Finite Group Databasebeta

← #34101200

Subgroups — #34101200

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#23757780C212yesmaximal, complemented
2#23757290C212yesmaximal, complemented
3#23757236C211yesmaximal, characteristic, complemented
4#23757030C211yesmaximal, characteristic, complemented
5#575×C157C211yesmaximal, characteristic, complemented
6C22×C4×D157C2211yescharacteristic
7C2×#14578938C2211yescharacteristic
8#19097752—22no—
9#19097747—22no—
10#19097742—22no—
11#19097739—22no—
12C4×C22⋊D157—24no—
13#19097730C2212yes—
14#19097698—24no—
15#19097683—22no—
16C2×#41×C157C2212yes—
17#137×C157—22no—
18AGL(1,ℤ/8)×C157—22no—
19#135×C157—22no—
20C2×M16×C157C2211yescharacteristic
21C23×D157D411yescharacteristic
22C2×C22⋊D157—24no—
23C22×Dic157D411yescharacteristic
24C2×C4×D157—21no—
25C2×C4×D157—22no—
26C2×C4×D157—22no—
27C2×C4×D157—21no—
28#14578938—22no—
29C2×#11929434—21no—
30C4⋊Dic157—22no—
31#14578933—24no—
32C22⋊Dic157—24no—
33C22⋊Dic157—22no—
34#14578931—24no—
35C4×Dic157D414yescomplemented
36#41×C157—22no—
37#41×C157—22no—
38#41×C157—22no—
39#41×C157—22no—
40C2×Q8×C157D412yescomplemented
41C2×D4×C157—22no—
42C2×D4×C157D412yescomplemented
43C22×C4×C157—22no—
44C22×C4×C157C2311yescharacteristic
45Q16×C157—22no—
46SD16×C157—24no—
47D8×C157—22no—
48M16×C157—22no—
49C2×C8×C157D412yescomplemented
50C22×D157—22no—
51C22×D157—21no—
52C22×D157—42no—
53C22⋊D157—48no—
54C2×Dic157—22no—
55C2×Dic157—24no—
56C2×Dic157—21no—
57C4×D157—41no—
58C4×D157—42no—
59C4×D157—41no—
60#11929434—41no—
61C23×C157—22no—
62C23×C157C2×D411yescharacteristic
63Q8×C157—22no—
64Q8×C157—22no—
65D4×C157—22no—
66D4×C157—22no—
67D4×C157—42no—
68D4×C157—42no—
69C2×C4×C157—22no—
70C2×C4×C157—42no—
71C2×C4×C157—42no—
72C2×C4×C157C2×D412yes—
73C2×C4×C157C2×D412yes—
74C2×C4×C157C2×D411yescharacteristic
75C2×C4×C157#4111yescharacteristic
76C8×C157—22no—
77C22×C157—41no—
78C22×C157—44no—
79C22×C157—42no—
80C22×C157#12012yes—
81C22×C157#12111yescharacteristic
82C2×D157—24no—
83C2×D157—22no—
84C2×D157—42no—
85C2×D157—41no—
86C2×D157—41no—
87C4×C157—42no—
88C4×C157#12011yescharacteristic
89C4×C157#12112yes—
90C4×C157#12711yescharacteristic
91Dic157—44no—
92Dic157—41no—
93C2×C157—22no—
94C2×C157—21no—
95C2×C157—82no—
96C2×C157#39211yescharacteristic
97D157—42no—
98C157#201011yescharacteristic, complemented, Sylow
99#2010—1571nomaximal, Sylow
100#575D15711yescharacteristic, complemented
101#525—1572no—
102#421—1572no—
103#407—1571no—
104H(3,ℤ/4)—1571no—
105C2×#41C2×D15712yes—
106C23×C4—1571no—
107#137—22no—
108AGL(1,ℤ/8)—22no—
109#135—22no—
110C2×M16—1571no—
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—3142no—
120C24—1571no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C22⋊D15712yescomplemented
126C2×D4—22no—
127C2×D4—3144no—
128C2×D4C22⋊D15712yescomplemented
129C22×C4—22no—
130C22×C4—3142no—
131C22×C4—3141no—
132C22×C4—3142no—
133C22×C4—3141no—
134C22×C4—1571no—
135C22×C4C22×D15711yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—3142no—
141C2×C8—3141no—
142C2×C8C22⋊D15712yescomplemented
143C4⋊C4—3144no—
144C4⋊C4—3142no—
145C22⋊C4—3144no—
146C22⋊C4—3144no—
147C22⋊C4—3142no—
148C42—1574no—
149C23—22no—
150C23—3142no—
151C23—3141no—
152C23—6282no—
153C23D4×D15711yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—42no—
159D4—42no—
160D4—6288no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—3144no—
165C2×C4—3142no—
166C2×C4—3141no—
167C2×C4—6281no—
168C2×C4—6282no—
169C2×C4—6281no—
170C2×C4D4×D15712yes—
171C2×C4C2×C22⋊D15712yes—
172C2×C4C2×C22⋊D15711yescharacteristic
173C2×C4#1457895311yescharacteristic
174C8—22no—
175C8—6281no—
176C22—41no—
177C22—44no—
178C22—42no—
179C22—3144no—
180C22—3142no—
181C22—6282no—
182C22—6281no—
183C22—6281no—
184C22#1909773912yes—
185C22#1909774211yescharacteristic
186C4—42no—
187C4—6284no—
188C4—6281no—
189C4#1909774011yescharacteristic
190C4#1909774312yes—
191C4#1909776711yescharacteristic
192C2—22no—
193C2—21no—
194C2—82no—
195C2—6282no—
196C2#2375718111yescharacteristic
subgroupG/H
centerC4#19097767
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#575×C157C2
socleC2×C157#392
hypercenter#575D157
hypocenterC157#2010
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #23757780C2semidirect
2. #23757290C2semidirect
3. #23757236C2semidirect
4. #23757030C2semidirect
5. #575×C157C2semidirect
35. C4×Dic157D4semidirect
40. C2×Q8×C157D4semidirect
42. C2×D4×C157D4semidirect
49. C2×C8×C157D4semidirect
98. C157#2010semidirect
100. #575D157semidirect
125. C2×Q8C22⋊D157semidirect
128. C2×D4C22⋊D157semidirect
142. C2×C8C22⋊D157semidirect

Maximal subgroups

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

subgroupindex
#237577802
#237572902
#237572362
#237570302
#575×C1572
#2010157