Finite Group Databasebeta

← #13073799

Subgroups — #13073799

Order 1408.

584 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 147 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×#66950C211yesmaximal, characteristic, complemented
2C2×#66946C211yesmaximal, characteristic
3C11×#400C211yesmaximal, characteristic, complemented
4#10622605C211yesmaximal, characteristic, complemented
5#10622592C211yesmaximal, characteristic, complemented
6#10622286C211yesmaximal, characteristic, complemented
7#10622281C212yesmaximal, complemented
8#10622280C212yesmaximal, complemented
9#10622278C212yesmaximal
10D11×#95C211yesmaximal, characteristic, complemented
11#10622268C212yesmaximal, complemented
12C22×D44C2211yescharacteristic
13C22×C4×D11C2212yes—
14C22×C4×D11C2211yescharacteristic
15C22×C4×D11C2211yescharacteristic
16C22×Dic22C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×(C2×D11)⋊C4C2211yescharacteristic
20C2×(C2×D11)⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×C4⋊Dic11C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2212yes—
27C2×C4×Dic11C2211yescharacteristic
28#66950—24no—
29#66946—24no—
30C11×#95C2212yes—
31C11×#95C2211yescharacteristic
32C11×#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2211yescharacteristic
37C23×D11C2311yescharacteristic
38C23×D11C2311yescharacteristic
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2312yes—
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×Dic11C2311yescharacteristic
45C22×Dic11C2312yes—
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2312yes—
48C2×D44—22no—
49C2×D44—22no—
50C2×D44Q814yescomplemented
51C2×C4×D11—22no—
52C2×C4×D11—24no—
53C2×C4×D11—24no—
54C2×C4×D11—42no—
55C2×C4×D11—42no—
56C2×C4×D11—42no—
57C2×C4×D11D414yes—
58C2×Dic22—22no—
59C2×Dic22—42no—
60C11×C4⋊C4—22no—
61C11×C4⋊C4—22no—
62(C2×D11)⋊C4—24no—
63(C2×D11)⋊C4—22no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—22no—
66(C2×D11)⋊C4—42no—
67C4⋊Dic11—24no—
68Dic11⋊C4—24no—
69Dic11⋊C4—42no—
70C4×Dic11—22no—
71#2564—111nomaximal, Sylow
72C23×C11C2411yescharacteristic
73C22×D11—22no—
74C22×D11—22no—
75C22×D11—21no—
76C22×D11—22no—
77C22×D11—21no—
78C22×D11—22no—
79C22×D11C2×D412yes—
80C22×D11C2×Q812yes—
81C22×D11C2×Q812yes—
82C22×D11#4112yes—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11C2×D412yes—
95C2×C4×C11C2×Q812yes—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—21no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11C2×D412yes—
105C2×Dic11#4114yes—
106D44—28no—
107C4×D11—44no—
108C4×D11—48no—
109C4×D11—44no—
110Dic22—44no—
111C2×C22⋊Q8—111no—
112C2×C4×D4—111no—
113#400D1111yescharacteristic, complemented
114#399—111no—
115#395—111no—
116#393—111no—
117#387—112no—
118#386—112no—
119#385—112no—
120#380—112no—
121C2×#95—111no—
122C22×C11C22×D411yescharacteristic
123C22×C11C22×Q811yescharacteristic
124C22×C11C2×#4111yescharacteristic
125C22×C11C2×#4112yes—
126C22×C11H(5,𝔽2)12yes—
127C2×D11—22no—
128C2×D11—22no—
129C2×D11—24no—
130C2×D11—24no—
131C2×D11—22no—
132C2×D11—24no—
133C2×D11—41no—
134C2×D11—41no—
135C2×D11—42no—
136C2×D11C22⋊Q814yes—
137C4×C11—22no—
138C4×C11—22no—
139C4×C11—42no—
140C4×C11—41no—
141C4×C11—42no—
142Dic11—22no—
143Dic11—24no—
144Dic11—41no—
145Dic11—42no—
146C22×Q8—111no—
147C22×D4—111no—
148C23×C4—111no—
149C23×C4—112no—
150C23×C4—111no—
151C22⋊Q8—224no—
152C4×D4—224no—
153C2×C4⋊C4—112no—
154C2×C4⋊C4—112no—
155C2×C4⋊C4—112no—
156C2×C4⋊C4C2×D1111yescharacteristic
157C2×C4⋊C4C2×D1111yescharacteristic
158C2×C22⋊C4—111no—
159C2×C22⋊C4—111no—
160C2×C22⋊C4—112no—
161C2×C22⋊C4—112no—
162C2×C22⋊C4—112no—
163C2×C42—111no—
164#95—112no—
165#95—111no—
166#95—112no—
167#95—112no—
168#95C2×D1111yescharacteristic
169#95C2×D1112yes—
170#95C2×D1112yes—
171C2×C11C2×C22⋊Q811yescharacteristic
172C2×C11#53211yescharacteristic
173C2×C11#53411yescharacteristic
174C2×C11#55112yes—
175C2×C11#55412yes—
176D11—24no—
177D11—42no—
178C24—111no—
179C24—111no—
180C2×Q8—222no—
181C2×Q8—442no—
182C2×D4—114no—
183C2×D4—222no—
184C2×D4—222no—
185C22×C4—112no—
186C22×C4—111no—
187C22×C4—114no—
188C22×C4—111no—
189C22×C4—112no—
190C22×C4—222no—
191C22×C4—224no—
192C22×C4—224no—
193C22×C4—442no—
194C22×C4—442no—
195C22×C4—442no—
196C22×C4C22×D1112yes—
197C22×C4C22×D1112yes—
198C22×C4C22×D1111yescharacteristic
199C22×C4C22×D1111yescharacteristic
200C22×C4C22×D1111yescharacteristic
201C4⋊C4—22no—
202C4⋊C4—22no—
203C4⋊C4—224no—
204C4⋊C4—224no—
205C4⋊C4—442no—
206C22⋊C4—224no—
207C22⋊C4—222no—
208C22⋊C4—224no—
209C22⋊C4—222no—
210C22⋊C4—442no—
211C42—222no—
212C11#256411yescharacteristic, complemented, Sylow
213C23—112no—
214C23—112no—
215C23—112no—
216C23—112no—
217C23—222no—
218C23—222no—
219C23—221no—
220C23—222no—
221C23—221no—
222C23—222no—
223C23C23×D1111yescharacteristic
224Q8—444no—
225D4—228no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—112no—
238C2×C4—114no—
239C2×C4—222no—
240C2×C4—222no—
241C2×C4—222no—
242C2×C4—221no—
243C2×C4—222no—
244C2×C4—222no—
245C2×C4—222no—
246C2×C4—222no—
247C2×C4—444no—
248C2×C4—448no—
249C2×C4—444no—
250C2×C4D4×D1112yes—
251C2×C4Q8×D1112yes—
252C22—114no—
253C22—224no—
254C22—222no—
255C22—222no—
256C22—224no—
257C22—222no—
258C22—224no—
259C22—442no—
260C22—441no—
261C22—441no—
262C22C2×D4×D1111yescharacteristic
263C22C2×Q8×D1111yescharacteristic
264C22#41×D1111yescharacteristic
265C22#41×D1112yes—
266C22#6704212yes—
267C4—22no—
268C4—22no—
269C4—42no—
270C4—41no—
271C4—42no—
272C4—224no—
273C4—222no—
274C4—442no—
275C4—441no—
276C2—224no—
277C2—442no—
278C2D11×C22⋊Q811yescharacteristic
279C2#1062318411yescharacteristic
280C2#1062319911yescharacteristic
281C2#1062322112yes—
282C2#1062323612yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#400C2
prime radicalC22×D44C22
hypercenter#400D11
hypocenterC11#2564
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#66950C2semidirect
3. C11×#400C2semidirect
4. #10622605C2semidirect
5. #10622592C2semidirect
6. #10622286C2semidirect
7. #10622281C2semidirect
8. #10622280C2semidirect
10. D11×#95C2semidirect
11. #10622268C2semidirect
50. C2×D44Q8semidirect
113. #400D11semidirect
212. C11#2564semidirect

Maximal subgroups

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

subgroupindex
C2×#669502
C2×#669462
C11×#4002
#106226052
#106225922
#106222862
#106222812
#106222802
#106222782
D11×#952
#106222682
#256411