Finite Group Databasebeta

← C11×#32934 #14610127

Subgroups — C11×#32934 #14610127

Order 2816.

1378 conjugacy classes of subgroups; only the 310 normal subgroups are shown.

normal subgroups only

This group has 1378 conjugacy classes of subgroups — too many to draw. Only its 310 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×#131C211yesmaximal, characteristic
2C2×C11×#467C213yesmaximal, complemented
3C11×#2616C212yesmaximal
4C11×#1894C216yesmaximal, complemented
5C11×#1808C213yesmaximal, complemented
6C22×C11×#41C2211yescharacteristic
7C22×C11×Q16C2211yescharacteristic
8C2×C11×#131—212no—
9C22×C11×M16C2213yes—
10C23×C8×C11C2213yes—
11C2×C11×C22⋊Q8C2216yes—
12C11×#467—212no—
13C2×C11×#107C2213yes—
14C2×C11×#103C2216yes—
15C11×#395—22no—
16C11×#394—26no—
17C11×#380C2216yes—
18C11×#340C2216yes—
19C2×C11×#41—26no—
20C2×C11×#41—26no—
21C22×Q8×C11D411yescharacteristic
22C22×Q8×C11C2312yes—
23C22×D4×C11D413yes—
24C23×C4×C11C2313yes—
25C2×C11×Q16—26no—
26C11×#131—232no—
27C2×C11×M16—26no—
28C2×C11×M16—212no—
29C22×C8×C11—212no—
30C22×C8×C11D4112yes—
31C22×C8×C11C2313yes—
32C22×C8×C11C2311yescharacteristic
33C11×C22⋊Q8—212no—
34C11×C22⋊Q8—212no—
35C2×C11×C4⋊C4—26no—
36C2×C11×C4⋊C4C2316yes—
37C2×C11×C22⋊C4—26no—
38C2×C11×C22⋊C4—26no—
39C11×#107—26no—
40C11×#103—212no—
41C11×#95—26no—
42#32934C1111yesmaximal, characteristic, direct product factor, Sylow
43C24×C11C2×D413yes—
44C11×#41—28no—
45C11×#41—224no—
46C2×Q8×C11—26no—
47C2×Q8×C11—26no—
48C2×Q8×C11—26no—
49C2×D4×C11—212no—
50C2×D4×C11—26no—
51C22×C4×C11—26no—
52C22×C4×C11—26no—
53C22×C4×C11—26no—
54C22×C4×C11—22no—
55C22×C4×C11C2×D413yes—
56C22×C4×C11C2×D416yes—
57C22×C4×C11#4116yes—
58C22×C4×C11C2411yescharacteristic
59C11×Q16—44no—
60C11×M16—224no—
61C2×C8×C11—224no—
62C2×C8×C11—26no—
63C2×C8×C11C2×D416yes—
64C2×C8×C11C2×D416yes—
65C11×C4⋊C4—26no—
66C11×C4⋊C4—26no—
67C11×C4⋊C4—412no—
68C11×C22⋊C4—412no—
69C11×C22⋊C4—86no—
70C22×#131C2×C1111yescharacteristic
71C2×#467C2×C1113yescomplemented
72#2616C2×C1112yes—
73#1894C2×C1116yescomplemented
74#1808C2×C1113yescomplemented
75C23×C11—26no—
76C23×C11—23no—
77C23×C11—26no—
78C23×C11—23no—
79C23×C11#12116yes—
80C23×C11C22×D411yescharacteristic
81Q8×C11—28no—
82Q8×C11—42no—
83Q8×C11—46no—
84D4×C11—224no—
85C2×C4×C11—26no—
86C2×C4×C11—26no—
87C2×C4×C11—26no—
88C2×C4×C11—212no—
89C2×C4×C11—46no—
90C2×C4×C11—46no—
91C2×C4×C11—46no—
92C2×C4×C11—46no—
93C2×C4×C11#12116yes—
94C2×C4×C11C22×D413yes—
95C2×C4×C11C2×#4113yes—
96C8×C11—26no—
97C8×C11#12014yes—
98C22×#41C22×C1111yescharacteristic
99C22×Q16C22×C1111yescharacteristic
100C2×#131—212no—
101C22×M16C22×C1113yes—
102C23×C8C22×C1113yes—
103C2×C22⋊Q8C22×C1116yes—
104#467—212no—
105C2×#107C22×C1113yes—
106C2×#103C22×C1116yes—
107#395—22no—
108#394—26no—
109#380C22×C1116yes—
110#340C22×C1116yes—
111C22×C11—26no—
112C22×C11—26no—
113C22×C11—26no—
114C22×C11—46no—
115C22×C11—46no—
116C22×C11C2×#12113yes—
117C22×C11#57611yescharacteristic
118C22×C11#57813yes—
119C4×C11—26no—
120C4×C11—82no—
121C4×C11—86no—
122C4×C11C2×#12011yescharacteristic
123C4×C11#52513yes—
124C2×#41—26no—
125C2×#41—26no—
126C22×Q8D4×C1111yescharacteristic
127C22×Q8C23×C1112yes—
128C22×D4D4×C1113yes—
129C23×C4C23×C1113yes—
130C2×Q16—26no—
131#131—232no—
132C2×M16—26no—
133C2×M16—212no—
134C22×C8—212no—
135C22×C8D4×C11112yes—
136C22×C8C23×C1113yes—
137C22×C8C23×C1111yescharacteristic
138C22⋊Q8—212no—
139C22⋊Q8—212no—
140C2×C4⋊C4—26no—
141C2×C4⋊C4C23×C1116yes—
142C2×C22⋊C4—26no—
143C2×C22⋊C4—26no—
144#107—26no—
145#103—212no—
146#95—26no—
147C2×C11—46no—
148C2×C11#284711yescharacteristic
149C2×C11#305913yes—
150C2×C11#306113yes—
151C24C2×D4×C1113yes—
152#41—28no—
153#41—224no—
154C2×Q8—26no—
155C2×Q8—26no—
156C2×Q8—26no—
157C2×D4—212no—
158C2×D4—26no—
159C22×C4—26no—
160C22×C4—26no—
161C22×C4—26no—
162C22×C4—22no—
163C22×C4C2×D4×C1113yes—
164C22×C4C2×D4×C1116yes—
165C22×C4C11×#4116yes—
166C22×C4C24×C1111yescharacteristic
167Q16—44no—
168M16—224no—
169C2×C8—26no—
170C2×C8—224no—
171C2×C8C2×D4×C1116yes—
172C2×C8C2×D4×C1116yes—
173C4⋊C4—26no—
174C4⋊C4—26no—
175C4⋊C4—412no—
176C22⋊C4—412no—
177C22⋊C4—86no—
178C11#3293411yescharacteristic, direct product factor, Sylow
179C23—26no—
180C23—23no—
181C23—26no—
182C23—23no—
183C23C11×#12116yes—
184C23C22×D4×C1111yescharacteristic
185Q8—28no—
186Q8—42no—
187Q8—46no—
188D4—224no—
189C2×C4—26no—
190C2×C4—26no—
191C2×C4—26no—
192C2×C4—212no—
193C2×C4—46no—
194C2×C4—46no—
195C2×C4—46no—
196C2×C4—46no—
197C2×C4C11×#12116yes—
198C2×C4C22×D4×C1113yes—
199C2×C4C2×C11×#4113yes—
200C8—26no—
201C8C11×#12014yes—
202C22—26no—
203C22—26no—
204C22—26no—
205C22—46no—
206C22—46no—
207C22C2×C11×#12113yes—
208C22C11×#57611yescharacteristic
209C22C11×#57813yes—
210C4—26no—
211C4—86no—
212C4—82no—
213C4C2×C11×#12011yescharacteristic
214C4C11×#52513yes—
215C2—46no—
216C2C11×#284711yescharacteristic
217C2C11×#305913yes—
218C2C11×#306113yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#467C2semidirect
4. C11×#1894C2semidirect
5. C11×#1808C2semidirect
42. #32934C11direct (N × H)
71. C2×#467C2×C11semidirect
73. #1894C2×C11semidirect
74. #1808C2×C11semidirect
178. C11#32934direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1312
C2×C11×#4672
C11×#26162
C11×#18942
C11×#18082
#3293411