Finite Group Databasebeta

← C22×C11×#353 #14610545

Subgroups — C22×C11×#353 #14610545

Order 2816.

2062 conjugacy classes of subgroups; only the 382 normal subgroups are shown.

normal subgroups only

This group has 2062 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×#127C211yesmaximal, characteristic
2C22×C11×#99C212yesmaximal, complemented
3C2×C11×#353C2112yesmaximal, direct product factor
4C23×D4×C11—22no—
5C23×D4×C11C411yescharacteristic, complemented
6C23×D4×C11C2211yescharacteristic
7C2×C11×#127—26no—
8C2×C11×#127C416yescomplemented
9C2×C11×#127C2216yes—
10C22×C11×C22⋊C4—22no—
11C22×C42×C11C411yescharacteristic, complemented
12C2×C11×#99—26no—
13C2×C11×#99C22112yescomplemented
14C11×#353C22116yesdirect product factor
15C25×C11—21no—
16C25×C11D412yes—
17C22×D4×C11—212no—
18C22×D4×C11—212no—
19C22×D4×C11—23no—
20C22×D4×C11—43no—
21C22×D4×C11—41no—
22C22×D4×C11—43no—
23C22×D4×C11—41no—
24C22×D4×C11—416no—
25C22×D4×C11C2×C413yes—
26C22×D4×C11C2×C416yescomplemented
27C22×D4×C11D416yes—
28C22×D4×C11C2313yes—
29C23×C4×C11—21no—
30C23×C4×C11—42no—
31C23×C4×C11C2×C411yescharacteristic
32C11×#127—212no—
33C11×#127—212no—
34C11×#127C2×C4112yescomplemented
35C11×#127C2314yes—
36C2×C11×C22⋊C4—212no—
37C2×C11×C22⋊C4—46no—
38C2×C42×C11—23no—
39C2×C42×C11C2×C416yescomplemented
40C11×#99—212no—
41C11×#99C2318yescomplemented
42C22×#353C1111yesmaximal, characteristic, direct product factor, Sylow
43C24×C11—22no—
44C24×C11—26no—
45C24×C11—26no—
46C24×C11—48no—
47C24×C11—48no—
48C24×C11—43no—
49C24×C11—41no—
50C24×C11C22⋊C416yes—
51C24×C11C22⋊C411yescharacteristic
52C24×C11C2×D416yes—
53C2×D4×C11—224no—
54C2×D4×C11—28no—
55C2×D4×C11—26no—
56C2×D4×C11—43no—
57C2×D4×C11—43no—
58C2×D4×C11—46no—
59C2×D4×C11—46no—
60C2×D4×C11—43no—
61C2×D4×C11—43no—
62C2×D4×C11—448no—
63C2×D4×C11—448no—
64C2×D4×C11—46no—
65C2×D4×C11—46no—
66C2×D4×C11—46no—
67C2×D4×C11—46no—
68C2×D4×C11C22⋊C416yes—
69C2×D4×C11C22×C413yes—
70C2×D4×C11C22×C414yescomplemented
71C2×D4×C11C2×D416yes—
72C2×D4×C11C2411yescharacteristic
73C22×C4×C11—28no—
74C22×C4×C11—23no—
75C22×C4×C11—21no—
76C22×C4×C11—26no—
77C22×C4×C11—412no—
78C22×C4×C11—88no—
79C22×C4×C11C22⋊C413yes—
80C22×C4×C11C22×C413yes—
81C11×C22⋊C4—28no—
82C11×C22⋊C4—412no—
83C42×C11—26no—
84C42×C11C22×C414yescomplemented
85C22×#127C2×C1111yescharacteristic
86C22×#99C2×C1112yescomplemented
87C2×#353C2×C11112yesdirect product factor
88C23×C11—24no—
89C23×C11—26no—
90C23×C11—26no—
91C23×C11—26no—
92C23×C11—26no—
93C23×C11—24no—
94C23×C11—412no—
95C23×C11—412no—
96C23×C11—424no—
97C23×C11—48no—
98C23×C11—46no—
99C23×C11—46no—
100C23×C11—812no—
101C23×C11—812no—
102C23×C11—84no—
103C23×C11#9913yes—
104C23×C11#9911yescharacteristic
105C23×C11C2×C22⋊C413yes—
106C23×C11C2×C22⋊C416yes—
107C23×C11C22×D412yes—
108D4×C11—46no—
109D4×C11—43no—
110D4×C11—46no—
111D4×C11—41no—
112D4×C11—44no—
113D4×C11—448no—
114D4×C11—416no—
115D4×C11—412no—
116C2×C4×C11—224no—
117C2×C4×C11—24no—
118C2×C4×C11—23no—
119C2×C4×C11—23no—
120C2×C4×C11—23no—
121C2×C4×C11—23no—
122C2×C4×C11—48no—
123C2×C4×C11—824no—
124C2×C4×C11C2×C22⋊C413yes—
125C2×C4×C11C23×C411yescharacteristic
126C23×D4—22no—
127C23×D4C4×C1111yescharacteristic, complemented
128C23×D4C22×C1111yescharacteristic
129C2×#127—26no—
130C2×#127C4×C1116yescomplemented
131C2×#127C22×C1116yes—
132C22×C22⋊C4—22no—
133C22×C42C4×C1111yescharacteristic, complemented
134C2×#99—26no—
135C2×#99C22×C11112yescomplemented
136#353C22×C11116yesdirect product factor
137C22×C11—26no—
138C22×C11—26no—
139C22×C11—22no—
140C22×C11—26no—
141C22×C11—46no—
142C22×C11—42no—
143C22×C11—48no—
144C22×C11—412no—
145C22×C11—412no—
146C22×C11—44no—
147C22×C11—86no—
148C22×C11—86no—
149C22×C11—812no—
150C22×C11—812no—
151C22×C11#35314yesdirect product factor
152C22×C11C2×#9913yes—
153C22×C11C2×#9913yes—
154C22×C11C22×C22⋊C411yescharacteristic
155C4×C11—28no—
156C4×C11—23no—
157C4×C11—21no—
158C4×C11—88no—
159C25—21no—
160C25D4×C1112yes—
161C22×D4—212no—
162C22×D4—212no—
163C22×D4—23no—
164C22×D4—41no—
165C22×D4—43no—
166C22×D4—43no—
167C22×D4—41no—
168C22×D4—416no—
169C22×D4C2×C4×C1113yes—
170C22×D4C2×C4×C1116yescomplemented
171C22×D4D4×C1116yes—
172C22×D4C23×C1113yes—
173C23×C4—21no—
174C23×C4—42no—
175C23×C4C2×C4×C1111yescharacteristic
176#127—212no—
177#127—212no—
178#127C2×C4×C11112yescomplemented
179#127C23×C1114yes—
180C2×C22⋊C4—212no—
181C2×C22⋊C4—46no—
182C2×C42—23no—
183C2×C42C2×C4×C1116yescomplemented
184#99—212no—
185#99C23×C1118yescomplemented
186C2×C11—21no—
187C2×C11—23no—
188C2×C11—42no—
189C2×C11—46no—
190C2×C11—84no—
191C2×C11C2×#35316yesdirect product factor
192C2×C11C22×#9911yescharacteristic
193C24—22no—
194C24—26no—
195C24—26no—
196C24—48no—
197C24—48no—
198C24—43no—
199C24—41no—
200C24C11×C22⋊C411yescharacteristic
201C24C11×C22⋊C416yes—
202C24C2×D4×C1116yes—
203C2×D4—224no—
204C2×D4—28no—
205C2×D4—26no—
206C2×D4—43no—
207C2×D4—43no—
208C2×D4—46no—
209C2×D4—46no—
210C2×D4—43no—
211C2×D4—43no—
212C2×D4—46no—
213C2×D4—46no—
214C2×D4—448no—
215C2×D4—448no—
216C2×D4—46no—
217C2×D4—46no—
218C2×D4C11×C22⋊C416yes—
219C2×D4C22×C4×C1113yes—
220C2×D4C22×C4×C1114yescomplemented
221C2×D4C2×D4×C1116yes—
222C2×D4C24×C1111yescharacteristic
223C22×C4—28no—
224C22×C4—23no—
225C22×C4—21no—
226C22×C4—26no—
227C22×C4—412no—
228C22×C4—88no—
229C22×C4C11×C22⋊C413yes—
230C22×C4C22×C4×C1113yes—
231C22⋊C4—28no—
232C22⋊C4—412no—
233C42—26no—
234C42C22×C4×C1114yescomplemented
235C11C22×#35311yescharacteristic, direct product factor, Sylow
236C23—24no—
237C23—26no—
238C23—26no—
239C23—26no—
240C23—26no—
241C23—24no—
242C23—412no—
243C23—412no—
244C23—424no—
245C23—48no—
246C23—46no—
247C23—46no—
248C23—812no—
249C23—812no—
250C23—84no—
251C23C11×#9913yes—
252C23C11×#9911yescharacteristic
253C23C2×C11×C22⋊C413yes—
254C23C2×C11×C22⋊C416yes—
255C23C22×D4×C1112yes—
256D4—46no—
257D4—43no—
258D4—46no—
259D4—41no—
260D4—44no—
261D4—448no—
262D4—416no—
263D4—412no—
264C2×C4—224no—
265C2×C4—24no—
266C2×C4—23no—
267C2×C4—23no—
268C2×C4—23no—
269C2×C4—23no—
270C2×C4—48no—
271C2×C4—824no—
272C2×C4C2×C11×C22⋊C413yes—
273C2×C4C23×C4×C1111yescharacteristic
274C22—26no—
275C22—26no—
276C22—22no—
277C22—26no—
278C22—46no—
279C22—42no—
280C22—48no—
281C22—412no—
282C22—412no—
283C22—44no—
284C22—86no—
285C22—86no—
286C22—812no—
287C22—812no—
288C22C11×#35314yesdirect product factor
289C22C2×C11×#9913yes—
290C22C2×C11×#9913yes—
291C22C22×C11×C22⋊C411yescharacteristic
292C4—28no—
293C4—23no—
294C4—21no—
295C4—88no—
296C2—21no—
297C2—23no—
298C2—42no—
299C2—46no—
300C2—84no—
301C2C2×C11×#35316yesdirect product factor
302C2C22×C11×#9911yescharacteristic
subgroupG/H
center, socleC23×C11#99
commutatorC2×C4C23×C4×C11
Frattini, cosocleC2×D4C24×C11
prime radicalC22×C11×#127C2
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
2. C22×C11×#99C2semidirect
3. C2×C11×#353C2direct (N × H)
5. C23×D4×C11C4semidirect
8. C2×C11×#127C4semidirect
11. C22×C42×C11C4semidirect
13. C2×C11×#99C22semidirect
14. C11×#353C22direct (N × H)
26. C22×D4×C11C2×C4semidirect
34. C11×#127C2×C4semidirect
39. C2×C42×C11C2×C4semidirect
41. C11×#99C23semidirect
42. C22×#353C11direct (N × H)
70. C2×D4×C11C22×C4semidirect
84. C42×C11C22×C4semidirect
86. C22×#99C2×C11semidirect
87. C2×#353C2×C11direct (N × H)
127. C23×D4C4×C11semidirect
130. C2×#127C4×C11semidirect
133. C22×C42C4×C11semidirect
135. C2×#99C22×C11semidirect
136. #353C22×C11direct (N × H)
151. C22×C11#353direct (N × H)
170. C22×D4C2×C4×C11semidirect
178. #127C2×C4×C11semidirect
183. C2×C42C2×C4×C11semidirect
185. #99C23×C11semidirect
191. C2×C11C2×#353direct (N × H)
220. C2×D4C22×C4×C11semidirect
234. C42C22×C4×C11semidirect
235. C11C22×#353direct (N × H)
288. C22C11×#353direct (N × H)
301. C2C2×C11×#353direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1272
C22×C11×#992
C2×C11×#3532
C22×#35311