Finite Group Databasebeta

← #34099210

Subgroups — #34099210

Order 20096.

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

normal subgroups only

This group has 236 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#23757980C211yesmaximal, characteristic, complemented
2#23757646C211yesmaximal, characteristic, complemented
3#23757474C211yesmaximal, characteristic, complemented
4#23757468C211yesmaximal, characteristic
5#23757021C211yesmaximal, characteristic, complemented
6#23757005C211yesmaximal, characteristic, complemented
7D4⋊C8×C157C211yesmaximal, characteristic, complemented
8C2×#14578943—22no—
9C2×#14578943—21no—
10C2×#14578939—21no—
11#19097771C2211yescharacteristic
12#19097768C2211yescharacteristic
13#19097762—21no—
14#19097750—21no—
15#19097748—22no—
16C4×Dic314C2211yescharacteristic
17D4×Dic157—21no—
18C2×C4⋊Dic157—21no—
19C4⋊#11929434C2211yescharacteristic
20#19097693—21no—
21#19097691—21no—
22C4×D4×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4×C8×C157C2211yescharacteristic
25C2×Dic314D411yescharacteristic
26C2×Dic314D412yes—
27C2×D628—21no—
28C2×D628—21no—
29C2×D628—21no—
30C22×Dic157—22no—
31#14578943—44no—
32#14578943—42no—
33#14578939—42no—
34C2×#11929434—21no—
35C4⋊Dic157—22no—
36C4⋊Dic157—21no—
37C4⋊Dic157—21no—
38C4⋊Dic157D411yescharacteristic
39#14578933—22no—
40#14578933—21no—
41C22⋊Dic157—22no—
42C4×Dic157—21no—
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—41no—
51Dic314—21no—
52Dic314—21no—
53Dic314—42no—
54D628—42no—
55D628—41no—
56D628—41no—
57D628—41no—
58D628—41no—
59C2×Dic157—21no—
60C2×Dic157—22no—
61C2×Dic157—21no—
62C2×Dic157—82no—
63#11929434—41no—
64C23×C157—21no—
65D4×C157—21no—
66D4×C157SD1612yescomplemented
67C2×C4×C157—21no—
68C2×C4×C157—41no—
69C2×C4×C157—41no—
70C2×C4×C157C2×D411yescharacteristic
71C2×C4×C157C2×D411yescharacteristic
72C2×C4×C157C2×D411yescharacteristic
73C8×C157—22no—
74C8×C157—41no—
75C22×C157—22no—
76C22×C157—41no—
77C22×C157—41no—
78C22×C157#12011yescharacteristic
79C2×D157—81no—
80C2×D157—81no—
81C2×D157—81no—
82C4×C157—21no—
83C4×C157—41no—
84C4×C157C2×SD1611yescharacteristic
85C4×C157#13511yescharacteristic
86C4×C157AGL(1,ℤ/8)11yescharacteristic
87C4×C157#13711yescharacteristic
88Dic157—41no—
89Dic157—41no—
90Dic157—42no—
91C2×C157—42no—
92C2×C157#44811yescharacteristic
93C2×C157#44911yescharacteristic
94C2×C157#45311yescharacteristic
95D157—161no—
96C157#162211yescharacteristic, complemented, Sylow
97#1622—1571nomaximal, Sylow
98#554—1571no—
99#492—1571no—
100#460—1571no—
101#459—1571no—
102#333—1571no—
103Q8⋊C8—1571no—
104D4⋊C8D15711yescharacteristic, complemented
105C2×SD16—3141no—
106C2×SD16—3142no—
107C2×D8—3141no—
108C4⋊Q8—1571no—
109#127—1571no—
110#125—3141no—
111C22⋊Q8—3142no—
112C22⋊Q8—3141no—
113C4×Q8—1571no—
114C4×D4—3141no—
115C4×D4C2×D15711yescharacteristic
116C2×C4⋊C4—3141no—
117C4⋊C8—1571no—
118C4⋊C8C2×D15711yescharacteristic
119#102—3141no—
120#102—3141no—
121C4×C8C2×D15711yescharacteristic
122C2×Q8—1571no—
123C2×Q8—1572no—
124C2×D4—3141no—
125C2×D4—3141no—
126C2×D4—3141no—
127C2×D4D62811yescharacteristic
128C22×C4—21no—
129C22×C4—3142no—
130SD16—6284no—
131SD16—6282no—
132D8—6282no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—3141no—
136C4⋊C4—3142no—
137C4⋊C4—3142no—
138C4⋊C4—3141no—
139C4⋊C4—3141no—
140C4⋊C4—3141no—
141C4⋊C4—1571no—
142C4⋊C4D62811yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—3142no—
145C42—3141no—
146C42C22×D15711yescharacteristic
147C23—21no—
148C23—6281no—
149Q8—3141no—
150Q8—3141no—
151Q8—6282no—
152D4—21no—
153D4—6282no—
154D4—6281no—
155D4—6281no—
156D4—6281no—
157D4—6281no—
158D4#1457894312yescomplemented
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—3141no—
163C2×C4—3141no—
164C2×C4—3142no—
165C2×C4—12562no—
166C2×C4D4×D15711yescharacteristic
167C2×C4D4×D15711yescharacteristic
168C2×C4C2×D62811yescharacteristic
169C8—22no—
170C8—41no—
171C8—6281no—
172C22—22no—
173C22—41no—
174C22—41no—
175C22—12561no—
176C22—12561no—
177C22—12561no—
178C22#1909774111yescharacteristic
179C4—21no—
180C4—41no—
181C4—6281no—
182C4—6281no—
183C4—6282no—
184C4C2×#1457894311yescharacteristic
185C4#1909779211yescharacteristic
186C4#1909779511yescharacteristic
187C4#1909780411yescharacteristic
188C2—42no—
189C2—25121no—
190C2#2375741411yescharacteristic
191C2#2375741911yescharacteristic
192C2#2375744211yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
FittingD4⋊C8×C157C2
socleC22×C157#120
prime radical#23757468C2
hypercenterD4⋊C8D157
hypocenterC157#1622
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. #23757980C2semidirect
2. #23757646C2semidirect
3. #23757474C2semidirect
5. #23757021C2semidirect
6. #23757005C2semidirect
7. D4⋊C8×C157C2semidirect
66. D4×C157SD16semidirect
96. C157#1622semidirect
104. D4⋊C8D157semidirect
158. D4#14578943semidirect

Maximal subgroups

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

subgroupindex
#237579802
#237576462
#237574742
#237574682
#237570212
#237570052
D4⋊C8×C1572
#1622157