Finite Group Databasebeta

← #22591096

Subgroups — #22591096

Order 9088.

484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 181 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×#14556107C211yesmaximal, characteristic
2#17985903C212yesmaximal, complemented
3#17985893C212yesmaximal
4#17985887C212yesmaximal
5#17985884C212yesmaximal, complemented
6#17985883C212yesmaximal, complemented
7#17985862C211yesmaximal, characteristic
8C4×Dic71⋊C4C212yesmaximal, complemented
9C4×C22⋊C4×C71C211yesmaximal, characteristic
10C22×Dic142C2211yescharacteristic
11#14556107C418yescomplemented
12C2×C4⋊Dic71C2211yescharacteristic
13C2×Dic71⋊C4C2212yes—
14C2×Dic71⋊C4C2212yes—
15C2×Dic71⋊C4C2212yes—
16C2×C22⋊Dic71C2211yescharacteristic
17C2×C22⋊Dic71C2211yescharacteristic
18C2×C22⋊Dic71C2212yes—
19C2×C4×Dic71C2212yes—
20C2×C4×Dic71C2212yes—
21C71⋊#95C2212yes—
22C71⋊#95C2212yes—
23C71⋊#95C2212yes—
24C71⋊#95C2212yes—
25C71⋊#95C2212yes—
26C71⋊#95C2212yes—
27C23×C4×C71C2211yescharacteristic
28C2×C22⋊C4×C71C2212yes—
29C2×C42×C71C2211yescharacteristic
30C2×C42×C71C2211yescharacteristic
31#95×C71C2212yes—
32C2×Dic142—41no—
33C2×Dic142—41no—
34C2×Dic142C2×C414yes—
35C22×Dic71C2312yes—
36C22×Dic71C2312yes—
37C22×Dic71C2312yes—
38C22×Dic71C2312yes—
39C4⋊Dic71C2×C414yes—
40Dic71⋊C4—24no—
41Dic71⋊C4—42no—
42Dic71⋊C4C2×C418yes—
43C22⋊Dic71—41no—
44C22⋊Dic71—41no—
45C22⋊Dic71C2×C418yes—
46C4×Dic71—24no—
47C4×Dic71—42no—
48C24×C71C2311yescharacteristic
49C22×C4×C71—41no—
50C22×C4×C71—41no—
51C22×C4×C71C2×C414yes—
52C22×C4×C71C2312yes—
53C22×C4×C71C2311yescharacteristic
54C22×C4×C71C2311yescharacteristic
55C22×C4×C71C2312yes—
56C22⋊C4×C71—24no—
57C42×C71—41no—
58C42×C71—41no—
59C23×C71—22no—
60C23×C71—21no—
61C23×C71—21no—
62C23×C71—22no—
63C23×C71C22×C412yes—
64C23×C71C2411yescharacteristic
65C2×C4×C71—21no—
66C2×C4×C71—21no—
67C2×C4×C71—22no—
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—44no—
75C2×C4×C71C22×C412yes—
76C2×C4×C71C22×C412yes—
77C2×C4×C71#4114yes—
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×Dic71C22×C414yes—
89C2×Dic71C22×C414yes—
90Dic142—44no—
91C22×C71—22no—
92C22×C71—22no—
93C22×C71—22no—
94C22×C71—42no—
95C22×C71—42no—
96C22×C71C23×C411yescharacteristic
97C22×C71C2×#4112yes—
98C22×C71H(5,𝔽2)11yescharacteristic
99C22×C71H(5,𝔽2)11yescharacteristic
100C22×C712−1+412yes—
101C4×C71—22no—
102C4×C71—22no—
103C4×C71—24no—
104C4×C71—42no—
105Dic71—24no—
106Dic71—24no—
107Dic71—42no—
108Dic71—42no—
109C2×C71—42no—
110C2×C71C4×#4111yescharacteristic
111C2×C71#51811yescharacteristic
112C2×C71#51911yescharacteristic
113C2×C71#53912yes—
114C2×C71#54212yes—
115#2332—711nomaximal, Sylow
116C71#233211yescharacteristic, complemented, Sylow
117C2×C22⋊Q8—711no—
118#391—712no—
119#388—712no—
120#388—712no—
121#387—712no—
122#387—712no—
123#381—711no—
124C4×C4⋊C4—712no—
125C4×C22⋊C4D7111yescharacteristic
126C22×Q8—711no—
127C23×C4C2×D7111yescharacteristic
128C22⋊Q8—718no—
129C2×C4⋊C4—712no—
130C2×C4⋊C4—712no—
131C2×C4⋊C4—711no—
132C2×C4⋊C4—712no—
133C2×C22⋊C4—711no—
134C2×C22⋊C4—711no—
135C2×C22⋊C4—712no—
136C2×C22⋊C4C2×D7112yes—
137C2×C42—712no—
138C2×C42—712no—
139C2×C42C2×D7111yescharacteristic
140C2×C42C2×D7111yescharacteristic
141#95—712no—
142#95—712no—
143#95—712no—
144#95—712no—
145#95—712no—
146#95—712no—
147#95C2×D7112yes—
148C24C22×D7111yescharacteristic
149C2×Q8—2841no—
150C2×Q8—2841no—
151C2×Q8—714no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—712no—
155C22×C4—712no—
156C22×C4—712no—
157C22×C4—712no—
158C22×C4C4×D7114yes—
159C22×C4C22×D7112yes—
160C22×C4C22×D7111yescharacteristic
161C22×C4C22×D7111yescharacteristic
162C22×C4C22×D7112yes—
163C4⋊C4—2842no—
164C4⋊C4—718no—
165C4⋊C4—714no—
166C4⋊C4—1424no—
167C22⋊C4—24no—
168C22⋊C4—2841no—
169C22⋊C4—2841no—
170C22⋊C4—718no—
171C42—41no—
172C42—41no—
173C42—2842no—
174C42—1424no—
175C23—22no—
176C23—21no—
177C23—21no—
178C23—22no—
179C23C2×C4×D7112yes—
180C23C23×D7111yescharacteristic
181Q8—2844no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—44no—
192C2×C4—714no—
193C2×C4—714no—
194C2×C4—1422no—
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×C4C2×C4×D7112yes—
205C2×C4C2×C4×D7112yes—
206C2×C4#1176586514yes—
207C22—22no—
208C22—22no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22C22×C4×D7111yescharacteristic
213C22C2×#1176586512yes—
214C22#1455617311yescharacteristic
215C22#1455617311yescharacteristic
216C22#1455617512yes—
217C4—24no—
218C4—22no—
219C4—22no—
220C4—42no—
221C4—2842no—
222C4—2842no—
223C4—1424no—
224C4—1424no—
225C2—42no—
226C2C4×#1176586511yescharacteristic
227C2#1798647211yescharacteristic
228C2#1798647611yescharacteristic
229C2#1798659112yes—
230C2#1798661412yes—
subgroupG/H
center, FrattiniC23C23×D71
commutatorC22×C71C23×C4
FittingC4×C22⋊C4×C71C2
socleC23×C71C24
hypercenterC4×C22⋊C4D71
hypocenterC71#2332
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #17985903C2semidirect
5. #17985884C2semidirect
6. #17985883C2semidirect
8. C4×Dic71⋊C4C2semidirect
11. #14556107C4semidirect
116. C71#2332semidirect