Finite Group Databasebeta

← C11×#10388 #14587581

Subgroups — C11×#10388 #14587581

Order 2816.

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

normal subgroups only

This group has 594 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×#2608C211yesmaximal, characteristic, complemented
2C11×#1789C212yesmaximal
3C11×#1782C211yesmaximal, characteristic
4C11×#1306C211yesmaximal, characteristic, complemented
5C11×#1284C212yesmaximal, complemented
6C22×C11×#41C2211yescharacteristic
7C2×C11×#104—22no—
8C2×C11×#104—22no—
9C2×C11×#99—22no—
10C11×#407C2212yes—
11C11×#396—22no—
12C11×#389—22no—
13C11×#387—22no—
14C11×#381C2211yescharacteristic
15C11×#381C2211yescharacteristic
16C4×C11×C22⋊C4C2212yes—
17C2×C11×#41—22no—
18C2×C11×#41—22no—
19C2×C11×#41—44no—
20C22×Q8×C11Q811yescharacteristic
21C22×D4×C11—21no—
22C22×D4×C11Q811yescharacteristic
23C23×C4×C11—21no—
24C23×C4×C11C2311yescharacteristic
25C2×C11×M16—22no—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C22⋊C4—22no—
30C2×C11×C22⋊C4—21no—
31C2×C11×C22⋊C4D412yes—
32C2×C42×C11D412yes—
33C2×C42×C11D412yes—
34C11×#104—44no—
35C11×#104—44no—
36C11×#99—44no—
37C11×C22⋊C8—22no—
38C11×C22⋊C8—22no—
39C11×#95—22no—
40C11×#95—22no—
41C11×#95—22no—
42C11×#95—22no—
43#10388C1111yesmaximal, characteristic, direct product factor, Sylow
44C24×C11—21no—
45C24×C11C2×D411yescharacteristic
46C11×#41—24no—
47C11×#41—24no—
48C11×#41—42no—
49C11×#41—42no—
50C11×#41—44no—
51C11×#41—44no—
52C2×Q8×C11—22no—
53C2×Q8×C11—42no—
54C2×D4×C11—24no—
55C2×D4×C11—22no—
56C2×D4×C11—42no—
57C2×D4×C11—42no—
58C2×D4×C11—41no—
59C2×D4×C11—41no—
60C22×C4×C11—22no—
61C22×C4×C11—21no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11—42no—
68C22×C4×C11—41no—
69C22×C4×C11C2×D412yes—
70C22×C4×C11C2×Q811yescharacteristic
71C22×C4×C11#4112yes—
72C22×C4×C11#4111yescharacteristic
73C11×M16—42no—
74C11×M16—42no—
75C2×C8×C11—42no—
76C11×C4⋊C4—44no—
77C11×C4⋊C4—44no—
78C11×C4⋊C4—82no—
79C11×C22⋊C4—44no—
80C11×C22⋊C4—42no—
81C11×C22⋊C4—42no—
82C42×C11—42no—
83C42×C11—42no—
84#2608C2×C1111yescharacteristic, complemented
85#1789C2×C1112yes—
86#1782C2×C1111yescharacteristic
87#1306C2×C1111yescharacteristic, complemented
88#1284C2×C1112yescomplemented
89C23×C11—22no—
90C23×C11—22no—
91C23×C11—42no—
92C23×C11—41no—
93C23×C11—41no—
94C23×C11—82no—
95C23×C11#12011yescharacteristic
96C23×C11C22⋊Q811yescharacteristic
97C23×C11#12411yescharacteristic
98Q8×C11—24no—
99Q8×C11—42no—
100D4×C11—24no—
101D4×C11—42no—
102D4×C11—44no—
103D4×C11—44no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—24no—
107C2×C4×C11—22no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—42no—
111C2×C4×C11—44no—
112C2×C4×C11—44no—
113C2×C4×C11—42no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—81no—
124C2×C4×C11—82no—
125C2×C4×C11C22⋊Q812yes—
126C2×C4×C11#12412yes—
127C8×C11—82no—
128C22×#41C22×C1111yescharacteristic
129C2×#104—22no—
130C2×#104—22no—
131C2×#99—22no—
132#407C22×C1112yes—
133#396—22no—
134#389—22no—
135#387—22no—
136#381C22×C1111yescharacteristic
137#381C22×C1111yescharacteristic
138C4×C22⋊C4C22×C1112yes—
139C22×C11—22no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—22no—
143C22×C11—22no—
144C22×C11—42no—
145C22×C11—82no—
146C22×C11—82no—
147C22×C11—82no—
148C22×C11—82no—
149C22×C11#39311yescharacteristic
150C22×C11B(4,𝔽2)12yes—
151C4×C11—22no—
152C4×C11—22no—
153C4×C11—44no—
154C4×C11—42no—
155C4×C11—82no—
156C4×C11—82no—
157C4×C11—161no—
158C2×#41—22no—
159C2×#41—22no—
160C2×#41—44no—
161C22×Q8Q8×C1111yescharacteristic
162C22×D4—21no—
163C22×D4Q8×C1111yescharacteristic
164C23×C4—21no—
165C23×C4C23×C1111yescharacteristic
166C2×M16—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C22⋊C4—22no—
171C2×C22⋊C4—21no—
172C2×C22⋊C4D4×C1112yes—
173C2×C42D4×C1112yes—
174C2×C42D4×C1112yes—
175#104—44no—
176#104—44no—
177#99—44no—
178C22⋊C8—22no—
179C22⋊C8—22no—
180#95—22no—
181#95—22no—
182#95—22no—
183#95—22no—
184C2×C11—22no—
185C2×C11—41no—
186C2×C11—41no—
187C2×C11—82no—
188C2×C11#202911yescharacteristic
189C2×C11#203112yes—
190C24—21no—
191C24C2×D4×C1111yescharacteristic
192#41—24no—
193#41—24no—
194#41—42no—
195#41—42no—
196#41—44no—
197#41—44no—
198C2×Q8—22no—
199C2×Q8—42no—
200C2×D4—24no—
201C2×D4—22no—
202C2×D4—42no—
203C2×D4—42no—
204C2×D4—41no—
205C2×D4—41no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—41no—
215C22×C4C2×D4×C1112yes—
216C22×C4C2×Q8×C1111yescharacteristic
217C22×C4C11×#4112yes—
218C22×C4C11×#4111yescharacteristic
219M16—42no—
220M16—42no—
221C2×C8—42no—
222C4⋊C4—44no—
223C4⋊C4—44no—
224C4⋊C4—82no—
225C22⋊C4—44no—
226C22⋊C4—42no—
227C22⋊C4—42no—
228C42—42no—
229C42—42no—
230C11#1038811yescharacteristic, direct product factor, Sylow
231C23—22no—
232C23—22no—
233C23—42no—
234C23—41no—
235C23—41no—
236C23—82no—
237C23C11×#12011yescharacteristic
238C23C11×C22⋊Q811yescharacteristic
239C23C11×#12411yescharacteristic
240Q8—24no—
241Q8—42no—
242D4—24no—
243D4—42no—
244D4—44no—
245D4—44no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—24no—
249C2×C4—22no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—44no—
254C2×C4—44no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—81no—
266C2×C4—82no—
267C2×C4C11×C22⋊Q812yes—
268C2×C4C11×#12412yes—
269C8—82no—
270C22—22no—
271C22—21no—
272C22—21no—
273C22—22no—
274C22—22no—
275C22—42no—
276C22—82no—
277C22—82no—
278C22—82no—
279C22—82no—
280C22C11×#39311yescharacteristic
281C22C11×B(4,𝔽2)12yes—
282C4—22no—
283C4—22no—
284C4—44no—
285C4—42no—
286C4—82no—
287C4—82no—
288C4—161no—
289C2—22no—
290C2—41no—
291C2—41no—
292C2—82no—
293C2C11×#202911yescharacteristic
294C2C11×#203112yes—
subgroupG/H
center, socleC22×C11#393
commutator, Frattini, cosocleC23×C4C23×C11
prime radicalC22×C11×#41C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2608C2semidirect
4. C11×#1306C2semidirect
5. C11×#1284C2semidirect
43. #10388C11direct (N × H)
84. #2608C2×C11semidirect
87. #1306C2×C11semidirect
88. #1284C2×C11semidirect
230. C11#10388direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26082
C11×#17892
C11×#17822
C11×#13062
C11×#12842
#1038811