Finite Group Databasebeta

← C11×#10392 #14587585

Subgroups — C11×#10392 #14587585

Order 2816.

746 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 746 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2842C211yesmaximal, characteristic, complemented
2C11×#1781C211yesmaximal, characteristic
3C11×#1781C212yesmaximal
4C11×#1304C211yesmaximal, characteristic, complemented
5C11×#1304C212yesmaximal, complemented
6C23×D4×C11C2211yescharacteristic
7C2×C11×#99—24no—
8C2×C11×#99—22no—
9C11×#399—22no—
10C11×#396—24no—
11C11×#379C2212yes—
12C11×#379C2211yescharacteristic
13C11×#379C2211yescharacteristic
14C11×#379C2212yes—
15C25×C11Q811yescharacteristic
16C25×C11C2311yescharacteristic
17C22×D4×C11—22no—
18C22×D4×C11—21no—
19C22×D4×C11—22no—
20C22×D4×C11—21no—
21C22×D4×C11—44no—
22C23×C4×C11Q811yescharacteristic
23C2×C11×C4⋊C4—24no—
24C2×C11×C4⋊C4—22no—
25C2×C11×C22⋊C4—22no—
26C2×C11×C22⋊C4—21no—
27C2×C11×C22⋊C4—22no—
28C2×C11×C22⋊C4—22no—
29C2×C11×C22⋊C4—22no—
30C2×C11×C22⋊C4—22no—
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4D414yes—
34C2×C11×C22⋊C4D412yes—
35C11×#99—48no—
36C11×#99—44no—
37C11×#95—22no—
38#10392C1111yesmaximal, characteristic, direct product factor, Sylow
39C24×C11—22no—
40C24×C11—21no—
41C24×C11—42no—
42C24×C11—42no—
43C24×C11—82no—
44C24×C11—82no—
45C24×C11C2×D412yes—
46C24×C11C2×D411yescharacteristic
47C24×C11C2×Q811yescharacteristic
48C24×C11#4112yes—
49C24×C11#4111yescharacteristic
50C2×D4×C11—28no—
51C2×D4×C11—24no—
52C2×D4×C11—44no—
53C2×D4×C11—42no—
54C2×D4×C11—44no—
55C2×D4×C11—42no—
56C2×D4×C11—44no—
57C2×D4×C11—42no—
58C2×D4×C11—41no—
59C2×D4×C11—42no—
60C2×D4×C11—41no—
61C22×C4×C11—22no—
62C22×C4×C11—21no—
63C22×C4×C11—22no—
64C22×C4×C11—24no—
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11—41no—
68C11×C4⋊C4—84no—
69C11×C4⋊C4—82no—
70C11×C22⋊C4—44no—
71C11×C22⋊C4—42no—
72C11×C22⋊C4—44no—
73C11×C22⋊C4—42no—
74C11×C22⋊C4—82no—
75C11×C22⋊C4—82no—
76C11×C22⋊C4—82no—
77C11×C22⋊C4—82no—
78C11×C22⋊C4—82no—
79C11×C22⋊C4—82no—
80#2842C2×C1111yescharacteristic, complemented
81#1781C2×C1111yescharacteristic
82#1781C2×C1112yes—
83#1304C2×C1111yescharacteristic, complemented
84#1304C2×C1112yescomplemented
85C23×C11—24no—
86C23×C11—22no—
87C23×C11—24no—
88C23×C11—22no—
89C23×C11—41no—
90C23×C11—42no—
91C23×C11—42no—
92C23×C11—42no—
93C23×C11—42no—
94C23×C11—42no—
95C23×C11—42no—
96C23×C11—42no—
97C23×C11—42no—
98C23×C11—41no—
99C23×C11—42no—
100C23×C11—41no—
101C23×C11—41no—
102C23×C11—82no—
103C23×C11—82no—
104C23×C11—82no—
105C23×C11—88no—
106C23×C11—88no—
107C23×C11#12011yescharacteristic
108C23×C11C22⋊Q812yes—
109C23×C11C22⋊Q811yescharacteristic
110C23×C11#12412yes—
111C23×C11#12411yescharacteristic
112D4×C11—48no—
113D4×C11—44no—
114D4×C11—44no—
115C2×C4×C11—24no—
116C2×C4×C11—22no—
117C2×C4×C11—42no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—44no—
121C2×C4×C11—44no—
122C2×C4×C11—44no—
123C2×C4×C11—44no—
124C2×C4×C11—42no—
125C2×C4×C11—82no—
126C2×C4×C11—81no—
127C2×C4×C11—82no—
128C2×C4×C11—82no—
129C2×C4×C11—82no—
130C23×D4C22×C1111yescharacteristic
131C2×#99—24no—
132C2×#99—22no—
133#399—22no—
134#396—24no—
135#379C22×C1112yes—
136#379C22×C1111yescharacteristic
137#379C22×C1111yescharacteristic
138#379C22×C1112yes—
139C22×C11—22no—
140C22×C11—22no—
141C22×C11—21no—
142C22×C11—22no—
143C22×C11—21no—
144C22×C11—22no—
145C22×C11—22no—
146C22×C11—22no—
147C22×C11—22no—
148C22×C11—22no—
149C22×C11—22no—
150C22×C11—44no—
151C22×C11—42no—
152C22×C11—84no—
153C22×C11—82no—
154C22×C11—82no—
155C22×C11—84no—
156C22×C11—84no—
157C22×C11—82no—
158C22×C11—84no—
159C22×C11—82no—
160C22×C11—82no—
161C22×C11#39311yescharacteristic
162C22×C11B(4,𝔽2)12yes—
163C4×C11—42no—
164C4×C11—82no—
165C4×C11—84no—
166C4×C11—162no—
167C4×C11—161no—
168C25Q8×C1111yescharacteristic
169C25C23×C1111yescharacteristic
170C22×D4—22no—
171C22×D4—21no—
172C22×D4—22no—
173C22×D4—21no—
174C22×D4—44no—
175C23×C4Q8×C1111yescharacteristic
176C2×C4⋊C4—24no—
177C2×C4⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—21no—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4—22no—
183C2×C22⋊C4—22no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4D4×C1114yes—
187C2×C22⋊C4D4×C1112yes—
188#99—48no—
189#99—44no—
190#95—22no—
191C2×C11—22no—
192C2×C11—42no—
193C2×C11—41no—
194C2×C11—42no—
195C2×C11—41no—
196C2×C11—82no—
197C2×C11#202911yescharacteristic
198C2×C11#203212yes—
199C24—22no—
200C24—21no—
201C24—42no—
202C24—42no—
203C24—82no—
204C24—82no—
205C24C2×D4×C1112yes—
206C24C2×D4×C1111yescharacteristic
207C24C2×Q8×C1111yescharacteristic
208C24C11×#4112yes—
209C24C11×#4111yescharacteristic
210C2×D4—28no—
211C2×D4—24no—
212C2×D4—44no—
213C2×D4—42no—
214C2×D4—44no—
215C2×D4—42no—
216C2×D4—44no—
217C2×D4—42no—
218C2×D4—41no—
219C2×D4—42no—
220C2×D4—41no—
221C22×C4—22no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—24no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—41no—
228C4⋊C4—84no—
229C4⋊C4—82no—
230C22⋊C4—44no—
231C22⋊C4—42no—
232C22⋊C4—44no—
233C22⋊C4—42no—
234C22⋊C4—82no—
235C22⋊C4—82no—
236C22⋊C4—82no—
237C22⋊C4—82no—
238C22⋊C4—82no—
239C22⋊C4—82no—
240C11#1039211yescharacteristic, direct product factor, Sylow
241C23—24no—
242C23—22no—
243C23—24no—
244C23—22no—
245C23—41no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23—42no—
250C23—42no—
251C23—42no—
252C23—42no—
253C23—42no—
254C23—41no—
255C23—42no—
256C23—41no—
257C23—41no—
258C23—82no—
259C23—82no—
260C23—82no—
261C23—88no—
262C23—88no—
263C23C11×#12011yescharacteristic
264C23C11×C22⋊Q812yes—
265C23C11×C22⋊Q811yescharacteristic
266C23C11×#12412yes—
267C23C11×#12411yescharacteristic
268D4—48no—
269D4—44no—
270D4—44no—
271C2×C4—24no—
272C2×C4—22no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—44no—
277C2×C4—44no—
278C2×C4—44no—
279C2×C4—44no—
280C2×C4—42no—
281C2×C4—82no—
282C2×C4—81no—
283C2×C4—82no—
284C2×C4—82no—
285C2×C4—82no—
286C22—22no—
287C22—22no—
288C22—21no—
289C22—22no—
290C22—21no—
291C22—22no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—44no—
298C22—42no—
299C22—84no—
300C22—82no—
301C22—82no—
302C22—84no—
303C22—84no—
304C22—82no—
305C22—84no—
306C22—82no—
307C22—82no—
308C22C11×#39311yescharacteristic
309C22C11×B(4,𝔽2)12yes—
310C4—42no—
311C4—82no—
312C4—84no—
313C4—162no—
314C4—161no—
315C2—22no—
316C2—42no—
317C2—41no—
318C2—42no—
319C2—41no—
320C2—82no—
321C2C11×#202911yescharacteristic
322C2C11×#203212yes—
subgroupG/H
center, socleC22×C11#393
commutator, Frattini, cosocleC25C23×C11
prime radicalC23×D4×C11C22
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2842C2semidirect
4. C11×#1304C2semidirect
5. C11×#1304C2semidirect
38. #10392C11direct (N × H)
80. #2842C2×C11semidirect
83. #1304C2×C11semidirect
84. #1304C2×C11semidirect
240. C11#10392direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28422
C11×#17812
C11×#13042
#1039211