Finite Group Databasebeta

← #22586675

Subgroups — #22586675

Order 9088.

316 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 69 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×(C22⋊D71)⋊C4C211yesmaximal, characteristic
2#17985961C212yesmaximal, complemented
3#17985724C212yesmaximal, complemented
4#17985723C211yesmaximal, characteristic, complemented
5#323×C71C211yesmaximal, characteristic, complemented
6C22×C22⋊D71C411yescharacteristic
7C23×Dic71C411yescharacteristic
8C22×C4×D71C2211yescharacteristic
9C2×#11765848—22no—
10(C22⋊D71)⋊C4—22no—
11(C22⋊D71)⋊C4—22no—
12C2×Dic71⋊C4C2211yescharacteristic
13C2×(C2×D71)⋊C4C411yescharacteristic
14C2×C4×Dic71C411yescharacteristic
15C22⋊(C71⋊C8)C2212yes—
16(C2×D71)⋊C8—22no—
17C2×C22⋊C4×C71C2211yescharacteristic
18C22⋊C8×C71C2212yes—
19C23×D71C2×C411yescharacteristic
20C2×C22⋊D71—22no—
21C2×C22⋊D71—22no—
22C2×C22⋊D71—22no—
23C22×Dic71—21no—
24C22×Dic71—21no—
25C22×Dic71—42no—
26C22×Dic71C2×C411yescharacteristic
27C22×Dic71C2×C411yescharacteristic
28C22×Dic71C2×C411yescharacteristic
29C2×C4×D71—42no—
30C2×C4×D71D412yes—
31C2×C4×D71D412yes—
32#11765848—44no—
33C2×C71⋊C8—22no—
34Dic71⋊C4—22no—
35(C2×D71)⋊C4—22no—
36C4×Dic71—21no—
37C4×Dic71—21no—
38C24×C71C2×C411yescharacteristic
39C22×C4×C71C2×C411yescharacteristic
40C22×C4×C71C2311yescharacteristic
41C2×C8×C71—22no—
42C22⋊C4×C71—22no—
43C23×C71—21no—
44C23×C71—21no—
45C23×C71—41no—
46C23×C71—41no—
47C23×C71M1612yescomplemented
48C23×C71C22×C411yescharacteristic
49C22×D71—21no—
50C22×D71—21no—
51C22×D71—41no—
52C22×D71—41no—
53C22×D71C22⋊C412yes—
54C2×C4×C71—21no—
55C2×C4×C71—41no—
56C2×C4×C71—41no—
57C2×C4×C71C2×D412yes—
58C22⋊D71—28no—
59C2×Dic71—21no—
60C2×Dic71—21no—
61C2×Dic71—22no—
62C2×Dic71—21no—
63C2×Dic71—42no—
64C2×Dic71—42no—
65C2×Dic71—41no—
66C2×Dic71C22⋊C411yescharacteristic
67C2×Dic71C22⋊C411yescharacteristic
68C2×Dic71M1612yescomplemented
69C4×D71—24no—
70C4×D71—42no—
71C8×C71—42no—
72C71⋊C8—42no—
73C22×C71—21no—
74C22×C71—21no—
75C22×C71—22no—
76C22×C71—42no—
77C22×C71—42no—
78C22×C71—41no—
79C22×C71—41no—
80C22×C71C2×C22⋊C411yescharacteristic
81C22×C71C2×M1611yescharacteristic
82C22×C71C2×M1611yescharacteristic
83C2×D71—22no—
84C2×D71—22no—
85C2×D71—22no—
86C2×D71—42no—
87C2×D71—42no—
88C4×C71—22no—
89C4×C71—41no—
90Dic71—22no—
91Dic71—21no—
92Dic71—41no—
93Dic71#9912yes—
94C2×C71—21no—
95C2×C71—21no—
96C2×C71—42no—
97C2×C71#40711yescharacteristic
98C2×C71C2×#9911yescharacteristic
99C2×C71#41311yescharacteristic
100D71—42no—
101#1465—711nomaximal, Sylow
102C71#146511yescharacteristic, complemented, Sylow
103C2×C4×D4—711no—
104#407—712no—
105#324—712no—
106#323—711no—
107#323D7111yescharacteristic, complemented
108C22×D4—711no—
109C23×C4—711no—
110C23×C4—711no—
111C2×M16—1422no—
112C4×D4—1422no—
113C4×D4—1422no—
114C2×C4⋊C4—711no—
115C2×C22⋊C4—711no—
116C2×C22⋊C4C2×D7111yescharacteristic
117C2×C42—711no—
118C22⋊C8—712no—
119C22⋊C8—1422no—
120C22⋊C8C2×D7112yes—
121C24—711no—
122C24C4×D7111yescharacteristic
123C2×D4—1422no—
124C2×D4—1422no—
125C2×D4—1422no—
126C22×C4—2842no—
127C22×C4—2842no—
128C22×C4—712no—
129C22×C4—711no—
130C22×C4—711no—
131C22×C4—711no—
132C22×C4—712no—
133C22×C4—1421no—
134C22×C4—1421no—
135C22×C4C4×D7111yescharacteristic
136C22×C4C22×D7111yescharacteristic
137M16—2844no—
138C2×C8—22no—
139C2×C8—1422no—
140C4⋊C4—1422no—
141C22⋊C4—22no—
142C22⋊C4—1422no—
143C42—1421no—
144C42—1421no—
145C23—21no—
146C23—21no—
147C23—41no—
148C23—41no—
149C23—2841no—
150C23—2841no—
151C23—712no—
152C23—1421no—
153C23—1421no—
154C23#1176584812yescomplemented
155C23C2×C4×D7111yescharacteristic
156D4—1428no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—2842no—
161C2×C4—2842no—
162C2×C4—2842no—
163C2×C4—2841no—
164C2×C4—711no—
165C2×C4—711no—
166C2×C4—712no—
167C2×C4—1424no—
168C2×C4—1421no—
169C2×C4—1422no—
170C2×C4—1421no—
171C2×C4—1421no—
172C2×C4D4×D7112yes—
173C8—42no—
174C8—2842no—
175C22—21no—
176C22—21no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—2842no—
183C22—2842no—
184C22—1422no—
185C22—1422no—
186C22—1422no—
187C22C22⋊C4×D7111yescharacteristic
188C22M16×D7111yescharacteristic
189C22C2×#1176584811yescharacteristic
190C4—22no—
191C4—41no—
192C4—2841no—
193C4—712no—
194C4—1422no—
195C4—1421no—
196C2—21no—
197C2—21no—
198C2—42no—
199C2—2842no—
200C2#1798596111yescharacteristic
201C2#99×D7111yescharacteristic
202C2#1798598011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D71
commutatorC23×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#323×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#323D71
hypocenterC71#1465
LCSG ▷ C23×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #17985961C2semidirect
3. #17985724C2semidirect
4. #17985723C2semidirect
5. #323×C71C2semidirect
47. C23×C71M16semidirect
68. C2×Dic71M16semidirect
102. C71#1465semidirect
107. #323D71semidirect
154. C23#11765848semidirect