Finite Group Databasebeta

← #34102084

Subgroups — #34102084

Order 20096.

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

normal subgroups only

This group has 226 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#23758073C211yesmaximal, characteristic, complemented
2#23757711C212yesmaximal, complemented
3#23757526C211yesmaximal, characteristic, complemented
4#23757084C212yesmaximal, complemented
5#349×C157C211yesmaximal, characteristic, complemented
6C2×#14578954—21no—
7#19097804—22no—
8#19097799—22no—
9#19097793—21no—
10#19097793C2212yes—
11C2×D1256C2211yescharacteristic, complemented
12#19097745—21no—
13#19097716—22no—
14D2512—22no—
15#19097703C2211yescharacteristic, complemented
16#19097693—21no—
17C2×M16×C157C2211yescharacteristic
18M32×C157C2212yescomplemented
19#14578954—22no—
20#14578954—22no—
21#14578954—41no—
22#14578954—41no—
23C2×Dic314—21no—
24C2×D628—21no—
25C2×D628—21no—
26C2×C22⋊D157—41no—
27C2×C22⋊D157—41no—
28C2×C4×D157—41no—
29Dic628—21no—
30Dic628D412yescomplemented
31#14578943—22no—
32#14578943—22no—
33D1256—21no—
34D1256—22no—
35D1256D412yescomplemented
36C4⋊Dic157—21no—
37#14578931—41no—
38C22×C4×C157D411yescharacteristic
39M16×C157—22no—
40C2×C8×C157D411yescharacteristic
41C2×C8×C157C2311yescharacteristic
42C16×C157—22no—
43C22×D157—41no—
44C22×D157—41no—
45Dic314—22no—
46Dic314—41no—
47D628—22no—
48D628—41no—
49D628—41no—
50D628—41no—
51C22⋊D157—42no—
52C22⋊D157—42no—
53C22⋊D157—82no—
54C2×Dic157—41no—
55C2×Dic157—41no—
56C4×D157—42no—
57C4×D157—42no—
58C23×C157D811yescharacteristic
59C2×C4×C157—21no—
60C2×C4×C157—21no—
61C2×C4×C157D811yescharacteristic
62C2×C4×C157C2×D411yescharacteristic
63C8×C157—21no—
64C8×C157C2×D412yes—
65C22×C157—21no—
66C22×C157—41no—
67C22×C157C2×D811yescharacteristic
68C2×D157—42no—
69C2×D157—82no—
70C2×D157—81no—
71C2×D157—81no—
72C2×D157—81no—
73C4×C157—21no—
74C4×C157#12011yescharacteristic
75C4×C157AGL(1,ℤ/8)11yescharacteristic
76Dic157—42no—
77Dic157—81no—
78C2×C157—21no—
79C2×C157—41no—
80C2×C157#44711yescharacteristic
81D157—82no—
82D157—161no—
83C157#219011yescharacteristic, complemented, Sylow
84#2190—1571nomaximal, Sylow
85#575—1571no—
86#509—1572no—
87#469—1571no—
88#360—1572no—
89#349D15711yescharacteristic, complemented
90C2×#41—3141no—
91#137—3142no—
92AGL(1,ℤ/8)—3142no—
93#135—3141no—
94#135—1572no—
95C2×D8—1571no—
96C2×M16C2×D15711yescharacteristic
97#121—3141no—
98SD32—3142no—
99D16—3142no—
100M32C2×D15712yescomplemented
101#106—1571no—
102#102—3141no—
103#41—3142no—
104#41—3142no—
105#41—6281no—
106#41—6281no—
107C2×Q8—3141no—
108C2×D4—3141no—
109C2×D4—3141no—
110C2×D4—6281no—
111C2×D4—6281no—
112C22×C4—6281no—
113C22×C4D62811yescharacteristic
114Q16—3141no—
115Q16—1572no—
116SD16—3142no—
117SD16—3142no—
118D8—3141no—
119D8—3142no—
120D8—1572no—
121M16—22no—
122C2×C8D62811yescharacteristic
123C2×C8C22×D15711yescharacteristic
124C4⋊C4—3141no—
125C22⋊C4—6281no—
126C16—22no—
127C23—6281no—
128C23—6281no—
129C23D125611yescharacteristic
130Q8—3142no—
131Q8—6281no—
132D4—3142no—
133D4—6281no—
134D4—6282no—
135D4—6282no—
136D4—6281no—
137D4—6281no—
138D4—12562no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—6282no—
142C2×C4—6281no—
143C2×C4—6282no—
144C2×C4—6281no—
145C2×C4D125611yescharacteristic
146C2×C4C2×D62811yescharacteristic
147C8—21no—
148C8D4×D15712yes—
149C22—21no—
150C22—41no—
151C22—6282no—
152C22—12561no—
153C22—12561no—
154C22—12562no—
155C22—12561no—
156C22C2×D125611yescharacteristic
157C4—21no—
158C4—6282no—
159C4—12561no—
160C4#1909774111yescharacteristic
161C4#1909779911yescharacteristic
162C2—21no—
163C2—41no—
164C2—25121no—
165C2—12562no—
166C2#2375740911yescharacteristic
subgroupG/H
centerC2#23757409
commutator, cosocleC2×C8×C157C23
FrattiniC2×C8C22×D157
Fitting#349×C157C2
socleC2×C157#447
hypercenter#349D157
hypocenterC157#2190
LCSG ▷ C2×C8×C157 ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
1. #23758073C2semidirect
2. #23757711C2semidirect
3. #23757526C2semidirect
4. #23757084C2semidirect
5. #349×C157C2semidirect
11. C2×D1256C22semidirect
15. #19097703C22semidirect
18. M32×C157C22semidirect
30. Dic628D4semidirect
35. D1256D4semidirect
83. C157#2190semidirect
89. #349D157semidirect
100. M32C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237580732
#237577112
#237575262
#237570842
#349×C1572
#2190157