Finite Group Databasebeta

← #34116407

Subgroups — #34116407

Order 20096.

258 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 54 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#23758252C212yesmaximal, complemented
2#23758179C212yesmaximal, complemented
3#23758177C212yesmaximal, complemented
4#23757819C211yesmaximal, characteristic
5#19097850—22no—
6#19097830C2214yes—
7#19097829—22no—
8C2×#14578954C2211yescharacteristic
9#19097769C411yescharacteristic, complemented
10#19097767C2211yescharacteristic
11#19097760C2211yescharacteristic
12#19097758C411yescharacteristic, complemented
13#19097743—22no—
14C4×C22⋊D157—22no—
15C2×C4×Dic157C411yescharacteristic, complemented
16C2×#41×C157C411yescharacteristic, complemented
17C4⋊#10597845—42no—
18C22⋊#10597845—24no—
19C4×#10597845—42no—
20#14578954—41no—
21#14578954—41no—
22C2×Dic314C2×C411yescharacteristic
23C2×D628C2311yescharacteristic
24C2×C22⋊D157—22no—
25C2×C22⋊D157D412yes—
26C22×Dic157—21no—
27C2×C4×D157D412yes—
28#14578933—22no—
29C22⋊Dic157—22no—
30#14578931—22no—
31C4×Dic157—21no—
32C4×Dic157C2×C411yescharacteristic
33C4×Dic157C2×C411yescharacteristic
34#41×C157—41no—
35#41×C157—41no—
36C2×Q8×C157C2×C411yescharacteristic
37C2×D4×C157—21no—
38C2×D4×C157C2×C411yescharacteristic
39C22×C4×C157—21no—
40C22×C4×C157C2×C411yescharacteristic
41C2×#10597845—44no—
42C22×D157C2×D412yes—
43Dic314—41no—
44D628—41no—
45C22⋊D157—42no—
46C22⋊D157—44no—
47C2×Dic157—21no—
48C2×Dic157—21no—
49C2×Dic157—42no—
50C2×Dic157C22⋊C412yes—
51C4×D157—22no—
52C4×D157—22no—
53C23×C157—21no—
54C23×C157C22⋊C411yescharacteristic
55Q8×C157—41no—
56D4×C157—41no—
57D4×C157—42no—
58C2×C4×C157—21no—
59C2×C4×C157—21no—
60C2×C4×C157—21no—
61C2×C4×C157—41no—
62C2×C4×C157—41no—
63C2×C4×C157C22⋊C411yescharacteristic
64C2×C4×C157C22×C411yescharacteristic
65C22×C157—21no—
66C22×C157—41no—
67C22×C157—42no—
68C22×C157—41no—
69C22×C157C2×C22⋊C411yescharacteristic
70C2×D157—22no—
71C2×D157—42no—
72#10597845—84no—
73C4×C157—21no—
74C4×C157—41no—
75C4×C157#9911yescharacteristic
76C4×C157#9911yescharacteristic
77Dic157—22no—
78Dic157—22no—
79Dic157—41no—
80C2×C157—21no—
81C2×C157—41no—
82C2×C157—81no—
83C2×C157C2×#9911yescharacteristic
84D157—42no—
85C157#212611yescharacteristic, complemented, Sylow
86#2126—1571nomaximal, Sylow
87#532—1571no—
88#410—1572no—
89#354—1572no—
90#353—1572no—
91C2×#41—1571no—
92C2×#41#1059784511yescharacteristic, complemented
93C4⋊Q8—1571no—
94#127—1571no—
95#124—1571no—
96#124—1571no—
97#121—3142no—
98C4×D4—3142no—
99#117—3142no—
100C2×C42—1571no—
101#99—3142no—
102#99—1574no—
103#41—41no—
104#41—41no—
105#41—6281no—
106#41—6281no—
107C2×Q8—1571no—
108C2×Q8C2×#1059784511yescharacteristic
109C2×D4—21no—
110C2×D4—3142no—
111C2×D4—1572no—
112C2×D4—1571no—
113C2×D4C2×#1059784511yescharacteristic
114C22×C4—21no—
115C22×C4—3141no—
116C22×C4—1572no—
117C22×C4C2×#1059784511yescharacteristic
118C4⋊C4—3142no—
119C4⋊C4—6282no—
120C22⋊C4—3142no—
121C22⋊C4—3142no—
122C22⋊C4—3144no—
123C42—3141no—
124C42—6282no—
125C42—1571no—
126C42—1571no—
127C23—21no—
128C23—1572no—
129C23C22⋊#1059784511yescharacteristic
130Q8—41no—
131Q8—6281no—
132D4—41no—
133D4—42no—
134D4—6281no—
135D4—6282no—
136D4—6284no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—3141no—
143C2×C4—3142no—
144C2×C4—3142no—
145C2×C4—3141no—
146C2×C4—6282no—
147C2×C4—6284no—
148C2×C4—1572no—
149C2×C4C22⋊#1059784511yescharacteristic
150C2×C4C22×#1059784511yescharacteristic
151C22—21no—
152C22—41no—
153C22—42no—
154C22—41no—
155C22—3142no—
156C22—6282no—
157C22C2×C22⋊#1059784511yescharacteristic
158C4—21no—
159C4—41no—
160C4—3142no—
161C4—3142no—
162C4—6281no—
163C4—12564no—
164C4#1909782911yescharacteristic
165C4#1909782911yescharacteristic
166C2—21no—
167C2—41no—
168C2—81no—
169C2—6282no—
170C2C2×#1909782911yescharacteristic
subgroupG/H
centerC4#19097829
commutatorC2×C4×C157C22×C4
FrattiniC2×C4C22×#10597845
FittingC2×#41×C157C4
socleC2×C157C2×#99
prime radical#23757819C2
cosocleC2×D628C23
hypercenterC2×#41#10597845
hypocenterC157#2126
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #23758252C2semidirect
2. #23758179C2semidirect
3. #23758177C2semidirect
9. #19097769C4semidirect
12. #19097758C4semidirect
15. C2×C4×Dic157C4semidirect
16. C2×#41×C157C4semidirect
85. C157#2126semidirect
92. C2×#41#10597845semidirect

Maximal subgroups

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

subgroupindex
#237582522
#237581792
#237581772
#237578192
#2126157