Finite Group Databasebeta

← C11×#32899 #14610092

Subgroups — C11×#32899 #14610092

Order 2816.

3866 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 3866 conjugacy classes of subgroups — too many to draw. Only its 366 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
1C2×C11×#585C211yesmaximal, characteristic, complemented
2C2×C11×B(4,𝔽2)C214yesmaximal, complemented
3C11×#2404C213yesmaximal, complemented
4C11×#1790C214yesmaximal, complemented
5C11×#1782C213yesmaximal, complemented
6C11×#585—216no—
7C2×C11×2−1+4—23no—
8C2×C11×H(5,𝔽2)—23no—
9C2×C11×H(5,𝔽2)C2214yes—
10C22×C11×#41—26no—
11C22×C11×#41C2213yes—
12C2×C11×#120C2216yescomplemented
13C22×C11×C22⋊C4C2211yescharacteristic, complemented
14C11×B(4,𝔽2)—216no—
15C2×C11×#99C22112yescomplemented
16C11×#393—23no—
17C11×#392—23no—
18C11×#386—26no—
19C11×#386C2216yescomplemented
20C11×#381C2213yescomplemented
21C25×C11C2311yescharacteristic
22C11×2−1+4—248no—
23C11×H(5,𝔽2)—248no—
24C11×H(5,𝔽2)—224no—
25C11×H(5,𝔽2)D4116yescomplemented
26C2×C11×#41—24no—
27C2×C11×#41—212no—
28C2×C11×#41—248no—
29C2×C11×#41—248no—
30C2×C11×#41—224no—
31C2×C11×#41—26no—
32C2×C11×#41—212no—
33C2×C11×#41—26no—
34C22×Q8×C11—26no—
35C22×Q8×C11D413yescomplemented
36C22×D4×C11—26no—
37C22×D4×C11—212no—
38C22×D4×C11—26no—
39C22×D4×C11D413yescomplemented
40C22×D4×C11C2316yes—
41C23×C4×C11—24no—
42C23×C4×C11D416yescomplemented
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C11×#120—224no—
46C2×C11×C22⋊C4—23no—
47C2×C11×C22⋊C4—23no—
48C2×C11×C22⋊C4—26no—
49C2×C11×C22⋊C4—26no—
50C2×C11×C22⋊C4C2316yes—
51C11×#99—224no—
52C11×#95—23no—
53C11×#95—23no—
54C11×#95—26no—
55#32899C1111yesmaximal, characteristic, direct product factor, Sylow
56C24×C11—24no—
57C24×C11—23no—
58C24×C11—24no—
59C24×C11—42no—
60C24×C11—81no—
61C24×C11C2×D416yes—
62C24×C11C2411yescharacteristic
63C11×#41—232no—
64C11×#41—248no—
65C11×#41—296no—
66C11×#41—248no—
67C11×#41—248no—
68C11×#41—248no—
69C2×Q8×C11—24no—
70C2×Q8×C11—248no—
71C2×Q8×C11—26no—
72C2×Q8×C11—212no—
73C2×D4×C11—212no—
74C2×D4×C11—248no—
75C2×D4×C11—248no—
76C2×D4×C11—248no—
77C2×D4×C11—212no—
78C2×D4×C11—212no—
79C2×D4×C11—212no—
80C2×D4×C11—26no—
81C2×D4×C11—412no—
82C2×D4×C11—412no—
83C2×D4×C11—86no—
84C2×D4×C11C2×D4124yes—
85C22×C4×C11—212no—
86C22×C4×C11—232no—
87C22×C4×C11—212no—
88C22×C4×C11—24no—
89C22×C4×C11—26no—
90C22×C4×C11—26no—
91C22×C4×C11—212no—
92C22×C4×C11—26no—
93C22×C4×C11—23no—
94C22×C4×C11—81no—
95C22×C4×C11C2×D413yes—
96C22×C4×C11C2×D416yes—
97C22×C4×C11C2×D413yes—
98C11×C22⋊C4—212no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—43no—
101C11×C22⋊C4—412no—
102C11×C22⋊C4—86no—
103C2×#585C2×C1111yescharacteristic, complemented
104C2×B(4,𝔽2)C2×C1114yescomplemented
105#2404C2×C1113yescomplemented
106#1790C2×C1114yescomplemented
107#1782C2×C1113yescomplemented
108C23×C11—216no—
109C23×C11—26no—
110C23×C11—26no—
111C23×C11—26no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11—46no—
115C23×C11—46no—
116C23×C11—46no—
117C23×C11—43no—
118C23×C11—46no—
119C23×C11—41no—
120C23×C11—88no—
121C23×C11—84no—
122C23×C11—84no—
123C23×C11#120112yes—
124C23×C11C22×D413yes—
125C23×C11C22×D414yes—
126Q8×C11—216no—
127Q8×C11—224no—
128D4×C11—248no—
129D4×C11—224no—
130D4×C11—248no—
131D4×C11—824no—
132C2×C4×C11—224no—
133C2×C4×C11—248no—
134C2×C4×C11—224no—
135C2×C4×C11—26no—
136C2×C4×C11—26no—
137C2×C4×C11—26no—
138C2×C4×C11—26no—
139C2×C4×C11—46no—
140C2×C4×C11—46no—
141C2×C4×C11—46no—
142C2×C4×C11—46no—
143C2×C4×C11—41no—
144C2×C4×C11#120112yes—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12013yes—
147#585—216no—
148C2×2−1+4—23no—
149C2×H(5,𝔽2)—23no—
150C2×H(5,𝔽2)C22×C1114yes—
151C22×#41—26no—
152C22×#41C22×C1113yes—
153C2×#120C22×C1116yescomplemented
154C22×C22⋊C4C22×C1111yescharacteristic, complemented
155B(4,𝔽2)—216no—
156C2×#99C22×C11112yescomplemented
157#393—23no—
158#392—23no—
159#386—26no—
160#386C22×C1116yescomplemented
161#381C22×C1113yescomplemented
162C22×C11—23no—
163C22×C11—23no—
164C22×C11—212no—
165C22×C11—44no—
166C22×C11—412no—
167C22×C11—412no—
168C22×C11—46no—
169C22×C11—46no—
170C22×C11—42no—
171C22×C11—86no—
172C22×C11—86no—
173C22×C11—816no—
174C22×C11—81no—
175C22×C11—81no—
176C22×C11C2×#12016yes—
177C22×C11C2×#12011yescharacteristic
178C4×C11—21no—
179C4×C11—212no—
180C4×C11—23no—
181C4×C11—86no—
182C4×C11—81no—
183C25C23×C1111yescharacteristic
1842−1+4—248no—
185H(5,𝔽2)—248no—
186H(5,𝔽2)—224no—
187H(5,𝔽2)D4×C11116yescomplemented
188C2×#41—24no—
189C2×#41—212no—
190C2×#41—248no—
191C2×#41—248no—
192C2×#41—224no—
193C2×#41—26no—
194C2×#41—212no—
195C2×#41—26no—
196C22×Q8—26no—
197C22×Q8D4×C1113yescomplemented
198C22×D4—26no—
199C22×D4—212no—
200C22×D4—26no—
201C22×D4D4×C1113yescomplemented
202C22×D4C23×C1116yes—
203C23×C4—24no—
204C23×C4D4×C1116yescomplemented
205C23×C4C23×C1111yescharacteristic
206C23×C4C23×C1111yescharacteristic
207#120—224no—
208C2×C22⋊C4—23no—
209C2×C22⋊C4—23no—
210C2×C22⋊C4—26no—
211C2×C22⋊C4—26no—
212C2×C22⋊C4C23×C1116yes—
213#99—224no—
214#95—23no—
215#95—23no—
216#95—26no—
217C2×C11—26no—
218C2×C11—412no—
219C2×C11—82no—
220C2×C11#284611yescharacteristic
221C2×C11#302511yescharacteristic
222C2×C11#302711yescharacteristic
223C24—24no—
224C24—23no—
225C24—24no—
226C24—42no—
227C24—81no—
228C24C2×D4×C1116yes—
229C24C24×C1111yescharacteristic
230#41—232no—
231#41—248no—
232#41—296no—
233#41—248no—
234#41—248no—
235#41—248no—
236C2×Q8—24no—
237C2×Q8—248no—
238C2×Q8—26no—
239C2×Q8—212no—
240C2×D4—212no—
241C2×D4—248no—
242C2×D4—248no—
243C2×D4—248no—
244C2×D4—212no—
245C2×D4—212no—
246C2×D4—212no—
247C2×D4—26no—
248C2×D4—412no—
249C2×D4—412no—
250C2×D4—86no—
251C2×D4C2×D4×C11124yes—
252C22×C4—212no—
253C22×C4—232no—
254C22×C4—212no—
255C22×C4—24no—
256C22×C4—26no—
257C22×C4—26no—
258C22×C4—212no—
259C22×C4—26no—
260C22×C4—23no—
261C22×C4—81no—
262C22×C4C2×D4×C1113yes—
263C22×C4C2×D4×C1116yes—
264C22×C4C2×D4×C1113yes—
265C22⋊C4—212no—
266C22⋊C4—41no—
267C22⋊C4—43no—
268C22⋊C4—412no—
269C22⋊C4—86no—
270C11#3289911yescharacteristic, direct product factor, Sylow
271C23—216no—
272C23—26no—
273C23—26no—
274C23—26no—
275C23—41no—
276C23—41no—
277C23—46no—
278C23—46no—
279C23—46no—
280C23—43no—
281C23—41no—
282C23—46no—
283C23—88no—
284C23—84no—
285C23—84no—
286C23C11×#120112yes—
287C23C22×D4×C1113yes—
288C23C22×D4×C1114yes—
289Q8—216no—
290Q8—224no—
291D4—248no—
292D4—224no—
293D4—248no—
294D4—824no—
295C2×C4—224no—
296C2×C4—248no—
297C2×C4—224no—
298C2×C4—26no—
299C2×C4—26no—
300C2×C4—26no—
301C2×C4—26no—
302C2×C4—46no—
303C2×C4—46no—
304C2×C4—46no—
305C2×C4—46no—
306C2×C4—41no—
307C2×C4C11×#12011yescharacteristic
308C2×C4C11×#12013yes—
309C2×C4C11×#120112yes—
310C22—23no—
311C22—23no—
312C22—212no—
313C22—44no—
314C22—412no—
315C22—412no—
316C22—46no—
317C22—46no—
318C22—42no—
319C22—86no—
320C22—86no—
321C22—816no—
322C22—81no—
323C22—81no—
324C22C2×C11×#12016yes—
325C22C2×C11×#12011yescharacteristic
326C4—21no—
327C4—212no—
328C4—23no—
329C4—86no—
330C4—81no—
331C2—26no—
332C2—412no—
333C2—82no—
334C2C11×#284611yescharacteristic
335C2C11×#302511yescharacteristic
336C2C11×#302711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC24C24×C11
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#585C2semidirect
2. C2×C11×B(4,𝔽2)C2semidirect
3. C11×#2404C2semidirect
4. C11×#1790C2semidirect
5. C11×#1782C2semidirect
12. C2×C11×#120C22semidirect
13. C22×C11×C22⋊C4C22semidirect
15. C2×C11×#99C22semidirect
19. C11×#386C22semidirect
20. C11×#381C22semidirect
25. C11×H(5,𝔽2)D4semidirect
35. C22×Q8×C11D4semidirect
39. C22×D4×C11D4semidirect
42. C23×C4×C11D4semidirect
55. #32899C11direct (N × H)
103. C2×#585C2×C11semidirect
104. C2×B(4,𝔽2)C2×C11semidirect
105. #2404C2×C11semidirect
106. #1790C2×C11semidirect
107. #1782C2×C11semidirect
153. C2×#120C22×C11semidirect
154. C22×C22⋊C4C22×C11semidirect
156. C2×#99C22×C11semidirect
160. #386C22×C11semidirect
161. #381C22×C11semidirect
187. H(5,𝔽2)D4×C11semidirect
197. C22×Q8D4×C11semidirect
201. C22×D4D4×C11semidirect
204. C23×C4D4×C11semidirect
270. C11#32899direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5852
C2×C11×B(4,𝔽2)2
C11×#24042
C11×#17902
C11×#17822
#3289911