Finite Group Databasebeta

← #14640802

Subgroups — #14640802

Order 2816.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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#13068693C211yesmaximal, characteristic
2#13068382C211yesmaximal, characteristic
3C11×#1464C211yesmaximal, characteristic
4C2×C11×#117C2211yescharacteristic
5C11×#432—21no—
6#10622824—21no—
7C2×C22⋊(C11⋊C8)—21no—
8C2×#66867C411yescharacteristic, complemented
9C2×C4×C11⋊C8C411yescharacteristic, complemented
10C11×#324C412yescomplemented
11C11×#323—21no—
12#10622164—21no—
13#10622164C412yes—
14#10622162—21no—
15C23×C4×C11D411yescharacteristic
16C11×#117—41no—
17C11×#117—41no—
18C2×C11×C4⋊C4C2×C411yescharacteristic
19C2×C11×C4⋊C4Q811yescharacteristic
20C2×C11×C22⋊C4C2×C411yescharacteristic
21C2×C11×C22⋊C4D411yescharacteristic
22C2×C42×C11C2×C411yescharacteristic
23C2×C42×C11D411yescharacteristic
24C2×C22⋊Dic11—22no—
25C22×C11⋊C8—21no—
26C22×C11⋊C8—21no—
27C11×C4⋊C8—41no—
28C11×C22⋊C8—22no—
29C11×#97—41no—
30C11⋊#95—41no—
31C11⋊#95—41no—
32C22⋊(C11⋊C8)—24no—
33#66867—41no—
34C4×C11⋊C8—41no—
35#7214—111nomaximal, Sylow
36C24×C11C22⋊C411yescharacteristic
37C22×C4×C11—22no—
38C22×C4×C11—21no—
39C22×C4×C11—21no—
40C22×C4×C11—41no—
41C22×C4×C11C4211yescharacteristic
42C22×C4×C11C22⋊C411yescharacteristic
43C22×C4×C11C22⋊C411yescharacteristic
44C22×C4×C11C4⋊C411yescharacteristic
45C22×C4×C11C4⋊C411yescharacteristic
46C22×C4×C11C4⋊C411yescharacteristic
47C22×Dic11—42no—
48C2×C8×C11—42no—
49C11×C4⋊C4—41no—
50C11×C4⋊C4—41no—
51C11×C22⋊C4—41no—
52C11×C22⋊C4—41no—
53C42×C11—21no—
54C42×C11—21no—
55C42×C11—21no—
56C42×C11—21no—
57C22⋊Dic11—42no—
58C22⋊Dic11—42no—
59C2×C11⋊C8—22no—
60C2×C11⋊C8—22no—
61C2×C11⋊C8—41no—
62C2×C11⋊C8—41no—
63C2×C11⋊C8—41no—
64C2×C11⋊C8—41no—
65#1820—111no—
66#1750—111no—
67#1464D1111yescharacteristic
68C23×C11—21no—
69C23×C11—21no—
70C23×C11—41no—
71C23×C11—41no—
72C23×C11#9511yescharacteristic
73C23×C11#10412yes—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—42no—
84C2×C4×C11—42no—
85C2×C4×C11—41no—
86C2×C4×C11—41no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11#9911yescharacteristic
90C2×C4×C11#9911yescharacteristic
91C2×Dic11—82no—
92C2×Dic11—82no—
93C2×Dic11—82no—
94C8×C11—82no—
95C11⋊C8—42no—
96C11⋊C8—42no—
97C2×#117C2×D1111yescharacteristic
98#432—21no—
99C2×C22⋊C8—221no—
100C2×#97—111no—
101C2×C4×C8—111no—
102#381—221no—
103#342—112no—
104#342—221no—
105#336—221no—
106#324Dic1112yescomplemented
107#323—21no—
108C22×C11—21no—
109C22×C11—21no—
110C22×C11—22no—
111C22×C11—42no—
112C22×C11—41no—
113C22×C11—41no—
114C22×C11—81no—
115C22×C11H(3,ℤ/4)11yescharacteristic
116C22×C11#33911yescharacteristic
117C22×C11#34211yescharacteristic
118C4×C11—21no—
119C4×C11—21no—
120C4×C11—41no—
121C4×C11—41no—
122C4×C11—41no—
123C4×C11—41no—
124C4×C11—41no—
125Dic11—162no—
126C23×C4D4411yescharacteristic
127C22×C8—221no—
128C22×C8—221no—
129#117—41no—
130#117—41no—
131C2×C4⋊C4Dic2211yescharacteristic
132C2×C4⋊C4C2×Dic1111yescharacteristic
133C2×C22⋊C4—222no—
134C2×C22⋊C4C4×D1111yescharacteristic
135C2×C22⋊C4C22⋊D1111yescharacteristic
136C2×C42C4×D1111yescharacteristic
137C2×C42C22⋊D1111yescharacteristic
138C4⋊C8—41no—
139C22⋊C8—22no—
140C22⋊C8—224no—
141#97—41no—
142#97—441no—
143C4×C8—441no—
144#95—441no—
145#95—441no—
146C2×C11—21no—
147C2×C11—21no—
148C2×C11—42no—
149C2×C11#128411yescharacteristic
150C2×C11#139111yescharacteristic
151C2×C11#139511yescharacteristic
152C24(C2×D11)⋊C411yescharacteristic
153C22×C4—22no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—41no—
157C22×C4—442no—
158C22×C4C4×Dic1111yescharacteristic
159C22×C4Dic11⋊C411yescharacteristic
160C22×C4Dic11⋊C411yescharacteristic
161C22×C4C4⋊Dic1111yescharacteristic
162C22×C4(C2×D11)⋊C411yescharacteristic
163C22×C4C22⋊Dic1111yescharacteristic
164C2×C8—42no—
165C2×C8—222no—
166C2×C8—222no—
167C2×C8—441no—
168C2×C8—441no—
169C2×C8—441no—
170C2×C8—441no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C22⋊C4—41no—
174C22⋊C4—41no—
175C22⋊C4—442no—
176C22⋊C4—442no—
177C42—21no—
178C42—21no—
179C42—21no—
180C42—21no—
181C11#721411yescharacteristic, complemented, Sylow
182C23—21no—
183C23—21no—
184C23—41no—
185C23—41no—
186C23#6688912yes—
187C23C11⋊#9511yescharacteristic
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—882no—
204C2×C4—882no—
205C2×C4—882no—
206C2×C4#6687011yescharacteristic
207C2×C4#6687011yescharacteristic
208C8—82no—
209C8—442no—
210C8—442no—
211C22—21no—
212C22—21no—
213C22—22no—
214C22—42no—
215C22—41no—
216C22—41no—
217C22—81no—
218C22#1062216511yescharacteristic
219C22#1062219311yescharacteristic
220C22#1062219511yescharacteristic
221C4—21no—
222C4—21no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—41no—
227C4—41no—
228C4—1762no—
229C2—21no—
230C2—21no—
231C2—42no—
232C2#1306647011yescharacteristic
233C2#1306673611yescharacteristic
234C2#1306674611yescharacteristic
subgroupG/H
centerC22#10622165
commutatorC22×C4×C11C42
FrattiniC2×#117C2×D11
FittingC11×#1464C2
socleC22×C11#342
prime radicalC24×C11C22⋊C4
cosocleC2×C11×#117C22
hypercenter#1464D11
hypocenterC11#7214
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
8. C2×#66867C4semidirect
9. C2×C4×C11⋊C8C4semidirect
10. C11×#324C4semidirect
106. #324Dic11semidirect
181. C11#7214semidirect

Maximal subgroups

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

subgroupindex
#130686932
#130683822
C11×#14642
#721411