Finite Group Databasebeta

← #34099320

Subgroups — #34099320

Order 20096.

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

normal subgroups only

This group has 212 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#23758008C211yesmaximal, characteristic
2#23757621C211yesmaximal, characteristic
3#23757555C211yesmaximal, characteristic, complemented
4#23757016C211yesmaximal, characteristic
5Q8⋊#11929434C211yesmaximal, characteristic, complemented
6#23757003C211yesmaximal, characteristic, complemented
7#462×C157C211yesmaximal, characteristic, complemented
8#19097768C2211yescharacteristic
9#19097760—21no—
10#19097759—21no—
11#19097756—22no—
12C4×Dic314C2211yescharacteristic
13C4×D628—21no—
14#19097733—21no—
15#19097702—21no—
16C4⋊#11929434C2211yescharacteristic
17#19097694—21no—
18#19097691—22no—
19C4×#11929434C2211yescharacteristic
20C2×Q16×C157—21no—
21C4⋊Q8×C157C2211yescharacteristic
22C4×Q8×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24#103×C157—21no—
25C2×Dic314D411yescharacteristic
26C2×D628—21no—
27C2×D628—21no—
28C2×D628D412yes—
29C2×C4×D157—22no—
30C2×#11929434—21no—
31C2×#11929434—21no—
32C4⋊Dic157D411yescharacteristic
33#14578933—21no—
34#14578931—22no—
35#14578931—22no—
36#14578931—22no—
37C4×Dic157—21no—
38C2×Q8×C157—21no—
39C2×Q8×C157D411yescharacteristic
40Q16×C157—42no—
41C2×C8×C157—21no—
42C4⋊C4×C157—21no—
43C4⋊C4×C157—21no—
44C4⋊C4×C157—21no—
45C4⋊C4×C157D411yescharacteristic
46C42×C157—21no—
47C42×C157C2311yescharacteristic
48C22×D157—22no—
49Dic314—21no—
50Dic314—21no—
51D628—42no—
52D628—41no—
53D628—41no—
54D628—41no—
55D628—41no—
56C2×Dic157—21no—
57C2×Dic157—21no—
58C4×D157—82no—
59#11929434—41no—
60#11929434—41no—
61Q8×C157—21no—
62Q8×C157—21no—
63Q8×C157—41no—
64Q8×C157—41no—
65C2×C4×C157—21no—
66C2×C4×C157—21no—
67C2×C4×C157—41no—
68C2×C4×C157C2×D411yescharacteristic
69C2×C4×C157C2×D411yescharacteristic
70C2×C4×C157C2×D411yescharacteristic
71C8×C157—41no—
72C22×C157#12011yescharacteristic
73C2×D157—42no—
74C2×D157—42no—
75C2×D157—42no—
76C4×C157—21no—
77C4×C157—41no—
78C4×C157—41no—
79C4×C157—81no—
80C4×C157#13511yescharacteristic
81C4×C157#13511yescharacteristic
82C4×C157AGL(1,ℤ/8)11yescharacteristic
83C4×C157#13711yescharacteristic
84Dic157—41no—
85Dic157—41no—
86C2×C157#44911yescharacteristic
87C2×C157#45211yescharacteristic
88C2×C157#45511yescharacteristic
89D157—82no—
90C157#164011yescharacteristic, complemented, Sylow
91#1640—1571nomaximal, Sylow
92#559—1571no—
93#486—1571no—
94#475—1571no—
95#462D15711yescharacteristic, complemented
96#331—1571no—
97Q8⋊C8—1571no—
98Q8⋊C8—1571no—
99C2×Q16—21no—
100C4⋊Q8C2×D15711yescharacteristic
101#127—1571no—
102#124—3141no—
103#124—3141no—
104#123—3142no—
105C4×Q8—1571no—
106C4×Q8C2×D15711yescharacteristic
107C4×D4—3141no—
108C4×D4—3141no—
109#106—3141no—
110C4⋊C8—1571no—
111C4⋊C8C2×D15711yescharacteristic
112#103—21no—
113#103—3141no—
114#102—3142no—
115C4×C8—1571no—
116C2×Q8—21no—
117C2×Q8—1571no—
118C2×Q8C22⋊D15711yescharacteristic
119C2×D4—3141no—
120C2×D4—3141no—
121C2×D4—1572no—
122C22×C4—3142no—
123Q16—42no—
124C2×C8—21no—
125C2×C8—3141no—
126C2×C8—3141no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—3141no—
131C4⋊C4—1571no—
132C4⋊C4C22⋊D15711yescharacteristic
133C22⋊C4—3142no—
134C22⋊C4—3142no—
135C22⋊C4—3142no—
136C42—21no—
137C42—3141no—
138C42C22×D15711yescharacteristic
139C23—3142no—
140Q8—21no—
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—3141no—
145Q8—3141no—
146D4—6282no—
147D4—6281no—
148D4—6281no—
149D4—6281no—
150D4—6281no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—3141no—
155C2×C4—3141no—
156C2×C4—12562no—
157C2×C4D4×D15711yescharacteristic
158C2×C4D4×D15711yescharacteristic
159C2×C4C2×C22⋊D15711yescharacteristic
160C8—41no—
161C8—6281no—
162C8—6281no—
163C22—6282no—
164C22—6282no—
165C22—6282no—
166C22#1909773911yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—81no—
171C4—6281no—
172C4—6281no—
173C4#1909779111yescharacteristic
174C4#1909779411yescharacteristic
175C4#1909779711yescharacteristic
176C4#1909780311yescharacteristic
177C2—12562no—
178C2#2375741611yescharacteristic
179C2#2375743411yescharacteristic
180C2#2375744911yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#462×C157C2
socleC22×C157#120
prime radical#19097768C22
hypercenter#462D157
hypocenterC157#1640
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. #23757555C2semidirect
5. Q8⋊#11929434C2semidirect
6. #23757003C2semidirect
7. #462×C157C2semidirect
90. C157#1640semidirect
95. #462D157semidirect

Maximal subgroups

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

subgroupindex
#237580082
#237576212
#237575552
#237570162
Q8⋊#119294342
#237570032
#462×C1572
#1640157