Finite Group Databasebeta

← #34101204

Subgroups — #34101204

Order 20096.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#23758073C211yesmaximal, characteristic, complemented
2#23757785C212yesmaximal, complemented
3#23757291C212yesmaximal, complemented
4#23757236C211yesmaximal, characteristic, complemented
5H(3,ℤ/4)×C157C211yesmaximal, characteristic, complemented
6C2×#14578954C2212yes—
7C22×C4×D157C2211yescharacteristic
8#19097804—22no—
9#19097799—22no—
10#19097793—22no—
11C2×#14578938C2211yescharacteristic
12#19097755—22no—
13#19097751—22no—
14#19097746—22no—
15#19097741—22no—
16C4×D628—24no—
17#19097699—24no—
18#19097683—22no—
19C2×M16×C157C2211yescharacteristic
20#117×C157C2212yes—
21C23×D157D411yescharacteristic
22#14578954—22no—
23#14578954—22no—
24#14578954—22no—
25#14578954—22no—
26C2×Dic314D412yescomplemented
27C2×D628—24no—
28C2×D628D412yescomplemented
29C2×C22⋊D157—22no—
30C22×Dic157D411yescharacteristic
31C2×C4×D157—21no—
32C2×C4×D157—22no—
33C2×C4×D157—22no—
34C2×C4×D157—22no—
35C2×C4×D157—21no—
36Dic628—22no—
37#14578943—24no—
38D1256—22no—
39#14578938—22no—
40C2×#11929434—21no—
41C4⋊Dic157—24no—
42#14578931—24no—
43#14578931—24no—
44C22×C4×C157C2311yescharacteristic
45M16×C157—22no—
46C2×C8×C157D412yescomplemented
47C4⋊C4×C157—22no—
48C22⋊C4×C157—22no—
49C42×C157D414yescomplemented
50C22×D157—22no—
51C22×D157—21no—
52C22×D157—22no—
53C22×D157—42no—
54Dic314—22no—
55Dic314—22no—
56D628—22no—
57D628—22no—
58D628—48no—
59C22⋊D157—42no—
60C22⋊D157—42no—
61C2×Dic157—22no—
62C2×Dic157—22no—
63C2×Dic157—21no—
64C4×D157—41no—
65C4×D157—42no—
66C4×D157—42no—
67C4×D157—41no—
68C4×D157—42no—
69#11929434—41no—
70C23×C157C2×D411yescharacteristic
71C2×C4×C157—24no—
72C2×C4×C157C2×D412yes—
73C2×C4×C157C2×D411yescharacteristic
74C2×C4×C157C2×D412yes—
75C2×C4×C157#4111yescharacteristic
76C8×C157—22no—
77C22×C157—41no—
78C22×C157#12012yes—
79C22×C157#12111yescharacteristic
80C2×D157—24no—
81C2×D157—22no—
82C2×D157—42no—
83C2×D157—41no—
84C2×D157—41no—
85C2×D157—44no—
86C2×D157—42no—
87C4×C157—44no—
88C4×C157#12011yescharacteristic
89C4×C157#12112yes—
90C4×C157#12711yescharacteristic
91Dic157—41no—
92Dic157—42no—
93C2×C157—22no—
94C2×C157—21no—
95C2×C157#39211yescharacteristic
96D157—42no—
97D157—82no—
98C157#201011yescharacteristic, complemented, Sylow
99#2010—1571nomaximal, Sylow
100#575—1571no—
101#525—1572no—
102#421—1572no—
103#407—1571no—
104H(3,ℤ/4)D15711yescharacteristic, complemented
105C2×#41—1572no—
106C23×C4—1571no—
107#137—3142no—
108AGL(1,ℤ/8)—3142no—
109#135—3142no—
110C2×M16—1571no—
111C2×M16C2×D15711yescharacteristic
112#123—3142no—
113C22⋊Q8—3142no—
114#121—3142no—
115#120—3142no—
116C4×D4—3144no—
117#117C2×D15712yes—
118#104—3144no—
119C22⋊C8—3142no—
120C24—1571no—
121#41—3142no—
122#41—3142no—
123#41—3142no—
124#41—3142no—
125C2×Q8—1572no—
126C2×D4—3144no—
127C2×D4—3142no—
128C2×D4—1572no—
129C22×C4—3142no—
130C22×C4—3141no—
131C22×C4—3142no—
132C22×C4—3142no—
133C22×C4—3141no—
134C22×C4—1571no—
135C22×C4C22×D15711yescharacteristic
136Q16—3142no—
137SD16—3144no—
138D8—3142no—
139M16—22no—
140M16—3142no—
141C2×C8—3141no—
142C2×C8D62812yescomplemented
143C4⋊C4—22no—
144C4⋊C4—3144no—
145C22⋊C4—22no—
146C22⋊C4—3144no—
147C22⋊C4—3144no—
148C42D62814yescomplemented
149C23—3142no—
150C23—3141no—
151C23—3142no—
152C23—6282no—
153C23D4×D15711yescharacteristic
154Q8—3142no—
155Q8—3142no—
156D4—3142no—
157D4—3142no—
158D4—6288no—
159D4—6282no—
160D4—6282no—
161C2×C4—24no—
162C2×C4—3142no—
163C2×C4—3142no—
164C2×C4—3141no—
165C2×C4—6281no—
166C2×C4—6282no—
167C2×C4—6282no—
168C2×C4—6281no—
169C2×C4—6282no—
170C2×C4D4×D15712yes—
171C2×C4C2×D62811yescharacteristic
172C2×C4C2×D62812yes—
173C2×C4#1457895511yescharacteristic
174C8—22no—
175C8—6281no—
176C22—41no—
177C22—3144no—
178C22—3142no—
179C22—6282no—
180C22—6281no—
181C22—6284no—
182C22—6281no—
183C22—6282no—
184C22#1909774112yes—
185C22#1909774611yescharacteristic
186C4—44no—
187C4—6281no—
188C4—6282no—
189C4#1909774111yescharacteristic
190C4#1909774612yes—
191C4#1909776811yescharacteristic
192C2—22no—
193C2—21no—
194C2—6282no—
195C2—12562no—
196C2#2375718311yescharacteristic
subgroupG/H
centerC4#19097768
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
FittingH(3,ℤ/4)×C157C2
socleC2×C157#392
hypercenterH(3,ℤ/4)D157
hypocenterC157#2010
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #23758073C2semidirect
2. #23757785C2semidirect
3. #23757291C2semidirect
4. #23757236C2semidirect
5. H(3,ℤ/4)×C157C2semidirect
26. C2×Dic314D4semidirect
28. C2×D628D4semidirect
46. C2×C8×C157D4semidirect
49. C42×C157D4semidirect
98. C157#2010semidirect
104. H(3,ℤ/4)D157semidirect
142. C2×C8D628semidirect
148. C42D628semidirect

Maximal subgroups

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

subgroupindex
#237580732
#237577852
#237572912
#237572362
H(3,ℤ/4)×C1572
#2010157