Finite Group Databasebeta

← #16846690

Subgroups — #16846690

Order 3968.

244 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 83 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#14521602C211yesmaximal, characteristic
2#14521072C211yesmaximal, characteristic
3#14520895C211yesmaximal, characteristic
4#14520810C211yesmaximal, characteristic
5#14520809C211yesmaximal, characteristic
6#14520808C211yesmaximal, characteristic
7C31×#339C211yesmaximal, characteristic
8C2×M16×C31C2211yescharacteristic
9C31×#117C2211yescharacteristic
10C2×C42×C31C2211yescharacteristic
11#11758503C2211yescharacteristic
12C2×C4×Dic31C2211yescharacteristic
13C2×C4×Dic31C2211yescharacteristic
14C2×#92474C2211yescharacteristic
15#11758467C412yescomplemented
16#11758465C412yescomplemented
17#11758455—22no—
18C4×Dic62—22no—
19C31⋊#95—22no—
20Dic31⋊C8—22no—
21C22×C4×C31—21no—
22C22×C4×C31C2311yescharacteristic
23C22×Dic31—21no—
24C22×Dic31D412yes—
25C2×Dic62—22no—
26M16×C31—21no—
27M16×C31—21no—
28C2×C8×C31—21no—
29C4⋊C4×C31C2×C412yes—
30C22⋊C4×C31—21no—
31C42×C31—21no—
32C42×C31—21no—
33C42×C31Q812yescomplemented
34C22⋊Dic31—21no—
35C4⋊Dic31—22no—
36C4⋊Dic31C2×C412yes—
37Dic31⋊C4—22no—
38Dic31⋊C4—22no—
39C4×Dic31—21no—
40C4×Dic31—21no—
41C4×Dic31C2×C411yescharacteristic
42C4×Dic31C2×C411yescharacteristic
43C4×Dic31D412yes—
44C4×Dic31Q812yescomplemented
45#92474—21no—
46#92474—21no—
47C2×C31⋊C8—21no—
48C23×C31C2×D411yescharacteristic
49C2×C4×C31—22no—
50C2×C4×C31—22no—
51C2×C4×C31—42no—
52C2×C4×C31C22×C411yescharacteristic
53C2×C4×C31C2×D411yescharacteristic
54C2×C4×C31C2×Q811yescharacteristic
55C2×C4×C31C2×Q811yescharacteristic
56C2×C4×C31#4111yescharacteristic
57C2×C4×C31#4111yescharacteristic
58C2×Dic31—22no—
59C2×Dic31—22no—
60C2×Dic31—42no—
61C2×Dic31—42no—
62C2×Dic31C22⋊C412yes—
63C2×Dic31C22⋊C412yes—
64Dic62—44no—
65C8×C31—41no—
66C31⋊C8—41no—
67#1995—311nomaximal, Sylow
68C22×C31—22no—
69C22×C31C2×C22⋊C411yescharacteristic
70C22×C31C22⋊Q811yescharacteristic
71C22×C31C22⋊Q811yescharacteristic
72C4×C31—42no—
73C4×C31—42no—
74C4×C31C4×Q811yescharacteristic
75C4×C31C4×Q811yescharacteristic
76C4×C31#12411yescharacteristic
77C4×C31C4⋊Q811yescharacteristic
78Dic31—22no—
79Dic31—22no—
80Dic31—42no—
81Dic31—42no—
82#533—311no—
83#423—311no—
84#376—311no—
85#339—311no—
86#339—311no—
87#339—311no—
88#339D3111yescharacteristic
89C2×C31—21no—
90C2×C31—21no—
91C2×C31#39111yescharacteristic
92C2×C31#42112yes—
93C2×M16—311no—
94C2×M16C2×D3111yescharacteristic
95C4⋊Q8—312no—
96#125—312no—
97C22⋊Q8—622no—
98C4×Q8—622no—
99#117—311no—
100#117C2×D3111yescharacteristic
101C2×C42—311no—
102C2×C42—311no—
103C2×C42C2×D3111yescharacteristic
104C4⋊C8—622no—
105#95—622no—
106C31#199511yescharacteristic, complemented, Sylow
107C2×Q8—622no—
108C22×C4—21no—
109C22×C4—312no—
110C22×C4—621no—
111C22×C4C22×D3111yescharacteristic
112M16—21no—
113M16—21no—
114M16—621no—
115M16—621no—
116C2×C8—21no—
117C2×C8—621no—
118C4⋊C4—312no—
119C4⋊C4—622no—
120C4⋊C4—622no—
121C4⋊C4—622no—
122C4⋊C4C4×D3112yes—
123C22⋊C4—21no—
124C22⋊C4—621no—
125C42—21no—
126C42—21no—
127C42—311no—
128C42—311no—
129C42—312no—
130C42—312no—
131C42—621no—
132C42—621no—
133C42Dic6212yescomplemented
134C23D4×D3111yescharacteristic
135Q8—1244no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—312no—
140C2×C4—312no—
141C2×C4—622no—
142C2×C4—622no—
143C2×C4—1242no—
144C2×C4—1242no—
145C2×C4C2×Dic6211yescharacteristic
146C2×C4C2×C4×D3111yescharacteristic
147C2×C4#9249511yescharacteristic
148C2×C4D4×D3111yescharacteristic
149C2×C4#9249711yescharacteristic
150C2×C4Q8×D3111yescharacteristic
151C8—41no—
152C8—1241no—
153C22—22no—
154C22#1175845511yescharacteristic
155C22C22⋊C4×D3111yescharacteristic
156C22#1175847311yescharacteristic
157C4—42no—
158C4—42no—
159C4—622no—
160C4—622no—
161C4—1242no—
162C4—1242no—
163C4C4×Dic6211yescharacteristic
164C4#1175846211yescharacteristic
165C4#1175846411yescharacteristic
166C4#1175846511yescharacteristic
167C2—21no—
168C2—21no—
169C2#1452095311yescharacteristic
170C2#1452106412yes—
subgroupG/H
centerC2×C4D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#339C2
socleC22×C31C2×C22⋊C4
prime radicalC23×C31C2×D4
cosocleC22×C4×C31C23
hypercenter#339D31
hypocenterC31#1995
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
15. #11758467C4semidirect
16. #11758465C4semidirect
33. C42×C31Q8semidirect
44. C4×Dic31Q8semidirect
106. C31#1995semidirect
133. C42Dic62semidirect

Maximal subgroups

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

subgroupindex
#145216022
#145210722
#145208952
#145208102
#145208092
#145208082
C31×#3392
#199531