Finite Group Databasebeta

← #20242725

Subgroups — #20242725

Order 6016.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#15689873C211yesmaximal, characteristic
2#15689532C211yesmaximal, characteristic, complemented
3#15689492C211yesmaximal, characteristic, complemented
4#15689482C211yesmaximal, characteristic
5#15688864C211yesmaximal, characteristic, complemented
6#15688864C211yesmaximal, characteristic, complemented
7C47×#329C211yesmaximal, characteristic
8#13094024C2211yescharacteristic
9#13094022—21no—
10#13094017—21no—
11#13094017—21no—
12#13094016C2211yescharacteristic
13#13094016C2211yescharacteristic
14#13094005—21no—
15#13094001—21no—
16#13094001—21no—
17#13093958—21no—
18#13093956—21no—
19#13093949—21no—
20#13093949—21no—
21#13093948—21no—
22#13093945—21no—
23#13093935C2211yescharacteristic
24#124×C47C2211yescharacteristic
25#97×C47C2211yescharacteristic
26#97×C47C2211yescharacteristic
27C2×Q8×C47D411yescharacteristic
28C2×D4×C47D411yescharacteristic
29C22×Dic47—21no—
30C2×Dic94—21no—
31C2×Dic94—21no—
32C2×C8×C47—21no—
33C2×C8×C47—21no—
34C22⋊C4×C47—21no—
35C22⋊C4×C47—21no—
36C42×C47C2311yescharacteristic
37C22⋊Dic47—21no—
38C22⋊Dic47—21no—
39C22⋊Dic47—21no—
40C4⋊Dic47—21no—
41C4⋊Dic47—21no—
42C4⋊Dic47D411yescharacteristic
43C4⋊Dic47D411yescharacteristic
44C4⋊Dic47D411yescharacteristic
45C4⋊Dic47D411yescharacteristic
46Dic47⋊C4—21no—
47Dic47⋊C4—21no—
48Dic47⋊C4—21no—
49Dic47⋊C4—21no—
50Dic47⋊C4—21no—
51Dic47⋊C4—21no—
52C4×Dic47—21no—
53C2×C47⋊C8—21no—
54C23×C47—21no—
55Q8×C47—41no—
56D4×C47—41no—
57C2×C4×C47—21no—
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47C2×D411yescharacteristic
61C2×Dic47—21no—
62C2×Dic47—21no—
63C2×Dic47—21no—
64C2×Dic47—21no—
65C2×Dic47—41no—
66C2×Dic47—81no—
67Dic94—42no—
68Dic94—81no—
69C8×C47—22no—
70C8×C47—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—
80Dic47—41no—
81Dic47—41no—
82Dic47—41no—
83Dic47—41no—
84Dic47—81no—
85#1664—471nomaximal, Sylow
86C2×C47—81no—
87C2×C47#45411yescharacteristic
88C2×C47#45511yescharacteristic
89C2×C47#45611yescharacteristic
90#563—471no—
91#501—471no—
92#491—471no—
93#489—471no—
94#330—471no—
95#330—471no—
96#329D4711yescharacteristic
97C47#166411yescharacteristic, complemented, Sylow
98C4⋊Q8—471no—
99C4⋊Q8—941no—
100#126—941no—
101#126—941no—
102#125—471no—
103#125—471no—
104#124C2×D4711yescharacteristic
105#123—941no—
106C22⋊Q8—941no—
107C22⋊Q8—941no—
108#107—941no—
109#106—941no—
110#103—941no—
111#103—941no—
112#103—941no—
113#102—941no—
114#97—471no—
115#97C2×D4711yescharacteristic
116#97C2×D4711yescharacteristic
117C2×Q8—941no—
118C2×Q8—941no—
119C2×Q8D18811yescharacteristic
120C2×D4D18811yescharacteristic
121C22×C4—941no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—941no—
125C4⋊C4—471no—
126C4⋊C4—471no—
127C4⋊C4—471no—
128C4⋊C4—471no—
129C4⋊C4—941no—
130C4⋊C4—941no—
131C4⋊C4—941no—
132C4⋊C4—941no—
133C4⋊C4—941no—
134C4⋊C4—941no—
135C4⋊C4—941no—
136C4⋊C4—941no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—941no—
140C22⋊C4—941no—
141C22⋊C4—941no—
142C42—941no—
143C42C22×D4711yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—3761no—
147Q8—1882no—
148D4—41no—
149C2×C4—21no—
150C2×C4—941no—
151C2×C4—941no—
152C2×C4—941no—
153C2×C4—941no—
154C2×C4—3761no—
155C2×C4—1881no—
156C2×C4C2×D18811yescharacteristic
157C2×C4D4×D4711yescharacteristic
158C2×C4D4×D4711yescharacteristic
159C8—22no—
160C8—41no—
161C8—1881no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#1309399411yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—3761no—
171C4—1881no—
172C4—1881no—
173C4—1881no—
174C4—1881no—
175C2—81no—
176C2#1568929711yescharacteristic
177C2#1568930311yescharacteristic
178C2#1568930711yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#329C2
socleC22×C47#120
hypercenter#329D47
hypocenterC47#1664
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #15689532C2semidirect
3. #15689492C2semidirect
5. #15688864C2semidirect
6. #15688864C2semidirect
97. C47#1664semidirect