Finite Group Databasebeta

← #22586940

Subgroups — #22586940

Order 9088.

212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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
1#125×D71C211yesmaximal, characteristic
2#17986054C211yesmaximal, characteristic
3#17985951C211yesmaximal, characteristic
4#17985741C211yesmaximal, characteristic, complemented
5#17985740C211yesmaximal, characteristic, complemented
6#17985740C211yesmaximal, characteristic, complemented
7#330×C71C211yesmaximal, characteristic, complemented
8C2×#11765848—21no—
9#14556120C2211yescharacteristic
10#14556119C411yescharacteristic
11#14556119C411yescharacteristic
12#14556118—21no—
13#14556118—21no—
14C4⋊C4×D71—21no—
15C4⋊C4×D71—21no—
16C4⋊C4×D71C411yescharacteristic
17C4⋊C4×D71C411yescharacteristic
18C42×D71C2211yescharacteristic
19Dic71⋊C8—21no—
20(C2×D71)⋊C8—21no—
21#14556039C2211yescharacteristic
22#14556039C2211yescharacteristic
23C8×Dic71—21no—
24#125×C71C2211yescharacteristic
25#97×C71C2211yescharacteristic
26#97×C71C2211yescharacteristic
27C2×C4×D71—21no—
28C2×C4×D71—21no—
29C2×C4×D71C2×C411yescharacteristic
30C2×C4×D71D411yescharacteristic
31C2×C4×D71D411yescharacteristic
32#11765848—24no—
33C2×C71⋊C8—21no—
34C2×C71⋊C8—21no—
35C4⋊Dic71—21no—
36C4⋊Dic71—21no—
37C4⋊Dic71C2×C411yescharacteristic
38C4⋊Dic71C2×C411yescharacteristic
39Dic71⋊C4—21no—
40Dic71⋊C4—21no—
41Dic71⋊C4—21no—
42Dic71⋊C4—21no—
43Dic71⋊C4—21no—
44Dic71⋊C4—21no—
45C4×Dic71C2×C411yescharacteristic
46C4×Dic71D411yescharacteristic
47C4×Dic71D411yescharacteristic
48C2×C8×C71—21no—
49C2×C8×C71—21no—
50C4⋊C4×C71—21no—
51C4⋊C4×C71—21no—
52C4⋊C4×C71C2×C411yescharacteristic
53C4⋊C4×C71C2×C411yescharacteristic
54C42×C71C2311yescharacteristic
55C22×D71C22⋊C411yescharacteristic
56C2×C4×C71—21no—
57C2×C4×C71—21no—
58C2×C4×C71C22×C411yescharacteristic
59C2×C4×C71C2×D411yescharacteristic
60C2×C4×C71C2×D411yescharacteristic
61C2×Dic71—21no—
62C2×Dic71—21no—
63C2×Dic71C22⋊C411yescharacteristic
64C2×Dic71C22⋊C411yescharacteristic
65C2×Dic71C22⋊C411yescharacteristic
66C4×D71—22no—
67C4×D71—22no—
68C4×D71—41no—
69C4×D71—42no—
70C4×D71—42no—
71C8×C71—22no—
72C8×C71—41no—
73C71⋊C8—22no—
74C71⋊C8—41no—
75C22×C71C2×C22⋊C411yescharacteristic
76C2×D71—21no—
77C2×D71—21no—
78C2×D71#10412yes—
79C4×C71—21no—
80C4×C71—21no—
81C4×C71—21no—
82C4×C71—41no—
83C4×C71—41no—
84Dic71—21no—
85Dic71—21no—
86Dic71—41no—
87Dic71—41no—
88Dic71#10112yes—
89C2×C71C2×#10111yescharacteristic
90C2×C71C2×#10411yescharacteristic
91C2×C71#42111yescharacteristic
92D71—22no—
93#1528—711nomaximal, Sylow
94C71#152811yescharacteristic, complemented, Sylow
95C2×#125—711no—
96#432—711no—
97C4×M16—711no—
98#330—711no—
99#330—711no—
100#330—711no—
101#330D7111yescharacteristic, complemented
102C2×M16—1421no—
103#125—711no—
104#125—711no—
105#125—711no—
106#125—1421no—
107#125—1421no—
108#125C2×D7111yescharacteristic
109C2×C4⋊C4—711no—
110C2×C4⋊C4—711no—
111C2×C4⋊C4—1421no—
112C2×C4⋊C4—1421no—
113C2×C42—711no—
114C4⋊C8—1421no—
115C22⋊C8—1421no—
116#97—711no—
117#97—711no—
118#97C2×D7111yescharacteristic
119#97C2×D7111yescharacteristic
120C4×C8—1421no—
121C22×C4—711no—
122C22×C4—711no—
123C22×C4—711no—
124C22×C4—1421no—
125C22×C4—1421no—
126M16—1424no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—1421no—
130C2×C8—1421no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—711no—
134C4⋊C4—711no—
135C4⋊C4—1421no—
136C4⋊C4—1421no—
137C4⋊C4—1421no—
138C4⋊C4—1421no—
139C4⋊C4—1421no—
140C4⋊C4—1421no—
141C4⋊C4—1421no—
142C4⋊C4—1421no—
143C4⋊C4C4×D7111yescharacteristic
144C4⋊C4C4×D7111yescharacteristic
145C42—711no—
146C42—711no—
147C42—711no—
148C42C22×D7111yescharacteristic
149C23—711no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—2841no—
153C2×C4—2842no—
154C2×C4—2842no—
155C2×C4—711no—
156C2×C4—711no—
157C2×C4—711no—
158C2×C4—1422no—
159C2×C4—1422no—
160C2×C4—1421no—
161C2×C4—1421no—
162C2×C4C2×C4×D7111yescharacteristic
163C2×C4D4×D7111yescharacteristic
164C2×C4D4×D7111yescharacteristic
165C8—22no—
166C8—41no—
167C8—2841no—
168C8—1422no—
169C22—712no—
170C22—1421no—
171C22—1421no—
172C22C22⋊C4×D7111yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—2841no—
179C4—2841no—
180C4—712no—
181C4—1421no—
182C4—1421no—
183C2—1422no—
184C2#101×D7111yescharacteristic
185C2#104×D7111yescharacteristic
186C2#1798601411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D71
commutatorC2×C4×C71C22×C4
FrattiniC42C22×D71
Fitting#330×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#330D71
hypocenterC71#1528
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
4. #17985741C2semidirect
5. #17985740C2semidirect
6. #17985740C2semidirect
7. #330×C71C2semidirect
94. C71#1528semidirect
101. #330D71semidirect