Finite Group Databasebeta

← #44536906

Subgroups — #44536906

Order 31424.

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#30628384C211yesmaximal, characteristic
2#30628368C211yesmaximal, characteristic, complemented
3#30628335C211yesmaximal, characteristic, complemented
4#30628264C211yesmaximal, characteristic, complemented
5#30628263C211yesmaximal, characteristic, complemented
6#30628255C211yesmaximal, characteristic, complemented
7#137×C491C211yesmaximal, characteristic, complemented
8#21463328—21no—
9#21463328C2211yescharacteristic
10#21463327—22no—
11#21463327—21no—
12C2×Dic982—21no—
13C2×Dic982C2211yescharacteristic
14Q8×D491—21no—
15#21463318—21no—
16#21463315—21no—
17#21463312C2211yescharacteristic
18Dic491⋊C4—22no—
19C4×Dic491C2211yescharacteristic
20#41×C491C2211yescharacteristic
21C2×Q8×C491C2211yescharacteristic
22Q16×C491—21no—
23SD16×C491—21no—
24M16×C491C2211yescharacteristic
25Dic982—22no—
26Dic982—21no—
27Dic982—21no—
28Dic982D411yescharacteristic
29D1964D411yescharacteristic
30C22⋊D491—22no—
31C22⋊D491—21no—
32C2×Dic491—22no—
33C2×Dic491—21no—
34C2×Dic491D412yes—
35C4×D491—22no—
36C4×D491—21no—
37C491⋊C8—21no—
38Q8×C491—21no—
39Q8×C491—21no—
40Q8×C491D411yescharacteristic
41D4×C491—21no—
42D4×C491D411yescharacteristic
43C2×C4×C491—21no—
44C2×C4×C491—21no—
45C2×C4×C491C2311yescharacteristic
46C8×C491—21no—
47C22×C491—21no—
48C22×C491C2×D411yescharacteristic
49C2×D491—21no—
50C4×C491—21no—
51C4×C491—41no—
52C4×C491C2×D411yescharacteristic
53C4×C491C2×D411yescharacteristic
54Dic491—22no—
55Dic491—21no—
56Dic491—22no—
57C2×C491—21no—
58C2×C491—41no—
59C2×C491#12011yescharacteristic
60D491—41no—
61C491#45611yescharacteristic, complemented, Sylow
62#456—4911nomaximal, Sylow
632−1+4—4911no—
64#137—4911no—
65#137D49111yescharacteristic, complemented
66C4⋊Q8—4911no—
67#104—4911no—
68#104—4911no—
69#101—4911no—
70#41—9821no—
71#41—9821no—
72#41—9822no—
73#41—4911no—
74#41C2×D49111yescharacteristic
75C2×Q8—9821no—
76C2×Q8—9821no—
77C2×Q8—4911no—
78C2×Q8C2×D49111yescharacteristic
79Q16—21no—
80Q16—9821no—
81SD16—21no—
82SD16—9821no—
83M16—4911no—
84M16C2×D49111yescharacteristic
85C4⋊C4—9822no—
86C42—4911no—
87Q8—21no—
88Q8—21no—
89Q8—9822no—
90Q8—9821no—
91Q8—9821no—
92Q8—4911no—
93Q8C22⋊D49111yescharacteristic
94D4—21no—
95D4—9822no—
96D4—9821no—
97D4—4911no—
98D4C22⋊D49111yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—9822no—
102C2×C4—9822no—
103C2×C4—9821no—
104C2×C4—9821no—
105C2×C4—4912no—
106C2×C4C22×D49111yescharacteristic
107C8—21no—
108C8—9821no—
109C22—21no—
110C22—9821no—
111C22D4×D49111yescharacteristic
112C4—21no—
113C4—41no—
114C4—9822no—
115C4—9821no—
116C4—9822no—
117C4D4×D49111yescharacteristic
118C4C2×C22⋊D49111yescharacteristic
119C2—21no—
120C2—41no—
121C2—19641no—
122C2#3062830511yescharacteristic
subgroupG/H
centerC2#30628305
commutator, cosocleC2×C4×C491C23
FrattiniC2×C4C22×D491
Fitting#137×C491C2
socleC2×C491#120
prime radical#30628384C2
hypercenter#137D491
hypocenterC491#456
LCSG ▷ C2×C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #30628368C2semidirect
3. #30628335C2semidirect
4. #30628264C2semidirect
5. #30628263C2semidirect
6. #30628255C2semidirect
7. #137×C491C2semidirect
61. C491#456semidirect
65. #137D491semidirect

Maximal subgroups

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

subgroupindex
#306283842
#306283682
#306283352
#306282642
#306282632
#306282552
#137×C4912
#456491