Finite Group Databasebeta

← #34099138

Subgroups — #34099138

Order 20096.

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

normal subgroups only

This group has 254 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#23757586C212yesmaximal, complemented
3#23757006C212yesmaximal, complemented
4#23756999C211yesmaximal, characteristic, complemented
5#398×C157C211yesmaximal, characteristic, complemented
6C2×#14578954—21no—
7#19097751—22no—
8#19097746—22no—
9#19097745—21no—
10#19097745C2212yes—
11#19097704—22no—
12#19097691—22no—
13C22⋊#11929434C2212yes—
14C2×C4⋊C4×C157—21no—
15C2×C4⋊C4×C157C2211yescharacteristic
16C2×C4⋊C4×C157C2211yescharacteristic
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—
39C4⋊C4×C157—42no—
40C22×D157—22no—
41Dic314—42no—
42D628—42no—
43D628—42no—
44D628—81no—
45C22⋊D157—42no—
46C22⋊D157—42no—
47C2×Dic157—22no—
48C4×D157—44no—
49#11929434—42no—
50C23×C157C2×D411yescharacteristic
51C2×C4×C157—21no—
52C2×C4×C157—21no—
53C2×C4×C157—22no—
54C2×C4×C157—21no—
55C2×C4×C157—41no—
56C2×C4×C157—41no—
57C2×C4×C157—41no—
58C2×C4×C157—41no—
59C2×C4×C157—41no—
60C2×C4×C157—41no—
61C2×C4×C157—41no—
62C2×C4×C157D812yes—
63C2×C4×C157C2×D412yes—
64C22×C157—21no—
65C22×C157—21no—
66C22×C157#12011yescharacteristic
67C22×C157C2×D811yescharacteristic
68C22×C157AGL(1,ℤ/8)11yescharacteristic
69C2×D157—42no—
70C2×D157—42no—
71C2×D157—42no—
72C4×C157—22no—
73C4×C157—22no—
74C4×C157—42no—
75C4×C157—41no—
76C4×C157—81no—
77Dic157—42no—
78C2×C157—21no—
79C2×C157—21no—
80C2×C157#44711yescharacteristic
81C2×C157#45611yescharacteristic
82C2×C157#45811yescharacteristic
83D157—82no—
84C157#161011yescharacteristic, complemented, Sylow
85#1610—1571nomaximal, Sylow
86#537—1571no—
87#480—1572no—
88#398D15711yescharacteristic, complemented
89#327—1572no—
90#324—1571no—
91C2×#41—3141no—
92C22⋊Q8—3142no—
93#121—3142no—
94#121—3141no—
95#121—1572no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4C2×D15711yescharacteristic
98C2×C4⋊C4C2×D15711yescharacteristic
99#107—3142no—
100#102—3142no—
101C22⋊C8—1572no—
102#95—21no—
103#95C2×D15711yescharacteristic
104#41—6282no—
105#41—6282no—
106C2×Q8—3141no—
107C2×D4—3141no—
108C2×D4—3141no—
109C2×D4—3142no—
110C2×D4—1572no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—3142no—
114C22×C4C22⋊D15711yescharacteristic
115C22×C4C22⋊D15711yescharacteristic
116C22×C4C22×D15711yescharacteristic
117C2×C8—3142no—
118C4⋊C4—22no—
119C4⋊C4—22no—
120C4⋊C4—42no—
121C4⋊C4—3141no—
122C4⋊C4—1572no—
123C22⋊C4—3142no—
124C22⋊C4—3142no—
125C23—3142no—
126C23C2×C22⋊D15711yescharacteristic
127Q8—6282no—
128D4—6282no—
129D4—6282no—
130D4—6282no—
131D4—6282no—
132D4—12561no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—3142no—
145C2×C4—6284no—
146C2×C4#1457893912yes—
147C2×C4D4×D15712yes—
148C8—6282no—
149C22—21no—
150C22—21no—
151C22—6282no—
152C22—6282no—
153C22—6282no—
154C22#1909773911yescharacteristic
155C22C2×#1457893911yescharacteristic
156C22#1909779611yescharacteristic
157C4—22no—
158C4—22no—
159C4—42no—
160C4—41no—
161C4—81no—
162C4—6282no—
163C2—21no—
164C2—21no—
165C2—12562no—
166C2#2375740611yescharacteristic
167C2#2375745511yescharacteristic
168C2#2375746211yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#398×C157C2
socleC22×C157#120
prime radical#23757854C2
hypercenter#398D157
hypocenterC157#1610
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
2. #23757586C2semidirect
3. #23757006C2semidirect
4. #23756999C2semidirect
5. #398×C157C2semidirect
84. C157#1610semidirect
88. #398D157semidirect

Maximal subgroups

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

subgroupindex
#237578542
#237575862
#237570062
#237569992
#398×C1572
#1610157