Finite Group Databasebeta

← #14738845

Subgroups — #14738845

Order 2816.

584 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079989C211yesmaximal, characteristic
2#13079640C211yesmaximal, characteristic
3#13079162C211yesmaximal, characteristic, complemented
4#13068134C211yesmaximal, characteristic, complemented
5#13068129C211yesmaximal, characteristic, complemented
6#13068122C211yesmaximal, characteristic, complemented
7#13068115C211yesmaximal, characteristic, complemented
8#13068010C211yesmaximal, characteristic, complemented
9#13068005C211yesmaximal, characteristic, complemented
10#13067998C211yesmaximal, characteristic, complemented
11#13067991C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067324C211yesmaximal, characteristic, complemented
14#13067287C211yesmaximal, characteristic, complemented
15C11×#2969C211yesmaximal, characteristic
16C11×#529C2211yescharacteristic
17#10623001C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C11×#446C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C11×#436—21no—
22C11×#436C2211yescharacteristic
23C11×#435—21no—
24C8×D4×C11C2211yescharacteristic
25C11×#433—21no—
26C11×#431C2211yescharacteristic
27C11×#405—21no—
28C4×C11×M16C2211yescharacteristic
29#10622734—21no—
30#10622734—21no—
31#10622682—21no—
32#10622676—21no—
33#10622673—21no—
34#10622667—21no—
35#10622665—21no—
36#10622663—21no—
37#10622655—21no—
38#10622653—21no—
39#10622644C2211yescharacteristic
40#10622644C2211yescharacteristic
41#10622644C2211yescharacteristic
42#10622634C2211yescharacteristic
43#10622632C2211yescharacteristic
44#10622632C2211yescharacteristic
45#10622632C2211yescharacteristic
46#10622621C2211yescharacteristic
47#10622539C2211yescharacteristic
48#10622537C2211yescharacteristic
49#10622315—21no—
50#10622315—21no—
51#10622295C2211yescharacteristic
52#10622295C2211yescharacteristic
53#10622293C2211yescharacteristic
54#10622293C2211yescharacteristic
55#10622124C2211yescharacteristic
56#10622124C2211yescharacteristic
57#10622124C2211yescharacteristic
58#10622124C2211yescharacteristic
59#10622124C2211yescharacteristic
60#10622124C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C22×Dic22—21no—
68C2×C11×M16—21no—
69C2×C11×M16D411yescharacteristic
70C2×C11×M16D411yescharacteristic
71C22×C8×C11—21no—
72C11×#126—21no—
73C11×#125D411yescharacteristic
74C11×#124D411yescharacteristic
75C11×#123—21no—
76C11×C22⋊Q8D411yescharacteristic
77C11×#121D411yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11C2311yescharacteristic
81C11×#117—21no—
82C2×C42×C11C2311yescharacteristic
83C2×#4326—21no—
84C2×#4326—21no—
85C2×#4326—21no—
86C2×#4324—21no—
87C2×#4324—21no—
88C2×#4324—21no—
89#66979—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92#66977—21no—
93#66977—21no—
94C2×#4318—21no—
95#66923—21no—
96#66922—21no—
97#66922—21no—
98#66922—21no—
99#66922C2311yescharacteristic
100#66922C2311yescharacteristic
101#66922C2311yescharacteristic
102#66922C2311yescharacteristic
103C4×Dic22—21no—
104C4×Dic22—21no—
105C11×C4⋊C8—21no—
106C11×C4⋊C8—21no—
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×C22⋊C8—21no—
110C11×C22⋊C8—21no—
111C11×C22⋊C8—21no—
112C11×#97—21no—
113C11×#97D411yescharacteristic
114C11×#97D411yescharacteristic
115C4×C8×C11—21no—
116C4×C8×C11—21no—
117C4×C8×C11C2311yescharacteristic
118C4×C8×C11C2311yescharacteristic
119#66899—21no—
120#66896—21no—
121C22⋊(C11⋊C8)—21no—
122#66882—21no—
123#66882—21no—
124#66882—21no—
125#66882—21no—
126#66881—21no—
127#66881—21no—
128#66881—21no—
129#66881—21no—
130#66874—21no—
131#66874—21no—
132#66874—21no—
133#66874—21no—
134#66874—21no—
135#66874—21no—
136#66872—21no—
137#66871—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143#66867—21no—
144#19378—111nomaximal, Sylow
145C2×Q8×C11C2×D411yescharacteristic
146C2×D4×C11—21no—
147C2×D4×C11C2×D411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C22×Dic11—41no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—41no—
158C2×Dic22—81no—
159C2×Dic22—81no—
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—42no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—42no—
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⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4C2×D411yescharacteristic
175C11×C4⋊C4C2×D411yescharacteristic
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C42×C11—21no—
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11#4111yescharacteristic
185C42×C11C2411yescharacteristic
186C22⋊Dic11—41no—
187#4326—81no—
188#4326—81no—
189#4326—81no—
190#4324—81no—
191#4324—81no—
192#4324—81no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—41no—
202C4⋊Dic11—41no—
203Dic11⋊C4—41no—
204Dic11⋊C4—41no—
205C4×Dic11—41no—
206#4318—81no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211#3252—111no—
212#3218—111no—
213#3165—111no—
214#2969D1111yescharacteristic
215#1694—111no—
216#1693—111no—
217#1692—111no—
218#1691—111no—
219#1674—111no—
220#1673—111no—
221#1672—111no—
222#1671—111no—
223#1569—111no—
224#1554—111no—
225#1546—111no—
226C23×C11—21no—
227C23×C11#12111yescharacteristic
228Q8×C11—21no—
229Q8×C11—21no—
230D4×C11—21no—
231D4×C11—21no—
232D4×C11—81no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
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—
253C2×Dic11—82no—
254Dic22—41no—
255Dic22—41no—
256Dic22—41no—
257Dic22—41no—
258Dic22—41no—
259Dic22—41no—
260Dic22—82no—
261Dic22—81no—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—41no—
265C8×C11—41no—
266C8×C11#13712yes—
267C8×C11#13712yes—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272#533—111no—
273C2×C4⋊Q8—111no—
274#529C2×D1111yescharacteristic
275#501—221no—
276#501—221no—
277#500—111no—
278#500—111no—
279#498—111no—
280#498—111no—
281#497—221no—
282#491—221no—
283#479—221no—
284#477—111no—
285#476—111no—
286#470—221no—
287#468—221no—
288#464—221no—
289#462—111no—
290#462—111no—
291#462—111no—
292#461—111no—
293#461—111no—
294#461—111no—
295#451—221no—
296#448—221no—
297#446C2×D1111yescharacteristic
298C8×Q8C2×D1111yescharacteristic
299#436—21no—
300#436C2×D1111yescharacteristic
301#435—21no—
302C8×D4C2×D1111yescharacteristic
303#433—21no—
304#432—111no—
305#431C2×D1111yescharacteristic
306#428—221no—
307#428—221no—
308#423—111no—
309#405—21no—
310C4×M16C2×D1111yescharacteristic
311#335—111no—
312#335—111no—
313#334—111no—
314#334—111no—
315#333—111no—
316#333—111no—
317#332—111no—
318#332—111no—
319#332—111no—
320#332—111no—
321#332—111no—
322#332—111no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11C2×#12111yescharacteristic
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11C2×#13711yescharacteristic
338C4×C11C2×#13711yescharacteristic
339C4×C11#57611yescharacteristic
340C4×C11#57711yescharacteristic
341Dic11—81no—
342Dic11—81no—
343Dic11—81no—
344Dic11—81no—
345C22×Q8—221no—
346C2×Q16—221no—
347C2×Q16—221no—
348C2×Q16—221no—
349C2×SD16—221no—
350C2×SD16—221no—
351C2×SD16—221no—
352C2×M16—21no—
353C2×M16—221no—
354C2×M16C22⋊D1111yescharacteristic
355C2×M16C22⋊D1111yescharacteristic
356C22×C8—21no—
357C4⋊Q8—111no—
358C4⋊Q8—111no—
359C4⋊Q8—111no—
360C4⋊Q8—111no—
361C4⋊Q8—221no—
362C4⋊Q8—221no—
363C4⋊Q8—221no—
364#126—21no—
365#125—221no—
366#125D4411yescharacteristic
367#124D4411yescharacteristic
368#123—21no—
369C22⋊Q8—221no—
370C22⋊Q8—221no—
371C22⋊Q8D4411yescharacteristic
372#121D4411yescharacteristic
373C4×Q8—221no—
374C4×Q8—221no—
375C4×Q8C22×D1111yescharacteristic
376C4×D4—21no—
377C4×D4C22×D1111yescharacteristic
378#117—21no—
379#117—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C42C22×D1111yescharacteristic
383#107—221no—
384#107—221no—
385#107—221no—
386#107—221no—
387#107—221no—
388#106—221no—
389#106—221no—
390#106—221no—
391#106—221no—
392#106—221no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8—111no—
396C4⋊C8—111no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—221no—
400C4⋊C8C22×D1111yescharacteristic
401C4⋊C8C22×D1111yescharacteristic
402#103—221no—
403#103—221no—
404#103—221no—
405#103—221no—
406#103—221no—
407#103—221no—
408#103—221no—
409#102—221no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—221no—
414#97—21no—
415#97—221no—
416#97C22⋊D1111yescharacteristic
417#97C22⋊D1111yescharacteristic
418C4×C8—21no—
419C4×C8—21no—
420C4×C8C22×D1111yescharacteristic
421C4×C8C22×D1111yescharacteristic
422C2×C11—41no—
423C2×C11—81no—
424C2×C11#303911yescharacteristic
425C2×C11#306211yescharacteristic
426C2×C11#306911yescharacteristic
427C2×Q8—221no—
428C2×Q8—221no—
429C2×Q8—221no—
430C2×Q8—221no—
431C2×Q8—441no—
432C2×Q8—881no—
433C2×Q8—881no—
434C2×Q8C2×D4411yescharacteristic
435C2×D4—21no—
436C2×D4C2×D4411yescharacteristic
437C22×C4—21no—
438C22×C4—441no—
439C22×C4C2×D4411yescharacteristic
440C22×C4#433911yescharacteristic
441C22×C4C2×C22⋊D1111yescharacteristic
442Q16—881no—
443Q16—881no—
444Q16—881no—
445SD16—881no—
446SD16—881no—
447SD16—881no—
448M16—22no—
449M16—22no—
450M16—42no—
451M16—881no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—42no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8C2×C22⋊D1111yescharacteristic
460C2×C8C2×C22⋊D1111yescharacteristic
461C2×C8C2×C22⋊D1111yescharacteristic
462C2×C8C2×C22⋊D1111yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—441no—
476C4⋊C4—441no—
477C4⋊C4—441no—
478C4⋊C4—441no—
479C4⋊C4C2×D4411yescharacteristic
480C4⋊C4C2×D4411yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—441no—
487C42—21no—
488C42—441no—
489C42C2×D4411yescharacteristic
490C42#433911yescharacteristic
491C42C2×C22⋊D1111yescharacteristic
492C42C23×D1111yescharacteristic
493C11#1937811yescharacteristic, complemented, Sylow
494C23—21no—
495C23#6698311yescharacteristic
496Q8—21no—
497Q8—21no—
498Q8—441no—
499Q8—441no—
500Q8—441no—
501Q8—441no—
502Q8—441no—
503Q8—441no—
504Q8—881no—
505Q8—882no—
506D4—21no—
507D4—21no—
508D4—81no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—882no—
524C2×C4#6698311yescharacteristic
525C2×C4#6698311yescharacteristic
526C2×C4#6698311yescharacteristic
527C2×C4C22×D4411yescharacteristic
528C2×C4C2×#433911yescharacteristic
529C2×C4C22×C22⋊D1111yescharacteristic
530C8—21no—
531C8—21no—
532C8—41no—
533C8—41no—
534C8—441no—
535C8—441no—
536C8—441no—
537C8—441no—
538C8#6700412yes—
539C8#6700412yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22C2×#6698311yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—881no—
555C4—881no—
556C4—881no—
557C4—881no—
558C4#1062328211yescharacteristic
559C4#1062328311yescharacteristic
560C4C2×#6700411yescharacteristic
561C4C2×#6700411yescharacteristic
562C2—41no—
563C2—81no—
564C2#1307810311yescharacteristic
565C2#1307829611yescharacteristic
566C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2969C2
socleC22×C11C2×#121
prime radicalC11×#121D4
hypercenter#2969D11
hypocenterC11#19378
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2969

Complements

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

NH ≅ G/Ntype
3. #13079162C2semidirect
4. #13068134C2semidirect
5. #13068129C2semidirect
6. #13068122C2semidirect
7. #13068115C2semidirect
8. #13068010C2semidirect
9. #13068005C2semidirect
10. #13067998C2semidirect
11. #13067991C2semidirect
12. #13067383C2semidirect
13. #13067324C2semidirect
14. #13067287C2semidirect
493. C11#19378semidirect

Maximal subgroups

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

subgroupindex
#130799892
#130796402
#130791622
#130681342
#130681292
#130681222
#130681152
#130680102
#130680052
#130679982
#130679912
#130673832
#130673242
#130672872
C11×#29692
#1937811