Finite Group Databasebeta

← #14664853

Subgroups — #14664853

Order 2816.

464 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 111 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#13070227C211yesmaximal, characteristic, complemented
2#13068641C211yesmaximal, characteristic, complemented
3#13066625C214yesmaximal, complemented
4C2×C11×#466C211yesmaximal, characteristic
5C22×C11×D8C411yescharacteristic, complemented
6C23×C8×C11C2211yescharacteristic
7C2×C11×#121—21no—
8C11×#466—21no—
9C11×#466—21no—
10C11×#466C412yescomplemented
11C11×#466C2212yes—
12C2×C11×#107C411yescharacteristic, complemented
13C2×C11×#102—21no—
14#10622825—21no—
15C2×#66881—21no—
16C2×#66876—21no—
17#10622189C2212yescomplemented
18C22⋊(C11⋊C16)—21no—
19C22⋊(C11⋊C16)C2212yescomplemented
20C22×D4×C11—21no—
21C22×D4×C11—41no—
22C23×C4×C11D411yescharacteristic
23C2×C11×D8—21no—
24C2×C11×D8—42no—
25C2×C11×D8C2×C412yes—
26C22×C8×C11—42no—
27C22×C8×C11C2×C411yescharacteristic
28C22×C8×C11C2×C411yescharacteristic
29C22×C8×C11D411yescharacteristic
30C22×C8×C11D411yescharacteristic
31C22×C8×C11D411yescharacteristic
32C22×C8×C11C2311yescharacteristic
33C11×#121—22no—
34C11×#121—22no—
35C11×#121—41no—
36C11×#121—41no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C22⋊C4—41no—
39C2×C22⋊Dic11—41no—
40C2×C4⋊Dic11—22no—
41C11×#107—21no—
42C11×#107C2×C412yes—
43C11×#102—22no—
44C11×#102—22no—
45C11⋊#95—41no—
46#66881—42no—
47#66876—42no—
48C2×C11⋊C16—22no—
49#11888—111nomaximal, Sylow
50C24×C11—41no—
51C24×C11D811yescharacteristic
52C2×D4×C11—22no—
53C2×D4×C11—42no—
54C2×D4×C11—42no—
55C2×D4×C11—42no—
56C2×D4×C11—42no—
57C2×D4×C11—41no—
58C2×D4×C11—84no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11D811yescharacteristic
65C22×C4×C11SD1611yescharacteristic
66C22×C4×C11SD1611yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—42no—
69C11×D8—42no—
70C11×D8—42no—
71C2×C8×C11—22no—
72C2×C8×C11—22no—
73C2×C8×C11—22no—
74C2×C8×C11—41no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C2×C8×C11C22⋊C411yescharacteristic
78C2×C8×C11C22⋊C411yescharacteristic
79C2×C8×C11C22×C411yescharacteristic
80C2×C8×C11C2×D411yescharacteristic
81C11×C4⋊C4—22no—
82C11×C4⋊C4—41no—
83C11×C22⋊C4—42no—
84C11×C22⋊C4—42no—
85C22⋊Dic11—82no—
86C4⋊Dic11—42no—
87C4⋊Dic11—42no—
88C11⋊C16—42no—
89C2×#466D1111yescharacteristic
90#2112—111no—
91#1807—111no—
92#1347—114no—
93C23×C11—22no—
94C23×C11—22no—
95C23×C11—41no—
96C23×C11—42no—
97C23×C11—82no—
98C23×C11—82no—
99C23×C11—82no—
100C23×C11#10211yescharacteristic
101C23×C11#10211yescharacteristic
102C23×C11C2×D811yescharacteristic
103D4×C11—42no—
104D4×C11—42no—
105D4×C11—82no—
106D4×C11—84no—
107D4×C11—84no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—42no—
118C2×C4×C11—82no—
119C2×C4×C11#10211yescharacteristic
120C2×C4×C11#10211yescharacteristic
121C2×C4×C11C2×C22⋊C411yescharacteristic
122C2×C4×C11C2×SD1611yescharacteristic
123C2×Dic11—82no—
124C2×Dic11—82no—
125C2×Dic11—82no—
126C8×C11—21no—
127C8×C11—21no—
128C8×C11—21no—
129C8×C11#9912yes—
130C22×D8Dic1111yescharacteristic, complemented
131C23×C8C2×D1111yescharacteristic
132C2×#121—21no—
133C2×M32—221no—
134#466—21no—
135#466—21no—
136#466Dic1112yescomplemented
137#466C2×D1112yes—
138C2×#107Dic1111yescharacteristic, complemented
139C2×#106—221no—
140C2×#102—21no—
141#380—221no—
142C22⋊C16—112no—
143C22⋊C16—221no—
144#340—112no—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11—44no—
153C22×C11—82no—
154C22×C11—82no—
155C22×C11—82no—
156C22×C11—164no—
157C22×C11#36012yes—
158C22×C11C2×#10211yescharacteristic
159C22×C11#50912yes—
160C4×C11—21no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—82no—
164C4×C11C2×#9911yescharacteristic
165C4×C11#42111yescharacteristic
166Dic11—162no—
167C22×D4—21no—
168C22×D4—41no—
169C23×C4C22⋊D1111yescharacteristic
170C2×D8—21no—
171C2×D8—42no—
172C2×D8C2×Dic1112yes—
173C22×C8—42no—
174C22×C8C2×Dic1111yescharacteristic
175C22×C8C2×Dic1111yescharacteristic
176C22×C8C22⋊D1111yescharacteristic
177C22×C8C22⋊D1111yescharacteristic
178C22×C8C22⋊D1111yescharacteristic
179C22×C8C22×D1111yescharacteristic
180#121—22no—
181#121—22no—
182#121—41no—
183#121—41no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—222no—
186C2×C22⋊C4—41no—
187C2×C22⋊C4—441no—
188M32—442no—
189C2×C16—222no—
190#107—21no—
191#107C2×Dic1112yes—
192#106—442no—
193#102—22no—
194#102—22no—
195#95—441no—
196C2×C11—22no—
197C2×C11—22no—
198C2×C11—41no—
199C2×C11—162no—
200C2×C11#151911yescharacteristic
201C2×C11#214011yescharacteristic
202C2×C11C2×#36011yescharacteristic
203C24—41no—
204C24#432311yescharacteristic
205C2×D4—22no—
206C2×D4—42no—
207C2×D4—42no—
208C2×D4—42no—
209C2×D4—42no—
210C2×D4—41no—
211C2×D4—84no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—442no—
216C22×C4#432311yescharacteristic
217C22×C4#432411yescharacteristic
218C22×C4#432411yescharacteristic
219C22×C4C22⋊Dic1111yescharacteristic
220C22×C4C22⋊Dic1111yescharacteristic
221C22×C4C2×C22⋊D1111yescharacteristic
222D8—42no—
223D8—42no—
224C2×C8—22no—
225C2×C8—22no—
226C2×C8—22no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8C22⋊Dic1111yescharacteristic
231C2×C8C22⋊Dic1111yescharacteristic
232C2×C8C22×Dic1111yescharacteristic
233C2×C8C2×C22⋊D1111yescharacteristic
234C4⋊C4—22no—
235C4⋊C4—41no—
236C4⋊C4—442no—
237C4⋊C4—442no—
238C22⋊C4—42no—
239C22⋊C4—42no—
240C22⋊C4—882no—
241C16—442no—
242C11#1188811yescharacteristic, complemented, Sylow
243C23—22no—
244C23—22no—
245C23—41no—
246C23—42no—
247C23—82no—
248C23—82no—
249C23—82no—
250C23#6689611yescharacteristic
251C23#6689611yescharacteristic
252C23C2×#432311yescharacteristic
253D4—42no—
254D4—42no—
255D4—82no—
256D4—84no—
257D4—84no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—82no—
269C2×C4—882no—
270C2×C4—882no—
271C2×C4—882no—
272C2×C4#6689611yescharacteristic
273C2×C4#6689611yescharacteristic
274C2×C4C2×#432411yescharacteristic
275C2×C4C2×C22⋊Dic1111yescharacteristic
276C8—21no—
277C8—21no—
278C8—21no—
279C8#6689812yes—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—44no—
288C22—82no—
289C22—82no—
290C22—82no—
291C22—164no—
292C22#1062220412yes—
293C22#1062276012yes—
294C22C2×#6689611yescharacteristic
295C4—21no—
296C4—21no—
297C4—21no—
298C4—82no—
299C4—1762no—
300C4C2×#6689811yescharacteristic
301C4#1062284911yescharacteristic
302C2—22no—
303C2—22no—
304C2—41no—
305C2—162no—
306C2#1306718411yescharacteristic
307C2#1307033211yescharacteristic
308C2C2×#1062220411yescharacteristic
subgroupG/H
centerC22C2×#66896
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
Fitting, prime radicalC2×C11×#466C2
socleC22×C11C2×#102
cosocleC22×C8×C11C23
hypercenterC2×#466D11
hypocenterC11#11888
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. #13070227C2semidirect
2. #13068641C2semidirect
3. #13066625C2semidirect
5. C22×C11×D8C4semidirect
10. C11×#466C4semidirect
12. C2×C11×#107C4semidirect
17. #10622189C22semidirect
19. C22⋊(C11⋊C16)C22semidirect
130. C22×D8Dic11semidirect
136. #466Dic11semidirect
138. C2×#107Dic11semidirect
242. C11#11888semidirect

Maximal subgroups

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

subgroupindex
#130702272
#130686412
#130666252
C2×C11×#4662
#1188811