Finite Group Databasebeta

← #44536899

Subgroups — #44536899

Order 31424.

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

normal subgroups only

This group has 146 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, complemented
2#30628365C211yesmaximal, characteristic, complemented
3#30628362C211yesmaximal, characteristic, complemented
4#30628325C211yesmaximal, characteristic, complemented
5#30628265C211yesmaximal, characteristic, complemented
6#30628255C211yesmaximal, characteristic, complemented
7#104×C491C211yesmaximal, characteristic, complemented
8#21463328—21no—
9#21463328C2211yescharacteristic
10#21463327—22no—
11#21463327—21no—
12C2×Dic982—21no—
13C2×Dic982C2211yescharacteristic
14Q8×D491—21no—
15C2×D1964C2211yescharacteristic
16#21463317—21no—
17#21463315—21no—
18D3928—21no—
19#21463313—21no—
20#21463312C2211yescharacteristic
21(C2×D491)⋊C4—22no—
22#41×C491C2211yescharacteristic
23M16×C491C2211yescharacteristic
24C42×C491C2211yescharacteristic
25C22×D491—21no—
26Dic982—22no—
27Dic982—21no—
28Dic982—21no—
29Dic982D411yescharacteristic
30D1964—21no—
31D1964—21no—
32D1964D411yescharacteristic
33C22⋊D491—22no—
34C22⋊D491—21no—
35C2×Dic491—22no—
36C2×Dic491D412yes—
37C4×D491—22no—
38C4×D491—21no—
39C491⋊C8—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—
50C2×D491—42no—
51C2×D491—41no—
52C4×C491—21no—
53C4×C491—41no—
54C4×C491C2×D411yescharacteristic
55C4×C491C2×D411yescharacteristic
56Dic491—21no—
57Dic491—22no—
58C2×C491—21no—
59C2×C491—41no—
60C2×C491#12011yescharacteristic
61D491—41no—
62D491—81no—
63C491#45411yescharacteristic, complemented, Sylow
64#454—4911nomaximal, Sylow
652−1+4—4911no—
66AGL(1,ℤ/8)—4911no—
67AGL(1,ℤ/8)—4911no—
68#124—4911no—
69#104—4911no—
70#104D49111yescharacteristic, complemented
71#101—4911no—
72#41—9821no—
73#41—9821no—
74#41—9822no—
75#41—4911no—
76#41C2×D49111yescharacteristic
77C2×Q8—9821no—
78C2×Q8—9821no—
79C2×Q8—4911no—
80C2×D4—4911no—
81SD16—9821no—
82SD16—9821no—
83D8—9821no—
84D8—9821no—
85M16—4911no—
86M16C2×D49111yescharacteristic
87C22⋊C4—9822no—
88C42C2×D49111yescharacteristic
89C23—9821no—
90Q8—9822no—
91Q8—9821no—
92Q8—9821no—
93Q8—4911no—
94Q8D196411yescharacteristic
95D4—21no—
96D4—9822no—
97D4—9821no—
98D4—9821no—
99D4—9821no—
100D4—4911no—
101D4D196411yescharacteristic
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—9822no—
105C2×C4—9822no—
106C2×C4—9821no—
107C2×C4—4912no—
108C2×C4C22×D49111yescharacteristic
109C8—21no—
110C8—9821no—
111C22—21no—
112C22—19642no—
113C22—19641no—
114C22—9821no—
115C22D4×D49111yescharacteristic
116C4—21no—
117C4—41no—
118C4—9821no—
119C4—9822no—
120C4D4×D49111yescharacteristic
121C4C2×D196411yescharacteristic
122C2—21no—
123C2—41no—
124C2—39281no—
125C2—19641no—
126C2#3062830711yescharacteristic
subgroupG/H
centerC2#30628307
commutator, cosocleC2×C4×C491C23
FrattiniC2×C4C22×D491
Fitting#104×C491C2
socleC2×C491#120
hypercenter#104D491
hypocenterC491#454
LCSG ▷ C2×C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
1. #30628384C2semidirect
2. #30628365C2semidirect
3. #30628362C2semidirect
4. #30628325C2semidirect
5. #30628265C2semidirect
6. #30628255C2semidirect
7. #104×C491C2semidirect
63. C491#454semidirect
70. #104D491semidirect

Maximal subgroups

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

subgroupindex
#306283842
#306283652
#306283622
#306283252
#306282652
#306282552
#104×C4912
#454491