Finite Group Databasebeta

← #14640887

Subgroups — #14640887

Order 2816.

322 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 71 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#13068909C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic
3C11×#1466C211yesmaximal, characteristic
4C2×C4×D4×C11C2211yescharacteristic
5C23×C11⋊C8C411yescharacteristic
6C11×#432—21no—
7#10622820—21no—
8C2×C22⋊(C11⋊C8)—21no—
9C2×C22⋊(C11⋊C8)C411yescharacteristic
10C11×#323—21no—
11C11×#323C412yes—
12#10622166C412yes—
13#10622163—21no—
14#10622162—21no—
15C22×D4×C11Q811yescharacteristic
16C23×C4×C11C2×C411yescharacteristic
17C23×C4×C11D411yescharacteristic
18C4×D4×C11—41no—
19C4×D4×C11—41no—
20C2×C11×C4⋊C4C2×C411yescharacteristic
21C2×C11×C22⋊C4C2×C411yescharacteristic
22C2×C11×C22⋊C4D411yescharacteristic
23C2×C42×C11D411yescharacteristic
24C2×#4318—41no—
25C22×C11⋊C8—21no—
26C22×C11⋊C8—21no—
27C22×C11⋊C8—42no—
28C22×C11⋊C8—41no—
29C11×C4⋊C8—41no—
30C11×C22⋊C8—22no—
31C11×#97—41no—
32C22⋊(C11⋊C8)—22no—
33C22⋊(C11⋊C8)—42no—
34C22⋊(C11⋊C8)—41no—
35C22⋊(C11⋊C8)—41no—
36#7247—111nomaximal, Sylow
37C24×C11C4⋊C411yescharacteristic
38C24×C11C4⋊C411yescharacteristic
39C2×D4×C11—22no—
40C2×D4×C11—41no—
41C2×D4×C11—41no—
42C22×C4×C11—21no—
43C22×C4×C11—21no—
44C22×C4×C11—21no—
45C22×C4×C11—21no—
46C22×C4×C11—41no—
47C22×C4×C11—41no—
48C22×C4×C11—41no—
49C22×C4×C11—41no—
50C22×C4×C11C4211yescharacteristic
51C22×C4×C11C22⋊C411yescharacteristic
52C22×C4×C11C22⋊C411yescharacteristic
53C22×C4×C11C22⋊C411yescharacteristic
54C22×C4×C11C4⋊C411yescharacteristic
55C2×C8×C11—42no—
56C11×C4⋊C4—41no—
57C11×C22⋊C4—41no—
58C11×C22⋊C4—41no—
59C42×C11—21no—
60C42×C11—21no—
61#4318—81no—
62#4318—81no—
63C2×C11⋊C8—22no—
64C2×C11⋊C8—41no—
65C2×C11⋊C8—42no—
66C2×C11⋊C8—41no—
67C2×C11⋊C8—41no—
68C2×C11⋊C8—42no—
69C2×C11⋊C8—42no—
70C2×C11⋊C8—41no—
71C2×C11⋊C8—41no—
72#1869—111no—
73#1466D1111yescharacteristic
74#1465—111no—
75C23×C11—21no—
76C23×C11—21no—
77C23×C11—21no—
78C23×C11—21no—
79C23×C11—21no—
80C23×C11—41no—
81C23×C11—41no—
82C23×C11—41no—
83C23×C11—41no—
84C23×C11#9511yescharacteristic
85C23×C11#10812yes—
86D4×C11—44no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—42no—
96C2×C4×C11—41no—
97C2×C4×C11—41no—
98C2×C4×C11—41no—
99C2×C4×C11—41no—
100C2×C4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11—41no—
103C2×C4×C11—81no—
104C2×C4×C11#9911yescharacteristic
105C2×C4×C11#9911yescharacteristic
106C8×C11—82no—
107C11⋊C8—42no—
108C11⋊C8—81no—
109C11⋊C8—82no—
110C23×C8—111no—
111C2×C4×D4C2×D1111yescharacteristic
112#432—21no—
113#407—221no—
114C2×C22⋊C8—111no—
115C2×C22⋊C8—221no—
116#336—221no—
117#324—112no—
118#323—21no—
119#323—221no—
120#323Dic1112yes—
121C22×C11—21no—
122C22×C11—21no—
123C22×C11—22no—
124C22×C11—42no—
125C22×C11—42no—
126C22×C11—42no—
127C22×C11—41no—
128C22×C11—41no—
129C22×C11—41no—
130C22×C11—41no—
131C22×C11—41no—
132C22×C11—81no—
133C22×C11#33811yescharacteristic
134C22×C11#34111yescharacteristic
135C22×C11#34211yescharacteristic
136C4×C11—21no—
137C4×C11—41no—
138C4×C11—41no—
139C4×C11—41no—
140C4×C11—41no—
141C4×C11AΣL(1,𝔽16)11yescharacteristic
142C4×C11#35211yescharacteristic
143C22×D4Dic2211yescharacteristic
144C23×C4C4×D1111yescharacteristic
145C23×C4D4411yescharacteristic
146C2×M16—441no—
147C22×C8—221no—
148C22×C8—221no—
149C22×C8—442no—
150C22×C8—441no—
151C4×D4—41no—
152C4×D4—41no—
153C2×C4⋊C4C4×D1111yescharacteristic
154C2×C22⋊C4C2×Dic1111yescharacteristic
155C2×C22⋊C4C22⋊D1111yescharacteristic
156C2×C42C22⋊D1111yescharacteristic
157C4⋊C8—41no—
158C22⋊C8—22no—
159C22⋊C8—222no—
160C22⋊C8—442no—
161C22⋊C8—441no—
162C22⋊C8—441no—
163#97—41no—
164C2×C11—21no—
165C2×C11—21no—
166C2×C11—42no—
167C2×C11—81no—
168C2×C11#129311yescharacteristic
169C2×C11#139011yescharacteristic
170C2×C11#139511yescharacteristic
171C24Dic11⋊C411yescharacteristic
172C24C4⋊Dic1111yescharacteristic
173C2×D4—22no—
174C2×D4—41no—
175C2×D4—41no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4C4×Dic1111yescharacteristic
185C22×C4Dic11⋊C411yescharacteristic
186C22×C4(C2×D11)⋊C411yescharacteristic
187C22×C4(C2×D11)⋊C411yescharacteristic
188C22×C4C22⋊Dic1111yescharacteristic
189M16—881no—
190M16—881no—
191C2×C8—42no—
192C2×C8—222no—
193C2×C8—441no—
194C2×C8—442no—
195C2×C8—441no—
196C2×C8—442no—
197C2×C8—442no—
198C2×C8—441no—
199C2×C8—441no—
200C2×C8—441no—
201C4⋊C4—41no—
202C22⋊C4—41no—
203C22⋊C4—41no—
204C42—21no—
205C42—21no—
206C11#724711yescharacteristic, complemented, Sylow
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—21no—
212C23—41no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23#6688612yes—
217C23C11⋊#9511yescharacteristic
218D4—44no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—81no—
236C2×C4#6687011yescharacteristic
237C2×C4#6687011yescharacteristic
238C8—82no—
239C8—442no—
240C8—881no—
241C8—882no—
242C22—21no—
243C22—21no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—41no—
252C22—41no—
253C22—81no—
254C22#1062216511yescharacteristic
255C22#1062219611yescharacteristic
256C22C11⋊#33811yescharacteristic
257C4—21no—
258C4—41no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4#1062211311yescharacteristic
263C4#1062211411yescharacteristic
264C2—21no—
265C2—21no—
266C2—42no—
267C2—81no—
268C2#1306649211yescharacteristic
269C2#1306673511yescharacteristic
270C2#1306674411yescharacteristic
subgroupG/H
centerC22#10622165
commutatorC22×C4×C11C42
FrattiniC2×C4×D4C2×D11
FittingC11×#1466C2
socleC22×C11#342
prime radicalC22×D4×C11Q8
cosocleC2×C4×D4×C11C22
hypercenter#1466D11
hypocenterC11#7247
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1466

Complements

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

NH ≅ G/Ntype
206. C11#7247semidirect

Maximal subgroups

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

subgroupindex
#130689092
#130669542
C11×#14662
#724711