Finite Group Databasebeta

← #22586677

Subgroups — #22586677

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×#14556090C211yesmaximal, characteristic
2#17985961C212yesmaximal, complemented
3#17985725C211yesmaximal, characteristic, complemented
4#17985722C212yesmaximal, complemented
5#324×C71C211yesmaximal, characteristic, complemented
6C22×D284C411yescharacteristic
7C22×C4×D71C411yescharacteristic
8C22×C4×D71C2211yescharacteristic
9C2×#11765848—22no—
10#14556090—22no—
11#14556090—22no—
12C2×(C2×D71)⋊C4C411yescharacteristic
13C2×(C2×D71)⋊C4C2211yescharacteristic
14C2×C4×Dic71C411yescharacteristic
15C22⋊(C71⋊C8)C2212yes—
16(C2×D71)⋊C8—22no—
17C2×C4⋊C4×C71C2211yescharacteristic
18C22⋊C8×C71C2212yes—
19C23×D71C2×C411yescharacteristic
20C23×D71C2×C411yescharacteristic
21C2×D284—22no—
22C2×D284—22no—
23C2×D284—22no—
24C22×Dic71C2×C411yescharacteristic
25C22×Dic71C2×C411yescharacteristic
26C2×C4×D71—21no—
27C2×C4×D71—21no—
28C2×C4×D71—42no—
29C2×C4×D71—42no—
30C2×C4×D71D412yes—
31C2×C4×D71D412yes—
32#11765848—44no—
33C2×C71⋊C8—22no—
34(C2×D71)⋊C4—22no—
35(C2×D71)⋊C4—22no—
36C4×Dic71—21no—
37C4×Dic71—21no—
38C22×C4×C71C2×C411yescharacteristic
39C22×C4×C71C2×C411yescharacteristic
40C22×C4×C71C2311yescharacteristic
41C2×C8×C71—22no—
42C4⋊C4×C71—22no—
43C23×C71C22×C411yescharacteristic
44C22×D71—21no—
45C22×D71—21no—
46C22×D71—21no—
47C22×D71—21no—
48C22×D71—41no—
49C22×D71—41no—
50C22×D71—41no—
51C22×D71—41no—
52C22×D71C22⋊C412yes—
53C22×D71M1612yescomplemented
54C2×C4×C71—21no—
55C2×C4×C71—21no—
56C2×C4×C71—21no—
57C2×C4×C71—41no—
58C2×C4×C71—41no—
59C2×C4×C71M1612yescomplemented
60C2×C4×C71C2×D412yes—
61C2×Dic71—22no—
62C2×Dic71—21no—
63C2×Dic71—41no—
64C2×Dic71C22⋊C411yescharacteristic
65C2×Dic71C22⋊C411yescharacteristic
66D284—28no—
67C4×D71—24no—
68C4×D71—42no—
69C4×D71—42no—
70C4×D71—42no—
71C8×C71—42no—
72C71⋊C8—42no—
73C22×C71—21no—
74C22×C71—21no—
75C22×C71C2×C22⋊C411yescharacteristic
76C22×C71C2×M1611yescharacteristic
77C22×C71C2×M1611yescharacteristic
78C2×D71—22no—
79C2×D71—22no—
80C2×D71—22no—
81C2×D71—22no—
82C2×D71—42no—
83C2×D71—42no—
84C2×D71—42no—
85C2×D71—41no—
86C2×D71—41no—
87C2×D71—42no—
88C4×C71—22no—
89C4×C71—22no—
90C4×C71—41no—
91Dic71—21no—
92Dic71—41no—
93Dic71#9912yes—
94C2×C71—21no—
95C2×C71—21no—
96C2×C71#40711yescharacteristic
97C2×C71C2×#9911yescharacteristic
98C2×C71#41311yescharacteristic
99D71—42no—
100D71—42no—
101#1465—711nomaximal, Sylow
102C71#146511yescharacteristic, complemented, Sylow
103C2×C4×D4—711no—
104#407—712no—
105#324—711no—
106#324D7111yescharacteristic, complemented
107#323—712no—
108C22×D4—711no—
109C23×C4—711no—
110C23×C4—711no—
111C2×M16—1422no—
112C4×D4—1422no—
113C4×D4—1422no—
114C2×C4⋊C4C2×D7111yescharacteristic
115C2×C22⋊C4—711no—
116C2×C22⋊C4—711no—
117C2×C42—711no—
118C22⋊C8—712no—
119C22⋊C8—1422no—
120C22⋊C8C2×D7112yes—
121C24—711no—
122C24—711no—
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—712no—
132C22×C4—1421no—
133C22×C4—1421no—
134C22×C4C4×D7111yescharacteristic
135C22×C4C4×D7111yescharacteristic
136C22×C4C22×D7111yescharacteristic
137M16—2844no—
138C2×C8—22no—
139C2×C8—1422no—
140C4⋊C4—22no—
141C22⋊C4—1422no—
142C22⋊C4—1422no—
143C42—1421no—
144C42—1421no—
145C23—2841no—
146C23—2841no—
147C23—2841no—
148C23—2841no—
149C23—712no—
150C23—712no—
151C23—1421no—
152C23—1421no—
153C23—1421no—
154C23—1421no—
155C23C2×C4×D7111yescharacteristic
156D4—1428no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—2842no—
163C2×C4—2842no—
164C2×C4—2842no—
165C2×C4—2841no—
166C2×C4—711no—
167C2×C4—711no—
168C2×C4—1424no—
169C2×C4—1421no—
170C2×C4—1422no—
171C2×C4#1176584812yescomplemented
172C2×C4D4×D7112yes—
173C8—42no—
174C8—2842no—
175C22—21no—
176C22—21no—
177C22—2842no—
178C22—2842no—
179C22—2842no—
180C22—2842no—
181C22—2841no—
182C22—2841no—
183C22—1422no—
184C22—1422no—
185C22—1422no—
186C22—1422no—
187C22C22⋊C4×D7111yescharacteristic
188C22M16×D7111yescharacteristic
189C22C2×#1176584811yescharacteristic
190C4—22no—
191C4—22no—
192C4—41no—
193C4—2841no—
194C4—712no—
195C4—1421no—
196C2—21no—
197C2—21no—
198C2—2842no—
199C2—2842no—
200C2#1798596111yescharacteristic
201C2#99×D7111yescharacteristic
202C2#1798598211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D71
commutatorC23×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#324×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#324D71
hypocenterC71#1465
LCSG ▷ C23×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #17985961C2semidirect
3. #17985725C2semidirect
4. #17985722C2semidirect
5. #324×C71C2semidirect
53. C22×D71M16semidirect
59. C2×C4×C71M16semidirect
102. C71#1465semidirect
106. #324D71semidirect
171. C2×C4#11765848semidirect