Finite Group Databasebeta

← #34099163

Subgroups — #34099163

Order 20096.

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

normal subgroups only

This group has 236 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#23757609C212yesmaximal, complemented
3#23757209C211yesmaximal, characteristic
4#23757011C212yesmaximal, complemented
5#323×C157C211yesmaximal, characteristic
6#19097750—21no—
7#19097750C2212yes—
8#19097748—22no—
9#19097748—22no—
10C2×C4⋊Dic157C2211yescharacteristic
11C2×#14578933—21no—
12C2×C22⋊Dic157—21no—
13C2×C22⋊Dic157—21no—
14#19097705—22no—
15#19097696—22no—
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—
30#14578933—42no—
31C22⋊Dic157—22no—
32C22⋊Dic157—22no—
33C22⋊Dic157—42no—
34C24×C157D411yescharacteristic
35C22×C4×C157D411yescharacteristic
36C22×C4×C157C2311yescharacteristic
37C2×C8×C157—22no—
38C22⋊C4×C157—22no—
39Dic314—42no—
40Dic314—81no—
41C2×Dic157—22no—
42C2×Dic157—22no—
43C2×Dic157—22no—
44C2×Dic157—41no—
45C2×Dic157—41no—
46C2×Dic157—41no—
47C2×Dic157—41no—
48C2×Dic157—41no—
49C2×Dic157—81no—
50C2×Dic157—81no—
51C23×C157—21no—
52C23×C157—21no—
53C23×C157—41no—
54C23×C157—41no—
55C23×C157Q1612yes—
56C23×C157C2×D411yescharacteristic
57C2×C4×C157—21no—
58C2×C4×C157—41no—
59C2×C4×C157—41no—
60C2×C4×C157C2×D412yes—
61C8×C157—42no—
62C22×C157—21no—
63C22×C157—21no—
64C22×C157—22no—
65C22×C157—42no—
66C22×C157—41no—
67C22×C157—41no—
68C22×C157—81no—
69C22×C157#12011yescharacteristic
70C22×C157C2×Q1611yescharacteristic
71C22×C157#13711yescharacteristic
72C4×C157—22no—
73C4×C157—41no—
74Dic157—42no—
75Dic157—42no—
76Dic157—42no—
77Dic157—81no—
78C2×C157—21no—
79C2×C157—21no—
80C2×C157—42no—
81C2×C157#45111yescharacteristic
82C2×C157#45311yescharacteristic
83C2×C157#45811yescharacteristic
84C157#161411yescharacteristic, complemented, Sylow
85#1614—1571nomaximal, Sylow
86#543—1571no—
87#484—1572no—
88#399—1571no—
89#328—1572no—
90#323D15711yescharacteristic
91C22⋊Q8—3142no—
92C22⋊Q8—3142no—
93C22⋊Q8—3141no—
94C22⋊Q8—1572no—
95C2×C4⋊C4—3141no—
96C2×C4⋊C4—1571no—
97C2×C22⋊C4—3141no—
98C2×C22⋊C4—3141no—
99C2×C22⋊C4C2×D15711yescharacteristic
100#107—3142no—
101#103—3142no—
102C22⋊C8C2×D15712yes—
103#95—1571no—
104C24D62811yescharacteristic
105C2×Q8—3141no—
106C2×Q8—1572no—
107C22×C4—3141no—
108C22×C4—3141no—
109C22×C4—3141no—
110C22×C4—3141no—
111C22×C4D62811yescharacteristic
112C22×C4C22×D15711yescharacteristic
113C2×C8—22no—
114C4⋊C4—3142no—
115C4⋊C4—3141no—
116C4⋊C4—3142no—
117C4⋊C4—3142no—
118C4⋊C4—6282no—
119C4⋊C4—1572no—
120C22⋊C4—22no—
121C22⋊C4—3142no—
122C22⋊C4—3142no—
123C22⋊C4—6282no—
124C23—21no—
125C23—21no—
126C23—41no—
127C23—41no—
128C23Dic62812yes—
129C23C2×D62811yescharacteristic
130Q8—6282no—
131Q8—12561no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—3142no—
136C2×C4—3142no—
137C2×C4—3142no—
138C2×C4—6281no—
139C2×C4—6281no—
140C2×C4—6281no—
141C2×C4—6281no—
142C2×C4—6281no—
143C2×C4—12561no—
144C2×C4—12561no—
145C2×C4D4×D15712yes—
146C8—42no—
147C22—21no—
148C22—21no—
149C22—22no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22—81no—
154C22#1909774111yescharacteristic
155C22C2×Dic62811yescharacteristic
156C22#1909780411yescharacteristic
157C4—22no—
158C4—41no—
159C4—6282no—
160C4—6282no—
161C4—6282no—
162C4—12561no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#2375743111yescharacteristic
167C2#2375744311yescharacteristic
168C2#2375746411yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#323×C157C2
socleC22×C157#120
prime radicalC24×C157D4
hypercenter#323D157
hypocenterC157#1614
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. #23757609C2semidirect
4. #23757011C2semidirect
84. C157#1614semidirect

Maximal subgroups

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

subgroupindex
#237578992
#237576092
#237572092
#237570112
#323×C1572
#1614157