Finite Group Databasebeta

← #34099288

Subgroups — #34099288

Order 20096.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#23757926C211yesmaximal, characteristic
2#23757625C211yesmaximal, characteristic, complemented
3#23757564C211yesmaximal, characteristic, complemented
4#23757564C211yesmaximal, characteristic, complemented
5#23757000C211yesmaximal, characteristic, complemented
6#23757000C211yesmaximal, characteristic, complemented
7#332×C157C211yesmaximal, characteristic, complemented
8C2×#14578955—21no—
9#19097771C2211yescharacteristic
10#19097756—22no—
11#19097747—21no—
12#19097746—21no—
13C4×D628C2211yescharacteristic
14C4×D628C2211yescharacteristic
15C4⋊C4×D157—21no—
16#19097703—21no—
17#19097703—21no—
18#19097694—22no—
19#19097693—21no—
20#19097693—21no—
21C4×#11929434C2211yescharacteristic
22C4⋊Q8×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4⋊C8×C157C2211yescharacteristic
25#14578955—42no—
26#14578955—42no—
27C2×Dic314—21no—
28C2×D628—22no—
29C2×D628D411yescharacteristic
30C2×D628D411yescharacteristic
31C2×C4×D157—22no—
32C2×C4×D157—21no—
33C2×C4×D157—21no—
34C2×#11929434—21no—
35C4⋊Dic157—21no—
36C4⋊Dic157—21no—
37C4⋊Dic157D411yescharacteristic
38C4⋊Dic157D411yescharacteristic
39#14578933—22no—
40#14578931—22no—
41#14578931—21no—
42#14578931—21no—
43C2×Q8×C157—21no—
44C2×C8×C157—21no—
45C2×C8×C157—21no—
46C4⋊C4×C157—21no—
47C4⋊C4×C157D412yes—
48C42×C157C2311yescharacteristic
49C22×D157—21no—
50C22×D157—21no—
51Dic314—42no—
52D628—21no—
53D628—21no—
54D628—21no—
55D628—44no—
56D628SD1612yes—
57C2×Dic157—21no—
58C2×Dic157—21no—
59C2×Dic157—41no—
60C4×D157—44no—
61C4×D157—41no—
62C4×D157—41no—
63C4×D157—41no—
64C4×D157—41no—
65#11929434—41no—
66Q8×C157—41no—
67Q8×C157—41no—
68C2×C4×C157—22no—
69C2×C4×C157C2×D411yescharacteristic
70C2×C4×C157C2×D411yescharacteristic
71C2×C4×C157C2×D411yescharacteristic
72C8×C157—41no—
73C8×C157—41no—
74C22×C157#12011yescharacteristic
75C2×D157—22no—
76C2×D157—41no—
77C2×D157—41no—
78C2×D157—41no—
79C2×D157—41no—
80C2×D157—41no—
81C4×C157—21no—
82C4×C157—42no—
83C4×C157C2×SD1611yescharacteristic
84C4×C157#13511yescharacteristic
85C4×C157AGL(1,ℤ/8)11yescharacteristic
86C4×C157#13711yescharacteristic
87Dic157—41no—
88Dic157—41no—
89Dic157—81no—
90C2×C157#45011yescharacteristic
91C2×C157#45211yescharacteristic
92C2×C157#45411yescharacteristic
93D157—42no—
94D157—81no—
95C157#163511yescharacteristic, complemented, Sylow
96#1635—1571nomaximal, Sylow
97#547—1571no—
98#487—1571no—
99#476—1571no—
100#476—1571no—
101#332D15711yescharacteristic, complemented
102D4⋊C8—1571no—
103D4⋊C8—1571no—
104C2×#41—3141no—
105C4⋊Q8—1571no—
106C4⋊Q8C2×D15711yescharacteristic
107#123—3142no—
108C22⋊Q8—3141no—
109#121—3141no—
110C4×D4—1571no—
111C4×D4—1571no—
112C2×C4⋊C4—3141no—
113#106—3141no—
114#106—3141no—
115C4⋊C8C2×D15711yescharacteristic
116C4⋊C8C2×D15711yescharacteristic
117#103—3142no—
118#102—3141no—
119#102—3141no—
120C4×C8—1571no—
121#41—6282no—
122#41—6282no—
123C2×Q8—21no—
124C2×Q8—3141no—
125C2×D4—3142no—
126C2×D4—1571no—
127C2×D4—1571no—
128C22×C4—3142no—
129C22×C4—3141no—
130C22×C4—3141no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—3141no—
134C4⋊C4—21no—
135C4⋊C4—3142no—
136C4⋊C4—3141no—
137C4⋊C4—3141no—
138C4⋊C4—1571no—
139C4⋊C4—1571no—
140C4⋊C4D62812yes—
141C22⋊C4—3142no—
142C22⋊C4—3141no—
143C22⋊C4—3141no—
144C42C22×D15711yescharacteristic
145C23—3141no—
146C23—3141no—
147Q8—41no—
148Q8—41no—
149Q8—6282no—
150D4—3141no—
151D4—3141no—
152D4—3141no—
153D4—6284no—
154D4—1572no—
155C2×C4—22no—
156C2×C4—3141no—
157C2×C4—3141no—
158C2×C4—6284no—
159C2×C4—6281no—
160C2×C4—6281no—
161C2×C4—6281no—
162C2×C4—6281no—
163C2×C4—6281no—
164C2×C4D4×D15711yescharacteristic
165C2×C4D4×D15711yescharacteristic
166C2×C4C2×D62811yescharacteristic
167C8—41no—
168C8—41no—
169C8—6281no—
170C22—3142no—
171C22—6281no—
172C22—6281no—
173C22—6281no—
174C22—6281no—
175C22—6281no—
176C22#1909774111yescharacteristic
177C4—21no—
178C4—42no—
179C4—6281no—
180C4—6281no—
181C4—12561no—
182C4SD16×D15711yescharacteristic
183C4#1909779211yescharacteristic
184C4#1909779511yescharacteristic
185C4#1909780311yescharacteristic
186C2—6282no—
187C2—12561no—
188C2#2375742511yescharacteristic
189C2#2375743811yescharacteristic
190C2#2375744811yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#332×C157C2
socleC22×C157#120
prime radical#23757926C2
hypercenter#332D157
hypocenterC157#1635
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #23757625C2semidirect
3. #23757564C2semidirect
4. #23757564C2semidirect
5. #23757000C2semidirect
6. #23757000C2semidirect
7. #332×C157C2semidirect
95. C157#1635semidirect
101. #332D157semidirect

Maximal subgroups

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

subgroupindex
#237579262
#237576252
#237575642
#237570002
#332×C1572
#1635157