Finite Group Databasebeta

← C11×#19265 #14596458

Subgroups — C11×#19265 #14596458

Order 2816.

606 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3170C211yesmaximal, characteristic
2C11×#3113C212yesmaximal
3C2×C8×Q8×C11C211yesmaximal, characteristic
4C11×#1680C214yesmaximal, complemented
5C11×#1674C212yesmaximal, complemented
6C11×#1670C212yesmaximal, complemented
7C11×#1568C211yesmaximal, characteristic
8C11×#1552C212yesmaximal
9C11×#533C2212yes—
10C2×C4×Q8×C11C2211yescharacteristic
11C11×#500C2211yescharacteristic
12C11×#494C2211yescharacteristic
13C11×#487C2212yes—
14C11×#483—22no—
15C11×#475C2214yes—
16C11×#467—21no—
17C11×#467—21no—
18C11×#462C2214yes—
19C11×#451—22no—
20C8×Q8×C11—21no—
21C8×Q8×C11—21no—
22C8×Q8×C11C2212yes—
23C8×Q8×C11C2212yes—
24C11×#441—24no—
25C4×C11×Q16—21no—
26C4×C11×Q16—21no—
27C11×#432C2212yes—
28C2×C11×C4⋊C8—21no—
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C4×C8×C11—21no—
31C2×C4×C8×C11C2211yescharacteristic
32C11×#335C2212yes—
33C11×#334C2212yes—
34C11×#332C2214yes—
35C11×#332C2214yes—
36C22×Q8×C11D411yescharacteristic
37C2×C11×Q16—24no—
38C2×C11×Q16—21no—
39C2×C11×Q16—21no—
40C22×C8×C11—21no—
41C22×C8×C11D411yescharacteristic
42C22×C8×C11D411yescharacteristic
43C11×C4⋊Q8C2312yes—
44C11×C4⋊Q8C2312yes—
45C11×#125—22no—
46C11×C22⋊Q8—22no—
47C11×C22⋊Q8—22no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C4×Q8×C11D412yes—
53C4×Q8×C11C2312yes—
54C11×#117—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59C11×#107—21no—
60C11×#107—21no—
61C11×#106—24no—
62C11×C4⋊C8—22no—
63C11×C4⋊C8—22no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8C2312yes—
66C11×C4⋊C8C2314yes—
67C11×#103—24no—
68C11×#103—22no—
69C11×#103—22no—
70C11×#103—24no—
71C11×C22⋊C8—22no—
72C11×#97—22no—
73C4×C8×C11—22no—
74C4×C8×C11—22no—
75C4×C8×C11D411yescharacteristic
76C4×C8×C11D411yescharacteristic
77C4×C8×C11C2311yescharacteristic
78C4×C8×C11C2311yescharacteristic
79#19265C1111yesmaximal, characteristic, direct product factor, Sylow
80C2×Q8×C11—24no—
81C2×Q8×C11—21no—
82C2×Q8×C11—22no—
83C2×Q8×C11—22no—
84C2×Q8×C11C2×D412yes—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C11×Q16—42no—
91C11×Q16—42no—
92C11×Q16—48no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—24no—
96C2×C8×C11—41no—
97C2×C8×C11—42no—
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C11×C4⋊C4—22no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—42no—
110C11×C4⋊C4—42no—
111C11×C4⋊C4C2×D412yes—
112C11×C22⋊C4—42no—
113C42×C11—22no—
114C42×C11—22no—
115C42×C11—42no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119C42×C11C2411yescharacteristic
120#3170C2×C1111yescharacteristic
121#3113C2×C1112yes—
122C2×C8×Q8C2×C1111yescharacteristic
123#1680C2×C1114yescomplemented
124#1674C2×C1112yescomplemented
125#1670C2×C1112yescomplemented
126#1568C2×C1111yescharacteristic
127#1552C2×C1112yes—
128C23×C11#12111yescharacteristic
129Q8×C11—24no—
130Q8×C11—22no—
131Q8×C11—44no—
132Q8×C11—42no—
133Q8×C11—42no—
134Q8×C11#13514yes—
135C2×C4×C11—24no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—22no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11C22×D411yescharacteristic
149C2×C4×C11C22×D411yescharacteristic
150C2×C4×C11C2×#4111yescharacteristic
151C8×C11—21no—
152C8×C11—21no—
153C8×C11—21no—
154C8×C11—44no—
155C8×C11—42no—
156C8×C11#13712yes—
157#533C22×C1112yes—
158C2×C4×Q8C22×C1111yescharacteristic
159#500C22×C1111yescharacteristic
160#494C22×C1111yescharacteristic
161#487C22×C1112yes—
162#483—22no—
163#475C22×C1114yes—
164#467—21no—
165#467—21no—
166#462C22×C1114yes—
167#451—22no—
168C8×Q8—21no—
169C8×Q8—21no—
170C8×Q8C22×C1112yes—
171C8×Q8C22×C1112yes—
172#441—24no—
173C4×Q16—21no—
174C4×Q16—21no—
175#432C22×C1112yes—
176C2×C4⋊C8—21no—
177C2×C4⋊C8C22×C1111yescharacteristic
178C2×C4×C8—21no—
179C2×C4×C8C22×C1111yescharacteristic
180#335C22×C1112yes—
181#334C22×C1112yes—
182#332C22×C1114yes—
183#332C22×C1114yes—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11#47312yes—
187C22×C11C2×#12111yescharacteristic
188C4×C11—21no—
189C4×C11—24no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—42no—
194C4×C11—82no—
195C4×C11—82no—
196C4×C11C2×#13512yes—
197C4×C11C2×#13711yescharacteristic
198C4×C11#57511yescharacteristic
199C22×Q8D4×C1111yescharacteristic
200C2×Q16—24no—
201C2×Q16—21no—
202C2×Q16—21no—
203C22×C8—21no—
204C22×C8D4×C1111yescharacteristic
205C22×C8D4×C1111yescharacteristic
206C4⋊Q8C23×C1112yes—
207C4⋊Q8C23×C1112yes—
208#125—22no—
209C22⋊Q8—22no—
210C22⋊Q8—22no—
211C4×Q8—21no—
212C4×Q8—21no—
213C4×Q8—22no—
214C4×Q8—22no—
215C4×Q8D4×C1112yes—
216C4×Q8C23×C1112yes—
217#117—22no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4D4×C1111yescharacteristic
220C2×C42—21no—
221C2×C42C23×C1111yescharacteristic
222#107—21no—
223#107—21no—
224#106—24no—
225C4⋊C8—22no—
226C4⋊C8—22no—
227C4⋊C8—21no—
228C4⋊C8C23×C1112yes—
229C4⋊C8C23×C1114yes—
230#103—24no—
231#103—22no—
232#103—22no—
233#103—24no—
234C22⋊C8—22no—
235#97—22no—
236C4×C8—22no—
237C4×C8—22no—
238C4×C8D4×C1111yescharacteristic
239C4×C8D4×C1111yescharacteristic
240C4×C8C23×C1111yescharacteristic
241C4×C8C23×C1111yescharacteristic
242C2×C11—22no—
243C2×C11#303711yescharacteristic
244C2×C11#305011yescharacteristic
245C2×C11C2×#47311yescharacteristic
246C2×Q8—24no—
247C2×Q8—21no—
248C2×Q8—22no—
249C2×Q8—22no—
250C2×Q8C2×D4×C1112yes—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4C2×D4×C1111yescharacteristic
254C22×C4C2×D4×C1111yescharacteristic
255C22×C4C11×#4111yescharacteristic
256Q16—42no—
257Q16—48no—
258Q16—42no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—24no—
262C2×C8—41no—
263C2×C8—42no—
264C2×C8C2×D4×C1111yescharacteristic
265C2×C8C2×D4×C1111yescharacteristic
266C2×C8C2×D4×C1111yescharacteristic
267C2×C8C2×D4×C1111yescharacteristic
268C4⋊C4—22no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4C2×D4×C1112yes—
278C22⋊C4—42no—
279C42—22no—
280C42—22no—
281C42—42no—
282C42C2×D4×C1111yescharacteristic
283C42C2×D4×C1111yescharacteristic
284C42C11×#4111yescharacteristic
285C42C24×C1111yescharacteristic
286C11#1926511yescharacteristic, direct product factor, Sylow
287C23C11×#12111yescharacteristic
288Q8—24no—
289Q8—22no—
290Q8—44no—
291Q8—42no—
292Q8—42no—
293Q8C11×#13514yes—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4C11×#12111yescharacteristic
305C2×C4C11×#12111yescharacteristic
306C2×C4C11×#12111yescharacteristic
307C2×C4C22×D4×C1111yescharacteristic
308C2×C4C22×D4×C1111yescharacteristic
309C2×C4C2×C11×#4111yescharacteristic
310C8—21no—
311C8—21no—
312C8—21no—
313C8—44no—
314C8—42no—
315C8C11×#13712yes—
316C22—21no—
317C22—21no—
318C22C11×#47312yes—
319C22C2×C11×#12111yescharacteristic
320C4—21no—
321C4—24no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4—82no—
327C4—82no—
328C4C2×C11×#13512yes—
329C4C2×C11×#13711yescharacteristic
330C4C11×#57511yescharacteristic
331C2—22no—
332C2C11×#303711yescharacteristic
333C2C11×#305011yescharacteristic
334C2C2×C11×#47311yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC23×C11#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1680C2semidirect
5. C11×#1674C2semidirect
6. C11×#1670C2semidirect
79. #19265C11direct (N × H)
123. #1680C2×C11semidirect
124. #1674C2×C11semidirect
125. #1670C2×C11semidirect
286. C11#19265direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31702
C11×#31132
C2×C8×Q8×C112
C11×#16802
C11×#16742
C11×#16702
C11×#15682
C11×#15522
#1926511