Finite Group Databasebeta

← #13073520

Subgroups — #13073520

Order 1408.

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

normal subgroups only

This group has 604 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
1C2×D4×Dic11C211yesmaximal, characteristic
2C2×#66940C211yesmaximal, characteristic, complemented
3C2×#66931C212yesmaximal, complemented
4C11×#394C211yesmaximal, characteristic
5#10622835C211yesmaximal, characteristic
6#10622596C211yesmaximal, characteristic, complemented
7#10622564C212yesmaximal, complemented
8#10622558C212yesmaximal, complemented
9#10622555C212yesmaximal, complemented
10#10622274C211yesmaximal, characteristic, complemented
11#10622263C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C23×Dic11C2212yes—
14C22×Dic22C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C22⋊C4C2212yes—
17C2×C11×C22⋊C4C2212yes—
18C2×C22⋊Dic11C2212yes—
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2212yes—
21D4×Dic11—24no—
22C2×C4⋊Dic11C2212yes—
23C2×C4⋊Dic11C2211yescharacteristic
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2211yescharacteristic
27C2×Dic11⋊C4C2211yescharacteristic
28C2×C4×Dic11C2211yescharacteristic
29C2×C4×Dic11C2211yescharacteristic
30C2×C4×Dic11C2211yescharacteristic
31#66940—24no—
32#66931—28no—
33C11×#95C2211yescharacteristic
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C11⋊#95C2212yes—
38C24×C11C2312yes—
39C2×D4×C11—24no—
40C2×D4×C11—22no—
41C22×C4×C11C2312yes—
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C22×Dic11—24no—
46C22×Dic11—24no—
47C22×Dic11—24no—
48C22×Dic11C2312yes—
49C22×Dic11C2311yescharacteristic
50C22×Dic11C2312yes—
51C22×Dic11C2311yescharacteristic
52C22×Dic11C2311yescharacteristic
53C22×Dic11C2311yescharacteristic
54C2×Dic22—22no—
55C2×Dic22—22no—
56C2×Dic22D414yescomplemented
57C11×C4⋊C4—22no—
58C11×C22⋊C4—24no—
59C11×C22⋊C4—24no—
60C22⋊Dic11—24no—
61C22⋊Dic11—24no—
62C22⋊Dic11—24no—
63C4⋊Dic11—24no—
64C4⋊Dic11—22no—
65Dic11⋊C4—24no—
66Dic11⋊C4—22no—
67Dic11⋊C4—24no—
68Dic11⋊C4—22no—
69C4×Dic11—22no—
70C4×Dic11—22no—
71C4×Dic11D414yes—
72#2536—111nomaximal, Sylow
73C23×C11—22no—
74C23×C11—22no—
75C23×C11—22no—
76C23×C11—22no—
77C23×C11—22no—
78C23×C11—22no—
79C23×C11#4114yes—
80C23×C11C2411yescharacteristic
81D4×C11—28no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—22no—
85C2×C4×C11—21no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11C2×D412yes—
91C2×C4×C11C2×D412yes—
92C2×Dic11—21no—
93C2×Dic11—21no—
94C2×Dic11—22no—
95C2×Dic11—21no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—48no—
104C2×Dic11C2×D412yes—
105C2×Dic11C2×D412yes—
106C2×Dic11C2×D412yes—
107C2×Dic11C2×D412yes—
108C2×Dic11#4112yes—
109Dic22—28no—
110C2×C22⋊Q8—112no—
111C2×C4×Q8—111no—
112C2×C4×D4—111no—
113#398—111no—
114#398—111no—
115#394—111no—
116#394D1111yescharacteristic
117#388—112no—
118#388—112no—
119#382—111no—
120#380—112no—
121C22×C11—24no—
122C22×C11—24no—
123C22×C11—24no—
124C22×C11—42no—
125C22×C11—42no—
126C22×C11—42no—
127C22×C11—42no—
128C22×C11C22×D411yescharacteristic
129C22×C11C22×D411yescharacteristic
130C22×C11C2×#4112yes—
131C22×C11C2×#4111yescharacteristic
132C22×C112−1+412yes—
133C4×C11—22no—
134C4×C11—22no—
135C4×C11—41no—
136C4×C11—42no—
137Dic11—22no—
138Dic11—22no—
139Dic11—42no—
140Dic11—41no—
141Dic11—42no—
142Dic11#12114yes—
143C22×Q8—111no—
144C22×D4C2×D1111yescharacteristic
145C23×C4—112no—
146C22⋊Q8—228no—
147C4×Q8—224no—
148C4×D4—224no—
149C2×C4⋊C4—111no—
150C2×C4⋊C4—111no—
151C2×C4⋊C4—111no—
152C2×C4⋊C4—112no—
153C2×C4⋊C4—112no—
154C2×C4⋊C4—112no—
155C2×C4⋊C4C2×D1111yescharacteristic
156C2×C22⋊C4—112no—
157C2×C22⋊C4—112no—
158C2×C22⋊C4—112no—
159C2×C22⋊C4C2×D1112yes—
160C2×C22⋊C4C2×D1112yes—
161C2×C42—111no—
162C2×C42—111no—
163C2×C42—111no—
164#95—112no—
165#95—112no—
166#95—112no—
167#95—111no—
168#95C2×D1111yescharacteristic
169C2×C11—44no—
170C2×C11C2×#12111yescharacteristic
171C2×C11#52511yescharacteristic
172C2×C11#53611yescharacteristic
173C2×C11#54812yes—
174C2×C11#55212yes—
175C24C22×D1112yes—
176C2×Q8—114no—
177C2×Q8—222no—
178C2×Q8—222no—
179C2×D4—24no—
180C2×D4—22no—
181C22×C4—111no—
182C22×C4—111no—
183C22×C4—111no—
184C22×C4—112no—
185C22×C4—111no—
186C22×C4—112no—
187C22×C4—224no—
188C22×C4—224no—
189C22×C4—224no—
190C22×C4C22×D1112yes—
191C22×C4C22×D1111yescharacteristic
192C22×C4C22×D1111yescharacteristic
193C22×C4C22×D1111yescharacteristic
194C4⋊C4—22no—
195C4⋊C4—222no—
196C4⋊C4—224no—
197C4⋊C4—224no—
198C4⋊C4—222no—
199C4⋊C4—222no—
200C4⋊C4—224no—
201C22⋊C4—24no—
202C22⋊C4—24no—
203C22⋊C4—224no—
204C22⋊C4—224no—
205C22⋊C4—224no—
206C42—114no—
207C42—222no—
208C42—222no—
209C11#253611yescharacteristic, complemented, Sylow
210C23—22no—
211C23—22no—
212C23—22no—
213C23—22no—
214C23—22no—
215C23—22no—
216C23#434114yes—
217C23C23×D1111yescharacteristic
218Q8—228no—
219D4—28no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—112no—
229C2×C4—112no—
230C2×C4—112no—
231C2×C4—112no—
232C2×C4—112no—
233C2×C4—221no—
234C2×C4—221no—
235C2×C4—222no—
236C2×C4—221no—
237C2×C4—222no—
238C2×C4—222no—
239C2×C4—222no—
240C2×C4—222no—
241C2×C4—222no—
242C2×C4—222no—
243C2×C4—222no—
244C2×C4—448no—
245C2×C4D4×D1112yes—
246C2×C4D4×D1112yes—
247C22—24no—
248C22—24no—
249C22—24no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22C2×D4×D1111yescharacteristic
255C22C2×D4×D1111yescharacteristic
256C22C2×#434112yes—
257C22#41×D1111yescharacteristic
258C22#6704312yes—
259C4—22no—
260C4—22no—
261C4—41no—
262C4—42no—
263C4—114no—
264C4—222no—
265C4—222no—
266C4—441no—
267C4—442no—
268C4—442no—
269C2—44no—
270C2#1062311711yescharacteristic
271C2#1062312912yes—
272C2D11×#12111yescharacteristic
273C2#1062318112yes—
274C2#1062320611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
prime radicalC22×D4×C11C22
hypercenter#394D11
hypocenterC11#2536
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#66940C2semidirect
3. C2×#66931C2semidirect
6. #10622596C2semidirect
7. #10622564C2semidirect
8. #10622558C2semidirect
9. #10622555C2semidirect
10. #10622274C2semidirect
11. #10622263C2semidirect
56. C2×Dic22D4semidirect
209. C11#2536semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic112
C2×#669402
C2×#669312
C11×#3942
#106228352
#106225962
#106225642
#106225582
#106225552
#106222742
#106222632
#253611