Finite Group Databasebeta

← #13074481

Subgroups — #13074481

Order 1408.

500 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 131 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×#66989C211yesmaximal, characteristic
2C2×#66940C211yesmaximal, characteristic, complemented
3C11×#394C211yesmaximal, characteristic
4#10622835C211yesmaximal, characteristic
5#10622592C211yesmaximal, characteristic, complemented
6#10622564C212yesmaximal, complemented
7#10622562C212yesmaximal, complemented
8#10622560C212yesmaximal, complemented
9#10622558C212yesmaximal, complemented
10#10622269C211yesmaximal, characteristic, complemented
11#10622264C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C22×Dic22C2211yescharacteristic
14C22×Dic22C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C22⋊C4C2212yes—
17C2×C11×C22⋊C4C2212yes—
18C2×C22⋊Dic11C2212yes—
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2212yes—
21C2×C22⋊Dic11C2212yes—
22#66989—24no—
23C2×C4⋊Dic11C2212yes—
24C2×Dic11⋊C4C2211yescharacteristic
25C2×Dic11⋊C4C2211yescharacteristic
26C2×Dic11⋊C4C2212yes—
27C2×C4×Dic11C2211yescharacteristic
28C2×C4×Dic11C2211yescharacteristic
29C2×C4×Dic11C2211yescharacteristic
30#66940—24no—
31C11×#95C2211yescharacteristic
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2211yescharacteristic
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2312yes—
38C2×D4×C11—22no—
39C2×D4×C11—42no—
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C22×Dic11C2311yescharacteristic
49C22×Dic11C2311yescharacteristic
50C2×Dic22—22no—
51C2×Dic22—22no—
52C2×Dic22—22no—
53C2×Dic22—22no—
54C2×Dic22—42no—
55C11×C4⋊C4—22no—
56C11×C22⋊C4—24no—
57C11×C22⋊C4—42no—
58C22⋊Dic11—24no—
59C22⋊Dic11—24no—
60C22⋊Dic11—24no—
61C22⋊Dic11—42no—
62C4⋊Dic11—42no—
63Dic11⋊C4—22no—
64Dic11⋊C4—22no—
65Dic11⋊C4—42no—
66C4×Dic11—22no—
67C4×Dic11—22no—
68C4×Dic11D414yes—
69#2632—111nomaximal, Sylow
70C23×C11—22no—
71C23×C11—22no—
72C23×C11—22no—
73C23×C11—22no—
74C23×C11—22no—
75C23×C11—22no—
76C23×C11—22no—
77C23×C11C2411yescharacteristic
78D4×C11—44no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—21no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11C2×D412yes—
88C2×C4×C11#4112yes—
89C2×Dic11—21no—
90C2×Dic11—21no—
91C2×Dic11—21no—
92C2×Dic11—21no—
93C2×Dic11—22no—
94C2×Dic11—21no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11C2×D412yes—
103C2×Dic11C2×D412yes—
104C2×Dic11#4112yes—
105Dic22—28no—
106Dic22—44no—
107C2×#124—111no—
108C2×C4×Q8—111no—
109#399—112no—
110#395—111no—
111#395—111no—
112#394—111no—
113#394D1111yescharacteristic
114#393—112no—
115#388—112no—
116#388—112no—
117#383—111no—
118C22×C11—42no—
119C22×C11—42no—
120C22×C11—42no—
121C22×C11—42no—
122C22×C11—42no—
123C22×C11—42no—
124C22×C11—42no—
125C22×C11C22×D411yescharacteristic
126C22×C11C2×#4111yescharacteristic
127C22×C11C2×#4111yescharacteristic
128C22×C11H(5,𝔽2)12yes—
129C22×C112−1+412yes—
130C4×C11—22no—
131C4×C11—22no—
132C4×C11—41no—
133C4×C11—42no—
134Dic11—22no—
135Dic11—22no—
136Dic11—22no—
137Dic11—42no—
138Dic11—41no—
139Dic11—42no—
140C22×Q8—111no—
141C22×Q8—111no—
142C22×D4C2×D1111yescharacteristic
143#124—224no—
144C4×Q8—224no—
145C2×C4⋊C4—111no—
146C2×C4⋊C4—111no—
147C2×C4⋊C4—112no—
148C2×C4⋊C4—112no—
149C2×C4⋊C4C2×D1111yescharacteristic
150C2×C22⋊C4—112no—
151C2×C22⋊C4—112no—
152C2×C22⋊C4—112no—
153C2×C22⋊C4—112no—
154C2×C22⋊C4C2×D1112yes—
155C2×C22⋊C4C2×D1112yes—
156C2×C42—111no—
157C2×C42—111no—
158C2×C42—111no—
159#95—112no—
160#95—112no—
161#95—111no—
162#95—112no—
163#95—112no—
164#95C2×D1111yescharacteristic
165C2×C11—82no—
166C2×C11#52511yescharacteristic
167C2×C11#53511yescharacteristic
168C2×C11#53611yescharacteristic
169C2×C11#54212yes—
170C2×C11#54212yes—
171C24C22×D1112yes—
172C2×Q8—222no—
173C2×Q8—222no—
174C2×Q8—222no—
175C2×Q8—222no—
176C2×Q8—442no—
177C2×D4—22no—
178C2×D4—42no—
179C22×C4—111no—
180C22×C4—111no—
181C22×C4—111no—
182C22×C4—112no—
183C22×C4—112no—
184C22×C4—111no—
185C22×C4C22×D1112yes—
186C22×C4C22×D1111yescharacteristic
187C22×C4C22×D1111yescharacteristic
188C22×C4C22×D1111yescharacteristic
189C4⋊C4—22no—
190C4⋊C4—222no—
191C4⋊C4—222no—
192C4⋊C4—442no—
193C4⋊C4—442no—
194C22⋊C4—24no—
195C22⋊C4—42no—
196C22⋊C4—224no—
197C22⋊C4—224no—
198C22⋊C4—224no—
199C22⋊C4—442no—
200C42—114no—
201C42—222no—
202C42—222no—
203C11#263211yescharacteristic, complemented, Sylow
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—22no—
209C23—22no—
210C23—22no—
211C23C23×D1111yescharacteristic
212Q8—228no—
213Q8—444no—
214D4—44no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—112no—
224C2×C4—112no—
225C2×C4—112no—
226C2×C4—221no—
227C2×C4—221no—
228C2×C4—221no—
229C2×C4—221no—
230C2×C4—222no—
231C2×C4—221no—
232C2×C4—222no—
233C2×C4—222no—
234C2×C4—222no—
235C2×C4—222no—
236C2×C4—222no—
237C2×C4—222no—
238C2×C4—222no—
239C2×C4D4×D1112yes—
240C2×C4#434112yes—
241C22—42no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22C2×D4×D1111yescharacteristic
249C22C2×#434111yescharacteristic
250C22#6703712yes—
251C22#41×D1111yescharacteristic
252C22#6704312yes—
253C4—22no—
254C4—22no—
255C4—41no—
256C4—42no—
257C4—222no—
258C4—222no—
259C4—222no—
260C4—442no—
261C4—441no—
262C4—442no—
263C2—82no—
264C2#1062312311yescharacteristic
265C2#1062313412yes—
266C2#1062313711yescharacteristic
267C2#1062319312yes—
268C2#1062320611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
prime radicalC22×D4×C11C22
hypercenter#394D11
hypocenterC11#2632
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#66940C2semidirect
5. #10622592C2semidirect
6. #10622564C2semidirect
7. #10622562C2semidirect
8. #10622560C2semidirect
9. #10622558C2semidirect
10. #10622269C2semidirect
11. #10622264C2semidirect
203. C11#2632semidirect

Maximal subgroups

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

subgroupindex
C2×#669892
C2×#669402
C11×#3942
#106228352
#106225922
#106225642
#106225622
#106225602
#106225582
#106222692
#106222642
#263211