Finite Group Databasebeta

← C11×#7962 #14585155

Subgroups — C11×#7962 #14585155

Order 2816.

608 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2920C211yesmaximal, characteristic
2C2×C11×#423C211yesmaximal, characteristic
3C11×#2283C211yesmaximal, characteristic
4C11×#1286C214yesmaximal, complemented
5C22×C11×M16—21no—
6C22×C42×C11C2211yescharacteristic
7C11×#432—21no—
8C11×#432—21no—
9C11×#431C412yescomplemented
10C11×#431C2212yes—
11C11×#423—21no—
12C11×#423—21no—
13C11×#423—21no—
14C11×#423C412yescomplemented
15C11×#423C2212yes—
16C2×C11×C4⋊C8—21no—
17C2×C11×C4⋊C8C412yescomplemented
18C11×#407—21no—
19C4×C11×M16C412yescomplemented
20C11×#383C412yes—
21C11×#382C2212yes—
22C11×#381—21no—
23C11×#380—21no—
24C4×C11×C4⋊C4—21no—
25C4×C11×C22⋊C4C412yes—
26C11×#376—21no—
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C2×C11×M16—22no—
31C2×C11×M16—22no—
32C2×C11×M16—22no—
33C2×C11×M16—44no—
34C22×C8×C11—22no—
35C2×C11×C4⋊C4—22no—
36C2×C11×C22⋊C4—22no—
37C2×C42×C11—22no—
38C2×C42×C11C2×C411yescharacteristic
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11C2×C411yescharacteristic
41C2×C42×C11C2×C411yescharacteristic
42C2×C42×C11C2×C411yescharacteristic
43C2×C42×C11D411yescharacteristic
44C2×C42×C11D411yescharacteristic
45C2×C42×C11D411yescharacteristic
46C2×C42×C11D411yescharacteristic
47C2×C42×C11Q811yescharacteristic
48C2×C42×C11Q811yescharacteristic
49C2×C42×C11C2311yescharacteristic
50C11×C4⋊C8—22no—
51C11×C4⋊C8—22no—
52C11×C4⋊C8—22no—
53C11×C4⋊C8—22no—
54C11×C4⋊C8—22no—
55C11×C4⋊C8C2×C414yes—
56C11×C22⋊C8—22no—
57C11×C22⋊C8—22no—
58C11×#97—22no—
59C4×C8×C11C2×C414yes—
60C11×#95—22no—
61C11×#95—22no—
62C11×#95—22no—
63C11×#95C2×C414yes—
64#7962C1111yesmaximal, characteristic, direct product factor, Sylow
65C24×C11C22⋊C411yescharacteristic
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—24no—
69C22×C4×C11—42no—
70C22×C4×C11—42no—
71C22×C4×C11C4211yescharacteristic
72C22×C4×C11C4211yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C4⋊C411yescharacteristic
81C22×C4×C11C4⋊C411yescharacteristic
82C22×C4×C11C4⋊C411yescharacteristic
83C22×C4×C11C4⋊C411yescharacteristic
84C22×C4×C11C4⋊C411yescharacteristic
85C22×C4×C11C4⋊C411yescharacteristic
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C11×M16—44no—
90C11×M16—44no—
91C11×M16—44no—
92C2×C8×C11—24no—
93C2×C8×C11—24no—
94C2×C8×C11—44no—
95C11×C4⋊C4—42no—
96C11×C4⋊C4—42no—
97C11×C22⋊C4—44no—
98C42×C11—44no—
99C42×C11C4211yescharacteristic
100C42×C11C4211yescharacteristic
101C42×C11C22⋊C411yescharacteristic
102C42×C11C22⋊C411yescharacteristic
103C42×C11C22⋊C411yescharacteristic
104C42×C11C22⋊C411yescharacteristic
105C42×C11C4⋊C411yescharacteristic
106C42×C11C4⋊C411yescharacteristic
107C42×C11C4⋊C411yescharacteristic
108C42×C11C4⋊C411yescharacteristic
109C42×C11C4⋊C411yescharacteristic
110C42×C11C4⋊C411yescharacteristic
111C42×C11C22×C411yescharacteristic
112C42×C11C22×C411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×Q811yescharacteristic
115#2920C2×C1111yescharacteristic
116C2×#423C2×C1111yescharacteristic
117#2283C2×C1111yescharacteristic
118#1286C2×C1114yescomplemented
119C23×C11—22no—
120C23×C11—22no—
121C23×C11—41no—
122C23×C11#9511yescharacteristic
123C23×C11#9511yescharacteristic
124C23×C11C2×C22⋊C411yescharacteristic
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—44no—
145C2×C4×C11—44no—
146C2×C4×C11—44no—
147C2×C4×C11#9511yescharacteristic
148C2×C4×C11#9511yescharacteristic
149C2×C4×C11#9511yescharacteristic
150C2×C4×C11#9511yescharacteristic
151C2×C4×C11#9511yescharacteristic
152C2×C4×C11#9511yescharacteristic
153C2×C4×C11C2×C4211yescharacteristic
154C2×C4×C11C2×C22⋊C411yescharacteristic
155C2×C4×C11C2×C22⋊C411yescharacteristic
156C2×C4×C11C2×C4⋊C411yescharacteristic
157C2×C4×C11C2×C4⋊C411yescharacteristic
158C2×C4×C11C2×C4⋊C411yescharacteristic
159C2×C4×C11AGL(1,ℤ/8)12yes—
160C2×C4×C11#13712yes—
161C8×C11—44no—
162C8×C11—44no—
163C22×M16—21no—
164C22×C42C22×C1111yescharacteristic
165#432—21no—
166#432—21no—
167#431C4×C1112yescomplemented
168#431C22×C1112yes—
169#423—21no—
170#423—21no—
171#423—21no—
172#423C4×C1112yescomplemented
173#423C22×C1112yes—
174C2×C4⋊C8—21no—
175C2×C4⋊C8C4×C1112yescomplemented
176#407—21no—
177C4×M16C4×C1112yescomplemented
178#383C4×C1112yes—
179#382C22×C1112yes—
180#381—21no—
181#380—21no—
182C4×C4⋊C4—21no—
183C4×C22⋊C4C4×C1112yes—
184#376—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—44no—
193C22×C11H(3,ℤ/4)12yes—
194C22×C11C2×#9511yescharacteristic
195C22×C11#41712yes—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—84no—
206C4×C11#34412yes—
207C4×C11#41811yescharacteristic
208C4×C11#41911yescharacteristic
209C4×C11#42812yes—
210C23×C4C2×C4×C1111yescharacteristic
211C23×C4D4×C1111yescharacteristic
212C23×C4D4×C1111yescharacteristic
213C2×M16—22no—
214C2×M16—22no—
215C2×M16—22no—
216C2×M16—44no—
217C22×C8—22no—
218C2×C4⋊C4—22no—
219C2×C22⋊C4—22no—
220C2×C42—22no—
221C2×C42C2×C4×C1111yescharacteristic
222C2×C42C2×C4×C1111yescharacteristic
223C2×C42C2×C4×C1111yescharacteristic
224C2×C42C2×C4×C1111yescharacteristic
225C2×C42C2×C4×C1111yescharacteristic
226C2×C42D4×C1111yescharacteristic
227C2×C42D4×C1111yescharacteristic
228C2×C42D4×C1111yescharacteristic
229C2×C42D4×C1111yescharacteristic
230C2×C42Q8×C1111yescharacteristic
231C2×C42Q8×C1111yescharacteristic
232C2×C42C23×C1111yescharacteristic
233C4⋊C8—22no—
234C4⋊C8—22no—
235C4⋊C8—22no—
236C4⋊C8—22no—
237C4⋊C8—22no—
238C4⋊C8C2×C4×C1114yes—
239C22⋊C8—22no—
240C22⋊C8—22no—
241#97—22no—
242C4×C8C2×C4×C1114yes—
243#95—22no—
244#95—22no—
245#95—22no—
246#95C2×C4×C1114yes—
247C2×C11—22no—
248C2×C11—22no—
249C2×C11—41no—
250C2×C11C2×H(3,ℤ/4)11yescharacteristic
251C2×C11#173611yescharacteristic
252C2×C11C2×#34411yescharacteristic
253C24C11×C22⋊C411yescharacteristic
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—24no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4C42×C1111yescharacteristic
260C22×C4C42×C1111yescharacteristic
261C22×C4C11×C22⋊C411yescharacteristic
262C22×C4C11×C22⋊C411yescharacteristic
263C22×C4C11×C22⋊C411yescharacteristic
264C22×C4C11×C22⋊C411yescharacteristic
265C22×C4C11×C22⋊C411yescharacteristic
266C22×C4C11×C22⋊C411yescharacteristic
267C22×C4C11×C22⋊C411yescharacteristic
268C22×C4C11×C4⋊C411yescharacteristic
269C22×C4C11×C4⋊C411yescharacteristic
270C22×C4C11×C4⋊C411yescharacteristic
271C22×C4C11×C4⋊C411yescharacteristic
272C22×C4C11×C4⋊C411yescharacteristic
273C22×C4C11×C4⋊C411yescharacteristic
274C22×C4C22×C4×C1111yescharacteristic
275C22×C4C2×D4×C1111yescharacteristic
276C22×C4C2×D4×C1111yescharacteristic
277M16—44no—
278M16—44no—
279M16—44no—
280C2×C8—24no—
281C2×C8—24no—
282C2×C8—44no—
283C4⋊C4—42no—
284C4⋊C4—42no—
285C22⋊C4—44no—
286C42—44no—
287C42C42×C1111yescharacteristic
288C42C42×C1111yescharacteristic
289C42C11×C22⋊C411yescharacteristic
290C42C11×C22⋊C411yescharacteristic
291C42C11×C22⋊C411yescharacteristic
292C42C11×C22⋊C411yescharacteristic
293C42C11×C4⋊C411yescharacteristic
294C42C11×C4⋊C411yescharacteristic
295C42C11×C4⋊C411yescharacteristic
296C42C11×C4⋊C411yescharacteristic
297C42C11×C4⋊C411yescharacteristic
298C42C11×C4⋊C411yescharacteristic
299C42C22×C4×C1111yescharacteristic
300C42C22×C4×C1111yescharacteristic
301C42C2×D4×C1111yescharacteristic
302C42C2×Q8×C1111yescharacteristic
303C11#796211yescharacteristic, direct product factor, Sylow
304C23—22no—
305C23—22no—
306C23—41no—
307C23C11×#9511yescharacteristic
308C23C11×#9511yescharacteristic
309C23C2×C11×C22⋊C411yescharacteristic
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—44no—
332C2×C4C11×#9511yescharacteristic
333C2×C4C11×#9511yescharacteristic
334C2×C4C11×#9511yescharacteristic
335C2×C4C11×#9511yescharacteristic
336C2×C4C11×#9511yescharacteristic
337C2×C4C11×#9511yescharacteristic
338C2×C4C2×C42×C1111yescharacteristic
339C2×C4C2×C11×C22⋊C411yescharacteristic
340C2×C4C2×C11×C22⋊C411yescharacteristic
341C2×C4C2×C11×C4⋊C411yescharacteristic
342C2×C4C2×C11×C4⋊C411yescharacteristic
343C2×C4C2×C11×C4⋊C411yescharacteristic
344C2×C4C11×AGL(1,ℤ/8)12yes—
345C2×C4C11×#13712yes—
346C8—44no—
347C8—44no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—44no—
356C22C11×H(3,ℤ/4)12yes—
357C22C2×C11×#9511yescharacteristic
358C22C11×#41712yes—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—84no—
369C4C11×#34412yes—
370C4C11×#41811yescharacteristic
371C4C11×#41911yescharacteristic
372C4C11×#42812yes—
373C2—22no—
374C2—22no—
375C2—41no—
376C2C2×C11×H(3,ℤ/4)11yescharacteristic
377C2C11×#173611yescharacteristic
378C2C2×C11×#34411yescharacteristic
subgroupG/H
center, socleC22×C11C2×#95
commutatorC2×C4C2×C42×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC24×C11C22⋊C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1286C2semidirect
9. C11×#431C4semidirect
14. C11×#423C4semidirect
17. C2×C11×C4⋊C8C4semidirect
19. C4×C11×M16C4semidirect
64. #7962C11direct (N × H)
118. #1286C2×C11semidirect
167. #431C4×C11semidirect
172. #423C4×C11semidirect
175. C2×C4⋊C8C4×C11semidirect
177. C4×M16C4×C11semidirect
303. C11#7962direct (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×#4232
C11×#22832
C11×#12862
#796211