Finite Group Databasebeta

← #34099244

Subgroups — #34099244

Order 20096.

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

normal subgroups only

This group has 216 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#23757993C211yesmaximal, characteristic, complemented
2#23757619C211yesmaximal, characteristic, complemented
3#23757470C211yesmaximal, characteristic, complemented
4#23757020C211yesmaximal, characteristic, complemented
5#23757003C211yesmaximal, characteristic, complemented
6D4⋊#11929434C211yesmaximal, characteristic, complemented
7#459×C157C211yesmaximal, characteristic
8C2×#14578942—21no—
9#19097771C2211yescharacteristic
10#19097764—22no—
11#19097758—21no—
12#19097750—21no—
13C4×Dic314C2211yescharacteristic
14#19097736—21no—
15#19097730—21no—
16C4⋊#11929434C2211yescharacteristic
17#19097692—22no—
18#19097692—21no—
19C4×#11929434C2211yescharacteristic
20C2×D8×C157—21no—
21#127×C157C2211yescharacteristic
22C4×D4×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24#102×C157—21no—
25C2×Dic314—21no—
26C2×Dic314D411yescharacteristic
27#14578942—42no—
28C2×#11929434—21no—
29C2×#11929434—21no—
30C4⋊Dic157—21no—
31C4⋊Dic157D411yescharacteristic
32C4⋊Dic157D412yes—
33#14578933—22no—
34#14578933—21no—
35C22⋊Dic157—22no—
36C22⋊Dic157—22no—
37C4×Dic157—22no—
38C4×Dic157—21no—
39C2×D4×C157—21no—
40C2×D4×C157—21no—
41C2×D4×C157—21no—
42C2×D4×C157D411yescharacteristic
43C22×C4×C157—21no—
44D8×C157—42no—
45C2×C8×C157—21no—
46C4⋊C4×C157D411yescharacteristic
47C22⋊C4×C157—21no—
48C42×C157C2311yescharacteristic
49Dic314—21no—
50Dic314—21no—
51Dic314—41no—
52Dic314—41no—
53C2×Dic157—22no—
54C2×Dic157—21no—
55C2×Dic157—21no—
56#11929434—41no—
57#11929434—41no—
58C23×C157—21no—
59C23×C157—41no—
60D4×C157—21no—
61D4×C157—21no—
62D4×C157—42no—
63D4×C157—41no—
64D4×C157—41no—
65D4×C157—41no—
66D4×C157—41no—
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—41no—
74C22×C157—41no—
75C22×C157—41no—
76C22×C157—41no—
77C22×C157—81no—
78C22×C157—81no—
79C22×C157—81no—
80C22×C157#12011yescharacteristic
81C4×C157—21no—
82C4×C157—41no—
83C4×C157#13511yescharacteristic
84C4×C157#13511yescharacteristic
85C4×C157AGL(1,ℤ/8)11yescharacteristic
86C4×C157AGL(1,ℤ/8)11yescharacteristic
87Dic157—41no—
88Dic157—42no—
89Dic157—41no—
90C2×C157—81no—
91C2×C157—161no—
92C2×C157#44911yescharacteristic
93C2×C157#44911yescharacteristic
94C2×C157#45411yescharacteristic
95C157#162811yescharacteristic, complemented, Sylow
96#1628—1571nomaximal, Sylow
97#556—1571no—
98#486—1571no—
99#460—1571no—
100#459D15711yescharacteristic
101#332—1571no—
102Q8⋊C8—1571no—
103D4⋊C8—1571no—
104C2×SD16—3141no—
105C2×D8—21no—
106C4⋊Q8—1571no—
107#127C2×D15711yescharacteristic
108#126—3142no—
109#124—3141no—
110C22⋊Q8—3141no—
111C4×Q8—3141no—
112C4×Q8—1571no—
113C4×D4C2×D15711yescharacteristic
114#117—3141no—
115C4⋊C8—1571no—
116C4⋊C8C2×D15711yescharacteristic
117#102—21no—
118#102—3141no—
119#102—3142no—
120C4×C8—1571no—
121C2×Q8—3141no—
122C2×Q8—1571no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4C22⋊D15711yescharacteristic
127C22×C4—21no—
128SD16—6282no—
129D8—42no—
130C2×C8—21no—
131C2×C8—3141no—
132C2×C8—3141no—
133C4⋊C4—3142no—
134C4⋊C4—3141no—
135C4⋊C4—3141no—
136C4⋊C4—1571no—
137C4⋊C4—1572no—
138C4⋊C4C22⋊D15711yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—3142no—
141C22⋊C4—3142no—
142C42—3142no—
143C42—3141no—
144C42C22×D15711yescharacteristic
145C23—21no—
146C23—41no—
147Q8—3141no—
148Q8—3141no—
149Q8—6281no—
150Q8—6281no—
151D4—21no—
152D4—21no—
153D4—42no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—3141no—
162C2×C4—3141no—
163C2×C4—3142no—
164C2×C4D4×D15711yescharacteristic
165C2×C4D4×D15711yescharacteristic
166C2×C4C2×C22⋊D15711yescharacteristic
167C8—41no—
168C8—6281no—
169C8—6281no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—81no—
174C22—81no—
175C22—81no—
176C22#1909773911yescharacteristic
177C4—21no—
178C4—41no—
179C4—6281no—
180C4—6282no—
181C4—6281no—
182C4#1909779011yescharacteristic
183C4#1909779111yescharacteristic
184C4#1909779511yescharacteristic
185C4#1909779711yescharacteristic
186C2—81no—
187C2—161no—
188C2#2375741511yescharacteristic
189C2#2375741611yescharacteristic
190C2#2375744411yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting, prime radical#459×C157C2
socleC22×C157#120
hypercenter#459D157
hypocenterC157#1628
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #23757993C2semidirect
2. #23757619C2semidirect
3. #23757470C2semidirect
4. #23757020C2semidirect
5. #23757003C2semidirect
6. D4⋊#11929434C2semidirect
95. C157#1628semidirect

Maximal subgroups

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

subgroupindex
#237579932
#237576192
#237574702
#237570202
#237570032
D4⋊#119294342
#459×C1572
#1628157