Finite Group Databasebeta

← #34099354

Subgroups — #34099354

Order 20096.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#23758003C211yesmaximal, characteristic
2#23757555C211yesmaximal, characteristic
3#23757480C211yesmaximal, characteristic
4#23757022C211yesmaximal, characteristic
5#23757005C211yesmaximal, characteristic
6#23757005C211yesmaximal, characteristic
7#487×C157C211yesmaximal, characteristic
8C2×#14578944—21no—
9#19097770—21no—
10#19097770—21no—
11#19097769—22no—
12C4×Dic314C2211yescharacteristic
13C4×Dic314C2211yescharacteristic
14#19097736—21no—
15#19097736—21no—
16#19097702—21no—
17C4⋊#11929434C2211yescharacteristic
18C4⋊#11929434C2211yescharacteristic
19#19097695—21no—
20#19097694—21no—
21C4⋊Q8×C157C2211yescharacteristic
22C4⋊Q8×C157C2211yescharacteristic
23#103×C157—22no—
24C4×C8×C157C2211yescharacteristic
25C2×Dic314—22no—
26C2×Dic314D411yescharacteristic
27C2×Dic314D411yescharacteristic
28#14578944—42no—
29C2×#11929434—21no—
30C2×#11929434—21no—
31C4⋊Dic157D411yescharacteristic
32C4⋊Dic157D411yescharacteristic
33#14578933—22no—
34#14578933—22no—
35#14578933—21no—
36#14578933—21no—
37C4×Dic157—22no—
38C4×Dic157—21no—
39C4×Dic157—21no—
40C2×Q8×C157—21no—
41C2×Q8×C157D412yes—
42C2×C8×C157—21no—
43C4⋊C4×C157—21no—
44C4⋊C4×C157—21no—
45C4⋊C4×C157—21no—
46C4⋊C4×C157—21no—
47C42×C157C2311yescharacteristic
48Dic314—21no—
49Dic314—21no—
50Dic314—82no—
51Dic314SD1612yes—
52Dic314Q1612yescomplemented
53C2×Dic157—21no—
54C2×Dic157—21no—
55C2×Dic157—21no—
56C2×Dic157—21no—
57#11929434—41no—
58#11929434—41no—
59Q8×C157—42no—
60Q8×C157—41no—
61Q8×C157—41no—
62C2×C4×C157—22no—
63C2×C4×C157—41no—
64C2×C4×C157C2×D411yescharacteristic
65C2×C4×C157C2×D411yescharacteristic
66C2×C4×C157C2×D411yescharacteristic
67C8×C157—41no—
68C22×C157#12011yescharacteristic
69C4×C157—21no—
70C4×C157—42no—
71C4×C157—81no—
72C4×C157C2×SD1611yescharacteristic
73C4×C157C2×Q1611yescharacteristic
74C4×C157#13711yescharacteristic
75C4×C157#13711yescharacteristic
76Dic157—22no—
77Dic157—22no—
78Dic157—41no—
79Dic157—41no—
80C2×C157#44811yescharacteristic
81C2×C157#45111yescharacteristic
82C2×C157#45511yescharacteristic
83C157#164511yescharacteristic, complemented, Sylow
84#1645—1571nomaximal, Sylow
85Q82—1571no—
86#487D15711yescharacteristic
87#475—1571no—
88#462—1571no—
89#333—1571no—
90Q8⋊C8—1571no—
91Q8⋊C8—1571no—
92C2×Q16—3141no—
93C4⋊Q8—3141no—
94C4⋊Q8—3141no—
95C4⋊Q8—3142no—
96C4⋊Q8C2×D15711yescharacteristic
97C4⋊Q8C2×D15711yescharacteristic
98C4×Q8—3141no—
99C4×Q8—3141no—
100C4×Q8—1571no—
101C4×Q8—1571no—
102#106—3141no—
103C4⋊C8—1571no—
104C4⋊C8—1571no—
105#103—22no—
106#103—3141no—
107#103—3141no—
108C4×C8C2×D15711yescharacteristic
109C2×Q8—21no—
110C2×Q8—3142no—
111C2×Q8—1571no—
112C2×Q8—1571no—
113C2×Q8C22⋊D15712yes—
114Q16—6282no—
115C2×C8—21no—
116C2×C8—3141no—
117C2×C8—3141no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—3142no—
123C4⋊C4—3142no—
124C4⋊C4—3141no—
125C4⋊C4—3141no—
126C4⋊C4—1571no—
127C4⋊C4—1571no—
128C42—3142no—
129C42—3141no—
130C42—3141no—
131C42C22×D15711yescharacteristic
132Q8—42no—
133Q8—41no—
134Q8—41no—
135Q8—3141no—
136Q8—3141no—
137Q8—1572no—
138Q8—1572no—
139Q8—12562no—
140C2×C4—22no—
141C2×C4—41no—
142C2×C4—3141no—
143C2×C4—3141no—
144C2×C4—3141no—
145C2×C4—3141no—
146C2×C4D4×D15711yescharacteristic
147C2×C4D4×D15711yescharacteristic
148C2×C4C2×C22⋊D15711yescharacteristic
149C8—41no—
150C8—6281no—
151C8—6281no—
152C22#1909773911yescharacteristic
153C4—21no—
154C4—42no—
155C4—81no—
156C4—3142no—
157C4—3142no—
158C4—6281no—
159C4—6281no—
160C4SD16×D15711yescharacteristic
161C4Q16×D15711yescharacteristic
162C4#1909780011yescharacteristic
163C4#1909780311yescharacteristic
164C2#2375741011yescharacteristic
165C2#2375742711yescharacteristic
166C2#2375745011yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#487×C157C2
socle, prime radicalC22×C157#120
hypercenter#487D157
hypocenterC157#1645
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
52. Dic314Q16semidirect
83. C157#1645semidirect

Maximal subgroups

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

subgroupindex
#237580032
#237575552
#237574802
#237570222
#237570052
#487×C1572
#1645157