Finite Group Databasebeta

← C22×C11×#354 #14610546

Subgroups — C22×C11×#354 #14610546

Order 2816.

1502 conjugacy classes of subgroups; only the 382 normal subgroups are shown.

normal subgroups only

This group has 1502 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×#99C212yesmaximal
3C2×C11×#354C2112yesmaximal, direct product factor
4C23×Q8×C11C411yescharacteristic, complemented
5C23×D4×C11C2211yescharacteristic
6C2×C11×#124—26no—
7C2×C11×#124C416yescomplemented
8C2×C11×#124C2216yes—
9C22×C11×C22⋊C4—22no—
10C22×C11×C22⋊C4—22no—
11C22×C42×C11C411yescharacteristic, complemented
12C2×C11×#99—26no—
13C2×C11×#99C22112yes—
14C11×#354C22116yesdirect product factor
15C25×C11D412yes—
16C22×Q8×C11—23no—
17C22×Q8×C11—43no—
18C22×Q8×C11—41no—
19C22×Q8×C11C2×C416yescomplemented
20C22×D4×C11—43no—
21C22×D4×C11—41no—
22C22×D4×C11C2×C413yes—
23C22×D4×C11D416yes—
24C22×D4×C11C2313yes—
25C23×C4×C11—21no—
26C23×C4×C11—21no—
27C23×C4×C11—42no—
28C23×C4×C11C2×C411yescharacteristic
29C11×#124—212no—
30C11×#124—212no—
31C11×#124C2×C4112yescomplemented
32C11×#124C2314yes—
33C2×C11×C22⋊C4—212no—
34C2×C11×C22⋊C4—212no—
35C2×C11×C22⋊C4—212no—
36C2×C11×C22⋊C4—46no—
37C2×C42×C11—23no—
38C2×C42×C11C2×C416yescomplemented
39C11×#99—212no—
40C11×#99C2318yes—
41C22×#354C1111yesmaximal, characteristic, direct product factor, Sylow
42C24×C11—22no—
43C24×C11—26no—
44C24×C11—48no—
45C24×C11C22⋊C416yes—
46C24×C11C22⋊C411yescharacteristic
47C24×C11C2×D416yes—
48C2×Q8×C11—26no—
49C2×Q8×C11—46no—
50C2×Q8×C11—46no—
51C2×Q8×C11—46no—
52C2×Q8×C11—46no—
53C2×Q8×C11C22×C414yescomplemented
54C2×D4×C11—43no—
55C2×D4×C11—43no—
56C2×D4×C11—46no—
57C2×D4×C11—46no—
58C2×D4×C11—43no—
59C2×D4×C11—43no—
60C2×D4×C11C22⋊C416yes—
61C2×D4×C11C22×C413yes—
62C2×D4×C11C2×D416yes—
63C2×D4×C11C2411yescharacteristic
64C22×C4×C11—23no—
65C22×C4×C11—21no—
66C22×C4×C11—26no—
67C22×C4×C11—26no—
68C22×C4×C11—44no—
69C22×C4×C11—43no—
70C22×C4×C11—41no—
71C22×C4×C11—412no—
72C22×C4×C11—88no—
73C22×C4×C11C22⋊C413yes—
74C22×C4×C11C22×C413yes—
75C11×C22⋊C4—224no—
76C11×C22⋊C4—28no—
77C11×C22⋊C4—28no—
78C11×C22⋊C4—412no—
79C42×C11—26no—
80C42×C11C22×C414yescomplemented
81C22×#124C2×C1111yescharacteristic
82C22×#99C2×C1112yes—
83C2×#354C2×C11112yesdirect product factor
84C23×C11—24no—
85C23×C11—26no—
86C23×C11—26no—
87C23×C11—26no—
88C23×C11—26no—
89C23×C11—412no—
90C23×C11—412no—
91C23×C11—48no—
92C23×C11—812no—
93C23×C11#9913yes—
94C23×C11#9911yescharacteristic
95C23×C11C2×C22⋊C413yes—
96C23×C11C2×C22⋊C416yes—
97C23×C11C22×D412yes—
98Q8×C11—44no—
99Q8×C11—412no—
100D4×C11—46no—
101D4×C11—43no—
102D4×C11—46no—
103D4×C11—41no—
104C2×C4×C11—23no—
105C2×C4×C11—23no—
106C2×C4×C11—23no—
107C2×C4×C11—23no—
108C2×C4×C11—24no—
109C2×C4×C11—24no—
110C2×C4×C11—412no—
111C2×C4×C11—46no—
112C2×C4×C11—46no—
113C2×C4×C11—48no—
114C2×C4×C11—824no—
115C2×C4×C11C2×C22⋊C413yes—
116C2×C4×C11C23×C411yescharacteristic
117C23×Q8C4×C1111yescharacteristic, complemented
118C23×D4C22×C1111yescharacteristic
119C2×#124—26no—
120C2×#124C4×C1116yescomplemented
121C2×#124C22×C1116yes—
122C22×C22⋊C4—22no—
123C22×C22⋊C4—22no—
124C22×C42C4×C1111yescharacteristic, complemented
125C2×#99—26no—
126C2×#99C22×C11112yes—
127#354C22×C11116yesdirect product factor
128C22×C11—26no—
129C22×C11—26no—
130C22×C11—22no—
131C22×C11—26no—
132C22×C11—46no—
133C22×C11—42no—
134C22×C11—412no—
135C22×C11—412no—
136C22×C11—86no—
137C22×C11—86no—
138C22×C11#35414yesdirect product factor
139C22×C11C2×#9913yes—
140C22×C11C2×#9913yes—
141C22×C11C22×C22⋊C411yescharacteristic
142C4×C11—23no—
143C4×C11—21no—
144C4×C11—44no—
145C4×C11—44no—
146C4×C11—88no—
147C25D4×C1112yes—
148C22×Q8—23no—
149C22×Q8—43no—
150C22×Q8—41no—
151C22×Q8C2×C4×C1116yescomplemented
152C22×D4—41no—
153C22×D4—43no—
154C22×D4C2×C4×C1113yes—
155C22×D4D4×C1116yes—
156C22×D4C23×C1113yes—
157C23×C4—21no—
158C23×C4—21no—
159C23×C4—42no—
160C23×C4C2×C4×C1111yescharacteristic
161#124—212no—
162#124—212no—
163#124C2×C4×C11112yescomplemented
164#124C23×C1114yes—
165C2×C22⋊C4—212no—
166C2×C22⋊C4—212no—
167C2×C22⋊C4—212no—
168C2×C22⋊C4—46no—
169C2×C42—23no—
170C2×C42C2×C4×C1116yescomplemented
171#99—212no—
172#99C23×C1118yes—
173C2×C11—21no—
174C2×C11—23no—
175C2×C11—42no—
176C2×C11—46no—
177C2×C11C2×#35416yesdirect product factor
178C2×C11C22×#9911yescharacteristic
179C24—22no—
180C24—26no—
181C24—48no—
182C24C11×C22⋊C411yescharacteristic
183C24C11×C22⋊C416yes—
184C24C2×D4×C1116yes—
185C2×Q8—26no—
186C2×Q8—46no—
187C2×Q8—46no—
188C2×Q8—46no—
189C2×Q8—46no—
190C2×Q8C22×C4×C1114yescomplemented
191C2×D4—43no—
192C2×D4—43no—
193C2×D4—46no—
194C2×D4—46no—
195C2×D4—43no—
196C2×D4—43no—
197C2×D4C11×C22⋊C416yes—
198C2×D4C22×C4×C1113yes—
199C2×D4C2×D4×C1116yes—
200C2×D4C24×C1111yescharacteristic
201C22×C4—23no—
202C22×C4—21no—
203C22×C4—26no—
204C22×C4—26no—
205C22×C4—44no—
206C22×C4—43no—
207C22×C4—41no—
208C22×C4—412no—
209C22×C4—88no—
210C22×C4C11×C22⋊C413yes—
211C22×C4C22×C4×C1113yes—
212C22⋊C4—224no—
213C22⋊C4—28no—
214C22⋊C4—28no—
215C22⋊C4—412no—
216C42—26no—
217C42C22×C4×C1114yescomplemented
218C11C22×#35411yescharacteristic, direct product factor, Sylow
219C23—24no—
220C23—26no—
221C23—26no—
222C23—26no—
223C23—26no—
224C23—412no—
225C23—412no—
226C23—48no—
227C23—812no—
228C23C11×#9913yes—
229C23C11×#9911yescharacteristic
230C23C2×C11×C22⋊C413yes—
231C23C2×C11×C22⋊C416yes—
232C23C22×D4×C1112yes—
233Q8—44no—
234Q8—412no—
235D4—46no—
236D4—43no—
237D4—46no—
238D4—41no—
239C2×C4—23no—
240C2×C4—23no—
241C2×C4—23no—
242C2×C4—23no—
243C2×C4—24no—
244C2×C4—24no—
245C2×C4—412no—
246C2×C4—46no—
247C2×C4—46no—
248C2×C4—48no—
249C2×C4—824no—
250C2×C4C2×C11×C22⋊C413yes—
251C2×C4C23×C4×C1111yescharacteristic
252C22—26no—
253C22—26no—
254C22—22no—
255C22—26no—
256C22—46no—
257C22—42no—
258C22—412no—
259C22—412no—
260C22—86no—
261C22—86no—
262C22C11×#35414yesdirect product factor
263C22C2×C11×#9913yes—
264C22C2×C11×#9913yes—
265C22C22×C11×C22⋊C411yescharacteristic
266C4—23no—
267C4—21no—
268C4—44no—
269C4—44no—
270C4—88no—
271C2—21no—
272C2—23no—
273C2—42no—
274C2—46no—
275C2C2×C11×#35416yesdirect product factor
276C2C22×C11×#9911yescharacteristic
subgroupG/H
center, socleC23×C11#99
commutatorC2×C4C23×C4×C11
Frattini, cosocleC2×D4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C11 ◁ C23×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#354C2direct (N × H)
4. C23×Q8×C11C4semidirect
7. C2×C11×#124C4semidirect
11. C22×C42×C11C4semidirect
14. C11×#354C22direct (N × H)
19. C22×Q8×C11C2×C4semidirect
31. C11×#124C2×C4semidirect
38. C2×C42×C11C2×C4semidirect
41. C22×#354C11direct (N × H)
53. C2×Q8×C11C22×C4semidirect
80. C42×C11C22×C4semidirect
83. C2×#354C2×C11direct (N × H)
117. C23×Q8C4×C11semidirect
120. C2×#124C4×C11semidirect
124. C22×C42C4×C11semidirect
127. #354C22×C11direct (N × H)
138. C22×C11#354direct (N × H)
151. C22×Q8C2×C4×C11semidirect
163. #124C2×C4×C11semidirect
170. C2×C42C2×C4×C11semidirect
177. C2×C11C2×#354direct (N × H)
190. C2×Q8C22×C4×C11semidirect
217. C42C22×C4×C11semidirect
218. C11C22×#354direct (N × H)
262. C22C11×#354direct (N × H)
275. C2C2×C11×#354direct (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×#992
C2×C11×#3542
C22×#35411