Finite Group Databasebeta

← #34099436

Subgroups — #34099436

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#23757662C211yesmaximal, characteristic
3#23757639C211yesmaximal, characteristic, complemented
4#23757638C211yesmaximal, characteristic, complemented
5#23757014C211yesmaximal, characteristic, complemented
6#23757012C211yesmaximal, characteristic, complemented
7#330×C157C211yesmaximal, characteristic, complemented
8C2×#14578943—21no—
9C2×D1256—21no—
10#19097770—21no—
11#19097768C2211yescharacteristic
12#19097766—21no—
13#19097766—21no—
14#19097763C2211yescharacteristic
15#19097759C2211yescharacteristic
16#19097756—21no—
17#19097751—21no—
18#19097749—21no—
19#19097693—21no—
20#19097693—21no—
21#19097691—21no—
22#19097691—21no—
23#19097682C2211yescharacteristic
24#125×C157C2211yescharacteristic
25#97×C157C2211yescharacteristic
26#97×C157C2211yescharacteristic
27C2×Dic314—21no—
28C2×Dic314D411yescharacteristic
29C2×D628—21no—
30C2×D628—21no—
31C2×D628—21no—
32C2×D628D411yescharacteristic
33C2×C4×D157—21no—
34#14578943—42no—
35D1256—42no—
36C2×#11929434—21no—
37C4⋊Dic157—21no—
38C4⋊Dic157D411yescharacteristic
39C4⋊Dic157D411yescharacteristic
40#14578933—21no—
41#14578933—21no—
42#14578933—21no—
43#14578931—21no—
44#14578931—21no—
45#14578931—21no—
46#14578931—21no—
47#14578931—21no—
48C4×Dic157—21no—
49C2×C8×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—
57C22×D157—41no—
58Dic314—41no—
59Dic314—81no—
60D628—41no—
61D628—42no—
62D628—42no—
63D628—41no—
64D628—41no—
65C2×Dic157—21no—
66C2×Dic157—21no—
67C2×Dic157—21no—
68C4×D157—81no—
69#11929434—41no—
70C2×C4×C157—21no—
71C2×C4×C157—21no—
72C2×C4×C157C2×D411yescharacteristic
73C2×C4×C157C2×D411yescharacteristic
74C2×C4×C157C2×D411yescharacteristic
75C8×C157—22no—
76C8×C157—41no—
77C22×C157#12011yescharacteristic
78C2×D157—41no—
79C2×D157—41no—
80C2×D157—41no—
81C2×D157—81no—
82C2×D157—81no—
83C2×D157—81no—
84C4×C157—21no—
85C4×C157—21no—
86C4×C157—21no—
87C4×C157—41no—
88C4×C157—41no—
89Dic157—41no—
90Dic157—41no—
91Dic157—41no—
92C2×C157#45311yescharacteristic
93C2×C157#45411yescharacteristic
94C2×C157#45411yescharacteristic
95D157—81no—
96D157—161no—
97C157#165711yescharacteristic, complemented, Sylow
98#1657—1571nomaximal, Sylow
99#563—1571no—
100#496—1571no—
101#490—1571no—
102#490—1571no—
103#330—1571no—
104#330D15711yescharacteristic, complemented
105#329—1571no—
106C2×SD16—3141no—
107C2×D8—3141no—
108C4⋊Q8—3141no—
109#127—1571no—
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—3141no—
119#102—3141no—
120#102—3141no—
121#102—3141no—
122#97—1571no—
123#97C2×D15711yescharacteristic
124#97C2×D15711yescharacteristic
125C2×Q8—3141no—
126C2×Q8—1571no—
127C2×D4—3141no—
128C2×D4—3141no—
129C2×D4—3141no—
130C2×D4—1571no—
131C22×C4—3141no—
132SD16—6282no—
133D8—6282no—
134C2×C8—21no—
135C2×C8—21no—
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⋊C4D62811yescharacteristic
146C4⋊C4D62811yescharacteristic
147C22⋊C4—3141no—
148C22⋊C4—3141no—
149C22⋊C4—3141no—
150C22⋊C4—3141no—
151C22⋊C4—3141no—
152C42—3141no—
153C42C22×D15711yescharacteristic
154C23—3141no—
155C23—6281no—
156Q8—6281no—
157Q8—12561no—
158D4—6281no—
159D4—6281no—
160D4—6281no—
161D4—6282no—
162D4—6282no—
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×D62811yescharacteristic
172C8—22no—
173C8—41no—
174C8—6281no—
175C22—6281no—
176C22—6281no—
177C22—6281no—
178C22—12561no—
179C22—12561no—
180C22—12561no—
181C22#1909774111yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—6281no—
188C4—6281no—
189C4—6281no—
190C2—25121no—
191C2—12561no—
192C2#2375744211yescharacteristic
193C2#2375744711yescharacteristic
194C2#2375744811yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#330×C157C2
socleC22×C157#120
prime radical#23757662C2
hypercenter#330D157
hypocenterC157#1657
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #23758027C2semidirect
3. #23757639C2semidirect
4. #23757638C2semidirect
5. #23757014C2semidirect
6. #23757012C2semidirect
7. #330×C157C2semidirect
97. C157#1657semidirect
104. #330D157semidirect

Maximal subgroups

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

subgroupindex
#237580272
#237576622
#237576392
#237576382
#237570142
#237570122
#330×C1572
#1657157