Finite Group Databasebeta

← #34099289

Subgroups — #34099289

Order 20096.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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#23757927C211yesmaximal, characteristic
2#23757624C211yesmaximal, characteristic, complemented
3#23757564C211yesmaximal, characteristic, complemented
4#23757563C211yesmaximal, characteristic, complemented
5#23757018C211yesmaximal, characteristic, complemented
6#23757002C211yesmaximal, characteristic, complemented
7D4⋊C8×C157C211yesmaximal, characteristic, complemented
8C2×#14578953—21no—
9#19097771C2211yescharacteristic
10#19097771C2211yescharacteristic
11#19097755—22no—
12#19097751—21no—
13#19097745—21no—
14C4×D628C2211yescharacteristic
15C2×C4⋊Dic157—21no—
16#19097703—21no—
17#19097702—21no—
18C4⋊#11929434C2211yescharacteristic
19#19097696—22no—
20#19097693—21no—
21#19097692—21no—
22C4×D4×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4×C8×C157C2211yescharacteristic
25#14578953—42no—
26#14578953—42no—
27C2×Dic314—21no—
28C2×Dic314—21no—
29C2×D628D411yescharacteristic
30C2×C22⋊D157—22no—
31C22×Dic157—22no—
32C2×C4×D157—21no—
33C2×#11929434—21no—
34C4⋊Dic157—22no—
35C4⋊Dic157—21no—
36C4⋊Dic157—21no—
37C4⋊Dic157—21no—
38C4⋊Dic157D412yes—
39C4⋊Dic157D411yescharacteristic
40#14578931—22no—
41#14578931—21no—
42C2×D4×C157D411yescharacteristic
43C22×C4×C157—21no—
44C2×C8×C157—21no—
45C2×C8×C157—21no—
46C4⋊C4×C157D411yescharacteristic
47C22⋊C4×C157—21no—
48C42×C157C2311yescharacteristic
49C22×D157—21no—
50Dic314—41no—
51Dic314—41no—
52Dic314—42no—
53D628—21no—
54D628—21no—
55C22⋊D157—44no—
56C2×Dic157—21no—
57C2×Dic157—22no—
58C2×Dic157—44no—
59C2×Dic157—41no—
60C4×D157—41no—
61C4×D157—41no—
62#11929434—41no—
63C23×C157—21no—
64D4×C157—21no—
65D4×C157SD1612yes—
66C2×C4×C157—21no—
67C2×C4×C157—41no—
68C2×C4×C157—41no—
69C2×C4×C157C2×D411yescharacteristic
70C2×C4×C157C2×D411yescharacteristic
71C2×C4×C157C2×D411yescharacteristic
72C8×C157—41no—
73C8×C157—41no—
74C22×C157—22no—
75C22×C157—41no—
76C22×C157—41no—
77C22×C157#12011yescharacteristic
78C2×D157—41no—
79C2×D157—41no—
80C2×D157—41no—
81C4×C157—21no—
82C4×C157—41no—
83C4×C157C2×SD1611yescharacteristic
84C4×C157#13511yescharacteristic
85C4×C157AGL(1,ℤ/8)11yescharacteristic
86C4×C157#13711yescharacteristic
87Dic157—41no—
88Dic157—42no—
89Dic157—81no—
90C2×C157—42no—
91C2×C157#45011yescharacteristic
92C2×C157#45211yescharacteristic
93C2×C157#45411yescharacteristic
94D157—81no—
95C157#163511yescharacteristic, complemented, Sylow
96#1635—1571nomaximal, Sylow
97#547—1571no—
98#487—1571no—
99#476—1571no—
100#476—1571no—
101#332—1571no—
102D4⋊C8—1571no—
103D4⋊C8D15711yescharacteristic, complemented
104C2×#41—3141no—
105C4⋊Q8—1571no—
106C4⋊Q8—1571no—
107#123—3142no—
108C22⋊Q8—3141no—
109#121—3141no—
110C4×D4—1571no—
111C4×D4C2×D15711yescharacteristic
112C2×C4⋊C4—3141no—
113#106—3141no—
114#106—3141no—
115C4⋊C8—1571no—
116C4⋊C8C2×D15711yescharacteristic
117#103—3142no—
118#102—3141no—
119#102—3141no—
120C4×C8C2×D15711yescharacteristic
121#41—6282no—
122#41—6282no—
123C2×Q8—3141no—
124C2×Q8—3141no—
125C2×D4—3142no—
126C2×D4—1571no—
127C2×D4D62811yescharacteristic
128C22×C4—21no—
129C22×C4—3142no—
130C22×C4—3141no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—3141no—
134C4⋊C4—3142no—
135C4⋊C4—3141no—
136C4⋊C4—3141no—
137C4⋊C4—3141no—
138C4⋊C4—1572no—
139C4⋊C4—1571no—
140C4⋊C4D62811yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—3142no—
143C22⋊C4—3141no—
144C42C22×D15711yescharacteristic
145C23—21no—
146C23—3141no—
147Q8—6282no—
148Q8—6281no—
149Q8—6281no—
150D4—21no—
151D4—3141no—
152D4—3141no—
153D4—6284no—
154D4#1457894312yes—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—3141no—
159C2×C4—3142no—
160C2×C4—6284no—
161C2×C4—6281no—
162C2×C4—6281no—
163C2×C4—6281no—
164C2×C4D4×D15711yescharacteristic
165C2×C4D4×D15711yescharacteristic
166C2×C4C2×D62811yescharacteristic
167C8—41no—
168C8—41no—
169C8—6281no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—6281no—
174C22—6281no—
175C22—6281no—
176C22#1909774111yescharacteristic
177C4—21no—
178C4—41no—
179C4—6281no—
180C4—6282no—
181C4—12561no—
182C4C2×#1457894311yescharacteristic
183C4#1909779011yescharacteristic
184C4#1909779911yescharacteristic
185C4#1909780011yescharacteristic
186C2—42no—
187C2—12561no—
188C2#2375742611yescharacteristic
189C2#2375743611yescharacteristic
190C2#2375744711yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
FittingD4⋊C8×C157C2
socleC22×C157#120
prime radical#23757927C2
hypercenterD4⋊C8D157
hypocenterC157#1635
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #23757624C2semidirect
3. #23757564C2semidirect
4. #23757563C2semidirect
5. #23757018C2semidirect
6. #23757002C2semidirect
7. D4⋊C8×C157C2semidirect
95. C157#1635semidirect
103. D4⋊C8D157semidirect

Maximal subgroups

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

subgroupindex
#237579272
#237576242
#237575642
#237575632
#237570182
#237570022
D4⋊C8×C1572
#1635157