Finite Group Databasebeta

← #22594108

Subgroups — #22594108

Order 9088.

528 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 143 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×#14556127C211yesmaximal, characteristic, complemented
2C2×#14556106C212yesmaximal
3C2×#14556086C211yesmaximal, characteristic
4#17985932C212yesmaximal, complemented
5#17985929C211yesmaximal, characteristic, complemented
6#17985928C212yesmaximal
7#17985926C211yesmaximal, characteristic
8#17985925C211yesmaximal, characteristic
9#17985903C212yesmaximal, complemented
10#17985863C211yesmaximal, characteristic, complemented
11#398×C71C211yesmaximal, characteristic, complemented
12C22×Dic142C2212yes—
13C22×C4×D71C2211yescharacteristic
14#14556127—24no—
15#14556106—28no—
16#14556086—24no—
17C2×C4⋊Dic71C2211yescharacteristic
18C2×C4⋊Dic71C2211yescharacteristic
19C2×Dic71⋊C4C2212yes—
20C2×Dic71⋊C4C2212yes—
21C2×Dic71⋊C4C2212yes—
22C2×(C2×D71)⋊C4C2211yescharacteristic
23C2×(C2×D71)⋊C4C2212yes—
24C2×(C2×D71)⋊C4C2212yes—
25C2×(C2×D71)⋊C4C2211yescharacteristic
26C2×C4×Dic71C2211yescharacteristic
27C2×C4×Dic71C2211yescharacteristic
28C71⋊#95C2211yescharacteristic
29C71⋊#95C2212yes—
30C71⋊#95C2212yes—
31C71⋊#95C2212yes—
32C71⋊#95C2212yes—
33C2×C4⋊C4×C71C2211yescharacteristic
34C2×C4⋊C4×C71C2211yescharacteristic
35C2×C4⋊C4×C71C2212yes—
36#95×C71C2211yescharacteristic
37#95×C71C2212yes—
38C23×D71C2311yescharacteristic
39C2×Dic142—24no—
40C2×Dic142—24no—
41C2×Dic142—24no—
42C22×Dic71C2312yes—
43C22×Dic71C2311yescharacteristic
44C22×Dic71C2312yes—
45C22×Dic71C2311yescharacteristic
46C22×Dic71C2311yescharacteristic
47C2×C4×D71—22no—
48C2×C4×D71—22no—
49C2×C4×D71D414yes—
50C4⋊Dic71—22no—
51C4⋊Dic71—22no—
52Dic71⋊C4—24no—
53Dic71⋊C4—24no—
54Dic71⋊C4—24no—
55(C2×D71)⋊C4—24no—
56(C2×D71)⋊C4—24no—
57(C2×D71)⋊C4—22no—
58(C2×D71)⋊C4—22no—
59C4×Dic71—22no—
60C4×Dic71D414yes—
61C22×C4×C71C2312yes—
62C22×C4×C71C2311yescharacteristic
63C22×C4×C71C2312yes—
64C22×C4×C71C2311yescharacteristic
65C22×C4×C71C2311yescharacteristic
66C4⋊C4×C71—22no—
67C4⋊C4×C71—24no—
68C4⋊C4×C71—22no—
69C23×C71C2411yescharacteristic
70C22×D71—21no—
71C22×D71—21no—
72C22×D71—22no—
73C22×D71—22no—
74C22×D71C2×D412yes—
75C2×C4×C71—21no—
76C2×C4×C71—21no—
77C2×C4×C71—22no—
78C2×C4×C71—21no—
79C2×C4×C71—22no—
80C2×C4×C71—22no—
81C2×C4×C71—22no—
82C2×C4×C71—22no—
83C2×C4×C71—22no—
84C2×C4×C71—22no—
85C2×C4×C71—22no—
86C2×C4×C71C2×D412yes—
87C2×C4×C71C2×D412yes—
88C2×Dic71—22no—
89C2×Dic71—21no—
90C2×Dic71—22no—
91C2×Dic71—22no—
92C2×Dic71—22no—
93C2×Dic71—22no—
94C2×Dic71—22no—
95C2×Dic71—22no—
96C2×Dic71—22no—
97C2×Dic71C2×D412yes—
98C2×Dic71C2×D412yes—
99C2×Dic71C2×D412yes—
100C2×Dic71#4112yes—
101C4×D71—28no—
102Dic142—48no—
103C22×C71C22×D411yescharacteristic
104C22×C71C22×D411yescharacteristic
105C22×C71C2×#4111yescharacteristic
106C22×C712−1+412yes—
107C22×C712−1+412yes—
108C2×D71—22no—
109C2×D71—24no—
110C2×D71—41no—
111C2×D71—41no—
112C2×D71—42no—
113C4×C71—22no—
114C4×C71—22no—
115C4×C71—42no—
116C4×C71—41no—
117C4×C71—42no—
118Dic71—22no—
119Dic71—42no—
120Dic71—42no—
121Dic71—41no—
122Dic71#12114yes—
123C2×C71C2×#12111yescharacteristic
124C2×C71#53611yescharacteristic
125C2×C71#53612yes—
126C2×C71#53611yescharacteristic
127C2×C71#54112yes—
128D71—42no—
129#2621—711nomaximal, Sylow
130C71#262111yescharacteristic, complemented, Sylow
131C2×C4⋊Q8—711no—
132C2×C22⋊Q8—712no—
133C2×#117—711no—
134#398—711no—
135#398—712no—
136#398D7111yescharacteristic, complemented
137#397—711no—
138#397—711no—
139#397—712no—
140#391—712no—
141#382—711no—
142C22×Q8—712no—
143C23×C4—711no—
144C4⋊Q8—1424no—
145C22⋊Q8—1428no—
146#117—1424no—
147C2×C4⋊C4—711no—
148C2×C4⋊C4—712no—
149C2×C4⋊C4—712no—
150C2×C4⋊C4—712no—
151C2×C4⋊C4—711no—
152C2×C4⋊C4C2×D7111yescharacteristic
153C2×C4⋊C4C2×D7112yes—
154C2×C4⋊C4C2×D7111yescharacteristic
155C2×C22⋊C4—711no—
156C2×C22⋊C4—711no—
157C2×C22⋊C4—712no—
158C2×C22⋊C4—712no—
159C2×C42—711no—
160C2×C42—711no—
161#95—712no—
162#95—711no—
163#95—712no—
164#95—712no—
165#95—712no—
166#95C2×D7111yescharacteristic
167#95C2×D7112yes—
168C24—711no—
169C2×Q8—1424no—
170C2×Q8—1424no—
171C2×Q8—1424no—
172C22×C4—711no—
173C22×C4—711no—
174C22×C4—714no—
175C22×C4—711no—
176C22×C4—712no—
177C22×C4—712no—
178C22×C4—1422no—
179C22×C4—1422no—
180C22×C4C22×D7111yescharacteristic
181C22×C4C22×D7112yes—
182C22×C4C22×D7112yes—
183C22×C4C22×D7111yescharacteristic
184C22×C4C22×D7111yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—24no—
187C4⋊C4—22no—
188C4⋊C4—1424no—
189C4⋊C4—1424no—
190C4⋊C4—1422no—
191C4⋊C4—1424no—
192C4⋊C4—1422no—
193C22⋊C4—1422no—
194C22⋊C4—1424no—
195C22⋊C4—1424no—
196C22⋊C4—1422no—
197C42—714no—
198C42—1422no—
199C23—712no—
200C23—1421no—
201C23—1421no—
202C23—1422no—
203C23—1422no—
204C23C23×D7111yescharacteristic
205Q8—2848no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—712no—
218C2×C4—712no—
219C2×C4—712no—
220C2×C4—712no—
221C2×C4—1428no—
222C2×C4—1421no—
223C2×C4—1422no—
224C2×C4—1422no—
225C2×C4—1422no—
226C2×C4—1422no—
227C2×C4—1422no—
228C2×C4—1422no—
229C2×C4—1422no—
230C2×C4—1422no—
231C2×C4D4×D7112yes—
232C2×C4D4×D7112yes—
233C22—2841no—
234C22—2841no—
235C22—2842no—
236C22—1424no—
237C22—1422no—
238C22C2×D4×D7111yescharacteristic
239C22C2×D4×D7111yescharacteristic
240C22#41×D7111yescharacteristic
241C22#1455617512yes—
242C22#1455617612yes—
243C4—22no—
244C4—22no—
245C4—41no—
246C4—42no—
247C4—42no—
248C4—2842no—
249C4—2841no—
250C4—2842no—
251C4—714no—
252C4—1422no—
253C2—2842no—
254C2#121×D7111yescharacteristic
255C2#1798657111yescharacteristic
256C2#1798657212yes—
257C2#1798657411yescharacteristic
258C2#1798660812yes—
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#398×C71C2
hypercenter#398D71
hypocenterC71#2621
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14556127C2semidirect
4. #17985932C2semidirect
5. #17985929C2semidirect
9. #17985903C2semidirect
10. #17985863C2semidirect
11. #398×C71C2semidirect
130. C71#2621semidirect
136. #398D71semidirect