Finite Group Databasebeta

← #42119240

Subgroups — #42119240

Order 27584.

142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 39 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#28352236C211yesmaximal, characteristic
2#28352220C211yesmaximal, characteristic, complemented
3#28352187C211yesmaximal, characteristic, complemented
4#28352116C211yesmaximal, characteristic, complemented
5#28352115C211yesmaximal, characteristic, complemented
6#28352107C211yesmaximal, characteristic, complemented
7#137×C431C211yesmaximal, characteristic, complemented
8#20293800—21no—
9#20293800C2211yescharacteristic
10#20293799—22no—
11#20293799—21no—
12C2×Dic862—21no—
13C2×Dic862C2211yescharacteristic
14Q8×D431—21no—
15#20293790—21no—
16#20293787—21no—
17#20293784C2211yescharacteristic
18Dic431⋊C4—22no—
19C4×Dic431C2211yescharacteristic
20#41×C431C2211yescharacteristic
21C2×Q8×C431C2211yescharacteristic
22Q16×C431—21no—
23SD16×C431—21no—
24M16×C431C2211yescharacteristic
25Dic862—22no—
26Dic862—21no—
27Dic862—21no—
28Dic862D411yescharacteristic
29D1724D411yescharacteristic
30C22⋊D431—22no—
31C22⋊D431—21no—
32C2×Dic431—22no—
33C2×Dic431—21no—
34C2×Dic431D412yes—
35C4×D431—22no—
36C4×D431—21no—
37C431⋊C8—21no—
38Q8×C431—21no—
39Q8×C431—21no—
40Q8×C431D411yescharacteristic
41D4×C431—21no—
42D4×C431D411yescharacteristic
43C2×C4×C431—21no—
44C2×C4×C431—21no—
45C2×C4×C431C2311yescharacteristic
46C8×C431—21no—
47C22×C431—21no—
48C22×C431C2×D411yescharacteristic
49C2×D431—21no—
50C4×C431—21no—
51C4×C431—41no—
52C4×C431C2×D411yescharacteristic
53C4×C431C2×D411yescharacteristic
54Dic431—22no—
55Dic431—21no—
56Dic431—22no—
57C2×C431—21no—
58C2×C431—41no—
59C2×C431#12011yescharacteristic
60D431—41no—
61C431#45611yescharacteristic, complemented, Sylow
62#456—4311nomaximal, Sylow
632−1+4—4311no—
64#137—4311no—
65#137D43111yescharacteristic, complemented
66C4⋊Q8—4311no—
67#104—4311no—
68#104—4311no—
69#101—4311no—
70#41—8621no—
71#41—8621no—
72#41—8622no—
73#41—4311no—
74#41C2×D43111yescharacteristic
75C2×Q8—8621no—
76C2×Q8—8621no—
77C2×Q8—4311no—
78C2×Q8C2×D43111yescharacteristic
79Q16—21no—
80Q16—8621no—
81SD16—21no—
82SD16—8621no—
83M16—4311no—
84M16C2×D43111yescharacteristic
85C4⋊C4—8622no—
86C42—4311no—
87Q8—21no—
88Q8—21no—
89Q8—8622no—
90Q8—8621no—
91Q8—8621no—
92Q8—4311no—
93Q8C22⋊D43111yescharacteristic
94D4—21no—
95D4—8622no—
96D4—8621no—
97D4—4311no—
98D4C22⋊D43111yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—8622no—
102C2×C4—8622no—
103C2×C4—8621no—
104C2×C4—8621no—
105C2×C4—4312no—
106C2×C4C22×D43111yescharacteristic
107C8—21no—
108C8—8621no—
109C22—21no—
110C22—8621no—
111C22D4×D43111yescharacteristic
112C4—21no—
113C4—41no—
114C4—8622no—
115C4—8621no—
116C4—8622no—
117C4D4×D43111yescharacteristic
118C4C2×C22⋊D43111yescharacteristic
119C2—21no—
120C2—41no—
121C2—17241no—
122C2#2835215711yescharacteristic
subgroupG/H
centerC2#28352157
commutator, cosocleC2×C4×C431C23
FrattiniC2×C4C22×D431
Fitting#137×C431C2
socleC2×C431#120
prime radical#28352236C2
hypercenter#137D431
hypocenterC431#456
LCSG ▷ C2×C4×C431 ▷ C2×C431 ▷ C431
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #28352220C2semidirect
3. #28352187C2semidirect
4. #28352116C2semidirect
5. #28352115C2semidirect
6. #28352107C2semidirect
7. #137×C431C2semidirect
61. C431#456semidirect
65. #137D431semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#283522362
#283522202
#283521872
#283521162
#283521152
#283521072
#137×C4312
#456431