Finite Group Databasebeta

← #13073792

Subgroups — #13073792

Order 1408.

584 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×C11C211yesmaximal, characteristic
2C2×#66977C211yesmaximal, characteristic, complemented
3#10622833C212yesmaximal
4#10622823C212yesmaximal, complemented
5C2×C11⋊#95C211yesmaximal, characteristic, complemented
6#10622599C211yesmaximal, characteristic, complemented
7#10622592C211yesmaximal, characteristic, complemented
8#10622562C211yesmaximal, characteristic, complemented
9#10622560C211yesmaximal, characteristic, complemented
10#10622555C212yesmaximal, complemented
11#10622546C212yesmaximal, complemented
12C22×D4×C11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C23×C4×C11C2211yescharacteristic
15C23×Dic11C2212yes—
16C22×Dic22C2211yescharacteristic
17C4×D4×C11—24no—
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C42×C11C2211yescharacteristic
22C2×C22⋊Dic11C2212yes—
23C2×C22⋊Dic11C2212yes—
24C2×C22⋊Dic11C2212yes—
25C2×C4⋊Dic11C2211yescharacteristic
26#66977—24no—
27C2×Dic11⋊C4C2212yes—
28C2×Dic11⋊C4C2212yes—
29C2×Dic11⋊C4C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2211yescharacteristic
37C24×C11C2311yescharacteristic
38C24×C11C2311yescharacteristic
39C2×D4×C11—22no—
40C2×D4×C11—22no—
41C2×D4×C11Q814yescomplemented
42C22×C4×C11—22no—
43C22×C4×C11—42no—
44C22×C4×C11—42no—
45C22×C4×C11D414yes—
46C22×C4×C11C2311yescharacteristic
47C22×C4×C11C2311yescharacteristic
48C22×C4×C11C2311yescharacteristic
49C22×C4×C11C2311yescharacteristic
50C22×C4×C11C2311yescharacteristic
51C22×Dic11—24no—
52C22×Dic11—24no—
53C22×Dic11—42no—
54C22×Dic11C2312yes—
55C22×Dic11C2312yes—
56C22×Dic11C2312yes—
57C22×Dic11C2312yes—
58C2×Dic22—22no—
59C2×Dic22—42no—
60C11×C4⋊C4—22no—
61C11×C22⋊C4—22no—
62C11×C22⋊C4—22no—
63C42×C11—22no—
64C22⋊Dic11—24no—
65C22⋊Dic11—24no—
66C22⋊Dic11—42no—
67C4⋊Dic11—22no—
68Dic11⋊C4—24no—
69Dic11⋊C4—24no—
70Dic11⋊C4—42no—
71#2564—111nomaximal, Sylow
72C23×C11—22no—
73C23×C11—22no—
74C23×C11—21no—
75C23×C11—22no—
76C23×C11—21no—
77C23×C11—22no—
78C23×C11C2×D412yes—
79C23×C11C2×Q812yes—
80C23×C11C2×Q812yes—
81C23×C11#4112yes—
82C23×C11C2411yescharacteristic
83D4×C11—28no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—44no—
93C2×C4×C11—44no—
94C2×C4×C11C2×D412yes—
95C2×C4×C11C2×D412yes—
96C2×C4×C11C2×Q812yes—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11—48no—
109C2×Dic11#4114yes—
110Dic22—44no—
111C2×C22⋊Q8—111no—
112C2×C4×D4D1111yescharacteristic
113#400—111no—
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×C11—22no—
123C22×C11—22no—
124C22×C11—24no—
125C22×C11—24no—
126C22×C11—22no—
127C22×C11—24no—
128C22×C11—41no—
129C22×C11—41no—
130C22×C11—42no—
131C22×C11C22⋊Q814yes—
132C22×C11C22×D411yescharacteristic
133C22×C11C22×Q811yescharacteristic
134C22×C11C2×#4111yescharacteristic
135C22×C11C2×#4112yes—
136C22×C11H(5,𝔽2)12yes—
137C4×C11—22no—
138C4×C11—22no—
139C4×C11—22no—
140C4×C11—41no—
141C4×C11—41no—
142Dic11—24no—
143Dic11—42no—
144Dic11—42no—
145Dic11—42no—
146C22×Q8—111no—
147C22×D4C2×D1111yescharacteristic
148C23×C4—112no—
149C23×C4C2×D1111yescharacteristic
150C23×C4C2×D1111yescharacteristic
151C22⋊Q8—224no—
152C4×D4—24no—
153C2×C4⋊C4—112no—
154C2×C4⋊C4—111no—
155C2×C4⋊C4—112no—
156C2×C4⋊C4—112no—
157C2×C4⋊C4C2×D1111yescharacteristic
158C2×C22⋊C4—112no—
159C2×C22⋊C4—112no—
160C2×C22⋊C4—112no—
161C2×C22⋊C4C2×D1111yescharacteristic
162C2×C22⋊C4C2×D1111yescharacteristic
163C2×C42C2×D1111yescharacteristic
164#95—112no—
165#95—111no—
166#95—111no—
167#95—112no—
168#95—112no—
169#95—112no—
170#95—112no—
171C2×C11—24no—
172C2×C11—42no—
173C2×C11C2×C22⋊Q811yescharacteristic
174C2×C11#53211yescharacteristic
175C2×C11#53411yescharacteristic
176C2×C11#55112yes—
177C2×C11#55412yes—
178C24C22×D1111yescharacteristic
179C24C22×D1111yescharacteristic
180C2×Q8—222no—
181C2×Q8—442no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4Dic2214yescomplemented
185C22×C4—22no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—112no—
189C22×C4—112no—
190C22×C4—112no—
191C22×C4—112no—
192C22×C4—224no—
193C22×C4—224no—
194C22×C4—442no—
195C22×C4C22⋊D1114yes—
196C22×C4C22×D1111yescharacteristic
197C22×C4C22×D1111yescharacteristic
198C22×C4C22×D1111yescharacteristic
199C22×C4C22×D1111yescharacteristic
200C22×C4C22×D1111yescharacteristic
201C4⋊C4—22no—
202C4⋊C4—224no—
203C4⋊C4—224no—
204C4⋊C4—222no—
205C4⋊C4—442no—
206C22⋊C4—22no—
207C22⋊C4—22no—
208C22⋊C4—224no—
209C22⋊C4—224no—
210C22⋊C4—442no—
211C42—22no—
212C11#256411yescharacteristic, complemented, Sylow
213C23—22no—
214C23—22no—
215C23—21no—
216C23—22no—
217C23—22no—
218C23—21no—
219C23C2×Dic2212yes—
220C23C2×Dic2212yes—
221C23#433912yes—
222C23C2×C22⋊D1112yes—
223C23C23×D1111yescharacteristic
224Q8—444no—
225D4—28no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—44no—
235C2×C4—44no—
236C2×C4—114no—
237C2×C4—222no—
238C2×C4—222no—
239C2×C4—222no—
240C2×C4—222no—
241C2×C4—222no—
242C2×C4—222no—
243C2×C4—222no—
244C2×C4—222no—
245C2×C4—222no—
246C2×C4—222no—
247C2×C4—222no—
248C2×C4—448no—
249C2×C4C2×Dic2212yes—
250C2×C4C2×C22⋊D1112yes—
251C2×C4C2×C22⋊D1112yes—
252C22—24no—
253C22—22no—
254C22—24no—
255C22—22no—
256C22—22no—
257C22—24no—
258C22—41no—
259C22—42no—
260C22—41no—
261C22#6697714yes—
262C22C22×Dic2211yescharacteristic
263C22C2×#433911yescharacteristic
264C22#6703712yes—
265C22#41×D1112yes—
266C22C22×C22⋊D1111yescharacteristic
267C4—22no—
268C4—22no—
269C4—22no—
270C4—41no—
271C4—41no—
272C4—224no—
273C4—442no—
274C4—442no—
275C4—442no—
276C2—24no—
277C2—42no—
278C2#1062307012yes—
279C2#1062308712yes—
280C2C2×#6697711yescharacteristic
281C2#1062333511yescharacteristic
282C2#1062336311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C4×D4×C11C2
prime radicalC22×D4×C11C22
hypercenterC2×C4×D4D11
hypocenterC11#2564
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#66977C2semidirect
4. #10622823C2semidirect
5. C2×C11⋊#95C2semidirect
6. #10622599C2semidirect
7. #10622592C2semidirect
8. #10622562C2semidirect
9. #10622560C2semidirect
10. #10622555C2semidirect
11. #10622546C2semidirect
41. C2×D4×C11Q8semidirect
184. C2×D4Dic22semidirect
212. C11#2564semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C112
C2×#669772
#106228332
#106228232
C2×C11⋊#952
#106225992
#106225922
#106225622
#106225602
#106225552
#106225462
#256411