Finite Group Databasebeta

← C11×#23896 #14601089

Subgroups — C11×#23896 #14601089

Order 2816.

1764 conjugacy classes of subgroups; only the 282 normal subgroups are shown.

normal subgroups only

This group has 1764 conjugacy classes of subgroups — too many to draw. Only its 282 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3485C212yesmaximal, complemented
2C11×#3026C214yesmaximal, complemented
3C11×#2022C214yesmaximal, complemented
4C11×#1913C214yesmaximal, complemented
5C11×#1782C211yesmaximal, characteristic, complemented
6C2×C11×H(5,𝔽2)C2212yescomplemented
7C22×C11×#41C2211yescharacteristic
8C11×#547—28no—
9C11×#546—28no—
10C11×#536—22no—
11C11×#534—22no—
12C11×#534C2214yes—
13C11×#534C2214yes—
14C11×#525—22no—
15C2×C11×#123—22no—
16C2×C11×#123C2214yescomplemented
17C11×#518C2212yescomplemented
18C11×#458—28no—
19C11×B(4,𝔽2)—28no—
20C2×C11×#99C2218yescomplemented
21C2×C11×#99C2214yescomplemented
22C11×#381C2212yescomplemented
23C11×#342C2214yescomplemented
24C11×H(5,𝔽2)—28no—
25C11×H(5,𝔽2)—44no—
26C2×C11×#41—28no—
27C2×C11×#41—22no—
28C2×C11×#41—24no—
29C2×C11×#41—42no—
30C22×Q8×C11D411yescharacteristic, complemented
31C22×D4×C11—22no—
32C22×D4×C11—24no—
33C22×D4×C11D411yescharacteristic, complemented
34C22×D4×C11C2314yes—
35C22×D4×C11C2312yes—
36C23×C4×C11D412yescomplemented
37C23×C4×C11C2311yescharacteristic
38C11×C4⋊Q8—24no—
39C11×#124—24no—
40C11×#123—28no—
41C11×#123—24no—
42C11×#123—24no—
43C11×#123—24no—
44C11×#123—24no—
45C11×#123—28no—
46C11×#123—28no—
47C11×#123D418yescomplemented
48C11×C22⋊Q8—24no—
49C11×C22⋊Q8—28no—
50C11×#121—24no—
51C11×#121—28no—
52C11×#121—28no—
53C11×#121—44no—
54C11×#120—24no—
55C11×#120—24no—
56C11×#120—28no—
57C11×#120D418yescomplemented
58C4×D4×C11—28no—
59C4×D4×C11—28no—
60C11×#117—22no—
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4—24no—
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4C2314yes—
67C2×C11×C22⋊C4C2314yes—
68C11×#99—28no—
69C11×#99—216no—
70C11×#95—42no—
71#23896C1111yesmaximal, characteristic, direct product factor, Sylow
72C24×C11—22no—
73C24×C11C2×D414yes—
74C24×C11C2×D412yes—
75C24×C11C2411yescharacteristic
76C11×#41—416no—
77C11×#41—44no—
78C11×#41—416no—
79C11×#41—44no—
80C2×Q8×C11—22no—
81C2×Q8×C11—24no—
82C2×Q8×C11—41no—
83C2×D4×C11—24no—
84C2×D4×C11—24no—
85C2×D4×C11—24no—
86C2×D4×C11—22no—
87C2×D4×C11—24no—
88C2×D4×C11—28no—
89C2×D4×C11—24no—
90C2×D4×C11—24no—
91C2×D4×C11—28no—
92C2×D4×C11—28no—
93C2×D4×C11—41no—
94C2×D4×C11—416no—
95C2×D4×C11—44no—
96C2×D4×C11—44no—
97C2×D4×C11—44no—
98C2×D4×C11C2×D418yes—
99C22×C4×C11—22no—
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11—24no—
103C22×C4×C11—22no—
104C22×C4×C11—24no—
105C22×C4×C11—24no—
106C22×C4×C11—24no—
107C22×C4×C11—24no—
108C22×C4×C11—42no—
109C22×C4×C11C2×D414yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D412yes—
113C11×C4⋊C4—28no—
114C11×C4⋊C4—28no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—28no—
117C11×C4⋊C4—44no—
118C11×C22⋊C4—28no—
119C11×C22⋊C4—24no—
120C11×C22⋊C4—28no—
121C11×C22⋊C4—28no—
122C11×C22⋊C4—24no—
123C11×C22⋊C4—28no—
124C11×C22⋊C4—28no—
125C11×C22⋊C4—48no—
126C11×C22⋊C4C2×D418yes—
127C42×C11—24no—
128#3485C2×C1112yescomplemented
129#3026C2×C1114yescomplemented
130#2022C2×C1114yescomplemented
131#1913C2×C1114yescomplemented
132#1782C2×C1111yescharacteristic, complemented
133C23×C11—22no—
134C23×C11—22no—
135C23×C11—24no—
136C23×C11—28no—
137C23×C11—44no—
138C23×C11—81no—
139C23×C11—82no—
140C23×C11—84no—
141C23×C11—84no—
142C23×C11#12014yes—
143C23×C11C22×D411yescharacteristic
144C23×C11C22×D414yes—
145C23×C11H(5,𝔽2)12yes—
146Q8×C11—44no—
147Q8×C11—44no—
148D4×C11—216no—
149D4×C11—44no—
150D4×C11—44no—
151D4×C11—48no—
152D4×C11—44no—
153D4×C11—44no—
154D4×C11—48no—
155D4×C11—88no—
156D4×C11—164no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—28no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—24no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—28no—
166C2×C4×C11—48no—
167C2×C4×C11—48no—
168C2×C4×C11—44no—
169C2×C4×C11—44no—
170C2×C4×C11—44no—
171C2×C4×C11—84no—
172C2×C4×C11—84no—
173C2×C4×C11—84no—
174C2×C4×C11#12014yes—
175C2×H(5,𝔽2)C22×C1112yescomplemented
176C22×#41C22×C1111yescharacteristic
177#547—28no—
178#546—28no—
179#536—22no—
180#534—22no—
181#534C22×C1114yes—
182#534C22×C1114yes—
183#525—22no—
184C2×#123—22no—
185C2×#123C22×C1114yescomplemented
186#518C22×C1112yescomplemented
187#458—28no—
188B(4,𝔽2)—28no—
189C2×#99C22×C1118yescomplemented
190C2×#99C22×C1114yescomplemented
191#381C22×C1112yescomplemented
192#342C22×C1114yescomplemented
193C22×C11—24no—
194C22×C11—42no—
195C22×C11—44no—
196C22×C11—41no—
197C22×C11—44no—
198C22×C11—44no—
199C22×C11—48no—
200C22×C11—44no—
201C22×C11—82no—
202C22×C11—88no—
203C22×C11—164no—
204C22×C11C2×#12012yes—
205C22×C11#53411yescharacteristic
206C22×C11D4214yes—
207C4×C11—24no—
208C4×C11—48no—
209C4×C11—41no—
210C4×C11—44no—
211C4×C11—41no—
212C4×C11—84no—
213H(5,𝔽2)—28no—
214H(5,𝔽2)—44no—
215C2×#41—28no—
216C2×#41—22no—
217C2×#41—24no—
218C2×#41—42no—
219C22×Q8D4×C1111yescharacteristic, complemented
220C22×D4—22no—
221C22×D4—24no—
222C22×D4D4×C1111yescharacteristic, complemented
223C22×D4C23×C1114yes—
224C22×D4C23×C1112yes—
225C23×C4D4×C1112yescomplemented
226C23×C4C23×C1111yescharacteristic
227C4⋊Q8—24no—
228#124—24no—
229#123—28no—
230#123—24no—
231#123—24no—
232#123—24no—
233#123—24no—
234#123—28no—
235#123—28no—
236#123D4×C1118yescomplemented
237C22⋊Q8—24no—
238C22⋊Q8—28no—
239#121—24no—
240#121—28no—
241#121—28no—
242#121—44no—
243#120—24no—
244#120—24no—
245#120—28no—
246#120D4×C1118yescomplemented
247C4×D4—28no—
248C4×D4—28no—
249#117—22no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—24no—
252C2×C22⋊C4—24no—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—24no—
255C2×C22⋊C4C23×C1114yes—
256C2×C22⋊C4C23×C1114yes—
257#99—28no—
258#99—216no—
259#95—42no—
260C2×C11—22no—
261C2×C11—24no—
262C2×C11—21no—
263C2×C11—44no—
264C2×C11—84no—
265C2×C11#240311yescharacteristic
266C24—22no—
267C24C2×D4×C1114yes—
268C24C2×D4×C1112yes—
269C24C24×C1111yescharacteristic
270#41—416no—
271#41—44no—
272#41—416no—
273#41—44no—
274C2×Q8—22no—
275C2×Q8—24no—
276C2×Q8—41no—
277C2×D4—24no—
278C2×D4—24no—
279C2×D4—24no—
280C2×D4—22no—
281C2×D4—24no—
282C2×D4—28no—
283C2×D4—24no—
284C2×D4—24no—
285C2×D4—28no—
286C2×D4—28no—
287C2×D4—41no—
288C2×D4—416no—
289C2×D4—44no—
290C2×D4—44no—
291C2×D4—44no—
292C2×D4C2×D4×C1118yes—
293C22×C4—22no—
294C22×C4—24no—
295C22×C4—24no—
296C22×C4—24no—
297C22×C4—22no—
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—24no—
301C22×C4—24no—
302C22×C4—42no—
303C22×C4C2×D4×C1114yes—
304C22×C4C2×D4×C1111yescharacteristic
305C22×C4C2×D4×C1111yescharacteristic
306C22×C4C2×D4×C1112yes—
307C4⋊C4—28no—
308C4⋊C4—28no—
309C4⋊C4—24no—
310C4⋊C4—28no—
311C4⋊C4—44no—
312C22⋊C4—28no—
313C22⋊C4—24no—
314C22⋊C4—28no—
315C22⋊C4—28no—
316C22⋊C4—24no—
317C22⋊C4—28no—
318C22⋊C4—28no—
319C22⋊C4—48no—
320C22⋊C4C2×D4×C1118yes—
321C42—24no—
322C11#2389611yescharacteristic, direct product factor, Sylow
323C23—22no—
324C23—22no—
325C23—24no—
326C23—28no—
327C23—44no—
328C23—81no—
329C23—82no—
330C23—84no—
331C23—84no—
332C23C11×#12014yes—
333C23C22×D4×C1111yescharacteristic
334C23C22×D4×C1114yes—
335C23C11×H(5,𝔽2)12yes—
336Q8—44no—
337Q8—44no—
338D4—216no—
339D4—44no—
340D4—44no—
341D4—48no—
342D4—44no—
343D4—44no—
344D4—48no—
345D4—88no—
346D4—164no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—28no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—24no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—28no—
356C2×C4—48no—
357C2×C4—48no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—84no—
362C2×C4—84no—
363C2×C4—84no—
364C2×C4C11×#12014yes—
365C22—24no—
366C22—42no—
367C22—44no—
368C22—41no—
369C22—44no—
370C22—44no—
371C22—48no—
372C22—44no—
373C22—82no—
374C22—88no—
375C22—164no—
376C22C2×C11×#12012yes—
377C22C11×#53411yescharacteristic
378C22D42×C1114yes—
379C4—24no—
380C4—48no—
381C4—41no—
382C4—44no—
383C4—41no—
384C4—84no—
385C2—22no—
386C2—24no—
387C2—21no—
388C2—44no—
389C2—84no—
390C2C11×#240311yescharacteristic
subgroupG/H
center, socleC2×C11#2403
commutator, Frattini, cosocleC24C24×C11
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3485C2semidirect
2. C11×#3026C2semidirect
3. C11×#2022C2semidirect
4. C11×#1913C2semidirect
5. C11×#1782C2semidirect
6. C2×C11×H(5,𝔽2)C22semidirect
16. C2×C11×#123C22semidirect
17. C11×#518C22semidirect
20. C2×C11×#99C22semidirect
21. C2×C11×#99C22semidirect
22. C11×#381C22semidirect
23. C11×#342C22semidirect
30. C22×Q8×C11D4semidirect
33. C22×D4×C11D4semidirect
36. C23×C4×C11D4semidirect
47. C11×#123D4semidirect
57. C11×#120D4semidirect
71. #23896C11direct (N × H)
128. #3485C2×C11semidirect
129. #3026C2×C11semidirect
130. #2022C2×C11semidirect
131. #1913C2×C11semidirect
132. #1782C2×C11semidirect
175. C2×H(5,𝔽2)C22×C11semidirect
185. C2×#123C22×C11semidirect
186. #518C22×C11semidirect
189. C2×#99C22×C11semidirect
190. C2×#99C22×C11semidirect
191. #381C22×C11semidirect
192. #342C22×C11semidirect
219. C22×Q8D4×C11semidirect
222. C22×D4D4×C11semidirect
225. C23×C4D4×C11semidirect
236. #123D4×C11semidirect
246. #120D4×C11semidirect
322. C11#23896direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34852
C11×#30262
C11×#20222
C11×#19132
C11×#17822
#2389611