Finite Group Databasebeta

← #34116142

Subgroups — #34116142

Order 20096.

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

normal subgroups only

This group has 324 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
2#23758266C212yesmaximal
3D157⋊#101C211yesmaximal, characteristic
4#23758144C212yesmaximal
5C4⋊Q8×D157C211yesmaximal, characteristic
6D157⋊M16C2212yes—
7Q8×#10597845—24no—
8#19097850—22no—
9#19097850C2212yes—
10#19097834—24no—
11#19097832—22no—
12C2×Q8×D157C2211yescharacteristic
13C2×Q8×D157C2211yescharacteristic
14#19097771C411yescharacteristic, complemented
15#19097770—22no—
16#19097769C411yescharacteristic, complemented
17#19097769C411yescharacteristic, complemented
18C4⋊C4×D157—22no—
19C42×D157C2211yescharacteristic
20C4⋊Q8×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—
29C2×Dic314—21no—
30C2×Dic314C2×C411yescharacteristic
31C2×Dic314C2×C411yescharacteristic
32C2×Dic314D412yes—
33Q8×D157—22no—
34Q8×D157—22no—
35Q8×D157—22no—
36Q8×D157—22no—
37C2×C4×D157—21no—
38C2×C4×D157—21no—
39C2×C4×D157D412yes—
40C2×C4×D157C2311yescharacteristic
41C4⋊Dic157—22no—
42#14578933—22no—
43#14578933—22no—
44C4×Dic157—21no—
45C4×Dic157C2×C411yescharacteristic
46C2×Q8×C157C2×C411yescharacteristic
47C2×Q8×C157C2×C411yescharacteristic
48C4⋊C4×C157—22no—
49C42×C157C2×C411yescharacteristic
50C2×#10597845—24no—
51#11929441—42no—
52C22×D157C2×D411yescharacteristic
53Dic314—22no—
54Dic314—24no—
55Dic314—22no—
56Dic314—42no—
57C2×Dic157—21no—
58C2×Dic157—21no—
59C2×Dic157C22⋊C412yes—
60C2×Dic157C2×D411yescharacteristic
61C4×D157—24no—
62C4×D157—22no—
63C4×D157—22no—
64C4×D157—41no—
65C4×D157—41no—
66C4×D157C2×D412yes—
67C4×D157#4112yes—
68Q8×C157—22no—
69Q8×C157—22no—
70C2×C4×C157—21no—
71C2×C4×C157—21no—
72C2×C4×C157C22⋊C412yes—
73C2×C4×C157C22×C411yescharacteristic
74C22×C157C2×C22⋊C411yescharacteristic
75C2×D157—22no—
76C2×D157#12011yescharacteristic
77C2×D157#12311yescharacteristic
78#10597845—44no—
79C4×C157—22no—
80C4×C157—22no—
81C4×C157—41no—
82C4×C157C4×D412yes—
83Dic157—22no—
84Dic157—22no—
85Dic157—41no—
86Dic157#12112yes—
87C2×C157—21no—
88C2×C157#38611yescharacteristic
89D157—21no—
90D157#45612yes—
91C157#188611yescharacteristic, complemented, Sylow
92#1886—1571nomaximal, Sylow
93C2×C4⋊Q8—1571no—
94#519—1571no—
95#419—1572no—
96C2×#101—1571no—
97#339—1572no—
98C22×Q8—1571no—
99C22×Q8—1571no—
100C2×M16—1572no—
101C4⋊Q8—3142no—
102C4⋊Q8—1571no—
103C4⋊Q8—1571no—
104C4⋊Q8—1571no—
105C4⋊Q8#1059784511yescharacteristic, complemented
106C4×Q8—3144no—
107#117—3142no—
108#117—1572no—
109C2×C4⋊C4—3142no—
110C2×C42—1571no—
111#103—3144no—
112#101—3142no—
113C2×Q8—3141no—
114C2×Q8—3142no—
115C2×Q8—3142no—
116C2×Q8—3142no—
117C2×Q8—3142no—
118C2×Q8—1571no—
119C2×Q8—1572no—
120C2×Q8—1571no—
121C2×Q8C2×#1059784511yescharacteristic
122C2×Q8C2×#1059784511yescharacteristic
123C22×C4—3141no—
124C22×C4—3141no—
125C22×C4—1572no—
126C22×C4—1571no—
127M16—3142no—
128M16—3142no—
129C2×C8—3142no—
130C4⋊C4—22no—
131C4⋊C4—3142no—
132C4⋊C4—3142no—
133C4⋊C4—3144no—
134C4⋊C4—3142no—
135C4⋊C4—1574no—
136C22⋊C4—3142no—
137C42—3141no—
138C42—3144no—
139C42—3142no—
140C42—1571no—
141C42C2×#1059784511yescharacteristic
142C23—1571no—
143Q8—22no—
144Q8—22no—
145Q8—3144no—
146Q8—3142no—
147Q8—3142no—
148Q8—6282no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—3144no—
152C2×C4—3142no—
153C2×C4—3142no—
154C2×C4—3141no—
155C2×C4—3144no—
156C2×C4—3141no—
157C2×C4—6281no—
158C2×C4—6281no—
159C2×C4—1572no—
160C2×C4—1571no—
161C2×C4—1572no—
162C2×C4—1572no—
163C2×C4C22⋊#1059784512yes—
164C2×C4C22×#1059784511yescharacteristic
165C8—6282no—
166C22—3142no—
167C22—1571no—
168C22—1571no—
169C22C2×C22⋊#1059784511yescharacteristic
170C4—22no—
171C4—22no—
172C4—41no—
173C4—3142no—
174C4—3142no—
175C4—6284no—
176C4—6281no—
177C4—1572no—
178C4D4×#1059784512yes—
179C2—21no—
180C2—3141no—
181C2—1572no—
182C2#2375822111yescharacteristic
subgroupG/H
centerC2#23758221
commutatorC2×C4×C157C22×C4
FrattiniC2×C4C22×#10597845
FittingC4⋊Q8×C157C4
socleC2×C157#386
prime radicalC22×D157C2×D4
cosocleC2×C4×D157C23
hypercenterC4⋊Q8#10597845
hypocenterC157#1886
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
14. #19097771C4semidirect
16. #19097769C4semidirect
17. #19097769C4semidirect
20. C4⋊Q8×C157C4semidirect
91. C157#1886semidirect
105. C4⋊Q8#10597845semidirect

Maximal subgroups

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

subgroupindex
#237583412
#237582662
D157⋊#1012
#237581442
C4⋊Q8×D1572
#1886157