Finite Group Databasebeta

← #14808187

Subgroups — #14808187

Order 2816.

1096 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622678C211yesmaximal, characteristic, complemented
2C2×#10622683C211yesmaximal, characteristic, complemented
3#13074437C211yesmaximal, characteristic, complemented
4#13069802C212yesmaximal, complemented
5#13069795C212yesmaximal, complemented
6#13069582C211yesmaximal, characteristic, complemented
7#13069441C211yesmaximal, characteristic, complemented
8#13068877C212yesmaximal, complemented
9#13068863C212yesmaximal, complemented
10#13068382C211yesmaximal, characteristic, complemented
11C2×C11×#540C211yesmaximal, characteristic
12C11×#540—24no—
13C11×#540—24no—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#125C2211yescharacteristic
16C2×C11×#123—21no—
17C2×C11×#123—21no—
18C2×C11×#121—21no—
19C2×C11×#121—21no—
20C2×C11×#121C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C11×#117C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C2×#66896C2212yes—
27C2×#66896C2212yes—
28C2×#66896C2212yes—
29C2×#66896C2212yes—
30#10622825C2212yes—
31C2×C22⋊(C11⋊C8)C2212yes—
32#10622683—24no—
33#10622678—24no—
34#10622599—21no—
35#10622592—21no—
36C2×#66872C2212yes—
37C2×#66871C2212yes—
38#10622562—21no—
39#10622560—21no—
40#10622549C2211yescharacteristic
41#10622541C2212yes—
42C2×#66867C2211yescharacteristic
43C2×C4×C11⋊C8C2211yescharacteristic
44#10622167C2212yes—
45#10622167C2212yes—
46#10622162C2212yes—
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C22×D4×C11C2311yescharacteristic
52C22×D4×C11C2311yescharacteristic
53C23×C4×C11—21no—
54C23×C4×C11—21no—
55C23×C4×C11C2311yescharacteristic
56C22×Dic22—21no—
57C11×#127—22no—
58C11×#127D414yes—
59C11×#125—22no—
60C11×#125D414yes—
61C11×#123—28no—
62C11×#123—28no—
63C11×#121—28no—
64C11×#121—28no—
65C11×#121—22no—
66C11×#121—22no—
67C11×#121—22no—
68C11×#121—22no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C11×#117—22no—
74C11×#117—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4D411yescharacteristic
86C2×C11×C22⋊C4D411yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11—22no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2312yes—
92C2×C4⋊Dic11C2312yes—
93C2×Dic11⋊C4—22no—
94C22×C11⋊C8C2312yes—
95C22×C11⋊C8C2312yes—
96#66922—22no—
97#66922—22no—
98#66896—24no—
99#66896—24no—
100#66896—24no—
101#66896—24no—
102C11⋊#95—22no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—22no—
106C22⋊(C11⋊C8)—24no—
107#66872—24no—
108#66871—24no—
109#66867—22no—
110C4×C11⋊C8—22no—
111#25685—111nomaximal, Sylow
112C24×C11—21no—
113C24×C11—21no—
114C24×C11C2×D411yescharacteristic
115C2×D4×C11—24no—
116C2×D4×C11—24no—
117C2×D4×C11—24no—
118C2×D4×C11—24no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—82no—
126C2×D4×C11—82no—
127C2×D4×C11—82no—
128C2×D4×C11—82no—
129C2×D4×C11C2×D412yes—
130C2×D4×C11C2×D412yes—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—82no—
140C22×C4×C11—82no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—22no—
148C22×Dic11—22no—
149C2×Dic22—42no—
150C2×Dic22—82no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4C2×D412yes—
158C11×C4⋊C4C2×D412yes—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11C2×D412yes—
168C42×C11C2×D412yes—
169C22⋊Dic11—82no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11—42no—
175Dic11⋊C4—82no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8#4114yes—
182C2×#540D1111yescharacteristic
183C2×#501—111no—
184C2×#486—111no—
185#2628—111no—
186#2034—112no—
187#2033—112no—
188#1991—111no—
189#1961—111no—
190#1864—112no—
191#1862—112no—
192#1750—111no—
193C23×C11—21no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—21no—
197C23×C11—21no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11C22×D411yescharacteristic
209D4×C11—24no—
210D4×C11—24no—
211D4×C11—42no—
212D4×C11—42no—
213D4×C11—84no—
214D4×C11—84no—
215D4×C11—84no—
216D4×C11—84no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—84no—
233C2×C4×C11—84no—
234C2×C4×C11#12012yes—
235C2×C4×C11#12012yes—
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C2×#4112yes—
239C2×C4×C112−1+412yes—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246Dic22—84no—
247C11⋊C8—24no—
248C11⋊C8—42no—
249#540—24no—
250#540—24no—
251C2×C4⋊Q8—111no—
252C2×#127C2×D1111yescharacteristic
253C2×#125C2×D1111yescharacteristic
254C2×#123—21no—
255C2×#123—21no—
256C2×#121—21no—
257C2×#121—21no—
258C2×#121C2×D1111yescharacteristic
259C2×#121C2×D1111yescharacteristic
260C2×C4×D4C2×D1111yescharacteristic
261C2×C4×D4C2×D1111yescharacteristic
262C2×#117C2×D1111yescharacteristic
263#501—224no—
264#486—224no—
265C2×#107—112no—
266C2×#106—112no—
267C2×#102—112no—
268C2×#102—112no—
269C2×#102—112no—
270C2×#102—112no—
271C2×C22⋊C8—112no—
272C2×#97—111no—
273C2×C4×C8—111no—
274#400—221no—
275#399—221no—
276#395—221no—
277#393—221no—
278#389—112no—
279#382—111no—
280#380—112no—
281#340—112no—
282#340—112no—
283#336—112no—
284C22×C11—42no—
285C22×C11—41no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—41no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—41no—
294C22×C11—42no—
295C22×C11—82no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11C2×#12011yescharacteristic
300C22×C11#53211yescharacteristic
301C22×C11#53611yescharacteristic
302C22×C11#57612yes—
303C22×C11#57712yes—
304C4×C11—22no—
305C4×C11—22no—
306C4×C11—41no—
307C4×C11—41no—
308C4×C11—42no—
309C4×C11—41no—
310C4×C11—42no—
311C4×C11#54712yes—
312C4×C11#54812yes—
313Dic11—82no—
314Dic11—82no—
315C22×Q8—221no—
316C22×D4—21no—
317C22×D4—21no—
318C22×D4—21no—
319C22×D4—21no—
320C22×D4C22×D1111yescharacteristic
321C22×D4C22×D1111yescharacteristic
322C23×C4—21no—
323C23×C4—21no—
324C23×C4C22×D1111yescharacteristic
325C22×C8—112no—
326C22×C8—112no—
327C4⋊Q8—222no—
328C4⋊Q8—222no—
329#127—22no—
330#127C22⋊D1114yes—
331#125—22no—
332#125C22⋊D1114yes—
333#123—28no—
334#123—28no—
335#121—28no—
336#121—28no—
337#121—22no—
338#121—22no—
339#121—22no—
340#121—22no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—22no—
345#117—22no—
346#117—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—112no—
350C2×C4⋊C4—112no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4C22⋊D1111yescharacteristic
354C2×C4⋊C4C22⋊D1111yescharacteristic
355C2×C4⋊C4C22×D1111yescharacteristic
356C2×C4⋊C4C22×D1111yescharacteristic
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—222no—
362C2×C22⋊C4C22⋊D1111yescharacteristic
363C2×C22⋊C4C22⋊D1111yescharacteristic
364C2×C42C22×D1111yescharacteristic
365C2×C42C22×D1111yescharacteristic
366#107—224no—
367#106—224no—
368#102—224no—
369#102—224no—
370#102—224no—
371#102—224no—
372C22⋊C8—224no—
373#97—222no—
374C4×C8—222no—
375#95—222no—
376#95—221no—
377#95—221no—
378#95—222no—
379C2×C11—81no—
380C2×C11—82no—
381C2×C11—82no—
382C2×C11#243211yescharacteristic
383C2×C11#300811yescharacteristic
384C2×C11#300911yescharacteristic
385C2×C11#317912yes—
386C2×C11#324112yes—
387C24—21no—
388C24—21no—
389C24C2×C22⋊D1111yescharacteristic
390C2×Q8—442no—
391C2×Q8—882no—
392C2×D4—24no—
393C2×D4—24no—
394C2×D4—24no—
395C2×D4—24no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—82no—
403C2×D4—82no—
404C2×D4—82no—
405C2×D4—82no—
406C2×D4C2×C22⋊D1112yes—
407C2×D4C2×C22⋊D1112yes—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—82no—
417C22×C4—82no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4C2×C22⋊D1111yescharacteristic
421C22×C4C2×C22⋊D1111yescharacteristic
422C22×C4C2×C22⋊D1111yescharacteristic
423C22×C4C2×C22⋊D1111yescharacteristic
424C22×C4C2×C22⋊D1111yescharacteristic
425C22×C4C23×D1111yescharacteristic
426C2×C8—114no—
427C2×C8—222no—
428C2×C8—222no—
429C2×C8—222no—
430C2×C8—222no—
431C2×C8—222no—
432C4⋊C4—24no—
433C4⋊C4—24no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—222no—
439C4⋊C4—222no—
440C4⋊C4—222no—
441C4⋊C4—222no—
442C4⋊C4—442no—
443C4⋊C4—882no—
444C4⋊C4C2×C22⋊D1112yes—
445C4⋊C4C2×C22⋊D1112yes—
446C22⋊C4—24no—
447C22⋊C4—24no—
448C22⋊C4—24no—
449C22⋊C4—24no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—882no—
453C42—21no—
454C42—21no—
455C42C2×C22⋊D1112yes—
456C42C2×C22⋊D1112yes—
457C11#2568511yescharacteristic, complemented, Sylow
458C23—21no—
459C23—21no—
460C23—22no—
461C23—22no—
462C23—21no—
463C23—22no—
464C23—22no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23C22×C22⋊D1111yescharacteristic
474Q8—884no—
475D4—24no—
476D4—24no—
477D4—42no—
478D4—42no—
479D4—84no—
480D4—84no—
481D4—84no—
482D4—84no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—84no—
499C2×C4—84no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4#6700612yes—
507C2×C4#6700612yes—
508C2×C4#41×D1112yes—
509C2×C4#6704312yes—
510C2×C4C22×C22⋊D1111yescharacteristic
511C2×C4C22×C22⋊D1111yescharacteristic
512C8—224no—
513C8—442no—
514C22—42no—
515C22—42no—
516C22—41no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—41no—
521C22—42no—
522C22—42no—
523C22—41no—
524C22—42no—
525C22—82no—
526C22—82no—
527C22—82no—
528C22—82no—
529C22#1062335611yescharacteristic
530C22#1062336311yescharacteristic
531C22#1062336612yes—
532C22#1062336712yes—
533C22C2×#6700611yescharacteristic
534C4—22no—
535C4—22no—
536C4—41no—
537C4—41no—
538C4—42no—
539C4—41no—
540C4—42no—
541C4—882no—
542C4—882no—
543C4#1062335512yes—
544C4#1062336212yes—
545C2—81no—
546C2—82no—
547C2—82no—
548C2#1307224011yescharacteristic
549C2#1307788411yescharacteristic
550C2#1307789311yescharacteristic
551C2#1307930112yes—
552C2#1307986312yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#540C2
socleC23×C11C22×D4
hypercenterC2×#540D11
hypocenterC11#25685
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#10622678C2semidirect
2. C2×#10622683C2semidirect
3. #13074437C2semidirect
4. #13069802C2semidirect
5. #13069795C2semidirect
6. #13069582C2semidirect
7. #13069441C2semidirect
8. #13068877C2semidirect
9. #13068863C2semidirect
10. #13068382C2semidirect
457. C11#25685semidirect

Maximal subgroups

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

subgroupindex
C2×#106226782
C2×#106226832
#130744372
#130698022
#130697952
#130695822
#130694412
#130688772
#130688632
#130683822
C2×C11×#5402
#2568511