Finite Group Databasebeta

← #22594011

Subgroups — #22594011

Order 9088.

540 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14556084C212yesmaximal, complemented
2#17985929C211yesmaximal, characteristic, complemented
3#17985922C212yesmaximal, complemented
4#17985892C212yesmaximal, complemented
5#17985881C212yesmaximal, complemented
6#17985879C212yesmaximal
7#17985871C212yesmaximal, complemented
8#17985864C211yesmaximal, characteristic, complemented
9#394×C71C211yesmaximal, characteristic
10C23×Dic71C2212yes—
11#14556084—28no—
12C2×C4⋊Dic71C2211yescharacteristic
13C2×C4⋊Dic71C2211yescharacteristic
14C2×Dic71⋊C4C2212yes—
15C2×Dic71⋊C4C2212yes—
16C2×Dic71⋊C4C2212yes—
17C2×C22⋊Dic71C2212yes—
18C2×C22⋊Dic71C2212yes—
19C2×C22⋊Dic71C2212yes—
20C2×C4×Dic71C2212yes—
21C2×C4×Dic71C2211yescharacteristic
22C71⋊#95C2212yes—
23C71⋊#95C2212yes—
24C71⋊#95C2211yescharacteristic
25C71⋊#95C2212yes—
26C71⋊#95C2212yes—
27C22×D4×C71C2211yescharacteristic
28C2×C4⋊C4×C71C2211yescharacteristic
29C2×C22⋊C4×C71C2212yes—
30C2×C22⋊C4×C71C2212yes—
31#95×C71C2211yescharacteristic
32C22×Dic71—24no—
33C22×Dic71—24no—
34C22×Dic71—24no—
35C22×Dic71C2312yes—
36C22×Dic71C2312yes—
37C22×Dic71C2312yes—
38C22×Dic71C2312yes—
39C4⋊Dic71—41no—
40C4⋊Dic71—41no—
41Dic71⋊C4—24no—
42Dic71⋊C4—24no—
43Dic71⋊C4—24no—
44C22⋊Dic71—24no—
45C22⋊Dic71—24no—
46C22⋊Dic71—42no—
47C4×Dic71—24no—
48C4×Dic71D414yescomplemented
49C24×C71C2312yes—
50C2×D4×C71—24no—
51C2×D4×C71—41no—
52C22×C4×C71C2312yes—
53C22×C4×C71C2311yescharacteristic
54C22×C4×C71C2311yescharacteristic
55C22×C4×C71C2311yescharacteristic
56C4⋊C4×C71—41no—
57C22⋊C4×C71—24no—
58C22⋊C4×C71—24no—
59C23×C71—22no—
60C23×C71—22no—
61C23×C71—22no—
62C23×C71—22no—
63C23×C71—22no—
64C23×C71—22no—
65C23×C71#4114yes—
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—22no—
74C2×C4×C71—22no—
75C2×C4×C71—21no—
76C2×C4×C71—21no—
77C2×C4×C71C2×D412yes—
78C2×Dic71—216no—
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—
90C2×Dic71#4114yes—
91C22×C71—24no—
92C22×C71—24no—
93C22×C71—24no—
94C22×C71—42no—
95C22×C71—42no—
96C22×C71—42no—
97C22×C71—42no—
98C22×C71C22×D411yescharacteristic
99C22×C71C2×#4112yes—
100C22×C71C2×#4112yes—
101C22×C71H(5,𝔽2)11yescharacteristic
102C22×C712−1+411yescharacteristic
103C4×C71—22no—
104C4×C71—42no—
105C4×C71—41no—
106C4×C71—41no—
107Dic71—24no—
108Dic71—24no—
109Dic71—42no—
110Dic71—42no—
111C2×C71—44no—
112C2×C71#52512yes—
113C2×C71#53711yescharacteristic
114C2×C71#55111yescharacteristic
115C2×C71#55212yes—
116C2×C71#55511yescharacteristic
117#2609—711nomaximal, Sylow
118C71#260911yescharacteristic, complemented, Sylow
119C2×#117—712no—
120#398—711no—
121#396—712no—
122#394D7111yescharacteristic
123#388—712no—
124#387—712no—
125#386—712no—
126#385—712no—
127#382—711no—
128C22×D4C2×D7111yescharacteristic
129C23×C4—712no—
130#117—1428no—
131C2×C4⋊C4—711no—
132C2×C4⋊C4—711no—
133C2×C4⋊C4—712no—
134C2×C4⋊C4—712no—
135C2×C4⋊C4—712no—
136C2×C4⋊C4C2×D7111yescharacteristic
137C2×C22⋊C4—712no—
138C2×C22⋊C4—712no—
139C2×C22⋊C4—712no—
140C2×C22⋊C4C2×D7112yes—
141C2×C22⋊C4C2×D7112yes—
142C2×C42—711no—
143C2×C42—712no—
144#95—712no—
145#95—712no—
146#95—711no—
147#95—712no—
148#95—712no—
149#95C2×D7111yescharacteristic
150C24C22×D7112yes—
151C2×D4—24no—
152C2×D4—41no—
153C22×C4—712no—
154C22×C4—712no—
155C22×C4—712no—
156C22×C4—712no—
157C22×C4—1424no—
158C22×C4—1424no—
159C22×C4—1424no—
160C22×C4C22×D7111yescharacteristic
161C22×C4C22×D7111yescharacteristic
162C22×C4C22×D7112yes—
163C22×C4C22×D7111yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—2841no—
166C4⋊C4—2841no—
167C4⋊C4—1424no—
168C4⋊C4—1424no—
169C4⋊C4—1424no—
170C22⋊C4—24no—
171C22⋊C4—24no—
172C22⋊C4—2842no—
173C22⋊C4—1424no—
174C22⋊C4—1424no—
175C42—714no—
176C42—1424no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23#1176586414yes—
184C23C23×D7111yescharacteristic
185D4—44no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—21no—
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—14216no—
204C2×C4—1422no—
205C2×C4—1422no—
206C2×C4—1422no—
207C2×C4—1422no—
208C2×C4D4×D7112yes—
209C22—24no—
210C22—24no—
211C22—24no—
212C22—42no—
213C22—42no—
214C22—42no—
215C22—42no—
216C22C2×D4×D7111yescharacteristic
217C22#41×D7112yes—
218C22C2×#1176586412yes—
219C22#1455617311yescharacteristic
220C22#1455617511yescharacteristic
221C4—22no—
222C4—41no—
223C4—41no—
224C4—42no—
225C4—2842no—
226C4—2842no—
227C4—1424no—
228C4—1424no—
229C2—44no—
230C2#1798650912yes—
231C2#1798657611yescharacteristic
232C2#1798668011yescharacteristic
233C2#1798668612yes—
234C2#1798671111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#394×C71C2
hypercenter#394D71
hypocenterC71#2609
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14556084C2semidirect
2. #17985929C2semidirect
3. #17985922C2semidirect
4. #17985892C2semidirect
5. #17985881C2semidirect
7. #17985871C2semidirect
8. #17985864C2semidirect
48. C4×Dic71D4semidirect
118. C71#2609semidirect