Finite Group Databasebeta

← #16847406

Subgroups — #16847406

Order 3968.

230 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 73 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#14521033C212yesmaximal
2#14520848C214yesmaximal, complemented
3C31×#536C211yesmaximal, characteristic
4C2×#41×C31C2211yescharacteristic
5C22×Q8×C31C411yescharacteristic
6C31×C4⋊Q8C2212yes—
7C31×#124C412yes—
8C31×#123—22no—
9C31×C22⋊Q8—22no—
10C31×#117C411yescharacteristic
11C2×#92474—22no—
12#11758424C2214yes—
13#11758421—22no—
14#41×C31—42no—
15C2×Q8×C31—21no—
16C2×Q8×C31—42no—
17C2×Q8×C31C2×C412yes—
18C2×Q8×C31C2311yescharacteristic
19C2×D4×C31C2×C411yescharacteristic
20C2×D4×C31D412yes—
21C22×C4×C31—21no—
22C22×C4×C31C2×C411yescharacteristic
23C22×C4×C31D412yes—
24C4⋊C4×C31—21no—
25C4⋊C4×C31—24no—
26C22⋊C4×C31—21no—
27C22⋊C4×C31—24no—
28C42×C31C2×C412yes—
29#92474—24no—
30#92474—42no—
31C2×C31⋊C8—42no—
32C23×C31C22⋊C412yes—
33C23×C31C22⋊C411yescharacteristic
34Q8×C31—41no—
35Q8×C31—42no—
36Q8×C31—42no—
37D4×C31—41no—
38D4×C31—42no—
39C2×C4×C31—22no—
40C2×C4×C31—22no—
41C2×C4×C31—22no—
42C2×C4×C31—22no—
43C2×C4×C31—22no—
44C2×C4×C31—42no—
45C2×C4×C31C22⋊C411yescharacteristic
46C2×C4×C31C22×C411yescharacteristic
47C2×C4×C31C2×D412yes—
48C31⋊C8—44no—
49#2135—311nomaximal, Sylow
50C22×C31—21no—
51C22×C31—22no—
52C22×C31—42no—
53C22×C31—41no—
54C22×C31C2×C22⋊C411yescharacteristic
55C4×C31—22no—
56C4×C31—21no—
57C4×C31—42no—
58C4×C31—42no—
59C4×C31#9912yes—
60#536D3111yescharacteristic
61#413—312no—
62#356—314no—
63C2×C31—21no—
64C2×C31—41no—
65C2×C31—42no—
66C2×C31C2×#9911yescharacteristic
67C2×#41C2×D3111yescharacteristic
68C22×Q8Dic3111yescharacteristic
69C2×M16—622no—
70C4⋊Q8C2×D3112yes—
71#124Dic3112yes—
72#123—22no—
73C22⋊Q8—22no—
74#117Dic3111yescharacteristic
75#101—314no—
76#100—622no—
77C31#213511yescharacteristic, complemented, Sylow
78#41—42no—
79C2×Q8—21no—
80C2×Q8—42no—
81C2×Q8C2×Dic3112yes—
82C2×Q8C22×D3111yescharacteristic
83C2×D4C2×Dic3111yescharacteristic
84C2×D4C22⋊D3112yes—
85C22×C4—21no—
86C22×C4C2×Dic3111yescharacteristic
87C22×C4C22⋊D3112yes—
88M16—624no—
89M16—1242no—
90C2×C8—1242no—
91C4⋊C4—21no—
92C4⋊C4—24no—
93C22⋊C4—21no—
94C22⋊C4—24no—
95C42C2×Dic3112yes—
96C23C22⋊Dic3112yes—
97C23C22⋊Dic3111yescharacteristic
98Q8—41no—
99Q8—42no—
100Q8—42no—
101D4—41no—
102D4—42no—
103C2×C4—22no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—42no—
109C2×C4C22⋊Dic3111yescharacteristic
110C2×C4C22×Dic3111yescharacteristic
111C2×C4C2×C22⋊D3112yes—
112C8—1244no—
113C22—21no—
114C22—22no—
115C22—42no—
116C22—41no—
117C22C2×C22⋊Dic3111yescharacteristic
118C4—22no—
119C4—21no—
120C4—42no—
121C4—42no—
122C4#1175842212yes—
123C2—21no—
124C2—41no—
125C2—42no—
126C2C2×#1175842211yescharacteristic
subgroupG/H
centerC2C2×#11758422
commutatorC2×C4×C31C22×C4
FrattiniC2×Q8C22×D31
FittingC31×#536C2
socleC2×C31C2×#99
prime radicalC2×#41×C31C22
cosocleC2×Q8×C31C23
hypercenter#536D31
hypocenterC31#2135
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #14520848C2semidirect
77. C31#2135semidirect

Maximal subgroups

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

subgroupindex
#145210332
#145208482
C31×#5362
#213531