Finite Group Databasebeta

← #34099076

Subgroups — #34099076

Order 20096.

266 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 57 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#23757423C212yesmaximal
2#23757190C211yesmaximal, characteristic
3#23757010C212yesmaximal, complemented
4#23756999C211yesmaximal, characteristic, complemented
5#544×C157C211yesmaximal, characteristic, complemented
6C22×D628C2211yescharacteristic
7C2×#14578941—22no—
8C2×#14578931—21no—
9C2×#14578931—21no—
10#19097691—22no—
11C22⋊#11929434C2212yes—
12#19097678C2211yescharacteristic
13C4⋊Q8×C157—22no—
14#125×C157—22no—
15C22⋊Q8×C157—21no—
16C22⋊Q8×C157C2212yes—
17#117×C157—21no—
18C2×C4⋊C4×C157C2211yescharacteristic
19C23×D157—21no—
20C2×D628—22no—
21C2×D628—42no—
22C22×Dic157—21no—
23#14578941—44no—
24C2×#11929434—22no—
25#14578931—42no—
26#14578931—42no—
27C2×Q8×C157—21no—
28C2×Q8×C157D412yes—
29C22×C4×C157D411yescharacteristic
30C22×C4×C157D411yescharacteristic
31C22×C4×C157C2311yescharacteristic
32C4⋊C4×C157—21no—
33C4⋊C4×C157—21no—
34C4⋊C4×C157—21no—
35C4⋊C4×C157—22no—
36C4⋊C4×C157—22no—
37C4⋊C4×C157—22no—
38C4⋊C4×C157D412yes—
39C22⋊C4×C157—22no—
40C42×C157—22no—
41C22×D157—22no—
42C22×D157—41no—
43C22×D157—41no—
44C22×D157—41no—
45C22×D157—41no—
46C22×D157—41no—
47C22×D157—41no—
48D628—24no—
49D628—42no—
50C2×Dic157—41no—
51C2×Dic157—41no—
52C2×Dic157—41no—
53#11929434—42no—
54C23×C157C2×D411yescharacteristic
55Q8×C157—42no—
56Q8×C157—81no—
57C2×C4×C157—21no—
58C2×C4×C157—21no—
59C2×C4×C157—22no—
60C2×C4×C157—22no—
61C2×C4×C157—21no—
62C2×C4×C157—41no—
63C2×C4×C157—41no—
64C2×C4×C157SD1612yescomplemented
65C2×C4×C157C2×D412yes—
66C22×C157—21no—
67C22×C157—21no—
68C22×C157#12011yescharacteristic
69C22×C157C2×SD1611yescharacteristic
70C22×C157#13711yescharacteristic
71C2×D157—42no—
72C2×D157—42no—
73C2×D157—42no—
74C2×D157—81no—
75C2×D157—81no—
76C2×D157—81no—
77C2×D157—81no—
78C4×C157—22no—
79C4×C157—22no—
80C4×C157—42no—
81C4×C157—41no—
82C4×C157—42no—
83Dic157—81no—
84C2×C157—21no—
85C2×C157—21no—
86C2×C157#44811yescharacteristic
87C2×C157#45411yescharacteristic
88C2×C157B(4,𝔽2)11yescharacteristic
89D157—82no—
90C157#159911yescharacteristic, complemented, Sylow
91#1599—1571nomaximal, Sylow
92#544D15711yescharacteristic, complemented
93#450—1572no—
94#394—1571no—
95#328—1572no—
96#324—1571no—
97C22×D4—1571no—
98C2×SD16—3142no—
99C4⋊Q8—22no—
100#125—22no—
101C22⋊Q8—21no—
102C22⋊Q8C2×D15712yes—
103#117—21no—
104C2×C4⋊C4C2×D15711yescharacteristic
105C2×C22⋊C4—3141no—
106C2×C22⋊C4—3141no—
107#102—3142no—
108C22⋊C8—1572no—
109#95—1571no—
110C24—3141no—
111C2×Q8—21no—
112C2×Q8C22⋊D15712yes—
113C2×D4—3142no—
114C2×D4—6282no—
115C22×C4—3141no—
116C22×C4C22⋊D15711yescharacteristic
117C22×C4C22⋊D15711yescharacteristic
118C22×C4C22×D15711yescharacteristic
119SD16—6284no—
120C2×C8—3142no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—22no—
125C4⋊C4—22no—
126C4⋊C4—22no—
127C4⋊C4C22⋊D15712yes—
128C22⋊C4—22no—
129C22⋊C4—6282no—
130C22⋊C4—6282no—
131C42—22no—
132C23—3142no—
133C23—6281no—
134C23—6281no—
135C23—6281no—
136C23—6281no—
137C23—6281no—
138C23—6281no—
139C23C2×C22⋊D15711yescharacteristic
140Q8—42no—
141Q8—81no—
142D4—3144no—
143D4—6282no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—6281no—
152C2×C4—6281no—
153C2×C4—6281no—
154C2×C4#1457894112yescomplemented
155C2×C4C2×C22⋊D15712yes—
156C8—6282no—
157C22—21no—
158C22—21no—
159C22—6282no—
160C22—6282no—
161C22—6282no—
162C22—12561no—
163C22—12561no—
164C22—12561no—
165C22—12561no—
166C22#1909774011yescharacteristic
167C22C2×#1457894111yescharacteristic
168C22#1909780211yescharacteristic
169C4—22no—
170C4—22no—
171C4—42no—
172C4—41no—
173C4—42no—
174C4—12561no—
175C2—21no—
176C2—21no—
177C2—12562no—
178C2#2375741211yescharacteristic
179C2#2375744611yescharacteristic
180C2#2375746011yescharacteristic
subgroupG/H
centerC22#19097740
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#544×C157C2
socleC22×C157#120
prime radicalC22×D628C22
hypercenter#544D157
hypocenterC157#1599
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
3. #23757010C2semidirect
4. #23756999C2semidirect
5. #544×C157C2semidirect
64. C2×C4×C157SD16semidirect
90. C157#1599semidirect
92. #544D157semidirect
154. C2×C4#14578941semidirect

Maximal subgroups

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

subgroupindex
#237574232
#237571902
#237570102
#237569992
#544×C1572
#1599157