Finite Group Databasebeta

← #20241796

Subgroups — #20241796

Order 6016.

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

normal subgroups only

This group has 212 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
1#15689176C211yesmaximal, characteristic, complemented
2#15689176C211yesmaximal, characteristic, complemented
3Q8⋊(C47⋊C8)C212yesmaximal, complemented
4D4⋊(C47⋊C8)C212yesmaximal, complemented
5C47×#529C211yesmaximal, characteristic
6C4⋊(C47⋊C8)—21no—
7C4⋊(C47⋊C8)C2212yes—
8C22⋊(C47⋊C8)—21no—
9C22⋊(C47⋊C8)—21no—
10C4×C47⋊C8—21no—
11C4×C47⋊C8C2212yes—
12#126×C47—21no—
13#125×C47C411yescharacteristic
14#124×C47C411yescharacteristic
15#123×C47—21no—
16C22⋊Q8×C47C411yescharacteristic
17#121×C47C411yescharacteristic
18C4×Q8×C47C2211yescharacteristic
19C4×D4×C47—21no—
20C4×D4×C47C2211yescharacteristic
21#117×C47—21no—
22C2×C42×C47C2211yescharacteristic
23C2×Q8×C47C2×C411yescharacteristic
24C2×D4×C47—21no—
25C2×D4×C47C2×C411yescharacteristic
26C22×C4×C47—21no—
27C22×C4×C47C2×C411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×C4×C47D411yescharacteristic
30C4⋊C4×C47—21no—
31C4⋊C4×C47—21no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47C2×C411yescharacteristic
35C4⋊C4×C47C2×C411yescharacteristic
36C22⋊C4×C47—21no—
37C22⋊C4×C47—21no—
38C22⋊C4×C47—21no—
39C22⋊C4×C47—21no—
40C22⋊C4×C47—21no—
41C42×C47—21no—
42C42×C47C2×C411yescharacteristic
43C42×C47D411yescharacteristic
44C42×C47D411yescharacteristic
45C42×C47C2311yescharacteristic
46C2×C47⋊C8—22no—
47C2×C47⋊C8—22no—
48C23×C47—21no—
49C23×C47C22⋊C411yescharacteristic
50Q8×C47—22no—
51D4×C47—22no—
52D4×C47—42no—
53C2×C4×C47—22no—
54C2×C4×C47—22no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—41no—
59C2×C4×C47—42no—
60C2×C4×C47C22⋊C411yescharacteristic
61C2×C4×C47C22⋊C411yescharacteristic
62C2×C4×C47C22⋊C411yescharacteristic
63C2×C4×C47C22×C411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C47⋊C8—42no—
67C47⋊C8—42no—
68C22×C47—21no—
69C22×C47—21no—
70C22×C47—21no—
71C22×C47—41no—
72C22×C47—41no—
73C22×C47—41no—
74C22×C47C2×C22⋊C411yescharacteristic
75C4×C47—21no—
76C4×C47—21no—
77C4×C47—21no—
78C4×C47—21no—
79C4×C47—41no—
80C4×C47—41no—
81C4×C47—41no—
82C4×C47#13112yes—
83C4×C47#13512yes—
84#1482—471nomaximal, Sylow
85C2×C47—41no—
86C2×C47—81no—
87C2×C47#40811yescharacteristic
88C2×C47#41611yescharacteristic
89C2×C47#42111yescharacteristic
90#529D4711yescharacteristic
91#431—471no—
92#431—471no—
93Q8⋊C8—472no—
94D4⋊C8—472no—
95C47#148211yescharacteristic, complemented, Sylow
96#126—21no—
97#125Dic4711yescharacteristic
98#124Dic4711yescharacteristic
99#123—21no—
100C22⋊Q8Dic4711yescharacteristic
101#121Dic4711yescharacteristic
102C4×Q8C2×D4711yescharacteristic
103C4×D4—21no—
104C4×D4C2×D4711yescharacteristic
105#117—21no—
106C2×C42C2×D4711yescharacteristic
107C4⋊C8—472no—
108C4⋊C8—941no—
109C22⋊C8—941no—
110C22⋊C8—941no—
111C4×C8—472no—
112C4×C8—941no—
113C2×Q8C2×Dic4711yescharacteristic
114C2×D4—21no—
115C2×D4C2×Dic4711yescharacteristic
116C22×C4—21no—
117C22×C4C2×Dic4711yescharacteristic
118C22×C4C22⋊D4711yescharacteristic
119C22×C4C22⋊D4711yescharacteristic
120C2×C8—942no—
121C2×C8—942no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4C2×Dic4711yescharacteristic
127C4⋊C4C2×Dic4711yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—21no—
130C22⋊C4—21no—
131C22⋊C4—21no—
132C22⋊C4—21no—
133C42—21no—
134C42C2×Dic4711yescharacteristic
135C42C22⋊D4711yescharacteristic
136C42C22⋊D4711yescharacteristic
137C42C22×D4711yescharacteristic
138C23—21no—
139C23C22⋊Dic4711yescharacteristic
140Q8—22no—
141D4—22no—
142D4—42no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4C22⋊Dic4711yescharacteristic
151C2×C4C22⋊Dic4711yescharacteristic
152C2×C4C22⋊Dic4711yescharacteristic
153C2×C4C22×Dic4711yescharacteristic
154C2×C4C2×C22⋊D4711yescharacteristic
155C2×C4C2×C22⋊D4711yescharacteristic
156C8—1882no—
157C8—1882no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—41no—
162C22—41no—
163C22—41no—
164C22C2×C22⋊Dic4711yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—41no—
172C4#1309403112yes—
173C4#1309404412yes—
174C2—41no—
175C2—81no—
176C2#1568909011yescharacteristic
177C2#1568911911yescharacteristic
178C2#1568914011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#529C2
socleC22×C47C2×C22⋊C4
hypercenter#529D47
hypocenterC47#1482
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #15689176C2semidirect
2. #15689176C2semidirect
3. Q8⋊(C47⋊C8)C2semidirect
4. D4⋊(C47⋊C8)C2semidirect
95. C47#1482semidirect