Finite Group Databasebeta

← #20242722

Subgroups — #20242722

Order 6016.

184 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 49 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#15689533C211yesmaximal, characteristic, complemented
2#15689493C211yesmaximal, characteristic, complemented
3#15689482C211yesmaximal, characteristic
4#15688865C211yesmaximal, characteristic, complemented
5#15688865C211yesmaximal, characteristic, complemented
6#15688863C211yesmaximal, characteristic
7C47×#563C211yesmaximal, characteristic
8#13094024C2211yescharacteristic
9#13093957—21no—
10#13093955—21no—
11#13093948—21no—
12#13093947—21no—
13#13093947—21no—
14#13093945—21no—
15#13093935C2211yescharacteristic
16#13093935C2211yescharacteristic
17#13093935C2211yescharacteristic
18C4⋊Q8×C47—21no—
19#126×C47—21no—
20#126×C47—21no—
21#125×C47C2211yescharacteristic
22#125×C47C2211yescharacteristic
23#124×C47C2211yescharacteristic
24#123×C47—21no—
25C22⋊Q8×C47—21no—
26C22⋊Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47D411yescharacteristic
29C2×D4×C47D411yescharacteristic
30C22×C4×C47—21no—
31C2×Dic94—21no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47D411yescharacteristic
39C4⋊C4×C47D411yescharacteristic
40C4⋊C4×C47D411yescharacteristic
41C4⋊C4×C47D411yescharacteristic
42C22⋊C4×C47—21no—
43C22⋊C4×C47—21no—
44C22⋊C4×C47—21no—
45C22⋊C4×C47—21no—
46C22⋊C4×C47—21no—
47C42×C47—21no—
48C42×C47C2311yescharacteristic
49C4⋊Dic47—21no—
50C4⋊Dic47—21no—
51C2×C47⋊C8—21no—
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C23×C47—21no—
55Q8×C47—41no—
56Q8×C47—81no—
57D4×C47—41no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47—21no—
62C2×C4×C47—21no—
63C2×C4×C47—81no—
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×Dic47—41no—
68Dic94—42no—
69C47⋊C8—22no—
70C47⋊C8—41no—
71C47⋊C8—41no—
72C22×C47—41no—
73C22×C47—41no—
74C22×C47—41no—
75C22×C47#12011yescharacteristic
76C4×C47—21no—
77C4×C47—21no—
78C4×C47—21no—
79C4×C47—41no—
80C4×C47—41no—
81C4×C47—41no—
82C4×C47—41no—
83C4×C47—41no—
84Dic47—81no—
85#1664—471nomaximal, Sylow
86C2×C47—81no—
87C2×C47#45411yescharacteristic
88C2×C47#45511yescharacteristic
89C2×C47#45611yescharacteristic
90#563D4711yescharacteristic
91#501—471no—
92#491—471no—
93#489—471no—
94#330—471no—
95#330—471no—
96#329—471no—
97C47#166411yescharacteristic, complemented, Sylow
98C4⋊Q8—21no—
99C4⋊Q8—471no—
100#126—21no—
101#126—21no—
102#125C2×D4711yescharacteristic
103#125C2×D4711yescharacteristic
104#124C2×D4711yescharacteristic
105#123—21no—
106C22⋊Q8—21no—
107C22⋊Q8—21no—
108#107—941no—
109#106—941no—
110#103—941no—
111#103—941no—
112#103—941no—
113#102—941no—
114#97—471no—
115#97—471no—
116#97—471no—
117C2×Q8—21no—
118C2×Q8—941no—
119C2×Q8C22⋊D4711yescharacteristic
120C2×D4C22⋊D4711yescharacteristic
121C22×C4—21no—
122C2×C8—941no—
123C2×C8—941no—
124C2×C8—941no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—941no—
132C4⋊C4—941no—
133C4⋊C4C22⋊D4711yescharacteristic
134C4⋊C4C22⋊D4711yescharacteristic
135C4⋊C4C22⋊D4711yescharacteristic
136C4⋊C4C22⋊D4711yescharacteristic
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—21no—
141C22⋊C4—21no—
142C42—21no—
143C42C22×D4711yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—81no—
147Q8—1882no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—81no—
155C2×C4—1881no—
156C2×C4C2×C22⋊D4711yescharacteristic
157C2×C4C2×C22⋊D4711yescharacteristic
158C2×C4C2×C22⋊D4711yescharacteristic
159C8—942no—
160C8—1881no—
161C8—1881no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#1309399311yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—41no—
172C4—41no—
173C4—41no—
174C4—3761no—
175C2—81no—
176C2#1568929611yescharacteristic
177C2#1568930111yescharacteristic
178C2#1568930611yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#563C2
socleC22×C47#120
hypercenter#563D47
hypocenterC47#1664
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #15689533C2semidirect
2. #15689493C2semidirect
4. #15688865C2semidirect
5. #15688865C2semidirect
97. C47#1664semidirect