Finite Group Databasebeta

← #34099221

Subgroups — #34099221

Order 20096.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#23757988C211yesmaximal, characteristic, complemented
2#23757646C211yesmaximal, characteristic, complemented
3#23757469C211yesmaximal, characteristic, complemented
4#23757468C211yesmaximal, characteristic, complemented
5#23757021C211yesmaximal, characteristic, complemented
6#23757002C211yesmaximal, characteristic, complemented
7D4⋊C8×C157C211yesmaximal, characteristic, complemented
8C2×#14578943—22no—
9C2×D1256—21no—
10C2×#14578939—21no—
11#19097771C2211yescharacteristic
12#19097768C2211yescharacteristic
13#19097757—22no—
14#19097745—21no—
15#19097742—21no—
16C4×D628C2211yescharacteristic
17#19097730—21no—
18#19097729—21no—
19C4⋊#11929434C2211yescharacteristic
20#19097693—21no—
21#19097691—21no—
22C4×D4×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4×C8×C157C2211yescharacteristic
25C2×Dic314D412yes—
26C2×D628—21no—
27C2×D628—21no—
28C2×D628—21no—
29C2×D628D411yescharacteristic
30C2×C22⋊D157—22no—
31C2×C4×D157—21no—
32#14578943—44no—
33D1256—42no—
34#14578939—42no—
35C2×#11929434—21no—
36C4⋊Dic157—21no—
37C4⋊Dic157—21no—
38C4⋊Dic157D411yescharacteristic
39C22⋊Dic157—22no—
40#14578931—22no—
41#14578931—21no—
42C4×Dic157—22no—
43C2×D4×C157D411yescharacteristic
44C22×C4×C157—21no—
45C2×C8×C157—21no—
46C2×C8×C157—21no—
47C4⋊C4×C157D411yescharacteristic
48C22⋊C4×C157—21no—
49C42×C157C2311yescharacteristic
50C22×D157—21no—
51C22×D157—41no—
52Dic314—42no—
53D628—21no—
54D628—21no—
55D628—42no—
56D628—41no—
57D628—41no—
58D628—41no—
59D628—41no—
60C22⋊D157—82no—
61C2×Dic157—21no—
62C2×Dic157—22no—
63C4×D157—41no—
64C4×D157—41no—
65#11929434—41no—
66C23×C157—21no—
67D4×C157—21no—
68D4×C157—21no—
69C2×C4×C157—21no—
70C2×C4×C157—41no—
71C2×C4×C157—41no—
72C2×C4×C157C2×D411yescharacteristic
73C2×C4×C157C2×D411yescharacteristic
74C2×C4×C157C2×D411yescharacteristic
75C8×C157—22no—
76C8×C157—41no—
77C22×C157—41no—
78C22×C157—41no—
79C22×C157—41no—
80C22×C157#12011yescharacteristic
81C2×D157—41no—
82C2×D157—41no—
83C2×D157—41no—
84C2×D157—81no—
85C2×D157—81no—
86C2×D157—81no—
87C4×C157—21no—
88C4×C157—41no—
89C4×C157#13511yescharacteristic
90C4×C157#13511yescharacteristic
91C4×C157AGL(1,ℤ/8)11yescharacteristic
92C4×C157AGL(1,ℤ/8)11yescharacteristic
93Dic157—41no—
94Dic157—42no—
95C2×C157—81no—
96C2×C157#44911yescharacteristic
97C2×C157#44911yescharacteristic
98C2×C157#45311yescharacteristic
99D157—81no—
100D157—161no—
101C157#162411yescharacteristic, complemented, Sylow
102#1624—1571nomaximal, Sylow
103#555—1571no—
104#492—1571no—
105#459—1571no—
106#459—1571no—
107#333—1571no—
108D4⋊C8—1571no—
109D4⋊C8D15711yescharacteristic, complemented
110C2×SD16—3142no—
111C2×D8—3141no—
112C2×D8—3141no—
113C4⋊Q8—1571no—
114#127—1571no—
115#124—3142no—
116#121—3141no—
117#121—3141no—
118C4×D4—1571no—
119C4×D4C2×D15711yescharacteristic
120#117—3141no—
121#117—3141no—
122C4⋊C8—1571no—
123C4⋊C8C2×D15711yescharacteristic
124#102—3141no—
125#102—3141no—
126C4×C8C2×D15711yescharacteristic
127C2×Q8—1572no—
128C2×D4—3142no—
129C2×D4—3141no—
130C2×D4—3141no—
131C2×D4—3141no—
132C2×D4—1571no—
133C2×D4D62811yescharacteristic
134C22×C4—21no—
135C22×C4—3141no—
136SD16—6284no—
137D8—6282no—
138D8—6282no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—3141no—
142C4⋊C4—3141no—
143C4⋊C4—3141no—
144C4⋊C4—1571no—
145C4⋊C4D62811yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—3142no—
148C22⋊C4—3142no—
149C22⋊C4—3141no—
150C42—3142no—
151C42C22×D15711yescharacteristic
152C23—21no—
153C23—3141no—
154C23—6281no—
155Q8—6282no—
156D4—21no—
157D4—21no—
158D4—3141no—
159D4—3141no—
160D4—6282no—
161D4—6281no—
162D4—6281no—
163D4—6281no—
164D4—6281no—
165D4—12562no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—3141no—
170C2×C4—3142no—
171C2×C4—6281no—
172C2×C4—6281no—
173C2×C4D4×D15711yescharacteristic
174C2×C4D4×D15711yescharacteristic
175C2×C4C2×D62811yescharacteristic
176C8—22no—
177C8—41no—
178C8—6281no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—6281no—
183C22—6281no—
184C22—6281no—
185C22—12561no—
186C22—12561no—
187C22—12561no—
188C22#1909774111yescharacteristic
189C4—21no—
190C4—41no—
191C4—6281no—
192C4—6282no—
193C4#1909779211yescharacteristic
194C4#1909779311yescharacteristic
195C4#1909779511yescharacteristic
196C4#1909779911yescharacteristic
197C2—81no—
198C2—25121no—
199C2—12561no—
200C2#2375741911yescharacteristic
201C2#2375742011yescharacteristic
202C2#2375744211yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
FittingD4⋊C8×C157C2
socleC22×C157#120
hypercenterD4⋊C8D157
hypocenterC157#1624
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. #23757988C2semidirect
2. #23757646C2semidirect
3. #23757469C2semidirect
4. #23757468C2semidirect
5. #23757021C2semidirect
6. #23757002C2semidirect
7. D4⋊C8×C157C2semidirect
101. C157#1624semidirect
109. D4⋊C8D157semidirect

Maximal subgroups

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

subgroupindex
#237579882
#237576462
#237574692
#237574682
#237570212
#237570022
D4⋊C8×C1572
#1624157