Finite Group Databasebeta

← #34099355

Subgroups — #34099355

Order 20096.

200 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 59 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
1Q8×Dic314C211yesmaximal, characteristic
2#23757625C211yesmaximal, characteristic
3#23757555C211yesmaximal, characteristic
4#23757021C211yesmaximal, characteristic
5Q8⋊#11929434C211yesmaximal, characteristic
6#23757003C211yesmaximal, characteristic
7#462×C157C211yesmaximal, characteristic
8#19097771—21no—
9#19097771C2211yescharacteristic
10#19097770—21no—
11#19097770—22no—
12Q8×Dic157—21no—
13C4×Dic314—21no—
14C4×Dic314C2211yescharacteristic
15#19097702—21no—
16C4⋊#11929434C2211yescharacteristic
17#19097694—22no—
18#19097694—21no—
19C4×#11929434C2211yescharacteristic
20C2×Q16×C157—21no—
21C4⋊Q8×C157C2211yescharacteristic
22C4×Q8×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24#103×C157—21no—
25C2×Dic314—22no—
26C2×Dic314D411yescharacteristic
27C2×Dic314D412yes—
28C2×#11929434—21no—
29C2×#11929434—21no—
30C4⋊Dic157—22no—
31C4⋊Dic157—21no—
32C4⋊Dic157—21no—
33C4⋊Dic157D411yescharacteristic
34#14578933—22no—
35#14578933—21no—
36C4×Dic157—22no—
37C4×Dic157—21no—
38C2×Q8×C157—21no—
39C2×Q8×C157D411yescharacteristic
40Q16×C157—42no—
41C2×C8×C157—21no—
42C4⋊C4×C157—21no—
43C4⋊C4×C157—21no—
44C4⋊C4×C157—21no—
45C4⋊C4×C157D411yescharacteristic
46C42×C157—21no—
47C42×C157C2311yescharacteristic
48Dic314—21no—
49Dic314—42no—
50Dic314—82no—
51Dic314Q1612yescomplemented
52C2×Dic157—21no—
53C2×Dic157—21no—
54C2×Dic157—22no—
55#11929434—41no—
56#11929434—41no—
57Q8×C157—21no—
58Q8×C157—41no—
59Q8×C157—41no—
60Q8×C157SD1612yes—
61C2×C4×C157—21no—
62C2×C4×C157—21no—
63C2×C4×C157—41no—
64C2×C4×C157C2×D411yescharacteristic
65C2×C4×C157C2×D411yescharacteristic
66C2×C4×C157C2×D411yescharacteristic
67C8×C157—41no—
68C22×C157#12011yescharacteristic
69C4×C157—22no—
70C4×C157—21no—
71C4×C157—41no—
72C4×C157—81no—
73C4×C157C2×SD1611yescharacteristic
74C4×C157C2×Q1611yescharacteristic
75C4×C157#13711yescharacteristic
76C4×C157#13711yescharacteristic
77Dic157—22no—
78Dic157—42no—
79Dic157—41no—
80C2×C157#44811yescharacteristic
81C2×C157#45111yescharacteristic
82C2×C157#45511yescharacteristic
83C157#164511yescharacteristic, complemented, Sylow
84#1645—1571nomaximal, Sylow
85Q82—1571no—
86#487—1571no—
87#475—1571no—
88#462D15711yescharacteristic
89#333—1571no—
90Q8⋊C8—1571no—
91Q8⋊C8—1571no—
92C2×Q16—21no—
93C4⋊Q8—3141no—
94C4⋊Q8—3142no—
95C4⋊Q8—3141no—
96C4⋊Q8—1571no—
97C4⋊Q8C2×D15711yescharacteristic
98C4×Q8—3141no—
99C4×Q8—3141no—
100C4×Q8—1571no—
101C4×Q8C2×D15711yescharacteristic
102#106—3141no—
103C4⋊C8—1571no—
104C4⋊C8C2×D15711yescharacteristic
105#103—21no—
106#103—3141no—
107#103—3142no—
108C4×C8—1571no—
109C2×Q8—21no—
110C2×Q8—3142no—
111C2×Q8—1571no—
112C2×Q8—1572no—
113C2×Q8C22⋊D15711yescharacteristic
114Q16—42no—
115C2×C8—21no—
116C2×C8—3141no—
117C2×C8—3141no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—3142no—
122C4⋊C4—3142no—
123C4⋊C4—3141no—
124C4⋊C4—3141no—
125C4⋊C4—3141no—
126C4⋊C4—1571no—
127C4⋊C4C22⋊D15711yescharacteristic
128C42—21no—
129C42—3142no—
130C42—3141no—
131C42C22×D15711yescharacteristic
132Q8—21no—
133Q8—41no—
134Q8—41no—
135Q8—3141no—
136Q8—6282no—
137Q8—1572no—
138Q8—12562no—
139Q8#1457894212yes—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—3141no—
144C2×C4—3142no—
145C2×C4—3141no—
146C2×C4D4×D15711yescharacteristic
147C2×C4D4×D15711yescharacteristic
148C2×C4C2×C22⋊D15711yescharacteristic
149C8—41no—
150C8—6281no—
151C8—6281no—
152C22#1909773911yescharacteristic
153C4—22no—
154C4—21no—
155C4—41no—
156C4—81no—
157C4—3142no—
158C4—6282no—
159C4—6281no—
160C4C2×#1457894211yescharacteristic
161C4Q16×D15711yescharacteristic
162C4#1909780111yescharacteristic
163C4#1909780311yescharacteristic
164C2#2375741111yescharacteristic
165C2#2375742711yescharacteristic
166C2#2375744911yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#462×C157C2
socle, prime radicalC22×C157#120
hypercenter#462D157
hypocenterC157#1645
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

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

Maximal subgroups

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

subgroupindex
Q8×Dic3142
#237576252
#237575552
#237570212
Q8⋊#119294342
#237570032
#462×C1572
#1645157