Finite Group Databasebeta

← C11×#19211 #14596404

Subgroups — C11×#19211 #14596404

Order 2816.

570 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3249C212yesmaximal
2C11×#3160C211yesmaximal, characteristic
3C11×#2960C211yesmaximal, characteristic
4C11×#1692C214yesmaximal, complemented
5C11×#1676C212yesmaximal, complemented
6C11×#1674C212yesmaximal, complemented
7C2×C11×#335C211yesmaximal, characteristic
8C11×#1550C212yesmaximal
9C11×#533C2212yes—
10C11×#533C2211yescharacteristic
11C11×#500C2211yescharacteristic
12C11×#500C2211yescharacteristic
13C11×#499—21no—
14C11×#499—21no—
15C11×#498C2212yes—
16C11×#477—22no—
17C11×#477C2214yes—
18C11×#467—24no—
19C11×#462—22no—
20C11×#462C2214yes—
21C11×#446—21no—
22C11×#446C2212yes—
23C8×Q8×C11—21no—
24C8×Q8×C11C2212yes—
25C11×#427—21no—
26C11×#427—21no—
27C11×#424—21no—
28C11×#423C2211yescharacteristic
29C2×C11×C4⋊C8C2212yes—
30C11×#405—21no—
31C2×C4×C8×C11C2211yescharacteristic
32C11×#335C2212yes—
33C11×#335C2212yes—
34C11×#333C2214yes—
35C11×#332C2214yes—
36C2×C11×Q16—24no—
37C2×C11×M16—21no—
38C22×C8×C11—22no—
39C22×C8×C11D411yescharacteristic
40C22×C8×C11D411yescharacteristic
41C11×C4⋊Q8D411yescharacteristic
42C11×C4⋊Q8D411yescharacteristic
43C11×C4⋊Q8C2312yes—
44C11×C4⋊Q8C2312yes—
45C11×#125—22no—
46C11×#125—21no—
47C11×C22⋊Q8—21no—
48C11×C22⋊Q8—22no—
49C11×C22⋊Q8—22no—
50C11×C22⋊Q8D412yes—
51C4×Q8×C11—21no—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C4×Q8×C11C2312yes—
55C11×#117—21no—
56C11×#117—22no—
57C2×C42×C11C2311yescharacteristic
58C11×#107—21no—
59C11×#107—21no—
60C11×#107—21no—
61C11×#107—21no—
62C11×#107—24no—
63C11×#106—22no—
64C11×#106—22no—
65C11×C4⋊C8—22no—
66C11×C4⋊C8—22no—
67C11×C4⋊C8—22no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8C2312yes—
70C11×C4⋊C8C2314yes—
71C11×#103—24no—
72C11×#103—24no—
73C11×#97—22no—
74C4×C8×C11—22no—
75C4×C8×C11D411yescharacteristic
76C4×C8×C11D411yescharacteristic
77C4×C8×C11C2311yescharacteristic
78C4×C8×C11C2311yescharacteristic
79#19211C1111yesmaximal, characteristic, direct product factor, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—22no—
82C2×Q8×C11—22no—
83C2×Q8×C11C2×D412yes—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C11×Q16—84no—
88C11×M16—42no—
89C2×C8×C11—22no—
90C2×C8×C11—22no—
91C2×C8×C11—24no—
92C2×C8×C11—82no—
93C2×C8×C11Q1614yescomplemented
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—42no—
108C11×C4⋊C4—42no—
109C11×C4⋊C4C2×D412yes—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—42no—
112C42×C11—22no—
113C42×C11—42no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117C42×C11C2411yescharacteristic
118#3249C2×C1112yes—
119#3160C2×C1111yescharacteristic
120#2960C2×C1111yescharacteristic
121#1692C2×C1114yescomplemented
122#1676C2×C1112yescomplemented
123#1674C2×C1112yescomplemented
124C2×#335C2×C1111yescharacteristic
125#1550C2×C1112yes—
126C23×C11#12111yescharacteristic
127Q8×C11—22no—
128Q8×C11—22no—
129Q8×C11—42no—
130Q8×C11—42no—
131Q8×C11—42no—
132Q8×C11—82no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11C2×Q1612yes—
144C2×C4×C11#13712yes—
145C2×C4×C11C22×D411yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C2×#4111yescharacteristic
148C8×C11—21no—
149C8×C11—21no—
150C8×C11—42no—
151C8×C11—44no—
152C8×C11C2×Q1612yes—
153C8×C11C2×Q1612yes—
154#533C22×C1112yes—
155#533C22×C1111yescharacteristic
156#500C22×C1111yescharacteristic
157#500C22×C1111yescharacteristic
158#499—21no—
159#499—21no—
160#498C22×C1112yes—
161#477—22no—
162#477C22×C1114yes—
163#467—24no—
164#462—22no—
165#462C22×C1114yes—
166#446—21no—
167#446C22×C1112yes—
168C8×Q8—21no—
169C8×Q8C22×C1112yes—
170#427—21no—
171#427—21no—
172#424—21no—
173#423C22×C1111yescharacteristic
174C2×C4⋊C8C22×C1112yes—
175#405—21no—
176C2×C4×C8C22×C1111yescharacteristic
177#335C22×C1112yes—
178#335C22×C1112yes—
179#333C22×C1114yes—
180#332C22×C1114yes—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11#46212yes—
184C22×C11C2×#12111yescharacteristic
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—42no—
189C4×C11—42no—
190C4×C11—82no—
191C4×C11—82no—
192C4×C11#46212yes—
193C4×C11C22×Q1611yescharacteristic
194C4×C11C2×#13711yescharacteristic
195C4×C11#57611yescharacteristic
196C4×C11#57811yescharacteristic
197C2×Q16—24no—
198C2×M16—21no—
199C22×C8—22no—
200C22×C8D4×C1111yescharacteristic
201C22×C8D4×C1111yescharacteristic
202C4⋊Q8D4×C1111yescharacteristic
203C4⋊Q8D4×C1111yescharacteristic
204C4⋊Q8C23×C1112yes—
205C4⋊Q8C23×C1112yes—
206#125—22no—
207#125—21no—
208C22⋊Q8—21no—
209C22⋊Q8—22no—
210C22⋊Q8—22no—
211C22⋊Q8D4×C1112yes—
212C4×Q8—21no—
213C4×Q8—22no—
214C4×Q8—22no—
215C4×Q8C23×C1112yes—
216#117—21no—
217#117—22no—
218C2×C42C23×C1111yescharacteristic
219#107—21no—
220#107—21no—
221#107—21no—
222#107—21no—
223#107—24no—
224#106—22no—
225#106—22no—
226C4⋊C8—22no—
227C4⋊C8—22no—
228C4⋊C8—22no—
229C4⋊C8—21no—
230C4⋊C8C23×C1112yes—
231C4⋊C8C23×C1114yes—
232#103—24no—
233#103—24no—
234#97—22no—
235C4×C8—22no—
236C4×C8D4×C1111yescharacteristic
237C4×C8D4×C1111yescharacteristic
238C4×C8C23×C1111yescharacteristic
239C4×C8C23×C1111yescharacteristic
240C2×C11—22no—
241C2×C11C2×#46211yescharacteristic
242C2×C11#306111yescharacteristic
243C2×C11#306711yescharacteristic
244C2×Q8—21no—
245C2×Q8—22no—
246C2×Q8—22no—
247C2×Q8C2×D4×C1112yes—
248C22×C4C2×D4×C1111yescharacteristic
249C22×C4C2×D4×C1111yescharacteristic
250C22×C4C11×#4111yescharacteristic
251Q16—84no—
252M16—42no—
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—24no—
256C2×C8—82no—
257C2×C8C11×Q1614yescomplemented
258C2×C8C2×D4×C1111yescharacteristic
259C2×C8C2×D4×C1111yescharacteristic
260C2×C8C2×D4×C1111yescharacteristic
261C2×C8C2×D4×C1111yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4C2×D4×C1112yes—
274C22⋊C4—22no—
275C22⋊C4—42no—
276C42—22no—
277C42—42no—
278C42C2×D4×C1111yescharacteristic
279C42C2×D4×C1111yescharacteristic
280C42C11×#4111yescharacteristic
281C42C24×C1111yescharacteristic
282C11#1921111yescharacteristic, direct product factor, Sylow
283C23C11×#12111yescharacteristic
284Q8—22no—
285Q8—22no—
286Q8—42no—
287Q8—42no—
288Q8—42no—
289Q8—82no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4C11×#12111yescharacteristic
298C2×C4C11×#12111yescharacteristic
299C2×C4C11×#12111yescharacteristic
300C2×C4C2×C11×Q1612yes—
301C2×C4C11×#13712yes—
302C2×C4C22×D4×C1111yescharacteristic
303C2×C4C22×D4×C1111yescharacteristic
304C2×C4C2×C11×#4111yescharacteristic
305C8—21no—
306C8—21no—
307C8—42no—
308C8—44no—
309C8C2×C11×Q1612yes—
310C8C2×C11×Q1612yes—
311C22—21no—
312C22—21no—
313C22C11×#46212yes—
314C22C2×C11×#12111yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—42no—
319C4—42no—
320C4—82no—
321C4—82no—
322C4C11×#46212yes—
323C4C22×C11×Q1611yescharacteristic
324C4C2×C11×#13711yescharacteristic
325C4C11×#57611yescharacteristic
326C4C11×#57811yescharacteristic
327C2—22no—
328C2C2×C11×#46211yescharacteristic
329C2C11×#306111yescharacteristic
330C2C11×#306711yescharacteristic
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×#1692C2semidirect
5. C11×#1676C2semidirect
6. C11×#1674C2semidirect
79. #19211C11direct (N × H)
93. C2×C8×C11Q16semidirect
121. #1692C2×C11semidirect
122. #1676C2×C11semidirect
123. #1674C2×C11semidirect
257. C2×C8C11×Q16semidirect
282. C11#19211direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32492
C11×#31602
C11×#29602
C11×#16922
C11×#16762
C11×#16742
C2×C11×#3352
C11×#15502
#1921111