Finite Group Databasebeta

← C11×#11394 #14588587

Subgroups — C11×#11394 #14588587

Order 2816.

1090 conjugacy classes of subgroups; only the 254 normal subgroups are shown.

normal subgroups only

This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 254 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
3C2×C11×#342C213yesmaximal
4C11×#543—26no—
5C11×#543C414yescomplemented
6C2×C11×C22⋊Q8—26no—
7C22×C11×C22⋊C4C2211yescharacteristic
8C22×C11×C22⋊C4C2213yes—
9C22×C11×C22⋊C4C2213yes—
10C11×#342—26no—
11C11×#342—26no—
12C25×C11C2311yescharacteristic
13C22×Q8×C11—22no—
14C23×C4×C11—23no—
15C23×C4×C11—23no—
16C23×C4×C11Q812yescomplemented
17C11×C22⋊Q8—224no—
18C11×C22⋊Q8—224no—
19C2×C11×C4⋊C4—26no—
20C2×C11×C22⋊C4—23no—
21C2×C11×C22⋊C4—23no—
22C2×C11×C22⋊C4—23no—
23C2×C11×C22⋊C4—23no—
24C2×C11×C22⋊C4—23no—
25C2×C11×C22⋊C4—23no—
26C2×C11×C22⋊C4—23no—
27C2×C11×C22⋊C4—23no—
28C2×C11×C22⋊C4—23no—
29C2×C11×C22⋊C4—23no—
30C2×C11×C22⋊C4C2×C416yes—
31C2×C11×C22⋊C4D416yes—
32C2×C11×C22⋊C4D416yes—
33C2×C11×C22⋊C4Q816yescomplemented
34#11394C1111yesmaximal, characteristic, direct product factor, Sylow
35C24×C11—82no—
36C24×C11C22×C411yescharacteristic
37C24×C11C2×D413yes—
38C24×C11C2×D413yes—
39C24×C11C2×Q811yescharacteristic
40C24×C11C2×Q813yes—
41C24×C11#4113yes—
42C24×C11#4111yescharacteristic
43C2×Q8×C11—28no—
44C2×Q8×C11—84no—
45C22×C4×C11—26no—
46C22×C4×C11—26no—
47C22×C4×C11—26no—
48C22×C4×C11—26no—
49C22×C4×C11—26no—
50C22×C4×C11—43no—
51C22×C4×C11—43no—
52C22×C4×C11—86no—
53C22×C4×C11—86no—
54C22×C4×C11—82no—
55C11×C4⋊C4—224no—
56C11×C22⋊C4—26no—
57C11×C22⋊C4—26no—
58C11×C22⋊C4—26no—
59C11×C22⋊C4—26no—
60C11×C22⋊C4—26no—
61C11×C22⋊C4—43no—
62C11×C22⋊C4—41no—
63C11×C22⋊C4—43no—
64C11×C22⋊C4—43no—
65C11×C22⋊C4C22⋊C4112yes—
66C2×#543C2×C1111yescharacteristic
67C2×#342C2×C1113yes—
68C2×#342C2×C1113yes—
69C23×C11—46no—
70C23×C11—42no—
71C23×C11—46no—
72C23×C11—81no—
73C23×C11—83no—
74C23×C11—83no—
75C23×C11—81no—
76C23×C11C2×C22⋊C413yes—
77C23×C11C4×Q811yescharacteristic
78C23×C11C4×Q813yes—
79C23×C11#12011yescharacteristic
80C23×C11#12013yes—
81C23×C11C22⋊Q813yes—
82C23×C11C22⋊Q813yes—
83C23×C11C22⋊Q813yes—
84C23×C11C22⋊Q813yes—
85C23×C11#12413yes—
86C23×C11#12413yes—
87C23×C11C4⋊Q813yes—
88C23×C11C4⋊Q813yes—
89Q8×C11—88no—
90C2×C4×C11—212no—
91C2×C4×C11—412no—
92C2×C4×C11—46no—
93C2×C4×C11—42no—
94C2×C4×C11—86no—
95C2×C4×C11—86no—
96C2×C4×C11—86no—
97C2×C4×C11—86no—
98C2×C4×C11—86no—
99C2×C4×C11—86no—
100#543—26no—
101#543C4×C1114yescomplemented
102C2×C22⋊Q8—26no—
103C22×C22⋊C4C22×C1111yescharacteristic
104C22×C22⋊C4C22×C1113yes—
105C22×C22⋊C4C22×C1113yes—
106#342—26no—
107#342—26no—
108C22×C11—22no—
109C22×C11—26no—
110C22×C11—26no—
111C22×C11—43no—
112C22×C11—43no—
113C22×C11—43no—
114C22×C11—43no—
115C22×C11—41no—
116C22×C11—43no—
117C22×C11—43no—
118C22×C11—43no—
119C22×C11—43no—
120C22×C11—43no—
121C22×C11#37911yescharacteristic
122C22×C11#39113yes—
123C22×C11#39113yes—
124C22×C11#39313yes—
125C22×C11#39311yescharacteristic
126C22×C11#39511yescharacteristic
127C22×C11#39513yes—
128C4×C11—412no—
129C4×C11—86no—
130C4×C11—82no—
131C25C23×C1111yescharacteristic
132C22×Q8—22no—
133C23×C4—23no—
134C23×C4—23no—
135C23×C4Q8×C1112yescomplemented
136C22⋊Q8—224no—
137C22⋊Q8—224no—
138C2×C4⋊C4—26no—
139C2×C22⋊C4—23no—
140C2×C22⋊C4—23no—
141C2×C22⋊C4—23no—
142C2×C22⋊C4—23no—
143C2×C22⋊C4—23no—
144C2×C22⋊C4—23no—
145C2×C22⋊C4—23no—
146C2×C22⋊C4—23no—
147C2×C22⋊C4—23no—
148C2×C22⋊C4—23no—
149C2×C22⋊C4C2×C4×C1116yes—
150C2×C22⋊C4D4×C1116yes—
151C2×C22⋊C4D4×C1116yes—
152C2×C22⋊C4Q8×C1116yescomplemented
153C2×C11—21no—
154C2×C11—23no—
155C2×C11—23no—
156C2×C11—23no—
157C2×C11—21no—
158C2×C11—23no—
159C2×C11#144611yescharacteristic
160C2×C11#203212yes—
161C24—82no—
162C24C22×C4×C1111yescharacteristic
163C24C2×D4×C1113yes—
164C24C2×D4×C1113yes—
165C24C2×Q8×C1111yescharacteristic
166C24C2×Q8×C1113yes—
167C24C11×#4113yes—
168C24C11×#4111yescharacteristic
169C2×Q8—28no—
170C2×Q8—84no—
171C22×C4—26no—
172C22×C4—26no—
173C22×C4—26no—
174C22×C4—26no—
175C22×C4—26no—
176C22×C4—43no—
177C22×C4—43no—
178C22×C4—86no—
179C22×C4—86no—
180C22×C4—82no—
181C4⋊C4—224no—
182C22⋊C4—26no—
183C22⋊C4—26no—
184C22⋊C4—26no—
185C22⋊C4—26no—
186C22⋊C4—26no—
187C22⋊C4—43no—
188C22⋊C4—41no—
189C22⋊C4—43no—
190C22⋊C4—43no—
191C22⋊C4C11×C22⋊C4112yes—
192C11#1139411yescharacteristic, direct product factor, Sylow
193C23—46no—
194C23—42no—
195C23—46no—
196C23—81no—
197C23—83no—
198C23—83no—
199C23—81no—
200C23C2×C11×C22⋊C413yes—
201C23C4×Q8×C1111yescharacteristic
202C23C4×Q8×C1113yes—
203C23C11×#12011yescharacteristic
204C23C11×#12013yes—
205C23C11×C22⋊Q813yes—
206C23C11×C22⋊Q813yes—
207C23C11×C22⋊Q813yes—
208C23C11×C22⋊Q813yes—
209C23C11×#12413yes—
210C23C11×#12413yes—
211C23C11×C4⋊Q813yes—
212C23C11×C4⋊Q813yes—
213Q8—88no—
214C2×C4—212no—
215C2×C4—412no—
216C2×C4—46no—
217C2×C4—42no—
218C2×C4—86no—
219C2×C4—86no—
220C2×C4—86no—
221C2×C4—86no—
222C2×C4—86no—
223C2×C4—86no—
224C22—22no—
225C22—26no—
226C22—26no—
227C22—43no—
228C22—43no—
229C22—43no—
230C22—43no—
231C22—41no—
232C22—43no—
233C22—43no—
234C22—43no—
235C22—43no—
236C22—43no—
237C22C11×#37911yescharacteristic
238C22C11×#39113yes—
239C22C11×#39113yes—
240C22C11×#39313yes—
241C22C11×#39311yescharacteristic
242C22C11×#39511yescharacteristic
243C22C11×#39513yes—
244C4—412no—
245C4—86no—
246C4—82no—
247C2—21no—
248C2—23no—
249C2—23no—
250C2—23no—
251C2—21no—
252C2—23no—
253C2C11×#144611yescharacteristic
254C2C11×#203212yes—
subgroupG/H
center, socleC22×C11#393
commutatorC24C22×C4×C11
Frattini, cosocleC25C23×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
5. C11×#543C4semidirect
16. C23×C4×C11Q8semidirect
33. C2×C11×C22⋊C4Q8semidirect
34. #11394C11direct (N × H)
101. #543C4×C11semidirect
135. C23×C4Q8×C11semidirect
152. C2×C22⋊C4Q8×C11semidirect
192. C11#11394direct (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
#1139411