Finite Group Databasebeta

← C11×#23565 #14600758

Subgroups — C11×#23565 #14600758

Order 2816.

1334 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 1334 conjugacy classes of subgroups — too many to draw. Only its 366 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
1C2×C11×#543C211yesmaximal, characteristic
2C11×#2315C213yesmaximal
3C11×#2062C218yesmaximal, complemented
4C2×C11×#342C213yesmaximal
5C11×#543—26no—
6C11×#543C2214yes—
7C2×C11×C22⋊Q8—26no—
8C22×C11×C22⋊C4C2211yescharacteristic
9C22×C11×C22⋊C4C2213yes—
10C22×C11×C22⋊C4C2213yes—
11C11×#385—26no—
12C11×#385C22112yes—
13C11×#380—26no—
14C11×#342C22112yes—
15C25×C11C2311yescharacteristic
16C22×Q8×C11—22no—
17C23×C4×C11—23no—
18C23×C4×C11D416yes—
19C23×C4×C11C2312yes—
20C11×C22⋊Q8—224no—
21C11×C22⋊Q8—224no—
22C2×C11×C4⋊C4—26no—
23C2×C11×C4⋊C4—212no—
24C2×C11×C22⋊C4—23no—
25C2×C11×C22⋊C4—26no—
26C2×C11×C22⋊C4—26no—
27C2×C11×C22⋊C4—26no—
28C2×C11×C22⋊C4—23no—
29C2×C11×C22⋊C4—23no—
30C2×C11×C22⋊C4D416yes—
31C2×C11×C22⋊C4Q8112yescomplemented
32C2×C11×C22⋊C4C2316yes—
33C2×C11×C22⋊C4C2316yes—
34C11×#95—212no—
35#23565C1111yesmaximal, characteristic, direct product factor, Sylow
36C24×C11—82no—
37C24×C11C2×D413yes—
38C24×C11C2×D413yes—
39C24×C11C2×Q816yes—
40C24×C11#4112yes—
41C24×C11C2411yescharacteristic
42C2×Q8×C11—28no—
43C2×Q8×C11—84no—
44C22×C4×C11—26no—
45C22×C4×C11—26no—
46C22×C4×C11—26no—
47C22×C4×C11—212no—
48C22×C4×C11—26no—
49C22×C4×C11—82no—
50C22×C4×C11—86no—
51C22×C4×C11—86no—
52C22×C4×C11C2×D4112yes—
53C11×C4⋊C4—224no—
54C11×C4⋊C4—812no—
55C11×C22⋊C4—212no—
56C11×C22⋊C4—212no—
57C11×C22⋊C4—212no—
58C11×C22⋊C4—26no—
59C11×C22⋊C4—43no—
60C11×C22⋊C4—41no—
61C11×C22⋊C4C2×Q8112yescomplemented
62C2×#543C2×C1111yescharacteristic
63#2315C2×C1113yes—
64#2062C2×C1118yescomplemented
65C2×#342C2×C1113yes—
66C23×C11—46no—
67C23×C11—46no—
68C23×C11—42no—
69C23×C11—86no—
70C23×C11—82no—
71C23×C11#12013yes—
72C23×C11#12011yescharacteristic
73C23×C11C22⋊Q816yes—
74C23×C11C22⋊Q816yes—
75C23×C11C4⋊Q816yes—
76C23×C11C4⋊Q816yes—
77C23×C11C22×D413yes—
78C23×C11C22×Q813yes—
79C23×C11C2×#4111yescharacteristic
80Q8×C11—88no—
81C2×C4×C11—212no—
82C2×C4×C11—212no—
83C2×C4×C11—412no—
84C2×C4×C11—412no—
85C2×C4×C11—412no—
86C2×C4×C11—412no—
87C2×C4×C11—42no—
88C2×C4×C11—86no—
89C2×C4×C11—812no—
90#543—26no—
91#543C22×C1114yes—
92C2×C22⋊Q8—26no—
93C22×C22⋊C4C22×C1111yescharacteristic
94C22×C22⋊C4C22×C1113yes—
95C22×C22⋊C4C22×C1113yes—
96#385—26no—
97#385C22×C11112yes—
98#380—26no—
99#342C22×C11112yes—
100C22×C11—22no—
101C22×C11—26no—
102C22×C11—26no—
103C22×C11—46no—
104C22×C11—46no—
105C22×C11—46no—
106C22×C11—46no—
107C22×C11—43no—
108C22×C11—41no—
109C22×C11#39516yes—
110C22×C11#39512yes—
111C22×C11C2×#12011yescharacteristic
112C22×C11C2×C22⋊Q813yes—
113C22×C11C2×C4⋊Q813yes—
114C4×C11—412no—
115C4×C11—412no—
116C4×C11—82no—
117C25C23×C1111yescharacteristic
118C22×Q8—22no—
119C23×C4—23no—
120C23×C4D4×C1116yes—
121C23×C4C23×C1112yes—
122C22⋊Q8—224no—
123C22⋊Q8—224no—
124C2×C4⋊C4—26no—
125C2×C4⋊C4—212no—
126C2×C22⋊C4—26no—
127C2×C22⋊C4—26no—
128C2×C22⋊C4—23no—
129C2×C22⋊C4—26no—
130C2×C22⋊C4—23no—
131C2×C22⋊C4—23no—
132C2×C22⋊C4D4×C1116yes—
133C2×C22⋊C4Q8×C11112yescomplemented
134C2×C22⋊C4C23×C1116yes—
135C2×C22⋊C4C23×C1116yes—
136#95—212no—
137C2×C11—23no—
138C2×C11—23no—
139C2×C11—22no—
140C2×C11—26no—
141C2×C11C2×#39511yescharacteristic
142C2×C11#302612yes—
143C24—82no—
144C24C2×D4×C1113yes—
145C24C2×D4×C1113yes—
146C24C2×Q8×C1116yes—
147C24C11×#4112yes—
148C24C24×C1111yescharacteristic
149C2×Q8—28no—
150C2×Q8—84no—
151C22×C4—26no—
152C22×C4—26no—
153C22×C4—26no—
154C22×C4—212no—
155C22×C4—26no—
156C22×C4—82no—
157C22×C4—86no—
158C22×C4—86no—
159C22×C4C2×D4×C11112yes—
160C4⋊C4—224no—
161C4⋊C4—812no—
162C22⋊C4—212no—
163C22⋊C4—212no—
164C22⋊C4—212no—
165C22⋊C4—26no—
166C22⋊C4—43no—
167C22⋊C4—41no—
168C22⋊C4C2×Q8×C11112yescomplemented
169C11#2356511yescharacteristic, direct product factor, Sylow
170C23—46no—
171C23—46no—
172C23—42no—
173C23—86no—
174C23—82no—
175C23C11×#12013yes—
176C23C11×#12011yescharacteristic
177C23C11×C22⋊Q816yes—
178C23C11×C22⋊Q816yes—
179C23C11×C4⋊Q816yes—
180C23C11×C4⋊Q816yes—
181C23C22×D4×C1113yes—
182C23C22×Q8×C1113yes—
183C23C2×C11×#4111yescharacteristic
184Q8—88no—
185C2×C4—212no—
186C2×C4—212no—
187C2×C4—412no—
188C2×C4—412no—
189C2×C4—412no—
190C2×C4—412no—
191C2×C4—42no—
192C2×C4—86no—
193C2×C4—812no—
194C22—22no—
195C22—26no—
196C22—26no—
197C22—46no—
198C22—46no—
199C22—46no—
200C22—46no—
201C22—43no—
202C22—41no—
203C22C11×#39516yes—
204C22C11×#39512yes—
205C22C2×C11×#12011yescharacteristic
206C22C2×C11×C22⋊Q813yes—
207C22C2×C11×C4⋊Q813yes—
208C4—412no—
209C4—412no—
210C4—82no—
211C2—23no—
212C2—23no—
213C2—22no—
214C2—26no—
215C2C2×C11×#39511yescharacteristic
216C2C11×#302612yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC24C24×C11
prime radicalC25×C11C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2062C2semidirect
31. C2×C11×C22⋊C4Q8semidirect
35. #23565C11direct (N × H)
61. C11×C22⋊C4C2×Q8semidirect
64. #2062C2×C11semidirect
133. C2×C22⋊C4Q8×C11semidirect
168. C22⋊C4C2×Q8×C11semidirect
169. C11#23565direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5432
C11×#23152
C11×#20622
C2×C11×#3422
#2356511