Finite Group Databasebeta

← #34116144

Subgroups — #34116144

Order 20096.

344 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 68 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#23758341C211yesmaximal, characteristic, complemented
2#23758265C212yesmaximal
3D157⋊#101C211yesmaximal, characteristic, complemented
4#23758144C212yesmaximal, complemented
5#124×D157C211yesmaximal, characteristic
6D157⋊M16C2212yes—
7Q8×#10597845—24no—
8#19097850—22no—
9#19097850C2212yes—
10#19097833—24no—
11#19097832—22no—
12C2×Q8×D157C2211yescharacteristic
13C2×D4×D157C2211yescharacteristic
14#19097760C411yescharacteristic, complemented
15#19097759C411yescharacteristic, complemented
16#19097758C411yescharacteristic, complemented
17#19097757—22no—
18C22⋊C4×D157—22no—
19C42×D157C2211yescharacteristic
20#124×C157C411yescharacteristic, complemented
21#14578964—22no—
22#14578963—22no—
23D157⋊C8—22no—
24C4⋊#10597845—24no—
25C4⋊#10597845D414yes—
26C22⋊#10597845—22no—
27C4×#10597845—24no—
28C4×#10597845—22no—
29C23×D157—21no—
30C2×Dic314C2×C411yescharacteristic
31C2×Dic314D412yes—
32Q8×D157—22no—
33Q8×D157—22no—
34C2×D628C2×C411yescharacteristic
35C2×C22⋊D157—21no—
36D4×D157—22no—
37D4×D157—22no—
38C2×C4×D157—21no—
39C2×C4×D157D412yes—
40C2×C4×D157C2311yescharacteristic
41C22⋊Dic157—22no—
42#14578931—22no—
43#14578931—22no—
44C4×Dic157—21no—
45C4×Dic157C2×C411yescharacteristic
46C2×Q8×C157C2×C411yescharacteristic
47C2×D4×C157C2×C411yescharacteristic
48C22⋊C4×C157—22no—
49C42×C157C2×C411yescharacteristic
50C2×#10597845—24no—
51#11929441—42no—
52C22×D157—21no—
53C22×D157—44no—
54C22×D157—41no—
55C22×D157—41no—
56C22×D157C2×D411yescharacteristic
57Dic314—22no—
58Dic314—24no—
59D628—22no—
60C22⋊D157—42no—
61C2×Dic157—21no—
62C2×Dic157C22⋊C412yes—
63C2×Dic157C2×D411yescharacteristic
64C4×D157—22no—
65C4×D157—22no—
66C4×D157—42no—
67C4×D157C2×D412yes—
68C4×D157#4112yes—
69C23×C157—21no—
70Q8×C157—22no—
71D4×C157—22no—
72C2×C4×C157—21no—
73C2×C4×C157C22⋊C412yes—
74C2×C4×C157C22×C411yescharacteristic
75C22×C157—42no—
76C22×C157—41no—
77C22×C157C2×C22⋊C411yescharacteristic
78C2×D157—22no—
79C2×D157—42no—
80C2×D157—41no—
81C2×D157—82no—
82C2×D157—82no—
83C2×D157#12011yescharacteristic
84C2×D157#12311yescharacteristic
85#10597845—44no—
86C4×C157—22no—
87C4×C157—41no—
88C4×C157C4×D412yes—
89Dic157—22no—
90Dic157—41no—
91Dic157#12112yes—
92C2×C157—21no—
93C2×C157—81no—
94C2×C157#38611yescharacteristic
95D157—21no—
96D157—81no—
97D157#45412yes—
98C157#188811yescharacteristic, complemented, Sylow
99#1888—1571nomaximal, Sylow
100C2×#124—1571no—
101#519—1571no—
102#418—1572no—
103C2×#101—1571no—
104#339—1572no—
105C22×Q8—1571no—
106C22×D4—1571no—
107C2×M16—1572no—
108#124—3142no—
109#124—1571no—
110#124—1571no—
111#124—1571no—
112#124#1059784511yescharacteristic, complemented
113C4×Q8—3144no—
114#117—3142no—
115#117—1572no—
116C2×C22⋊C4—3142no—
117C2×C42—1571no—
118#102—3144no—
119#101—3142no—
120C24—3141no—
121C2×Q8—3142no—
122C2×Q8—3142no—
123C2×Q8—1572no—
124C2×Q8—1571no—
125C2×Q8C2×#1059784511yescharacteristic
126C2×D4—3142no—
127C2×D4—3142no—
128C2×D4—3141no—
129C2×D4—1571no—
130C2×D4C2×#1059784511yescharacteristic
131C22×C4—3141no—
132C22×C4—1572no—
133C22×C4—1571no—
134M16—3142no—
135M16—3142no—
136C2×C8—3142no—
137C4⋊C4—3144no—
138C4⋊C4—1574no—
139C22⋊C4—22no—
140C22⋊C4—3142no—
141C22⋊C4—3142no—
142C22⋊C4—3142no—
143C22⋊C4—3142no—
144C42—3141no—
145C42—3144no—
146C42—3142no—
147C42—1571no—
148C42C2×#1059784511yescharacteristic
149C23—21no—
150C23—3141no—
151C23—6284no—
152C23—6281no—
153C23—6281no—
154C23—1571no—
155Q8—22no—
156Q8—3144no—
157Q8—3142no—
158D4—22no—
159D4—3142no—
160D4—6282no—
161C2×C4—21no—
162C2×C4—3142no—
163C2×C4—3142no—
164C2×C4—3144no—
165C2×C4—3141no—
166C2×C4—6282no—
167C2×C4—1572no—
168C2×C4—1571no—
169C2×C4—1572no—
170C2×C4—1572no—
171C2×C4C22⋊#1059784512yes—
172C2×C4C22×#1059784511yescharacteristic
173C8—6282no—
174C22—42no—
175C22—41no—
176C22—3142no—
177C22—6282no—
178C22—6281no—
179C22—1571no—
180C22—1571no—
181C22—12562no—
182C22—12562no—
183C22C2×C22⋊#1059784511yescharacteristic
184C4—22no—
185C4—41no—
186C4—3142no—
187C4—6281no—
188C4—6284no—
189C4—1572no—
190C4D4×#1059784512yes—
191C2—21no—
192C2—81no—
193C2—3141no—
194C2—1572no—
195C2—12561no—
196C2#2375822111yescharacteristic
subgroupG/H
centerC2#23758221
commutatorC2×C4×C157C22×C4
FrattiniC2×C4C22×#10597845
Fitting#124×C157C4
socleC2×C157#386
prime radicalC2×D4×D157C22
cosocleC2×C4×D157C23
hypercenter#124#10597845
hypocenterC157#1888
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #23758341C2semidirect
3. D157⋊#101C2semidirect
4. #23758144C2semidirect
14. #19097760C4semidirect
15. #19097759C4semidirect
16. #19097758C4semidirect
20. #124×C157C4semidirect
98. C157#1888semidirect
112. #124#10597845semidirect

Maximal subgroups

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

subgroupindex
#237583412
#237582652
D157⋊#1012
#237581442
#124×D1572
#1888157