Finite Group Databasebeta

← #34099278

Subgroups — #34099278

Order 20096.

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×Dic314C211yesmaximal, characteristic
2#23757653C211yesmaximal, characteristic
3#23757569C211yesmaximal, characteristic
4#23757568C211yesmaximal, characteristic
5#23757021C211yesmaximal, characteristic
6#23757005C211yesmaximal, characteristic
7Q8⋊C8×C157C211yesmaximal, characteristic
8C2×Dic628—22no—
9#19097771—21no—
10#19097771C2211yescharacteristic
11#19097771C2211yescharacteristic
12#19097770—21no—
13#19097770—22no—
14Q8×Dic157—21no—
15C4×Dic314—21no—
16C4×Dic314C2211yescharacteristic
17#19097705—21no—
18#19097704—21no—
19C4⋊#11929434C2211yescharacteristic
20#19097696—21no—
21#19097695—21no—
22C4×Q8×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4×C8×C157C2211yescharacteristic
25C2×Dic314—22no—
26C2×Dic314—21no—
27C2×Dic314D411yescharacteristic
28C2×Dic314D412yes—
29Dic628—44no—
30C2×#11929434—21no—
31C4⋊Dic157—22no—
32C4⋊Dic157—21no—
33C4⋊Dic157—21no—
34C4⋊Dic157—21no—
35C4⋊Dic157—21no—
36C4⋊Dic157D411yescharacteristic
37#14578933—22no—
38#14578933—21no—
39C4×Dic157—22no—
40C4×Dic157—21no—
41C2×Q8×C157D411yescharacteristic
42C2×C8×C157—21no—
43C2×C8×C157—21no—
44C4⋊C4×C157—21no—
45C4⋊C4×C157D411yescharacteristic
46C42×C157—21no—
47C42×C157C2311yescharacteristic
48Dic314—21no—
49Dic314—42no—
50Dic314—42no—
51Dic314—82no—
52Dic314Q1612yescomplemented
53C2×Dic157—21no—
54C2×Dic157—21no—
55C2×Dic157—22no—
56C2×Dic157—41no—
57#11929434—41no—
58Q8×C157—21no—
59Q8×C157Q1612yescomplemented
60C2×C4×C157—21no—
61C2×C4×C157—21no—
62C2×C4×C157C2×D411yescharacteristic
63C2×C4×C157C2×D411yescharacteristic
64C2×C4×C157C2×D411yescharacteristic
65C8×C157—22no—
66C8×C157—41no—
67C22×C157#12011yescharacteristic
68C4×C157—22no—
69C4×C157—21no—
70C4×C157—41no—
71C4×C157C2×Q1611yescharacteristic
72C4×C157C2×Q1611yescharacteristic
73C4×C157#13711yescharacteristic
74C4×C157#13711yescharacteristic
75Dic157—22no—
76Dic157—42no—
77Dic157—41no—
78Dic157—81no—
79C2×C157#45111yescharacteristic
80C2×C157#45111yescharacteristic
81C2×C157#45311yescharacteristic
82C157#163311yescharacteristic, complemented, Sylow
83#1633—1571nomaximal, Sylow
84Q82—1571no—
85#494—1571no—
86#477—1571no—
87#477—1571no—
88#333—1571no—
89Q8⋊C8—1571no—
90Q8⋊C8D15711yescharacteristic
91C2×Q16—3142no—
92C4⋊Q8—3141no—
93C4⋊Q8—3142no—
94C4⋊Q8—3141no—
95C4⋊Q8—1571no—
96C4⋊Q8—1571no—
97C4×Q8—3141no—
98C4×Q8—3141no—
99C4×Q8—1571no—
100C4×Q8C2×D15711yescharacteristic
101#107—3141no—
102#107—3141no—
103C4⋊C8—1571no—
104C4⋊C8C2×D15711yescharacteristic
105#103—3141no—
106#103—3141no—
107C4×C8C2×D15711yescharacteristic
108C2×Q8—3142no—
109C2×Q8—3141no—
110C2×Q8—1571no—
111C2×Q8—1572no—
112C2×Q8D62811yescharacteristic
113Q16—6284no—
114C2×C8—21no—
115C2×C8—21no—
116C2×C8—3141no—
117C4⋊C4—21no—
118C4⋊C4—3142no—
119C4⋊C4—3142no—
120C4⋊C4—3141no—
121C4⋊C4—3141no—
122C4⋊C4—3141no—
123C4⋊C4—3141no—
124C4⋊C4—3141no—
125C4⋊C4—1571no—
126C4⋊C4D62811yescharacteristic
127C42—21no—
128C42—3142no—
129C42—3141no—
130C42C22×D15711yescharacteristic
131Q8—21no—
132Q8—3141no—
133Q8—6282no—
134Q8—6282no—
135Q8—1572no—
136Q8—12562no—
137Q8Dic62812yescomplemented
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—3141no—
141C2×C4—3142no—
142C2×C4—3141no—
143C2×C4—6281no—
144C2×C4D4×D15711yescharacteristic
145C2×C4D4×D15711yescharacteristic
146C2×C4C2×D62811yescharacteristic
147C8—22no—
148C8—41no—
149C8—6281no—
150C22#1909774111yescharacteristic
151C4—22no—
152C4—21no—
153C4—41no—
154C4—3142no—
155C4—6282no—
156C4—6281no—
157C4—12561no—
158C4Q16×D15711yescharacteristic
159C4C2×Dic62811yescharacteristic
160C4#1909780011yescharacteristic
161C4#1909780411yescharacteristic
162C2#2375743011yescharacteristic
163C2#2375743111yescharacteristic
164C2#2375744211yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
FittingQ8⋊C8×C157C2
socle, prime radicalC22×C157#120
hypercenterQ8⋊C8D157
hypocenterC157#1633
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
52. Dic314Q16semidirect
59. Q8×C157Q16semidirect
82. C157#1633semidirect
137. Q8Dic628semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic3142
#237576532
#237575692
#237575682
#237570212
#237570052
Q8⋊C8×C1572
#1633157