Finite Group Databasebeta

← #34115508

Subgroups — #34115508

Order 20096.

238 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 58 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#23758291C211yesmaximal, characteristic, complemented
2#23758209C211yesmaximal, characteristic, complemented
3#23758127C212yesmaximal, complemented
4#23758124C212yesmaximal
5#23757802C211yesmaximal, characteristic
6C2×C4×#10597845—21no—
7#19097838—21no—
8#19097828C2212yes—
9C4×#11929441—21no—
10(C2×#10597845)⋊C4—21no—
11(C2×#10597845)⋊C4C2212yes—
12#19097764—21no—
13#19097763C411yescharacteristic, complemented
14#19097753—21no—
15#19097747C2211yescharacteristic
16#19097742C2211yescharacteristic
17Q8×Dic157C411yescharacteristic, complemented
18D4×Dic157C411yescharacteristic, complemented
19#19097731—21no—
20#19097727—21no—
21C42×D157C2211yescharacteristic
22#124×C157C411yescharacteristic, complemented
23C22×#10597845—22no—
24C2×#11929441—22no—
25C4×#10597845—24no—
26C2×C22⋊D157—21no—
27C22×Dic157—21no—
28C2×C4×D157D411yescharacteristic
29C2×C4×D157D411yescharacteristic
30C2×C4×D157C2311yescharacteristic
31C4⋊Dic157—21no—
32C4⋊Dic157C2×C411yescharacteristic
33C4⋊Dic157C2×C411yescharacteristic
34#14578933—21no—
35#14578933—21no—
36#14578933—21no—
37C22⋊Dic157—21no—
38C22⋊Dic157—21no—
39#14578931—21no—
40C4×Dic157—21no—
41C4×Dic157C2×C411yescharacteristic
42C4×Dic157D411yescharacteristic
43C4×Dic157D411yescharacteristic
44C2×Q8×C157C2×C411yescharacteristic
45C2×D4×C157C2×C411yescharacteristic
46C22⋊C4×C157—21no—
47C22⋊C4×C157—21no—
48C42×C157C2×C411yescharacteristic
49C2×#10597845—24no—
50C2×#10597845—42no—
51C2×#10597845—42no—
52#11929441—42no—
53C22×D157C2×D411yescharacteristic
54C22⋊D157—42no—
55C2×Dic157—21no—
56C2×Dic157—21no—
57C2×Dic157—42no—
58C2×Dic157C22⋊C411yescharacteristic
59C2×Dic157C22⋊C411yescharacteristic
60C2×Dic157C2×D411yescharacteristic
61C4×D157—22no—
62C4×D157—22no—
63C4×D157—41no—
64C23×C157—21no—
65Q8×C157—41no—
66D4×C157—41no—
67C2×C4×C157—21no—
68C2×C4×C157C22⋊C411yescharacteristic
69C2×C4×C157C22⋊C411yescharacteristic
70C2×C4×C157C22×C411yescharacteristic
71C22×C157—41no—
72C22×C157—41no—
73C22×C157—41no—
74C22×C157C2×C22⋊C411yescharacteristic
75C2×D157—21no—
76C2×D157—21no—
77C2×D157#13512yes—
78#10597845—44no—
79C4×C157—21no—
80C4×C157—21no—
81C4×C157—21no—
82C4×C157—41no—
83Dic157—21no—
84Dic157—21no—
85Dic157—41no—
86Dic157—41no—
87Dic157#10412yes—
88C2×C157—81no—
89C2×C157#41011yescharacteristic
90C2×C157#41611yescharacteristic
91C2×C157C2×#10411yescharacteristic
92D157—22no—
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#1059784511yescharacteristic, complemented
103#123—3141no—
104C22⋊Q8—1571no—
105#121—1571no—
106C4×Q8—1571no—
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×D4C2×#1059784511yescharacteristic
120C22×C4—3142no—
121C22×C4—3141no—
122C22×C4—1571no—
123C22×C4—1571no—
124C22×C4—1571no—
125C2×C8—3142no—
126C4⋊C4—3141no—
127C4⋊C4—3141no—
128C4⋊C4—3141no—
129C4⋊C4—3141no—
130C4⋊C4—1571no—
131C4⋊C4—1571no—
132C22⋊C4—21no—
133C22⋊C4—21no—
134C22⋊C4—3141no—
135C22⋊C4—3141no—
136C22⋊C4—3141no—
137C42—3141no—
138C42—3144no—
139C42—1571no—
140C42—1571no—
141C42—1571no—
142C42C2×#1059784511yescharacteristic
143C23—21no—
144C23—1571no—
145Q8—41no—
146D4—41no—
147D4—6282no—
148C2×C4—21no—
149C2×C4—3142no—
150C2×C4—3142no—
151C2×C4—3144no—
152C2×C4—3141no—
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—41no—
166C22—41no—
167C22—41no—
168C22—3141no—
169C22—3141no—
170C22—1572no—
171C22C2×C22⋊#1059784511yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—3141no—
177C4—3141no—
178C4—6284no—
179C4—6281no—
180C4—6281no—
181C4—1572no—
182C2—81no—
183C2—3142no—
184C2#2375825311yescharacteristic
185C2#2375826311yescharacteristic
186C2D157⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597845
commutatorC2×C4×C157C22×C4
FrattiniC2×C4C22×#10597845
Fitting#124×C157C4
socleC22×C157C2×C22⋊C4
prime radical#19097742C22
cosocleC2×C4×D157C23
hypercenter#124#10597845
hypocenterC157#1500
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #23758291C2semidirect
2. #23758209C2semidirect
3. #23758127C2semidirect
13. #19097763C4semidirect
17. Q8×Dic157C4semidirect
18. D4×Dic157C4semidirect
22. #124×C157C4semidirect
93. C157#1500semidirect
102. #124#10597845semidirect

Maximal subgroups

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

subgroupindex
#237582912
#237582092
#237581272
#237581242
#237578022
#1500157