Finite Group Databasebeta

← #16844848

Subgroups — #16844848

Order 3968.

214 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 55 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#14521759C211yesmaximal, characteristic
2#14521429C211yesmaximal, characteristic, complemented
3#14521344C211yesmaximal, characteristic, complemented
4#14521340C211yesmaximal, characteristic
5#14520797C211yesmaximal, characteristic, complemented
6#14520778C211yesmaximal, characteristic
7C31×Q8⋊C8C211yesmaximal, characteristic, complemented
8C4×Q8×C31C2211yescharacteristic
9#11758523—21no—
10C2×Dic124—22no—
11#11758473—22no—
12C4⋊C4×D31—21no—
13C4×D124—21no—
14C4×D124C2211yescharacteristic
15#11758447—21no—
16#11758446C2211yescharacteristic
17#11758446C2211yescharacteristic
18C31×C4⋊C8C2211yescharacteristic
19C4×C8×C31C2211yescharacteristic
20#11758423—21no—
21#11758409—21no—
22#11758405—21no—
23#11758395—21no—
24C4⋊(C31⋊C8)C2211yescharacteristic
25C2×Q8×C31D411yescharacteristic
26C2×D124D411yescharacteristic
27C2×C4×D31—21no—
28C2×C4×D31—22no—
29C2×Dic62—21no—
30C2×Dic62D412yes—
31C2×C8×C31—21no—
32C2×C8×C31—21no—
33C4⋊C4×C31—21no—
34C4⋊C4×C31D411yescharacteristic
35C42×C31—21no—
36C42×C31C2311yescharacteristic
37(C2×D31)⋊C4—22no—
38(C2×D31)⋊C4—21no—
39C4⋊Dic31—21no—
40C4⋊Dic31—21no—
41C4⋊Dic31—21no—
42C4⋊Dic31—21no—
43C4⋊Dic31D411yescharacteristic
44Dic31⋊C4—22no—
45Dic31⋊C4—22no—
46C2×C31⋊C8—21no—
47Dic124—44no—
48C22×D31—21no—
49Q8×C31—21no—
50Q8×C31—21no—
51C2×C4×C31—21no—
52C2×C4×C31—21no—
53C2×C4×C31C2×D411yescharacteristic
54C2×C4×C31C2×D411yescharacteristic
55C2×C4×C31C2×D411yescharacteristic
56C2×Dic31—21no—
57C2×Dic31—22no—
58C2×Dic31—41no—
59D124—21no—
60D124Q1612yescomplemented
61C4×D31—41no—
62C4×D31—41no—
63C4×D31—82no—
64Dic62—42no—
65Dic62—42no—
66C8×C31—22no—
67C8×C31—41no—
68C31⋊C8—41no—
69#1632—311nomaximal, Sylow
70C22×C31#12011yescharacteristic
71C2×D31—22no—
72C2×D31—41no—
73C2×D31—41no—
74C4×C31—21no—
75C4×C31—41no—
76C4×C31—41no—
77C4×C31C2×Q1611yescharacteristic
78C4×C31#13511yescharacteristic
79C4×C31#13711yescharacteristic
80C4×C31#13711yescharacteristic
81Dic31—41no—
82Dic31—42no—
83Dic31—81no—
84#554—311no—
85#494—311no—
86#477—311no—
87#476—311no—
88#333—311no—
89Q8⋊C8D3111yescharacteristic, complemented
90D4⋊C8—311no—
91C2×C31#45111yescharacteristic
92C2×C31#45211yescharacteristic
93C2×C31#45311yescharacteristic
94D31—42no—
95C2×Q16—622no—
96C4⋊Q8—311no—
97C4⋊Q8—311no—
98#125—621no—
99C22⋊Q8—622no—
100C22⋊Q8—621no—
101C4×Q8C2×D3111yescharacteristic
102C4×D4—311no—
103C4×D4—621no—
104C2×C4⋊C4—621no—
105#107—621no—
106#106—621no—
107C4⋊C8—311no—
108C4⋊C8C2×D3111yescharacteristic
109#103—621no—
110#102—621no—
111C4×C8C2×D3111yescharacteristic
112C31#163211yescharacteristic, complemented, Sylow
113C2×Q8—312no—
114C2×Q8—621no—
115C2×Q8D12411yescharacteristic
116C2×D4—311no—
117C22×C4—622no—
118C22×C4—621no—
119Q16—1244no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—621no—
123C4⋊C4—21no—
124C4⋊C4—311no—
125C4⋊C4—622no—
126C4⋊C4—622no—
127C4⋊C4—621no—
128C4⋊C4—621no—
129C4⋊C4—621no—
130C4⋊C4—621no—
131C4⋊C4D12411yescharacteristic
132C22⋊C4—622no—
133C22⋊C4—621no—
134C42—21no—
135C42C22×D3111yescharacteristic
136C23—621no—
137Q8—21no—
138Q8—21no—
139Q8—1242no—
140Q8—1242no—
141D4—312no—
142D4—621no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—621no—
146C2×C4—622no—
147C2×C4—1241no—
148C2×C4—1241no—
149C2×C4—1241no—
150C2×C4—2482no—
151C2×C4C2×D12411yescharacteristic
152C2×C4D4×D3111yescharacteristic
153C2×C4D4×D3111yescharacteristic
154C8—22no—
155C8—41no—
156C8—1241no—
157C22—622no—
158C22—1241no—
159C22—1241no—
160C22#1175845911yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—1241no—
165C4—1242no—
166C4—2481no—
167C4#1175848111yescharacteristic
168C4#1175848611yescharacteristic
169C4#1175849211yescharacteristic
170C4Q16×D3111yescharacteristic
171C2—1242no—
172C2#1452120611yescharacteristic
173C2#1452121311yescharacteristic
174C2#1452121811yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×Q8⋊C8C2
socleC22×C31#120
prime radicalC2×D124D4
hypercenterQ8⋊C8D31
hypocenterC31#1632
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #14521429C2semidirect
3. #14521344C2semidirect
5. #14520797C2semidirect
7. C31×Q8⋊C8C2semidirect
60. D124Q16semidirect
89. Q8⋊C8D31semidirect
112. C31#1632semidirect

Maximal subgroups

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

subgroupindex
#145217592
#145214292
#145213442
#145213402
#145207972
#145207782
C31×Q8⋊C82
#163231