Finite Group Databasebeta

← #14670052

Subgroups — #14670052

Order 2816.

342 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 95 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
1#13068720C212yesmaximal
2#13066745C212yesmaximal
3#13066739C211yesmaximal, characteristic
4#13066737C211yesmaximal, characteristic
5C11×#2922C211yesmaximal, characteristic
6C4×C11×#41C2211yescharacteristic
7C11×#433—22no—
8C11×#431—22no—
9C11×#424C411yescharacteristic, complemented
10C11×#424C411yescharacteristic, complemented
11C11×#408C2211yescharacteristic
12C11×#408C2211yescharacteristic
13C4×C11×M16C411yescharacteristic, complemented
14C2×C4×C8×C11C411yescharacteristic, complemented
15#10622853C2212yes—
16#10622850C2212yes—
17#10622169—22no—
18#10622161—22no—
19C2×C11×#41C2311yescharacteristic
20C2×C11×M16C2×C411yescharacteristic
21C2×C11×M16C2×C411yescharacteristic
22C22×C8×C11C2×C411yescharacteristic
23C22×C8×C11C2×C411yescharacteristic
24C4×Q8×C11—21no—
25C4×D4×C11—21no—
26C4×D4×C11—22no—
27C11×#117C2×C411yescharacteristic
28C11×#117D412yes—
29C2×C42×C11C2×C411yescharacteristic
30C2×C42×C11D412yes—
31#66979—22no—
32C2×#4318—22no—
33C11×C4⋊C8—22no—
34C11×C4⋊C8—22no—
35C11×C22⋊C8—22no—
36C11×C22⋊C8—22no—
37C11×#97—21no—
38C4×C8×C11—21no—
39C4×C8×C11—21no—
40C4×C8×C11—21no—
41#66900—22no—
42#66898—22no—
43#66898—22no—
44#66897—22no—
45#12864—111nomaximal, Sylow
46C11×#41—41no—
47C11×#41—41no—
48C2×Q8×C11#4111yescharacteristic
49C2×D4×C11#4111yescharacteristic
50C2×D4×C11#4112yes—
51C22×C4×C11—21no—
52C22×C4×C11—22no—
53C22×C4×C11C22×C411yescharacteristic
54C22×C4×C11C2×D412yes—
55C11×M16—41no—
56C11×M16—41no—
57C2×C8×C11—21no—
58C2×C8×C11—21no—
59C2×C8×C11—21no—
60C2×C8×C11—21no—
61C2×C8×C11—41no—
62C2×C8×C11—41no—
63C11×C4⋊C4—21no—
64C11×C4⋊C4—22no—
65C11×C22⋊C4—21no—
66C11×C22⋊C4—22no—
67C42×C11—21no—
68C42×C11—22no—
69C42×C11C22⋊C411yescharacteristic
70C42×C11C22⋊C412yes—
71C42×C11C22⋊C411yescharacteristic
72C22⋊Dic11—42no—
73C4⋊Dic11—42no—
74C4×Dic11—42no—
75#4318—42no—
76#4318—42no—
77C2×C11⋊C8—42no—
78#2922D1111yescharacteristic
79#1827—112no—
80#1395—112no—
81#1392—111no—
82#1391—111no—
83C23×C11#11711yescharacteristic
84C23×C11#12312yes—
85Q8×C11—41no—
86D4×C11—41no—
87D4×C11—42no—
88C2×C4×C11—21no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—42no—
96C2×C4×C11—44no—
97C2×C4×C11C2×C22⋊C411yescharacteristic
98C2×C4×C11#11711yescharacteristic
99C2×C4×C11#12312yes—
100C2×Dic11—82no—
101C8×C11—41no—
102C8×C11—41no—
103C8×C11—41no—
104C8×C11—41no—
105C11⋊C8—82no—
106C4×#41C2×D1111yescharacteristic
107#433—22no—
108#431—22no—
109#424Dic1111yescharacteristic, complemented
110#424Dic1111yescharacteristic, complemented
111#413—112no—
112#410—112no—
113#408C2×D1111yescharacteristic
114#408C2×D1111yescharacteristic
115C4×M16Dic1111yescharacteristic, complemented
116C2×C4×C8Dic1111yescharacteristic, complemented
117#339—222no—
118H(3,ℤ/4)—222no—
119C22×C11—21no—
120C22×C11—22no—
121C22×C11—41no—
122C22×C11—42no—
123C22×C11#38111yescharacteristic
124C4×C11—22no—
125C4×C11—21no—
126C4×C11—22no—
127C4×C11—42no—
128C4×C11—41no—
129C4×C11#41011yescharacteristic
130C4×C11#41011yescharacteristic
131Dic11—162no—
132C2×#41C22×D1111yescharacteristic
133C2×M16—222no—
134C2×M16C2×Dic1111yescharacteristic
135C2×M16C2×Dic1111yescharacteristic
136C22×C8C2×Dic1111yescharacteristic
137C22×C8C2×Dic1111yescharacteristic
138C4×Q8—21no—
139C4×D4—21no—
140C4×D4—22no—
141#117—222no—
142#117C2×Dic1111yescharacteristic
143#117C22⋊D1112yes—
144C2×C42C2×Dic1111yescharacteristic
145C2×C42C22⋊D1112yes—
146C4⋊C8—22no—
147C4⋊C8—22no—
148#101—222no—
149#100—222no—
150#99—222no—
151#99—222no—
152C22⋊C8—22no—
153C22⋊C8—22no—
154#97—21no—
155C4×C8—21no—
156C4×C8—21no—
157C4×C8—21no—
158C2×C11—21no—
159C2×C11—42no—
160C2×C11—41no—
161C2×C11#182011yescharacteristic
162#41—41no—
163#41—41no—
164C2×Q8#433911yescharacteristic
165C2×D4#433911yescharacteristic
166C2×D4#433912yes—
167C22×C4—21no—
168C22×C4—22no—
169C22×C4C22×Dic1111yescharacteristic
170C22×C4C2×C22⋊D1112yes—
171M16—41no—
172M16—41no—
173M16—442no—
174M16—442no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—442no—
182C4⋊C4—21no—
183C4⋊C4—22no—
184C4⋊C4—442no—
185C22⋊C4—21no—
186C22⋊C4—22no—
187C22⋊C4—442no—
188C42—21no—
189C42—22no—
190C42—442no—
191C42C22⋊Dic1111yescharacteristic
192C42C22⋊Dic1112yes—
193C42C22⋊Dic1111yescharacteristic
194C11#1286411yescharacteristic, complemented, Sylow
195C23#6697911yescharacteristic
196C23#6698212yes—
197Q8—41no—
198D4—42no—
199D4—41no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—42no—
208C2×C4—44no—
209C2×C4—882no—
210C2×C4#6697911yescharacteristic
211C2×C4#6698212yes—
212C2×C4C2×C22⋊Dic1111yescharacteristic
213C8—41no—
214C8—41no—
215C8—41no—
216C8—41no—
217C8—882no—
218C22—22no—
219C22—21no—
220C22—41no—
221C22—42no—
222C22#1062282411yescharacteristic
223C4—22no—
224C4—22no—
225C4—21no—
226C4—42no—
227C4—41no—
228C4—1762no—
229C4#1062285311yescharacteristic
230C4#1062285311yescharacteristic
231C2—21no—
232C2—42no—
233C2—41no—
234C2#1306869311yescharacteristic
subgroupG/H
centerC4#10622853
commutatorC22×C4×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#2922C2
socleC2×C11#1820
prime radical, cosocleC2×C11×#41C23
hypercenter#2922D11
hypocenterC11#12864
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C42 ◁ C4×#41 ◁ #2922

Complements

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

NH ≅ G/Ntype
9. C11×#424C4semidirect
10. C11×#424C4semidirect
13. C4×C11×M16C4semidirect
14. C2×C4×C8×C11C4semidirect
109. #424Dic11semidirect
110. #424Dic11semidirect
115. C4×M16Dic11semidirect
116. C2×C4×C8Dic11semidirect
194. C11#12864semidirect

Maximal subgroups

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

subgroupindex
#130687202
#130667452
#130667392
#130667372
C11×#29222
#1286411