Finite Group Databasebeta

← #34116178

Subgroups — #34116178

Order 20096.

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

normal subgroups only

This group has 312 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#23758353C211yesmaximal, characteristic
2#23758266C212yesmaximal, complemented
3#23758254C211yesmaximal, characteristic
4#23758140C212yesmaximal, complemented
5#23757848C211yesmaximal, characteristic
6#19097859—24no—
7D157⋊M16—22no—
8D157⋊M16C2212yes—
9#19097850C2212yes—
10#19097834—24no—
11#19097830—22no—
12C2×#14578955C2211yescharacteristic
13C2×Q8×D157C2211yescharacteristic
14#19097769C411yescharacteristic, complemented
15#19097760C411yescharacteristic, complemented
16#19097759C411yescharacteristic, complemented
17#19097756—22no—
18#19097749—22no—
19#19097728C2211yescharacteristic
20C4⋊Q8×C157C411yescharacteristic, complemented
21#14578964—24no—
22#14578964—22no—
23#14578963—22no—
24D157⋊C8—24no—
25D157⋊C8D414yes—
26C4⋊#10597845—22no—
27C22⋊#10597845—22no—
28C4×#10597845—22no—
29#14578955—22no—
30#14578955—22no—
31C2×Dic314—21no—
32C2×Dic314C2×C411yescharacteristic
33Q8×D157—22no—
34Q8×D157—22no—
35C2×D628C2×C411yescharacteristic
36C2×D628D412yes—
37C2×C4×D157—21no—
38C2×C4×D157D412yes—
39C2×C4×D157C2311yescharacteristic
40#14578933—21no—
41#14578933—22no—
42#14578931—22no—
43#14578931—22no—
44#14578931—21no—
45C4×Dic157C2×C411yescharacteristic
46C2×Q8×C157C2×C411yescharacteristic
47C2×Q8×C157C2×C411yescharacteristic
48C4⋊C4×C157—22no—
49C42×C157C2×C411yescharacteristic
50C2×#10597845—42no—
51#11929441—24no—
52C22×D157C22⋊C412yes—
53C22×D157C2×D411yescharacteristic
54Dic314—22no—
55Dic314—41no—
56Dic314—41no—
57D628—24no—
58D628—22no—
59C2×Dic157—21no—
60C2×Dic157—21no—
61C2×Dic157C2×D411yescharacteristic
62C4×D157—22no—
63C4×D157—22no—
64C4×D157—42no—
65C4×D157C2×D412yes—
66C4×D157#4112yes—
67Q8×C157—22no—
68Q8×C157—22no—
69C2×C4×C157—21no—
70C2×C4×C157—21no—
71C2×C4×C157C22⋊C412yes—
72C2×C4×C157C22×C411yescharacteristic
73C22×C157C2×C22⋊C411yescharacteristic
74C2×D157—22no—
75C2×D157—41no—
76C2×D157—42no—
77C2×D157#12112yes—
78#10597845—82no—
79C4×C157—22no—
80C4×C157—41no—
81C4×C157—41no—
82C4×C157C4×D412yes—
83Dic157—41no—
84Dic157—41no—
85Dic157#12011yescharacteristic
86Dic157#12311yescharacteristic
87C2×C157—21no—
88C2×C157#38611yescharacteristic
89D157—22no—
90D157—42no—
91C157#190911yescharacteristic, complemented, Sylow
92#1909—1571nomaximal, Sylow
93#568—1571no—
94#536—1571no—
95#419—1572no—
96#410—1571no—
97H(3,ℤ/4)—1572no—
98C2×#41—1571no—
99C22×Q8—1571no—
100#131—3144no—
101C2×M16—3142no—
102C2×M16—1572no—
103C4⋊Q8—1571no—
104C4⋊Q8#1059784511yescharacteristic, complemented
105#124—1571no—
106#124—1571no—
107#123—3142no—
108C22⋊Q8—3142no—
109#117—1572no—
110#117—1571no—
111#103—3144no—
112#99—3142no—
113#41—3142no—
114#41—3142no—
115C2×Q8—3141no—
116C2×Q8—3142no—
117C2×Q8—3142no—
118C2×Q8—1571no—
119C2×Q8C2×#1059784511yescharacteristic
120C2×Q8C2×#1059784511yescharacteristic
121C2×D4—1572no—
122C2×D4—1571no—
123C22×C4—3141no—
124C22×C4—1572no—
125C22×C4—1571no—
126M16—3144no—
127M16—3142no—
128M16—3142no—
129C2×C8—3144no—
130C2×C8—1574no—
131C4⋊C4—22no—
132C4⋊C4—3141no—
133C4⋊C4—3142no—
134C4⋊C4—3142no—
135C22⋊C4—3141no—
136C22⋊C4—3142no—
137C22⋊C4—3142no—
138C22⋊C4—3142no—
139C42—3142no—
140C42—1571no—
141C42C2×#1059784511yescharacteristic
142C23—1572no—
143C23—1571no—
144Q8—22no—
145Q8—22no—
146Q8—3142no—
147Q8—6281no—
148Q8—6281no—
149D4—3144no—
150D4—3142no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—3142no—
154C2×C4—3142no—
155C2×C4—3141no—
156C2×C4—3141no—
157C2×C4—6282no—
158C2×C4—6282no—
159C2×C4—1571no—
160C2×C4—1572no—
161C2×C4—1572no—
162C2×C4C22⋊#1059784512yes—
163C2×C4C22×#1059784511yescharacteristic
164C8—3144no—
165C22—3142no—
166C22—6281no—
167C22—6282no—
168C22—1572no—
169C22C2×C22⋊#1059784511yescharacteristic
170C4—22no—
171C4—41no—
172C4—41no—
173C4—6281no—
174C4—6281no—
175C4—1571no—
176C4—1571no—
177C4—12562no—
178C4D4×#1059784512yes—
179C2—21no—
180C2—3142no—
181C2—6282no—
182C2#2375822111yescharacteristic
subgroupG/H
centerC2#23758221
commutatorC2×C4×C157C22×C4
FrattiniC2×C4C22×#10597845
FittingC4⋊Q8×C157C4
socleC2×C157#386
prime radicalC2×#14578955C22
cosocleC2×C4×D157C23
hypercenterC4⋊Q8#10597845
hypocenterC157#1909
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #23758266C2semidirect
4. #23758140C2semidirect
14. #19097769C4semidirect
15. #19097760C4semidirect
16. #19097759C4semidirect
20. C4⋊Q8×C157C4semidirect
91. C157#1909semidirect
104. C4⋊Q8#10597845semidirect

Maximal subgroups

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

subgroupindex
#237583532
#237582662
#237582542
#237581402
#237578482
#1909157