Finite Group Databasebeta

← #34099227

Subgroups — #34099227

Order 20096.

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

normal subgroups only

This group has 256 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, complemented
2#23757620C211yesmaximal, characteristic, complemented
3#23757469C211yesmaximal, characteristic, complemented
4#23757468C211yesmaximal, characteristic, complemented
5#23757018C211yesmaximal, characteristic, complemented
6#23757002C211yesmaximal, characteristic, complemented
7D4⋊C8×C157C211yesmaximal, characteristic, complemented
8C2×#14578953—21no—
9C2×D1256—21no—
10C2×#14578939—21no—
11#19097771C2211yescharacteristic
12#19097768C2211yescharacteristic
13#19097755—22no—
14#19097751—21no—
15#19097745—21no—
16C4×D628C2211yescharacteristic
17C2×C4⋊Dic157—21no—
18C4⋊#11929434C2211yescharacteristic
19#19097693—22no—
20#19097693—21no—
21#19097691—21no—
22C4×D4×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4×C8×C157C2211yescharacteristic
25#14578953—42no—
26#14578953—42no—
27C2×Dic314—21no—
28C2×D628—21no—
29C2×D628—21no—
30C2×D628—21no—
31C2×D628D411yescharacteristic
32C2×C22⋊D157—22no—
33C22×Dic157—22no—
34C2×C4×D157—21no—
35D1256—42no—
36#14578939—42no—
37C2×#11929434—21no—
38C4⋊Dic157—22no—
39C4⋊Dic157—21no—
40C4⋊Dic157D411yescharacteristic
41C4⋊Dic157D412yes—
42#14578931—22no—
43#14578931—21no—
44C2×D4×C157D411yescharacteristic
45C22×C4×C157—21no—
46C2×C8×C157—21no—
47C2×C8×C157—21no—
48C4⋊C4×C157D411yescharacteristic
49C22⋊C4×C157—21no—
50C42×C157C2311yescharacteristic
51C22×D157—21no—
52C22×D157—41no—
53Dic314—41no—
54Dic314—41no—
55D628—21no—
56D628—21no—
57D628—42no—
58D628—41no—
59D628—41no—
60D628—41no—
61D628—41no—
62C22⋊D157—44no—
63C2×Dic157—21no—
64C2×Dic157—22no—
65C2×Dic157—44no—
66C4×D157—41no—
67C4×D157—41no—
68#11929434—41no—
69C23×C157—21no—
70D4×C157—21no—
71D4×C157D812yescomplemented
72C2×C4×C157—21no—
73C2×C4×C157—41no—
74C2×C4×C157—41no—
75C2×C4×C157C2×D411yescharacteristic
76C2×C4×C157C2×D411yescharacteristic
77C2×C4×C157C2×D411yescharacteristic
78C8×C157—41no—
79C8×C157—41no—
80C22×C157—22no—
81C22×C157—41no—
82C22×C157—41no—
83C22×C157#12011yescharacteristic
84C2×D157—41no—
85C2×D157—41no—
86C2×D157—41no—
87C2×D157—81no—
88C2×D157—81no—
89C2×D157—81no—
90C4×C157—21no—
91C4×C157—41no—
92C4×C157C2×D811yescharacteristic
93C4×C157#13511yescharacteristic
94C4×C157AGL(1,ℤ/8)11yescharacteristic
95C4×C157AGL(1,ℤ/8)11yescharacteristic
96Dic157—41no—
97Dic157—42no—
98C2×C157—42no—
99C2×C157#44711yescharacteristic
100C2×C157#44911yescharacteristic
101C2×C157#45411yescharacteristic
102D157—81no—
103D157—161no—
104C157#162511yescharacteristic, complemented, Sylow
105#1625—1571nomaximal, Sylow
106#547—1571no—
107#486—1571no—
108#459—1571no—
109#459—1571no—
110#332—1571no—
111D4⋊C8—1571no—
112D4⋊C8D15711yescharacteristic, complemented
113C2×#41—3141no—
114C2×D8—3141no—
115C2×D8—3141no—
116C4⋊Q8—1571no—
117#127—1571no—
118#123—3142no—
119C22⋊Q8—3141no—
120#121—3141no—
121C4×D4—1571no—
122C4×D4C2×D15711yescharacteristic
123C2×C4⋊C4—3141no—
124C4⋊C8—1571no—
125C4⋊C8C2×D15711yescharacteristic
126#102—3141no—
127#102—3142no—
128#102—3141no—
129C4×C8C2×D15711yescharacteristic
130#41—6282no—
131#41—6282no—
132C2×Q8—3141no—
133C2×D4—3142no—
134C2×D4—3141no—
135C2×D4—3141no—
136C2×D4—3141no—
137C2×D4—1571no—
138C2×D4D62811yescharacteristic
139C22×C4—21no—
140C22×C4—3142no—
141C22×C4—3141no—
142D8—6282no—
143D8—6282no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—3141no—
147C4⋊C4—3142no—
148C4⋊C4—3141no—
149C4⋊C4—1571no—
150C4⋊C4—1572no—
151C4⋊C4D62811yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—3142no—
154C22⋊C4—3141no—
155C42C22×D15711yescharacteristic
156C23—21no—
157C23—3141no—
158C23—6281no—
159Q8—6281no—
160Q8—6281no—
161D4—21no—
162D4—3141no—
163D4—3141no—
164D4—6282no—
165D4—6284no—
166D4—6281no—
167D4—6281no—
168D4—6281no—
169D4—6281no—
170D4D125612yescomplemented
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—3141no—
175C2×C4—3142no—
176C2×C4—6284no—
177C2×C4—6281no—
178C2×C4—6281no—
179C2×C4D4×D15711yescharacteristic
180C2×C4D4×D15711yescharacteristic
181C2×C4C2×D62811yescharacteristic
182C8—41no—
183C8—41no—
184C8—6281no—
185C22—22no—
186C22—41no—
187C22—41no—
188C22—6281no—
189C22—6281no—
190C22—6281no—
191C22—12561no—
192C22—12561no—
193C22—12561no—
194C22#1909774111yescharacteristic
195C4—21no—
196C4—41no—
197C4—6281no—
198C4—6282no—
199C4C2×D125611yescharacteristic
200C4#1909779211yescharacteristic
201C4#1909779511yescharacteristic
202C4#1909779911yescharacteristic
203C2—42no—
204C2—25121no—
205C2—12561no—
206C2#2375740911yescharacteristic
207C2#2375741911yescharacteristic
208C2#2375744711yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
FittingD4⋊C8×C157C2
socleC22×C157#120
hypercenterD4⋊C8D157
hypocenterC157#1625
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
1. #23757927C2semidirect
2. #23757620C2semidirect
3. #23757469C2semidirect
4. #23757468C2semidirect
5. #23757018C2semidirect
6. #23757002C2semidirect
7. D4⋊C8×C157C2semidirect
71. D4×C157D8semidirect
104. C157#1625semidirect
112. D4⋊C8D157semidirect
170. D4D1256semidirect

Maximal subgroups

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

subgroupindex
#237579272
#237576202
#237574692
#237574682
#237570182
#237570022
D4⋊C8×C1572
#1625157