Finite Group Databasebeta

← #34099222

Subgroups — #34099222

Order 20096.

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

normal subgroups only

This group has 256 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, complemented
2#23757465C211yesmaximal, characteristic, complemented
3#23757465C211yesmaximal, characteristic, complemented
4#23757019C211yesmaximal, characteristic, complemented
5#23757002C211yesmaximal, characteristic, complemented
6#23757002C211yesmaximal, characteristic, complemented
7#486×C157C211yesmaximal, characteristic, complemented
8C2×#14578955—21no—
9C2×#14578939—21no—
10C2×#14578939—21no—
11#19097756—22no—
12#19097747—21no—
13#19097746—21no—
14C4×D628C2211yescharacteristic
15C4×D628C2211yescharacteristic
16C4⋊C4×D157—21no—
17C4⋊#11929434C2211yescharacteristic
18C4⋊#11929434C2211yescharacteristic
19#19097692—21no—
20#19097692—21no—
21C4⋊Q8×C157C2211yescharacteristic
22#127×C157C2211yescharacteristic
23#102×C157—22no—
24C4×C8×C157C2211yescharacteristic
25#14578955—42no—
26#14578955—42no—
27C2×D628—22no—
28C2×D628D411yescharacteristic
29C2×D628D411yescharacteristic
30C2×C4×D157—22no—
31C2×C4×D157—21no—
32C2×C4×D157—21no—
33#14578939—42no—
34#14578939—42no—
35C2×#11929434—21no—
36C2×#11929434—21no—
37C4⋊Dic157D411yescharacteristic
38C4⋊Dic157D411yescharacteristic
39#14578933—22no—
40#14578931—22no—
41#14578931—21no—
42#14578931—21no—
43C2×Q8×C157—21no—
44C2×D4×C157—21no—
45C2×D4×C157—21no—
46C2×D4×C157—21no—
47C2×C8×C157—21no—
48C4⋊C4×C157—21no—
49C4⋊C4×C157D412yes—
50C42×C157C2311yescharacteristic
51C22×D157—21no—
52C22×D157—21no—
53D628—21no—
54D628—21no—
55D628—21no—
56D628—44no—
57D628D812yescomplemented
58C2×Dic157—21no—
59C2×Dic157—21no—
60C4×D157—44no—
61C4×D157—41no—
62C4×D157—41no—
63C4×D157—41no—
64C4×D157—41no—
65#11929434—41no—
66#11929434—41no—
67C23×C157—41no—
68Q8×C157—41no—
69Q8×C157—41no—
70D4×C157—42no—
71D4×C157—41no—
72D4×C157—41no—
73D4×C157—41no—
74D4×C157—41no—
75C2×C4×C157—22no—
76C2×C4×C157C2×D411yescharacteristic
77C2×C4×C157C2×D411yescharacteristic
78C2×C4×C157C2×D411yescharacteristic
79C8×C157—41no—
80C22×C157—81no—
81C22×C157—81no—
82C22×C157—81no—
83C22×C157#12011yescharacteristic
84C2×D157—22no—
85C2×D157—41no—
86C2×D157—41no—
87C2×D157—41no—
88C2×D157—41no—
89C2×D157—41no—
90C4×C157—21no—
91C4×C157—42no—
92C4×C157C2×D811yescharacteristic
93C4×C157#13511yescharacteristic
94C4×C157AGL(1,ℤ/8)11yescharacteristic
95C4×C157AGL(1,ℤ/8)11yescharacteristic
96Dic157—41no—
97Dic157—41no—
98C2×C157—161no—
99C2×C157#44711yescharacteristic
100C2×C157#44911yescharacteristic
101C2×C157#45411yescharacteristic
102D157—42no—
103D157—81no—
104C157#162511yescharacteristic, complemented, Sylow
105#1625—1571nomaximal, Sylow
106#547—1571no—
107#486D15711yescharacteristic, complemented
108#459—1571no—
109#459—1571no—
110#332—1571no—
111D4⋊C8—1571no—
112D4⋊C8—1571no—
113C2×#41—3141no—
114C2×D8—3141no—
115C2×D8—3141no—
116C4⋊Q8C2×D15711yescharacteristic
117#127C2×D15711yescharacteristic
118#123—3142no—
119C22⋊Q8—3141no—
120#121—3141no—
121C4×D4—1571no—
122C4×D4—1571no—
123C2×C4⋊C4—3141no—
124C4⋊C8—1571no—
125C4⋊C8—1571no—
126#102—22no—
127#102—3141no—
128#102—3141no—
129C4×C8C2×D15711yescharacteristic
130#41—6282no—
131#41—6282no—
132C2×Q8—21no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—3142no—
137C2×D4—1571no—
138C2×D4—1571no—
139C22×C4—3142no—
140C22×C4—3141no—
141C22×C4—3141no—
142D8—6282no—
143D8—6282no—
144C2×C8—21no—
145C2×C8—3141no—
146C2×C8—3141no—
147C4⋊C4—21no—
148C4⋊C4—3142no—
149C4⋊C4—1571no—
150C4⋊C4—1571no—
151C4⋊C4C22⋊D15712yes—
152C22⋊C4—3142no—
153C22⋊C4—3141no—
154C22⋊C4—3141no—
155C42C22×D15711yescharacteristic
156C23—41no—
157C23—3141no—
158C23—3141no—
159Q8—41no—
160Q8—41no—
161D4—42no—
162D4—41no—
163D4—41no—
164D4—41no—
165D4—41no—
166D4—3141no—
167D4—3141no—
168D4—3141no—
169D4—6284no—
170D4—1572no—
171C2×C4—22no—
172C2×C4—3141no—
173C2×C4—3141no—
174C2×C4—6284no—
175C2×C4—6281no—
176C2×C4—6281no—
177C2×C4—6281no—
178C2×C4—6281no—
179C2×C4D4×D15711yescharacteristic
180C2×C4D4×D15711yescharacteristic
181C2×C4C2×C22⋊D15711yescharacteristic
182C8—41no—
183C8—6281no—
184C8—6281no—
185C22—81no—
186C22—81no—
187C22—81no—
188C22—3142no—
189C22—6281no—
190C22—6281no—
191C22—6281no—
192C22—6281no—
193C22—6281no—
194C22#1909773911yescharacteristic
195C4—21no—
196C4—42no—
197C4—6281no—
198C4—6281no—
199C4D8×D15711yescharacteristic
200C4#1909779211yescharacteristic
201C4#1909779511yescharacteristic
202C4#1909779811yescharacteristic
203C2—161no—
204C2—6282no—
205C2—12561no—
206C2#2375740511yescharacteristic
207C2#2375741711yescharacteristic
208C2#2375744511yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#486×C157C2
socleC22×C157#120
hypercenter#486D157
hypocenterC157#1625
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #23757926C2semidirect
2. #23757465C2semidirect
3. #23757465C2semidirect
4. #23757019C2semidirect
5. #23757002C2semidirect
6. #23757002C2semidirect
7. #486×C157C2semidirect
57. D628D8semidirect
104. C157#1625semidirect
107. #486D157semidirect

Maximal subgroups

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

subgroupindex
#237579262
#237574652
#237570192
#237570022
#486×C1572
#1625157