Finite Group Databasebeta

← #34099194

Subgroups — #34099194

Order 20096.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#23758008C211yesmaximal, characteristic, complemented
2#23757649C211yesmaximal, characteristic
3#23757470C211yesmaximal, characteristic, complemented
4#23757016C211yesmaximal, characteristic, complemented
5Q8⋊#11929434C211yesmaximal, characteristic, complemented
6#23757003C211yesmaximal, characteristic, complemented
7#460×C157C211yesmaximal, characteristic, complemented
8C2×#14578942—21no—
9C2×#14578939—22no—
10#19097768C2211yescharacteristic
11#19097760—21no—
12#19097759—21no—
13#19097756—22no—
14C4×Dic314C2211yescharacteristic
15C4×D628—21no—
16#19097733—21no—
17C4⋊#11929434C2211yescharacteristic
18#19097692—21no—
19C4×#11929434C2211yescharacteristic
20C2×SD16×C157—21no—
21#127×C157C2211yescharacteristic
22C4×Q8×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24#102×C157—21no—
25C2×Dic314D411yescharacteristic
26C2×D628—21no—
27C2×D628—21no—
28C2×D628D412yes—
29C2×C4×D157—22no—
30#14578942—42no—
31#14578939—44no—
32C2×#11929434—21no—
33C2×#11929434—21no—
34C4⋊Dic157D411yescharacteristic
35#14578933—21no—
36#14578931—22no—
37#14578931—22no—
38#14578931—22no—
39C4×Dic157—21no—
40C2×Q8×C157D411yescharacteristic
41C2×D4×C157—21no—
42C2×D4×C157—21no—
43C2×D4×C157—21no—
44SD16×C157—42no—
45C2×C8×C157—21no—
46C4⋊C4×C157—21no—
47C4⋊C4×C157D411yescharacteristic
48C42×C157—21no—
49C42×C157C2311yescharacteristic
50C22×D157—22no—
51Dic314—21no—
52Dic314—21no—
53D628—42no—
54D628—41no—
55D628—41no—
56D628—41no—
57D628—41no—
58C2×Dic157—21no—
59C2×Dic157—21no—
60C4×D157—82no—
61#11929434—22no—
62#11929434—41no—
63C23×C157—41no—
64Q8×C157—21no—
65Q8×C157—21no—
66D4×C157—42no—
67D4×C157—41no—
68D4×C157—41no—
69D4×C157—41no—
70D4×C157—41no—
71C2×C4×C157—21no—
72C2×C4×C157—21no—
73C2×C4×C157C2×D411yescharacteristic
74C2×C4×C157C2×D411yescharacteristic
75C2×C4×C157C2×D411yescharacteristic
76C8×C157—41no—
77C22×C157—81no—
78C22×C157—81no—
79C22×C157—81no—
80C22×C157#12011yescharacteristic
81C2×D157—42no—
82C2×D157—42no—
83C2×D157—42no—
84C4×C157—21no—
85C4×C157—41no—
86C4×C157—41no—
87C4×C157#13511yescharacteristic
88C4×C157#13511yescharacteristic
89C4×C157AGL(1,ℤ/8)11yescharacteristic
90C4×C157AGL(1,ℤ/8)11yescharacteristic
91Dic157—41no—
92Dic157—41no—
93C2×C157—161no—
94C2×C157#44911yescharacteristic
95C2×C157#44911yescharacteristic
96C2×C157#45311yescharacteristic
97D157—82no—
98C157#162011yescharacteristic, complemented, Sylow
99#1620—1571nomaximal, Sylow
100#559—1571no—
101#493—1571no—
102#460—1571no—
103#460D15711yescharacteristic, complemented
104#331—1571no—
105Q8⋊C8—1571no—
106Q8⋊C8—1571no—
107C2×SD16—21no—
108C2×SD16—3141no—
109C2×D8—3142no—
110#127—1571no—
111#127C2×D15711yescharacteristic
112#124—3141no—
113#124—3141no—
114#123—3142no—
115C4×Q8—1571no—
116C4×Q8C2×D15711yescharacteristic
117C4×D4—3141no—
118C4×D4—3141no—
119C4⋊C8—1571no—
120C4⋊C8C2×D15711yescharacteristic
121#102—21no—
122#102—3141no—
123C4×C8—1571no—
124C2×Q8—1571no—
125C2×Q8C22⋊D15711yescharacteristic
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—3141no—
130C2×D4—3141no—
131C2×D4—1572no—
132C22×C4—3142no—
133SD16—42no—
134SD16—6282no—
135D8—6284no—
136C2×C8—21no—
137C2×C8—3141no—
138C2×C8—3141no—
139C4⋊C4—21no—
140C4⋊C4—3141no—
141C4⋊C4—1571no—
142C4⋊C4C22⋊D15711yescharacteristic
143C22⋊C4—3142no—
144C22⋊C4—3142no—
145C22⋊C4—3142no—
146C42—21no—
147C42—3141no—
148C42C22×D15711yescharacteristic
149C23—41no—
150C23—3142no—
151Q8—21no—
152Q8—21no—
153Q8—3141no—
154Q8—3141no—
155D4—42no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—41no—
160D4—6282no—
161D4—6281no—
162D4—6281no—
163D4—6281no—
164D4—6281no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—3141no—
168C2×C4—3141no—
169C2×C4—12562no—
170C2×C4D4×D15711yescharacteristic
171C2×C4D4×D15711yescharacteristic
172C2×C4C2×C22⋊D15711yescharacteristic
173C8—41no—
174C8—3142no—
175C8—6281no—
176C22—81no—
177C22—81no—
178C22—81no—
179C22—6282no—
180C22—6282no—
181C22—6282no—
182C22#1909773911yescharacteristic
183C4—21no—
184C4—41no—
185C4—41no—
186C4—6281no—
187C4—6281no—
188C4#1909779111yescharacteristic
189C4#1909779211yescharacteristic
190C4#1909779711yescharacteristic
191C4#1909779811yescharacteristic
192C2—161no—
193C2—12562no—
194C2#2375741611yescharacteristic
195C2#2375741711yescharacteristic
196C2#2375743911yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#460×C157C2
socleC22×C157#120
prime radical#23757649C2
hypercenter#460D157
hypocenterC157#1620
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #23758008C2semidirect
3. #23757470C2semidirect
4. #23757016C2semidirect
5. Q8⋊#11929434C2semidirect
6. #23757003C2semidirect
7. #460×C157C2semidirect
98. C157#1620semidirect
103. #460D157semidirect

Maximal subgroups

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

subgroupindex
#237580082
#237576492
#237574702
#237570162
Q8⋊#119294342
#237570032
#460×C1572
#1620157