Finite Group Databasebeta

← C11×#32882 #14610075

Subgroups — C11×#32882 #14610075

Order 2816.

3798 conjugacy classes of subgroups; only the 438 normal subgroups are shown.

normal subgroups only

This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 438 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
1C24×Q8×C11C211yesmaximal, characteristic
2C2×C11×#451C216yesmaximal, complemented
3C11×#2848C211yesmaximal, characteristic
4C11×#1787C216yesmaximal, complemented
5C11×#1779C211yesmaximal, characteristic
6C23×Q8×C11—224no—
7C23×Q8×C11—23no—
8C23×Q8×C11C2216yes—
9C24×C4×C11—21no—
10C24×C4×C11C2211yescharacteristic
11C22×C11×Q16C2214yescomplemented
12C2×C11×C22⋊Q8C2213yes—
13C11×#451—224no—
14C2×C11×#103C22112yescomplemented
15C2×C11×C22⋊C8C2216yes—
16C11×#385—23no—
17C11×#380C2213yes—
18C11×#379—21no—
19C25×C11D411yescharacteristic
20C22×Q8×C11—2128no—
21C22×Q8×C11—248no—
22C22×Q8×C11—224no—
23C22×Q8×C11—248no—
24C22×Q8×C11—212no—
25C22×Q8×C11—26no—
26C22×Q8×C11D4124yes—
27C22×Q8×C11C2311yescharacteristic
28C22×Q8×C11C2314yes—
29C23×C4×C11—224no—
30C23×C4×C11—26no—
31C23×C4×C11—212no—
32C23×C4×C11D413yes—
33C23×C4×C11C2313yes—
34C2×C11×Q16—224no—
35C22×C8×C11C2314yes—
36C11×C22⋊Q8—212no—
37C2×C11×C4⋊C4—23no—
38C2×C11×C4⋊C4C2313yes—
39C2×C11×C22⋊C4—23no—
40C2×C11×C22⋊C4—23no—
41C11×#103—224no—
42C11×C22⋊C8—212no—
43C11×#95—23no—
44#32882C1111yesmaximal, characteristic, direct product factor, Sylow
45C24×C11—26no—
46C24×C11—26no—
47C24×C11Q1614yescomplemented
48C24×C11C2×D413yes—
49C2×Q8×C11—2192no—
50C2×Q8×C11—296no—
51C2×Q8×C11—248no—
52C2×Q8×C11—296no—
53C2×Q8×C11—224no—
54C2×Q8×C11—212no—
55C2×Q8×C11—26no—
56C2×Q8×C11C2×D4124yes—
57C22×C4×C11—264no—
58C22×C4×C11—248no—
59C22×C4×C11—232no—
60C22×C4×C11—224no—
61C22×C4×C11—26no—
62C22×C4×C11—24no—
63C22×C4×C11—212no—
64C22×C4×C11—212no—
65C22×C4×C11—23no—
66C22×C4×C11—21no—
67C22×C4×C11C2×D413yes—
68C22×C4×C11C2×D4112yes—
69C22×C4×C11C2411yescharacteristic
70C11×Q16—416no—
71C2×C8×C11—212no—
72C11×C4⋊C4—26no—
73C11×C4⋊C4—46no—
74C11×C22⋊C4—46no—
75C11×C22⋊C4—46no—
76C24×Q8C2×C1111yescharacteristic
77C2×#451C2×C1116yescomplemented
78#2848C2×C1111yescharacteristic
79#1787C2×C1116yescomplemented
80#1779C2×C1111yescharacteristic
81C23×C11—28no—
82C23×C11—224no—
83C23×C11—26no—
84C23×C11—26no—
85C23×C11—224no—
86C23×C11#12016yes—
87C23×C11C2×Q1616yes—
88C23×C11#13716yes—
89C23×C11C22×D411yescharacteristic
90Q8×C11—296no—
91Q8×C11—224no—
92Q8×C11—44no—
93Q8×C11#120116yes—
94C2×C4×C11—296no—
95C2×C4×C11—224no—
96C2×C4×C11—224no—
97C2×C4×C11—26no—
98C2×C4×C11—224no—
99C2×C4×C11—43no—
100C2×C4×C11—43no—
101C2×C4×C11—46no—
102C2×C4×C11#12016yes—
103C2×C4×C11C22×D416yes—
104C8×C11—44no—
105C23×Q8—224no—
106C23×Q8—23no—
107C23×Q8C22×C1116yes—
108C24×C4—21no—
109C24×C4C22×C1111yescharacteristic
110C22×Q16C22×C1114yescomplemented
111C2×C22⋊Q8C22×C1113yes—
112#451—224no—
113C2×#103C22×C11112yescomplemented
114C2×C22⋊C8C22×C1116yes—
115#385—23no—
116#380C22×C1113yes—
117#379—21no—
118C22×C11—232no—
119C22×C11—26no—
120C22×C11—212no—
121C22×C11—26no—
122C22×C11—212no—
123C22×C11#451112yescomplemented
124C22×C11C2×#12013yes—
125C22×C11C22×Q1611yescharacteristic
126C22×C11C2×#13713yes—
127C4×C11—216no—
128C4×C11—26no—
129C4×C11—81no—
130C4×C11—83no—
131C4×C11C2×#12014yes—
132C25D4×C1111yescharacteristic
133C22×Q8—2128no—
134C22×Q8—248no—
135C22×Q8—224no—
136C22×Q8—248no—
137C22×Q8—212no—
138C22×Q8—26no—
139C22×Q8D4×C11124yes—
140C22×Q8C23×C1111yescharacteristic
141C22×Q8C23×C1114yes—
142C23×C4—224no—
143C23×C4—26no—
144C23×C4—212no—
145C23×C4D4×C1113yes—
146C23×C4C23×C1113yes—
147C2×Q16—224no—
148C22×C8C23×C1114yes—
149C22⋊Q8—212no—
150C2×C4⋊C4—23no—
151C2×C4⋊C4C23×C1113yes—
152C2×C22⋊C4—23no—
153C2×C22⋊C4—23no—
154#103—224no—
155C22⋊C8—212no—
156#95—23no—
157C2×C11—212no—
158C2×C11#284611yescharacteristic
159C2×C11C2×#45113yes—
160C2×C11#300413yes—
161C24—26no—
162C24—26no—
163C24C11×Q1614yescomplemented
164C24C2×D4×C1113yes—
165C2×Q8—2192no—
166C2×Q8—296no—
167C2×Q8—248no—
168C2×Q8—296no—
169C2×Q8—224no—
170C2×Q8—212no—
171C2×Q8—26no—
172C2×Q8C2×D4×C11124yes—
173C22×C4—264no—
174C22×C4—248no—
175C22×C4—232no—
176C22×C4—224no—
177C22×C4—26no—
178C22×C4—24no—
179C22×C4—212no—
180C22×C4—212no—
181C22×C4—23no—
182C22×C4—21no—
183C22×C4C2×D4×C1113yes—
184C22×C4C2×D4×C11112yes—
185C22×C4C24×C1111yescharacteristic
186Q16—416no—
187C2×C8—212no—
188C4⋊C4—26no—
189C4⋊C4—46no—
190C22⋊C4—46no—
191C22⋊C4—46no—
192C11#3288211yescharacteristic, direct product factor, Sylow
193C23—28no—
194C23—224no—
195C23—26no—
196C23—26no—
197C23—224no—
198C23C11×#12016yes—
199C23C2×C11×Q1616yes—
200C23C11×#13716yes—
201C23C22×D4×C1111yescharacteristic
202Q8—296no—
203Q8—224no—
204Q8—44no—
205Q8C11×#120116yes—
206C2×C4—296no—
207C2×C4—224no—
208C2×C4—224no—
209C2×C4—26no—
210C2×C4—224no—
211C2×C4—43no—
212C2×C4—43no—
213C2×C4—46no—
214C2×C4C11×#12016yes—
215C2×C4C22×D4×C1116yes—
216C8—44no—
217C22—232no—
218C22—212no—
219C22—26no—
220C22—212no—
221C22—26no—
222C22C11×#451112yescomplemented
223C22C2×C11×#12013yes—
224C22C22×C11×Q1611yescharacteristic
225C22C2×C11×#13713yes—
226C4—216no—
227C4—26no—
228C4—83no—
229C4—81no—
230C4C2×C11×#12014yes—
231C2—212no—
232C2C11×#284611yescharacteristic
233C2C2×C11×#45113yes—
234C2C11×#300413yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC25×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#451C2semidirect
4. C11×#1787C2semidirect
11. C22×C11×Q16C22semidirect
14. C2×C11×#103C22semidirect
44. #32882C11direct (N × H)
47. C24×C11Q16semidirect
77. C2×#451C2×C11semidirect
79. #1787C2×C11semidirect
110. C22×Q16C22×C11semidirect
113. C2×#103C22×C11semidirect
123. C22×C11#451semidirect
163. C24C11×Q16semidirect
192. C11#32882direct (N × H)
222. C22C11×#451semidirect

Maximal subgroups

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

subgroupindex
C24×Q8×C112
C2×C11×#4512
C11×#28482
C11×#17872
C11×#17792
#3288211