Finite Group Databasebeta

← C11×#9394 #14586587

Subgroups — C11×#9394 #14586587

Order 2816.

506 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 154 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×#2982C211yesmaximal, characteristic
2C11×#2546C211yesmaximal, characteristic
3C11×#1801C211yesmaximal, characteristic
4C11×#1546C212yesmaximal
5C11×#1303C212yesmaximal
6C2×C11×C4⋊Q8—21no—
7C2×C11×C4⋊Q8C2211yescharacteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C8×Q8×C11—24no—
10C11×#431—22no—
11C11×#431C2212yes—
12C11×#423C2212yes—
13C2×C11×#101—21no—
14C11×#398C414yes—
15C11×#391—21no—
16C11×#389—22no—
17C4×C11×C4⋊C4C2211yescharacteristic
18C11×#343—21no—
19C11×#332—24no—
20C22×Q8×C11—21no—
21C22×Q8×C11D411yescharacteristic
22C2×C11×M16—22no—
23C11×C4⋊Q8—22no—
24C11×C4⋊Q8—22no—
25C11×C4⋊Q8—42no—
26C11×C4⋊Q8—42no—
27C4×Q8×C11—22no—
28C4×Q8×C11—22no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—24no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4C2×C412yes—
33C2×C11×C4⋊C4C2×C412yes—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C42×C11—21no—
36C2×C42×C11D412yes—
37C2×C42×C11C2311yescharacteristic
38C11×C4⋊C8—24no—
39C11×C4⋊C8—22no—
40C11×C4⋊C8—22no—
41C11×C4⋊C8D414yes—
42C11×#101—42no—
43C11×C22⋊C8—22no—
44C4×C8×C11—24no—
45C4×C8×C11—22no—
46C11×#95—24no—
47C11×#95C2×C412yes—
48#9394C1111yesmaximal, characteristic, direct product factor, Sylow
49C2×Q8×C11—22no—
50C2×Q8×C11—22no—
51C2×Q8×C11—42no—
52C2×Q8×C11—41no—
53C2×Q8×C11—41no—
54C2×Q8×C11—42no—
55C2×Q8×C11D812yes—
56C2×Q8×C11SD1612yes—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11C22⋊C412yes—
60C22×C4×C11C22⋊C412yes—
61C22×C4×C11C22×C411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C11×M16—42no—
65C11×M16—42no—
66C2×C8×C11—24no—
67C2×C8×C11—42no—
68C11×C4⋊C4—24no—
69C11×C4⋊C4—24no—
70C11×C4⋊C4—22no—
71C11×C4⋊C4—24no—
72C11×C4⋊C4—48no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C42×C11—22no—
76C42×C11—22no—
77C42×C11—41no—
78C42×C11—41no—
79C42×C11C2×D412yes—
80C42×C11#4112yes—
81#2982C2×C1111yescharacteristic
82#2546C2×C1111yescharacteristic
83#1801C2×C1111yescharacteristic
84#1546C2×C1112yes—
85#1303C2×C1112yes—
86C23×C11C2×C22⋊C411yescharacteristic
87Q8×C11—24no—
88Q8×C11—24no—
89Q8×C11—82no—
90Q8×C11—82no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—24no—
95C2×C4×C11—22no—
96C2×C4×C11—41no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11#10214yes—
104C2×C4×C11C4×D412yes—
105C2×C4×C11#12011yescharacteristic
106C2×C4×C11#12112yes—
107C2×C4×C11#12311yescharacteristic
108C2×C4×C11C2×D811yescharacteristic
109C2×C4×C11C2×SD1611yescharacteristic
110C2×C4×C11#13512yes—
111C8×C11—44no—
112C8×C11—82no—
113C2×C4⋊Q8—21no—
114C2×C4⋊Q8C22×C1111yescharacteristic
115C2×C4×Q8C22×C1111yescharacteristic
116C8×Q8—24no—
117#431—22no—
118#431C22×C1112yes—
119#423C22×C1112yes—
120C2×#101—21no—
121#398C4×C1114yes—
122#391—21no—
123#389—22no—
124C4×C4⋊C4C22×C1111yescharacteristic
125#343—21no—
126#332—24no—
127C22×C11—21no—
128C22×C11—21no—
129C22×C11#38611yescharacteristic
130C22×C11C2×#10211yescharacteristic
131C22×C11#41611yescharacteristic
132C4×C11—21no—
133C4×C11—24no—
134C4×C11—22no—
135C4×C11—44no—
136C4×C11—42no—
137C4×C11—82no—
138C4×C11#45612yes—
139C4×C11#46512yes—
140C4×C11#46612yes—
141C22×Q8—21no—
142C22×Q8D4×C1111yescharacteristic
143C2×M16—22no—
144C4⋊Q8—22no—
145C4⋊Q8—22no—
146C4⋊Q8—42no—
147C4⋊Q8—42no—
148C4×Q8—22no—
149C4×Q8—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—24no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4C2×C4×C1112yes—
154C2×C4⋊C4C2×C4×C1112yes—
155C2×C4⋊C4D4×C1111yescharacteristic
156C2×C42—21no—
157C2×C42D4×C1112yes—
158C2×C42C23×C1111yescharacteristic
159C4⋊C8—24no—
160C4⋊C8—22no—
161C4⋊C8—22no—
162C4⋊C8D4×C1114yes—
163#101—42no—
164C22⋊C8—22no—
165C4×C8—24no—
166C4×C8—22no—
167#95—24no—
168#95C2×C4×C1112yes—
169C2×C11—21no—
170C2×C11—21no—
171C2×C11#188611yescharacteristic
172C2×C11#189311yescharacteristic
173C2×C11#191511yescharacteristic
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—42no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—42no—
180C2×Q8C11×D812yes—
181C2×Q8C11×SD1612yes—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4C11×C22⋊C412yes—
185C22×C4C11×C22⋊C412yes—
186C22×C4C22×C4×C1111yescharacteristic
187C22×C4C2×D4×C1111yescharacteristic
188C22×C4C2×D4×C1111yescharacteristic
189M16—42no—
190M16—42no—
191C2×C8—24no—
192C2×C8—42no—
193C4⋊C4—24no—
194C4⋊C4—24no—
195C4⋊C4—22no—
196C4⋊C4—24no—
197C4⋊C4—48no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C42—22no—
201C42—22no—
202C42—41no—
203C42—41no—
204C42C2×D4×C1112yes—
205C42C11×#4112yes—
206C11#939411yescharacteristic, direct product factor, Sylow
207C23C2×C11×C22⋊C411yescharacteristic
208Q8—24no—
209Q8—24no—
210Q8—82no—
211Q8—82no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—24no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4C11×#10214yes—
225C2×C4C4×D4×C1112yes—
226C2×C4C11×#12011yescharacteristic
227C2×C4C11×#12112yes—
228C2×C4C11×#12311yescharacteristic
229C2×C4C2×C11×D811yescharacteristic
230C2×C4C2×C11×SD1611yescharacteristic
231C2×C4C11×#13512yes—
232C8—44no—
233C8—82no—
234C22—21no—
235C22—21no—
236C22C11×#38611yescharacteristic
237C22C2×C11×#10211yescharacteristic
238C22C11×#41611yescharacteristic
239C4—21no—
240C4—24no—
241C4—22no—
242C4—44no—
243C4—42no—
244C4—82no—
245C4C11×#45612yes—
246C4C11×#46512yes—
247C4C11×#46612yes—
248C2—21no—
249C2—21no—
250C2C11×#188611yescharacteristic
251C2C11×#189311yescharacteristic
252C2C11×#191511yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC23×C11C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
48. #9394C11direct (N × H)
206. C11#9394direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29822
C11×#25462
C11×#18012
C11×#15462
C11×#13032
#939411