Finite Group Databasebeta

← #16844310

Subgroups — #16844310

Order 3968.

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

normal subgroups only

This group has 264 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×#11758452C211yesmaximal, characteristic
2C4×#92474C211yesmaximal, characteristic, complemented
3#14520788C214yesmaximal, complemented
4C31×#432C211yesmaximal, characteristic, complemented
5C22×D124C411yescharacteristic
6C22×Dic62C411yescharacteristic
7C2×C42×C31C2211yescharacteristic
8C2×(C2×D31)⋊C4—21no—
9C2×(C2×D31)⋊C4—21no—
10C2×#92474—21no—
11#11758452—21no—
12#11758452—21no—
13#11758452C412yes—
14#11758452C2212yes—
15C31×C4⋊C8—21no—
16C31×C22⋊C8—21no—
17C31×#97C2212yescomplemented
18#11758391C2212yescomplemented
19C4×C31⋊C8—21no—
20C23×D31—21no—
21C22×C4×C31C2×C411yescharacteristic
22C22×C4×C31D411yescharacteristic
23C22×C4×C31D411yescharacteristic
24C22×Dic31—21no—
25C2×D124—21no—
26C2×D124—42no—
27C2×D124C2×C412yes—
28C2×Dic62—21no—
29C2×Dic62—42no—
30C2×Dic62C2×C412yes—
31C2×C8×C31—22no—
32C42×C31C2×C411yescharacteristic
33C42×C31D411yescharacteristic
34C42×C31D411yescharacteristic
35C42×C31C2311yescharacteristic
36(C2×D31)⋊C4—22no—
37(C2×D31)⋊C4—22no—
38(C2×D31)⋊C4—22no—
39(C2×D31)⋊C4—22no—
40#92474—24no—
41C2×C31⋊C8—22no—
42C23×C31C22⋊C411yescharacteristic
43C22×D31—22no—
44C22×D31—42no—
45C22×D31—42no—
46C22×D31—42no—
47C2×C4×C31—22no—
48C2×C4×C31—22no—
49C2×C4×C31—41no—
50C2×C4×C31C22⋊C411yescharacteristic
51C2×C4×C31C22⋊C411yescharacteristic
52C2×C4×C31C22⋊C411yescharacteristic
53C2×C4×C31C22×C411yescharacteristic
54C2×C4×C31C2×D411yescharacteristic
55C2×C4×C31C2×D411yescharacteristic
56C2×Dic31—22no—
57C2×Dic31—42no—
58D124—42no—
59D124—42no—
60Dic62—42no—
61Dic62—42no—
62C8×C31—42no—
63C31⋊C8—24no—
64#1527—311nomaximal, Sylow
65C22×C31—21no—
66C22×C31—21no—
67C22×C31#10412yes—
68C22×C31C2×C22⋊C411yescharacteristic
69C2×D31—42no—
70C2×D31—42no—
71C2×D31—42no—
72C2×D31—84no—
73C4×C31—21no—
74C4×C31—21no—
75C4×C31—21no—
76C4×C31—21no—
77C4×C31—21no—
78C4×C31#10012yes—
79Dic31—42no—
80C2×#124—311no—
81#432D3111yescharacteristic, complemented
82C4×M16—311no—
83#329—314no—
84C2×C31—22no—
85C2×C31C2×#10011yescharacteristic
86C2×C31C2×#10411yescharacteristic
87C2×C31#42111yescharacteristic
88D31—82no—
89C22×Q8—311no—
90C22×D4—311no—
91C2×M16—621no—
92#124—312no—
93#124—312no—
94#124—621no—
95#124—621no—
96C2×C22⋊C4—621no—
97C2×C22⋊C4—621no—
98C2×C42C2×D3111yescharacteristic
99C4⋊C8—21no—
100C22⋊C8—21no—
101#97—312no—
102#97C2×D3112yescomplemented
103C4×C8—621no—
104C31#152711yescharacteristic, complemented, Sylow
105C24—621no—
106C2×Q8—312no—
107C2×Q8—621no—
108C2×Q8—1242no—
109C2×D4—312no—
110C2×D4—621no—
111C2×D4—1242no—
112C22×C4—621no—
113C22×C4C4×D3111yescharacteristic
114C22×C4D12411yescharacteristic
115C22×C4C22⋊D3111yescharacteristic
116M16—624no—
117C2×C8—22no—
118C2×C8—622no—
119C22⋊C4—622no—
120C22⋊C4—622no—
121C22⋊C4—622no—
122C22⋊C4—622no—
123C42C4×D3111yescharacteristic
124C42D12411yescharacteristic
125C42C22⋊D3111yescharacteristic
126C42C22×D3111yescharacteristic
127C23—622no—
128C23—1242no—
129C23—1242no—
130C23—1242no—
131C23(C2×D31)⋊C411yescharacteristic
132Q8—1242no—
133Q8—1242no—
134D4—1242no—
135D4—1242no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—41no—
139C2×C4—622no—
140C2×C4—1242no—
141C2×C4(C2×D31)⋊C411yescharacteristic
142C2×C4(C2×D31)⋊C411yescharacteristic
143C2×C4(C2×D31)⋊C411yescharacteristic
144C2×C4C2×C4×D3111yescharacteristic
145C2×C4C2×D12411yescharacteristic
146C2×C4C2×C22⋊D3111yescharacteristic
147C8—42no—
148C8—624no—
149C22—21no—
150C22—21no—
151C22—1242no—
152C22—1242no—
153C22—1242no—
154C22—2484no—
155C22#1175841312yes—
156C22C2×(C2×D31)⋊C411yescharacteristic
157C4—21no—
158C4—21no—
159C4—21no—
160C4—21no—
161C4—21no—
162C4—1242no—
163C4#1175841112yes—
164C2—22no—
165C2—2482no—
166C2C2×#1175841111yescharacteristic
167C2C2×#1175841311yescharacteristic
168C2#1452106711yescharacteristic
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×#432C2
socleC22×C31C2×C22⋊C4
prime radicalC22×D124C4
cosocleC42×C31C23
hypercenter#432D31
hypocenterC31#1527
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C4×#92474C2semidirect
3. #14520788C2semidirect
4. C31×#432C2semidirect
17. C31×#97C22semidirect
18. #11758391C22semidirect
81. #432D31semidirect
102. #97C2×D31semidirect
104. C31#1527semidirect

Maximal subgroups

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

subgroupindex
C2×#117584522
C4×#924742
#145207882
C31×#4322
#152731