Finite Group Databasebeta

← C11×#7965 #14585158

Subgroups — C11×#7965 #14585158

Order 2816.

542 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2920C211yesmaximal, characteristic
2C11×#2920C211yesmaximal, characteristic
3C2×C11×#431C211yesmaximal, characteristic
4C11×#1287C214yesmaximal, complemented
5C22×C42×C11C2211yescharacteristic
6C11×#432—21no—
7C11×#432C412yes—
8C11×#432C2212yes—
9C11×#432C2212yes—
10C11×#431—21no—
11C11×#431—21no—
12C11×#431—21no—
13C11×#431—21no—
14C11×#431—21no—
15C11×#431C412yes—
16C11×#431C412yes—
17C11×#431C2212yes—
18C11×#423—21no—
19C11×#423—21no—
20C2×C11×C4⋊C8—21no—
21C11×#407—21no—
22C11×#407C412yes—
23C2×C11×C22⋊C8—21no—
24C4×C11×M16—21no—
25C4×C11×M16C412yes—
26C2×C4×C8×C11C412yes—
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11Q811yescharacteristic
30C2×C11×M16—22no—
31C2×C11×M16—22no—
32C22×C8×C11—22no—
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11C2×C411yescharacteristic
37C2×C42×C11C2×C411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×C42×C11Q811yescharacteristic
44C2×C42×C11C2311yescharacteristic
45C11×C4⋊C8—22no—
46C11×C4⋊C8—22no—
47C11×C4⋊C8—22no—
48C11×C4⋊C8—22no—
49C11×C4⋊C8—22no—
50C11×C4⋊C8—22no—
51C11×C22⋊C8—22no—
52C11×C22⋊C8—22no—
53C11×C22⋊C8—22no—
54C11×C22⋊C8—22no—
55C11×C22⋊C8—22no—
56C11×C22⋊C8C2×C414yes—
57C11×#97—22no—
58C11×#97C2×C414yes—
59C4×C8×C11—22no—
60C4×C8×C11—22no—
61C4×C8×C11—22no—
62C4×C8×C11C2×C414yes—
63#7965C1111yesmaximal, characteristic, direct product factor, Sylow
64C24×C11C4⋊C411yescharacteristic
65C22×C4×C11—24no—
66C22×C4×C11—42no—
67C22×C4×C11—42no—
68C22×C4×C11C4211yescharacteristic
69C22×C4×C11C4211yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C4⋊C411yescharacteristic
77C22×C4×C11C4⋊C411yescharacteristic
78C22×C4×C11C4⋊C411yescharacteristic
79C22×C4×C11C4⋊C411yescharacteristic
80C22×C4×C11C4⋊C411yescharacteristic
81C22×C4×C11C4⋊C411yescharacteristic
82C22×C4×C11C4⋊C411yescharacteristic
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×Q811yescharacteristic
86C11×M16—44no—
87C11×M16—44no—
88C2×C8×C11—24no—
89C2×C8×C11—24no—
90C2×C8×C11—24no—
91C2×C8×C11—44no—
92C42×C11C4211yescharacteristic
93C42×C11C4211yescharacteristic
94C42×C11C22⋊C411yescharacteristic
95C42×C11C22⋊C411yescharacteristic
96C42×C11C22⋊C411yescharacteristic
97C42×C11C22⋊C411yescharacteristic
98C42×C11C22⋊C411yescharacteristic
99C42×C11C22⋊C411yescharacteristic
100C42×C11C4⋊C411yescharacteristic
101C42×C11C4⋊C411yescharacteristic
102C42×C11C4⋊C411yescharacteristic
103C42×C11C4⋊C411yescharacteristic
104C42×C11C22×C411yescharacteristic
105C42×C11C22×C411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108#2920C2×C1111yescharacteristic
109#2920C2×C1111yescharacteristic
110C2×#431C2×C1111yescharacteristic
111#1287C2×C1114yescomplemented
112C23×C11—22no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11#9511yescharacteristic
116C23×C11#9511yescharacteristic
117C23×C11C2×C4⋊C411yescharacteristic
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11#9511yescharacteristic
136C2×C4×C11#9511yescharacteristic
137C2×C4×C11#9511yescharacteristic
138C2×C4×C11#9511yescharacteristic
139C2×C4×C11#9511yescharacteristic
140C2×C4×C11#9511yescharacteristic
141C2×C4×C11#10814yes—
142C2×C4×C11C2×C4211yescharacteristic
143C2×C4×C11C2×C22⋊C411yescharacteristic
144C2×C4×C11C2×C22⋊C411yescharacteristic
145C2×C4×C11C2×C22⋊C411yescharacteristic
146C2×C4×C11C2×C4⋊C411yescharacteristic
147C2×C4×C11C2×C4⋊C411yescharacteristic
148C8×C11—44no—
149C8×C11—44no—
150C8×C11—44no—
151C22×C42C22×C1111yescharacteristic
152#432—21no—
153#432C4×C1112yes—
154#432C22×C1112yes—
155#432C22×C1112yes—
156#431—21no—
157#431—21no—
158#431—21no—
159#431—21no—
160#431—21no—
161#431C4×C1112yes—
162#431C4×C1112yes—
163#431C22×C1112yes—
164#423—21no—
165#423—21no—
166C2×C4⋊C8—21no—
167#407—21no—
168#407C4×C1112yes—
169C2×C22⋊C8—21no—
170C4×M16—21no—
171C4×M16C4×C1112yes—
172C2×C4×C8C4×C1112yes—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—44no—
182C22×C11#34112yes—
183C22×C11C2×#9511yescharacteristic
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11H(3,ℤ/4)12yes—
193C4×C11#34112yes—
194C4×C11#34412yes—
195C4×C11C2×#10812yes—
196C23×C4C2×C4×C1111yescharacteristic
197C23×C4D4×C1111yescharacteristic
198C23×C4Q8×C1111yescharacteristic
199C2×M16—22no—
200C2×M16—22no—
201C22×C8—22no—
202C2×C42C2×C4×C1111yescharacteristic
203C2×C42C2×C4×C1111yescharacteristic
204C2×C42C2×C4×C1111yescharacteristic
205C2×C42C2×C4×C1111yescharacteristic
206C2×C42C2×C4×C1111yescharacteristic
207C2×C42D4×C1111yescharacteristic
208C2×C42D4×C1111yescharacteristic
209C2×C42D4×C1111yescharacteristic
210C2×C42D4×C1111yescharacteristic
211C2×C42D4×C1111yescharacteristic
212C2×C42Q8×C1111yescharacteristic
213C2×C42C23×C1111yescharacteristic
214C4⋊C8—22no—
215C4⋊C8—22no—
216C4⋊C8—22no—
217C4⋊C8—22no—
218C4⋊C8—22no—
219C4⋊C8—22no—
220C22⋊C8—22no—
221C22⋊C8—22no—
222C22⋊C8—22no—
223C22⋊C8—22no—
224C22⋊C8—22no—
225C22⋊C8C2×C4×C1114yes—
226#97—22no—
227#97C2×C4×C1114yes—
228C4×C8—22no—
229C4×C8—22no—
230C4×C8—22no—
231C4×C8C2×C4×C1114yes—
232C2×C11—22no—
233C2×C11—41no—
234C2×C11—41no—
235C2×C11C2×H(3,ℤ/4)11yescharacteristic
236C2×C11C2×#34111yescharacteristic
237C2×C11C2×#34411yescharacteristic
238C24C11×C4⋊C411yescharacteristic
239C22×C4—24no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4C42×C1111yescharacteristic
243C22×C4C42×C1111yescharacteristic
244C22×C4C11×C22⋊C411yescharacteristic
245C22×C4C11×C22⋊C411yescharacteristic
246C22×C4C11×C22⋊C411yescharacteristic
247C22×C4C11×C22⋊C411yescharacteristic
248C22×C4C11×C22⋊C411yescharacteristic
249C22×C4C11×C22⋊C411yescharacteristic
250C22×C4C11×C4⋊C411yescharacteristic
251C22×C4C11×C4⋊C411yescharacteristic
252C22×C4C11×C4⋊C411yescharacteristic
253C22×C4C11×C4⋊C411yescharacteristic
254C22×C4C11×C4⋊C411yescharacteristic
255C22×C4C11×C4⋊C411yescharacteristic
256C22×C4C11×C4⋊C411yescharacteristic
257C22×C4C22×C4×C1111yescharacteristic
258C22×C4C2×D4×C1111yescharacteristic
259C22×C4C2×Q8×C1111yescharacteristic
260M16—44no—
261M16—44no—
262C2×C8—24no—
263C2×C8—24no—
264C2×C8—24no—
265C2×C8—44no—
266C42C42×C1111yescharacteristic
267C42C42×C1111yescharacteristic
268C42C11×C22⋊C411yescharacteristic
269C42C11×C22⋊C411yescharacteristic
270C42C11×C22⋊C411yescharacteristic
271C42C11×C22⋊C411yescharacteristic
272C42C11×C22⋊C411yescharacteristic
273C42C11×C22⋊C411yescharacteristic
274C42C11×C4⋊C411yescharacteristic
275C42C11×C4⋊C411yescharacteristic
276C42C11×C4⋊C411yescharacteristic
277C42C11×C4⋊C411yescharacteristic
278C42C22×C4×C1111yescharacteristic
279C42C22×C4×C1111yescharacteristic
280C42C2×D4×C1111yescharacteristic
281C42C2×D4×C1111yescharacteristic
282C11#796511yescharacteristic, direct product factor, Sylow
283C23—22no—
284C23—41no—
285C23—41no—
286C23C11×#9511yescharacteristic
287C23C11×#9511yescharacteristic
288C23C2×C11×C4⋊C411yescharacteristic
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4C11×#9511yescharacteristic
307C2×C4C11×#9511yescharacteristic
308C2×C4C11×#9511yescharacteristic
309C2×C4C11×#9511yescharacteristic
310C2×C4C11×#9511yescharacteristic
311C2×C4C11×#9511yescharacteristic
312C2×C4C11×#10814yes—
313C2×C4C2×C42×C1111yescharacteristic
314C2×C4C2×C11×C22⋊C411yescharacteristic
315C2×C4C2×C11×C22⋊C411yescharacteristic
316C2×C4C2×C11×C22⋊C411yescharacteristic
317C2×C4C2×C11×C4⋊C411yescharacteristic
318C2×C4C2×C11×C4⋊C411yescharacteristic
319C8—44no—
320C8—44no—
321C8—44no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—44no—
331C22C11×#34112yes—
332C22C2×C11×#9511yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4C11×H(3,ℤ/4)12yes—
342C4C11×#34112yes—
343C4C11×#34412yes—
344C4C2×C11×#10812yes—
345C2—22no—
346C2—41no—
347C2—41no—
348C2C2×C11×H(3,ℤ/4)11yescharacteristic
349C2C2×C11×#34111yescharacteristic
350C2C2×C11×#34411yescharacteristic
subgroupG/H
centerC2×C4×C11#95
commutatorC2×C4C2×C42×C11
Frattini, cosocleC2×C42C23×C11
socleC22×C11C2×#95
prime radicalC24×C11C4⋊C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1287C2semidirect
63. #7965C11direct (N × H)
111. #1287C2×C11semidirect
282. C11#7965direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29202
C2×C11×#4312
C11×#12872
#796511