Finite Group Databasebeta

← #34099170

Subgroups — #34099170

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#23757872C211yesmaximal, characteristic
2#23757606C211yesmaximal, characteristic, complemented
3#23757592C211yesmaximal, characteristic
4#23757213C211yesmaximal, characteristic, complemented
5#23757006C211yesmaximal, characteristic
6#23756998C211yesmaximal, characteristic, complemented
7#328×C157C211yesmaximal, characteristic, complemented
8#19097766—21no—
9#19097762—21no—
10#19097756—21no—
11#19097755—21no—
12#19097747—21no—
13#19097745C2211yescharacteristic
14#19097731—21no—
15C2×C4⋊Dic157C2211yescharacteristic
16C2×#14578933C2211yescharacteristic
17#19097704—21no—
18#19097703—21no—
19#19097695—21no—
20#19097693—21no—
21C22⋊#11929434C2211yescharacteristic
22#19097678—21no—
23#19097678—21no—
24C22⋊Q8×C157C2211yescharacteristic
25C22⋊C8×C157C2211yescharacteristic
26#95×C157C2211yescharacteristic
27C2×D628D411yescharacteristic
28C2×C22⋊D157—21no—
29C22×Dic157—21no—
30C22×Dic157D411yescharacteristic
31C22×Dic157D411yescharacteristic
32C2×C4×D157—21no—
33C2×#11929434—21no—
34C4⋊Dic157—21no—
35C4⋊Dic157—21no—
36C4⋊Dic157—21no—
37C4⋊Dic157—21no—
38C4⋊Dic157D411yescharacteristic
39#14578933—21no—
40#14578933—21no—
41#14578933—21no—
42#14578931—21no—
43#14578931—21no—
44#14578931—21no—
45#14578931—21no—
46C4×Dic157—21no—
47C2×Q8×C157D411yescharacteristic
48C22×C4×C157—21no—
49C22×C4×C157C2311yescharacteristic
50C2×C8×C157—21no—
51C4⋊C4×C157—21no—
52C4⋊C4×C157D411yescharacteristic
53C22⋊C4×C157—21no—
54C22×D157—21no—
55D628—41no—
56C22⋊D157—41no—
57C22⋊D157—41no—
58C2×Dic157—21no—
59C2×Dic157—21no—
60C2×Dic157—21no—
61C2×Dic157—21no—
62C2×Dic157—21no—
63C2×Dic157—41no—
64C2×Dic157—42no—
65C2×Dic157—41no—
66C4×D157—81no—
67#11929434—41no—
68C23×C157C2×D411yescharacteristic
69Q8×C157—41no—
70C2×C4×C157—21no—
71C2×C4×C157—21no—
72C2×C4×C157—41no—
73C2×C4×C157—41no—
74C2×C4×C157—41no—
75C2×C4×C157—41no—
76C2×C4×C157C2×D411yescharacteristic
77C2×C4×C157C2×D411yescharacteristic
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—
91C4×C157—81no—
92Dic157—41no—
93Dic157—41no—
94Dic157—41no—
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#328D15711yescharacteristic, complemented
109#327—1571no—
110#324—1571no—
111#126—3141no—
112#125—3141no—
113#123—3141no—
114#123—3141no—
115C22⋊Q8—3141no—
116C22⋊Q8C2×D15711yescharacteristic
117#121—1571no—
118C4×D4—3141no—
119C2×C4⋊C4—1571no—
120C2×C4⋊C4—1571no—
121#107—3141no—
122#106—3141no—
123#103—3141no—
124#102—3141no—
125C22⋊C8—1571no—
126C22⋊C8C2×D15711yescharacteristic
127#95—3141no—
128#95—3141no—
129#95C2×D15711yescharacteristic
130C2×Q8D62811yescharacteristic
131C2×D4—3141no—
132C2×D4—1571no—
133C22×C4—21no—
134C22×C4—3141no—
135C22×C4—3141no—
136C22×C4—1571no—
137C22×C4—1571no—
138C22×C4C22×D15711yescharacteristic
139C2×C8—21no—
140C2×C8—3141no—
141C4⋊C4—21no—
142C4⋊C4—3141no—
143C4⋊C4—3141no—
144C4⋊C4—3141no—
145C4⋊C4—3141no—
146C4⋊C4—3141no—
147C4⋊C4—3141no—
148C4⋊C4—3141no—
149C4⋊C4—1571no—
150C4⋊C4D62811yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—3141no—
153C22⋊C4—3141no—
154C22⋊C4—3141no—
155C22⋊C4—3141no—
156C42—3141no—
157C23—3141no—
158C23D4×D15711yescharacteristic
159Q8—41no—
160D4—6281no—
161D4—6281no—
162D4—6281no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—3141no—
170C2×C4—3141no—
171C2×C4—3141no—
172C2×C4—3141no—
173C2×C4—3141no—
174C2×C4—6281no—
175C2×C4—6282no—
176C2×C4—6281no—
177C2×C4—12561no—
178C2×C4D4×D15711yescharacteristic
179C2×C4C2×D62811yescharacteristic
180C8—41no—
181C8—6281no—
182C22—21no—
183C22—21no—
184C22—6281no—
185C22—6281no—
186C22—6281no—
187C22#1909774111yescharacteristic
188C22#1909779211yescharacteristic
189C22#1909780311yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—6281no—
196C4—6281no—
197C4—6281no—
198C4—12561no—
199C2—21no—
200C2—21no—
201C2—12561no—
202C2#2375743811yescharacteristic
203C2#2375744711yescharacteristic
204C2#2375746411yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#328×C157C2
socleC22×C157#120
prime radical#19097745C22
hypercenter#328D157
hypocenterC157#1615
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #23757606C2semidirect
4. #23757213C2semidirect
6. #23756998C2semidirect
7. #328×C157C2semidirect
102. C157#1615semidirect
108. #328D157semidirect

Maximal subgroups

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

subgroupindex
#237578722
#237576062
#237575922
#237572132
#237570062
#237569982
#328×C1572
#1615157