Finite Group Databasebeta

← #22595604

Subgroups — #22595604

Order 9088.

484 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#17985935C211yesmaximal, characteristic, complemented
2#17985928C212yesmaximal, complemented
3#17985917C212yesmaximal, complemented
4#17985908C211yesmaximal, characteristic
5#17985899C212yesmaximal, complemented
6#17985891C212yesmaximal, complemented
7#17985881C212yesmaximal, complemented
8#17985878C212yesmaximal, complemented
9#381×C71C211yesmaximal, characteristic, complemented
10C22×D284C2211yescharacteristic
11C22×C22⋊D71C2212yes—
12C2×C4⋊Dic71C2211yescharacteristic
13C2×Dic71⋊C4C2212yes—
14C2×Dic71⋊C4C2212yes—
15C2×C22⋊Dic71C2212yes—
16C2×(C2×D71)⋊C4C2212yes—
17C2×(C2×D71)⋊C4C2212yes—
18C2×(C2×D71)⋊C4C2212yes—
19C2×(C2×D71)⋊C4C2212yes—
20C2×(C2×D71)⋊C4C2212yes—
21C2×C4×Dic71C2212yes—
22C71⋊#95C2212yes—
23C71⋊#95C2212yes—
24C71⋊#95C2211yescharacteristic
25C71⋊#95C2211yescharacteristic
26C23×C4×C71C2211yescharacteristic
27C2×C22⋊C4×C71C2211yescharacteristic
28C2×C22⋊C4×C71C2211yescharacteristic
29#95×C71C2212yes—
30#95×C71C2212yes—
31C23×D71C2312yes—
32C2×D284—41no—
33C2×D284—42no—
34C2×C22⋊D71—24no—
35C2×C22⋊D71—24no—
36C2×C22⋊D71—42no—
37C22×Dic71C2312yes—
38C22×Dic71C2312yes—
39C22×Dic71C2312yes—
40C4⋊Dic71—41no—
41Dic71⋊C4—24no—
42Dic71⋊C4—42no—
43C22⋊Dic71—42no—
44(C2×D71)⋊C4—24no—
45(C2×D71)⋊C4—42no—
46(C2×D71)⋊C4—42no—
47(C2×D71)⋊C4—42no—
48(C2×D71)⋊C4—42no—
49C4×Dic71—42no—
50C24×C71C2311yescharacteristic
51C22×C4×C71—22no—
52C22×C4×C71—41no—
53C22×C4×C71—41no—
54C22×C4×C71C2311yescharacteristic
55C22×C4×C71C2311yescharacteristic
56C22×C4×C71C2312yes—
57C22×C4×C71C2312yes—
58C22⋊C4×C71—41no—
59C22⋊C4×C71—41no—
60C23×C71—22no—
61C23×C71—21no—
62C23×C71—21no—
63C23×C71—22no—
64C23×C71#4112yes—
65C23×C71C2411yescharacteristic
66C22×D71—22no—
67C22×D71—22no—
68C22×D71—22no—
69C22×D71—22no—
70C22×D71—22no—
71C22×D71—22no—
72C22×D71—22no—
73C2×C4×C71—22no—
74C2×C4×C71—22no—
75C2×C4×C71—22no—
76C2×C4×C71—22no—
77C2×C4×C71—21no—
78C2×C4×C71—21no—
79C2×C4×C71—22no—
80C2×C4×C71—22no—
81C2×C4×C71—22no—
82C2×C4×C71—22no—
83C2×C4×C71—44no—
84C22⋊D71—48no—
85C2×Dic71—22no—
86C2×Dic71—22no—
87C2×Dic71—22no—
88C2×Dic71—22no—
89C2×Dic71—22no—
90C2×Dic71—22no—
91C2×Dic71—22no—
92C2×Dic71—22no—
93C2×Dic71#4114yes—
94D284—44no—
95C22×C71—22no—
96C22×C71—24no—
97C22×C71—42no—
98C22×C71—41no—
99C22×C71—41no—
100C22×C71C2×#4112yes—
101C22×C71C2×#4111yescharacteristic
102C22×C71H(5,𝔽2)11yescharacteristic
103C22×C71H(5,𝔽2)11yescharacteristic
104C22×C71H(5,𝔽2)12yes—
105C2×D71—42no—
106C2×D71—42no—
107C2×D71—42no—
108C2×D71—42no—
109C2×D71—42no—
110C2×D71—42no—
111C2×D71—42no—
112C4×C71—42no—
113C4×C71—42no—
114C4×C71—41no—
115C4×C71—41no—
116Dic71—24no—
117Dic71—42no—
118Dic71—42no—
119C2×C71—42no—
120C2×C71#53811yescharacteristic
121C2×C71#54012yes—
122C2×C71#55112yes—
123C2×C71#55911yescharacteristic
124C2×C71#56011yescharacteristic
125D71—82no—
126#2752—711nomaximal, Sylow
127C71#275211yescharacteristic, complemented, Sylow
128#399—711no—
129#397—712no—
130#394—712no—
131#392—711no—
132#390—712no—
133#388—712no—
134#387—712no—
135#386—712no—
136#381D7111yescharacteristic, complemented
137C22×D4—712no—
138C22×D4—711no—
139C23×C4C2×D7111yescharacteristic
140C2×C4⋊C4—712no—
141C2×C4⋊C4—711no—
142C2×C4⋊C4—712no—
143C2×C22⋊C4—712no—
144C2×C22⋊C4—712no—
145C2×C22⋊C4—712no—
146C2×C22⋊C4—712no—
147C2×C22⋊C4—712no—
148C2×C22⋊C4—712no—
149C2×C22⋊C4C2×D7111yescharacteristic
150C2×C22⋊C4C2×D7111yescharacteristic
151C2×C42—712no—
152#95—712no—
153#95—712no—
154#95—711no—
155#95—711no—
156#95C2×D7112yes—
157#95C2×D7112yes—
158C24—712no—
159C24C22×D7111yescharacteristic
160C2×D4—2841no—
161C2×D4—2842no—
162C2×D4—2842no—
163C2×D4—1424no—
164C2×D4—1424no—
165C22×C4—22no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—712no—
169C22×C4—712no—
170C22×C4—712no—
171C22×C4C22×D7112yes—
172C22×C4C22×D7111yescharacteristic
173C22×C4C22×D7111yescharacteristic
174C22×C4C22×D7112yes—
175C4⋊C4—2842no—
176C4⋊C4—2841no—
177C4⋊C4—1424no—
178C22⋊C4—41no—
179C22⋊C4—41no—
180C22⋊C4—2842no—
181C22⋊C4—2842no—
182C22⋊C4—2842no—
183C22⋊C4—2842no—
184C22⋊C4—2842no—
185C22⋊C4—1424no—
186C42—2842no—
187C23—22no—
188C23—21no—
189C23—21no—
190C23—22no—
191C23—1422no—
192C23—1422no—
193C23—1422no—
194C23—1422no—
195C23—1422no—
196C23—1422no—
197C23—1422no—
198C23#1176586512yes—
199C23C23×D7111yescharacteristic
200D4—2844no—
201D4—2848no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—44no—
213C2×C4—714no—
214C2×C4—1422no—
215C2×C4—1422no—
216C2×C4—1422no—
217C2×C4—1422no—
218C2×C4—1422no—
219C2×C4—1422no—
220C2×C4—1422no—
221C2×C4—1422no—
222C22—22no—
223C22—24no—
224C22—42no—
225C22—41no—
226C22—41no—
227C22—2842no—
228C22—2842no—
229C22—2842no—
230C22—2842no—
231C22—2842no—
232C22—2842no—
233C22—2842no—
234C22#41×D7112yes—
235C22C2×#1176586511yescharacteristic
236C22#1455617311yescharacteristic
237C22#1455617311yescharacteristic
238C22#1455617412yes—
239C4—42no—
240C4—42no—
241C4—41no—
242C4—41no—
243C4—2842no—
244C4—2842no—
245C4—1424no—
246C2—42no—
247C2—5682no—
248C2#1798658711yescharacteristic
249C2#1798660112yes—
250C2#1798667312yes—
251C2#1798673311yescharacteristic
252C2#1798673911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#381×C71C2
hypercenter#381D71
hypocenterC71#2752
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. #17985935C2semidirect
2. #17985928C2semidirect
3. #17985917C2semidirect
5. #17985899C2semidirect
6. #17985891C2semidirect
7. #17985881C2semidirect
8. #17985878C2semidirect
9. #381×C71C2semidirect
127. C71#2752semidirect
136. #381D71semidirect