Finite Group Databasebeta

← #16844347

Subgroups — #16844347

Order 3968.

194 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 59 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#14521605C211yesmaximal, characteristic
2#14521104C212yesmaximal
3#14520791C211yesmaximal, characteristic, complemented
4#14520790C212yesmaximal, complemented
5C31×#330C211yesmaximal, characteristic, complemented
6C31×#125C2211yescharacteristic
7#11758473—22no—
8#11758469C412yes—
9#11758465C412yes—
10#11758464—22no—
11C42×D31C2211yescharacteristic
12#11758447C2211yescharacteristic
13C31×#97C2212yes—
14(C2×D31)⋊C8—22no—
15Dic31⋊C8—22no—
16#11758391C2212yes—
17C2×C4×D31C2×C411yescharacteristic
18C2×C4×D31D412yes—
19C2×Dic62—22no—
20C2×C8×C31—22no—
21C4⋊C4×C31—22no—
22C4⋊C4×C31C2×C412yes—
23C42×C31C2311yescharacteristic
24(C2×D31)⋊C4—22no—
25C4⋊Dic31C2×C412yes—
26Dic31⋊C4—22no—
27Dic31⋊C4—22no—
28C4×Dic31—22no—
29C4×Dic31C2×C411yescharacteristic
30C4×Dic31D412yes—
31C2×C31⋊C8—22no—
32C22×D31C22⋊C411yescharacteristic
33C2×C4×C31—22no—
34C2×C4×C31C22×C411yescharacteristic
35C2×C4×C31C2×D412yes—
36C2×Dic31—22no—
37C2×Dic31C22⋊C412yes—
38C2×Dic31C22⋊C411yescharacteristic
39C4×D31—22no—
40C4×D31—42no—
41Dic62—44no—
42C8×C31—42no—
43C31⋊C8—42no—
44#1537—311nomaximal, Sylow
45C22×C31C2×C22⋊C411yescharacteristic
46C2×D31—21no—
47C2×D31—22no—
48C4×C31—21no—
49C4×C31—22no—
50C4×C31—42no—
51Dic31—22no—
52Dic31—42no—
53Dic31#10112yes—
54#533—311no—
55#432—312no—
56#330—311no—
57#330—312no—
58#330D3111yescharacteristic, complemented
59C2×C31C2×#10111yescharacteristic
60C2×C31#42112yes—
61D31—41no—
62C4⋊Q8—312no—
63#125—311no—
64#125C2×D3111yescharacteristic
65C22⋊Q8—622no—
66C4×Q8—622no—
67#117—312no—
68C2×C42—311no—
69C4⋊C8—622no—
70C22⋊C8—622no—
71#97—312no—
72#97C2×D3112yes—
73C31#153711yescharacteristic, complemented, Sylow
74C2×Q8—622no—
75C22×C4—311no—
76C22×C4—312no—
77C2×C8—22no—
78C2×C8—622no—
79C4⋊C4—22no—
80C4⋊C4—312no—
81C4⋊C4—622no—
82C4⋊C4—622no—
83C4⋊C4C4×D3112yes—
84C22⋊C4—622no—
85C42—311no—
86C42—312no—
87C42—622no—
88C42C22×D3111yescharacteristic
89C23—311no—
90Q8—1244no—
91C2×C4—22no—
92C2×C4—311no—
93C2×C4—312no—
94C2×C4—622no—
95C2×C4—622no—
96C2×C4—1242no—
97C2×C4C2×C4×D3111yescharacteristic
98C2×C4D4×D3112yes—
99C8—42no—
100C8—1242no—
101C22—621no—
102C22—622no—
103C22C22⋊C4×D3111yescharacteristic
104C4—21no—
105C4—22no—
106C4—42no—
107C4—312no—
108C4—622no—
109C4—1242no—
110C2—1241no—
111C2#101×D3111yescharacteristic
112C2#1452106412yes—
subgroupG/H
centerC22C22⋊C4×D31
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×#330C2
socleC22×C31C2×C22⋊C4
prime radicalC22×D31C22⋊C4
cosocleC42×C31C23
hypercenter#330D31
hypocenterC31#1537
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #14520791C2semidirect
4. #14520790C2semidirect
5. C31×#330C2semidirect
58. #330D31semidirect
73. C31#1537semidirect

Maximal subgroups

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

subgroupindex
#145216052
#145211042
#145207912
#145207902
C31×#3302
#153731