Finite Group Databasebeta

← #34099224

Subgroups — #34099224

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#23757928C211yesmaximal, characteristic, complemented
2#23757619C211yesmaximal, characteristic, complemented
3#23757465C211yesmaximal, characteristic, complemented
4#23757018C211yesmaximal, characteristic, complemented
5D4⋊#11929434C211yesmaximal, characteristic, complemented
6#23757000C211yesmaximal, characteristic, complemented
7#459×C157C211yesmaximal, characteristic, complemented
8C2×#14578954—21no—
9C2×#14578939—21no—
10#19097771C2211yescharacteristic
11#19097753—22no—
12#19097750—21no—
13#19097742—21no—
14C4×D628C2211yescharacteristic
15C4⋊C4×D157—21no—
16C4⋊#11929434C2211yescharacteristic
17#19097692—22no—
18#19097692—21no—
19C4×#11929434C2211yescharacteristic
20C2×D8×C157—21no—
21#127×C157C2211yescharacteristic
22C4×D4×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24#102×C157—21no—
25#14578954—42no—
26#14578954—42no—
27C2×Dic314—21no—
28C2×D628D411yescharacteristic
29C2×C22⋊D157—22no—
30C2×C4×D157—22no—
31C2×C4×D157—21no—
32#14578939—42no—
33C2×#11929434—21no—
34C2×#11929434—21no—
35C4⋊Dic157—21no—
36C4⋊Dic157D411yescharacteristic
37C4⋊Dic157D412yes—
38#14578933—22no—
39C22⋊Dic157—22no—
40#14578931—21no—
41C2×D4×C157—21no—
42C2×D4×C157—21no—
43C2×D4×C157—21no—
44C2×D4×C157D411yescharacteristic
45C22×C4×C157—21no—
46D8×C157—42no—
47C2×C8×C157—21no—
48C4⋊C4×C157D411yescharacteristic
49C22⋊C4×C157—21no—
50C42×C157C2311yescharacteristic
51C22×D157—21no—
52Dic314—41no—
53Dic314—41no—
54D628—21no—
55D628D812yescomplemented
56C22⋊D157—44no—
57C2×Dic157—22no—
58C2×Dic157—21no—
59C4×D157—44no—
60C4×D157—41no—
61C4×D157—41no—
62#11929434—41no—
63#11929434—41no—
64C23×C157—21no—
65C23×C157—41no—
66D4×C157—21no—
67D4×C157—21no—
68D4×C157—42no—
69D4×C157—41no—
70D4×C157—41no—
71D4×C157—41no—
72D4×C157—41no—
73C2×C4×C157—21no—
74C2×C4×C157—41no—
75C2×C4×C157—41no—
76C2×C4×C157C2×D411yescharacteristic
77C2×C4×C157C2×D411yescharacteristic
78C2×C4×C157C2×D411yescharacteristic
79C8×C157—41no—
80C22×C157—41no—
81C22×C157—41no—
82C22×C157—41no—
83C22×C157—81no—
84C22×C157—81no—
85C22×C157—81no—
86C22×C157#12011yescharacteristic
87C2×D157—22no—
88C2×D157—41no—
89C2×D157—41no—
90C4×C157—21no—
91C4×C157—41no—
92C4×C157C2×D811yescharacteristic
93C4×C157#13511yescharacteristic
94C4×C157AGL(1,ℤ/8)11yescharacteristic
95C4×C157AGL(1,ℤ/8)11yescharacteristic
96Dic157—42no—
97Dic157—41no—
98C2×C157—81no—
99C2×C157—161no—
100C2×C157#44711yescharacteristic
101C2×C157#44911yescharacteristic
102C2×C157#45411yescharacteristic
103D157—42no—
104C157#162511yescharacteristic, complemented, Sylow
105#1625—1571nomaximal, Sylow
106#547—1571no—
107#486—1571no—
108#459—1571no—
109#459D15711yescharacteristic, complemented
110#332—1571no—
111D4⋊C8—1571no—
112D4⋊C8—1571no—
113C2×#41—3141no—
114C2×D8—21no—
115C2×D8—3141no—
116C4⋊Q8—1571no—
117#127C2×D15711yescharacteristic
118#123—3142no—
119C22⋊Q8—3141no—
120#121—3141no—
121C4×D4—1571no—
122C4×D4C2×D15711yescharacteristic
123C2×C4⋊C4—3141no—
124C4⋊C8—1571no—
125C4⋊C8C2×D15711yescharacteristic
126#102—21no—
127#102—3141no—
128#102—3142no—
129C4×C8—1571no—
130#41—6282no—
131#41—6282no—
132C2×Q8—3141no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—3142no—
137C2×D4—1571no—
138C2×D4C22⋊D15711yescharacteristic
139C22×C4—21no—
140C22×C4—3142no—
141C22×C4—3141no—
142D8—42no—
143D8—6282no—
144C2×C8—21no—
145C2×C8—3141no—
146C2×C8—3141no—
147C4⋊C4—3142no—
148C4⋊C4—3141no—
149C4⋊C4—1571no—
150C4⋊C4—1572no—
151C4⋊C4C22⋊D15711yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—3142no—
154C22⋊C4—3141no—
155C42C22×D15711yescharacteristic
156C23—21no—
157C23—41no—
158C23—3141no—
159Q8—6281no—
160Q8—6281no—
161D4—21no—
162D4—21no—
163D4—42no—
164D4—41no—
165D4—41no—
166D4—41no—
167D4—41no—
168D4—3141no—
169D4—6284no—
170D4—1572no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—3141no—
175C2×C4—3142no—
176C2×C4—6284no—
177C2×C4—6281no—
178C2×C4—6281no—
179C2×C4D4×D15711yescharacteristic
180C2×C4D4×D15711yescharacteristic
181C2×C4C2×C22⋊D15711yescharacteristic
182C8—41no—
183C8—6281no—
184C8—6281no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—81no—
189C22—81no—
190C22—81no—
191C22—3142no—
192C22—6281no—
193C22—6281no—
194C22#1909773911yescharacteristic
195C4—21no—
196C4—41no—
197C4—6282no—
198C4—6281no—
199C4D8×D15711yescharacteristic
200C4#1909779111yescharacteristic
201C4#1909779511yescharacteristic
202C4#1909779711yescharacteristic
203C2—81no—
204C2—161no—
205C2—6282no—
206C2#2375740511yescharacteristic
207C2#2375741611yescharacteristic
208C2#2375744411yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#459×C157C2
socleC22×C157#120
hypercenter#459D157
hypocenterC157#1625
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #23757928C2semidirect
2. #23757619C2semidirect
3. #23757465C2semidirect
4. #23757018C2semidirect
5. D4⋊#11929434C2semidirect
6. #23757000C2semidirect
7. #459×C157C2semidirect
55. D628D8semidirect
104. C157#1625semidirect
109. #459D157semidirect

Maximal subgroups

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

subgroupindex
#237579282
#237576192
#237574652
#237570182
D4⋊#119294342
#237570002
#459×C1572
#1625157