Finite Group Databasebeta

← #20242001

Subgroups — #20242001

Order 6016.

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#15689679C211yesmaximal, characteristic
2#15689178C211yesmaximal, characteristic
3#97×D47C211yesmaximal, characteristic
4#15688865C211yesmaximal, characteristic, complemented
5#15688864C211yesmaximal, characteristic, complemented
6#15688864C211yesmaximal, characteristic, complemented
7C47×#330C211yesmaximal, characteristic, complemented
8C2×C8×D47—21no—
9#13094023C411yescharacteristic
10#13094023C411yescharacteristic
11#13094016C2211yescharacteristic
12#13094002—21no—
13#13094002—21no—
14#13093989—21no—
15#13093989—21no—
16#13093982C411yescharacteristic
17#13093982C411yescharacteristic
18C42×D47C2211yescharacteristic
19Dic47⋊C8—21no—
20(C2×D47)⋊C8—21no—
21#13093935C2211yescharacteristic
22#13093935C2211yescharacteristic
23#13093934—21no—
24#125×C47C2211yescharacteristic
25#97×C47C2211yescharacteristic
26#97×C47C2211yescharacteristic
27C2×C4×D47C2×C411yescharacteristic
28C2×C4×D47D411yescharacteristic
29C2×C4×D47D411yescharacteristic
30C2×Dic94—21no—
31C2×Dic94—21no—
32C2×C8×C47—21no—
33C2×C8×C47—21no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47—21no—
36C4⋊C4×C47C2×C411yescharacteristic
37C4⋊C4×C47C2×C411yescharacteristic
38C42×C47C2311yescharacteristic
39(C2×D47)⋊C4—21no—
40(C2×D47)⋊C4—21no—
41C4⋊Dic47C2×C411yescharacteristic
42C4⋊Dic47C2×C411yescharacteristic
43Dic47⋊C4—21no—
44Dic47⋊C4—21no—
45Dic47⋊C4—21no—
46Dic47⋊C4—21no—
47C4×Dic47—21no—
48C4×Dic47—21no—
49C4×Dic47C2×C411yescharacteristic
50C4×Dic47D411yescharacteristic
51C4×Dic47D411yescharacteristic
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C8×D47—24no—
55C22×D47C22⋊C411yescharacteristic
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47C22×C411yescharacteristic
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47C2×D411yescharacteristic
61C2×Dic47—21no—
62C2×Dic47—21no—
63C2×Dic47C22⋊C411yescharacteristic
64C2×Dic47C22⋊C411yescharacteristic
65C2×Dic47C22⋊C411yescharacteristic
66C4×D47—22no—
67C4×D47—22no—
68C4×D47—41no—
69Dic94—42no—
70Dic94—42no—
71C8×C47—22no—
72C8×C47—41no—
73C47⋊C8—22no—
74C47⋊C8—41no—
75C22×C47C2×C22⋊C411yescharacteristic
76C2×D47—21no—
77C2×D47—21no—
78C2×D47#10112yes—
79C4×C47—21no—
80C4×C47—21no—
81C4×C47—21no—
82C4×C47—41no—
83C4×C47—41no—
84Dic47—21no—
85Dic47—21no—
86Dic47—41no—
87Dic47—41no—
88Dic47#10412yes—
89#1531—471nomaximal, Sylow
90C2×C47C2×#10111yescharacteristic
91C2×C47C2×#10411yescharacteristic
92C2×C47#42111yescharacteristic
93D47—22no—
94#533—471no—
95#432—471no—
96C2×#97—471no—
97#330—471no—
98#330—471no—
99#330—471no—
100#330D4711yescharacteristic, complemented
101C47#153111yescharacteristic, complemented, Sylow
102C22×C8—941no—
103C4⋊Q8—471no—
104C4⋊Q8—471no—
105#125—471no—
106#125C2×D4711yescharacteristic
107C22⋊Q8—941no—
108C22⋊Q8—941no—
109C4×Q8—941no—
110C4×Q8—941no—
111#117—471no—
112#117—471no—
113C2×C42—471no—
114C4⋊C8—941no—
115C22⋊C8—941no—
116#97—471no—
117#97—471no—
118#97—941no—
119#97C2×D4711yescharacteristic
120#97C2×D4711yescharacteristic
121C2×Q8—941no—
122C2×Q8—941no—
123C22×C4—471no—
124C22×C4—471no—
125C22×C4—471no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—944no—
129C2×C8—941no—
130C2×C8—941no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—471no—
134C4⋊C4—471no—
135C4⋊C4—941no—
136C4⋊C4—941no—
137C4⋊C4—941no—
138C4⋊C4—941no—
139C4⋊C4C4×D4711yescharacteristic
140C4⋊C4C4×D4711yescharacteristic
141C22⋊C4—941no—
142C22⋊C4—941no—
143C42—471no—
144C42—471no—
145C42—471no—
146C42—941no—
147C42—941no—
148C42C22×D4711yescharacteristic
149C23—471no—
150Q8—1882no—
151Q8—1882no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—471no—
155C2×C4—471no—
156C2×C4—471no—
157C2×C4—942no—
158C2×C4—942no—
159C2×C4—941no—
160C2×C4—941no—
161C2×C4—1881no—
162C2×C4C2×C4×D4711yescharacteristic
163C2×C4D4×D4711yescharacteristic
164C2×C4D4×D4711yescharacteristic
165C8—22no—
166C8—41no—
167C8—942no—
168C8—1881no—
169C22—472no—
170C22—941no—
171C22—941no—
172C22C22⋊C4×D4711yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—472no—
179C4—941no—
180C4—941no—
181C4—1881no—
182C4—1881no—
183C2—942no—
184C2#101×D4711yescharacteristic
185C2#104×D4711yescharacteristic
186C2#1568913811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#330C2
socleC22×C47C2×C22⋊C4
hypercenter#330D47
hypocenterC47#1531
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
4. #15688865C2semidirect
5. #15688864C2semidirect
6. #15688864C2semidirect
7. C47×#330C2semidirect
100. #330D47semidirect
101. C47#1531semidirect