Finite Group Databasebeta

← #22586861

Subgroups — #22586861

Order 9088.

294 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 77 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×#14556107C211yesmaximal, characteristic
2C4×C22⋊Dic71C211yesmaximal, characteristic
3#17985737C214yesmaximal, complemented
4#407×C71C211yesmaximal, characteristic
5C22×Dic142C411yescharacteristic, complemented
6#14556107—21no—
7#14556107—21no—
8#14556107C412yescomplemented
9#14556107C2212yes—
10C2×C4⋊Dic71C411yescharacteristic, complemented
11C2×Dic71⋊C4—21no—
12C2×C22⋊Dic71—21no—
13C2×C22⋊Dic71—21no—
14C2×C4×Dic71—21no—
15C71⋊#95C2212yes—
16C23×C4×C71C2211yescharacteristic
17C2×M16×C71—21no—
18C22⋊C8×C71—21no—
19C22⋊C8×C71C2212yes—
20C2×Dic142—21no—
21C2×Dic142—42no—
22C2×Dic142C2×C412yes—
23C22×Dic71—21no—
24C22×Dic71—21no—
25C22×Dic71—22no—
26C4⋊Dic71—21no—
27C4⋊Dic71C2×C412yes—
28Dic71⋊C4—22no—
29Dic71⋊C4—22no—
30C22⋊Dic71—24no—
31C22⋊Dic71—22no—
32C22⋊Dic71—22no—
33C4×Dic71—42no—
34C24×C71D411yescharacteristic
35C22×C4×C71—42no—
36C22×C4×C71C2×C411yescharacteristic
37C22×C4×C71C2×C411yescharacteristic
38C22×C4×C71D411yescharacteristic
39C22×C4×C71D411yescharacteristic
40C22×C4×C71D411yescharacteristic
41C22×C4×C71C2311yescharacteristic
42M16×C71—42no—
43C2×C8×C71—22no—
44C23×C71—22no—
45C23×C71—22no—
46C23×C71—41no—
47C23×C71C22⋊C411yescharacteristic
48C23×C71C22⋊C411yescharacteristic
49C23×C71C2×D411yescharacteristic
50C2×C4×C71—22no—
51C2×C4×C71—22no—
52C2×C4×C71—22no—
53C2×C4×C71—41no—
54C2×C4×C71—41no—
55C2×C4×C71—41no—
56C2×C4×C71C22⋊C411yescharacteristic
57C2×C4×C71C22⋊C411yescharacteristic
58C2×C4×C71C22×C411yescharacteristic
59C2×C4×C71C2×D411yescharacteristic
60C2×Dic71—24no—
61C2×Dic71—22no—
62C2×Dic71—22no—
63C2×Dic71—42no—
64C2×Dic71—42no—
65C2×Dic71—42no—
66C2×Dic71—42no—
67Dic142—42no—
68Dic142—42no—
69C8×C71—42no—
70C22×C71—21no—
71C22×C71—21no—
72C22×C71—21no—
73C22×C71—21no—
74C22×C71—21no—
75C22×C71—21no—
76C22×C71—21no—
77C22×C71—44no—
78C22×C71#10412yes—
79C22×C71C2×C22⋊C411yescharacteristic
80C22×C71#13712yes—
81C4×C71—21no—
82C4×C71—21no—
83C4×C71—21no—
84C4×C71#9912yes—
85Dic71—44no—
86Dic71—42no—
87Dic71—42no—
88C2×C71—22no—
89C2×C71—22no—
90C2×C71—41no—
91C2×C71C2×#9911yescharacteristic
92C2×C71#41911yescharacteristic
93C2×C71C2×#10411yescharacteristic
94#1508—711nomaximal, Sylow
95C71#150811yescharacteristic, complemented, Sylow
96C2×C22⋊Q8—711no—
97#407D7111yescharacteristic
98C4×C22⋊C4—711no—
99#328—714no—
100C22×Q8—711no—
101C23×C4C2×D7111yescharacteristic
102C2×M16—21no—
103C22⋊Q8—712no—
104C22⋊Q8—712no—
105C22⋊Q8—1421no—
106C22⋊Q8—1421no—
107C2×C4⋊C4—711no—
108C2×C4⋊C4—1421no—
109C2×C22⋊C4—1421no—
110C2×C22⋊C4—1421no—
111C2×C42—1421no—
112C22⋊C8—21no—
113C22⋊C8C2×D7112yes—
114#95—712no—
115C24D28411yescharacteristic
116C2×Q8—2842no—
117C2×Q8—712no—
118C2×Q8—1421no—
119C22×C4—42no—
120C22×C4—1421no—
121C22×C4—1421no—
122C22×C4—1422no—
123C22×C4C4×D7111yescharacteristic
124C22×C4C4×D7111yescharacteristic
125C22×C4D28411yescharacteristic
126C22×C4C22⋊D7111yescharacteristic
127C22×C4C22⋊D7111yescharacteristic
128C22×C4C22×D7111yescharacteristic
129M16—42no—
130C2×C8—22no—
131C4⋊C4—712no—
132C4⋊C4—1422no—
133C4⋊C4—1421no—
134C4⋊C4—1422no—
135C22⋊C4—1424no—
136C22⋊C4—1422no—
137C22⋊C4—1422no—
138C42—2842no—
139C23—22no—
140C23—22no—
141C23—41no—
142C23(C2×D71)⋊C411yescharacteristic
143C23(C2×D71)⋊C411yescharacteristic
144C23C2×D28411yescharacteristic
145Q8—2842no—
146Q8—2842no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—2842no—
154C2×C4—2842no—
155C2×C4—2842no—
156C2×C4—2842no—
157C2×C4—1424no—
158C2×C4—1422no—
159C2×C4—1422no—
160C2×C4(C2×D71)⋊C411yescharacteristic
161C2×C4(C2×D71)⋊C411yescharacteristic
162C2×C4C2×C4×D7111yescharacteristic
163C2×C4C2×C22⋊D7111yescharacteristic
164C8—42no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—21no—
171C22—21no—
172C22—44no—
173C22#1455605412yes—
174C22C2×(C2×D71)⋊C411yescharacteristic
175C22#1455616112yes—
176C4—21no—
177C4—21no—
178C4—21no—
179C4—2844no—
180C4—2842no—
181C4—2842no—
182C4#1455604212yes—
183C2—22no—
184C2—22no—
185C2—41no—
186C2C2×#1455604211yescharacteristic
187C2#1798600911yescharacteristic
188C2C2×#1455605411yescharacteristic
subgroupG/H
centerC22C2×(C2×D71)⋊C4
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#407×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#407D71
hypocenterC71#1508
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #17985737C2semidirect
5. C22×Dic142C4semidirect
8. #14556107C4semidirect
10. C2×C4⋊Dic71C4semidirect
95. C71#1508semidirect