Finite Group Databasebeta

← #34099169

Subgroups — #34099169

Order 20096.

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

normal subgroups only

This group has 208 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#23757870C211yesmaximal, characteristic
2#23757609C211yesmaximal, characteristic, complemented
3#23757592C211yesmaximal, characteristic
4#23757212C211yesmaximal, characteristic, complemented
5#23757011C211yesmaximal, characteristic, complemented
6#23757008C211yesmaximal, characteristic
7#324×C157C211yesmaximal, characteristic, complemented
8#19097766—21no—
9#19097761—21no—
10#19097756—21no—
11#19097754—21no—
12#19097750C2211yescharacteristic
13#19097749—21no—
14#19097745C2211yescharacteristic
15C4×C22⋊D157—21no—
16C2×C4⋊Dic157C2211yescharacteristic
17#19097705—21no—
18#19097703—21no—
19#19097696—21no—
20#19097693—21no—
21#19097678—21no—
22#19097678—21no—
23#19097678C2211yescharacteristic
24C2×C4⋊C4×C157C2211yescharacteristic
25C22⋊C8×C157C2211yescharacteristic
26C22⋊C8×C157C2211yescharacteristic
27C2×Dic314D411yescharacteristic
28C2×D628D411yescharacteristic
29C2×C22⋊D157—21no—
30C22×Dic157—21no—
31C22×Dic157—21no—
32C2×C4×D157—21no—
33C4⋊Dic157—21no—
34C4⋊Dic157—21no—
35C4⋊Dic157D411yescharacteristic
36C4⋊Dic157D411yescharacteristic
37#14578933—21no—
38#14578933—21no—
39#14578933—21no—
40#14578933—21no—
41C22⋊Dic157—21no—
42#14578931—21no—
43#14578931—21no—
44#14578931—21no—
45#14578931—21no—
46C4×Dic157—21no—
47C22×C4×C157D411yescharacteristic
48C22×C4×C157D411yescharacteristic
49C22×C4×C157C2311yescharacteristic
50C2×C8×C157—21no—
51C2×C8×C157—21no—
52C4⋊C4×C157—21no—
53C4⋊C4×C157—21no—
54C22×D157—21no—
55Dic314—41no—
56D628—41no—
57C22⋊D157—41no—
58C22⋊D157—41no—
59C2×Dic157—21no—
60C2×Dic157—21no—
61C2×Dic157—21no—
62C2×Dic157—41no—
63C2×Dic157—41no—
64C2×Dic157—42no—
65C2×Dic157—41no—
66C2×Dic157—41no—
67C4×D157—81no—
68C23×C157C2×D411yescharacteristic
69C2×C4×C157—21no—
70C2×C4×C157—21no—
71C2×C4×C157—21no—
72C2×C4×C157—21no—
73C2×C4×C157—41no—
74C2×C4×C157—41no—
75C2×C4×C157C2×D411yescharacteristic
76C2×C4×C157C2×D411yescharacteristic
77C8×C157—41no—
78C8×C157—41no—
79C22×C157—21no—
80C22×C157—21no—
81C22×C157#12011yescharacteristic
82C22×C157#13511yescharacteristic
83C22×C157#13711yescharacteristic
84C2×D157—41no—
85C2×D157—41no—
86C2×D157—41no—
87C4×C157—21no—
88C4×C157—21no—
89C4×C157—41no—
90C4×C157—41no—
91Dic157—41no—
92Dic157—41no—
93Dic157—41no—
94Dic157—81no—
95Dic157—81no—
96C2×C157—21no—
97C2×C157—21no—
98C2×C157#45211yescharacteristic
99C2×C157#45411yescharacteristic
100C2×C157#45811yescharacteristic
101D157—81no—
102C157#161511yescharacteristic, complemented, Sylow
103#1615—1571nomaximal, Sylow
104#539—1571no—
105#484—1571no—
106#481—1571no—
107#400—1571no—
108#328—1571no—
109#327—1571no—
110#324D15711yescharacteristic, complemented
111#126—3141no—
112#125—3141no—
113#123—3141no—
114#123—3141no—
115C22⋊Q8—3141no—
116C22⋊Q8—1571no—
117#121—1571no—
118C4×D4—3141no—
119C2×C4⋊C4—1571no—
120C2×C4⋊C4C2×D15711yescharacteristic
121#107—3141no—
122#106—3141no—
123#103—3141no—
124#102—3141no—
125C22⋊C8C2×D15711yescharacteristic
126C22⋊C8C2×D15711yescharacteristic
127#95—3141no—
128#95—3141no—
129#95—1571no—
130C2×Q8—1571no—
131C2×D4—3141no—
132C2×D4—1571no—
133C22×C4—3141no—
134C22×C4—3141no—
135C22×C4—3141no—
136C22×C4D62811yescharacteristic
137C22×C4D62811yescharacteristic
138C22×C4C22×D15711yescharacteristic
139C2×C8—21no—
140C2×C8—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—3141no—
144C4⋊C4—3141no—
145C4⋊C4—3141no—
146C4⋊C4—3141no—
147C4⋊C4—3141no—
148C4⋊C4—3141no—
149C4⋊C4—1571no—
150C4⋊C4—1571no—
151C22⋊C4—3141no—
152C22⋊C4—3141no—
153C22⋊C4—3141no—
154C22⋊C4—3141no—
155C22⋊C4—3141no—
156C42—3141no—
157C23—3141no—
158C23C2×D62811yescharacteristic
159Q8—6281no—
160D4—6281no—
161D4—6281no—
162D4—6281no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—3141no—
170C2×C4—3141no—
171C2×C4—3141no—
172C2×C4—6281no—
173C2×C4—6281no—
174C2×C4—6282no—
175C2×C4—6281no—
176C2×C4—6281no—
177C2×C4—12561no—
178C2×C4D4×D15711yescharacteristic
179C2×C4D4×D15711yescharacteristic
180C8—41no—
181C8—41no—
182C22—21no—
183C22—21no—
184C22—6281no—
185C22—6281no—
186C22—6281no—
187C22#1909774111yescharacteristic
188C22#1909779311yescharacteristic
189C22#1909780411yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—6281no—
195C4—6281no—
196C4—6281no—
197C4—12561no—
198C4—12561no—
199C2—21no—
200C2—21no—
201C2—12561no—
202C2#2375743711yescharacteristic
203C2#2375744811yescharacteristic
204C2#2375746411yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#324×C157C2
socleC22×C157#120
prime radical#19097745C22
hypercenter#324D157
hypocenterC157#1615
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #23757609C2semidirect
4. #23757212C2semidirect
5. #23757011C2semidirect
7. #324×C157C2semidirect
102. C157#1615semidirect
110. #324D157semidirect

Maximal subgroups

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

subgroupindex
#237578702
#237576092
#237575922
#237572122
#237570112
#237570082
#324×C1572
#1615157