Finite Group Databasebeta

← #34098757

Subgroups — #34098757

Order 20096.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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#23757807C211yesmaximal, characteristic
2C2×#19097682C211yesmaximal, characteristic, complemented
3#23757014C212yesmaximal, complemented
4#23757012C212yesmaximal, complemented
5#432×C157C211yesmaximal, characteristic, complemented
6C22×#11929434—21no—
7#19097765—21no—
8#19097763C2211yescharacteristic
9#19097759C2211yescharacteristic
10#19097754—21no—
11#19097750C411yescharacteristic
12#19097745C411yescharacteristic
13C4×Dic314C411yescharacteristic
14C4×D628C411yescharacteristic
15C4×C22⋊D157—21no—
16#19097728—21no—
17#19097682—21no—
18#19097682C2212yes—
19C2×C42×C157C2211yescharacteristic
20C4⋊C8×C157—21no—
21C22⋊C8×C157—21no—
22#97×C157C2212yes—
23C2×Dic314C2×C411yescharacteristic
24C2×D628C2×C411yescharacteristic
25C2×C22⋊D157—21no—
26C2×C4×D157—21no—
27C2×#11929434—24no—
28C2×#11929434—22no—
29C4⋊Dic157C2×C411yescharacteristic
30C4⋊Dic157C2×C411yescharacteristic
31#14578933—21no—
32#14578933—21no—
33#14578933—21no—
34#14578933—21no—
35C22⋊Dic157—21no—
36#14578931—21no—
37#14578931—21no—
38#14578931—21no—
39#14578931—21no—
40C4×Dic157—21no—
41C22×C4×C157C2×C411yescharacteristic
42C22×C4×C157D411yescharacteristic
43C22×C4×C157D411yescharacteristic
44C2×C8×C157—22no—
45C42×C157C2×C411yescharacteristic
46C42×C157D411yescharacteristic
47C42×C157D411yescharacteristic
48C42×C157C2311yescharacteristic
49C22×D157—21no—
50Dic314—41no—
51D628—41no—
52C22⋊D157—42no—
53C2×Dic157—21no—
54C2×Dic157—21no—
55C2×Dic157—21no—
56C4×D157—42no—
57#11929434—24no—
58C23×C157C22⋊C411yescharacteristic
59C2×C4×C157—22no—
60C2×C4×C157—41no—
61C2×C4×C157—41no—
62C2×C4×C157C22⋊C411yescharacteristic
63C2×C4×C157C22⋊C411yescharacteristic
64C2×C4×C157C22⋊C411yescharacteristic
65C2×C4×C157C22×C411yescharacteristic
66C2×C4×C157C2×D411yescharacteristic
67C2×C4×C157C2×D411yescharacteristic
68C8×C157—42no—
69C22×C157—21no—
70C22×C157—21no—
71C22×C157#10412yes—
72C22×C157C2×C22⋊C411yescharacteristic
73C2×D157—41no—
74C2×D157—41no—
75C2×D157—41no—
76C4×C157—21no—
77C4×C157—21no—
78C4×C157—21no—
79C4×C157—21no—
80C4×C157—21no—
81C4×C157—21no—
82Dic157—41no—
83Dic157—41no—
84Dic157—41no—
85C2×C157—22no—
86C2×C157#41311yescharacteristic
87C2×C157C2×#10411yescharacteristic
88C2×C157#42111yescharacteristic
89D157—81no—
90C157#153211yescharacteristic, complemented, Sylow
91#1532—1571nomaximal, Sylow
92#529—1571no—
93#432D15711yescharacteristic, complemented
94C2×#97—1571no—
95#330—1572no—
96#329—1572no—
97C22×C8—3141no—
98#126—3141no—
99#125—1571no—
100#124—1571no—
101#123—3141no—
102C22⋊Q8—1571no—
103#121—1571no—
104C4×Q8—1571no—
105C4×D4—3141no—
106C4×D4—1571no—
107#117—3141no—
108C2×C42C2×D15711yescharacteristic
109C4⋊C8—21no—
110C22⋊C8—21no—
111#97—3141no—
112#97—1572no—
113#97C2×D15712yes—
114C2×Q8—1571no—
115C2×D4—3141no—
116C2×D4—1571no—
117C22×C4—3141no—
118C22×C4C4×D15711yescharacteristic
119C22×C4C22⋊D15711yescharacteristic
120C22×C4D62811yescharacteristic
121C2×C8—22no—
122C2×C8—3144no—
123C2×C8—3142no—
124C4⋊C4—3141no—
125C4⋊C4—3141no—
126C4⋊C4—3141no—
127C4⋊C4—3141no—
128C4⋊C4—1571no—
129C4⋊C4—1571no—
130C22⋊C4—3141no—
131C22⋊C4—3141no—
132C22⋊C4—3141no—
133C22⋊C4—3141no—
134C22⋊C4—3141no—
135C42—3141no—
136C42C4×D15711yescharacteristic
137C42C22⋊D15711yescharacteristic
138C42D62811yescharacteristic
139C42C22×D15711yescharacteristic
140C23—3141no—
141C23#1457893111yescharacteristic
142Q8—6281no—
143D4—6281no—
144D4—6282no—
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—3141no—
149C2×C4—3141no—
150C2×C4—3141no—
151C2×C4—6282no—
152C2×C4#1457893111yescharacteristic
153C2×C4#1457893111yescharacteristic
154C2×C4#1457893111yescharacteristic
155C2×C4C2×C4×D15711yescharacteristic
156C2×C4C2×C22⋊D15711yescharacteristic
157C2×C4C2×D62811yescharacteristic
158C8—42no—
159C8—3144no—
160C22—21no—
161C22—21no—
162C22—6281no—
163C22—6281no—
164C22—6281no—
165C22#1909769712yes—
166C22C2×#1457893111yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—6281no—
174C4—6281no—
175C4—6281no—
176C2—22no—
177C2—12561no—
178C2#2375725511yescharacteristic
179C2C2×#1909769711yescharacteristic
180C2#2375729111yescharacteristic
subgroupG/H
centerC22C2×#14578931
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
Fitting#432×C157C2
socleC22×C157C2×C22⋊C4
prime radical#19097745C4
cosocleC42×C157C23
hypercenter#432D157
hypocenterC157#1532
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×#19097682C2semidirect
3. #23757014C2semidirect
4. #23757012C2semidirect
5. #432×C157C2semidirect
90. C157#1532semidirect
93. #432D157semidirect

Maximal subgroups

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

subgroupindex
#237578072
C2×#190976822
#237570142
#237570122
#432×C1572
#1532157