Finite Group Databasebeta

← #34101079

Subgroups — #34101079

Order 20096.

260 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 93 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#23757830C211yesmaximal, characteristic
2C4×#14578938C211yesmaximal, characteristic
3#23757033C214yesmaximal
4C4×C4⋊C4×C157C211yesmaximal, characteristic
5C2×#14578938C2212yes—
6#19097771C411yescharacteristic, complemented
7#19097771C411yescharacteristic, complemented
8#19097763C412yescomplemented
9#19097750—21no—
10#19097750—21no—
11C4×Dic314—21no—
12C4×Dic314—21no—
13#19097730C2212yes—
14#19097682—21no—
15C4×#11929434—21no—
16C2×C4⋊C4×C157—21no—
17C2×C42×C157C2212yes—
18C2×C42×C157C2211yescharacteristic
19#95×C157—21no—
20C2×Dic314—21no—
21C2×Dic314—21no—
22#14578938—22no—
23#14578938Q814yescomplemented
24C2×#11929434—22no—
25C4⋊Dic157—21no—
26C4⋊Dic157—21no—
27C4⋊Dic157C2×C412yes—
28C4⋊Dic157C2×C412yes—
29#14578933—22no—
30#14578933—22no—
31C22⋊Dic157—22no—
32C4×Dic157—22no—
33C22×C4×C157—22no—
34C22×C4×C157D411yescharacteristic
35C22×C4×C157D411yescharacteristic
36C22×C4×C157C2311yescharacteristic
37C4⋊C4×C157—24no—
38C42×C157—24no—
39C42×C157C2×C411yescharacteristic
40C42×C157C2×C411yescharacteristic
41C42×C157D411yescharacteristic
42C42×C157D411yescharacteristic
43Dic314—42no—
44Dic314—42no—
45C2×Dic157—22no—
46C2×Dic157—22no—
47#11929434—24no—
48C23×C157C2×D411yescharacteristic
49C2×C4×C157—22no—
50C2×C4×C157—24no—
51C2×C4×C157—41no—
52C2×C4×C157—42no—
53C2×C4×C157—42no—
54C2×C4×C157C22⋊C411yescharacteristic
55C2×C4×C157C22⋊C411yescharacteristic
56C2×C4×C157C22⋊C411yescharacteristic
57C2×C4×C157C22⋊C411yescharacteristic
58C2×C4×C157C22×C411yescharacteristic
59C2×C4×C157C2×D411yescharacteristic
60C2×C4×C157C2×Q812yes—
61C2×C4×C157#4112yes—
62C22×C157—21no—
63C22×C157—21no—
64C22×C157C2×C22⋊C411yescharacteristic
65C22×C157#12411yescharacteristic
66C22×C157C4⋊Q811yescharacteristic
67C4×C157—21no—
68C4×C157—21no—
69C4×C157—21no—
70C4×C157—44no—
71C4×C157#10412yes—
72C4×C157C4×Q812yes—
73C4×C157C22⋊Q812yes—
74Dic157—42no—
75Dic157—42no—
76C2×C157—21no—
77C2×C157—21no—
78C2×C157#39111yescharacteristic
79C2×C157C2×#10411yescharacteristic
80C2×C157#42111yescharacteristic
81C157#198611yescharacteristic, complemented, Sylow
82#1986—1571nomaximal, Sylow
83#533—1571no—
84C4×M16—1571no—
85C4×C4⋊C4D15711yescharacteristic
86#339—1574no—
87C2×M16—1572no—
88C4⋊Q8—1571no—
89C4⋊Q8—1571no—
90#125—1572no—
91C22⋊Q8—3141no—
92C22⋊Q8—3141no—
93C4×Q8—3141no—
94C4×Q8—3141no—
95#117—1572no—
96C2×C4⋊C4—21no—
97C2×C42C2×D15712yes—
98C2×C42C2×D15711yescharacteristic
99#97—3141no—
100C4×C8—3141no—
101#95—21no—
102C2×Q8—3141no—
103C2×Q8—3141no—
104C22×C4—22no—
105C22×C4C22⋊D15711yescharacteristic
106C22×C4C22⋊D15711yescharacteristic
107C22×C4C22×D15711yescharacteristic
108M16—3142no—
109M16—1574no—
110C2×C8—3142no—
111C4⋊C4—24no—
112C4⋊C4—3142no—
113C4⋊C4—3142no—
114C4⋊C4—3141no—
115C4⋊C4—3141no—
116C4⋊C4—1572no—
117C4⋊C4—1572no—
118C22⋊C4—3142no—
119C42—24no—
120C42—3142no—
121C42C4×D15711yescharacteristic
122C42C4×D15711yescharacteristic
123C42D62811yescharacteristic
124C42D62811yescharacteristic
125C23C2×C22⋊D15711yescharacteristic
126Q8—6282no—
127Q8—6282no—
128C2×C4—22no—
129C2×C4—24no—
130C2×C4—41no—
131C2×C4—42no—
132C2×C4—42no—
133C2×C4—3142no—
134C2×C4—3142no—
135C2×C4#1457893111yescharacteristic
136C2×C4#1457893111yescharacteristic
137C2×C4#1457893111yescharacteristic
138C2×C4#1457893111yescharacteristic
139C2×C4C2×C4×D15711yescharacteristic
140C2×C4C2×D62811yescharacteristic
141C2×C4Q8×D15712yes—
142C2×C4#1457895312yes—
143C8—3144no—
144C22—21no—
145C22—21no—
146C22C2×#1457893111yescharacteristic
147C22#1909775811yescharacteristic
148C22#1909776911yescharacteristic
149C4—21no—
150C4—21no—
151C4—21no—
152C4—44no—
153C4—6282no—
154C4—6282no—
155C4#1909769912yes—
156C4#1909773612yes—
157C4#1909775112yes—
158C2—21no—
159C2—21no—
160C2#2375717811yescharacteristic
161C2C2×#1909769911yescharacteristic
162C2#2375729111yescharacteristic
subgroupG/H
centerC2×C4C2×D628
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
FittingC4×C4⋊C4×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC23×C157C2×D4
cosocleC22×C4×C157C23
hypercenterC4×C4⋊C4D157
hypocenterC157#1986
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. #19097771C4semidirect
7. #19097771C4semidirect
8. #19097763C4semidirect
23. #14578938Q8semidirect
81. C157#1986semidirect

Maximal subgroups

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

subgroupindex
#237578302
C4×#145789382
#237570332
C4×C4⋊C4×C1572
#1986157