Finite Group Databasebeta

← #34099205

Subgroups — #34099205

Order 20096.

236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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#23757984C211yesmaximal, characteristic, complemented
2#23757470C211yesmaximal, characteristic, complemented
3#23757465C211yesmaximal, characteristic
4#23757022C211yesmaximal, characteristic, complemented
5#23757005C211yesmaximal, characteristic, complemented
6#23757002C211yesmaximal, characteristic, complemented
7#492×C157C211yesmaximal, characteristic, complemented
8C2×#14578942—21no—
9C2×#14578939—21no—
10#19097762—21no—
11#19097751—21no—
12#19097747—22no—
13C4×Dic314C2211yescharacteristic
14C4×D628C2211yescharacteristic
15#19097733—21no—
16C4⋊C4×D157—21no—
17C4⋊#11929434C2211yescharacteristic
18C4⋊#11929434C2211yescharacteristic
19#19097692—21no—
20#19097692—21no—
21C2×SD16×C157—22no—
22C4⋊Q8×C157C2211yescharacteristic
23#127×C157C2211yescharacteristic
24C4×C8×C157C2211yescharacteristic
25C2×Dic314D411yescharacteristic
26C2×D628D411yescharacteristic
27C2×C4×D157—22no—
28C2×C4×D157—21no—
29#14578942—42no—
30#14578939—42no—
31C2×#11929434—21no—
32C2×#11929434—21no—
33C4⋊Dic157—22no—
34C4⋊Dic157D411yescharacteristic
35C4⋊Dic157D411yescharacteristic
36#14578933—22no—
37#14578933—21no—
38#14578931—22no—
39#14578931—21no—
40C4×Dic157—21no—
41C2×Q8×C157D412yes—
42C2×D4×C157—21no—
43C2×D4×C157—21no—
44C2×D4×C157—21no—
45SD16×C157—44no—
46C2×C8×C157—21no—
47C4⋊C4×C157—21no—
48C4⋊C4×C157—21no—
49C42×C157C2311yescharacteristic
50C22×D157—21no—
51Dic314—21no—
52Dic314—21no—
53D628—21no—
54D628SD1612yescomplemented
55C2×Dic157—21no—
56C2×Dic157—21no—
57C2×Dic157—21no—
58C4×D157—41no—
59C4×D157—41no—
60C4×D157—82no—
61#11929434—41no—
62#11929434—41no—
63C23×C157—41no—
64Q8×C157—42no—
65D4×C157—42no—
66D4×C157—41no—
67D4×C157—41no—
68D4×C157—41no—
69D4×C157—41no—
70C2×C4×C157—22no—
71C2×C4×C157C2×D411yescharacteristic
72C2×C4×C157C2×D411yescharacteristic
73C2×C4×C157C2×D411yescharacteristic
74C8×C157—22no—
75C22×C157—81no—
76C22×C157—81no—
77C22×C157—81no—
78C22×C157#12011yescharacteristic
79C2×D157—22no—
80C2×D157—41no—
81C2×D157—41no—
82C4×C157—21no—
83C4×C157—42no—
84C4×C157C2×SD1611yescharacteristic
85C4×C157#13511yescharacteristic
86C4×C157AGL(1,ℤ/8)11yescharacteristic
87C4×C157#13711yescharacteristic
88Dic157—41no—
89Dic157—41no—
90Dic157—41no—
91C2×C157—161no—
92C2×C157#44811yescharacteristic
93C2×C157#44911yescharacteristic
94C2×C157#45311yescharacteristic
95D157—42no—
96C157#162211yescharacteristic, complemented, Sylow
97#1622—1571nomaximal, Sylow
98#554—1571no—
99#492D15711yescharacteristic, complemented
100#460—1571no—
101#459—1571no—
102#333—1571no—
103Q8⋊C8—1571no—
104D4⋊C8—1571no—
105C2×SD16—22no—
106C2×SD16—3141no—
107C2×D8—3141no—
108C4⋊Q8C2×D15711yescharacteristic
109#127C2×D15711yescharacteristic
110#125—3141no—
111C22⋊Q8—3141no—
112C22⋊Q8—3142no—
113C4×Q8—1571no—
114C4×D4—3141no—
115C4×D4—1571no—
116C2×C4⋊C4—3141no—
117C4⋊C8—1571no—
118C4⋊C8—1571no—
119#102—3141no—
120#102—3141no—
121C4×C8C2×D15711yescharacteristic
122C2×Q8—1571no—
123C2×Q8C22⋊D15712yes—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—1571no—
128C22×C4—3142no—
129C22×C4—3141no—
130SD16—44no—
131SD16—6282no—
132D8—6282no—
133C2×C8—21no—
134C2×C8—3141no—
135C2×C8—3141no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—3142no—
139C4⋊C4—3142no—
140C4⋊C4—3141no—
141C4⋊C4—1571no—
142C4⋊C4—1571no—
143C22⋊C4—3142no—
144C22⋊C4—3141no—
145C42—3141no—
146C42C22×D15711yescharacteristic
147C23—41no—
148C23—3141no—
149Q8—42no—
150Q8—3141no—
151Q8—3141no—
152D4—42no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—3141no—
158D4—1572no—
159C2×C4—22no—
160C2×C4—3141no—
161C2×C4—3141no—
162C2×C4—3141no—
163C2×C4—6281no—
164C2×C4—6281no—
165C2×C4—12562no—
166C2×C4D4×D15711yescharacteristic
167C2×C4D4×D15711yescharacteristic
168C2×C4C2×C22⋊D15711yescharacteristic
169C8—22no—
170C8—6281no—
171C8—6281no—
172C22—81no—
173C22—81no—
174C22—81no—
175C22—3142no—
176C22—6281no—
177C22—6281no—
178C22#1909773911yescharacteristic
179C4—21no—
180C4—42no—
181C4—6281no—
182C4—6281no—
183C4—6281no—
184C4SD16×D15711yescharacteristic
185C4#1909779211yescharacteristic
186C4#1909779811yescharacteristic
187C4#1909780011yescharacteristic
188C2—161no—
189C2—6282no—
190C2#2375741011yescharacteristic
191C2#2375741711yescharacteristic
192C2#2375744011yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#492×C157C2
socleC22×C157#120
prime radical#23757465C2
hypercenter#492D157
hypocenterC157#1622
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #23757984C2semidirect
2. #23757470C2semidirect
4. #23757022C2semidirect
5. #23757005C2semidirect
6. #23757002C2semidirect
7. #492×C157C2semidirect
54. D628SD16semidirect
96. C157#1622semidirect
99. #492D157semidirect

Maximal subgroups

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

subgroupindex
#237579842
#237574702
#237574652
#237570222
#237570052
#237570022
#492×C1572
#1622157