Finite Group Databasebeta

← #34115509

Subgroups — #34115509

Order 20096.

238 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 60 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#23758292C211yesmaximal, characteristic, complemented
2#23758209C211yesmaximal, characteristic, complemented
3#23758127C212yesmaximal, complemented
4#23758125C212yesmaximal
5#23757810C211yesmaximal, characteristic
6C2×C4×#10597845—21no—
7C4⋊#11929441—21no—
8#19097828C2212yes—
9C4×#11929441—21no—
10(C2×#10597845)⋊C4—21no—
11(C2×#10597845)⋊C4C2212yes—
12#19097766—21no—
13#19097762C411yescharacteristic, complemented
14#19097760C411yescharacteristic, complemented
15#19097756—21no—
16#19097747C2211yescharacteristic
17#19097746C2211yescharacteristic
18C4×D628—21no—
19C4×D628C411yescharacteristic, complemented
20#19097728—21no—
21C42×D157C2211yescharacteristic
22C4×Q8×C157C411yescharacteristic, complemented
23C22×#10597845—22no—
24C2×#11929441—22no—
25C4×#10597845—24no—
26C2×D628—21no—
27C2×D628C2×C411yescharacteristic
28C2×C4×D157—21no—
29C2×C4×D157D411yescharacteristic
30C2×C4×D157D411yescharacteristic
31C2×C4×D157C2311yescharacteristic
32C4⋊Dic157—21no—
33C4⋊Dic157C2×C411yescharacteristic
34#14578933—21no—
35#14578933—21no—
36#14578931—21no—
37#14578931—21no—
38#14578931—21no—
39#14578931—21no—
40#14578931—21no—
41C4×Dic157C2×C411yescharacteristic
42C4×Dic157D411yescharacteristic
43C4×Dic157D411yescharacteristic
44C2×Q8×C157C2×C411yescharacteristic
45C4⋊C4×C157—21no—
46C4⋊C4×C157C2×C411yescharacteristic
47C42×C157—21no—
48C42×C157C2×C411yescharacteristic
49C2×#10597845—24no—
50C2×#10597845—42no—
51C2×#10597845—42no—
52#11929441—42no—
53C22×D157—21no—
54C22×D157C2×D411yescharacteristic
55D628—41no—
56D628—42no—
57C2×Dic157—21no—
58C2×Dic157C22⋊C411yescharacteristic
59C2×Dic157C22⋊C411yescharacteristic
60C2×Dic157C2×D411yescharacteristic
61C4×D157—22no—
62C4×D157—22no—
63C4×D157—41no—
64C4×D157—42no—
65Q8×C157—41no—
66C2×C4×C157—21no—
67C2×C4×C157—21no—
68C2×C4×C157C22⋊C411yescharacteristic
69C2×C4×C157C22⋊C411yescharacteristic
70C2×C4×C157C22×C411yescharacteristic
71C22×C157C2×C22⋊C411yescharacteristic
72C2×D157—21no—
73C2×D157—21no—
74C2×D157—41no—
75C2×D157—41no—
76C2×D157—41no—
77C2×D157#13512yes—
78#10597845—44no—
79C4×C157—21no—
80C4×C157—21no—
81C4×C157—41no—
82C4×C157—41no—
83C4×C157#10412yes—
84Dic157—21no—
85Dic157—21no—
86Dic157—21no—
87Dic157—41no—
88C2×C157#41011yescharacteristic
89C2×C157#41611yescharacteristic
90C2×C157C2×#10411yescharacteristic
91D157—22no—
92D157—81no—
93C157#150011yescharacteristic, complemented, Sylow
94#1500—1571nomaximal, Sylow
95#529—1571no—
96#431—1571no—
97#376—1571no—
98#328—1572no—
99#327—1572no—
100#126—3141no—
101#125—1571no—
102#124—1571no—
103#123—3141no—
104C22⋊Q8—1571no—
105#121—1571no—
106C4×Q8#1059784511yescharacteristic, complemented
107C4×D4—3141no—
108C4×D4—1571no—
109#117—3141no—
110C2×C42—3141no—
111C2×C42—1571no—
112C4⋊C8—3141no—
113C22⋊C8—1572no—
114C4×C8—3141no—
115#95—3141no—
116#95—1572no—
117C2×Q8C2×#1059784511yescharacteristic
118C2×D4—3141no—
119C2×D4—1571no—
120C22×C4—3142no—
121C22×C4—3141no—
122C22×C4—1571no—
123C22×C4—1571no—
124C22×C4—1571no—
125C2×C8—3142no—
126C4⋊C4—21no—
127C4⋊C4—3141no—
128C4⋊C4—3141no—
129C4⋊C4—3141no—
130C4⋊C4—1571no—
131C4⋊C4C2×#1059784511yescharacteristic
132C22⋊C4—3141no—
133C22⋊C4—3141no—
134C22⋊C4—3141no—
135C22⋊C4—3141no—
136C22⋊C4—3141no—
137C42—21no—
138C42—3144no—
139C42—1571no—
140C42—1571no—
141C42—1571no—
142C42C2×#1059784511yescharacteristic
143C23—3141no—
144C23—1571no—
145Q8—41no—
146D4—6281no—
147D4—6282no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—3142no—
151C2×C4—3142no—
152C2×C4—3144no—
153C2×C4—3141no—
154C2×C4—6281no—
155C2×C4—6282no—
156C2×C4—6282no—
157C2×C4—6282no—
158C2×C4—1571no—
159C2×C4—1571no—
160C2×C4—1571no—
161C2×C4C22⋊#1059784511yescharacteristic
162C2×C4C22⋊#1059784511yescharacteristic
163C2×C4C22×#1059784511yescharacteristic
164C8—6282no—
165C22—3141no—
166C22—3141no—
167C22—6281no—
168C22—6281no—
169C22—6281no—
170C22—1572no—
171C22C2×C22⋊#1059784511yescharacteristic
172C4—21no—
173C4—21no—
174C4—41no—
175C4—41no—
176C4—3141no—
177C4—3141no—
178C4—3141no—
179C4—6284no—
180C4—6281no—
181C4#1909783612yes—
182C2—3142no—
183C2—12561no—
184C2#2375825211yescharacteristic
185C2#2375826311yescharacteristic
186C2C2×#1909783611yescharacteristic
subgroupG/H
centerC2×C4C22⋊#10597845
commutatorC2×C4×C157C22×C4
FrattiniC2×C4C22×#10597845
FittingC4×Q8×C157C4
socleC22×C157C2×C22⋊C4
prime radical#19097746C22
cosocleC2×C4×D157C23
hypercenterC4×Q8#10597845
hypocenterC157#1500
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #23758292C2semidirect
2. #23758209C2semidirect
3. #23758127C2semidirect
13. #19097762C4semidirect
14. #19097760C4semidirect
19. C4×D628C4semidirect
22. C4×Q8×C157C4semidirect
93. C157#1500semidirect
106. C4×Q8#10597845semidirect

Maximal subgroups

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

subgroupindex
#237582922
#237582092
#237581272
#237581252
#237578102
#1500157