Finite Group Databasebeta

← #22586850

Subgroups — #22586850

Order 9088.

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

normal subgroups only

This group has 228 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
1#17986551C211yesmaximal, characteristic
2#17986053C211yesmaximal, characteristic
3#17985844C211yesmaximal, characteristic
4#17985737C211yesmaximal, characteristic
5#17985736C211yesmaximal, characteristic
6#17985735C211yesmaximal, characteristic
7#328×C71C211yesmaximal, characteristic
8#14556127C411yescharacteristic, complemented
9#14556126C411yescharacteristic, complemented
10#14556118—21no—
11#14556107C2211yescharacteristic
12#14556105—21no—
13Q8×Dic71C411yescharacteristic, complemented
14#14556093—21no—
15#14556093C411yescharacteristic, complemented
16#14556084—21no—
17C2×C4×Dic71—21no—
18C2×C4×Dic71C2211yescharacteristic
19Dic71⋊C8—21no—
20C22⋊(C71⋊C8)C2211yescharacteristic
21#14556038—21no—
22C71⋊#95—21no—
23C71⋊#95C2211yescharacteristic
24C22⋊Q8×C71C2211yescharacteristic
25C22⋊C8×C71C2211yescharacteristic
26#95×C71C2211yescharacteristic
27C2×Dic142—21no—
28C2×Dic142C2×C411yescharacteristic
29C22×Dic71—21no—
30C22×Dic71D411yescharacteristic
31C22×Dic71D411yescharacteristic
32C2×C71⋊C8—21no—
33C4⋊Dic71—21no—
34C4⋊Dic71C2×C411yescharacteristic
35Dic71⋊C4—21no—
36Dic71⋊C4—21no—
37Dic71⋊C4—21no—
38Dic71⋊C4—21no—
39Dic71⋊C4—21no—
40C22⋊Dic71—21no—
41C4×Dic71—24no—
42C4×Dic71—21no—
43C4×Dic71—21no—
44C4×Dic71C2×C411yescharacteristic
45C4×Dic71C2×C411yescharacteristic
46C4×Dic71D411yescharacteristic
47C4×Dic71D411yescharacteristic
48C2×Q8×C71C2×C411yescharacteristic
49C22×C4×C71—21no—
50C22×C4×C71C2311yescharacteristic
51C2×C8×C71—21no—
52C4⋊C4×C71—21no—
53C4⋊C4×C71C2×C411yescharacteristic
54C22⋊C4×C71—21no—
55C23×C71C2×D411yescharacteristic
56Q8×C71—41no—
57C2×C4×C71—22no—
58C2×C4×C71—21no—
59C2×C4×C71—21no—
60C2×C4×C71—41no—
61C2×C4×C71—41no—
62C2×C4×C71—41no—
63C2×C4×C71C22×C411yescharacteristic
64C2×C4×C71C2×D411yescharacteristic
65C2×Dic71—21no—
66C2×Dic71—21no—
67C2×Dic71—22no—
68C2×Dic71—22no—
69C2×Dic71—21no—
70C2×Dic71—21no—
71C2×Dic71—41no—
72C2×Dic71—41no—
73C2×Dic71C22⋊C411yescharacteristic
74C2×Dic71C22⋊C411yescharacteristic
75C2×Dic71C22⋊C411yescharacteristic
76C2×Dic71C22⋊C411yescharacteristic
77Dic142—42no—
78Dic142—41no—
79C8×C71—41no—
80C71⋊C8—41no—
81C22×C71—21no—
82C22×C71—21no—
83C22×C71C2×C22⋊C411yescharacteristic
84C22×C71#13711yescharacteristic
85C22×C71#13711yescharacteristic
86C4×C71—21no—
87C4×C71—21no—
88C4×C71—42no—
89C4×C71—41no—
90C4×C71—41no—
91Dic71—21no—
92Dic71—21no—
93Dic71—21no—
94Dic71—42no—
95Dic71—41no—
96Dic71—41no—
97Dic71#10412yes—
98C2×C71—21no—
99C2×C71—21no—
100C2×C71#41011yescharacteristic
101C2×C71#41911yescharacteristic
102C2×C71C2×#10411yescharacteristic
103#1506—711nomaximal, Sylow
104C71#150611yescharacteristic, complemented, Sylow
105#533—711no—
106#432—711no—
107#376—711no—
108#328—711no—
109#328—711no—
110#328—711no—
111#328D7111yescharacteristic
112C4⋊Q8—711no—
113C4⋊Q8—711no—
114#125—1421no—
115C22⋊Q8—711no—
116C22⋊Q8—1421no—
117C22⋊Q8C2×D7111yescharacteristic
118C4×Q8—711no—
119C4×Q8—711no—
120C4×Q8—1421no—
121#117—1421no—
122C2×C42—711no—
123C2×C42—1421no—
124C4⋊C8—1421no—
125C22⋊C8—711no—
126C22⋊C8C2×D7111yescharacteristic
127#97—1421no—
128#95—711no—
129#95—1421no—
130#95C2×D7111yescharacteristic
131C2×Q8—711no—
132C2×Q8—1421no—
133C2×Q8C4×D7111yescharacteristic
134C22×C4—21no—
135C22×C4—711no—
136C22×C4—711no—
137C22×C4—1421no—
138C22×C4C22×D7111yescharacteristic
139C2×C8—21no—
140C2×C8—1421no—
141C4⋊C4—21no—
142C4⋊C4—711no—
143C4⋊C4—1421no—
144C4⋊C4—1421no—
145C4⋊C4—1421no—
146C4⋊C4—1421no—
147C4⋊C4—1421no—
148C4⋊C4—1421no—
149C4⋊C4C4×D7111yescharacteristic
150C22⋊C4—21no—
151C22⋊C4—1421no—
152C42—711no—
153C42—711no—
154C42—711no—
155C42—711no—
156C42—1421no—
157C42—1421no—
158C42—1424no—
159C23D4×D7111yescharacteristic
160Q8—41no—
161Q8—2841no—
162Q8—2842no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—2841no—
170C2×C4—2841no—
171C2×C4—711no—
172C2×C4—711no—
173C2×C4—711no—
174C2×C4—711no—
175C2×C4—1422no—
176C2×C4—1421no—
177C2×C4—1421no—
178C2×C4—1422no—
179C2×C4—1421no—
180C2×C4—1421no—
181C2×C4C2×C4×D7111yescharacteristic
182C2×C4D4×D7111yescharacteristic
183C8—41no—
184C8—2841no—
185C22—21no—
186C22—21no—
187C22C22⋊C4×D7111yescharacteristic
188C22#1455615711yescharacteristic
189C22#1455616011yescharacteristic
190C4—21no—
191C4—21no—
192C4—42no—
193C4—41no—
194C4—41no—
195C4—2842no—
196C4—2841no—
197C4—2841no—
198C4—712no—
199C4—1421no—
200C4—1421no—
201C4—1421no—
202C2—21no—
203C2—21no—
204C2#1798597111yescharacteristic
205C2#1798600611yescharacteristic
206C2#104×D7111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D71
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#328×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#328D71
hypocenterC71#1506
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #14556127C4semidirect
9. #14556126C4semidirect
13. Q8×Dic71C4semidirect
15. #14556093C4semidirect
104. C71#1506semidirect