Finite Group Databasebeta

← #14731587

Subgroups — #14731587

Order 2816.

1006 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079631C212yesmaximal, complemented
2C2×#10622698C211yesmaximal, characteristic, complemented
3#13067699C212yesmaximal, complemented
4#13067694C212yesmaximal, complemented
5#13067688C214yesmaximal, complemented
6#13067342C211yesmaximal, characteristic, complemented
7#13067076C212yesmaximal, complemented
8C11×#3544C211yesmaximal, characteristic, complemented
9C11×#563—22no—
10Q82×C11C2211yescharacteristic, complemented
11C11×#555C2211yescharacteristic, complemented
12C11×#554C2212yescomplemented
13C11×#552—22no—
14C11×#547—22no—
15C11×#544—22no—
16C11×#542—22no—
17C11×#536—22no—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C11×#529C2212yes—
20C22×#4325—22no—
21C2×#66927C2211yescharacteristic
22#10622698—22no—
23#10622698C2212yes—
24#10622698C2212yes—
25#10622680—22no—
26#10622671—22no—
27#10622659—22no—
28#10622649—22no—
29#10622640C2214yes—
30#10622628C2214yes—
31#10622539C2212yes—
32C2×C4×C11⋊C8C2211yescharacteristic
33#10622184C2212yescomplemented
34#10622184C2212yescomplemented
35Q8⋊(C11⋊C8)C2214yescomplemented
36D4⋊(C11⋊C8)C2214yescomplemented
37C2×C11×#41—22no—
38C22×Q8×C11D412yes—
39C22×D44—21no—
40C22×D44—22no—
41C11×C4⋊Q8—22no—
42C11×C4⋊Q8—22no—
43C11×C4⋊Q8—22no—
44C11×C4⋊Q8—22no—
45C11×C4⋊Q8D412yes—
46C11×C4⋊Q8C2311yescharacteristic
47C11×C4⋊Q8C2311yescharacteristic
48C11×#126—24no—
49C11×#126—22no—
50C11×#125—24no—
51C11×#125—22no—
52C11×#125D412yes—
53C11×#124—22no—
54C11×#124—22no—
55C11×#124D412yes—
56C11×#123—24no—
57C11×#123—24no—
58C11×#123—22no—
59C11×C22⋊Q8—24no—
60C11×C22⋊Q8—24no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8D412yes—
64C11×#121—22no—
65C11×#121D412yes—
66C4×Q8×C11—22no—
67C4×Q8×C11C2312yes—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11C2312yes—
71C11×#117—22no—
72C11×#117—22no—
73C11×#117—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—22no—
76C2×C42×C11C2311yescharacteristic
77C2×#4325—24no—
78C2×#4325—24no—
79C2×#4325—24no—
80C2×#4325—48no—
81C2×#4323—24no—
82C22×C11⋊C8—21no—
83#66927—22no—
84#66927—21no—
85#66927C2312yes—
86C22⋊(C11⋊C8)—22no—
87#66873—24no—
88#66873—24no—
89C4⋊(C11⋊C8)C2314yes—
90#66867—22no—
91C4×C11⋊C8—21no—
92C4×C11⋊C8C2312yes—
93#18684—111nomaximal, Sylow
94C23×D11—41no—
95C11×#41—84no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—44no—
99C2×Q8×C11C2×D412yes—
100C2×Q8×C11C2×D412yes—
101C2×Q8×C11C2×D412yes—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11C2×D412yes—
105C22×C4×C11—22no—
106C22×C4×C11—24no—
107C22×C4×C11—22no—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D411yescharacteristic
110C2×D44—24no—
111C2×D44—22no—
112C2×D44—44no—
113C2×D44—42no—
114C2×D44—41no—
115C2×D44—84no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4C2×D412yes—
127C11×C4⋊C4C2×D412yes—
128C11×C22⋊C4—24no—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—22no—
131C11×C22⋊C4—22no—
132C11×C22⋊C4—22no—
133C11×C22⋊C4—22no—
134C11×C22⋊C4—22no—
135C42×C11—22no—
136C42×C11—22no—
137C42×C11—22no—
138C42×C11C2×D411yescharacteristic
139C42×C11C2×D412yes—
140C42×C11C2411yescharacteristic
141#4325—48no—
142#4325—48no—
143#4325—84no—
144#4323—84no—
145C2×C11⋊C8—24no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—24no—
148#3544D1111yescharacteristic, complemented
149#3217—112no—
150C2×#492—111no—
151#1624—112no—
152#1623—112no—
153#1622—114no—
154#1558—111no—
155#1494—112no—
156C23×C11—22no—
157C23×C11#12011yescharacteristic
158C22×D11—42no—
159C22×D11—84no—
160C22×D11—82no—
161Q8×C11—24no—
162Q8×C11—42no—
163Q8×C11—42no—
164Q8×C11—82no—
165Q8×C11—82no—
166D4×C11—24no—
167D4×C11—44no—
168D4×C11—82no—
169C2×C4×C11—22no—
170C2×C4×C11—24no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—44no—
177C2×C4×C11—44no—
178C2×C4×C11—84no—
179C2×C4×C11#12012yes—
180C2×C4×C11#12011yescharacteristic
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11C22×D412yes—
183D44—44no—
184D44—44no—
185D44—44no—
186D44—82no—
187D44—84no—
188C11⋊C8—24no—
189C11⋊C8—44no—
190C22×SD16—222no—
191#563—22no—
192Q82C2×D1111yescharacteristic, complemented
193#555C2×D1111yescharacteristic, complemented
194#554C2×D1112yescomplemented
195#552—22no—
196#547—22no—
197#544—22no—
198#542—22no—
199#536—22no—
200C2×C4⋊Q8C2×D1111yescharacteristic
201C2×#127—111no—
202#529C2×D1112yes—
203#496—222no—
204#492—112no—
205#492—112no—
206#492—222no—
207#490—222no—
208#460—114no—
209#459—114no—
210#450—222no—
211#447—222no—
212#432—112no—
213C2×C4×C8—111no—
214#333—112no—
215#333—112no—
216Q8⋊C8—114no—
217D4⋊C8—114no—
218C22×C11—22no—
219C22×C11—42no—
220C22×C11—42no—
221C22×C11—42no—
222C22×C11#45312yes—
223C22×C11C2×#12011yescharacteristic
224C2×D11—84no—
225C2×D11—82no—
226C2×D11—164no—
227C4×C11—22no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—42no—
231C4×C11—42no—
232C4×C11—42no—
233C4×C11—42no—
234C4×C11—42no—
235C4×C11#57714yes—
236C2×#41—22no—
237C22×Q8C22⋊D1112yes—
238C22×D4—221no—
239C22×D4—222no—
240C2×SD16—224no—
241C2×SD16—224no—
242C2×SD16—224no—
243C2×SD16—448no—
244C2×D8—224no—
245C22×C8—221no—
246C4⋊Q8—22no—
247C4⋊Q8—22no—
248C4⋊Q8—22no—
249C4⋊Q8—22no—
250C4⋊Q8C22⋊D1112yes—
251C4⋊Q8C22×D1111yescharacteristic
252C4⋊Q8C22×D1111yescharacteristic
253#127—112no—
254#127—222no—
255#127—221no—
256#126—24no—
257#126—22no—
258#125—24no—
259#125—22no—
260#125C22⋊D1112yes—
261#124—22no—
262#124—22no—
263#124C22⋊D1112yes—
264#123—24no—
265#123—24no—
266#123—22no—
267C22⋊Q8—24no—
268C22⋊Q8—24no—
269C22⋊Q8—24no—
270C22⋊Q8—22no—
271C22⋊Q8C22⋊D1112yes—
272#121—22no—
273#121C22⋊D1112yes—
274C4×Q8—22no—
275C4×Q8C22×D1112yes—
276C4×D4—22no—
277C4×D4—22no—
278C4×D4C22×D1112yes—
279#117—22no—
280#117—22no—
281#117—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C42C22×D1111yescharacteristic
285C4⋊C8—114no—
286#102—224no—
287#102—224no—
288C22⋊C8—222no—
289#97—222no—
290C4×C8—112no—
291C4×C8—221no—
292C2×C11—22no—
293C2×C11—82no—
294C2×C11#301012yes—
295C2×C11C2×#45311yescharacteristic
296D11—162no—
297C24—441no—
298#41—84no—
299C2×Q8—22no—
300C2×Q8—22no—
301C2×Q8—44no—
302C2×Q8C2×C22⋊D1112yes—
303C2×Q8C2×C22⋊D1112yes—
304C2×Q8C2×C22⋊D1112yes—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—224no—
308C2×D4—222no—
309C2×D4—444no—
310C2×D4—442no—
311C2×D4—441no—
312C2×D4—884no—
313C2×D4C2×C22⋊D1112yes—
314C22×C4—22no—
315C22×C4—24no—
316C22×C4—22no—
317C22×C4C2×C22⋊D1112yes—
318C22×C4C2×C22⋊D1111yescharacteristic
319SD16—448no—
320SD16—448no—
321SD16—884no—
322D8—884no—
323C2×C8—224no—
324C2×C8—222no—
325C2×C8—224no—
326C4⋊C4—24no—
327C4⋊C4—24no—
328C4⋊C4—24no—
329C4⋊C4—24no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4C2×C22⋊D1112yes—
337C4⋊C4C2×C22⋊D1112yes—
338C22⋊C4—24no—
339C22⋊C4—24no—
340C22⋊C4—22no—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C22⋊C4—22no—
344C22⋊C4—22no—
345C42—22no—
346C42—22no—
347C42—22no—
348C42C2×C22⋊D1111yescharacteristic
349C42C2×C22⋊D1112yes—
350C42C23×D1111yescharacteristic
351C11#1868411yescharacteristic, complemented, Sylow
352C23—22no—
353C23—442no—
354C23—884no—
355C23—882no—
356C23#6700611yescharacteristic
357Q8—24no—
358Q8—42no—
359Q8—42no—
360Q8—82no—
361Q8—82no—
362D4—24no—
363D4—44no—
364D4—82no—
365D4—444no—
366D4—444no—
367D4—444no—
368D4—882no—
369D4—884no—
370C2×C4—22no—
371C2×C4—24no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—44no—
378C2×C4—44no—
379C2×C4—84no—
380C2×C4#6700612yes—
381C2×C4#6700611yescharacteristic
382C2×C4C22×C22⋊D1111yescharacteristic
383C2×C4C22×C22⋊D1112yes—
384C8—224no—
385C8—444no—
386C22—22no—
387C22—42no—
388C22—42no—
389C22—42no—
390C22—884no—
391C22—882no—
392C22—1764no—
393C22#1062285412yes—
394C22C2×#6700611yescharacteristic
395C4—22no—
396C4—21no—
397C4—21no—
398C4—42no—
399C4—42no—
400C4—42no—
401C4—42no—
402C4—42no—
403C4#1062336814yes—
404C2—22no—
405C2—82no—
406C2—1762no—
407C2#1307790212yes—
408C2C2×#1062285411yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3544C2
socleC22×C11C2×#120
hypercenter#3544D11
hypocenterC11#18684
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3544

Complements

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

NH ≅ G/Ntype
1. #13079631C2semidirect
2. C2×#10622698C2semidirect
3. #13067699C2semidirect
4. #13067694C2semidirect
5. #13067688C2semidirect
6. #13067342C2semidirect
7. #13067076C2semidirect
8. C11×#3544C2semidirect
10. Q82×C11C22semidirect
11. C11×#555C22semidirect
12. C11×#554C22semidirect
33. #10622184C22semidirect
34. #10622184C22semidirect
35. Q8⋊(C11⋊C8)C22semidirect
36. D4⋊(C11⋊C8)C22semidirect
148. #3544D11semidirect
192. Q82C2×D11semidirect
193. #555C2×D11semidirect
194. #554C2×D11semidirect
351. C11#18684semidirect

Maximal subgroups

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

subgroupindex
#130796312
C2×#106226982
#130676992
#130676942
#130676882
#130673422
#130670762
C11×#35442
#1868411