Finite Group Databasebeta

← #14640380

Subgroups — #14640380

Order 2816.

364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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#13068684C211yesmaximal, characteristic
2#13068378C211yesmaximal, characteristic
3C11×#1749C211yesmaximal, characteristic
4C22×C42×C11C2211yescharacteristic
5C2×C11×C22⋊C8—21no—
6C2×C11×#97—21no—
7C2×C22⋊(C11⋊C8)—21no—
8C2×C22⋊(C11⋊C8)C412yes—
9C2×#66867—21no—
10C11×#336C412yes—
11#10622162—21no—
12#10622162—21no—
13#10622162C412yes—
14C23×C4×C11C2×C411yescharacteristic
15C23×C4×C11D411yescharacteristic
16C23×C4×C11Q811yescharacteristic
17C22×C8×C11—22no—
18C2×C42×C11—42no—
19C2×C42×C11C2×C411yescharacteristic
20C2×C42×C11C2×C411yescharacteristic
21C2×C42×C11D411yescharacteristic
22C2×C42×C11D411yescharacteristic
23C22×C11⋊C8—22no—
24C22×C11⋊C8—22no—
25C11×C22⋊C8—24no—
26C11×#97—42no—
27C22⋊(C11⋊C8)—24no—
28C22⋊(C11⋊C8)—42no—
29#66867—42no—
30#7046—111nomaximal, Sylow
31C24×C11C4⋊C411yescharacteristic
32C22×C4×C11—22no—
33C22×C4×C11—22no—
34C22×C4×C11—22no—
35C22×C4×C11—22no—
36C22×C4×C11—41no—
37C22×C4×C11—41no—
38C22×C4×C11—41no—
39C22×C4×C11—41no—
40C22×C4×C11—41no—
41C22×C4×C11C4211yescharacteristic
42C22×C4×C11C22⋊C411yescharacteristic
43C22×C4×C11C22⋊C411yescharacteristic
44C22×C4×C11C22⋊C411yescharacteristic
45C22×C4×C11C4⋊C411yescharacteristic
46C22×C4×C11C4⋊C411yescharacteristic
47C2×C8×C11—24no—
48C2×C8×C11—42no—
49C2×C8×C11—42no—
50C42×C11—22no—
51C42×C11—22no—
52C42×C11—41no—
53C42×C11—41no—
54C2×C11⋊C8—24no—
55C2×C11⋊C8—42no—
56C2×C11⋊C8—42no—
57C2×C11⋊C8—42no—
58C2×C11⋊C8—42no—
59C2×C11⋊C8—42no—
60#1817—111no—
61#1749—111no—
62#1749D1111yescharacteristic
63C23×C11—21no—
64C23×C11—21no—
65C23×C11—21no—
66C23×C11—21no—
67C23×C11—21no—
68C23×C11—21no—
69C23×C11#9511yescharacteristic
70C23×C11#10812yes—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11—21no—
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—21no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—44no—
87C2×C4×C11—44no—
88C2×C4×C11—44no—
89C2×C4×C11#9912yes—
90C2×C4×C11#10412yes—
91C2×C4×C11#10412yes—
92C8×C11—44no—
93C11⋊C8—44no—
94C11⋊C8—82no—
95C22×C42C2×D1111yescharacteristic
96C2×C22⋊C8—21no—
97C2×C22⋊C8—112no—
98C2×C22⋊C8—221no—
99C2×#97—21no—
100C2×#97—221no—
101#336—112no—
102#336—221no—
103#336—221no—
104#336Dic1112yes—
105C22×C11—22no—
106C22×C11—22no—
107C22×C11—22no—
108C22×C11—41no—
109C22×C11—41no—
110C22×C11—41no—
111C22×C11—41no—
112C22×C11#33811yescharacteristic
113C22×C11#33911yescharacteristic
114C22×C11#33911yescharacteristic
115C22×C11#34111yescharacteristic
116C22×C11#34211yescharacteristic
117C22×C11#34411yescharacteristic
118C22×C11#34411yescharacteristic
119C4×C11—22no—
120C4×C11—22no—
121C4×C11—22no—
122C4×C11—41no—
123C4×C11—41no—
124C4×C11—41no—
125C23×C4Dic2211yescharacteristic
126C23×C4C4×D1111yescharacteristic
127C23×C4C22⋊D1111yescharacteristic
128C22×C8—22no—
129C22×C8—222no—
130C22×C8—222no—
131C2×C42—42no—
132C2×C42C4×D1111yescharacteristic
133C2×C42D4411yescharacteristic
134C2×C42C2×Dic1111yescharacteristic
135C2×C42C22⋊D1111yescharacteristic
136C22⋊C8—24no—
137C22⋊C8—224no—
138C22⋊C8—442no—
139#97—42no—
140#97—442no—
141C2×C11—42no—
142C2×C11#129111yescharacteristic
143C2×C11#129111yescharacteristic
144C2×C11#129311yescharacteristic
145C2×C11#129711yescharacteristic
146C2×C11#130211yescharacteristic
147C2×C11#130211yescharacteristic
148C2×C11#130611yescharacteristic
149C24Dic11⋊C411yescharacteristic
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4C4×Dic1111yescharacteristic
160C22×C4Dic11⋊C411yescharacteristic
161C22×C4C4⋊Dic1111yescharacteristic
162C22×C4(C2×D11)⋊C411yescharacteristic
163C22×C4(C2×D11)⋊C411yescharacteristic
164C22×C4C22⋊Dic1111yescharacteristic
165C2×C8—24no—
166C2×C8—42no—
167C2×C8—42no—
168C2×C8—224no—
169C2×C8—442no—
170C2×C8—442no—
171C2×C8—442no—
172C2×C8—442no—
173C2×C8—442no—
174C42—22no—
175C42—22no—
176C42—41no—
177C42—41no—
178C11#704611yescharacteristic, complemented, Sylow
179C23—21no—
180C23—21no—
181C23—21no—
182C23—21no—
183C23—21no—
184C23—21no—
185C23#6688612yes—
186C23C11⋊#9511yescharacteristic
187C2×C4—21no—
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—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—44no—
203C2×C4—44no—
204C2×C4—44no—
205C2×C4#6686912yes—
206C2×C4#6687012yes—
207C2×C4#6690112yes—
208C8—44no—
209C8—444no—
210C8—882no—
211C22—22no—
212C22—22no—
213C22—22no—
214C22—41no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22#1062216111yescharacteristic
219C22#1062216511yescharacteristic
220C22#1062217011yescharacteristic
221C22#1062219411yescharacteristic
222C22#1062219611yescharacteristic
223C22#1062219711yescharacteristic
224C22C11⋊#33811yescharacteristic
225C4—22no—
226C4—22no—
227C4—22no—
228C4—41no—
229C4—41no—
230C4—41no—
231C2—42no—
232C2#1306648711yescharacteristic
233C2#1306648811yescharacteristic
234C2#1306649211yescharacteristic
235C2#1306650211yescharacteristic
236C2#1306651411yescharacteristic
237C2#1306651511yescharacteristic
238C2#1306652511yescharacteristic
subgroupG/H
centerC23C11⋊#95
commutatorC22×C4×C11C42
FrattiniC22×C42C2×D11
FittingC11×#1749C2
socleC23×C11#95
prime radicalC24×C11C4⋊C4
cosocleC22×C42×C11C22
hypercenter#1749D11
hypocenterC11#7046
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
178. C11#7046semidirect

Maximal subgroups

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

subgroupindex
#130686842
#130683782
C11×#17492
#704611