Finite Group Databasebeta

← C11×#11388 #14588581

Subgroups — C11×#11388 #14588581

Order 2816.

878 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#544C211yesmaximal, characteristic
2C11×#1742C211yesmaximal, characteristic
3C11×#1740C211yesmaximal, characteristic
4C11×#1736C212yesmaximal
5C11×#1733C212yesmaximal
6C22×C11×M16C2212yes—
7C11×#544—24no—
8C11×#544—24no—
9C2×C11×C4⋊Q8—21no—
10C2×C11×C4⋊Q8C412yescomplemented
11C2×C11×#125—21no—
12C2×C11×#125C412yescomplemented
13C2×C11×C22⋊Q8—22no—
14C2×C11×#117C2212yes—
15C2×C11×#117C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C11×#343—21no—
19C11×#343—21no—
20C11×#342—22no—
21C11×#340—24no—
22C11×#339—24no—
23C22×Q8×C11—22no—
24C23×C4×C11—21no—
25C23×C4×C11C2311yescharacteristic
26C2×C11×M16—22no—
27C2×C11×M16—22no—
28C2×C11×M16—22no—
29C2×C11×M16—22no—
30C2×C11×M16—22no—
31C2×C11×M16Q814yescomplemented
32C22×C8×C11—22no—
33C11×C4⋊Q8—28no—
34C11×C4⋊Q8—24no—
35C11×C4⋊Q8—24no—
36C11×#125—28no—
37C11×#125—24no—
38C11×#125—24no—
39C11×C22⋊Q8—216no—
40C11×#117—22no—
41C11×#117—22no—
42C11×#117—22no—
43C11×#117—22no—
44C11×#117—22no—
45C11×#117—22no—
46C11×#117D414yes—
47C11×#117Q814yescomplemented
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4C2×C412yes—
55C2×C11×C4⋊C4C2×C411yescharacteristic
56C2×C11×C4⋊C4C2×C411yescharacteristic
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4D414yes—
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4D412yes—
63C2×C42×C11—21no—
64C2×C42×C11—22no—
65C2×C42×C11C2×C412yes—
66#11388C1111yesmaximal, characteristic, direct product factor, Sylow
67C24×C11C2×D411yescharacteristic
68C2×Q8×C11—28no—
69C2×Q8×C11—84no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—22no—
73C22×C4×C11—24no—
74C22×C4×C11—42no—
75C22×C4×C11—82no—
76C22×C4×C11C22⋊C412yes—
77C22×C4×C11C22⋊C412yes—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D412yes—
80C22×C4×C11C2×D412yes—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×Q812yes—
83C22×C4×C11C2×Q812yes—
84C22×C4×C11#4112yes—
85C22×C4×C11#4112yes—
86C11×M16—24no—
87C11×M16—24no—
88C11×M16—42no—
89C11×M16—42no—
90C2×C8×C11—24no—
91C2×C8×C11—42no—
92C2×C8×C11—42no—
93C11×C4⋊C4—28no—
94C11×C4⋊C4—28no—
95C11×C4⋊C4—28no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—24no—
103C11×C4⋊C4—42no—
104C11×C4⋊C4C22⋊C414yes—
105C11×C4⋊C4C22⋊C412yes—
106C11×C4⋊C4C22⋊C412yes—
107C11×C22⋊C4—24no—
108C11×C22⋊C4—24no—
109C11×C22⋊C4—24no—
110C11×C22⋊C4—42no—
111C42×C11—22no—
112C42×C11—22no—
113C42×C11—24no—
114C42×C11—24no—
115C42×C11—42no—
116C2×#544C2×C1111yescharacteristic
117#1742C2×C1111yescharacteristic
118#1740C2×C1111yescharacteristic
119#1736C2×C1112yes—
120#1733C2×C1112yes—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11C2×C22⋊C411yescharacteristic
124C23×C11#12012yes—
125C23×C11C22⋊Q812yes—
126C23×C11#12411yescharacteristic
127C23×C11C4⋊Q811yescharacteristic
128Q8×C11—88no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—24no—
134C2×C4×C11—42no—
135C2×C4×C11—44no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—44no—
140C2×C4×C11—84no—
141C2×C4×C11—82no—
142C2×C4×C11—82no—
143C2×C4×C11C2×C22⋊C411yescharacteristic
144C2×C4×C11C2×C22⋊C411yescharacteristic
145C2×C4×C11C4×Q812yes—
146C2×C4×C11C4×Q812yes—
147C2×C4×C11#12012yes—
148C2×C4×C11C22⋊Q812yes—
149C2×C4×C11C22⋊Q812yes—
150C2×C4×C11C22⋊Q812yes—
151C2×C4×C11C22⋊Q812yes—
152C2×C4×C11C22⋊Q812yes—
153C2×C4×C11#12412yes—
154C2×C4×C11#12412yes—
155C2×C4×C11#12411yescharacteristic
156C2×C4×C11C4⋊Q812yes—
157C2×C4×C11C4⋊Q812yes—
158C2×C4×C11C4⋊Q811yescharacteristic
159C8×C11—44no—
160C22×M16C22×C1112yes—
161#544—24no—
162#544—24no—
163C2×C4⋊Q8—21no—
164C2×C4⋊Q8C4×C1112yescomplemented
165C2×#125—21no—
166C2×#125C4×C1112yescomplemented
167C2×C22⋊Q8—22no—
168C2×#117C22×C1112yes—
169C2×#117C22×C1111yescharacteristic
170C2×#117C22×C1111yescharacteristic
171C22×C4⋊C4C22×C1111yescharacteristic
172#343—21no—
173#343—21no—
174#342—22no—
175#340—24no—
176#339—24no—
177C22×C11—21no—
178C22×C11—22no—
179C22×C11—21no—
180C22×C11—22no—
181C22×C11—42no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11#37911yescharacteristic
185C22×C11#39111yescharacteristic
186C22×C11#39111yescharacteristic
187C22×C11#39312yes—
188C22×C11#39512yes—
189C4×C11—44no—
190C4×C11—42no—
191C4×C11—42no—
192C4×C11—42no—
193C4×C11—42no—
194C4×C11—84no—
195C4×C11#39112yes—
196C4×C11#39112yes—
197C4×C11#39312yes—
198C4×C11#39512yes—
199C22×Q8—22no—
200C23×C4—21no—
201C23×C4C23×C1111yescharacteristic
202C2×M16—22no—
203C2×M16—22no—
204C2×M16—22no—
205C2×M16—22no—
206C2×M16—22no—
207C2×M16Q8×C1114yescomplemented
208C22×C8—22no—
209C4⋊Q8—28no—
210C4⋊Q8—24no—
211C4⋊Q8—24no—
212#125—28no—
213#125—24no—
214#125—24no—
215C22⋊Q8—216no—
216#117—22no—
217#117—22no—
218#117—22no—
219#117—22no—
220#117—22no—
221#117—22no—
222#117D4×C1114yes—
223#117Q8×C1114yescomplemented
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4C2×C4×C1112yes—
231C2×C4⋊C4C2×C4×C1111yescharacteristic
232C2×C4⋊C4C2×C4×C1111yescharacteristic
233C2×C4⋊C4D4×C1111yescharacteristic
234C2×C4⋊C4D4×C1111yescharacteristic
235C2×C4⋊C4D4×C1114yes—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4D4×C1112yes—
239C2×C42—21no—
240C2×C42—22no—
241C2×C42C2×C4×C1112yes—
242C2×C11—22no—
243C2×C11—21no—
244C2×C11—21no—
245C2×C11—22no—
246C2×C11#144611yescharacteristic
247C2×C11#179511yescharacteristic
248C2×C11#179611yescharacteristic
249C24C2×D4×C1111yescharacteristic
250C2×Q8—28no—
251C2×Q8—84no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—24no—
256C22×C4—42no—
257C22×C4—82no—
258C22×C4C11×C22⋊C412yes—
259C22×C4C11×C22⋊C412yes—
260C22×C4C22×C4×C1111yescharacteristic
261C22×C4C2×D4×C1112yes—
262C22×C4C2×D4×C1112yes—
263C22×C4C2×D4×C1111yescharacteristic
264C22×C4C2×Q8×C1112yes—
265C22×C4C2×Q8×C1112yes—
266C22×C4C11×#4112yes—
267C22×C4C11×#4112yes—
268M16—24no—
269M16—24no—
270M16—42no—
271M16—42no—
272C2×C8—24no—
273C2×C8—42no—
274C2×C8—42no—
275C4⋊C4—28no—
276C4⋊C4—28no—
277C4⋊C4—28no—
278C4⋊C4—22no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—24no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—24no—
285C4⋊C4—42no—
286C4⋊C4C11×C22⋊C414yes—
287C4⋊C4C11×C22⋊C412yes—
288C4⋊C4C11×C22⋊C412yes—
289C22⋊C4—24no—
290C22⋊C4—24no—
291C22⋊C4—24no—
292C22⋊C4—42no—
293C42—22no—
294C42—22no—
295C42—24no—
296C42—24no—
297C42—42no—
298C11#1138811yescharacteristic, direct product factor, Sylow
299C23—41no—
300C23—41no—
301C23C2×C11×C22⋊C411yescharacteristic
302C23C11×#12012yes—
303C23C11×C22⋊Q812yes—
304C23C11×#12411yescharacteristic
305C23C11×C4⋊Q811yescharacteristic
306Q8—88no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—24no—
312C2×C4—42no—
313C2×C4—44no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—44no—
318C2×C4—84no—
319C2×C4—82no—
320C2×C4—82no—
321C2×C4C2×C11×C22⋊C411yescharacteristic
322C2×C4C2×C11×C22⋊C411yescharacteristic
323C2×C4C4×Q8×C1112yes—
324C2×C4C4×Q8×C1112yes—
325C2×C4C11×#12012yes—
326C2×C4C11×C22⋊Q812yes—
327C2×C4C11×C22⋊Q812yes—
328C2×C4C11×C22⋊Q812yes—
329C2×C4C11×C22⋊Q812yes—
330C2×C4C11×C22⋊Q812yes—
331C2×C4C11×#12412yes—
332C2×C4C11×#12412yes—
333C2×C4C11×#12411yescharacteristic
334C2×C4C11×C4⋊Q812yes—
335C2×C4C11×C4⋊Q812yes—
336C2×C4C11×C4⋊Q811yescharacteristic
337C8—44no—
338C22—21no—
339C22—22no—
340C22—21no—
341C22—22no—
342C22—42no—
343C22—41no—
344C22—41no—
345C22C11×#37911yescharacteristic
346C22C11×#39111yescharacteristic
347C22C11×#39111yescharacteristic
348C22C11×#39312yes—
349C22C11×#39512yes—
350C4—44no—
351C4—42no—
352C4—42no—
353C4—42no—
354C4—42no—
355C4—84no—
356C4C11×#39112yes—
357C4C11×#39112yes—
358C4C11×#39312yes—
359C4C11×#39512yes—
360C2—22no—
361C2—21no—
362C2—21no—
363C2—22no—
364C2C11×#144611yescharacteristic
365C2C11×#179511yescharacteristic
366C2C11×#179611yescharacteristic
subgroupG/H
center, socleC22×C11#379
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
10. C2×C11×C4⋊Q8C4semidirect
12. C2×C11×#125C4semidirect
31. C2×C11×M16Q8semidirect
47. C11×#117Q8semidirect
66. #11388C11direct (N × H)
164. C2×C4⋊Q8C4×C11semidirect
166. C2×#125C4×C11semidirect
207. C2×M16Q8×C11semidirect
223. #117Q8×C11semidirect
298. C11#11388direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5442
C11×#17422
C11×#17402
C11×#17362
C11×#17332
#1138811