Finite Group Databasebeta

← #34099433

Subgroups — #34099433

Order 20096.

206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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#23758027C211yesmaximal, characteristic, complemented
2#23757660C211yesmaximal, characteristic
3#23757637C211yesmaximal, characteristic, complemented
4#23757015C211yesmaximal, characteristic, complemented
5#23757014C211yesmaximal, characteristic, complemented
6#23757012C211yesmaximal, characteristic, complemented
7#490×C157C211yesmaximal, characteristic, complemented
8C2×#14578942—21no—
9C2×#14578939—21no—
10#19097770—21no—
11#19097766—21no—
12#19097766—21no—
13#19097763C2211yescharacteristic
14#19097759C2211yescharacteristic
15#19097756—21no—
16#19097751—21no—
17#19097749—21no—
18#19097692—21no—
19#19097692—21no—
20#19097682C2211yescharacteristic
21#19097682C2211yescharacteristic
22#127×C157C2211yescharacteristic
23#125×C157C2211yescharacteristic
24#102×C157—21no—
25#102×C157—21no—
26#97×C157C2211yescharacteristic
27C2×Dic314—21no—
28C2×Dic314D411yescharacteristic
29C2×D628D411yescharacteristic
30C2×C4×D157—21no—
31#14578942—42no—
32#14578939—42no—
33C2×#11929434—21no—
34C2×#11929434—21no—
35C4⋊Dic157—21no—
36C4⋊Dic157D411yescharacteristic
37C4⋊Dic157D411yescharacteristic
38#14578933—21no—
39#14578933—21no—
40#14578933—21no—
41#14578931—21no—
42#14578931—21no—
43#14578931—21no—
44#14578931—21no—
45#14578931—21no—
46C4×Dic157—21no—
47C2×D4×C157—21no—
48C2×D4×C157—21no—
49C2×D4×C157—21no—
50C2×C8×C157—21no—
51C4⋊C4×C157—21no—
52C4⋊C4×C157—21no—
53C4⋊C4×C157D411yescharacteristic
54C4⋊C4×C157D411yescharacteristic
55C42×C157C2311yescharacteristic
56C22×D157—21no—
57Dic314—41no—
58Dic314—81no—
59D628—41no—
60C2×Dic157—21no—
61C2×Dic157—21no—
62C2×Dic157—21no—
63C4×D157—81no—
64#11929434—22no—
65#11929434—41no—
66C23×C157—41no—
67D4×C157—42no—
68D4×C157—42no—
69D4×C157—41no—
70D4×C157—41no—
71C2×C4×C157—21no—
72C2×C4×C157—21no—
73C2×C4×C157C2×D411yescharacteristic
74C2×C4×C157C2×D411yescharacteristic
75C2×C4×C157C2×D411yescharacteristic
76C8×C157—41no—
77C22×C157—81no—
78C22×C157—81no—
79C22×C157—81no—
80C22×C157#12011yescharacteristic
81C2×D157—41no—
82C2×D157—41no—
83C2×D157—41no—
84C4×C157—21no—
85C4×C157—21no—
86C4×C157—21no—
87C4×C157—41no—
88C4×C157—41no—
89Dic157—41no—
90Dic157—41no—
91Dic157—41no—
92C2×C157—161no—
93C2×C157#45311yescharacteristic
94C2×C157#45411yescharacteristic
95C2×C157#45411yescharacteristic
96D157—81no—
97C157#165711yescharacteristic, complemented, Sylow
98#1657—1571nomaximal, Sylow
99#563—1571no—
100#496—1571no—
101#490—1571no—
102#490D15711yescharacteristic, complemented
103#330—1571no—
104#330—1571no—
105#329—1571no—
106C2×SD16—3141no—
107C2×D8—3141no—
108C4⋊Q8—3141no—
109#127C2×D15711yescharacteristic
110#126—3141no—
111#126—3141no—
112#125—1571no—
113#125C2×D15711yescharacteristic
114#124—1571no—
115#123—3141no—
116C22⋊Q8—3141no—
117C22⋊Q8—3141no—
118#102—21no—
119#102—21no—
120#102—3141no—
121#102—3141no—
122#97—1571no—
123#97—1571no—
124#97C2×D15711yescharacteristic
125C2×Q8—3141no—
126C2×Q8—1571no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—1571no—
131C22×C4—3141no—
132SD16—6282no—
133D8—6282no—
134C2×C8—21no—
135C2×C8—3141no—
136C2×C8—3141no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—3141no—
140C4⋊C4—3141no—
141C4⋊C4—3141no—
142C4⋊C4—3141no—
143C4⋊C4—1571no—
144C4⋊C4—1571no—
145C4⋊C4C22⋊D15711yescharacteristic
146C4⋊C4C22⋊D15711yescharacteristic
147C22⋊C4—3141no—
148C22⋊C4—3141no—
149C22⋊C4—3141no—
150C22⋊C4—3141no—
151C22⋊C4—3141no—
152C42—3141no—
153C42C22×D15711yescharacteristic
154C23—41no—
155C23—3141no—
156Q8—6281no—
157Q8—12561no—
158D4—41no—
159D4—41no—
160D4—42no—
161D4—42no—
162D4—6281no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—3141no—
166C2×C4—3141no—
167C2×C4—3141no—
168C2×C4—12561no—
169C2×C4D4×D15711yescharacteristic
170C2×C4D4×D15711yescharacteristic
171C2×C4C2×C22⋊D15711yescharacteristic
172C8—41no—
173C8—3142no—
174C8—6281no—
175C22—81no—
176C22—81no—
177C22—81no—
178C22—6281no—
179C22—6281no—
180C22—6281no—
181C22#1909773911yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—6281no—
188C4—6281no—
189C4—6281no—
190C2—161no—
191C2—12561no—
192C2#2375743911yescharacteristic
193C2#2375744411yescharacteristic
194C2#2375744511yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#490×C157C2
socleC22×C157#120
prime radical#23757660C2
hypercenter#490D157
hypocenterC157#1657
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #23758027C2semidirect
3. #23757637C2semidirect
4. #23757015C2semidirect
5. #23757014C2semidirect
6. #23757012C2semidirect
7. #490×C157C2semidirect
97. C157#1657semidirect
102. #490D157semidirect

Maximal subgroups

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

subgroupindex
#237580272
#237576602
#237576372
#237570152
#237570142
#237570122
#490×C1572
#1657157