Finite Group Databasebeta

← #22596411

Subgroups — #22596411

Order 9088.

456 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14556121C212yesmaximal, complemented
2#17985933C212yesmaximal, complemented
3#17985929C211yesmaximal, characteristic, complemented
4#17985922C212yesmaximal, complemented
5#17985922C212yesmaximal, complemented
6#17985922C212yesmaximal, complemented
7#17985913C212yesmaximal
8#17985868C211yesmaximal, characteristic, complemented
9#394×C71C211yesmaximal, characteristic
10#14556121—28no—
11C2×C4⋊Dic71C2212yes—
12C2×C4⋊Dic71C2211yescharacteristic
13C2×C4⋊Dic71C2211yescharacteristic
14C2×Dic71⋊C4C2212yes—
15C2×Dic71⋊C4C2212yes—
16C2×Dic71⋊C4C2212yes—
17C2×Dic71⋊C4C2212yes—
18C2×Dic71⋊C4C2212yes—
19C2×C22⋊Dic71C2212yes—
20C2×C22⋊Dic71C2212yes—
21C2×C22⋊Dic71C2212yes—
22C2×C22⋊Dic71C2212yes—
23C2×C4×Dic71C2211yescharacteristic
24C71⋊#95C2212yes—
25C71⋊#95C2211yescharacteristic
26C71⋊#95C2212yes—
27C22×D4×C71C2211yescharacteristic
28C2×C4⋊C4×C71C2211yescharacteristic
29C2×C22⋊C4×C71C2212yes—
30C2×C22⋊C4×C71C2212yes—
31#95×C71C2211yescharacteristic
32C22×Dic71C2312yes—
33C22×Dic71C2312yes—
34C22×Dic71C2312yes—
35C22×Dic71C2312yes—
36C4⋊Dic71—24no—
37C4⋊Dic71—41no—
38C4⋊Dic71—41no—
39Dic71⋊C4—24no—
40Dic71⋊C4—24no—
41Dic71⋊C4—42no—
42Dic71⋊C4—42no—
43Dic71⋊C4—42no—
44C22⋊Dic71—24no—
45C22⋊Dic71—24no—
46C22⋊Dic71—42no—
47C22⋊Dic71—42no—
48C4×Dic71D414yescomplemented
49C24×C71C2312yes—
50C2×D4×C71—41no—
51C2×D4×C71—42no—
52C22×C4×C71C2312yes—
53C22×C4×C71C2311yescharacteristic
54C22×C4×C71C2311yescharacteristic
55C22×C4×C71C2311yescharacteristic
56C4⋊C4×C71—41no—
57C22⋊C4×C71—24no—
58C22⋊C4×C71—42no—
59C23×C71—22no—
60C23×C71—22no—
61C23×C71—22no—
62C23×C71—22no—
63C23×C71—22no—
64C23×C71—22no—
65C23×C71—22no—
66C23×C71C2411yescharacteristic
67D4×C71—44no—
68C2×C4×C71—21no—
69C2×C4×C71—21no—
70C2×C4×C71—22no—
71C2×C4×C71—22no—
72C2×C4×C71—22no—
73C2×C4×C71—21no—
74C2×C4×C71—21no—
75C2×C4×C71—22no—
76C2×C4×C71—22no—
77C2×C4×C71C2×D412yes—
78C2×Dic71—22no—
79C2×Dic71—22no—
80C2×Dic71—22no—
81C2×Dic71—22no—
82C2×Dic71—22no—
83C2×Dic71—22no—
84C2×Dic71—22no—
85C2×Dic71—22no—
86C2×Dic71—22no—
87C2×Dic71—22no—
88C2×Dic71—22no—
89C2×Dic71C2×D414yes—
90C22×C71—42no—
91C22×C71—42no—
92C22×C71—42no—
93C22×C71—42no—
94C22×C71—42no—
95C22×C71—42no—
96C22×C71—42no—
97C22×C71C22×D411yescharacteristic
98C22×C71H(5,𝔽2)11yescharacteristic
99C22×C71H(5,𝔽2)12yes—
100C22×C712−1+411yescharacteristic
101C22×C712−1+412yes—
102C4×C71—22no—
103C4×C71—42no—
104C4×C71—41no—
105C4×C71—41no—
106Dic71—24no—
107Dic71—42no—
108Dic71—42no—
109Dic71—42no—
110C2×C71—82no—
111C2×C71#53711yescharacteristic
112C2×C71#53712yes—
113C2×C71#56011yescharacteristic
114C2×C71#56311yescharacteristic
115C2×C71#56312yes—
116#2823—711nomaximal, Sylow
117C71#282311yescharacteristic, complemented, Sylow
118C2×#126—712no—
119#398—711no—
120#398—712no—
121#396—712no—
122#396—712no—
123#396—712no—
124#394—712no—
125#394D7111yescharacteristic
126#384—711no—
127C22×D4C2×D7111yescharacteristic
128#126—1428no—
129C2×C4⋊C4—712no—
130C2×C4⋊C4—712no—
131C2×C4⋊C4—711no—
132C2×C4⋊C4—712no—
133C2×C4⋊C4—711no—
134C2×C4⋊C4—712no—
135C2×C4⋊C4—712no—
136C2×C4⋊C4—712no—
137C2×C4⋊C4C2×D7111yescharacteristic
138C2×C22⋊C4—712no—
139C2×C22⋊C4—712no—
140C2×C22⋊C4—712no—
141C2×C22⋊C4—712no—
142C2×C22⋊C4C2×D7112yes—
143C2×C22⋊C4C2×D7112yes—
144C2×C42—711no—
145#95—712no—
146#95—711no—
147#95—712no—
148#95C2×D7111yescharacteristic
149C24C22×D7112yes—
150C2×D4—41no—
151C2×D4—42no—
152C22×C4—712no—
153C22×C4—712no—
154C22×C4—712no—
155C22×C4—712no—
156C22×C4C22×D7111yescharacteristic
157C22×C4C22×D7112yes—
158C22×C4C22×D7111yescharacteristic
159C22×C4C22×D7111yescharacteristic
160C4⋊C4—41no—
161C4⋊C4—2842no—
162C4⋊C4—2842no—
163C4⋊C4—2842no—
164C4⋊C4—2841no—
165C4⋊C4—2841no—
166C4⋊C4—1424no—
167C4⋊C4—1424no—
168C4⋊C4—1424no—
169C22⋊C4—24no—
170C22⋊C4—42no—
171C22⋊C4—2842no—
172C22⋊C4—2842no—
173C22⋊C4—1424no—
174C22⋊C4—1424no—
175C42—714no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23C23×D7111yescharacteristic
184D4—44no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—714no—
195C2×C4—1422no—
196C2×C4—1422no—
197C2×C4—1422no—
198C2×C4—1422no—
199C2×C4—1422no—
200C2×C4—1422no—
201C2×C4—1422no—
202C2×C4—1422no—
203C2×C4—1422no—
204C2×C4—1422no—
205C2×C4—1422no—
206C2×C4D4×D7112yes—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—42no—
214C22C2×D4×D7111yescharacteristic
215C22#1455617311yescharacteristic
216C22#1455617312yes—
217C22#1455617511yescharacteristic
218C22#1455617512yes—
219C4—22no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—2842no—
224C4—2842no—
225C4—2842no—
226C4—1424no—
227C2—82no—
228C2#1798657611yescharacteristic
229C2#1798657812yes—
230C2#1798673811yescharacteristic
231C2#1798674911yescharacteristic
232C2#1798675212yes—
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#394×C71C2
hypercenter#394D71
hypocenterC71#2823
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14556121C2semidirect
2. #17985933C2semidirect
3. #17985929C2semidirect
4. #17985922C2semidirect
5. #17985922C2semidirect
6. #17985922C2semidirect
8. #17985868C2semidirect
48. C4×Dic71D4semidirect
117. C71#2823semidirect