Finite Group Databasebeta

← #34099407

Subgroups — #34099407

Order 20096.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#23757997C211yesmaximal, characteristic
2#23757669C211yesmaximal, characteristic, complemented
3#23757554C211yesmaximal, characteristic
4#23757484C211yesmaximal, characteristic, complemented
5#23757003C211yesmaximal, characteristic, complemented
6#23757000C211yesmaximal, characteristic
7#332×C157C211yesmaximal, characteristic, complemented
8C2×Dic628—21no—
9#19097771C2211yescharacteristic
10#19097766—22no—
11#19097760—21no—
12#19097751—21no—
13Q8×Dic157—21no—
14C4×Dic314C2211yescharacteristic
15C4×D628C2211yescharacteristic
16#19097729—21no—
17#19097705—21no—
18#19097702—22no—
19#19097696—21no—
20#19097693—21no—
21C4×#11929434C2211yescharacteristic
22C4⋊Q8×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4⋊C8×C157C2211yescharacteristic
25C2×Dic314—21no—
26C2×Dic314D411yescharacteristic
27C2×D628D411yescharacteristic
28C2×C4×D157—21no—
29Dic628—42no—
30C2×#11929434—21no—
31C4⋊Dic157—22no—
32C4⋊Dic157—21no—
33C4⋊Dic157—21no—
34C4⋊Dic157D411yescharacteristic
35C4⋊Dic157D411yescharacteristic
36#14578933—21no—
37#14578931—22no—
38#14578931—22no—
39#14578931—21no—
40C4×Dic157—22no—
41C4×Dic157—21no—
42C2×Q8×C157—21no—
43C2×C8×C157—21no—
44C2×C8×C157—21no—
45C4⋊C4×C157—21no—
46C4⋊C4×C157D412yes—
47C42×C157C2311yescharacteristic
48C22×D157—21no—
49Dic314—21no—
50Dic314—21no—
51Dic314—41no—
52Dic314—41no—
53D628—21no—
54D628—21no—
55C2×Dic157—21no—
56C2×Dic157—21no—
57C2×Dic157—21no—
58C2×Dic157—41no—
59C4×D157—41no—
60C4×D157—41no—
61#11929434—22no—
62Q8×C157—41no—
63Q8×C157—41no—
64C2×C4×C157—22no—
65C2×C4×C157C2×D411yescharacteristic
66C2×C4×C157C2×D411yescharacteristic
67C2×C4×C157C2×D411yescharacteristic
68C8×C157—41no—
69C8×C157—41no—
70C22×C157#12011yescharacteristic
71C2×D157—41no—
72C2×D157—41no—
73C2×D157—41no—
74C4×C157—21no—
75C4×C157—42no—
76C4×C157#13511yescharacteristic
77C4×C157#13511yescharacteristic
78C4×C157AGL(1,ℤ/8)11yescharacteristic
79C4×C157#13711yescharacteristic
80Dic157—41no—
81Dic157—41no—
82Dic157—41no—
83Dic157—81no—
84C2×C157#44911yescharacteristic
85C2×C157#45211yescharacteristic
86C2×C157#45611yescharacteristic
87D157—81no—
88C157#165211yescharacteristic, complemented, Sylow
89#1652—1571nomaximal, Sylow
90#556—1571no—
91#498—1571no—
92#474—1571no—
93#462—1571no—
94#332D15711yescharacteristic, complemented
95Q8⋊C8—1571no—
96D4⋊C8—1571no—
97C2×Q16—3141no—
98C4⋊Q8—1571no—
99C4⋊Q8C2×D15711yescharacteristic
100#126—3142no—
101#124—3141no—
102C22⋊Q8—3141no—
103C4×Q8—3141no—
104C4×Q8—1571no—
105C4×D4—1571no—
106#117—3141no—
107#107—3141no—
108#106—3142no—
109C4⋊C8C2×D15711yescharacteristic
110C4⋊C8C2×D15711yescharacteristic
111#103—3141no—
112#102—3141no—
113C4×C8—1571no—
114C2×Q8—21no—
115C2×Q8—3141no—
116C2×Q8—1571no—
117C2×D4—1571no—
118C22×C4—3141no—
119Q16—6282no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—3141no—
123C4⋊C4—21no—
124C4⋊C4—3142no—
125C4⋊C4—3141no—
126C4⋊C4—3141no—
127C4⋊C4—3141no—
128C4⋊C4—1571no—
129C4⋊C4—1571no—
130C4⋊C4D62812yes—
131C22⋊C4—3142no—
132C22⋊C4—3142no—
133C22⋊C4—3141no—
134C42—3142no—
135C42—3141no—
136C42C22×D15711yescharacteristic
137C23—3141no—
138Q8—41no—
139Q8—41no—
140Q8—3141no—
141Q8—3141no—
142Q8—6281no—
143Q8—6281no—
144D4—3141no—
145D4—3141no—
146C2×C4—22no—
147C2×C4—3141no—
148C2×C4—3141no—
149C2×C4—3141no—
150C2×C4—6281no—
151C2×C4—6281no—
152C2×C4—6281no—
153C2×C4D4×D15711yescharacteristic
154C2×C4D4×D15711yescharacteristic
155C2×C4C2×D62811yescharacteristic
156C8—41no—
157C8—41no—
158C8—3142no—
159C22—6281no—
160C22—6281no—
161C22—6281no—
162C22#1909774111yescharacteristic
163C4—21no—
164C4—42no—
165C4—6281no—
166C4—6281no—
167C4—6281no—
168C4—12561no—
169C4#1909779011yescharacteristic
170C4#1909779411yescharacteristic
171C4#1909779811yescharacteristic
172C4#1909780011yescharacteristic
173C2—12561no—
174C2#2375742111yescharacteristic
175C2#2375743611yescharacteristic
176C2#2375745811yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#332×C157C2
socleC22×C157#120
prime radicalC2×D628D4
hypercenter#332D157
hypocenterC157#1652
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #23757669C2semidirect
4. #23757484C2semidirect
5. #23757003C2semidirect
7. #332×C157C2semidirect
88. C157#1652semidirect
94. #332D157semidirect

Maximal subgroups

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

subgroupindex
#237579972
#237576692
#237575542
#237574842
#237570032
#237570002
#332×C1572
#1652157