Finite Group Databasebeta

← #22586928

Subgroups — #22586928

Order 9088.

234 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C4×#11765849C211yesmaximal, characteristic, complemented
2C2×#14556039C211yesmaximal, characteristic, complemented
3#17985741C212yesmaximal, complemented
4#17985739C212yesmaximal, complemented
5#529×C71C211yesmaximal, characteristic
6C2×#11765849—21no—
7C22×C71⋊C8—21no—
8#14556039—21no—
9#14556039C2212yes—
10#14556039C2212yes—
11C4×C71⋊C8—21no—
12#126×C71—21no—
13#125×C71C2211yescharacteristic
14#124×C71C2211yescharacteristic
15#123×C71—21no—
16C22⋊Q8×C71C411yescharacteristic
17#121×C71C411yescharacteristic
18C4×Q8×C71C411yescharacteristic
19C4×D4×C71—21no—
20C4×D4×C71C411yescharacteristic
21#117×C71—21no—
22C2×C42×C71C2211yescharacteristic
23#11765849—24no—
24C2×C71⋊C8—24no—
25C2×C71⋊C8—22no—
26C2×C71⋊C8—22no—
27C2×Q8×C71C2×C411yescharacteristic
28C2×D4×C71—21no—
29C2×D4×C71C2×C411yescharacteristic
30C22×C4×C71—21no—
31C22×C4×C71C2×C411yescharacteristic
32C22×C4×C71D411yescharacteristic
33C22×C4×C71D411yescharacteristic
34C4⋊C4×C71—21no—
35C4⋊C4×C71—21no—
36C4⋊C4×C71—21no—
37C4⋊C4×C71—21no—
38C4⋊C4×C71C2×C411yescharacteristic
39C4⋊C4×C71C2×C411yescharacteristic
40C22⋊C4×C71—21no—
41C22⋊C4×C71—21no—
42C22⋊C4×C71—21no—
43C22⋊C4×C71—21no—
44C22⋊C4×C71—21no—
45C42×C71—21no—
46C42×C71C2×C411yescharacteristic
47C42×C71D411yescharacteristic
48C42×C71D411yescharacteristic
49C42×C71C2311yescharacteristic
50C23×C71—21no—
51C23×C71C22⋊C411yescharacteristic
52Q8×C71—41no—
53D4×C71—41no—
54D4×C71—42no—
55C2×C4×C71—22no—
56C2×C4×C71—22no—
57C2×C4×C71—21no—
58C2×C4×C71—21no—
59C2×C4×C71—21no—
60C2×C4×C71—41no—
61C2×C4×C71—42no—
62C2×C4×C71C22⋊C411yescharacteristic
63C2×C4×C71C22⋊C411yescharacteristic
64C2×C4×C71C22⋊C411yescharacteristic
65C2×C4×C71C22×C411yescharacteristic
66C2×C4×C71C2×D411yescharacteristic
67C2×C4×C71C2×D411yescharacteristic
68C71⋊C8—24no—
69C71⋊C8—24no—
70C22×C71—21no—
71C22×C71—21no—
72C22×C71—41no—
73C22×C71—41no—
74C22×C71—41no—
75C22×C71#10412yes—
76C22×C71C2×C22⋊C411yescharacteristic
77C4×C71—21no—
78C4×C71—21no—
79C4×C71—21no—
80C4×C71—21no—
81C4×C71—21no—
82C4×C71—41no—
83C4×C71—41no—
84C4×C71—41no—
85C4×C71#10412yes—
86C2×C71—22no—
87C2×C71—81no—
88C2×C71#41311yescharacteristic
89C2×C71C2×#10411yescharacteristic
90C2×C71C2×#10411yescharacteristic
91#1524—711nomaximal, Sylow
92C71#152411yescharacteristic, complemented, Sylow
93#529D7111yescharacteristic
94C4×M16—711no—
95C2×#97—711no—
96#330—712no—
97#329—712no—
98C2×M16—1421no—
99C22×C8—1421no—
100#126—21no—
101#125C2×D7111yescharacteristic
102#124C2×D7111yescharacteristic
103#123—21no—
104C22⋊Q8Dic7111yescharacteristic
105#121Dic7111yescharacteristic
106C4×Q8Dic7111yescharacteristic
107C4×D4—21no—
108C4×D4Dic7111yescharacteristic
109#117—21no—
110C2×C42C2×D7111yescharacteristic
111#97—712no—
112#97—712no—
113#97—1421no—
114C4×C8—1421no—
115C2×Q8C2×Dic7111yescharacteristic
116C2×D4—21no—
117C2×D4C2×Dic7111yescharacteristic
118C22×C4—21no—
119C22×C4C2×Dic7111yescharacteristic
120C22×C4C22⋊D7111yescharacteristic
121C22×C4C22⋊D7111yescharacteristic
122M16—1424no—
123C2×C8—1424no—
124C2×C8—1422no—
125C2×C8—1422no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4C2×Dic7111yescharacteristic
131C4⋊C4C2×Dic7111yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—21no—
136C22⋊C4—21no—
137C42—21no—
138C42C2×Dic7111yescharacteristic
139C42C22⋊D7111yescharacteristic
140C42C22⋊D7111yescharacteristic
141C42C22×D7111yescharacteristic
142C23—21no—
143C23C22⋊Dic7111yescharacteristic
144Q8—41no—
145D4—41no—
146D4—42no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—42no—
154C2×C4C22⋊Dic7111yescharacteristic
155C2×C4C22⋊Dic7111yescharacteristic
156C2×C4C22⋊Dic7111yescharacteristic
157C2×C4C22×Dic7111yescharacteristic
158C2×C4C2×C22⋊D7111yescharacteristic
159C2×C4C2×C22⋊D7111yescharacteristic
160C8—1424no—
161C8—1424no—
162C22—21no—
163C22—21no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22#1455605512yes—
168C22C2×C22⋊Dic7111yescharacteristic
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—41no—
175C4—41no—
176C4—41no—
177C4#1455605512yes—
178C2—22no—
179C2—81no—
180C2#1798598311yescharacteristic
181C2C2×#1455605511yescharacteristic
182C2C2×#1455605511yescharacteristic
subgroupG/H
centerC2×C4C22⋊Dic71
commutatorC2×C4×C71C22×C4
FrattiniC42C22×D71
Fitting#529×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#529D71
hypocenterC71#1524
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C4×#11765849C2semidirect
2. C2×#14556039C2semidirect
3. #17985741C2semidirect
4. #17985739C2semidirect
92. C71#1524semidirect