Finite Group Databasebeta

← #34102092

Subgroups — #34102092

Order 20096.

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

normal subgroups only

This group has 220 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#23758074C211yesmaximal, characteristic, complemented
2#23757709C211yesmaximal, characteristic, complemented
3#23757540C211yesmaximal, characteristic, complemented
4#23757086C211yesmaximal, characteristic, complemented
5#23757081C211yesmaximal, characteristic, complemented
6#23757056C211yesmaximal, characteristic, complemented
7C2×D16×C157C211yesmaximal, characteristic, complemented
8#19097816—21no—
9#19097797—21no—
10#19097797—21no—
11#19097795—22no—
12#19097793C2211yescharacteristic
13#19097790—21no—
14D8×D157—21no—
15#19097777C2211yescharacteristic
16#19097715—21no—
17#19097712—21no—
18#19097711C2211yescharacteristic, complemented
19#19097707C2211yescharacteristic, complemented
20#19097688—21no—
21C2×D8×C157C2211yescharacteristic
22C2×D8×C157C2211yescharacteristic, complemented
23D16×C157—22no—
24C2×C16×C157C2211yescharacteristic, complemented
25#14578954—21no—
26#14578954D411yescharacteristic
27#14578953—22no—
28#14578953—41no—
29C2×C22⋊D157—42no—
30D4×D157—22no—
31D4×D157—41no—
32Dic628D411yescharacteristic
33#14578943—21no—
34#14578942—22no—
35#14578942—41no—
36D1256D411yescharacteristic
37#14578939—22no—
38#14578939—41no—
39#14578938—21no—
40#14578938D411yescharacteristic
41#14578937—21no—
42C8×D157—21no—
43#14578929—21no—
44C2×D4×C157—21no—
45C2×D4×C157—21no—
46D8×C157—21no—
47D8×C157—21no—
48D8×C157—21no—
49D8×C157D412yes—
50C2×C8×C157C2311yescharacteristic
51C16×C157—21no—
52C22×D157—42no—
53Dic314—21no—
54Dic314D811yescharacteristic
55D628—21no—
56D628D811yescharacteristic
57C22⋊D157—21no—
58C22⋊D157—42no—
59C22⋊D157—42no—
60C22⋊D157—41no—
61C2×Dic157—42no—
62C4×D157—21no—
63C4×D157—41no—
64#11929434—21no—
65#11929434—41no—
66C23×C157—41no—
67C23×C157—41no—
68D4×C157—22no—
69D4×C157—41no—
70D4×C157—41no—
71D4×C157—41no—
72C2×C4×C157C2×D411yescharacteristic
73C8×C157C2×D411yescharacteristic
74C8×C157C2×D411yescharacteristic
75C22×C157—42no—
76C22×C157—81no—
77C22×C157—161no—
78C22×C157—161no—
79C22×C157AGL(1,ℤ/8)11yescharacteristic
80C2×D157—21no—
81C2×D157—41no—
82C2×D157—162no—
83C4×C157#12011yescharacteristic
84C4×C157C2×D811yescharacteristic
85Dic157—21no—
86Dic157—41no—
87C2×C157—21no—
88C2×C157—82no—
89C2×C157—161no—
90C2×C157#44711yescharacteristic
91D157—41no—
92D157—81no—
93C157#219211yescharacteristic, complemented, Sylow
94#2192—1571nomaximal, Sylow
95#576—1571no—
96#509—1571no—
97C2×D16D15711yescharacteristic, complemented
98#472—1571no—
99#361—1571no—
100#359—1571no—
101#350—1571no—
102H(5,𝔽2)—3141no—
103AGL(1,ℤ/8)—3142no—
104AGL(1,ℤ/8)—3141no—
105AGL(1,ℤ/8)—3141no—
106#135—3141no—
107#135—1571no—
108C2×D8—3141no—
109C2×D8C2×D15711yescharacteristic
110C2×D8C2×D15711yescharacteristic, complemented
111#131—1571no—
112SD32—3141no—
113D16—22no—
114D16—3141no—
115M32—1571no—
116C2×C16C2×D15711yescharacteristic, complemented
117#108—1571no—
118#100—3141no—
119#41—3142no—
120#41—3141no—
121#41—6281no—
122#41—1571no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—3142no—
126C2×D4—6281no—
127C2×D4—6282no—
128Q16—1571no—
129SD16—3142no—
130SD16—3141no—
131SD16—6281no—
132D8—21no—
133D8—21no—
134D8—21no—
135D8—3142no—
136D8—6281no—
137D8—1571no—
138D8C22⋊D15712yes—
139M16—3141no—
140M16—3141no—
141M16—1571no—
142C2×C8—3141no—
143C2×C8C22×D15711yescharacteristic
144C16—21no—
145C16—3141no—
146C23—41no—
147C23—41no—
148C23—6282no—
149Q8—3141no—
150Q8—1571no—
151D4—22no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—3141no—
156D4—3141no—
157D4—6282no—
158D4—6282no—
159D4—6281no—
160D4—1571no—
161C2×C4—3141no—
162C2×C4—6282no—
163C2×C4—6281no—
164C2×C4D4×D15711yescharacteristic
165C8—3141no—
166C8—6281no—
167C8D4×D15711yescharacteristic
168C8C2×C22⋊D15711yescharacteristic
169C22—42no—
170C22—81no—
171C22—161no—
172C22—161no—
173C22—3141no—
174C22—6281no—
175C22—25122no—
176C22#1909779511yescharacteristic
177C4—3141no—
178C4—6281no—
179C4#1909773911yescharacteristic
180C4D8×D15711yescharacteristic
181C2—21no—
182C2—82no—
183C2—161no—
184C2—6281no—
185C2—12561no—
186C2#2375740511yescharacteristic
subgroupG/H
centerC2#23757405
commutator, cosocleC2×C8×C157C23
FrattiniC2×C8C22×D157
FittingC2×D16×C157C2
socleC2×C157#447
hypercenterC2×D16D157
hypocenterC157#2192
LCSG ▷ C2×C8×C157 ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #23758074C2semidirect
2. #23757709C2semidirect
3. #23757540C2semidirect
4. #23757086C2semidirect
5. #23757081C2semidirect
6. #23757056C2semidirect
7. C2×D16×C157C2semidirect
18. #19097711C22semidirect
19. #19097707C22semidirect
22. C2×D8×C157C22semidirect
24. C2×C16×C157C22semidirect
93. C157#2192semidirect
97. C2×D16D157semidirect
110. C2×D8C2×D157semidirect
116. C2×C16C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237580742
#237577092
#237575402
#237570862
#237570812
#237570562
C2×D16×C1572
#2192157