Finite Group Databasebeta

← #16847400

Subgroups — #16847400

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
1C2×#11758424C212yesmaximal, complemented
2#14520848C212yesmaximal, complemented
3#14520846C212yesmaximal, complemented
4C31×#536C211yesmaximal, characteristic
5C2×#41×C31C411yescharacteristic
6C22×Q8×C31C2211yescharacteristic
7C31×C4⋊Q8C411yescharacteristic
8C31×C4⋊Q8C2211yescharacteristic
9C31×#124C411yescharacteristic
10C31×#124C2211yescharacteristic
11C31×#123—22no—
12C31×C22⋊Q8—22no—
13C31×#117C411yescharacteristic
14C2×#92474—22no—
15#11758424—22no—
16#11758424C2214yes—
17#41×C31—42no—
18C2×Q8×C31—42no—
19C2×Q8×C31C2×C411yescharacteristic
20C2×Q8×C31C2×C411yescharacteristic
21C2×Q8×C31D412yes—
22C2×Q8×C31C2311yescharacteristic
23C2×D4×C31—21no—
24C2×D4×C31C2×C411yescharacteristic
25C22×C4×C31—21no—
26C22×C4×C31C2×C411yescharacteristic
27C22×C4×C31D412yes—
28C4⋊C4×C31—21no—
29C4⋊C4×C31—22no—
30C4⋊C4×C31—22no—
31C22⋊C4×C31—21no—
32C22⋊C4×C31—22no—
33C22⋊C4×C31—22no—
34C42×C31C2×C411yescharacteristic
35C42×C31C2×C411yescharacteristic
36#92474—24no—
37#92474—42no—
38C2×C31⋊C8—42no—
39C23×C31—21no—
40C23×C31C22⋊C411yescharacteristic
41Q8×C31—41no—
42Q8×C31—42no—
43Q8×C31—41no—
44Q8×C31—41no—
45D4×C31—41no—
46D4×C31—42no—
47C2×C4×C31—22no—
48C2×C4×C31—22no—
49C2×C4×C31—22no—
50C2×C4×C31—21no—
51C2×C4×C31—21no—
52C2×C4×C31—21no—
53C2×C4×C31—42no—
54C2×C4×C31C22⋊C412yes—
55C2×C4×C31C22⋊C411yescharacteristic
56C2×C4×C31C22×C411yescharacteristic
57C2×C4×C31C2×D412yes—
58C31⋊C8—44no—
59#2133—311nomaximal, Sylow
60C22×C31—41no—
61C22×C31—42no—
62C22×C31—41no—
63C22×C31#9912yes—
64C22×C31C2×C22⋊C411yescharacteristic
65C4×C31—22no—
66C4×C31—21no—
67C4×C31—22no—
68C4×C31—21no—
69C4×C31—41no—
70C4×C31—41no—
71C4×C31—41no—
72#536D3111yescharacteristic
73C2×#101—312no—
74#356—312no—
75#355—312no—
76C2×C31—21no—
77C2×C31—22no—
78C2×C31—81no—
79C2×C31C2×#9911yescharacteristic
80C2×#41Dic3111yescharacteristic
81C22×Q8C2×D3111yescharacteristic
82C2×M16—622no—
83C4⋊Q8Dic3111yescharacteristic
84C4⋊Q8C2×D3111yescharacteristic
85#124Dic3111yescharacteristic
86#124C2×D3111yescharacteristic
87#123—22no—
88C22⋊Q8—22no—
89#117Dic3111yescharacteristic
90#101—314no—
91#101—622no—
92C31#213311yescharacteristic, complemented, Sylow
93#41—42no—
94C2×Q8—42no—
95C2×Q8C2×Dic3111yescharacteristic
96C2×Q8C2×Dic3111yescharacteristic
97C2×Q8C22⋊D3112yes—
98C2×Q8C22×D3111yescharacteristic
99C2×D4—21no—
100C2×D4C2×Dic3111yescharacteristic
101C22×C4—21no—
102C22×C4C2×Dic3111yescharacteristic
103C22×C4C22⋊D3112yes—
104M16—624no—
105M16—1242no—
106C2×C8—1242no—
107C4⋊C4—21no—
108C4⋊C4—22no—
109C4⋊C4—22no—
110C22⋊C4—21no—
111C22⋊C4—22no—
112C22⋊C4—22no—
113C42C2×Dic3111yescharacteristic
114C42C2×Dic3111yescharacteristic
115C23—21no—
116C23C22⋊Dic3111yescharacteristic
117Q8—41no—
118Q8—42no—
119Q8—41no—
120Q8—41no—
121D4—41no—
122D4—42no—
123C2×C4—22no—
124C2×C4—22no—
125C2×C4—22no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—42no—
130C2×C4C22⋊Dic3112yes—
131C2×C4C22⋊Dic3111yescharacteristic
132C2×C4C22×Dic3111yescharacteristic
133C2×C4C2×C22⋊D3112yes—
134C8—1244no—
135C22—41no—
136C22—42no—
137C22—41no—
138C22#1175842212yes—
139C22C2×C22⋊Dic3111yescharacteristic
140C4—22no—
141C4—21no—
142C4—22no—
143C4—21no—
144C4—41no—
145C4—41no—
146C4—41no—
147C2—21no—
148C2—22no—
149C2—81no—
150C2C2×#1175842211yescharacteristic
subgroupG/H
centerC2C2×#11758422
commutatorC2×C4×C31C22×C4
FrattiniC2×Q8C22×D31
FittingC31×#536C2
socleC2×C31C2×#99
prime radicalC2×#41×C31C4
cosocleC2×Q8×C31C23
hypercenter#536D31
hypocenterC31#2133
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C23 ◁ C22×Q8 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#11758424C2semidirect
2. #14520848C2semidirect
3. #14520846C2semidirect
92. C31#2133semidirect

Maximal subgroups

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

subgroupindex
C2×#117584242
#145208482
#145208462
C31×#5362
#213331