Finite Group Databasebeta

← #34100331

Subgroups — #34100331

Order 20096.

360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C22×C4⋊Dic157C211yesmaximal, characteristic
2C2×#19097703C212yesmaximal, complemented
3#23757133C211yesmaximal, characteristic
4#23757036C212yesmaximal, complemented
5C2×C22⋊C8×C157C211yesmaximal, characteristic
6C23×Dic157—21no—
7C2×C4⋊Dic157—24no—
8C2×C4⋊Dic157—21no—
9C2×C4⋊Dic157C2211yescharacteristic
10C2×C4⋊Dic157C2211yescharacteristic
11C2×C4⋊Dic157C2212yes—
12C2×C22⋊Dic157—21no—
13#19097703—24no—
14#19097678—21no—
15C23×C4×C157C2211yescharacteristic
16C22×C8×C157C2212yes—
17C22⋊C8×C157C414yescomplemented
18C22×Dic157—24no—
19C22×Dic157—22no—
20C22×Dic157—21no—
21C22×Dic157—21no—
22C22×Dic157—42no—
23C22×Dic157—42no—
24C4⋊Dic157—24no—
25C4⋊Dic157—22no—
26C4⋊Dic157—22no—
27C4⋊Dic157—22no—
28C4⋊Dic157D414yes—
29C22⋊Dic157—42no—
30C24×C157D411yescharacteristic
31C22×C4×C157—22no—
32C22×C4×C157—22no—
33C22×C4×C157C2×C412yes—
34C22×C4×C157D411yescharacteristic
35C22×C4×C157Q812yes—
36C22×C4×C157C2311yescharacteristic
37C2×C8×C157—22no—
38C2×C8×C157—22no—
39C2×C8×C157C2×C414yescomplemented
40C2×Dic157—24no—
41C2×Dic157—48no—
42C2×Dic157—42no—
43C2×Dic157—42no—
44C2×Dic157—41no—
45C2×Dic157—41no—
46C2×Dic157—41no—
47C2×Dic157—41no—
48C2×Dic157—41no—
49C2×Dic157—41no—
50C23×C157—21no—
51C23×C157—21no—
52C23×C157—21no—
53C23×C157—21no—
54C23×C157C4⋊C412yes—
55C23×C157SD1612yes—
56C23×C157SD1612yes—
57C23×C157C2×D411yescharacteristic
58C2×C4×C157—21no—
59C2×C4×C157—21no—
60C2×C4×C157—24no—
61C2×C4×C157—24no—
62C2×C4×C157C4⋊C412yes—
63C2×C4×C157C22×C411yescharacteristic
64C2×C4×C157C2×D412yes—
65C2×C4×C157C2×Q811yescharacteristic
66C2×C4×C157#4112yes—
67C8×C157—24no—
68C22×C157—22no—
69C22×C157—22no—
70C22×C157—22no—
71C22×C157—22no—
72C22×C157—22no—
73C22×C157—22no—
74C22×C157#10614yescomplemented
75C22×C157C2×C4⋊C411yescharacteristic
76C22×C157#12011yescharacteristic
77C22×C157#12311yescharacteristic
78C22×C157C2×SD1611yescharacteristic
79C22×C157C2×SD1611yescharacteristic
80C22×C157AGL(1,ℤ/8)11yescharacteristic
81C22×C157#13711yescharacteristic
82C4×C157—22no—
83C4×C157C4×D412yes—
84C4×C157C22⋊Q812yes—
85Dic157—44no—
86Dic157—81no—
87Dic157—81no—
88C2×C157—24no—
89C2×C157#38511yescharacteristic
90C2×C157C2×#10611yescharacteristic
91C2×C157#42811yescharacteristic
92C2×C157#44811yescharacteristic
93C2×C157#45011yescharacteristic
94C2×C157#48111yescharacteristic
95C2×C157#48311yescharacteristic
96C157#185311yescharacteristic, complemented, Sylow
97#1853—1571nomaximal, Sylow
98C22×C4⋊C4—1571no—
99C2×#106—1572no—
100C2×C22⋊C8D15711yescharacteristic
101#380—1571no—
102#340—1572no—
103C23×C4—3141no—
104C23×C4C2×D15711yescharacteristic
105C22×C8C2×D15712yes—
106C2×C4⋊C4—3141no—
107C2×C4⋊C4—3144no—
108C2×C4⋊C4—1571no—
109C2×C4⋊C4—1571no—
110C2×C4⋊C4—1572no—
111C2×C22⋊C4—3141no—
112#106—3144no—
113C22⋊C8Dic15714yescomplemented
114#95—3141no—
115C24D62811yescharacteristic
116C22×C4—22no—
117C22×C4—22no—
118C22×C4—3144no—
119C22×C4—3142no—
120C22×C4—3141no—
121C22×C4—3141no—
122C22×C4—6282no—
123C22×C4—6282no—
124C22×C4C2×Dic15712yes—
125C22×C4D62811yescharacteristic
126C22×C4Dic31412yes—
127C22×C4C22×D15711yescharacteristic
128C2×C8—22no—
129C2×C8—22no—
130C2×C8C2×Dic15714yescomplemented
131C4⋊C4—3144no—
132C4⋊C4—3142no—
133C4⋊C4—3142no—
134C4⋊C4—3142no—
135C4⋊C4—1574no—
136C22⋊C4—6282no—
137C23—21no—
138C23—21no—
139C23—21no—
140C23—21no—
141C23C4⋊Dic15712yes—
142C23#1457894312yes—
143C23#1457894312yes—
144C23C2×D62811yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—24no—
148C2×C4—24no—
149C2×C4—3144no—
150C2×C4—6288no—
151C2×C4—6282no—
152C2×C4—6282no—
153C2×C4—6281no—
154C2×C4—6281no—
155C2×C4—6281no—
156C2×C4—6281no—
157C2×C4—6281no—
158C2×C4—6281no—
159C2×C4C4⋊Dic15712yes—
160C2×C4C22×Dic15711yescharacteristic
161C2×C4D4×D15712yes—
162C2×C4C2×Dic31411yescharacteristic
163C2×C4#1457895312yes—
164C8—24no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—22no—
169C22—22no—
170C22—22no—
171C22#1909770314yescomplemented
172C22C2×C4⋊Dic15711yescharacteristic
173C22#1909774111yescharacteristic
174C22#1909775511yescharacteristic
175C22C2×#1457894311yescharacteristic
176C22C2×#1457894311yescharacteristic
177C22#1909779911yescharacteristic
178C22#1909780411yescharacteristic
179C4—22no—
180C4—6284no—
181C4—12561no—
182C4—12561no—
183C4D4×Dic15712yes—
184C4#1909774812yes—
185C2—24no—
186C2#2375714811yescharacteristic
187C2C2×#1909770311yescharacteristic
188C2#2375731511yescharacteristic
189C2#2375741411yescharacteristic
190C2#2375742611yescharacteristic
191C2#2375759211yescharacteristic
192C2#2375760411yescharacteristic
subgroupG/H
centerC23C2×D628
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
FittingC2×C22⋊C8×C157C2
socleC23×C157C2×D4
prime radicalC24×C157D4
cosocleC22×C4×C157C23
hypercenterC2×C22⋊C8D157
hypocenterC157#1853
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#19097703C2semidirect
4. #23757036C2semidirect
17. C22⋊C8×C157C4semidirect
39. C2×C8×C157C2×C4semidirect
74. C22×C157#106semidirect
96. C157#1853semidirect
113. C22⋊C8Dic157semidirect
130. C2×C8C2×Dic157semidirect
171. C22#19097703semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊Dic1572
C2×#190977032
#237571332
#237570362
C2×C22⋊C8×C1572
#1853157