Finite Group Databasebeta

← C11×#11390 #14588583

Subgroups — C11×#11390 #14588583

Order 2816.

1358 conjugacy classes of subgroups; only the 270 normal subgroups are shown.

normal subgroups only

This group has 1358 conjugacy classes of subgroups — too many to draw. Only its 270 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
2C2×C11×#342C213yesmaximal
3C11×C22⋊#95C213yesmaximal
4C24×C4×C11C2211yescharacteristic
5C11×#543—26no—
6C11×#543C414yescomplemented
7C2×C11×C22⋊Q8—26no—
8C22×C11×C22⋊C4C2213yes—
9C22×C11×C22⋊C4C2213yes—
10C2×C11×#95—26no—
11C11×#342—26no—
12C25×C11C2311yescharacteristic
13C22×Q8×C11—22no—
14C23×C4×C11—23no—
15C23×C4×C11—23no—
16C23×C4×C11—23no—
17C23×C4×C11—44no—
18C23×C4×C11D416yes—
19C23×C4×C11Q812yescomplemented
20C11×C22⋊Q8—224no—
21C11×C22⋊Q8—224no—
22C2×C11×C4⋊C4—26no—
23C2×C11×C22⋊C4—26no—
24C2×C11×C22⋊C4—26no—
25C2×C11×C22⋊C4—26no—
26C2×C11×C22⋊C4—26no—
27C2×C11×C22⋊C4—23no—
28C2×C11×C22⋊C4C2×C416yes—
29C2×C11×C22⋊C4D416yes—
30C2×C11×C22⋊C4Q816yescomplemented
31C11×#95—412no—
32#11390C1111yesmaximal, characteristic, direct product factor, Sylow
33C24×C11—42no—
34C24×C11—42no—
35C24×C11C22×C411yescharacteristic
36C24×C11C2×D413yes—
37C24×C11C2×D413yes—
38C24×C11C2×Q813yes—
39C24×C11C2×Q811yescharacteristic
40C24×C11#4111yescharacteristic
41C24×C11#4113yes—
42C2×Q8×C11—28no—
43C2×Q8×C11—82no—
44C2×Q8×C11—82no—
45C22×C4×C11—212no—
46C22×C4×C11—26no—
47C22×C4×C11—26no—
48C22×C4×C11—26no—
49C22×C4×C11—26no—
50C22×C4×C11—44no—
51C22×C4×C11—412no—
52C22×C4×C11—46no—
53C22×C4×C11—41no—
54C22×C4×C11—43no—
55C22×C4×C11—46no—
56C22×C4×C11—46no—
57C22×C4×C11—46no—
58C22×C4×C11—46no—
59C22×C4×C11—43no—
60C22×C4×C11—43no—
61C22×C4×C11C22⋊C4112yes—
62C11×C4⋊C4—224no—
63C11×C22⋊C4—212no—
64C11×C22⋊C4—212no—
65C11×C22⋊C4—212no—
66C11×C22⋊C4—46no—
67C2×#543C2×C1111yescharacteristic
68C2×#342C2×C1113yes—
69C22⋊#95C2×C1113yes—
70C23×C11—26no—
71C23×C11—26no—
72C23×C11—41no—
73C23×C11—43no—
74C23×C11—42no—
75C23×C11—46no—
76C23×C11—46no—
77C23×C11—41no—
78C23×C11—42no—
79C23×C11—43no—
80C23×C11C2×C22⋊C413yes—
81C23×C11C4×Q813yes—
82C23×C11C4×Q811yescharacteristic
83C23×C11#12013yes—
84C23×C11#12011yescharacteristic
85C23×C11C22⋊Q813yes—
86C23×C11C22⋊Q813yes—
87C23×C11C22⋊Q816yes—
88C23×C11#12413yes—
89C23×C11#12413yes—
90C23×C11C4⋊Q813yes—
91C23×C11C4⋊Q813yes—
92Q8×C11—88no—
93C2×C4×C11—212no—
94C2×C4×C11—212no—
95C2×C4×C11—46no—
96C2×C4×C11—412no—
97C2×C4×C11—42no—
98C2×C4×C11—44no—
99C2×C4×C11—46no—
100C2×C4×C11—46no—
101C2×C4×C11—412no—
102C2×C4×C11—412no—
103C2×C4×C11—46no—
104C2×C4×C11—86no—
105C2×C4×C11—83no—
106C2×C4×C11—83no—
107C2×C4×C11—86no—
108C24×C4C22×C1111yescharacteristic
109#543—26no—
110#543C4×C1114yescomplemented
111C2×C22⋊Q8—26no—
112C22×C22⋊C4C22×C1113yes—
113C22×C22⋊C4C22×C1113yes—
114C2×#95—26no—
115#342—26no—
116C22×C11—26no—
117C22×C11—26no—
118C22×C11—23no—
119C22×C11—23no—
120C22×C11—23no—
121C22×C11—23no—
122C22×C11—26no—
123C22×C11—26no—
124C22×C11—41no—
125C22×C11—43no—
126C22×C11—46no—
127C22×C11—43no—
128C22×C11—43no—
129C22×C11#37911yescharacteristic
130C22×C11#39113yes—
131C22×C11#39113yes—
132C22×C11#39313yes—
133C22×C11#39311yescharacteristic
134C22×C11#39513yes—
135C22×C11#39511yescharacteristic
136C22×C11B(4,𝔽2)12yes—
137C22×C11#45812yes—
138C4×C11—44no—
139C4×C11—412no—
140C4×C11—86no—
141C25C23×C1111yescharacteristic
142C22×Q8—22no—
143C23×C4—23no—
144C23×C4—23no—
145C23×C4—23no—
146C23×C4—44no—
147C23×C4D4×C1116yes—
148C23×C4Q8×C1112yescomplemented
149C22⋊Q8—224no—
150C22⋊Q8—224no—
151C2×C4⋊C4—26no—
152C2×C22⋊C4—26no—
153C2×C22⋊C4—26no—
154C2×C22⋊C4—26no—
155C2×C22⋊C4—26no—
156C2×C22⋊C4—23no—
157C2×C22⋊C4C2×C4×C1116yes—
158C2×C22⋊C4D4×C1116yes—
159C2×C22⋊C4Q8×C1116yescomplemented
160#95—412no—
161C2×C11—23no—
162C2×C11—23no—
163C2×C11—23no—
164C2×C11—23no—
165C2×C11#144611yescharacteristic
166C2×C11#179012yes—
167C2×C11#202911yescharacteristic
168C2×C11#203011yescharacteristic
169C2×C11#206212yes—
170C24—42no—
171C24—42no—
172C24C22×C4×C1111yescharacteristic
173C24C2×D4×C1113yes—
174C24C2×D4×C1113yes—
175C24C2×Q8×C1113yes—
176C24C2×Q8×C1111yescharacteristic
177C24C11×#4111yescharacteristic
178C24C11×#4113yes—
179C2×Q8—28no—
180C2×Q8—82no—
181C2×Q8—82no—
182C22×C4—212no—
183C22×C4—26no—
184C22×C4—26no—
185C22×C4—26no—
186C22×C4—26no—
187C22×C4—44no—
188C22×C4—412no—
189C22×C4—46no—
190C22×C4—41no—
191C22×C4—43no—
192C22×C4—46no—
193C22×C4—46no—
194C22×C4—46no—
195C22×C4—46no—
196C22×C4—43no—
197C22×C4—43no—
198C22×C4C11×C22⋊C4112yes—
199C4⋊C4—224no—
200C22⋊C4—212no—
201C22⋊C4—212no—
202C22⋊C4—212no—
203C22⋊C4—46no—
204C11#1139011yescharacteristic, direct product factor, Sylow
205C23—26no—
206C23—26no—
207C23—41no—
208C23—43no—
209C23—42no—
210C23—46no—
211C23—41no—
212C23—46no—
213C23—43no—
214C23—42no—
215C23C2×C11×C22⋊C413yes—
216C23C4×Q8×C1113yes—
217C23C4×Q8×C1111yescharacteristic
218C23C11×#12013yes—
219C23C11×#12011yescharacteristic
220C23C11×C22⋊Q813yes—
221C23C11×C22⋊Q813yes—
222C23C11×C22⋊Q816yes—
223C23C11×#12413yes—
224C23C11×#12413yes—
225C23C11×C4⋊Q813yes—
226C23C11×C4⋊Q813yes—
227Q8—88no—
228C2×C4—212no—
229C2×C4—212no—
230C2×C4—46no—
231C2×C4—412no—
232C2×C4—42no—
233C2×C4—44no—
234C2×C4—46no—
235C2×C4—46no—
236C2×C4—412no—
237C2×C4—412no—
238C2×C4—46no—
239C2×C4—86no—
240C2×C4—83no—
241C2×C4—83no—
242C2×C4—86no—
243C22—23no—
244C22—23no—
245C22—23no—
246C22—23no—
247C22—26no—
248C22—26no—
249C22—26no—
250C22—26no—
251C22—41no—
252C22—43no—
253C22—46no—
254C22—43no—
255C22—43no—
256C22C11×#37911yescharacteristic
257C22C11×#39113yes—
258C22C11×#39113yes—
259C22C11×#39313yes—
260C22C11×#39311yescharacteristic
261C22C11×#39513yes—
262C22C11×#39511yescharacteristic
263C22C11×B(4,𝔽2)12yes—
264C22C11×#45812yes—
265C4—44no—
266C4—412no—
267C4—86no—
268C2—23no—
269C2—23no—
270C2—23no—
271C2—23no—
272C2C11×#144611yescharacteristic
273C2C11×#179012yes—
274C2C11×#202911yescharacteristic
275C2C11×#203011yescharacteristic
276C2C11×#206212yes—
subgroupG/H
center, socleC23×C11#120
commutatorC24C22×C4×C11
Frattini, cosocleC25C23×C11
prime radicalC25×C11C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
6. C11×#543C4semidirect
19. C23×C4×C11Q8semidirect
30. C2×C11×C22⋊C4Q8semidirect
32. #11390C11direct (N × H)
110. #543C4×C11semidirect
148. C23×C4Q8×C11semidirect
159. C2×C22⋊C4Q8×C11semidirect
204. C11#11390direct (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
C2×C11×#3422
C11×C22⋊#952
#1139011