Finite Group Databasebeta

← #16844334

Subgroups — #16844334

Order 3968.

248 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 69 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
2#14521106C211yesmaximal, 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—
10#11758452—21no—
11#11758452—21no—
12#11758452C412yes—
13#11758452C2212yes—
14C31×C4⋊C8—21no—
15C31×C22⋊C8—21no—
16C31×#97C2212yescomplemented
17C22⋊(C31⋊C8)—21no—
18C4⋊(C31⋊C8)—21no—
19#11758391C2212yescomplemented
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—
40C2×C31⋊C8—22no—
41C23×C31C22⋊C411yescharacteristic
42C22×D31—22no—
43C22×D31—42no—
44C22×D31—42no—
45C22×D31—42no—
46C2×C4×C31—22no—
47C2×C4×C31—41no—
48C2×C4×C31—41no—
49C2×C4×C31C22⋊C411yescharacteristic
50C2×C4×C31C22⋊C411yescharacteristic
51C2×C4×C31C22⋊C411yescharacteristic
52C2×C4×C31C22×C411yescharacteristic
53C2×C4×C31C2×D411yescharacteristic
54C2×C4×C31C2×D411yescharacteristic
55C2×Dic31—22no—
56C2×Dic31—42no—
57D124—42no—
58D124—42no—
59Dic62—42no—
60Dic62—42no—
61C8×C31—42no—
62C31⋊C8—42no—
63#1533—311nomaximal, Sylow
64C22×C31—21no—
65C22×C31—21no—
66C22×C31#10012yes—
67C22×C31C2×C22⋊C411yescharacteristic
68C2×D31—42no—
69C2×D31—42no—
70C2×D31—42no—
71C2×D31—84no—
72C4×C31—21no—
73C4×C31—21no—
74C4×C31—21no—
75C4×C31—21no—
76C4×C31—21no—
77C4×C31—21no—
78Dic31—42no—
79C2×#124—311no—
80#432—311no—
81#432D3111yescharacteristic, complemented
82#329—314no—
83C2×C31—22no—
84C2×C31C2×#10011yescharacteristic
85C2×C31#42111yescharacteristic
86C2×C31#42111yescharacteristic
87D31—82no—
88C22×Q8—311no—
89C22×D4—311no—
90#124—312no—
91#124—312no—
92#124—621no—
93#124—621no—
94C2×C22⋊C4—621no—
95C2×C22⋊C4—621no—
96C2×C42C2×D3111yescharacteristic
97C4⋊C8—21no—
98C4⋊C8—621no—
99C22⋊C8—21no—
100C22⋊C8—621no—
101#97—312no—
102#97C2×D3112yescomplemented
103C31#153311yescharacteristic, complemented, Sylow
104C24—621no—
105C2×Q8—312no—
106C2×Q8—621no—
107C2×Q8—1242no—
108C2×D4—312no—
109C2×D4—621no—
110C2×D4—1242no—
111C22×C4—621no—
112C22×C4C4×D3111yescharacteristic
113C22×C4D12411yescharacteristic
114C22×C4C22⋊D3111yescharacteristic
115C2×C8—22no—
116C2×C8—622no—
117C22⋊C4—622no—
118C22⋊C4—622no—
119C22⋊C4—622no—
120C22⋊C4—622no—
121C42C4×D3111yescharacteristic
122C42D12411yescharacteristic
123C42C22⋊D3111yescharacteristic
124C42C22×D3111yescharacteristic
125C23—622no—
126C23—1242no—
127C23—1242no—
128C23—1242no—
129C23(C2×D31)⋊C411yescharacteristic
130Q8—1242no—
131Q8—1242no—
132D4—1242no—
133D4—1242no—
134C2×C4—22no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—622no—
138C2×C4—1242no—
139C2×C4(C2×D31)⋊C411yescharacteristic
140C2×C4(C2×D31)⋊C411yescharacteristic
141C2×C4(C2×D31)⋊C411yescharacteristic
142C2×C4C2×C4×D3111yescharacteristic
143C2×C4C2×D12411yescharacteristic
144C2×C4C2×C22⋊D3111yescharacteristic
145C8—42no—
146C8—1242no—
147C22—21no—
148C22—21no—
149C22—1242no—
150C22—1242no—
151C22—1242no—
152C22—2484no—
153C22#1175841112yes—
154C22C2×(C2×D31)⋊C411yescharacteristic
155C4—21no—
156C4—21no—
157C4—21no—
158C4—21no—
159C4—21no—
160C4—21no—
161C4—1242no—
162C2—22no—
163C2—2482no—
164C2C2×#1175841111yescharacteristic
165C2#1452106511yescharacteristic
166C2#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#1533
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. #14521106C2semidirect
3. #14520788C2semidirect
4. C31×#432C2semidirect
16. C31×#97C22semidirect
19. #11758391C22semidirect
81. #432D31semidirect
102. #97C2×D31semidirect
103. C31#1533semidirect

Maximal subgroups

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

subgroupindex
C2×#117584522
#145211062
#145207882
C31×#4322
#153331