Finite Group Databasebeta

← #14652892

Subgroups — #14652892

Order 2816.

590 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 151 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#13068733C211yesmaximal, characteristic, complemented
2#13068469C211yesmaximal, characteristic, complemented
3C2×#10622185C212yesmaximal, complemented
4C2×#10622182C212yesmaximal
5C11×#2858C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C11×#127C2211yescharacteristic
8C2×C11×#124—22no—
9C11×#390—21no—
10C11×#390—21no—
11C11×#390C414yes—
12C43×C11C2211yescharacteristic
13C2×C4⋊(C11⋊C8)C2212yes—
14C2×C4⋊(C11⋊C8)C2212yes—
15C2×#66867—21no—
16#10622185—24no—
17#10622182—24no—
18#10622162—21no—
19#10622162—22no—
20C22×Q8×C11—21no—
21C22×D4×C11—21no—
22C22×D4×C11—21no—
23C22×D4×C11C2×C412yes—
24C11×C4⋊Q8—22no—
25C11×C4⋊Q8—22no—
26C11×#127—22no—
27C11×#127—22no—
28C11×#124—48no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4C2×C412yes—
31C2×C11×C22⋊C4—24no—
32C2×C11×C22⋊C4—24no—
33C2×C42×C11C2×C412yes—
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D412yes—
36C2×C42×C11D411yescharacteristic
37C2×C42×C11C2311yescharacteristic
38C22×C11⋊C8—22no—
39C22×C11⋊C8—22no—
40C4⋊(C11⋊C8)—22no—
41C4⋊(C11⋊C8)—22no—
42C4⋊(C11⋊C8)—22no—
43C4⋊(C11⋊C8)D414yes—
44#66867—42no—
45#9710—111nomaximal, Sylow
46C24×C11—22no—
47C2×Q8×C11—41no—
48C2×Q8×C11—41no—
49C2×Q8×C11—44no—
50C2×D4×C11—24no—
51C2×D4×C11—44no—
52C2×D4×C11—42no—
53C2×D4×C11—41no—
54C2×D4×C11—41no—
55C2×D4×C11—42no—
56C2×D4×C11—44no—
57C2×D4×C11—41no—
58C2×D4×C11—41no—
59C22×C4×C11—22no—
60C22×C4×C11C22⋊C412yes—
61C22×C4×C11C22⋊C412yes—
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C11×C4⋊C4—24no—
66C11×C4⋊C4—42no—
67C11×C22⋊C4—48no—
68C11×C22⋊C4—48no—
69C42×C11—22no—
70C42×C11—21no—
71C42×C11—24no—
72C42×C11—21no—
73C42×C11—42no—
74C42×C11C2×D412yes—
75C42×C11#4112yes—
76C2×C11⋊C8—24no—
77C2×C11⋊C8—42no—
78C2×C11⋊C8—42no—
79C2×C11⋊C8—42no—
80C2×C11⋊C8—44no—
81#2858D1111yescharacteristic
82#1831—111no—
83#1767—111no—
84C2×#332—112no—
85C2×#331—112no—
86C23×C11—42no—
87C23×C11—44no—
88C23×C11—42no—
89C23×C11—42no—
90C23×C11—44no—
91C23×C11C2×C22⋊C411yescharacteristic
92Q8×C11—82no—
93Q8×C11—82no—
94D4×C11—84no—
95D4×C11—82no—
96D4×C11—82no—
97D4×C11—82no—
98D4×C11—82no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—42no—
107C2×C4×C11—44no—
108C2×C4×C11C4×D412yes—
109C2×C4×C11#12112yes—
110C2×C4×C11#12411yescharacteristic
111C2×C4×C11#12711yescharacteristic
112C2×C4×C11#13512yes—
113C2×C4×C11AGL(1,ℤ/8)14yes—
114C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C11#13711yescharacteristic
116C11⋊C8—44no—
117C11⋊C8—82no—
118C2×C4⋊Q8C2×D1111yescharacteristic
119C2×#127C2×D1111yescharacteristic
120C2×#124—22no—
121C2×C4⋊C8—112no—
122C2×C4⋊C8—112no—
123C2×#97—221no—
124#390—21no—
125#390—21no—
126#390Dic1114yes—
127C43C2×D1111yescharacteristic
128#336—222no—
129#336—221no—
130#332—224no—
131#331—224no—
132C22×C11—84no—
133C22×C11—84no—
134C22×C11—82no—
135C22×C11—82no—
136C22×C11—82no—
137C22×C11#39011yescharacteristic
138C22×C11#41312yes—
139C22×C11#41611yescharacteristic
140C22×C11#41711yescharacteristic
141C22×C11#41812yes—
142C4×C11—22no—
143C4×C11—42no—
144C4×C11—42no—
145C4×C11—82no—
146C4×C11#46312yes—
147C4×C11#46412yes—
148C4×C11#49012yes—
149C4×C11#49612yes—
150C22×Q8—21no—
151C22×D4—21no—
152C22×D4—21no—
153C22×D4C2×Dic1112yes—
154C22×C8—222no—
155C22×C8—222no—
156C4⋊Q8—22no—
157C4⋊Q8—22no—
158#127—22no—
159#127—22no—
160#124—48no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4C2×Dic1112yes—
163C2×C22⋊C4—24no—
164C2×C22⋊C4—24no—
165C2×C42C2×Dic1112yes—
166C2×C42C22⋊D1112yes—
167C2×C42C22⋊D1111yescharacteristic
168C2×C42C22⋊D1111yescharacteristic
169C2×C42C22×D1111yescharacteristic
170C4⋊C8—114no—
171C4⋊C8—222no—
172C4⋊C8—222no—
173C4⋊C8—222no—
174#97—442no—
175C2×C11—162no—
176C2×C11#155312yes—
177C2×C11#155712yes—
178C2×C11#196111yescharacteristic
179C2×C11#196711yescharacteristic
180C2×C11#198311yescharacteristic
181C24—22no—
182C2×Q8—44no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×D4—24no—
186C2×D4—44no—
187C2×D4—44no—
188C2×D4—41no—
189C2×D4—42no—
190C2×D4—41no—
191C2×D4—41no—
192C2×D4—42no—
193C2×D4—41no—
194C22×C4—22no—
195C22×C4C22⋊Dic1112yes—
196C22×C4C22⋊Dic1112yes—
197C22×C4C22×Dic1111yescharacteristic
198C22×C4C2×C22⋊D1111yescharacteristic
199C22×C4C2×C22⋊D1111yescharacteristic
200C2×C8—224no—
201C2×C8—442no—
202C2×C8—442no—
203C2×C8—444no—
204C2×C8—442no—
205C4⋊C4—24no—
206C4⋊C4—42no—
207C22⋊C4—48no—
208C22⋊C4—48no—
209C42—24no—
210C42—21no—
211C42—22no—
212C42—21no—
213C42—42no—
214C42D4×D1112yes—
215C42#434112yes—
216C11#971011yescharacteristic, complemented, Sylow
217C23—44no—
218C23—42no—
219C23—42no—
220C23—42no—
221C23—44no—
222C23C2×C22⋊Dic1111yescharacteristic
223Q8—82no—
224Q8—82no—
225D4—84no—
226D4—82no—
227D4—82no—
228D4—82no—
229D4—82no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—44no—
238C2×C4—42no—
239C2×C4#6698514yes—
240C2×C4D4×Dic1112yes—
241C2×C4#6698911yescharacteristic
242C2×C4#6699112yes—
243C2×C4#6699311yescharacteristic
244C2×C4#6700211yescharacteristic
245C2×C4#6700312yes—
246C2×C4#6700411yescharacteristic
247C8—444no—
248C8—882no—
249C22—84no—
250C22—84no—
251C22—82no—
252C22—82no—
253C22—82no—
254C22#1062282812yes—
255C22#1062283411yescharacteristic
256C22#1062284511yescharacteristic
257C22#1062284611yescharacteristic
258C22#1062285012yes—
259C4—22no—
260C4—42no—
261C4—42no—
262C4—82no—
263C4#1062266712yes—
264C4#1062267012yes—
265C4#1062268412yes—
266C4#1062268712yes—
267C2—162no—
268C2#1306732112yes—
269C2#1306733812yes—
270C2#1306944111yescharacteristic
271C2#1306946611yescharacteristic
272C2#1306954911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2858C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#127C22
cosocleC2×C42×C11C23
hypercenter#2858D11
hypocenterC11#9710
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #2858

Complements

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

NH ≅ G/Ntype
1. #13068733C2semidirect
2. #13068469C2semidirect
3. C2×#10622185C2semidirect
216. C11#9710semidirect

Maximal subgroups

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

subgroupindex
#130687332
#130684692
C2×#106221852
C2×#106221822
C11×#28582
#971011