Finite Group Databasebeta

← #34099444

Subgroups — #34099444

Order 20096.

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

normal subgroups only

This group has 228 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#23758015C211yesmaximal, characteristic
2#23757667C211yesmaximal, characteristic, complemented
3#23757633C211yesmaximal, characteristic, complemented
4#23757632C211yesmaximal, characteristic, complemented
5#23757012C211yesmaximal, characteristic, complemented
6#23757012C211yesmaximal, characteristic, complemented
7#329×C157C211yesmaximal, characteristic, complemented
8C2×Dic628—21no—
9C2×#14578943—21no—
10#19097771C2211yescharacteristic, complemented
11#19097760—21no—
12#19097759C2211yescharacteristic
13#19097759C2211yescharacteristic
14#19097757—21no—
15#19097757—21no—
16#19097741—21no—
17#19097741—21no—
18#19097739—21no—
19#19097696—21no—
20#19097695—21no—
21#19097693—21no—
22#19097692—21no—
23#19097682C2211yescharacteristic, complemented
24#124×C157C2211yescharacteristic
25#97×C157C2211yescharacteristic, complemented
26#97×C157C2211yescharacteristic, complemented
27C23×D157—21no—
28C2×Dic314—21no—
29C2×Dic314D411yescharacteristic
30C2×Dic314D411yescharacteristic
31C2×D628—21no—
32C2×D628D411yescharacteristic
33C2×D628D411yescharacteristic
34C2×C22⋊D157—21no—
35C2×C22⋊D157—21no—
36Dic628—42no—
37#14578943—42no—
38C2×#11929434—21no—
39C4⋊Dic157—21no—
40C4⋊Dic157—21no—
41C22⋊Dic157—21no—
42#14578931—21no—
43#14578931—21no—
44#14578931—21no—
45#14578931—21no—
46#14578931—21no—
47#14578931—21no—
48C4×Dic157—21no—
49C2×Q8×C157D411yescharacteristic
50C2×D4×C157D411yescharacteristic
51C2×C8×C157—21no—
52C2×C8×C157—21no—
53C22⋊C4×C157—21no—
54C22⋊C4×C157—21no—
55C42×C157C2311yescharacteristic
56C22×D157—21no—
57C22×D157—21no—
58C22×D157—81no—
59C22×D157—81no—
60C22×D157—81no—
61Dic314—41no—
62Dic314—41no—
63Dic314—41no—
64Dic314—41no—
65D628—41no—
66D628—41no—
67D628—81no—
68C22⋊D157—81no—
69C22⋊D157—81no—
70C2×Dic157—21no—
71C2×Dic157—21no—
72C2×Dic157—41no—
73#11929434—41no—
74C23×C157—21no—
75Q8×C157—41no—
76D4×C157—41no—
77C2×C4×C157—21no—
78C2×C4×C157C2×D411yescharacteristic
79C2×C4×C157C2×D411yescharacteristic
80C2×C4×C157C2×D411yescharacteristic
81C8×C157—22no—
82C8×C157—41no—
83C22×C157—41no—
84C22×C157—41no—
85C22×C157—41no—
86C22×C157#12011yescharacteristic
87C2×D157—41no—
88C2×D157—41no—
89C2×D157—41no—
90C2×D157—41no—
91C2×D157—41no—
92C2×D157—41no—
93C2×D157—84no—
94C4×C157—21no—
95C4×C157—21no—
96C4×C157—21no—
97C4×C157—41no—
98Dic157—41no—
99Dic157—41no—
100Dic157—81no—
101C2×C157—81no—
102C2×C157#45311yescharacteristic
103C2×C157#45511yescharacteristic
104C2×C157#45511yescharacteristic
105D157—81no—
106D157—81no—
107C157#165911yescharacteristic, complemented, Sylow
108#1659—1571nomaximal, Sylow
109H(3,𝔽4)—1571no—
110#497—1571no—
111#489—1571no—
112#489—1571no—
113#329—1571no—
114#329—1571no—
115#329D15711yescharacteristic, complemented
116C2×Q16—3141no—
117C2×SD16—3141no—
118C4⋊Q8—1571no—
119#124—3141no—
120#124—3141no—
121#124—3141no—
122#124—1571no—
123#124—1571no—
124#124C2×D15711yescharacteristic
125#120—3141no—
126#120—3141no—
127#120—3141no—
128#103—3141no—
129#103—3141no—
130#102—3141no—
131#102—3141no—
132#97—1571no—
133#97C2×D15711yescharacteristic, complemented
134#97C2×D15711yescharacteristic, complemented
135C24—3141no—
136C2×Q8—3141no—
137C2×Q8—1571no—
138C2×Q8—1571no—
139C2×Q8D62811yescharacteristic
140C2×D4—3141no—
141C2×D4—3141no—
142C2×D4—3141no—
143C2×D4—1571no—
144C2×D4—1571no—
145C2×D4D62811yescharacteristic
146Q16—6282no—
147SD16—6282no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—3141no—
151C4⋊C4—3141no—
152C4⋊C4—3141no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—3141no—
156C22⋊C4—3141no—
157C22⋊C4—3141no—
158C22⋊C4—3141no—
159C22⋊C4—3141no—
160C22⋊C4—3141no—
161C22⋊C4—3141no—
162C42—3141no—
163C42C22×D15711yescharacteristic
164C23—21no—
165C23—3141no—
166C23—3141no—
167C23—12561no—
168C23—12561no—
169C23—12561no—
170Q8—41no—
171Q8—6281no—
172Q8—6281no—
173Q8—6281no—
174Q8—6281no—
175D4—41no—
176D4—6281no—
177D4—6281no—
178D4—12561no—
179D4—12561no—
180D4—12561no—
181C2×C4—21no—
182C2×C4—3141no—
183C2×C4—3141no—
184C2×C4—6281no—
185C2×C4D4×D15711yescharacteristic
186C2×C4D4×D15711yescharacteristic
187C2×C4C2×D62811yescharacteristic
188C8—22no—
189C8—41no—
190C8—6281no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—6281no—
195C22—6281no—
196C22—6281no—
197C22—6281no—
198C22—6281no—
199C22—6281no—
200C22—12564no—
201C22#1909774111yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—6281no—
207C4—6281no—
208C4—12561no—
209C2—81no—
210C2—12561no—
211C2—12561no—
212C2#2375744211yescharacteristic
213C2#2375745211yescharacteristic
214C2#2375745311yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#329×C157C2
socleC22×C157#120
prime radical#23758015C2
hypercenter#329D157
hypocenterC157#1659
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #23757667C2semidirect
3. #23757633C2semidirect
4. #23757632C2semidirect
5. #23757012C2semidirect
6. #23757012C2semidirect
7. #329×C157C2semidirect
10. #19097771C22semidirect
23. #19097682C22semidirect
25. #97×C157C22semidirect
26. #97×C157C22semidirect
107. C157#1659semidirect
115. #329D157semidirect
133. #97C2×D157semidirect
134. #97C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237580152
#237576672
#237576332
#237576322
#237570122
#329×C1572
#1659157