Finite Group Databasebeta

← #16844850

Subgroups — #16844850

Order 3968.

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

normal subgroups only

This group has 206 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
1Q8×Dic62C211yesmaximal, characteristic
2#14521428C211yesmaximal, characteristic
3#14521341C211yesmaximal, characteristic
4#14520797C211yesmaximal, characteristic
5Q8⋊(C31⋊C8)C211yesmaximal, characteristic
6#14520779C211yesmaximal, characteristic
7C31×#477C211yesmaximal, characteristic
8C31×C4⋊Q8C2211yescharacteristic
9C4×Q8×C31C2211yescharacteristic
10Q8×Dic31—21no—
11C2×#92482—22no—
12#11758465—22no—
13#11758465—21no—
14#11758446—21no—
15#11758446C2211yescharacteristic
16C4×Dic62—21no—
17C4×Dic62C2211yescharacteristic
18C31×#107—21no—
19C31×C4⋊C8C2211yescharacteristic
20C31×#103—21no—
21#11758398—21no—
22#11758395—21no—
23C4⋊(C31⋊C8)C2211yescharacteristic
24C4×C31⋊C8C2211yescharacteristic
25C2×Q8×C31—21no—
26C2×Q8×C31D411yescharacteristic
27C2×Dic62—22no—
28C2×Dic62D411yescharacteristic
29C2×Dic62D412yes—
30C2×C8×C31—21no—
31C4⋊C4×C31—21no—
32C4⋊C4×C31—21no—
33C4⋊C4×C31—21no—
34C4⋊C4×C31D411yescharacteristic
35C42×C31—21no—
36C42×C31C2311yescharacteristic
37#92482—44no—
38C4⋊Dic31—22no—
39C4⋊Dic31—21no—
40C4⋊Dic31—21no—
41C4⋊Dic31D411yescharacteristic
42Dic31⋊C4—22no—
43Dic31⋊C4—21no—
44C4×Dic31—22no—
45C4×Dic31—21no—
46C2×C31⋊C8—21no—
47C2×C31⋊C8—21no—
48Q8×C31—21no—
49Q8×C31—42no—
50Q8×C31Q1612yescomplemented
51C2×C4×C31—21no—
52C2×C4×C31—21no—
53C2×C4×C31—41no—
54C2×C4×C31C2×D411yescharacteristic
55C2×C4×C31C2×D411yescharacteristic
56C2×C4×C31C2×D411yescharacteristic
57C2×Dic31—21no—
58C2×Dic31—22no—
59C2×Dic31—21no—
60Dic62—21no—
61Dic62—42no—
62Dic62—82no—
63Dic62Q1612yescomplemented
64C8×C31—41no—
65C31⋊C8—22no—
66C31⋊C8—41no—
67#1633—311nomaximal, Sylow
68C22×C31#12011yescharacteristic
69C4×C31—22no—
70C4×C31—21no—
71C4×C31—41no—
72C4×C31—81no—
73C4×C31C2×Q1611yescharacteristic
74C4×C31C2×Q1611yescharacteristic
75C4×C31#13711yescharacteristic
76C4×C31#13711yescharacteristic
77Dic31—22no—
78Dic31—42no—
79Dic31—41no—
80Q82—311no—
81#494—311no—
82#477—311no—
83#477D3111yescharacteristic
84#333—311no—
85Q8⋊C8—311no—
86Q8⋊C8—311no—
87C2×C31#45111yescharacteristic
88C2×C31#45111yescharacteristic
89C2×C31#45311yescharacteristic
90C2×Q16—622no—
91C4⋊Q8—311no—
92C4⋊Q8—621no—
93C4⋊Q8—622no—
94C4⋊Q8—621no—
95C4⋊Q8C2×D3111yescharacteristic
96C4×Q8—311no—
97C4×Q8—621no—
98C4×Q8—621no—
99C4×Q8C2×D3111yescharacteristic
100#107—21no—
101#107—621no—
102C4⋊C8—311no—
103C4⋊C8C2×D3111yescharacteristic
104#103—21no—
105#103—621no—
106C4×C8—311no—
107C31#163311yescharacteristic, complemented, Sylow
108C2×Q8—21no—
109C2×Q8—311no—
110C2×Q8—312no—
111C2×Q8—622no—
112C2×Q8C22⋊D3111yescharacteristic
113Q16—1244no—
114C2×C8—21no—
115C2×C8—621no—
116C2×C8—621no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—311no—
121C4⋊C4—622no—
122C4⋊C4—622no—
123C4⋊C4—621no—
124C4⋊C4—621no—
125C4⋊C4—621no—
126C4⋊C4C22⋊D3111yescharacteristic
127C42—21no—
128C42—622no—
129C42—621no—
130C42C22×D3111yescharacteristic
131Q8—21no—
132Q8—42no—
133Q8—312no—
134Q8—621no—
135Q8—1242no—
136Q8—2482no—
137Q8#9248212yescomplemented
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—621no—
142C2×C4—621no—
143C2×C4—622no—
144C2×C4D4×D3111yescharacteristic
145C2×C4D4×D3111yescharacteristic
146C2×C4C2×C22⋊D3111yescharacteristic
147C8—41no—
148C8—622no—
149C8—1241no—
150C22#1175851411yescharacteristic
151C4—22no—
152C4—21no—
153C4—41no—
154C4—81no—
155C4—622no—
156C4—1242no—
157C4—1241no—
158C4Q16×D3111yescharacteristic
159C4#1175849511yescharacteristic
160C4C2×#9248211yescharacteristic
161C4#1175852811yescharacteristic
162C2#1452120311yescharacteristic
163C2#1452120411yescharacteristic
164C2#1452121511yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#477C2
socle, prime radicalC22×C31#120
hypercenter#477D31
hypocenterC31#1633
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
50. Q8×C31Q16semidirect
63. Dic62Q16semidirect
107. C31#1633semidirect
137. Q8#92482semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic622
#145214282
#145213412
#145207972
Q8⋊(C31⋊C8)2
#145207792
C31×#4772
#163331