Finite Group Databasebeta

← C11×#13298 #14590491

Subgroups — C11×#13298 #14590491

Order 2816.

556 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2542C211yesmaximal, characteristic
2C11×#1799C211yesmaximal, characteristic
3C4×C11×#99C211yesmaximal, characteristic
4C11×#1393C214yesmaximal
5C2×C11×C4⋊Q8C411yescharacteristic, complemented
6C2×C11×C22⋊Q8—21no—
7C2×C11×C22⋊Q8—21no—
8C2×C4×D4×C11C2211yescharacteristic
9C2×C11×#99C2212yes—
10C2×C11×#99C2212yes—
11C11×#399—21no—
12C11×#399—21no—
13C11×#390C2212yes—
14C11×#384C412yescomplemented
15C11×#380—21no—
16C4×C11×C4⋊C4C411yescharacteristic, complemented
17C4×C11×C22⋊C4—21no—
18C11×#342—21no—
19C11×#342—21no—
20C22×Q8×C11—21no—
21C22×D4×C11C2311yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C11×C4⋊Q8—41no—
25C11×C4⋊Q8—41no—
26C11×C22⋊Q8—44no—
27C11×C22⋊Q8—44no—
28C4×D4×C11—41no—
29C4×D4×C11—41no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4—22no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—41no—
35C2×C11×C4⋊C4C2×C412yes—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C22⋊C4—22no—
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4D411yescharacteristic
42C2×C11×C22⋊C4D411yescharacteristic
43C2×C42×C11—41no—
44C2×C42×C11C2×C411yescharacteristic
45C2×C42×C11C2×C412yes—
46C11×#99—22no—
47C11×#99—24no—
48C11×#99Q814yescomplemented
49C11×#95—21no—
50C11×#95—41no—
51C11×#95—41no—
52#13298C1111yesmaximal, characteristic, direct product factor, Sylow
53C24×C11C2×D411yescharacteristic
54C24×C11C2×D411yescharacteristic
55C2×Q8×C11—42no—
56C2×Q8×C11—42no—
57C2×Q8×C11—41no—
58C2×Q8×C11—41no—
59C2×D4×C11—41no—
60C2×D4×C11—41no—
61C2×D4×C11C2×Q812yes—
62C2×D4×C11#4112yes—
63C22×C4×C11—22no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—22no—
69C22×C4×C11—42no—
70C22×C4×C11—42no—
71C22×C4×C11—42no—
72C22×C4×C11—42no—
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22×C411yescharacteristic
78C11×C4⋊C4—24no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—44no—
81C11×C4⋊C4—44no—
82C11×C4⋊C4—42no—
83C11×C4⋊C4—42no—
84C11×C4⋊C4—82no—
85C11×C22⋊C4—24no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—44no—
89C11×C22⋊C4—44no—
90C11×C22⋊C4—42no—
91C11×C22⋊C4—42no—
92C11×C22⋊C4—42no—
93C42×C11—21no—
94C42×C11—21no—
95C42×C11—42no—
96C42×C11—82no—
97#2542C2×C1111yescharacteristic
98#1799C2×C1111yescharacteristic
99C4×#99C2×C1111yescharacteristic
100#1393C2×C1114yes—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11C2×C22⋊C411yescharacteristic
110C23×C11C22⋊Q812yes—
111C23×C11#12411yescharacteristic
112C23×C11C4⋊Q811yescharacteristic
113Q8×C11—82no—
114Q8×C11—82no—
115D4×C11—42no—
116D4×C11—42no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—22no—
120C2×C4×C11—24no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—44no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11—82no—
138C2×C4×C11—82no—
139C2×C4×C11—82no—
140C2×C4×C11—82no—
141C2×C4×C11—82no—
142C2×C4×C11#9911yescharacteristic
143C2×C4×C11#9911yescharacteristic
144C2×C4×C11C4×Q812yes—
145C2×C4⋊Q8C4×C1111yescharacteristic, complemented
146C2×C22⋊Q8—21no—
147C2×C22⋊Q8—21no—
148C2×C4×D4C22×C1111yescharacteristic
149C2×#99C22×C1112yes—
150C2×#99C22×C1112yes—
151#399—21no—
152#399—21no—
153#390C22×C1112yes—
154#384C4×C1112yescomplemented
155#380—21no—
156C4×C4⋊C4C4×C1111yescharacteristic, complemented
157C4×C22⋊C4—21no—
158#342—21no—
159#342—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—22no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—42no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—81no—
173C22×C11—81no—
174C22×C11#39111yescharacteristic
175C22×C11C2×#9911yescharacteristic
176C22×C11#41011yescharacteristic
177C4×C11—21no—
178C4×C11—22no—
179C4×C11—44no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11—84no—
184C4×C11—82no—
185C4×C11—162no—
186C4×C11#35312yes—
187C22×Q8—21no—
188C22×D4C23×C1111yescharacteristic
189C23×C4D4×C1111yescharacteristic
190C23×C4D4×C1111yescharacteristic
191C4⋊Q8—41no—
192C4⋊Q8—41no—
193C22⋊Q8—44no—
194C22⋊Q8—44no—
195C4×D4—41no—
196C4×D4—41no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—41no—
202C2×C4⋊C4C2×C4×C1112yes—
203C2×C4⋊C4C2×C4×C1111yescharacteristic
204C2×C22⋊C4—22no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4—22no—
207C2×C22⋊C4—22no—
208C2×C22⋊C4D4×C1111yescharacteristic
209C2×C22⋊C4D4×C1111yescharacteristic
210C2×C42—41no—
211C2×C42C2×C4×C1111yescharacteristic
212C2×C42C2×C4×C1112yes—
213#99—22no—
214#99—24no—
215#99Q8×C1114yescomplemented
216#95—21no—
217#95—41no—
218#95—41no—
219C2×C11—21no—
220C2×C11—21no—
221C2×C11—42no—
222C2×C11—41no—
223C2×C11—41no—
224C2×C11#199611yescharacteristic
225C2×C11C2×#35311yescharacteristic
226C2×C11#212911yescharacteristic
227C24C2×D4×C1111yescharacteristic
228C24C2×D4×C1111yescharacteristic
229C2×Q8—42no—
230C2×Q8—42no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×D4—41no—
234C2×D4—41no—
235C2×D4C2×Q8×C1112yes—
236C2×D4C11×#4112yes—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—22no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4C11×C22⋊C411yescharacteristic
248C22×C4C11×C22⋊C411yescharacteristic
249C22×C4C11×C22⋊C411yescharacteristic
250C22×C4C11×C22⋊C411yescharacteristic
251C22×C4C22×C4×C1111yescharacteristic
252C4⋊C4—24no—
253C4⋊C4—41no—
254C4⋊C4—42no—
255C4⋊C4—44no—
256C4⋊C4—44no—
257C4⋊C4—42no—
258C4⋊C4—82no—
259C22⋊C4—24no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—44no—
263C22⋊C4—44no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C42—21no—
268C42—21no—
269C42—42no—
270C42—82no—
271C11#1329811yescharacteristic, direct product factor, Sylow
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23C2×C11×C22⋊C411yescharacteristic
281C23C11×C22⋊Q812yes—
282C23C11×#12411yescharacteristic
283C23C11×C4⋊Q811yescharacteristic
284Q8—82no—
285Q8—82no—
286D4—42no—
287D4—42no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—24no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—44no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4C11×#9911yescharacteristic
314C2×C4C11×#9911yescharacteristic
315C2×C4C4×Q8×C1112yes—
316C22—21no—
317C22—21no—
318C22—22no—
319C22—21no—
320C22—21no—
321C22—42no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—81no—
329C22—81no—
330C22C11×#39111yescharacteristic
331C22C2×C11×#9911yescharacteristic
332C22C11×#41011yescharacteristic
333C4—21no—
334C4—22no—
335C4—44no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—84no—
340C4—82no—
341C4—162no—
342C4C11×#35312yes—
343C2—21no—
344C2—21no—
345C2—42no—
346C2—41no—
347C2—41no—
348C2C11×#199611yescharacteristic
349C2C2×C11×#35311yescharacteristic
350C2C11×#212911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC22×D4C23×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×C11×C4⋊Q8C4semidirect
14. C11×#384C4semidirect
16. C4×C11×C4⋊C4C4semidirect
48. C11×#99Q8semidirect
52. #13298C11direct (N × H)
145. C2×C4⋊Q8C4×C11semidirect
154. #384C4×C11semidirect
156. C4×C4⋊C4C4×C11semidirect
215. #99Q8×C11semidirect
271. C11#13298direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25422
C11×#17992
C4×C11×#992
C11×#13932
#1329811