Finite Group Databasebeta

← #34102095

Subgroups — #34102095

Order 20096.

220 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 49 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#23758078C211yesmaximal, characteristic, complemented
2#23757711C211yesmaximal, characteristic, complemented
3C2×D2512C211yesmaximal, characteristic, complemented
4#23757543C211yesmaximal, characteristic, complemented
5#23757087C211yesmaximal, characteristic, complemented
6#23757081C211yesmaximal, characteristic, complemented
7#350×C157C211yesmaximal, characteristic, complemented
8#19097817—21no—
9#19097799—22no—
10#19097799—21no—
11#19097796—21no—
12#19097793—21no—
13#19097793C2211yescharacteristic
14C2×D1256—21no—
15C2×D1256C2211yescharacteristic
16C2×D1256C2211yescharacteristic, complemented
17#19097716—21no—
18D2512—22no—
19D2512—21no—
20#19097707C2211yescharacteristic, complemented
21#19097687—21no—
22#131×C157C2211yescharacteristic
23M32×C157C2211yescharacteristic, complemented
24C2×C16×C157C2211yescharacteristic, complemented
25#14578955—41no—
26#14578954—22no—
27#14578954—21no—
28C2×D628—22no—
29C2×D628—21no—
30C2×D628—21no—
31D4×D157—42no—
32D4×D157—41no—
33Dic628D411yescharacteristic
34#14578943—22no—
35#14578943—21no—
36#14578941—41no—
37D1256—22no—
38D1256—21no—
39D1256—21no—
40D1256—21no—
41D1256D411yescharacteristic
42D1256D412yes—
43#14578939—41no—
44#14578938—21no—
45#41×C157D411yescharacteristic
46M16×C157—21no—
47M16×C157D411yescharacteristic
48C2×C8×C157—21no—
49C2×C8×C157C2311yescharacteristic
50C16×C157—21no—
51C16×C157—21no—
52C22×D157—42no—
53C22×D157—41no—
54C22×D157—41no—
55Dic314—21no—
56D628—21no—
57D628—22no—
58D628—42no—
59D628—41no—
60D628—41no—
61D628—41no—
62C22⋊D157—42no—
63C22⋊D157—41no—
64C4×D157—42no—
65C4×D157—41no—
66#11929434—41no—
67Q8×C157D811yescharacteristic
68D4×C157—21no—
69D4×C157D811yescharacteristic
70C2×C4×C157—21no—
71C2×C4×C157C2×D411yescharacteristic
72C8×C157—21no—
73C8×C157C2×D411yescharacteristic
74C8×C157C2×D411yescharacteristic
75C22×C157—21no—
76C22×C157AGL(1,ℤ/8)11yescharacteristic
77C2×D157—42no—
78C2×D157—41no—
79C2×D157—81no—
80C2×D157—161no—
81C2×D157—162no—
82C2×D157—161no—
83C4×C157—21no—
84C4×C157#12011yescharacteristic
85C4×C157C2×D811yescharacteristic
86Dic157—41no—
87C2×C157—21no—
88C2×C157—41no—
89C2×C157#44711yescharacteristic
90D157—82no—
91D157—81no—
92D157—161no—
93C157#219211yescharacteristic, complemented, Sylow
94#2192—1571nomaximal, Sylow
95#576—1571no—
96#509—1571no—
97C2×D16—1571no—
98#472—1571no—
99#361—1571no—
100#359—1571no—
101#350D15711yescharacteristic, complemented
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×D8—1571no—
110C2×D8—1571no—
111#131C2×D15711yescharacteristic
112SD32—3141no—
113D16—3142no—
114D16—3141no—
115M32C2×D15711yescharacteristic, complemented
116C2×C16C2×D15711yescharacteristic, complemented
117#108—1571no—
118#100—3141no—
119#41—3142no—
120#41—3141no—
121#41—6281no—
122#41D62811yescharacteristic
123C2×D4—3142no—
124C2×D4—3141no—
125C2×D4—3141no—
126C2×D4—6282no—
127C2×D4—6281no—
128Q16—1571no—
129SD16—3142no—
130SD16—3141no—
131SD16—6281no—
132D8—3142no—
133D8—3141no—
134D8—3141no—
135D8—3141no—
136D8—6281no—
137D8—1571no—
138D8—1572no—
139M16—21no—
140M16—3141no—
141M16D62811yescharacteristic
142C2×C8—21no—
143C2×C8C22×D15711yescharacteristic
144C16—21no—
145C16—21no—
146C23—6282no—
147C23—6281no—
148C23—6281no—
149Q8—3141no—
150Q8D125611yescharacteristic
151D4—21no—
152D4—3141no—
153D4—3142no—
154D4—6282no—
155D4—6282no—
156D4—6281no—
157D4—6281no—
158D4—6281no—
159D4—6281no—
160D4D125611yescharacteristic
161C2×C4—21no—
162C2×C4—6282no—
163C2×C4—6281no—
164C2×C4C2×D62811yescharacteristic
165C8—21no—
166C8—6281no—
167C8D4×D15711yescharacteristic
168C8D4×D15711yescharacteristic
169C22—21no—
170C22—6282no—
171C22—6281no—
172C22—25121no—
173C22—25121no—
174C22—25122no—
175C22—12561no—
176C22#1909779911yescharacteristic
177C4—21no—
178C4—6281no—
179C4#1909774111yescharacteristic
180C4C2×D125611yescharacteristic
181C2—21no—
182C2—41no—
183C2—25121no—
184C2—12562no—
185C2—12561no—
186C2#2375740911yescharacteristic
subgroupG/H
centerC2#23757409
commutator, cosocleC2×C8×C157C23
FrattiniC2×C8C22×D157
Fitting#350×C157C2
socleC2×C157#447
hypercenter#350D157
hypocenterC157#2192
LCSG ▷ C2×C8×C157 ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #350

Complements

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

NH ≅ G/Ntype
1. #23758078C2semidirect
2. #23757711C2semidirect
3. C2×D2512C2semidirect
4. #23757543C2semidirect
5. #23757087C2semidirect
6. #23757081C2semidirect
7. #350×C157C2semidirect
16. C2×D1256C22semidirect
20. #19097707C22semidirect
23. M32×C157C22semidirect
24. C2×C16×C157C22semidirect
93. C157#2192semidirect
101. #350D157semidirect
115. M32C2×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
#237580782
#237577112
C2×D25122
#237575432
#237570872
#237570812
#350×C1572
#2192157