Finite Group Databasebeta

← #16844333

Subgroups — #16844333

Order 3968.

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

normal subgroups only

This group has 248 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#124×D31C211yesmaximal, characteristic
2#14521104C212yesmaximal, complemented
3#14520789C211yesmaximal, characteristic, complemented
4#14520788C212yesmaximal, complemented
5C31×#329C211yesmaximal, characteristic, complemented
6C2×Q8×D31C411yescharacteristic
7C2×D4×D31C411yescharacteristic
8C31×#124C2211yescharacteristic
9#11758524C411yescharacteristic
10#11758513C411yescharacteristic
11#11758462—22no—
12C22⋊C4×D31—22no—
13#11758452C2211yescharacteristic
14C42×D31C2211yescharacteristic
15C31×#97C2212yescomplemented
16(C2×D31)⋊C8—22no—
17Dic31⋊C8—22no—
18#11758391C2212yescomplemented
19C23×D31—21no—
20C2×Q8×C31C2×C411yescharacteristic
21C2×D4×C31C2×C411yescharacteristic
22C2×C22⋊D31—21no—
23Q8×D31—42no—
24D4×D31—42no—
25C2×D124C2×C411yescharacteristic
26C2×C4×D31—21no—
27C2×C4×D31C2×C411yescharacteristic
28C2×C4×D31D412yes—
29C2×Dic62—21no—
30C2×Dic62C2×C411yescharacteristic
31C2×C8×C31—22no—
32C22⋊C4×C31—22no—
33C42×C31C2311yescharacteristic
34C22⋊Dic31—22no—
35(C2×D31)⋊C4—22no—
36(C2×D31)⋊C4—22no—
37C4×Dic31C2×C411yescharacteristic
38C4×Dic31D412yes—
39C2×C31⋊C8—22no—
40C23×C31—21no—
41C22×D31—21no—
42C22×D31—44no—
43C22×D31—42no—
44C22×D31C22⋊C411yescharacteristic
45Q8×C31—41no—
46D4×C31—41no—
47C2×C4×C31—21no—
48C2×C4×C31C22×C411yescharacteristic
49C2×C4×C31C2×D412yes—
50C22⋊D31—42no—
51C2×Dic31—21no—
52C2×Dic31C22⋊C412yes—
53C2×Dic31C22⋊C411yescharacteristic
54D124—41no—
55C4×D31—22no—
56C4×D31—42no—
57C4×D31—42no—
58Dic62—42no—
59Dic62—41no—
60C8×C31—42no—
61C31⋊C8—42no—
62#1533—311nomaximal, Sylow
63C22×C31—41no—
64C22×C31—42no—
65C22×C31C2×C22⋊C411yescharacteristic
66C2×D31—22no—
67C2×D31—41no—
68C2×D31—42no—
69C2×D31—84no—
70C2×D31#10012yes—
71C4×C31—21no—
72C4×C31—22no—
73C4×C31—41no—
74Dic31—21no—
75Dic31—22no—
76Dic31—41no—
77C2×#124—311no—
78#432—312no—
79#329—311no—
80#329—312no—
81#329D3111yescharacteristic, complemented
82C2×C31—81no—
83C2×C31C2×#10011yescharacteristic
84C2×C31#42112yes—
85D31—22no—
86D31—81no—
87C22×Q8—311no—
88C22×D4—311no—
89#124—311no—
90#124—311no—
91#124—311no—
92#124—622no—
93#124C2×D3111yescharacteristic
94C2×C22⋊C4—622no—
95C2×C42—311no—
96C4⋊C8—622no—
97C22⋊C8—622no—
98#97—312no—
99#97C2×D3112yescomplemented
100C31#153311yescharacteristic, complemented, Sylow
101C24—621no—
102C2×Q8—311no—
103C2×Q8—621no—
104C2×Q8—1242no—
105C2×Q8C4×D3111yescharacteristic
106C2×D4—311no—
107C2×D4—621no—
108C2×D4—1242no—
109C2×D4C4×D3111yescharacteristic
110C22×C4—311no—
111C22×C4—312no—
112C22×C4—621no—
113C2×C8—22no—
114C2×C8—622no—
115C22⋊C4—22no—
116C22⋊C4—622no—
117C22⋊C4—622no—
118C22⋊C4—622no—
119C42—311no—
120C42—312no—
121C42C22×D3111yescharacteristic
122C23—21no—
123C23—311no—
124C23—621no—
125C23—1242no—
126C23—1244no—
127Q8—41no—
128Q8—1241no—
129Q8—1242no—
130D4—41no—
131D4—1241no—
132D4—1242no—
133C2×C4—21no—
134C2×C4—312no—
135C2×C4—311no—
136C2×C4—622no—
137C2×C4—621no—
138C2×C4—1242no—
139C2×C4—1242no—
140C2×C4C2×C4×D3111yescharacteristic
141C2×C4D4×D3112yes—
142C8—42no—
143C8—1242no—
144C22—41no—
145C22—42no—
146C22—312no—
147C22—622no—
148C22—1241no—
149C22—1242no—
150C22—2484no—
151C22C22⋊C4×D3111yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—621no—
156C4—622no—
157C4—1241no—
158C2—81no—
159C2—622no—
160C2—2481no—
161C2#100×D3111yescharacteristic
162C2#1452106412yes—
subgroupG/H
centerC22C22⋊C4×D31
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×#329C2
socleC22×C31C2×C22⋊C4
prime radicalC2×D4×D31C4
cosocleC42×C31C23
hypercenter#329D31
hypocenterC31#1533
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #14521104C2semidirect
3. #14520789C2semidirect
4. #14520788C2semidirect
5. C31×#329C2semidirect
15. C31×#97C22semidirect
18. #11758391C22semidirect
81. #329D31semidirect
99. #97C2×D31semidirect
100. C31#1533semidirect

Maximal subgroups

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

subgroupindex
#124×D312
#145211042
#145207892
#145207882
C31×#3292
#153331