Finite Group Databasebeta

← #14780342

Subgroups — #14780342

Order 2816.

688 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079073C211yesmaximal, characteristic
2#13069110C212yesmaximal, complemented
3#13069108C212yesmaximal, complemented
4#13069092C212yesmaximal, complemented
5#13069086C212yesmaximal, complemented
6#13069010C211yesmaximal, characteristic, complemented
7#13068998C212yesmaximal
8#13068762C212yesmaximal, complemented
9C11×#1886C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C11×#519C2211yescharacteristic
12#10623343C2211yescharacteristic
13C2×#66995C2212yes—
14C2×#66995C2212yes—
15#10623276C2212yes—
16#10623008C2211yescharacteristic
17C11×#419C2212yes—
18C2×C11×#101C2211yescharacteristic
19C2×#66900C2211yescharacteristic
20#10622838C2212yes—
21#10622752C2212yes—
22#10622705C412yescomplemented
23#10622699C414yescomplemented
24#10622698C412yescomplemented
25#10622619C2212yes—
26#10622618C2212yes—
27C4×#4318C2211yescharacteristic
28C11×#339C2212yes—
29C11⋊#338C2212yes—
30#10622197C2212yes—
31#10622171C2212yes—
32#10622169C2212yes—
33#10622161C2212yes—
34C22×Q8×C11C2311yescharacteristic
35C22×Q8×C11C2311yescharacteristic
36C2×#4339C2312yes—
37C2×C11×M16C2312yes—
38C11×C4⋊Q8—41no—
39C11×C4⋊Q8C2×C412yes—
40C11×C4⋊Q8C2×C412yes—
41C4×Q8×C11—42no—
42C11×#117—41no—
43C11×#117C2312yes—
44C2×C11×C4⋊C4—41no—
45C2×C42×C11C2311yescharacteristic
46Q8×Dic11—42no—
47C2×#4326C2×C414yes—
48C2×#4326C2×C414yes—
49#66995—42no—
50#66995—42no—
51#66995—42no—
52#66995—42no—
53C2×#4325C2×C414yes—
54C2×#4325C2×C414yes—
55#66983—41no—
56#66979—41no—
57#66979C2312yes—
58C2×#4318C2312yes—
59C2×#4318C2312yes—
60#66960—42no—
61M16×D11—42no—
62#66954—42no—
63#66928C2×C412yes—
64#66927C2×C411yescharacteristic
65C4×D44—41no—
66#66922C2×C411yescharacteristic
67C11×#103—42no—
68C11×#101—41no—
69#66900—41no—
70#66899—42no—
71#66889—42no—
72#66870—42no—
73#66869—42no—
74#66867C2×C412yes—
75C4×C11⋊C8C2×C412yes—
76#23360—111nomaximal, Sylow
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—22no—
80C2×Q8×C11—22no—
81C2×Q8×C11—22no—
82C2×Q8×C11—22no—
83C2×Q8×C11C22×C412yes—
84C2×Q8×C11C22×C412yes—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11C2411yescharacteristic
89C2×C22⋊D11—22no—
90#4339—22no—
91#4339—22no—
92#4339—22no—
93#4339—22no—
94C2×D44—41no—
95C2×D44C22×C412yes—
96C2×C4×D11—22no—
97C2×Dic22C22×C412yes—
98C11×M16—22no—
99C11×M16—22no—
100C2×C8×C11—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—42no—
103C11×C4⋊C4—42no—
104C11×C4⋊C4—42no—
105C11×C22⋊C4—22no—
106C42×C11—21no—
107C42×C11—22no—
108C42×C11—42no—
109C42×C11C22×C411yescharacteristic
110C42×C11C22×C411yescharacteristic
111C22⋊Dic11—22no—
112#4326—44no—
113#4326—44no—
114#4325—44no—
115#4325—44no—
116(C2×D11)⋊C4—42no—
117C4⋊Dic11—22no—
118C4⋊Dic11—41no—
119C4⋊Dic11—42no—
120C4×Dic11—22no—
121C4×Dic11—42no—
122#4318—22no—
123#4318—22no—
124#4318—22no—
125#4318—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8C22×C414yes—
128#4313—44no—
129C8×D11—44no—
130#3152—111no—
131#1905—112no—
132#1905—112no—
133#1902—112no—
134#1902—112no—
135#1886—111no—
136#1886D1111yescharacteristic, complemented
137#1884—112no—
138#1841—112no—
139C23×C11H(5,𝔽2)11yescharacteristic
140C22×D11—22no—
141Q8×C11—24no—
142Q8×C11—24no—
143Q8×C11—42no—
144Q8×C11—42no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11C23×C411yescharacteristic
156C2×C4×C11H(5,𝔽2)12yes—
157C2×C4×C11H(5,𝔽2)11yescharacteristic
158C2×C4×C11H(5,𝔽2)12yes—
159C22⋊D11—42no—
160C22⋊D11—42no—
161C2×Dic11—22no—
162C2×Dic11—42no—
163D44—22no—
164D44—22no—
165D44—82no—
166C4×D11—42no—
167C4×D11—42no—
168Dic22—22no—
169Dic22—22no—
170C8×C11—42no—
171C11⋊C8—24no—
172C11⋊C8—42no—
173C2×#137—112no—
174C2×#137—112no—
175#568—112no—
176#532—111no—
177C2×C4⋊Q8C2×D1111yescharacteristic
178#519—111no—
179#519C2×D1111yescharacteristic
180#497—114no—
181#494—112no—
182#492—112no—
183#421—112no—
184#421—112no—
185#419—112no—
186#419C2×D1112yes—
187C2×#101—111no—
188C2×#101C2×D1111yescharacteristic
189#410—112no—
190C4×M16—111no—
191#344—112no—
192#344—112no—
193#339—112no—
194#339C2×D1112yes—
195#338—112no—
196H(3,ℤ/4)—112no—
197C22×C11—41no—
198C22×C11#51811yescharacteristic
199C22×C11#56011yescharacteristic
200C22×C11#56011yescharacteristic
201C2×D11—42no—
202C2×D11—82no—
203C4×C11—22no—
204C4×C11—41no—
205C4×C11—42no—
206C4×C11—42no—
207C4×C11—82no—
208C4×C11#51812yes—
209C4×C11#56012yes—
210Dic11—42no—
211Dic11—82no—
212C2×#41—112no—
213C22×Q8C22×D1111yescharacteristic
214C22×Q8C22×D1111yescharacteristic
215#137—442no—
216#137—442no—
217#137—442no—
218#137—442no—
219C2×Q16—114no—
220C2×Q16—114no—
221C2×SD16—114no—
222C2×SD16—114no—
223#131—442no—
224#131—442no—
225C2×M16—112no—
226C2×M16—112no—
227C2×M16—442no—
228C2×M16C22×D1112yes—
229C4⋊Q8—41no—
230C4⋊Q8—111no—
231C4⋊Q8C4×D1112yes—
232C4⋊Q8C4×D1112yes—
233#127—111no—
234#124—112no—
235#121—441no—
236C4×Q8—42no—
237C4×Q8—442no—
238C4×D4—441no—
239#117—41no—
240#117—112no—
241#117—441no—
242#117C22×D1112yes—
243C2×C4⋊C4—41no—
244C2×C42C22×D1111yescharacteristic
245#104—442no—
246#104—442no—
247#103—42no—
248#103—442no—
249#101—41no—
250#101—441no—
251#99—442no—
252#97—112no—
253C4×C8—112no—
254C2×C11—21no—
255C2×C11—21no—
256C2×C11—21no—
257C2×C11#238011yescharacteristic
258D11—82no—
259#41—222no—
260#41—222no—
261#41—222no—
262#41—222no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8—22no—
266C2×Q8—22no—
267C2×Q8—22no—
268C2×Q8—22no—
269C2×Q8—112no—
270C2×Q8C2×C4×D1112yes—
271C2×Q8C2×C4×D1112yes—
272C2×D4—112no—
273C2×D4—222no—
274C2×D4—441no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—222no—
279C22×C4C23×D1111yescharacteristic
280Q16—444no—
281Q16—444no—
282SD16—444no—
283SD16—444no—
284M16—22no—
285M16—22no—
286M16—222no—
287M16—222no—
288M16—222no—
289M16—222no—
290M16—444no—
291C2×C8—22no—
292C2×C8—114no—
293C2×C8—222no—
294C2×C8—444no—
295C4⋊C4—22no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—222no—
300C4⋊C4—441no—
301C4⋊C4—442no—
302C22⋊C4—22no—
303C22⋊C4—222no—
304C22⋊C4—442no—
305C42—21no—
306C42—22no—
307C42—42no—
308C42—222no—
309C42—442no—
310C42C2×C4×D1111yescharacteristic
311C42C2×C4×D1111yescharacteristic
312C11#2336011yescharacteristic, complemented, Sylow
313C23—222no—
314C23#6703711yescharacteristic
315Q8—24no—
316Q8—24no—
317Q8—42no—
318Q8—42no—
319Q8—222no—
320Q8—222no—
321D4—222no—
322D4—222no—
323D4—442no—
324D4—442no—
325D4—882no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—222no—
337C2×C4—442no—
338C2×C4—442no—
339C2×C4—442no—
340C2×C4C22×C4×D1111yescharacteristic
341C2×C4#6703712yes—
342C2×C4#6703711yescharacteristic
343C2×C4#6704212yes—
344C8—42no—
345C8—224no—
346C8—442no—
347C22—41no—
348C22—442no—
349C22—882no—
350C22#1062301711yescharacteristic
351C22#1062312611yescharacteristic
352C22#1062319711yescharacteristic
353C4—22no—
354C4—41no—
355C4—42no—
356C4—42no—
357C4—82no—
358C4—442no—
359C4—882no—
360C4#1062307612yes—
361C4#1062315112yes—
362C2—21no—
363C2—21no—
364C2—21no—
365C2—882no—
366C2#1307179111yescharacteristic
subgroupG/H
centerC2#13071791
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1886C2
socleC2×C11#2380
prime radical#10623008C22
cosocleC22×C4×C11C24
hypercenter#1886D11
hypocenterC11#23360
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1886

Complements

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

NH ≅ G/Ntype
2. #13069110C2semidirect
3. #13069108C2semidirect
4. #13069092C2semidirect
5. #13069086C2semidirect
6. #13069010C2semidirect
8. #13068762C2semidirect
9. C11×#1886C2semidirect
22. #10622705C4semidirect
23. #10622699C4semidirect
24. #10622698C4semidirect
136. #1886D11semidirect
312. C11#23360semidirect

Maximal subgroups

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

subgroupindex
#130790732
#130691102
#130691082
#130690922
#130690862
#130690102
#130689982
#130687622
C11×#18862
#2336011