—
410#102—21no—
411#102—21no—
412#102—221no—
413#102—221no—
414#102C22⋊D1111yescharacteristic
415#102C22⋊D1111yescharacteristic
416C22⋊C8—221no—
417C22⋊C8—221no—
418#97—21no—
419#97—221no—
420C4×C8—111no—
421C4×C8—111no—
422C4×C8C22×D1111yescharacteristic
423C2×C11—42no—
424C2×C11—42no—
425C2×C11#327311yescharacteristic
426C2×C11D4×Q1611yescharacteristic
427C2×C11#329111yescharacteristic
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—41no—
431C2×Q8—42no—
432C2×Q8—81no—
433C2×Q8—111no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8—441no—
437C2×Q8—442no—
438C2×Q8—881no—
439C2×Q8D4×D1111yescharacteristic
440C2×D4C2×C22⋊D1111yescharacteristic
441C2×D4C2×C22⋊D1111yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—441no—
447C22×C4—441no—
448Q16—441no—
449Q16—882no—
450Q16—881no—
451Q16—881no—
452D8#432614yescomplemented
453C2×C8—21no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—881no—
461C2×C8—881no—
462C2×C8C2×C22⋊D1111yescharacteristic
463C2×C8C2×C22⋊D1111yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—111no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—441no—
479C4⋊C4—441no—
480C4⋊C4—441no—
481C4⋊C4D4×D1111yescharacteristic
482C4⋊C4C2×C22⋊D1111yescharacteristic
483C4⋊C4C2×C22⋊D1111yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—441no—
489C22⋊C4—441no—
490C42—21no—
491C42—221no—
492C42C23×D1111yescharacteristic
493C11#1992711yescharacteristic, complemented, Sylow
494C23—21no—
495C23—21no—
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—82no—
502Q8—221no—
503Q8—221no—
504Q8—441no—
505Q8—441no—
506Q8—881no—
507Q8—882no—
508D4—21no—
509D4—21no—
510D4C2×#432612yes—
511D4C2×#432612yes—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—82no—
523C2×C4—161no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—882no—
529C2×C4—1761no—
530C2×C4C2×D4×D1111yescharacteristic
531C2×C4#6703711yescharacteristic
532C2×C4C22×C22⋊D1111yescharacteristic
533C8—21no—
534C8—41no—
535C8—222no—
536C8—221no—
537C8—221no—
538C8—441no—
539C8—441no—
540C8—441no—
541C8C2×#432612yes—
542C22—22no—
543C22—22no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22D4×C22⋊D1111yescharacteristic
549C4—21no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—81no—
555C4—81no—
556C4—441no—
557C4—441no—
558C4—881no—
559C4—881no—
560C4#1062330411yescharacteristic
561C4#1062330511yescharacteristic
562C4C22×#432611yescharacteristic
563C4#1062336911yescharacteristic
564C2—42no—
565C2—42no—
566C2#1308022111yescharacteristic
567C2D4×#432611yescharacteristic
568C2#1308040711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3384C2
socleC22×C11D42
prime radicalC2×C11×D8D4
hypercenter#3384D11
hypocenterC11#19927
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. #13080492C2semidirect
3. #13080486C2semidirect
4. #13068211C2semidirect
5. #13068122C2semidirect
6. #13068119C2semidirect
7. #13068069C2semidirect
8. #13068065C2semidirect
9. #13067865C2semidirect
10. #13067864C2semidirect
11. #13067750C2semidirect
12. #13067748C2semidirect
13. #13067511C2semidirect
165. C11×D8Q16semidirect
452. D8#4326semidirect
493. C11#19927semidirect

Maximal subgroups

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

subgroupindex
#130815132
#130804922
#130804862
#130682112
#130681222
#130681192
#130680692
#130680652
#130678652
#130678642
#130677502
#130677482
#130675112
D8×C11⋊C82
C11×#33842
#1992711