Finite Group Databasebeta

← C11×#8914 #14586107

Subgroups — C11×#8914 #14586107

Order 2816.

468 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 134 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×#2379C211yesmaximal, characteristic
2C11×#1959C211yesmaximal, characteristic
3C11×#1836C212yesmaximal, complemented
4C2×C11×#329C211yesmaximal, characteristic
5C11×#1295C212yesmaximal, complemented
6C2×C11×#124C2211yescharacteristic
7C2×C11×#103—21no—
8C2×C11×#102—21no—
9C2×C11×#97C2211yescharacteristic
10C2×C11×#97C2212yes—
11C11×#391—21no—
12C11×#388—22no—
13C11×#386—21no—
14C11×#385—22no—
15C11×#384C2211yescharacteristic
16C11×#382C2212yes—
17C11×#340—22no—
18C11×#340—22no—
19C11×#329C414yescomplemented
20C22×Q8×C11D411yescharacteristic
21C22×D4×C11D411yescharacteristic
22C23×C4×C11—21no—
23C22×C8×C11—22no—
24C22×C8×C11—21no—
25C11×#124—22no—
26C11×#124C2×C412yes—
27C11×#124Q812yes—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4D412yes—
32C2×C11×C4⋊C4D412yes—
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4—21no—
36C2×C42×C11—21no—
37C2×C42×C11C2311yescharacteristic
38C11×#103—42no—
39C11×#102—42no—
40C11×#97—22no—
41C11×#97—22no—
42C11×#97C2×C414yescomplemented
43C11×#95—22no—
44C11×#95—22no—
45C11×#95—22no—
46#8914C1111yesmaximal, characteristic, direct product factor, Sylow
47C24×C11—21no—
48C2×Q8×C11—21no—
49C2×Q8×C11—41no—
50C2×Q8×C11—41no—
51C2×Q8×C11C4⋊C412yes—
52C2×D4×C11—21no—
53C2×D4×C11—41no—
54C2×D4×C11—41no—
55C2×D4×C11C4⋊C412yes—
56C22×C4×C11—21no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—41no—
60C22×C4×C11—81no—
61C22×C4×C11—82no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D412yes—
64C2×C8×C11—22no—
65C2×C8×C11—24no—
66C2×C8×C11—42no—
67C2×C8×C11—42no—
68C2×C8×C11—41no—
69C2×C8×C11—41no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—44no—
75C11×C4⋊C4—81no—
76C11×C22⋊C4—24no—
77C11×C22⋊C4—24no—
78C11×C22⋊C4—81no—
79C11×C22⋊C4—82no—
80C42×C11—81no—
81C42×C11C22×C411yescharacteristic
82C42×C11C2×Q811yescharacteristic
83C42×C11#4112yes—
84#2379C2×C1111yescharacteristic
85#1959C2×C1111yescharacteristic
86#1836C2×C1112yescomplemented
87C2×#329C2×C1111yescharacteristic
88#1295C2×C1112yescomplemented
89C23×C11—22no—
90C23×C11—41no—
91C23×C11—42no—
92C23×C11—42no—
93C23×C11—41no—
94C23×C11#12011yescharacteristic
95Q8×C11—42no—
96Q8×C11—81no—
97D4×C11—42no—
98D4×C11—81no—
99C2×C4×C11—21no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—21no—
103C2×C4×C11—22no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—84no—
113C2×C4×C11—81no—
114C2×C4×C11—82no—
115C2×C4×C11C2×C4⋊C411yescharacteristic
116C2×C4×C11C4×D412yes—
117C2×C4×C11C22⋊Q812yes—
118C2×C4×C11#12311yescharacteristic
119C8×C11—42no—
120C8×C11—44no—
121C2×#124C22×C1111yescharacteristic
122C2×#103—21no—
123C2×#102—21no—
124C2×#97C22×C1111yescharacteristic
125C2×#97C22×C1112yes—
126#391—21no—
127#388—22no—
128#386—21no—
129#385—22no—
130#384C22×C1111yescharacteristic
131#382C22×C1112yes—
132#340—22no—
133#340—22no—
134#329C4×C1114yescomplemented
135C22×C11—42no—
136C22×C11—44no—
137C22×C11—81no—
138C22×C11—81no—
139C22×C11—82no—
140C22×C11#38511yescharacteristic
141C22×C11#45311yescharacteristic
142C22×C11#45412yes—
143C22×C11#45511yescharacteristic
144C22×C11#45512yes—
145C4×C11—21no—
146C4×C11—21no—
147C4×C11—22no—
148C4×C11—22no—
149C4×C11—42no—
150C4×C11—82no—
151C4×C11—82no—
152C4×C11—161no—
153C22×Q8D4×C1111yescharacteristic
154C22×D4D4×C1111yescharacteristic
155C23×C4—21no—
156C22×C8—22no—
157C22×C8—21no—
158#124—22no—
159#124C2×C4×C1112yes—
160#124Q8×C1112yes—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4D4×C1112yes—
165C2×C4⋊C4D4×C1112yes—
166C2×C22⋊C4—22no—
167C2×C22⋊C4—22no—
168C2×C22⋊C4—21no—
169C2×C42—21no—
170C2×C42C23×C1111yescharacteristic
171#103—42no—
172#102—42no—
173#97—22no—
174#97—22no—
175#97C2×C4×C1114yescomplemented
176#95—22no—
177#95—22no—
178#95—22no—
179C2×C11—82no—
180C2×C11#165711yescharacteristic
181C2×C11#165911yescharacteristic
182C2×C11#166212yes—
183C2×C11#185611yescharacteristic
184C2×C11#186012yes—
185C24—21no—
186C2×Q8—21no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8C11×C4⋊C412yes—
190C2×D4—21no—
191C2×D4—41no—
192C2×D4—41no—
193C2×D4C11×C4⋊C412yes—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—41no—
198C22×C4—81no—
199C22×C4—82no—
200C22×C4C2×D4×C1111yescharacteristic
201C22×C4C2×D4×C1112yes—
202C2×C8—22no—
203C2×C8—24no—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—41no—
207C2×C8—41no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—44no—
213C4⋊C4—81no—
214C22⋊C4—24no—
215C22⋊C4—24no—
216C22⋊C4—81no—
217C22⋊C4—82no—
218C42—81no—
219C42C22×C4×C1111yescharacteristic
220C42C2×Q8×C1111yescharacteristic
221C42C11×#4112yes—
222C11#891411yescharacteristic, direct product factor, Sylow
223C23—22no—
224C23—41no—
225C23—42no—
226C23—42no—
227C23—41no—
228C23C11×#12011yescharacteristic
229Q8—42no—
230Q8—81no—
231D4—42no—
232D4—81no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—84no—
247C2×C4—81no—
248C2×C4—82no—
249C2×C4C2×C11×C4⋊C411yescharacteristic
250C2×C4C4×D4×C1112yes—
251C2×C4C11×C22⋊Q812yes—
252C2×C4C11×#12311yescharacteristic
253C8—42no—
254C8—44no—
255C22—42no—
256C22—44no—
257C22—81no—
258C22—81no—
259C22—82no—
260C22C11×#38511yescharacteristic
261C22C11×#45311yescharacteristic
262C22C11×#45412yes—
263C22C11×#45512yes—
264C22C11×#45511yescharacteristic
265C4—21no—
266C4—21no—
267C4—22no—
268C4—22no—
269C4—42no—
270C4—82no—
271C4—82no—
272C4—161no—
273C2—82no—
274C2C11×#165711yescharacteristic
275C2C11×#165911yescharacteristic
276C2C11×#166212yes—
277C2C11×#185611yescharacteristic
278C2C11×#186012yes—
subgroupG/H
center, socleC23×C11#120
commutatorC42C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1836C2semidirect
5. C11×#1295C2semidirect
19. C11×#329C4semidirect
42. C11×#97C2×C4semidirect
46. #8914C11direct (N × H)
86. #1836C2×C11semidirect
88. #1295C2×C11semidirect
134. #329C4×C11semidirect
175. #97C2×C4×C11semidirect
222. C11#8914direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23792
C11×#19592
C11×#18362
C2×C11×#3292
C11×#12952
#891411