Finite Group Databasebeta

← #14641572

Subgroups — #14641572

Order 2816.

290 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×#10622180C211yesmaximal, characteristic
2#13069433C211yesmaximal, characteristic
3C2×C11×#354C211yesmaximal, characteristic
4C2×C11×#124C2211yescharacteristic
5C2×C11×#99—21no—
6C2×#66900—21no—
7C2×#66899—21no—
8C2×#66896—21no—
9#10622548C411yescharacteristic, complemented
10C2×#66867C411yescharacteristic, complemented
11C11×#354—21no—
12C11×#354C412yescomplemented
13#10622180—21no—
14#10622180C412yescomplemented
15C22×Q8×C11D411yescharacteristic
16C22×D4×C11D411yescharacteristic
17C11×#124—41no—
18C11×#124C2×C411yescharacteristic
19C11×#124C2×C411yescharacteristic
20C11×#124D411yescharacteristic
21C11×#124Q811yescharacteristic
22C2×C11×C22⋊C4—41no—
23C2×C11×C22⋊C4—41no—
24C2×C42×C11C2×C411yescharacteristic
25C2×C4⋊Dic11—21no—
26C2×C4⋊Dic11—41no—
27C2×#4318—41no—
28C22×C11⋊C8—21no—
29C11×#99—22no—
30C11×#99—41no—
31#66900—22no—
32#66900—41no—
33#66899—42no—
34#66896—42no—
35#66867—41no—
36#7508—111nomaximal, Sylow
37C24×C11—21no—
38C2×Q8×C11—21no—
39C2×Q8×C11—41no—
40C2×Q8×C11—41no—
41C2×Q8×C11C22⋊C411yescharacteristic
42C2×Q8×C11C4⋊C411yescharacteristic
43C2×D4×C11—21no—
44C2×D4×C11—41no—
45C2×D4×C11—41no—
46C2×D4×C11C22⋊C411yescharacteristic
47C2×D4×C11C4⋊C411yescharacteristic
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11—81no—
51C22×C4×C11C22⋊C411yescharacteristic
52C22×Dic11—41no—
53C11×C22⋊C4—41no—
54C11×C22⋊C4—41no—
55C11×C22⋊C4—41no—
56C11×C22⋊C4—41no—
57C11×C22⋊C4—42no—
58C11×C22⋊C4—81no—
59C42×C11—21no—
60C42×C11C4211yescharacteristic
61C42×C11C4⋊C411yescharacteristic
62C4⋊Dic11—41no—
63C4⋊Dic11—41no—
64C4⋊Dic11—82no—
65#4318—42no—
66#4318—81no—
67C2×C11⋊C8—22no—
68C2×C11⋊C8—41no—
69C2×C11⋊C8—41no—
70C2×C11⋊C8—81no—
71C2×#355—111no—
72C2×#354D1111yescharacteristic
73#1959—111no—
74C23×C11—21no—
75C23×C11—21no—
76C23×C11—41no—
77C23×C11—41no—
78C23×C11—81no—
79C23×C11—81no—
80C23×C11#9911yescharacteristic
81Q8×C11—41no—
82Q8×C11—41no—
83Q8×C11—81no—
84D4×C11—41no—
85D4×C11—41no—
86D4×C11—81no—
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—41no—
94C2×C4×C11—41no—
95C2×C4×C11—41no—
96C2×C4×C11—41no—
97C2×C4×C11—82no—
98C2×C4×C11—161no—
99C2×C4×C11—161no—
100C2×C4×C11#9511yescharacteristic
101C2×C4×C11#9911yescharacteristic
102C2×Dic11—82no—
103C2×Dic11—81no—
104C11⋊C8—42no—
105C11⋊C8—82no—
106C2×#124C2×D1111yescharacteristic
107C2×#103—221no—
108C2×#102—221no—
109C2×#101—221no—
110C2×#99—21no—
111C2×#97—111no—
112#384—111no—
113#355—112no—
114#355—221no—
115#354—21no—
116#354Dic1112yescomplemented
117C22×C11—21no—
118C22×C11—21no—
119C22×C11—41no—
120C22×C11—41no—
121C22×C11—81no—
122C22×C11—81no—
123C22×C11—81no—
124C22×C11—81no—
125C22×C11—161no—
126C22×C11#34211yescharacteristic
127C22×C11#35311yescharacteristic
128C22×C11#35411yescharacteristic
129C4×C11—21no—
130C4×C11—21no—
131C4×C11—41no—
132C4×C11—41no—
133C4×C11—41no—
134C4×C11—41no—
135C4×C11—162no—
136Dic11—161no—
137C22×Q8D4411yescharacteristic
138C22×D4C22⋊D1111yescharacteristic
139C2×M16—441no—
140C22×C8—221no—
141#124—41no—
142#124Dic2211yescharacteristic
143#124C4×D1111yescharacteristic
144#124C2×Dic1111yescharacteristic
145#124C22⋊D1111yescharacteristic
146C2×C4⋊C4—221no—
147C2×C4⋊C4—441no—
148C2×C22⋊C4—41no—
149C2×C22⋊C4—41no—
150C2×C42C4×D1111yescharacteristic
151#103—442no—
152#102—442no—
153#101—222no—
154#101—441no—
155#99—22no—
156#99—41no—
157#97—441no—
158C2×C11—21no—
159C2×C11—21no—
160C2×C11—81no—
161C2×C11—81no—
162C2×C11#139311yescharacteristic
163C2×C11#140611yescharacteristic
164C2×C11#140711yescharacteristic
165C24—21no—
166C2×Q8—21no—
167C2×Q8—41no—
168C2×Q8—41no—
169C2×Q8C4⋊Dic1111yescharacteristic
170C2×Q8(C2×D11)⋊C411yescharacteristic
171C2×D4—21no—
172C2×D4—41no—
173C2×D4—41no—
174C2×D4Dic11⋊C411yescharacteristic
175C2×D4C22⋊Dic1111yescharacteristic
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—81no—
179C22×C4—441no—
180C22×C4(C2×D11)⋊C411yescharacteristic
181M16—442no—
182M16—881no—
183C2×C8—222no—
184C2×C8—441no—
185C2×C8—441no—
186C2×C8—881no—
187C4⋊C4—441no—
188C4⋊C4—441no—
189C4⋊C4—882no—
190C22⋊C4—41no—
191C22⋊C4—41no—
192C22⋊C4—41no—
193C22⋊C4—41no—
194C22⋊C4—42no—
195C22⋊C4—81no—
196C42—21no—
197C42C4×Dic1111yescharacteristic
198C42Dic11⋊C411yescharacteristic
199C11#750811yescharacteristic, complemented, Sylow
200C23—21no—
201C23—21no—
202C23—41no—
203C23—41no—
204C23—81no—
205C23—81no—
206C23#6687011yescharacteristic
207Q8—41no—
208Q8—41no—
209Q8—81no—
210D4—41no—
211D4—41no—
212D4—81no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—82no—
224C2×C4—161no—
225C2×C4—161no—
226C2×C4—882no—
227C2×C4—881no—
228C2×C4#6687011yescharacteristic
229C2×C4C11⋊#9511yescharacteristic
230C8—442no—
231C8—882no—
232C22—21no—
233C22—21no—
234C22—41no—
235C22—41no—
236C22—81no—
237C22—81no—
238C22—81no—
239C22—81no—
240C22—161no—
241C22#1062211111yescharacteristic
242C22#1062211211yescharacteristic
243C22#1062216511yescharacteristic
244C4—21no—
245C4—21no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—162no—
251C4—1761no—
252C2—21no—
253C2—21no—
254C2—81no—
255C2—81no—
256C2#1306674011yescharacteristic
257C2#1306677211yescharacteristic
258C2#1306677511yescharacteristic
subgroupG/H
centerC22#10622112
commutatorC42×C11C42
FrattiniC2×#124C2×D11
FittingC2×C11×#354C2
socleC22×C11#353
prime radicalC22×D4×C11D4
cosocleC2×C11×#124C22
hypercenterC2×#354D11
hypocenterC11#7508
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×#124 ◁ C2×#354

Complements

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

NH ≅ G/Ntype
9. #10622548C4semidirect
10. C2×#66867C4semidirect
12. C11×#354C4semidirect
14. #10622180C4semidirect
116. #354Dic11semidirect
199. C11#7508semidirect

Maximal subgroups

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

subgroupindex
C2×#106221802
#130694332
C2×C11×#3542
#750811