Finite Group Databasebeta

← #22594655

Subgroups — #22594655

Order 9088.

544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14556127C212yesmaximal, complemented
2C2×#14556107C212yesmaximal
3#17985935C211yesmaximal, characteristic
4#17985932C212yesmaximal, complemented
5#17985920C212yesmaximal, complemented
6#17985911C211yesmaximal, characteristic
7#17985892C212yesmaximal
8#17985886C212yesmaximal, complemented
9#385×C71C211yesmaximal, characteristic
10C22×Dic142C2211yescharacteristic
11C22×Dic142C2212yes—
12#14556127—28no—
13#14556107—28no—
14C2×C4⋊Dic71C2212yes—
15C2×C4⋊Dic71C2212yes—
16C2×C4⋊Dic71C2211yescharacteristic
17C2×Dic71⋊C4C2212yes—
18C2×Dic71⋊C4C2212yes—
19C2×Dic71⋊C4C2212yes—
20C2×C22⋊Dic71C2212yes—
21C2×C22⋊Dic71C2212yes—
22C2×C4×Dic71C2212yes—
23C71⋊#95C2211yescharacteristic
24C71⋊#95C2212yes—
25C71⋊#95C2212yes—
26C71⋊#95C2212yes—
27C71⋊#95C2211yescharacteristic
28C23×C4×C71C2211yescharacteristic
29C2×C4⋊C4×C71C2212yes—
30C2×C22⋊C4×C71C2211yescharacteristic
31C2×C22⋊C4×C71C2211yescharacteristic
32#95×C71C2212yes—
33C2×Dic142—24no—
34C2×Dic142—24no—
35C2×Dic142—24no—
36C2×Dic142—41no—
37C2×Dic142—42no—
38C22×Dic71C2312yes—
39C22×Dic71C2312yes—
40C22×Dic71C2312yes—
41C22×Dic71C2312yes—
42C4⋊Dic71—24no—
43C4⋊Dic71—24no—
44C4⋊Dic71—41no—
45Dic71⋊C4—24no—
46Dic71⋊C4—24no—
47Dic71⋊C4D418yes—
48C22⋊Dic71—24no—
49C22⋊Dic71—24no—
50C4×Dic71—24no—
51C24×C71C2311yescharacteristic
52C22×C4×C71—24no—
53C22×C4×C71—41no—
54C22×C4×C71C2311yescharacteristic
55C22×C4×C71C2311yescharacteristic
56C22×C4×C71C2312yes—
57C22×C4×C71C2312yes—
58C4⋊C4×C71—24no—
59C22⋊C4×C71—41no—
60C22⋊C4×C71Q814yescomplemented
61C23×C71—22no—
62C23×C71—21no—
63C23×C71—22no—
64C23×C71—21no—
65C23×C71C2×Q812yes—
66C23×C71C2411yescharacteristic
67C2×C4×C71—22no—
68C2×C4×C71—22no—
69C2×C4×C71—22no—
70C2×C4×C71—22no—
71C2×C4×C71—22no—
72C2×C4×C71—21no—
73C2×C4×C71—21no—
74C2×C4×C71—22no—
75C2×C4×C71—44no—
76C2×C4×C71C2×D414yes—
77C2×C4×C71C2×Q814yes—
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×Dic71C2×D414yes—
89C2×Dic71C2×D414yes—
90Dic142—44no—
91Dic142—48no—
92C22×C71—22no—
93C22×C71—24no—
94C22×C71—42no—
95C22×C71—41no—
96C22×C71—41no—
97C22×C71C22×D412yes—
98C22×C71C22×Q811yescharacteristic
99C22×C71H(5,𝔽2)11yescharacteristic
100C22×C712−1+412yes—
101C22×C712−1+411yescharacteristic
102C4×C71—24no—
103C4×C71—24no—
104C4×C71—41no—
105C4×C71—41no—
106Dic71—24no—
107Dic71—24no—
108Dic71—42no—
109Dic71—42no—
110C2×C71—42no—
111C2×C71#53612yes—
112C2×C71#54411yescharacteristic
113C2×C71D4211yescharacteristic
114C2×C71D4×Q812yes—
115C2×C71#56311yescharacteristic
116#2677—711nomaximal, Sylow
117C71#267711yescharacteristic, complemented, Sylow
118C2×C4⋊Q8—712no—
119C2×C22⋊Q8—712no—
120#399—711no—
121#398—712no—
122#395—712no—
123#393—711no—
124#388—712no—
125#387—712no—
126#385D7111yescharacteristic
127C22×Q8—712no—
128C22×Q8—711no—
129C23×C4C2×D7111yescharacteristic
130C4⋊Q8—1428no—
131C22⋊Q8—1428no—
132C2×C4⋊C4—711no—
133C2×C4⋊C4—712no—
134C2×C4⋊C4—712no—
135C2×C4⋊C4—712no—
136C2×C4⋊C4—712no—
137C2×C4⋊C4—712no—
138C2×C4⋊C4C2×D7112yes—
139C2×C22⋊C4—712no—
140C2×C22⋊C4—712no—
141C2×C22⋊C4C2×D7111yescharacteristic
142C2×C22⋊C4C2×D7111yescharacteristic
143C2×C42—712no—
144#95—711no—
145#95—712no—
146#95—712no—
147#95—712no—
148#95—711no—
149#95C2×D7112yes—
150C24C22×D7111yescharacteristic
151C2×Q8—2842no—
152C2×Q8—2841no—
153C2×Q8—1424no—
154C2×Q8—1424no—
155C2×Q8—1424no—
156C22×C4—24no—
157C22×C4—41no—
158C22×C4—712no—
159C22×C4—712no—
160C22×C4—712no—
161C22×C4—712no—
162C22×C4C22×D7111yescharacteristic
163C22×C4C22×D7111yescharacteristic
164C22×C4C22×D7112yes—
165C22×C4C22×D7112yes—
166C4⋊C4—24no—
167C4⋊C4—2841no—
168C4⋊C4—718no—
169C4⋊C4—1424no—
170C4⋊C4—1424no—
171C4⋊C4—1424no—
172C4⋊C4—1424no—
173C22⋊C4—41no—
174C22⋊C4—1424no—
175C22⋊C4—1424no—
176C22⋊C4Dic14214yescomplemented
177C42—1424no—
178C23—22no—
179C23—21no—
180C23—22no—
181C23—21no—
182C23C2×Dic14212yes—
183C23C23×D7111yescharacteristic
184Q8—2848no—
185Q8—2844no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—44no—
195C2×C4—714no—
196C2×C4—714no—
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×C4—1422no—
207C2×C4D4×D7114yes—
208C2×C4C2×Dic14214yes—
209C22—22no—
210C22—24no—
211C22—42no—
212C22—41no—
213C22—41no—
214C22C2×D4×D7112yes—
215C22C22×Dic14211yescharacteristic
216C22#1455617311yescharacteristic
217C22#1455617512yes—
218C22#1455617611yescharacteristic
219C4—24no—
220C4—24no—
221C4—41no—
222C4—41no—
223C4—2842no—
224C4—2842no—
225C4—1424no—
226C4—1424no—
227C2—42no—
228C2#1798657212yes—
229C2#1798663011yescharacteristic
230C2#1798663111yescharacteristic
231C2D4×Dic14212yes—
232C2#1798675211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#385×C71C2
hypercenter#385D71
hypocenterC71#2677
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#14556127C2semidirect
4. #17985932C2semidirect
5. #17985920C2semidirect
8. #17985886C2semidirect
60. C22⋊C4×C71Q8semidirect
117. C71#2677semidirect
176. C22⋊C4Dic142semidirect