Finite Group Databasebeta

← #34116137

Subgroups — #34116137

Order 20096.

332 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 66 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#23758351C211yesmaximal, characteristic, complemented
2#23758272C212yesmaximal, complemented
3#23758253C211yesmaximal, characteristic, complemented
4#23758144C212yesmaximal, complemented
5#23757822C211yesmaximal, characteristic
6#19097858—24no—
7D157⋊M16C2212yes—
8C2×#14578963—22no—
9#19097850C2212yes—
10#19097836—24no—
11#19097829—22no—
12C2×#14578955C2211yescharacteristic
13C2×#14578953C2211yescharacteristic
14#19097769C411yescharacteristic, complemented
15#19097767C411yescharacteristic, complemented
16#19097759C411yescharacteristic, complemented
17#19097744—22no—
18#19097731—22no—
19C42×D157C2211yescharacteristic
20#124×C157C411yescharacteristic, complemented
21#14578964D414yescomplemented
22#14578963—24no—
23#14578963—22no—
24D157⋊C8—22no—
25C2×#11929441—24no—
26C4⋊#10597845—22no—
27C22⋊#10597845—22no—
28C4×#10597845—22no—
29#14578955—22no—
30#14578955—22no—
31#14578953—22no—
32#14578953—22no—
33C2×Dic314C2×C411yescharacteristic
34C2×D628—21no—
35C2×D628C2×C411yescharacteristic
36C2×C22⋊D157—22no—
37C2×C22⋊D157D412yes—
38C22×Dic157D412yes—
39C2×C4×D157—21no—
40C2×C4×D157—21no—
41C2×C4×D157C2311yescharacteristic
42#14578933—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—42no—
51#11929441—24no—
52C22×D157—21no—
53C22×D157C2×D411yescharacteristic
54Dic314—22no—
55D628—22no—
56D628—42no—
57C22⋊D157—24no—
58C22⋊D157—44no—
59C2×Dic157—21no—
60C2×Dic157—22no—
61C2×Dic157—22no—
62C2×Dic157C22⋊C412yes—
63C2×Dic157C2×D411yescharacteristic
64C4×D157—42no—
65C4×D157—41no—
66C4×D157—41no—
67C4×D157C2×D412yes—
68C4×D157#4112yes—
69C23×C157C22⋊C412yes—
70Q8×C157—22no—
71D4×C157—22no—
72C2×C4×C157—21no—
73C2×C4×C157—21no—
74C2×C4×C157C22×C411yescharacteristic
75C22×C157—22no—
76C22×C157—42no—
77C22×C157C2×C22⋊C411yescharacteristic
78C2×D157—41no—
79C2×D157—42no—
80C2×D157—41no—
81C2×D157#12112yes—
82#10597845—82no—
83C4×C157—41no—
84C4×C157—41no—
85C4×C157C4×D412yes—
86Dic157—22no—
87Dic157—22no—
88Dic157#12011yescharacteristic
89Dic157#12311yescharacteristic
90C2×C157—21no—
91C2×C157—42no—
92C2×C157#38611yescharacteristic
93D157—22no—
94D157—81no—
95C157#188411yescharacteristic, complemented, Sylow
96#1884—1571nomaximal, Sylow
97#568—1571no—
98#532—1571no—
99#421—1572no—
100#410—1571no—
101#339—1572no—
102C2×#41—1571no—
103C2×#41—1571no—
104#131—3144no—
105C2×M16—3142no—
106C2×M16—1572no—
107C4⋊Q8—1571no—
108#127—1571no—
109#124—1571no—
110#124#1059784511yescharacteristic, complemented
111#121—3142no—
112C4×D4—3142no—
113#117—1572no—
114C2×C42—1571no—
115#104—3144no—
116#99—3142no—
117#41—3142no—
118#41—3142no—
119#41—3142no—
120#41—3142no—
121C2×Q8—1571no—
122C2×Q8C2×#1059784511yescharacteristic
123C2×D4—3141no—
124C2×D4—3142no—
125C2×D4—1572no—
126C2×D4—1571no—
127C2×D4C2×#1059784511yescharacteristic
128C22×C4—3141no—
129C22×C4—3141no—
130C22×C4—1572no—
131C22×C4—1571no—
132M16—3144no—
133M16—3142no—
134M16—1574no—
135C2×C8—3144no—
136C2×C8—3142no—
137C4⋊C4—3142no—
138C4⋊C4—3142no—
139C22⋊C4—22no—
140C22⋊C4—3142no—
141C22⋊C4—3142no—
142C42—3141no—
143C42—3142no—
144C42—1571no—
145C42C2×#1059784511yescharacteristic
146C23—3141no—
147C23—1571no—
148C23C22⋊#1059784512yes—
149Q8—22no—
150Q8—3142no—
151D4—22no—
152D4—3144no—
153D4—3142no—
154D4—6282no—
155D4—6284no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—3141no—
159C2×C4—3142no—
160C2×C4—3142no—
161C2×C4—6282no—
162C2×C4—6281no—
163C2×C4—6281no—
164C2×C4—6282no—
165C2×C4—1572no—
166C2×C4—1571no—
167C2×C4—1572no—
168C2×C4—1572no—
169C2×C4C22×#1059784511yescharacteristic
170C8—3144no—
171C22—22no—
172C22—42no—
173C22—6281no—
174C22—6282no—
175C22—6281no—
176C22—1572no—
177C22C2×C22⋊#1059784511yescharacteristic
178C4—41no—
179C4—41no—
180C4—3142no—
181C4—3142no—
182C4—1571no—
183C4—1571no—
184C4—12562no—
185C4D4×#1059784512yes—
186C2—21no—
187C2—42no—
188C2—3142no—
189C2—12561no—
190C2#2375822111yescharacteristic
subgroupG/H
centerC2#23758221
commutatorC2×C4×C157C22×C4
FrattiniC2×C4C22×#10597845
Fitting#124×C157C4
socleC2×C157#386
prime radical#23757822C2
cosocleC2×C4×D157C23
hypercenter#124#10597845
hypocenterC157#1884
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. #23758351C2semidirect
2. #23758272C2semidirect
3. #23758253C2semidirect
4. #23758144C2semidirect
14. #19097769C4semidirect
15. #19097767C4semidirect
16. #19097759C4semidirect
20. #124×C157C4semidirect
21. #14578964D4semidirect
95. C157#1884semidirect
110. #124#10597845semidirect

Maximal subgroups

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

subgroupindex
#237583512
#237582722
#237582532
#237581442
#237578222
#1884157