Finite Group Databasebeta

← C22×C11×#355 #14610556

Subgroups — C22×C11×#355 #14610556

Order 2816.

1382 conjugacy classes of subgroups; only the 382 normal subgroups are shown.

normal subgroups only

This group has 1382 conjugacy classes of subgroups — too many to draw. Only its 382 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
1C22×C11×#124C211yesmaximal, characteristic
2C22×C11×#101C212yesmaximal, complemented
3C2×C11×#355C2112yesmaximal, direct product factor
4C23×Q8×C11C2211yescharacteristic
5C23×D4×C11C411yescharacteristic
6C22×C11×M16—22no—
7C2×C11×#124—26no—
8C2×C11×#124C416yes—
9C2×C11×#124C2216yes—
10C22×C11×C22⋊C4—22no—
11C22×C42×C11C411yescharacteristic
12C2×C11×#101—26no—
13C2×C11×#101C22112yescomplemented
14C11×#355C22116yesdirect product factor
15C25×C11—21no—
16C22×Q8×C11—43no—
17C22×Q8×C11—41no—
18C22×Q8×C11C2×C413yes—
19C22×Q8×C11D416yes—
20C22×Q8×C11C2313yes—
21C22×D4×C11—23no—
22C22×D4×C11—43no—
23C22×D4×C11—41no—
24C22×D4×C11C2×C416yes—
25C23×C4×C11—21no—
26C23×C4×C11C2×C411yescharacteristic
27C23×C4×C11D412yes—
28C2×C11×M16—212no—
29C2×C11×M16—46no—
30C22×C8×C11—42no—
31C11×#124—212no—
32C11×#124—212no—
33C11×#124C2×C4112yes—
34C11×#124C2314yes—
35C2×C11×C22⋊C4—212no—
36C2×C11×C22⋊C4—212no—
37C2×C42×C11—23no—
38C2×C42×C11C2×C416yes—
39C11×#101—212no—
40C11×#101C2318yescomplemented
41C22×#355C1111yesmaximal, characteristic, direct product factor, Sylow
42C24×C11—26no—
43C24×C11—48no—
44C24×C11—43no—
45C24×C11—41no—
46C24×C11C22⋊C411yescharacteristic
47C2×Q8×C11—43no—
48C2×Q8×C11—43no—
49C2×Q8×C11—46no—
50C2×Q8×C11—46no—
51C2×Q8×C11—43no—
52C2×Q8×C11—43no—
53C2×Q8×C11C22⋊C416yes—
54C2×Q8×C11C22×C413yes—
55C2×Q8×C11C2×D416yes—
56C2×Q8×C11C2411yescharacteristic
57C2×D4×C11—26no—
58C2×D4×C11—46no—
59C2×D4×C11—46no—
60C2×D4×C11—46no—
61C2×D4×C11—46no—
62C2×D4×C11C22×C414yes—
63C22×C4×C11—26no—
64C22×C4×C11—23no—
65C22×C4×C11—22no—
66C22×C4×C11—21no—
67C22×C4×C11—26no—
68C22×C4×C11—44no—
69C22×C4×C11C22⋊C413yes—
70C22×C4×C11C22⋊C416yes—
71C22×C4×C11C22×C413yes—
72C22×C4×C11C2×D416yes—
73C11×M16—28no—
74C11×M16—412no—
75C2×C8×C11—412no—
76C11×C22⋊C4—224no—
77C11×C22⋊C4—28no—
78C42×C11—26no—
79C42×C11C22×C414yes—
80C22×#124C2×C1111yescharacteristic
81C22×#101C2×C1112yescomplemented
82C2×#355C2×C11112yesdirect product factor
83C23×C11—24no—
84C23×C11—24no—
85C23×C11—424no—
86C23×C11—46no—
87C23×C11—46no—
88C23×C11—812no—
89C23×C11—84no—
90C23×C11#9913yes—
91C23×C11#9911yescharacteristic
92C23×C11C2×C22⋊C413yes—
93Q8×C11—46no—
94Q8×C11—43no—
95Q8×C11—46no—
96Q8×C11—41no—
97D4×C11—44no—
98D4×C11—412no—
99C2×C4×C11—26no—
100C2×C4×C11—26no—
101C2×C4×C11—23no—
102C2×C4×C11—23no—
103C2×C4×C11—26no—
104C2×C4×C11—26no—
105C2×C4×C11—23no—
106C2×C4×C11—23no—
107C2×C4×C11—24no—
108C2×C4×C11—412no—
109C2×C4×C11C2×C22⋊C413yes—
110C2×C4×C11C2×C22⋊C416yes—
111C2×C4×C11C23×C411yescharacteristic
112C2×C4×C11C22×D412yes—
113C8×C11—48no—
114C23×Q8C22×C1111yescharacteristic
115C23×D4C4×C1111yescharacteristic
116C22×M16—22no—
117C2×#124—26no—
118C2×#124C4×C1116yes—
119C2×#124C22×C1116yes—
120C22×C22⋊C4—22no—
121C22×C42C4×C1111yescharacteristic
122C2×#101—26no—
123C2×#101C22×C11112yescomplemented
124#355C22×C11116yesdirect product factor
125C22×C11—26no—
126C22×C11—26no—
127C22×C11—48no—
128C22×C11—44no—
129C22×C11—812no—
130C22×C11—812no—
131C22×C11#35514yesdirect product factor
132C22×C11C2×#9913yes—
133C22×C11C2×#9913yes—
134C22×C11C22×C22⋊C411yescharacteristic
135C4×C11—23no—
136C4×C11—26no—
137C4×C11—21no—
138C4×C11—22no—
139C4×C11—44no—
140C25—21no—
141C22×Q8—41no—
142C22×Q8—43no—
143C22×Q8C2×C4×C1113yes—
144C22×Q8D4×C1116yes—
145C22×Q8C23×C1113yes—
146C22×D4—23no—
147C22×D4—43no—
148C22×D4—41no—
149C22×D4C2×C4×C1116yes—
150C23×C4—21no—
151C23×C4C2×C4×C1111yescharacteristic
152C23×C4D4×C1112yes—
153C2×M16—212no—
154C2×M16—46no—
155C22×C8—42no—
156#124—212no—
157#124—212no—
158#124C2×C4×C11112yes—
159#124C23×C1114yes—
160C2×C22⋊C4—212no—
161C2×C22⋊C4—212no—
162C2×C42—23no—
163C2×C42C2×C4×C1116yes—
164#101—212no—
165#101C23×C1118yescomplemented
166C2×C11—21no—
167C2×C11—23no—
168C2×C11—84no—
169C2×C11C2×#35516yesdirect product factor
170C2×C11C22×#9911yescharacteristic
171C24—26no—
172C24—48no—
173C24—43no—
174C24—41no—
175C24C11×C22⋊C411yescharacteristic
176C2×Q8—43no—
177C2×Q8—43no—
178C2×Q8—46no—
179C2×Q8—46no—
180C2×Q8—43no—
181C2×Q8—43no—
182C2×Q8C11×C22⋊C416yes—
183C2×Q8C22×C4×C1113yes—
184C2×Q8C2×D4×C1116yes—
185C2×Q8C24×C1111yescharacteristic
186C2×D4—26no—
187C2×D4—46no—
188C2×D4—46no—
189C2×D4—46no—
190C2×D4—46no—
191C2×D4C22×C4×C1114yes—
192C22×C4—22no—
193C22×C4—26no—
194C22×C4—23no—
195C22×C4—21no—
196C22×C4—26no—
197C22×C4—44no—
198C22×C4C11×C22⋊C413yes—
199C22×C4C11×C22⋊C416yes—
200C22×C4C22×C4×C1113yes—
201C22×C4C2×D4×C1116yes—
202M16—28no—
203M16—412no—
204C2×C8—412no—
205C22⋊C4—224no—
206C22⋊C4—28no—
207C42—26no—
208C42C22×C4×C1114yes—
209C11C22×#35511yescharacteristic, direct product factor, Sylow
210C23—24no—
211C23—24no—
212C23—424no—
213C23—46no—
214C23—46no—
215C23—812no—
216C23—84no—
217C23C11×#9913yes—
218C23C11×#9911yescharacteristic
219C23C2×C11×C22⋊C413yes—
220Q8—46no—
221Q8—43no—
222Q8—46no—
223Q8—41no—
224D4—44no—
225D4—412no—
226C2×C4—26no—
227C2×C4—26no—
228C2×C4—23no—
229C2×C4—23no—
230C2×C4—26no—
231C2×C4—26no—
232C2×C4—23no—
233C2×C4—23no—
234C2×C4—24no—
235C2×C4—412no—
236C2×C4C2×C11×C22⋊C413yes—
237C2×C4C2×C11×C22⋊C416yes—
238C2×C4C23×C4×C1111yescharacteristic
239C2×C4C22×D4×C1112yes—
240C8—48no—
241C22—26no—
242C22—26no—
243C22—48no—
244C22—44no—
245C22—812no—
246C22—812no—
247C22C11×#35514yesdirect product factor
248C22C2×C11×#9913yes—
249C22C2×C11×#9913yes—
250C22C22×C11×C22⋊C411yescharacteristic
251C4—22no—
252C4—23no—
253C4—26no—
254C4—21no—
255C4—44no—
256C2—21no—
257C2—23no—
258C2—84no—
259C2C2×C11×#35516yesdirect product factor
260C2C22×C11×#9911yescharacteristic
subgroupG/H
center, socleC23×C11#99
commutatorC2×C4C23×C4×C11
Frattini, cosocleC2×Q8C24×C11
prime radicalC23×D4×C11C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C11 ◁ C23×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×#101C2semidirect
3. C2×C11×#355C2direct (N × H)
13. C2×C11×#101C22semidirect
14. C11×#355C22direct (N × H)
40. C11×#101C23semidirect
41. C22×#355C11direct (N × H)
81. C22×#101C2×C11semidirect
82. C2×#355C2×C11direct (N × H)
123. C2×#101C22×C11semidirect
124. #355C22×C11direct (N × H)
131. C22×C11#355direct (N × H)
165. #101C23×C11semidirect
169. C2×C11C2×#355direct (N × H)
209. C11C22×#355direct (N × H)
247. C22C11×#355direct (N × H)
259. C2C2×C11×#355direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1242
C22×C11×#1012
C2×C11×#3552
C22×#35511