Finite Group Databasebeta

← #34102103

Subgroups — #34102103

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#23757711C211yesmaximal, characteristic, complemented
3C2×#19097714C211yesmaximal, characteristic, complemented
4#23757544C211yesmaximal, characteristic, complemented
5#23757079C211yesmaximal, characteristic, complemented
6#23757058C211yesmaximal, characteristic, complemented
7#362×C157C211yesmaximal, characteristic, complemented
8#19097819—21no—
9#19097803—22no—
10#19097802—21no—
11#19097799—21no—
12#19097794—21no—
13#19097793C2211yescharacteristic
14Q16×D157—21no—
15C2×D1256C2211yescharacteristic
16#19097777C2211yescharacteristic
17#19097716—21no—
18#19097714—22no—
19D2512—21no—
20C2×#14578929C2211yescharacteristic
21#19097687—21no—
22C2×Q16×C157C2211yescharacteristic
23M32×C157C2211yescharacteristic
24#108×C157C2211yescharacteristic
25#14578955—22no—
26#14578955—41no—
27#14578954—21no—
28#14578954—42no—
29#14578954D411yescharacteristic
30Q8×D157—22no—
31Q8×D157—41no—
32C2×D628—21no—
33Dic628D411yescharacteristic
34#14578944—22no—
35#14578943—21no—
36#14578943—41no—
37#14578941—22no—
38D1256—21no—
39D1256—21no—
40D1256—41no—
41D1256D411yescharacteristic
42#14578938D411yescharacteristic
43#14578937—21no—
44C8×D157—21no—
45#14578929—21no—
46C2×Q8×C157—21no—
47Q16×C157—21no—
48Q16×C157D412yes—
49M16×C157—21no—
50C2×C8×C157C2311yescharacteristic
51C16×C157—21no—
52C22×D157—41no—
53Dic314—21no—
54Dic314—42no—
55Dic314D811yescharacteristic
56D628—21no—
57D628—42no—
58D628—41no—
59D628—41no—
60D628D811yescharacteristic
61C22⋊D157—21no—
62C22⋊D157—41no—
63C4×D157—21no—
64C4×D157—42no—
65C4×D157—42no—
66C4×D157—41no—
67#11929434—21no—
68Q8×C157—22no—
69Q8×C157—41no—
70C2×C4×C157—41no—
71C2×C4×C157C2×D411yescharacteristic
72C8×C157—41no—
73C8×C157C2×D411yescharacteristic
74C8×C157C2×D411yescharacteristic
75C22×C157AGL(1,ℤ/8)11yescharacteristic
76C2×D157—21no—
77C2×D157—41no—
78C2×D157—81no—
79C2×D157—161no—
80C4×C157—42no—
81C4×C157#12011yescharacteristic
82C4×C157C2×D811yescharacteristic
83Dic157—21no—
84Dic157—41no—
85C2×C157—21no—
86C2×C157#44711yescharacteristic
87D157—41no—
88D157—81no—
89D157—161no—
90C157#219311yescharacteristic, complemented, Sylow
91#2193—1571nomaximal, Sylow
92#578—1571no—
93#509—1571no—
94C2×SD32—1571no—
95#472—1571no—
96#362D15711yescharacteristic, complemented
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×D8—1571no—
108#131—1571no—
109SD32—3141no—
110SD32—3142no—
111D16—3141no—
112M32C2×D15711yescharacteristic
113C2×C16—1571no—
114#108C2×D15711yescharacteristic
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—3141no—
125Q16—21no—
126Q16—3142no—
127Q16—1571no—
128Q16D62812yes—
129SD16—3142no—
130SD16—3141no—
131SD16—6281no—
132D8—3141no—
133D8—3141no—
134D8—6281no—
135D8—1571no—
136M16—21no—
137M16—3141no—
138M16—1571no—
139C2×C8—3141no—
140C2×C8C22×D15711yescharacteristic
141C16—21no—
142C16—3141no—
143C23—6281no—
144Q8—22no—
145Q8—41no—
146Q8—3141no—
147Q8—6282no—
148Q8—1571no—
149D4—3141no—
150D4—3141no—
151D4—6282no—
152D4—6281no—
153D4—6281no—
154D4—6281no—
155D4—1571no—
156C2×C4—41no—
157C2×C4—3141no—
158C2×C4—6282no—
159C2×C4—6282no—
160C2×C4—6281no—
161C2×C4D4×D15711yescharacteristic
162C8—41no—
163C8—3141no—
164C8D4×D15711yescharacteristic
165C8C2×D62811yescharacteristic
166C22—3141no—
167C22—6281no—
168C22—25121no—
169C22—12561no—
170C22#1909779811yescharacteristic
171C4—42no—
172C4—3141no—
173C4—6281no—
174C4#1909774111yescharacteristic
175C4D8×D15711yescharacteristic
176C2—21no—
177C2—6281no—
178C2—25121no—
179C2—12561no—
180C2#2375740811yescharacteristic
subgroupG/H
centerC2#23757408
commutator, cosocleC2×C8×C157C23
FrattiniC2×C8C22×D157
Fitting#362×C157C2
socleC2×C157#447
hypercenter#362D157
hypocenterC157#2193
LCSG ▷ C2×C8×C157 ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
1. #23758086C2semidirect
2. #23757711C2semidirect
3. C2×#19097714C2semidirect
4. #23757544C2semidirect
5. #23757079C2semidirect
6. #23757058C2semidirect
7. #362×C157C2semidirect
90. C157#2193semidirect
96. #362D157semidirect

Maximal subgroups

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

subgroupindex
#237580862
#237577112
C2×#190977142
#237575442
#237570792
#237570582
#362×C1572
#2193157