Finite Group Databasebeta

← #34101203

Subgroups — #34101203

Order 20096.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#23757784C212yesmaximal, complemented
3#23757289C212yesmaximal, complemented
4#23757030C211yesmaximal, characteristic, complemented
5#407×C157C211yesmaximal, characteristic, complemented
6C2×#14578954C2212yes—
7#19097804—22no—
8#19097799—22no—
9#19097793—22no—
10#19097754—22no—
11#19097750—22no—
12#19097745—22no—
13#19097740—22no—
14C4×C22⋊D157—24no—
15#19097730C2212yes—
16#19097697—24no—
17C23×C4×C157C2211yescharacteristic
18C2×M16×C157C2211yescharacteristic
19C2×M16×C157C2211yescharacteristic
20C22⋊C8×C157—22no—
21#14578954—22no—
22#14578954—22no—
23#14578954—22no—
24#14578954—22no—
25C2×Dic314D412yescomplemented
26C2×D628D412yescomplemented
27C2×C22⋊D157—24no—
28C2×C22⋊D157—22no—
29C2×C4×D157—22no—
30Dic628—22no—
31#14578943—24no—
32D1256—22no—
33C4⋊Dic157—22no—
34#14578933—24no—
35C22⋊Dic157—24no—
36C22⋊Dic157—22no—
37#14578931—24no—
38C4×Dic157D414yescomplemented
39C24×C157D411yescharacteristic
40C22×C4×C157—21no—
41C22×C4×C157—22no—
42C22×C4×C157—22no—
43C22×C4×C157—21no—
44C22×C4×C157D411yescharacteristic
45C22×C4×C157C2311yescharacteristic
46M16×C157—22no—
47M16×C157—22no—
48C2×C8×C157—21no—
49C2×C8×C157D412yescomplemented
50C22×D157—22no—
51Dic314—22no—
52Dic314—22no—
53D628—22no—
54D628—22no—
55C22⋊D157—48no—
56C22⋊D157—42no—
57C22⋊D157—42no—
58C2×Dic157—22no—
59C2×Dic157—24no—
60C4×D157—42no—
61C4×D157—42no—
62C23×C157—22no—
63C23×C157—21no—
64C23×C157—42no—
65C23×C157C2×D411yescharacteristic
66C2×C4×C157—22no—
67C2×C4×C157—21no—
68C2×C4×C157—41no—
69C2×C4×C157—42no—
70C2×C4×C157—41no—
71C2×C4×C157C2×D412yes—
72C2×C4×C157C2×D412yes—
73C2×C4×C157C2×D411yescharacteristic
74C2×C4×C157#4111yescharacteristic
75C8×C157—22no—
76C8×C157—41no—
77C22×C157—22no—
78C22×C157—24no—
79C22×C157—41no—
80C22×C157—42no—
81C22×C157—41no—
82C22×C157—41no—
83C22×C157#12012yes—
84C22×C157#12111yescharacteristic
85C2×D157—44no—
86C2×D157—42no—
87C4×C157—41no—
88C4×C157#12011yescharacteristic
89C4×C157#12112yes—
90C4×C157#12711yescharacteristic
91Dic157—44no—
92Dic157—42no—
93C2×C157—22no—
94C2×C157—21no—
95C2×C157—42no—
96C2×C157#39211yescharacteristic
97D157—82no—
98C157#201011yescharacteristic, complemented, Sylow
99#2010—1571nomaximal, Sylow
100#575—1571no—
101#525—1572no—
102#421—1572no—
103#407D15711yescharacteristic, complemented
104H(3,ℤ/4)—1571no—
105C2×#41—1572no—
106C23×C4C2×D15711yescharacteristic
107#137—3142no—
108AGL(1,ℤ/8)—3142no—
109#135—3142no—
110C2×M16C2×D15711yescharacteristic
111C2×M16C2×D15711yescharacteristic
112#123—3142no—
113C22⋊Q8—3142no—
114#121—3142no—
115#120—3142no—
116C4×D4—3144no—
117#117—1572no—
118#104—3144no—
119C22⋊C8—22no—
120C24D62811yescharacteristic
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—22no—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—3142no—
134C22×C4D62811yescharacteristic
135C22×C4C22×D15711yescharacteristic
136Q16—3142no—
137SD16—3144no—
138D8—3142no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8C22⋊D15712yescomplemented
143C4⋊C4—3144no—
144C4⋊C4—3142no—
145C22⋊C4—3144no—
146C22⋊C4—3144no—
147C22⋊C4—3142no—
148C42—1574no—
149C23—22no—
150C23—21no—
151C23—42no—
152C23—3142no—
153C23C2×D62811yescharacteristic
154Q8—3142no—
155Q8—3142no—
156D4—3142no—
157D4—3142no—
158D4—6288no—
159D4—6282no—
160D4—6282no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—3144no—
167C2×C4—3142no—
168C2×C4—6282no—
169C2×C4—6282no—
170C2×C4D4×D15712yes—
171C2×C4D4×D15712yes—
172C2×C4C2×C22⋊D15711yescharacteristic
173C2×C4#1457895411yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—6284no—
183C22—6282no—
184C22#1909774112yes—
185C22#1909774511yescharacteristic
186C4—41no—
187C4—6284no—
188C4—6282no—
189C4#1909773911yescharacteristic
190C4#1909774412yes—
191C4#1909776711yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—12562no—
196C2#2375718211yescharacteristic
subgroupG/H
centerC4#19097767
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#407×C157C2
socleC2×C157#392
hypercenter#407D157
hypocenterC157#2010
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #23758073C2semidirect
2. #23757784C2semidirect
3. #23757289C2semidirect
4. #23757030C2semidirect
5. #407×C157C2semidirect
25. C2×Dic314D4semidirect
26. C2×D628D4semidirect
38. C4×Dic157D4semidirect
49. C2×C8×C157D4semidirect
98. C157#2010semidirect
103. #407D157semidirect
142. C2×C8C22⋊D157semidirect

Maximal subgroups

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

subgroupindex
#237580732
#237577842
#237572892
#237570302
#407×C1572
#2010157