Finite Group Databasebeta

← #34099209

Subgroups — #34099209

Order 20096.

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

normal subgroups only

This group has 236 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#23757984C211yesmaximal, characteristic, complemented
2#23757647C211yesmaximal, characteristic, complemented
3#23757474C211yesmaximal, characteristic, complemented
4#23757469C211yesmaximal, characteristic
5#23757003C211yesmaximal, characteristic, complemented
6#23757000C211yesmaximal, characteristic, complemented
7#333×C157C211yesmaximal, characteristic, complemented
8C2×#14578943—21no—
9C2×#14578941—22no—
10C2×D1256—21no—
11#19097768C2211yescharacteristic
12#19097762—21no—
13#19097751—21no—
14#19097747—22no—
15C4×Dic314C2211yescharacteristic
16C4×D628C2211yescharacteristic
17#19097733—21no—
18C4⋊C4×D157—21no—
19#19097693—21no—
20#19097693—21no—
21C4×#11929434C2211yescharacteristic
22C4⋊Q8×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4⋊C8×C157C2211yescharacteristic
25C2×Dic314D411yescharacteristic
26C2×D628—21no—
27C2×D628—21no—
28C2×D628—21no—
29C2×D628D411yescharacteristic
30C2×C4×D157—22no—
31C2×C4×D157—21no—
32#14578943—42no—
33#14578941—44no—
34D1256—42no—
35C2×#11929434—21no—
36C4⋊Dic157—22no—
37C4⋊Dic157D411yescharacteristic
38C4⋊Dic157D411yescharacteristic
39#14578933—22no—
40#14578933—21no—
41#14578931—22no—
42#14578931—21no—
43C4×Dic157—21no—
44C2×Q8×C157D412yes—
45C2×C8×C157—21no—
46C2×C8×C157—21no—
47C4⋊C4×C157—21no—
48C4⋊C4×C157—21no—
49C42×C157C2311yescharacteristic
50C22×D157—21no—
51C22×D157—41no—
52Dic314—21no—
53Dic314—21no—
54D628—21no—
55D628—42no—
56D628—41no—
57D628—41no—
58D628—41no—
59D628—41no—
60D628SD1612yescomplemented
61C2×Dic157—21no—
62C2×Dic157—21no—
63C2×Dic157—21no—
64C4×D157—41no—
65C4×D157—41no—
66C4×D157—82no—
67#11929434—22no—
68Q8×C157—42no—
69C2×C4×C157—22no—
70C2×C4×C157C2×D411yescharacteristic
71C2×C4×C157C2×D411yescharacteristic
72C2×C4×C157C2×D411yescharacteristic
73C8×C157—41no—
74C8×C157—41no—
75C22×C157#12011yescharacteristic
76C2×D157—22no—
77C2×D157—41no—
78C2×D157—41no—
79C2×D157—81no—
80C2×D157—81no—
81C2×D157—81no—
82C4×C157—21no—
83C4×C157—42no—
84C4×C157C2×SD1611yescharacteristic
85C4×C157#13511yescharacteristic
86C4×C157AGL(1,ℤ/8)11yescharacteristic
87C4×C157#13711yescharacteristic
88Dic157—41no—
89Dic157—41no—
90Dic157—41no—
91C2×C157#44811yescharacteristic
92C2×C157#44911yescharacteristic
93C2×C157#45311yescharacteristic
94D157—42no—
95D157—161no—
96C157#162211yescharacteristic, complemented, Sylow
97#1622—1571nomaximal, Sylow
98#554—1571no—
99#492—1571no—
100#460—1571no—
101#459—1571no—
102#333D15711yescharacteristic, complemented
103Q8⋊C8—1571no—
104D4⋊C8—1571no—
105C2×SD16—3141no—
106C2×SD16—3142no—
107C2×D8—3141no—
108C4⋊Q8C2×D15711yescharacteristic
109#127—1571no—
110#125—3141no—
111C22⋊Q8—3141no—
112C22⋊Q8—3142no—
113C4×Q8—1571no—
114C4×D4—3141no—
115C4×D4—1571no—
116C2×C4⋊C4—3141no—
117C4⋊C8C2×D15711yescharacteristic
118C4⋊C8C2×D15711yescharacteristic
119#102—3141no—
120#102—3141no—
121C4×C8—1571no—
122C2×Q8—1571no—
123C2×Q8D62812yes—
124C2×D4—3141no—
125C2×D4—3141no—
126C2×D4—3141no—
127C2×D4—1571no—
128C22×C4—3142no—
129C22×C4—3141no—
130SD16—6282no—
131SD16—6284no—
132D8—6282no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—3141no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—3142no—
139C4⋊C4—3142no—
140C4⋊C4—3141no—
141C4⋊C4—1571no—
142C4⋊C4—1571no—
143C22⋊C4—3142no—
144C22⋊C4—3141no—
145C42—3141no—
146C42C22×D15711yescharacteristic
147C23—3141no—
148C23—6281no—
149Q8—42no—
150Q8—3141no—
151Q8—3141no—
152D4—3141no—
153D4—6282no—
154D4—6281no—
155D4—6281no—
156D4—6281no—
157D4—6281no—
158D4—1572no—
159C2×C4—22no—
160C2×C4—3141no—
161C2×C4—3141no—
162C2×C4—3141no—
163C2×C4—6281no—
164C2×C4—6281no—
165C2×C4—12562no—
166C2×C4D4×D15711yescharacteristic
167C2×C4D4×D15711yescharacteristic
168C2×C4C2×D62811yescharacteristic
169C8—41no—
170C8—41no—
171C8—3142no—
172C22—3142no—
173C22—6281no—
174C22—6281no—
175C22—12561no—
176C22—12561no—
177C22—12561no—
178C22#1909774111yescharacteristic
179C4—21no—
180C4—42no—
181C4—6281no—
182C4—6281no—
183C4—6281no—
184C4SD16×D15711yescharacteristic
185C4#1909779411yescharacteristic
186C4#1909779811yescharacteristic
187C4#1909780311yescharacteristic
188C2—6282no—
189C2—25121no—
190C2#2375741311yescharacteristic
191C2#2375742111yescharacteristic
192C2#2375744311yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#333×C157C2
socleC22×C157#120
prime radical#23757469C2
hypercenter#333D157
hypocenterC157#1622
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #23757984C2semidirect
2. #23757647C2semidirect
3. #23757474C2semidirect
5. #23757003C2semidirect
6. #23757000C2semidirect
7. #333×C157C2semidirect
60. D628SD16semidirect
96. C157#1622semidirect
102. #333D157semidirect

Maximal subgroups

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

subgroupindex
#237579842
#237576472
#237574742
#237574692
#237570032
#237570002
#333×C1572
#1622157