Finite Group Databasebeta

← #34099135

Subgroups — #34099135

Order 20096.

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

normal subgroups only

This group has 216 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#23757604C211yesmaximal, characteristic, complemented
3#23757587C211yesmaximal, characteristic
4#23757203C211yesmaximal, 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
17C2×#14578933—21no—
18#19097705—21no—
19#19097703—21no—
20#19097696—21no—
21#19097693—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—
41#14578933—42no—
42C22⋊Dic157—21no—
43#14578931—21no—
44#14578931—21no—
45#14578931—21no—
46#14578931—21no—
47C4×Dic157—21no—
48C22×C4×C157D411yescharacteristic
49C22×C4×C157D411yescharacteristic
50C22×C4×C157C2311yescharacteristic
51C2×C8×C157—21no—
52C2×C8×C157—21no—
53C4⋊C4×C157—21no—
54C4⋊C4×C157—21no—
55C22×D157—21no—
56Dic314—41no—
57D628—41no—
58C22⋊D157—41no—
59C22⋊D157—41no—
60C2×Dic157—22no—
61C2×Dic157—21no—
62C2×Dic157—21no—
63C2×Dic157—21no—
64C2×Dic157—41no—
65C2×Dic157—41no—
66C2×Dic157—41no—
67C2×Dic157—41no—
68C2×Dic157—41no—
69C4×D157—81no—
70C23×C157C2×D411yescharacteristic
71C2×C4×C157—21no—
72C2×C4×C157—21no—
73C2×C4×C157—21no—
74C2×C4×C157—21no—
75C2×C4×C157—41no—
76C2×C4×C157—41no—
77C2×C4×C157C2×D411yescharacteristic
78C2×C4×C157C2×D411yescharacteristic
79C8×C157—41no—
80C8×C157—41no—
81C22×C157—21no—
82C22×C157—21no—
83C22×C157#12011yescharacteristic
84C22×C157#13511yescharacteristic
85C22×C157AGL(1,ℤ/8)11yescharacteristic
86C2×D157—41no—
87C2×D157—41no—
88C2×D157—41no—
89C4×C157—21no—
90C4×C157—21no—
91C4×C157—41no—
92C4×C157—41no—
93Dic157—42no—
94Dic157—41no—
95Dic157—41no—
96Dic157—41no—
97Dic157—81no—
98C2×C157—21no—
99C2×C157—21no—
100C2×C157#44911yescharacteristic
101C2×C157#45611yescharacteristic
102C2×C157#45811yescharacteristic
103D157—81no—
104C157#160911yescharacteristic, complemented, Sylow
105#1609—1571nomaximal, Sylow
106#539—1571no—
107#483—1571no—
108#480—1571no—
109#398—1571no—
110#328—1571no—
111#327—1571no—
112#324D15711yescharacteristic, complemented
113#126—3141no—
114#125—3141no—
115#123—3141no—
116#123—3141no—
117C22⋊Q8—3141no—
118C22⋊Q8—1571no—
119#121—1571no—
120C4×D4—3141no—
121C2×C4⋊C4—3141no—
122C2×C4⋊C4—1571no—
123C2×C4⋊C4C2×D15711yescharacteristic
124#107—3141no—
125#106—3141no—
126#103—3141no—
127#102—3141no—
128C22⋊C8C2×D15711yescharacteristic
129C22⋊C8C2×D15711yescharacteristic
130#95—3141no—
131#95—1571no—
132C2×Q8—1571no—
133C2×D4—3141no—
134C2×D4—1571no—
135C22×C4—3141no—
136C22×C4—3141no—
137C22×C4—3141no—
138C22×C4D62811yescharacteristic
139C22×C4D62811yescharacteristic
140C22×C4C22×D15711yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—3141no—
146C4⋊C4—3141no—
147C4⋊C4—3141no—
148C4⋊C4—3141no—
149C4⋊C4—3141no—
150C4⋊C4—3141no—
151C4⋊C4—6282no—
152C4⋊C4—1571no—
153C4⋊C4—1571no—
154C22⋊C4—3141no—
155C22⋊C4—3141no—
156C22⋊C4—3141no—
157C22⋊C4—3141no—
158C22⋊C4—3141no—
159C42—3141no—
160C23—3141no—
161C23C2×D62811yescharacteristic
162Q8—6281no—
163D4—6281no—
164D4—6281no—
165D4—6281no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—3142no—
173C2×C4—3141no—
174C2×C4—3141no—
175C2×C4—3141no—
176C2×C4—6281no—
177C2×C4—6281no—
178C2×C4—6281no—
179C2×C4—6281no—
180C2×C4—6281no—
181C2×C4—12561no—
182C2×C4D4×D15711yescharacteristic
183C2×C4D4×D15711yescharacteristic
184C8—41no—
185C8—41no—
186C22—21no—
187C22—21no—
188C22—6281no—
189C22—6281no—
190C22—6281no—
191C22#1909774111yescharacteristic
192C22#1909779311yescharacteristic
193C22#1909779911yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—6282no—
199C4—6281no—
200C4—6281no—
201C4—6281no—
202C4—12561no—
203C2—21no—
204C2—21no—
205C2—12561no—
206C2#2375742011yescharacteristic
207C2#2375745811yescharacteristic
208C2#2375746411yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#324×C157C2
socleC22×C157#120
prime radical#19097745C22
hypercenter#324D157
hypocenterC157#1609
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. #23757604C2semidirect
4. #23757203C2semidirect
5. #23757011C2semidirect
7. #324×C157C2semidirect
104. C157#1609semidirect
112. #324D157semidirect

Maximal subgroups

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

subgroupindex
#237578702
#237576042
#237575872
#237572032
#237570112
#237570082
#324×C1572
#1609157