Finite Group Databasebeta

← #14737816

Subgroups — #14737816

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079195C211yesmaximal, characteristic, complemented
2#13078707C212yesmaximal, complemented
3#13068149C214yesmaximal, complemented
4#13068139C212yesmaximal, complemented
5#13068095C212yesmaximal, complemented
6#13067379C211yesmaximal, characteristic, complemented
7#13067309C212yesmaximal, complemented
8C2×C11×#436C211yesmaximal, characteristic, complemented
9C22×C11×M16—21no—
10C2×C4×D4×C11C2211yescharacteristic
11#10623008C2212yes—
12C11×#436—21no—
13C11×#436—21no—
14C11×#436C2212yes—
15C11×#436C2212yes—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×C22⋊C8—21no—
18C2×C4×C8×C11C2211yescharacteristic
19#10622830—22no—
20#10622728—21no—
21#10622728—21no—
22#10622628C2214yes—
23#10622627—24no—
24#10622621C2214yes—
25#10622581—22no—
26#10622539C2212yes—
27#10622308C2211yescharacteristic, complemented
28#10622307C2212yescomplemented
29C4×D88—21no—
30C4×D88—21no—
31#10622295C2211yescharacteristic, complemented
32#10622123C2214yescomplemented
33#10622119C2214yescomplemented
34#10622096C2212yescomplemented
35#10622095C2212yescomplemented
36C22×D4×C11D411yescharacteristic
37C23×C4×C11—21no—
38C2×#4339—22no—
39C2×C11×M16—22no—
40C2×C11×M16—22no—
41C2×C11×M16—44no—
42C22×C8×C11—21no—
43C22×C8×C11D411yescharacteristic
44C22×C8×C11D411yescharacteristic
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11D412yes—
48C4×D4×C11C2312yes—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C22⋊C4—21no—
51C2×C42×C11C2311yescharacteristic
52C2×#4323—24no—
53#66983—22no—
54#66983—22no—
55C2×D88—21no—
56C2×D88—21no—
57#66928—22no—
58#66927C2312yes—
59C4×D44—22no—
60C4×D44—22no—
61#66922C2312yes—
62C11×C4⋊C8—21no—
63C11×C4⋊C8C2312yes—
64C11×C22⋊C8—22no—
65C11×C22⋊C8—22no—
66C4×C8×C11D411yescharacteristic
67C4×C8×C11D411yescharacteristic
68C4×C8×C11C2311yescharacteristic
69C4×C8×C11C2311yescharacteristic
70#66896—24no—
71C22⋊(C11⋊C8)—22no—
72#66885—22no—
73#66885—22no—
74#66882—21no—
75#66882—21no—
76#66873—24no—
77#66872—24no—
78C4⋊(C11⋊C8)C2314yes—
79#66867—22no—
80#19283—111nomaximal, Sylow
81C24×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—42no—
84C2×D4×C11C2×D412yes—
85C22×C4×C11—21no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C2×C22⋊D11—42no—
94#4339—84no—
95C2×D44—22no—
96C2×D44—22no—
97C2×D44—22no—
98C2×C4×D11—42no—
99C2×Dic22—22no—
100C11×M16—44no—
101C11×M16—44no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—41no—
105C2×C8×C11—42no—
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11C2×D411yescharacteristic
110C11×C4⋊C4—21no—
111C11×C4⋊C4C2×D412yes—
112C11×C22⋊C4—22no—
113C11×C22⋊C4—22no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117C42×C11C2411yescharacteristic
118#4323—48no—
119(C2×D11)⋊C4—42no—
120(C2×D11)⋊C4—42no—
121C4⋊Dic11—22no—
122C4⋊Dic11—22no—
123C2×C11⋊C8—24no—
124D88—42no—
125D88—42no—
126#3169—111no—
127#3109—112no—
128C2×#436D1111yescharacteristic, complemented
129#1697—114no—
130#1695—112no—
131#1687—112no—
132#1568—111no—
133#1551—112no—
134C23×C11—22no—
135C23×C11—42no—
136C23×C11—42no—
137C23×C11—42no—
138C23×C11#12111yescharacteristic
139C22×D11—42no—
140D4×C11—24no—
141D4×C11—42no—
142C2×C4×C11—22no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—44no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11C22×D411yescharacteristic
155C2×C4×C11C22×D411yescharacteristic
156C2×C4×C11C2×#4111yescharacteristic
157C22⋊D11—84no—
158C2×Dic11—42no—
159D44—42no—
160D44—42no—
161D44—44no—
162D44—82no—
163C4×D11—84no—
164Dic22—82no—
165C8×C11—21no—
166C8×C11—21no—
167C8×C11—21no—
168C8×C11—42no—
169C8×C11AGL(1,ℤ/8)12yes—
170C11⋊C8—44no—
171C22×M16—21no—
172#532—112no—
173C2×C4×D4C2×D1111yescharacteristic
174#500—111no—
175#493—111no—
176#486—112no—
177#481—222no—
178#476—114no—
179#466—221no—
180#466—221no—
181#459—114no—
182#447—222no—
183#442—224no—
184C4×D8—221no—
185C4×D8—221no—
186#436—21no—
187#436—21no—
188#436C2×D1112yes—
189#436C2×D1112yes—
190#432—112no—
191C2×C4⋊C8C2×D1111yescharacteristic
192C2×C22⋊C8—21no—
193C2×C4×C8C2×D1111yescharacteristic
194#335—112no—
195#334—112no—
196#333—114no—
197#331—114no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—42no—
201C22×C11—42no—
202C22×C11—42no—
203C22×C11—84no—
204C22×C11#47212yes—
205C22×C11C2×#12111yescharacteristic
206C2×D11—82no—
207C2×D11—82no—
208C2×D11—82no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—42no—
214C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
215C4×C11#57512yes—
216C4×C11#57511yescharacteristic
217Dic11—82no—
218C2×#41—222no—
219C22×D4D4411yescharacteristic
220C23×C4—21no—
221C2×D8—224no—
222C2×D8—221no—
223C2×D8—221no—
224C2×M16—22no—
225C2×M16—22no—
226C2×M16—44no—
227C22×C8—21no—
228C22×C8C22⋊D1111yescharacteristic
229C22×C8C22⋊D1111yescharacteristic
230C4⋊Q8—112no—
231#127—112no—
232#124—222no—
233#121—222no—
234#121—222no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—222no—
238C4×D4—222no—
239C4×D4D4412yes—
240C4×D4C22×D1112yes—
241C2×C4⋊C4D4411yescharacteristic
242C2×C22⋊C4—21no—
243C2×C42C22×D1111yescharacteristic
244#107—221no—
245#107—221no—
246#106—224no—
247C4⋊C8—21no—
248C4⋊C8—114no—
249C4⋊C8C22×D1112yes—
250#102—224no—
251#102—222no—
252#102—222no—
253#102—224no—
254C22⋊C8—22no—
255C22⋊C8—22no—
256C22⋊C8—222no—
257#97—222no—
258C4×C8C22⋊D1111yescharacteristic
259C4×C8C22⋊D1111yescharacteristic
260C4×C8C22×D1111yescharacteristic
261C4×C8C22×D1111yescharacteristic
262C2×C11—22no—
263C2×C11—82no—
264C2×C11#303611yescharacteristic
265C2×C11#305411yescharacteristic
266C2×C11C2×#47211yescharacteristic
267D11—162no—
268C24—21no—
269#41—884no—
270C2×Q8—222no—
271C2×D4—21no—
272C2×D4—42no—
273C2×D4—222no—
274C2×D4—222no—
275C2×D4—222no—
276C2×D4—442no—
277C2×D4C2×D4412yes—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—442no—
284C22×C4C2×D4411yescharacteristic
285C22×C4#433911yescharacteristic
286C22×C4C2×C22⋊D1111yescharacteristic
287D8—442no—
288D8—448no—
289D8—442no—
290M16—44no—
291M16—44no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—41no—
295C2×C8—42no—
296C2×C8—224no—
297C2×C8C2×C22⋊D1111yescharacteristic
298C2×C8C2×C22⋊D1111yescharacteristic
299C2×C8C2×C22⋊D1111yescharacteristic
300C2×C8C2×C22⋊D1111yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—222no—
303C4⋊C4—222no—
304C4⋊C4C2×D4412yes—
305C22⋊C4—22no—
306C22⋊C4—22no—
307C22⋊C4—442no—
308C22⋊C4—442no—
309C42C2×D4411yescharacteristic
310C42#433911yescharacteristic
311C42C2×C22⋊D1111yescharacteristic
312C42C23×D1111yescharacteristic
313C11#1928311yescharacteristic, complemented, Sylow
314C23—22no—
315C23—42no—
316C23—42no—
317C23—42no—
318C23—442no—
319C23#6698311yescharacteristic
320Q8—882no—
321D4—24no—
322D4—42no—
323D4—444no—
324D4—442no—
325D4—442no—
326D4—882no—
327D4—884no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—22no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—442no—
338C2×C4—884no—
339C2×C4#6698311yescharacteristic
340C2×C4#6698311yescharacteristic
341C2×C4#6698311yescharacteristic
342C2×C4C22×D4411yescharacteristic
343C2×C4C2×#433911yescharacteristic
344C2×C4C22×C22⋊D1111yescharacteristic
345C8—21no—
346C8—21no—
347C8—21no—
348C8—42no—
349C8—444no—
350C8#6698512yes—
351C22—21no—
352C22—21no—
353C22—42no—
354C22—42no—
355C22—42no—
356C22—84no—
357C22—882no—
358C22—882no—
359C22—882no—
360C22#1062275512yes—
361C22C2×#6698311yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—42no—
367C4—882no—
368C4#1062327912yes—
369C4C2×#6698511yescharacteristic
370C4#1062335311yescharacteristic
371C2—22no—
372C2—82no—
373C2—1762no—
374C2#1307808011yescharacteristic
375C2#1307822511yescharacteristic
376C2C2×#1062275511yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#436C2
socleC22×C11C2×#121
hypercenterC2×#436D11
hypocenterC11#19283
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. #13079195C2semidirect
2. #13078707C2semidirect
3. #13068149C2semidirect
4. #13068139C2semidirect
5. #13068095C2semidirect
6. #13067379C2semidirect
7. #13067309C2semidirect
8. C2×C11×#436C2semidirect
27. #10622308C22semidirect
28. #10622307C22semidirect
31. #10622295C22semidirect
32. #10622123C22semidirect
33. #10622119C22semidirect
34. #10622096C22semidirect
35. #10622095C22semidirect
128. C2×#436D11semidirect
313. C11#19283semidirect

Maximal subgroups

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

subgroupindex
#130791952
#130787072
#130681492
#130681392
#130680952
#130673792
#130673092
C2×C11×#4362
#1928311