Finite Group Databasebeta

← #34099129

Subgroups — #34099129

Order 20096.

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

normal subgroups only

This group has 228 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#23757899C211yesmaximal, characteristic
2#23757604C212yesmaximal, complemented
3#23757198C211yesmaximal, characteristic
4#23757011C212yesmaximal, complemented
5#323×C157C211yesmaximal, characteristic
6#19097750—21no—
7#19097750C2212yes—
8#19097748—22no—
9#19097748—22no—
10C2×C4⋊Dic157C2211yescharacteristic
11C2×C22⋊Dic157—21no—
12C2×C22⋊Dic157—21no—
13#19097703—22no—
14#19097696—22no—
15#19097678—21no—
16#19097678C2211yescharacteristic
17C2×C22⋊C4×C157C2211yescharacteristic
18C22⋊C8×C157C2212yes—
19C2×Dic314—21no—
20C2×Dic314D412yes—
21C22×Dic157—21no—
22C22×Dic157—21no—
23C22×Dic157—21no—
24C22×Dic157—21no—
25C4⋊Dic157—21no—
26C4⋊Dic157—22no—
27C4⋊Dic157D412yes—
28#14578933—22no—
29#14578933—22no—
30C22⋊Dic157—22no—
31C22⋊Dic157—22no—
32C22⋊Dic157—42no—
33C24×C157D411yescharacteristic
34C22×C4×C157D411yescharacteristic
35C22×C4×C157C2311yescharacteristic
36C2×C8×C157—22no—
37C22⋊C4×C157—22no—
38Dic314—42no—
39Dic314—81no—
40C2×Dic157—22no—
41C2×Dic157—22no—
42C2×Dic157—41no—
43C2×Dic157—41no—
44C2×Dic157—41no—
45C2×Dic157—41no—
46C2×Dic157—41no—
47C2×Dic157—41no—
48C2×Dic157—81no—
49C2×Dic157—81no—
50C23×C157—21no—
51C23×C157—21no—
52C23×C157—41no—
53C23×C157—41no—
54C23×C157SD1612yes—
55C23×C157C2×D411yescharacteristic
56C2×C4×C157—21no—
57C2×C4×C157—41no—
58C2×C4×C157—41no—
59C2×C4×C157C2×D412yes—
60C8×C157—42no—
61C22×C157—21no—
62C22×C157—21no—
63C22×C157—22no—
64C22×C157—42no—
65C22×C157—41no—
66C22×C157—41no—
67C22×C157—81no—
68C22×C157#12011yescharacteristic
69C22×C157C2×SD1611yescharacteristic
70C22×C157#13711yescharacteristic
71C4×C157—22no—
72C4×C157—41no—
73Dic157—42no—
74Dic157—42no—
75Dic157—81no—
76Dic157—81no—
77C2×C157—21no—
78C2×C157—21no—
79C2×C157—42no—
80C2×C157#44811yescharacteristic
81C2×C157#45511yescharacteristic
82C2×C157#45811yescharacteristic
83C157#160811yescharacteristic, complemented, Sylow
84#1608—1571nomaximal, Sylow
85#543—1571no—
86#483—1572no—
87#397—1571no—
88#328—1572no—
89#323D15711yescharacteristic
90C22⋊Q8—3142no—
91C22⋊Q8—3142no—
92C22⋊Q8—3141no—
93C22⋊Q8—1572no—
94C2×C4⋊C4—1571no—
95C2×C22⋊C4—3141no—
96C2×C22⋊C4—3141no—
97C2×C22⋊C4C2×D15711yescharacteristic
98#106—3142no—
99#103—3142no—
100C22⋊C8C2×D15712yes—
101#95—3141no—
102#95—1571no—
103C24D62811yescharacteristic
104C2×Q8—3141no—
105C2×Q8—1572no—
106C22×C4—3141no—
107C22×C4—3141no—
108C22×C4—3141no—
109C22×C4—3141no—
110C22×C4D62811yescharacteristic
111C22×C4C22×D15711yescharacteristic
112C2×C8—22no—
113C4⋊C4—3142no—
114C4⋊C4—3141no—
115C4⋊C4—3142no—
116C4⋊C4—3142no—
117C4⋊C4—1572no—
118C22⋊C4—22no—
119C22⋊C4—3142no—
120C22⋊C4—3142no—
121C22⋊C4—6282no—
122C23—21no—
123C23—21no—
124C23—41no—
125C23—41no—
126C23#1457894312yes—
127C23C2×D62811yescharacteristic
128Q8—6282no—
129Q8—12561no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—3142no—
134C2×C4—3142no—
135C2×C4—6281no—
136C2×C4—6281no—
137C2×C4—6281no—
138C2×C4—6281no—
139C2×C4—6281no—
140C2×C4—6281no—
141C2×C4—12561no—
142C2×C4—12561no—
143C2×C4D4×D15712yes—
144C8—42no—
145C22—21no—
146C22—21no—
147C22—22no—
148C22—42no—
149C22—41no—
150C22—41no—
151C22—81no—
152C22#1909774111yescharacteristic
153C22C2×#1457894311yescharacteristic
154C22#1909780411yescharacteristic
155C4—22no—
156C4—41no—
157C4—6282no—
158C4—6282no—
159C4—12561no—
160C4—12561no—
161C2—21no—
162C2—21no—
163C2—42no—
164C2#2375741411yescharacteristic
165C2#2375745311yescharacteristic
166C2#2375746411yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#323×C157C2
socleC22×C157#120
prime radicalC24×C157D4
hypercenter#323D157
hypocenterC157#1608
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #23757604C2semidirect
4. #23757011C2semidirect
83. C157#1608semidirect

Maximal subgroups

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

subgroupindex
#237578992
#237576042
#237571982
#237570112
#323×C1572
#1608157