Finite Group Databasebeta

← C11×#7958 #14585151

Subgroups — C11×#7958 #14585151

Order 2816.

584 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2920C211yesmaximal, characteristic
2C2×C11×#431C211yesmaximal, characteristic
3C11×#2283C211yesmaximal, characteristic
4C11×#1286C214yesmaximal, complemented
5C22×C42×C11C2211yescharacteristic
6C11×#432—21no—
7C11×#432C412yescomplemented
8C11×#431—21no—
9C11×#431—21no—
10C11×#431—21no—
11C11×#431C412yescomplemented
12C11×#431C412yescomplemented
13C11×#431C2212yes—
14C11×#423C2212yes—
15C2×C11×C4⋊C8—21no—
16C11×#407—21no—
17C2×C11×C22⋊C8—21no—
18C4×C11×M16—21no—
19C2×C4×C8×C11C412yescomplemented
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—
31C22×C8×C11—22no—
32C2×C11×C4⋊C4—22no—
33C2×C11×C22⋊C4—22no—
34C2×C42×C11—22no—
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11C2×C411yescharacteristic
37C2×C42×C11C2×C411yescharacteristic
38C2×C42×C11C2×C411yescharacteristic
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×C42×C11D411yescharacteristic
44C2×C42×C11Q811yescharacteristic
45C2×C42×C11Q811yescharacteristic
46C2×C42×C11C2311yescharacteristic
47C11×C4⋊C8—22no—
48C11×C4⋊C8—22no—
49C11×C4⋊C8—22no—
50C11×C4⋊C8C2×C414yes—
51C11×C22⋊C8—22no—
52C11×C22⋊C8—22no—
53C11×C22⋊C8—22no—
54C11×C22⋊C8—22no—
55C11×#97—22no—
56C4×C8×C11—22no—
57C4×C8×C11—22no—
58C4×C8×C11C2×C414yes—
59C11×#95—22no—
60C11×#95—22no—
61C11×#95—22no—
62C11×#95C2×C414yes—
63#7958C1111yesmaximal, characteristic, direct product factor, Sylow
64C24×C11C22⋊C411yescharacteristic
65C22×C4×C11—24no—
66C22×C4×C11—24no—
67C22×C4×C11—42no—
68C22×C4×C11—42no—
69C22×C4×C11C4211yescharacteristic
70C22×C4×C11C4211yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C4⋊C411yescharacteristic
79C22×C4×C11C4⋊C411yescharacteristic
80C22×C4×C11C4⋊C411yescharacteristic
81C22×C4×C11C4⋊C411yescharacteristic
82C22×C4×C11C4⋊C411yescharacteristic
83C22×C4×C11C4⋊C411yescharacteristic
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C11×M16—44no—
88C2×C8×C11—24no—
89C2×C8×C11—24no—
90C2×C8×C11—44no—
91C11×C4⋊C4—44no—
92C11×C22⋊C4—44no—
93C42×C11—44no—
94C42×C11C4211yescharacteristic
95C42×C11C4211yescharacteristic
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×C11C4⋊C411yescharacteristic
105C42×C11C4⋊C411yescharacteristic
106C42×C11C22×C411yescharacteristic
107C42×C11C22×C411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×Q811yescharacteristic
110#2920C2×C1111yescharacteristic
111C2×#431C2×C1111yescharacteristic
112#2283C2×C1111yescharacteristic
113#1286C2×C1114yescomplemented
114C23×C11—22no—
115C23×C11—22no—
116C23×C11—41no—
117C23×C11#9511yescharacteristic
118C23×C11#9511yescharacteristic
119C23×C11C2×C22⋊C411yescharacteristic
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—22no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—44no—
138C2×C4×C11—44no—
139C2×C4×C11—44no—
140C2×C4×C11#9511yescharacteristic
141C2×C4×C11#9511yescharacteristic
142C2×C4×C11#9511yescharacteristic
143C2×C4×C11#9511yescharacteristic
144C2×C4×C11#9511yescharacteristic
145C2×C4×C11#9511yescharacteristic
146C2×C4×C11C2×C4211yescharacteristic
147C2×C4×C11C2×C22⋊C411yescharacteristic
148C2×C4×C11C2×C22⋊C411yescharacteristic
149C2×C4×C11C2×C4⋊C411yescharacteristic
150C2×C4×C11C2×C4⋊C411yescharacteristic
151C2×C4×C11C2×C4⋊C411yescharacteristic
152C2×C4×C11#13514yes—
153C8×C11—44no—
154C8×C11—44no—
155C22×C42C22×C1111yescharacteristic
156#432—21no—
157#432C4×C1112yescomplemented
158#431—21no—
159#431—21no—
160#431—21no—
161#431C4×C1112yescomplemented
162#431C4×C1112yescomplemented
163#431C22×C1112yes—
164#423C22×C1112yes—
165C2×C4⋊C8—21no—
166#407—21no—
167C2×C22⋊C8—21no—
168C4×M16—21no—
169C2×C4×C8C4×C1112yescomplemented
170#383C4×C1112yes—
171#382C22×C1112yes—
172#381—21no—
173#380—21no—
174C4×C4⋊C4—21no—
175C4×C22⋊C4C4×C1112yes—
176#376—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—44no—
185C22×C11H(3,ℤ/4)12yes—
186C22×C11C2×#9511yescharacteristic
187C22×C11#41612yes—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—84no—
198C4×C11#34412yes—
199C4×C11#41612yes—
200C4×C11#42712yes—
201C23×C4C2×C4×C1111yescharacteristic
202C23×C4D4×C1111yescharacteristic
203C23×C4D4×C1111yescharacteristic
204C2×M16—22no—
205C22×C8—22no—
206C2×C4⋊C4—22no—
207C2×C22⋊C4—22no—
208C2×C42—22no—
209C2×C42C2×C4×C1111yescharacteristic
210C2×C42C2×C4×C1111yescharacteristic
211C2×C42C2×C4×C1111yescharacteristic
212C2×C42C2×C4×C1111yescharacteristic
213C2×C42C2×C4×C1111yescharacteristic
214C2×C42D4×C1111yescharacteristic
215C2×C42D4×C1111yescharacteristic
216C2×C42D4×C1111yescharacteristic
217C2×C42D4×C1111yescharacteristic
218C2×C42Q8×C1111yescharacteristic
219C2×C42Q8×C1111yescharacteristic
220C2×C42C23×C1111yescharacteristic
221C4⋊C8—22no—
222C4⋊C8—22no—
223C4⋊C8—22no—
224C4⋊C8C2×C4×C1114yes—
225C22⋊C8—22no—
226C22⋊C8—22no—
227C22⋊C8—22no—
228C22⋊C8—22no—
229#97—22no—
230C4×C8—22no—
231C4×C8—22no—
232C4×C8C2×C4×C1114yes—
233#95—22no—
234#95—22no—
235#95—22no—
236#95C2×C4×C1114yes—
237C2×C11—22no—
238C2×C11—22no—
239C2×C11—41no—
240C2×C11C2×H(3,ℤ/4)11yescharacteristic
241C2×C11#173511yescharacteristic
242C2×C11C2×#34411yescharacteristic
243C24C11×C22⋊C411yescharacteristic
244C22×C4—24no—
245C22×C4—24no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4C42×C1111yescharacteristic
249C22×C4C42×C1111yescharacteristic
250C22×C4C11×C22⋊C411yescharacteristic
251C22×C4C11×C22⋊C411yescharacteristic
252C22×C4C11×C22⋊C411yescharacteristic
253C22×C4C11×C22⋊C411yescharacteristic
254C22×C4C11×C22⋊C411yescharacteristic
255C22×C4C11×C22⋊C411yescharacteristic
256C22×C4C11×C22⋊C411yescharacteristic
257C22×C4C11×C4⋊C411yescharacteristic
258C22×C4C11×C4⋊C411yescharacteristic
259C22×C4C11×C4⋊C411yescharacteristic
260C22×C4C11×C4⋊C411yescharacteristic
261C22×C4C11×C4⋊C411yescharacteristic
262C22×C4C11×C4⋊C411yescharacteristic
263C22×C4C22×C4×C1111yescharacteristic
264C22×C4C2×D4×C1111yescharacteristic
265C22×C4C2×D4×C1111yescharacteristic
266M16—44no—
267C2×C8—24no—
268C2×C8—24no—
269C2×C8—44no—
270C4⋊C4—44no—
271C22⋊C4—44no—
272C42—44no—
273C42C42×C1111yescharacteristic
274C42C42×C1111yescharacteristic
275C42C11×C22⋊C411yescharacteristic
276C42C11×C22⋊C411yescharacteristic
277C42C11×C22⋊C411yescharacteristic
278C42C11×C22⋊C411yescharacteristic
279C42C11×C4⋊C411yescharacteristic
280C42C11×C4⋊C411yescharacteristic
281C42C11×C4⋊C411yescharacteristic
282C42C11×C4⋊C411yescharacteristic
283C42C11×C4⋊C411yescharacteristic
284C42C11×C4⋊C411yescharacteristic
285C42C22×C4×C1111yescharacteristic
286C42C22×C4×C1111yescharacteristic
287C42C2×D4×C1111yescharacteristic
288C42C2×Q8×C1111yescharacteristic
289C11#795811yescharacteristic, direct product factor, Sylow
290C23—22no—
291C23—22no—
292C23—41no—
293C23C11×#9511yescharacteristic
294C23C11×#9511yescharacteristic
295C23C2×C11×C22⋊C411yescharacteristic
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—44no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4C11×#9511yescharacteristic
317C2×C4C11×#9511yescharacteristic
318C2×C4C11×#9511yescharacteristic
319C2×C4C11×#9511yescharacteristic
320C2×C4C11×#9511yescharacteristic
321C2×C4C11×#9511yescharacteristic
322C2×C4C2×C42×C1111yescharacteristic
323C2×C4C2×C11×C22⋊C411yescharacteristic
324C2×C4C2×C11×C22⋊C411yescharacteristic
325C2×C4C2×C11×C4⋊C411yescharacteristic
326C2×C4C2×C11×C4⋊C411yescharacteristic
327C2×C4C2×C11×C4⋊C411yescharacteristic
328C2×C4C11×#13514yes—
329C8—44no—
330C8—44no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—44no—
339C22C11×H(3,ℤ/4)12yes—
340C22C2×C11×#9511yescharacteristic
341C22C11×#41612yes—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—84no—
352C4C11×#34412yes—
353C4C11×#41612yes—
354C4C11×#42712yes—
355C2—22no—
356C2—22no—
357C2—41no—
358C2C2×C11×H(3,ℤ/4)11yescharacteristic
359C2C11×#173511yescharacteristic
360C2C2×C11×#34411yescharacteristic
subgroupG/H
centerC2×C4×C11#95
commutatorC2×C4C2×C42×C11
Frattini, cosocleC2×C42C23×C11
socleC22×C11C2×#95
prime radicalC24×C11C22⋊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×#1286C2semidirect
7. C11×#432C4semidirect
11. C11×#431C4semidirect
12. C11×#431C4semidirect
19. C2×C4×C8×C11C4semidirect
63. #7958C11direct (N × H)
113. #1286C2×C11semidirect
157. #432C4×C11semidirect
161. #431C4×C11semidirect
162. #431C4×C11semidirect
169. C2×C4×C8C4×C11semidirect
289. C11#7958direct (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×#22832
C11×#12862
#795811