Finite Group Databasebeta

← #22586694

Subgroups — #22586694

Order 9088.

204 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 63 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×#14556118C211yesmaximal, characteristic
2#17986053C211yesmaximal, characteristic
3#17986049C211yesmaximal, characteristic
4#17985725C211yesmaximal, characteristic
5#17985724C211yesmaximal, characteristic
6#17985724C211yesmaximal, characteristic
7#324×C71C211yesmaximal, characteristic
8#14556118—21no—
9#14556118—21no—
10#14556118—21no—
11#14556118—21no—
12C2×C4⋊Dic71C411yescharacteristic
13C2×Dic71⋊C4C411yescharacteristic
14C2×Dic71⋊C4C411yescharacteristic
15C2×Dic71⋊C4C411yescharacteristic
16C2×Dic71⋊C4C2211yescharacteristic
17C2×C4×Dic71C2211yescharacteristic
18Dic71⋊C8—21no—
19Dic71⋊C8—21no—
20C22⋊(C71⋊C8)C2211yescharacteristic
21C22⋊(C71⋊C8)C2211yescharacteristic
22#14556038—21no—
23C8×Dic71—21no—
24C2×C4⋊C4×C71C2211yescharacteristic
25C22⋊C8×C71C2211yescharacteristic
26C22⋊C8×C71C2211yescharacteristic
27C22×Dic71C2×C411yescharacteristic
28C22×Dic71C2×C411yescharacteristic
29C22×Dic71C2×C411yescharacteristic
30C22×Dic71C2×C411yescharacteristic
31C2×C71⋊C8—21no—
32C2×C71⋊C8—21no—
33C4⋊Dic71—21no—
34C4⋊Dic71—21no—
35Dic71⋊C4—21no—
36Dic71⋊C4—21no—
37Dic71⋊C4—21no—
38Dic71⋊C4—21no—
39Dic71⋊C4—21no—
40Dic71⋊C4—21no—
41Dic71⋊C4—21no—
42Dic71⋊C4—21no—
43C4×Dic71D411yescharacteristic
44C4×Dic71D411yescharacteristic
45C4×Dic71D411yescharacteristic
46C4×Dic71D411yescharacteristic
47C22×C4×C71C2×C411yescharacteristic
48C22×C4×C71C2×C411yescharacteristic
49C22×C4×C71C2311yescharacteristic
50C2×C8×C71—21no—
51C2×C8×C71—21no—
52C4⋊C4×C71—21no—
53C4⋊C4×C71—21no—
54C23×C71C22×C411yescharacteristic
55C2×C4×C71—21no—
56C2×C4×C71—21no—
57C2×C4×C71—21no—
58C2×C4×C71—21no—
59C2×C4×C71—41no—
60C2×C4×C71—41no—
61C2×C4×C71C2×D411yescharacteristic
62C2×C4×C71C2×D411yescharacteristic
63C2×Dic71—21no—
64C2×Dic71—21no—
65C2×Dic71—22no—
66C2×Dic71—21no—
67C2×Dic71—21no—
68C2×Dic71—21no—
69C2×Dic71—21no—
70C2×Dic71—41no—
71C2×Dic71C22⋊C411yescharacteristic
72C2×Dic71C22⋊C411yescharacteristic
73C2×Dic71C22⋊C411yescharacteristic
74C2×Dic71C22⋊C411yescharacteristic
75C8×C71—41no—
76C8×C71—41no—
77C71⋊C8—41no—
78C71⋊C8—41no—
79C22×C71—21no—
80C22×C71—21no—
81C22×C71C2×C22⋊C411yescharacteristic
82C22×C71#13111yescharacteristic
83C22×C71#13111yescharacteristic
84C4×C71—21no—
85C4×C71—21no—
86C4×C71—41no—
87C4×C71—41no—
88Dic71—21no—
89Dic71—21no—
90Dic71—21no—
91Dic71—41no—
92Dic71—41no—
93Dic71#10112yes—
94C2×C71—21no—
95C2×C71—21no—
96C2×C71#40811yescharacteristic
97C2×C71#41011yescharacteristic
98C2×C71C2×#10111yescharacteristic
99#1470—711nomaximal, Sylow
100C71#147011yescharacteristic, complemented, Sylow
101C2×#125—711no—
102#432—711no—
103#431—711no—
104#324—711no—
105#324—711no—
106#324—711no—
107#324D7111yescharacteristic
108#125—1421no—
109#125—1421no—
110#125—1421no—
111#125—1421no—
112C2×C4⋊C4—711no—
113C2×C4⋊C4—711no—
114C2×C4⋊C4—711no—
115C2×C4⋊C4—711no—
116C2×C4⋊C4—711no—
117C2×C4⋊C4C2×D7111yescharacteristic
118C2×C42—711no—
119C4⋊C8—1421no—
120C4⋊C8—1421no—
121C22⋊C8—711no—
122C22⋊C8—711no—
123C22⋊C8C2×D7111yescharacteristic
124C22⋊C8C2×D7111yescharacteristic
125#97—1421no—
126C4×C8—1421no—
127C22×C4—711no—
128C22×C4—711no—
129C22×C4—711no—
130C22×C4—711no—
131C22×C4C4×D7111yescharacteristic
132C22×C4C4×D7111yescharacteristic
133C22×C4C22×D7111yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—1421no—
137C2×C8—1421no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—1421no—
141C4⋊C4—1421no—
142C4⋊C4—1421no—
143C4⋊C4—1421no—
144C4⋊C4—1421no—
145C4⋊C4—1421no—
146C4⋊C4—1421no—
147C4⋊C4—1421no—
148C4⋊C4—1421no—
149C4⋊C4—1421no—
150C42—711no—
151C42—711no—
152C42—711no—
153C42—711no—
154C23C2×C4×D7111yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—2841no—
162C2×C4—711no—
163C2×C4—711no—
164C2×C4—711no—
165C2×C4—711no—
166C2×C4—1421no—
167C2×C4—1421no—
168C2×C4—1421no—
169C2×C4—1421no—
170C2×C4—1422no—
171C2×C4—1421no—
172C2×C4—1421no—
173C2×C4D4×D7111yescharacteristic
174C2×C4D4×D7111yescharacteristic
175C8—41no—
176C8—41no—
177C8—2841no—
178C8—2841no—
179C22—21no—
180C22—21no—
181C22C22⋊C4×D7111yescharacteristic
182C22#1455613411yescharacteristic
183C22#1455613611yescharacteristic
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—2841no—
189C4—2841no—
190C4—712no—
191C4—1421no—
192C4—1421no—
193C4—1421no—
194C2—21no—
195C2—21no—
196C2#1798596411yescharacteristic
197C2#1798597111yescharacteristic
198C2#101×D7111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D71
commutatorC23×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#324×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#324D71
hypocenterC71#1470
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
100. C71#1470semidirect