Finite Group Databasebeta

← C11×#23171 #14600364

Subgroups — C11×#23171 #14600364

Order 2816.

626 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3160C211yesmaximal, characteristic
2C11×#2962C212yesmaximal
3C11×#1986C212yesmaximal
4C11×#1946C212yesmaximal
5C11×#1922C214yesmaximal
6C4×C11×#108C211yesmaximal, characteristic
7C11×#1773C212yesmaximal
8C11×#1770C211yesmaximal, characteristic
9C11×#533C2212yes—
10C11×#500C411yescharacteristic, complemented
11C11×#500C411yescharacteristic, complemented
12C11×#499C412yescomplemented
13C11×#499C412yescomplemented
14C11×#498C412yescomplemented
15C11×#446—24no—
16C11×#446—22no—
17C8×Q8×C11—22no—
18C2×C11×#108C2211yescharacteristic
19C2×C11×#108C2211yescharacteristic
20C11×#427C2212yes—
21C11×#427C2212yes—
22C11×#424C2214yes—
23C2×C11×C4⋊C8C2211yescharacteristic
24C11×#405C2214yes—
25C4×C11×M16C2212yes—
26C2×C11×#97C2212yes—
27C2×C4×C8×C11C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C11×#341C2212yes—
30C11×#339C2214yes—
31C11×#339C2214yes—
32C11×#336C2212yes—
33C2×C11×M16C2312yes—
34C2×C11×M16C2312yes—
35C22×C8×C11C2311yescharacteristic
36C22×C8×C11C2312yes—
37C22×C8×C11C2311yescharacteristic
38C11×C4⋊Q8C2×C412yes—
39C11×C4⋊Q8C2×C412yes—
40C11×#125C2×C414yes—
41C11×C22⋊Q8—22no—
42C11×C22⋊Q8—22no—
43C4×Q8×C11—22no—
44C4×Q8×C11—22no—
45C11×#117C2314yes—
46C2×C11×C4⋊C4—21no—
47C2×C42×C11C2312yes—
48C2×C42×C11C2311yescharacteristic
49C11×#108—22no—
50C11×#108Q814yescomplemented
51C11×#107C2×C412yes—
52C11×#107C2×C412yes—
53C11×#107C2×C412yes—
54C11×#107C2×C412yes—
55C11×#106C2×C414yes—
56C11×#106C2×C414yes—
57C11×C4⋊C8—24no—
58C11×C4⋊C8—24no—
59C11×C4⋊C8D412yes—
60C11×C4⋊C8D412yes—
61C11×#97—24no—
62C11×#97—24no—
63C11×#97—22no—
64C4×C8×C11—24no—
65C4×C8×C11—22no—
66C4×C8×C11C2×C411yescharacteristic
67C4×C8×C11C2×C411yescharacteristic
68C4×C8×C11C2×C411yescharacteristic
69C4×C8×C11C2×C411yescharacteristic
70C11×#95—21no—
71#23171C1111yesmaximal, characteristic, direct product factor, Sylow
72C2×Q8×C11—22no—
73C2×Q8×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11#4111yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C22×C4×C11C2411yescharacteristic
78C11×M16—22no—
79C11×M16—22no—
80C11×M16—22no—
81C11×M16C2×Q814yes—
82C2×C8×C11—22no—
83C2×C8×C11—22no—
84C2×C8×C11—22no—
85C2×C8×C11—21no—
86C2×C8×C11—22no—
87C2×C8×C11—21no—
88C2×C8×C11C22×C411yescharacteristic
89C2×C8×C11C22×C411yescharacteristic
90C2×C8×C11C22×C411yescharacteristic
91C2×C8×C11C22×C411yescharacteristic
92C2×C8×C11C2×D414yes—
93C2×C8×C11C2×Q812yes—
94C2×C8×C11#4112yes—
95C11×C4⋊C4—24no—
96C11×C4⋊C4—24no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—42no—
100C11×C4⋊C4C22×C414yes—
101C11×C4⋊C4C22×C414yes—
102C11×C22⋊C4—24no—
103C42×C11—24no—
104C42×C11—22no—
105C42×C11—22no—
106C42×C11C22×C411yescharacteristic
107C42×C11C22×C411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110#3160C2×C1111yescharacteristic
111#2962C2×C1112yes—
112#1986C2×C1112yes—
113#1946C2×C1112yes—
114#1922C2×C1114yes—
115C4×#108C2×C1111yescharacteristic
116#1773C2×C1112yes—
117#1770C2×C1111yescharacteristic
118C23×C11C2×#4111yescharacteristic
119Q8×C11—44no—
120Q8×C11—82no—
121C2×C4×C11—22no—
122C2×C4×C11—24no—
123C2×C4×C11—24no—
124C2×C4×C11—41no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11C4×D411yescharacteristic
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11C4×D411yescharacteristic
132C2×C4×C11C23×C411yescharacteristic
133C2×C4×C11C22×D411yescharacteristic
134C2×C4×C11C22×Q811yescharacteristic
135C2×C4×C11C2×#4111yescharacteristic
136C2×C4×C112−1+411yescharacteristic
137C2×C4×C112−1+411yescharacteristic
138C8×C11—21no—
139C8×C11—21no—
140C8×C11—24no—
141C8×C11—24no—
142C8×C11—42no—
143C8×C11C4×Q812yes—
144C8×C11C4×Q812yes—
145#533C22×C1112yes—
146#500C4×C1111yescharacteristic, complemented
147#500C4×C1111yescharacteristic, complemented
148#499C4×C1112yescomplemented
149#499C4×C1112yescomplemented
150#498C4×C1112yescomplemented
151#446—24no—
152#446—22no—
153C8×Q8—22no—
154C2×#108C22×C1111yescharacteristic
155C2×#108C22×C1111yescharacteristic
156#427C22×C1112yes—
157#427C22×C1112yes—
158#424C22×C1114yes—
159C2×C4⋊C8C22×C1111yescharacteristic
160#405C22×C1114yes—
161C4×M16C22×C1112yes—
162C2×#97C22×C1112yes—
163C2×C4×C8C22×C1111yescharacteristic
164C4×C4⋊C4C22×C1111yescharacteristic
165#341C22×C1112yes—
166#339C22×C1114yes—
167#339C22×C1114yes—
168#336C22×C1112yes—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11C2×C4×D411yescharacteristic
172C22×C11#55611yescharacteristic
173C22×C11#55711yescharacteristic
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—44no—
178C4×C11—44no—
179C4×C11—82no—
180C4×C11#44412yes—
181C4×C11C2×C4×Q811yescharacteristic
182C4×C11#51911yescharacteristic
183C4×C11#54711yescharacteristic
184C4×C11D4×Q811yescharacteristic
185C2×M16C23×C1112yes—
186C2×M16C23×C1112yes—
187C22×C8C23×C1111yescharacteristic
188C22×C8C23×C1112yes—
189C22×C8C23×C1111yescharacteristic
190C4⋊Q8C2×C4×C1112yes—
191C4⋊Q8C2×C4×C1112yes—
192#125C2×C4×C1114yes—
193C22⋊Q8—22no—
194C22⋊Q8—22no—
195C4×Q8—22no—
196C4×Q8—22no—
197#117C23×C1114yes—
198C2×C4⋊C4—21no—
199C2×C42C23×C1112yes—
200C2×C42C23×C1111yescharacteristic
201#108—22no—
202#108Q8×C1114yescomplemented
203#107C2×C4×C1112yes—
204#107C2×C4×C1112yes—
205#107C2×C4×C1112yes—
206#107C2×C4×C1112yes—
207#106C2×C4×C1114yes—
208#106C2×C4×C1114yes—
209C4⋊C8—24no—
210C4⋊C8—24no—
211C4⋊C8D4×C1112yes—
212C4⋊C8D4×C1112yes—
213#97—24no—
214#97—24no—
215#97—22no—
216C4×C8—24no—
217C4×C8—22no—
218C4×C8C2×C4×C1111yescharacteristic
219C4×C8C2×C4×C1111yescharacteristic
220C4×C8C2×C4×C1111yescharacteristic
221C4×C8C2×C4×C1111yescharacteristic
222#95—21no—
223C2×C11—21no—
224C2×C11—21no—
225C2×C11#236511yescharacteristic
226C2×C11C2×#44411yescharacteristic
227C2×C11#295711yescharacteristic
228C2×Q8—22no—
229C2×Q8—22no—
230C22×C4—22no—
231C22×C4C11×#4111yescharacteristic
232C22×C4C11×#4111yescharacteristic
233C22×C4C24×C1111yescharacteristic
234M16—22no—
235M16—22no—
236M16—22no—
237M16C2×Q8×C1114yes—
238C2×C8—22no—
239C2×C8—22no—
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—22no—
243C2×C8—22no—
244C2×C8C22×C4×C1111yescharacteristic
245C2×C8C22×C4×C1111yescharacteristic
246C2×C8C22×C4×C1111yescharacteristic
247C2×C8C22×C4×C1111yescharacteristic
248C2×C8C2×D4×C1114yes—
249C2×C8C2×Q8×C1112yes—
250C2×C8C11×#4112yes—
251C4⋊C4—24no—
252C4⋊C4—24no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—42no—
256C4⋊C4C22×C4×C1114yes—
257C4⋊C4C22×C4×C1114yes—
258C22⋊C4—24no—
259C42—24no—
260C42—22no—
261C42—22no—
262C42C22×C4×C1111yescharacteristic
263C42C22×C4×C1111yescharacteristic
264C42C2×D4×C1111yescharacteristic
265C42C2×D4×C1111yescharacteristic
266C11#2317111yescharacteristic, direct product factor, Sylow
267C23C2×C11×#4111yescharacteristic
268Q8—44no—
269Q8—82no—
270C2×C4—22no—
271C2×C4—24no—
272C2×C4—24no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4C4×D4×C1111yescharacteristic
278C2×C4C4×D4×C1111yescharacteristic
279C2×C4C4×D4×C1111yescharacteristic
280C2×C4C4×D4×C1111yescharacteristic
281C2×C4C23×C4×C1111yescharacteristic
282C2×C4C22×D4×C1111yescharacteristic
283C2×C4C22×Q8×C1111yescharacteristic
284C2×C4C2×C11×#4111yescharacteristic
285C2×C4C11×2−1+411yescharacteristic
286C2×C4C11×2−1+411yescharacteristic
287C8—21no—
288C8—21no—
289C8—24no—
290C8—24no—
291C8—42no—
292C8C4×Q8×C1112yes—
293C8C4×Q8×C1112yes—
294C22—21no—
295C22—21no—
296C22C2×C4×D4×C1111yescharacteristic
297C22C11×#55611yescharacteristic
298C22C11×#55711yescharacteristic
299C4—21no—
300C4—21no—
301C4—21no—
302C4—44no—
303C4—44no—
304C4—82no—
305C4C11×#44412yes—
306C4C2×C4×Q8×C1111yescharacteristic
307C4C11×#51911yescharacteristic
308C4C11×#54711yescharacteristic
309C4D4×Q8×C1111yescharacteristic
310C2—21no—
311C2—21no—
312C2C11×#236511yescharacteristic
313C2C2×C11×#44411yescharacteristic
314C2C11×#295711yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC22×C11C2×C4×D4
prime radicalC23×C11C2×#41
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C11×C4⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
10. C11×#500C4semidirect
11. C11×#500C4semidirect
12. C11×#499C4semidirect
13. C11×#499C4semidirect
14. C11×#498C4semidirect
50. C11×#108Q8semidirect
71. #23171C11direct (N × H)
146. #500C4×C11semidirect
147. #500C4×C11semidirect
148. #499C4×C11semidirect
149. #499C4×C11semidirect
150. #498C4×C11semidirect
202. #108Q8×C11semidirect
266. C11#23171direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31602
C11×#29622
C11×#19862
C11×#19462
C11×#19222
C4×C11×#1082
C11×#17732
C11×#17702
#2317111