Finite Group Databasebeta

← #34099172

Subgroups — #34099172

Order 20096.

246 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 53 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#23757854C211yesmaximal, characteristic
2#23757591C212yesmaximal, complemented
3#23757006C212yesmaximal, complemented
4#23756999C211yesmaximal, characteristic, complemented
5#400×C157C211yesmaximal, characteristic, complemented
6C2×#14578954—21no—
7#19097751—22no—
8#19097746—22no—
9#19097745—21no—
10#19097745C2212yes—
11#19097702—22no—
12#19097691—22no—
13C22⋊#11929434C2212yes—
14C2×C4⋊C4×C157C2211yescharacteristic
15C2×C4⋊C4×C157C2211yescharacteristic
16#95×C157—21no—
17#95×C157—21no—
18#95×C157C2211yescharacteristic
19#14578954—42no—
20#14578954—42no—
21C2×Dic314—21no—
22C2×D628—21no—
23C2×D628—21no—
24C2×D628D412yes—
25C2×C22⋊D157—22no—
26C2×C4×D157—22no—
27C2×#11929434—22no—
28C4⋊Dic157—21no—
29C4⋊Dic157D412yes—
30#14578931—22no—
31#14578931—22no—
32C22×C4×C157—21no—
33C22×C4×C157—21no—
34C22×C4×C157D411yescharacteristic
35C22×C4×C157D411yescharacteristic
36C22×C4×C157C2311yescharacteristic
37C4⋊C4×C157—22no—
38C4⋊C4×C157—22no—
39C22×D157—22no—
40Dic314—42no—
41D628—42no—
42D628—42no—
43D628—81no—
44C22⋊D157—42no—
45C22⋊D157—42no—
46C2×Dic157—22no—
47C4×D157—44no—
48#11929434—42no—
49C23×C157C2×D411yescharacteristic
50C2×C4×C157—21no—
51C2×C4×C157—21no—
52C2×C4×C157—21no—
53C2×C4×C157—41no—
54C2×C4×C157—41no—
55C2×C4×C157—41no—
56C2×C4×C157—41no—
57C2×C4×C157—42no—
58C2×C4×C157—41no—
59C2×C4×C157—41no—
60C2×C4×C157SD1612yes—
61C2×C4×C157C2×D412yes—
62C22×C157—21no—
63C22×C157—21no—
64C22×C157#12011yescharacteristic
65C22×C157C2×SD1611yescharacteristic
66C22×C157AGL(1,ℤ/8)11yescharacteristic
67C2×D157—42no—
68C2×D157—42no—
69C2×D157—42no—
70C4×C157—22no—
71C4×C157—22no—
72C4×C157—41no—
73C4×C157—81no—
74C4×C157—81no—
75Dic157—42no—
76C2×C157—21no—
77C2×C157—21no—
78C2×C157#45011yescharacteristic
79C2×C157#45411yescharacteristic
80C2×C157#45811yescharacteristic
81D157—82no—
82C157#161611yescharacteristic, complemented, Sylow
83#1616—1571nomaximal, Sylow
84#537—1571no—
85#481—1572no—
86#400D15711yescharacteristic, complemented
87#327—1572no—
88#324—1571no—
89C2×#41—3141no—
90C22⋊Q8—3142no—
91#121—3142no—
92#121—3141no—
93#121—1572no—
94C2×C4⋊C4C2×D15711yescharacteristic
95C2×C4⋊C4C2×D15711yescharacteristic
96#106—3142no—
97#102—3142no—
98C22⋊C8—1572no—
99#95—21no—
100#95—21no—
101#95C2×D15711yescharacteristic
102#41—6282no—
103#41—6282no—
104C2×Q8—3141no—
105C2×D4—3141no—
106C2×D4—3141no—
107C2×D4—3142no—
108C2×D4—1572no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—3142no—
112C22×C4C22⋊D15711yescharacteristic
113C22×C4C22⋊D15711yescharacteristic
114C22×C4C22×D15711yescharacteristic
115C2×C8—3142no—
116C4⋊C4—22no—
117C4⋊C4—22no—
118C4⋊C4—3141no—
119C4⋊C4—1572no—
120C22⋊C4—3142no—
121C22⋊C4—3142no—
122C23—3142no—
123C23C2×C22⋊D15711yescharacteristic
124Q8—6282no—
125D4—6282no—
126D4—6282no—
127D4—6282no—
128D4—6282no—
129D4—12561no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—3142no—
141C2×C4—6284no—
142C2×C4#1457894112yes—
143C2×C4D4×D15712yes—
144C8—6282no—
145C22—21no—
146C22—21no—
147C22—6282no—
148C22—6282no—
149C22—6282no—
150C22#1909773911yescharacteristic
151C22C2×#1457894111yescharacteristic
152C22#1909779611yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—81no—
157C4—81no—
158C4—6282no—
159C2—21no—
160C2—21no—
161C2—12562no—
162C2#2375742311yescharacteristic
163C2#2375744511yescharacteristic
164C2#2375746211yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#400×C157C2
socleC22×C157#120
prime radical#23757854C2
hypercenter#400D157
hypocenterC157#1616
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #23757591C2semidirect
3. #23757006C2semidirect
4. #23756999C2semidirect
5. #400×C157C2semidirect
82. C157#1616semidirect
86. #400D157semidirect

Maximal subgroups

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

subgroupindex
#237578542
#237575912
#237570062
#237569992
#400×C1572
#1616157