Finite Group Databasebeta

← #34102099

Subgroups — #34102099

Order 20096.

210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 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#23758086C211yesmaximal, characteristic, complemented
2#23757709C211yesmaximal, characteristic, complemented
3#23757540C211yesmaximal, characteristic, complemented
4#23757089C211yesmaximal, characteristic, complemented
5#23757081C211yesmaximal, characteristic, complemented
6#23757056C211yesmaximal, characteristic, complemented
7C2×SD32×C157C211yesmaximal, characteristic, complemented
8#19097819—21no—
9#19097803—22no—
10#19097802—21no—
11#19097797—21no—
12#19097794—21no—
13#19097793C2211yescharacteristic
14Q16×D157—21no—
15#19097777C2211yescharacteristic
16#19097715—21no—
17#19097712—21no—
18#19097711C2211yescharacteristic
19#19097707C2211yescharacteristic
20#19097688—21no—
21C2×Q16×C157C2211yescharacteristic
22C2×D8×C157C2211yescharacteristic
23SD32×C157—22no—
24C2×C16×C157C2211yescharacteristic
25#14578955—22no—
26#14578955—41no—
27#14578954—21no—
28#14578954—42no—
29#14578954D411yescharacteristic
30Q8×D157—22no—
31Q8×D157—41no—
32Dic628D411yescharacteristic
33#14578944—22no—
34#14578943—21no—
35#14578942—41no—
36#14578941—22no—
37D1256D411yescharacteristic
38#14578939—41no—
39#14578938—21no—
40#14578938D411yescharacteristic
41#14578937—21no—
42C8×D157—21no—
43#14578929—21no—
44C2×Q8×C157—21no—
45C2×D4×C157—21no—
46Q16×C157—21no—
47Q16×C157D412yes—
48D8×C157—21no—
49D8×C157—21no—
50C2×C8×C157C2311yescharacteristic
51C16×C157—21no—
52Dic314—21no—
53Dic314—42no—
54Dic314D811yescharacteristic
55D628—21no—
56D628—42no—
57D628D811yescharacteristic
58C22⋊D157—21no—
59C22⋊D157—41no—
60C4×D157—21no—
61C4×D157—42no—
62C4×D157—42no—
63C4×D157—41no—
64#11929434—21no—
65#11929434—41no—
66C23×C157—41no—
67Q8×C157—22no—
68Q8×C157—41no—
69D4×C157—41no—
70D4×C157—41no—
71C2×C4×C157—41no—
72C2×C4×C157C2×D411yescharacteristic
73C8×C157C2×D411yescharacteristic
74C8×C157C2×D411yescharacteristic
75C22×C157—81no—
76C22×C157—161no—
77C22×C157AGL(1,ℤ/8)11yescharacteristic
78C2×D157—21no—
79C2×D157—41no—
80C4×C157—42no—
81C4×C157#12011yescharacteristic
82C4×C157C2×D811yescharacteristic
83Dic157—21no—
84Dic157—41no—
85C2×C157—21no—
86C2×C157—161no—
87C2×C157#44711yescharacteristic
88D157—41no—
89D157—81no—
90C157#219311yescharacteristic, complemented, Sylow
91#2193—1571nomaximal, Sylow
92#578—1571no—
93#509—1571no—
94C2×SD32D15711yescharacteristic, complemented
95#472—1571no—
96#362—1571no—
97#359—1571no—
98#350—1571no—
992−1+4—3141no—
100#137—3142no—
101#137—3141no—
102AGL(1,ℤ/8)—3141no—
103#135—3141no—
104#135—1571no—
105C2×Q16—3141no—
106C2×Q16C2×D15711yescharacteristic
107C2×D8C2×D15711yescharacteristic
108#131—1571no—
109SD32—22no—
110SD32—3141no—
111D16—3141no—
112M32—1571no—
113C2×C16C2×D15711yescharacteristic
114#108—1571no—
115#100—3141no—
116#41—3142no—
117#41—3141no—
118#41—6282no—
119#41—6281no—
120#41—1571no—
121C2×Q8—21no—
122C2×Q8—3142no—
123C2×Q8—6281no—
124C2×D4—21no—
125Q16—21no—
126Q16—3142no—
127Q16—1571no—
128Q16C22⋊D15712yes—
129SD16—3142no—
130SD16—3141no—
131SD16—6281no—
132D8—21no—
133D8—21no—
134D8—6281no—
135D8—1571no—
136M16—3141no—
137M16—3141no—
138M16—1571no—
139C2×C8—3141no—
140C2×C8C22×D15711yescharacteristic
141C16—21no—
142C16—3141no—
143C23—41no—
144Q8—22no—
145Q8—41no—
146Q8—3141no—
147Q8—6282no—
148Q8—1571no—
149D4—41no—
150D4—41no—
151D4—3141no—
152D4—3141no—
153D4—6282no—
154D4—6281no—
155D4—1571no—
156C2×C4—41no—
157C2×C4—3141no—
158C2×C4—6282no—
159C2×C4—6282no—
160C2×C4—6281no—
161C2×C4D4×D15711yescharacteristic
162C8—3141no—
163C8—6281no—
164C8D4×D15711yescharacteristic
165C8C2×C22⋊D15711yescharacteristic
166C22—81no—
167C22—161no—
168C22—3141no—
169C22—6281no—
170C22#1909779511yescharacteristic
171C4—42no—
172C4—3141no—
173C4—6281no—
174C4#1909773911yescharacteristic
175C4D8×D15711yescharacteristic
176C2—21no—
177C2—161no—
178C2—6281no—
179C2—12561no—
180C2#2375740511yescharacteristic
subgroupG/H
centerC2#23757405
commutator, cosocleC2×C8×C157C23
FrattiniC2×C8C22×D157
FittingC2×SD32×C157C2
socleC2×C157#447
hypercenterC2×SD32D157
hypocenterC157#2193
LCSG ▷ C2×C8×C157 ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #23758086C2semidirect
2. #23757709C2semidirect
3. #23757540C2semidirect
4. #23757089C2semidirect
5. #23757081C2semidirect
6. #23757056C2semidirect
7. C2×SD32×C157C2semidirect
90. C157#2193semidirect
94. C2×SD32D157semidirect

Maximal subgroups

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

subgroupindex
#237580862
#237577092
#237575402
#237570892
#237570812
#237570562
C2×SD32×C1572
#2193157