Finite Group Databasebeta

← #34099269

Subgroups — #34099269

Order 20096.

214 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 55 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#23757983C211yesmaximal, characteristic
2#23757652C211yesmaximal, characteristic, complemented
3#23757560C211yesmaximal, characteristic
4#23757021C211yesmaximal, characteristic, complemented
5Q8⋊#11929434C211yesmaximal, characteristic, complemented
6#23757000C211yesmaximal, characteristic
7#477×C157C211yesmaximal, characteristic, complemented
8C2×#14578944—22no—
9#19097771C2211yescharacteristic
10#19097763—21no—
11#19097749—22no—
12#19097747—21no—
13C4×D628—21no—
14C4×D628C2211yescharacteristic
15C4⋊C4×D157—21no—
16#19097702—21no—
17C4⋊#11929434C2211yescharacteristic
18#19097691—21no—
19C4×#11929434C2211yescharacteristic
20C4⋊Q8×C157C2211yescharacteristic
21C4×Q8×C157C2211yescharacteristic
22#107×C157—21no—
23C4⋊C8×C157C2211yescharacteristic
24#103×C157—21no—
25C2×Dic314D412yes—
26C2×D628D411yescharacteristic
27C2×C4×D157—22no—
28C2×C4×D157—21no—
29#14578944—44no—
30C2×#11929434—21no—
31C2×#11929434—21no—
32C4⋊Dic157—21no—
33C4⋊Dic157—21no—
34C4⋊Dic157D411yescharacteristic
35#14578933—22no—
36#14578933—22no—
37#14578931—22no—
38#14578931—21no—
39C2×Q8×C157—21no—
40C2×Q8×C157D411yescharacteristic
41C2×C8×C157—21no—
42C4⋊C4×C157—21no—
43C4⋊C4×C157—21no—
44C4⋊C4×C157—21no—
45C4⋊C4×C157D411yescharacteristic
46C42×C157—21no—
47C42×C157C2311yescharacteristic
48C22×D157—21no—
49Dic314—42no—
50D628—21no—
51D628Q1612yescomplemented
52C2×Dic157—22no—
53C2×Dic157—21no—
54C4×D157—41no—
55C4×D157—41no—
56C4×D157—82no—
57#11929434—22no—
58#11929434—41no—
59Q8×C157—21no—
60Q8×C157—21no—
61Q8×C157—42no—
62C2×C4×C157—21no—
63C2×C4×C157—21no—
64C2×C4×C157—41no—
65C2×C4×C157C2×D411yescharacteristic
66C2×C4×C157C2×D411yescharacteristic
67C2×C4×C157C2×D411yescharacteristic
68C8×C157—41no—
69C22×C157#12011yescharacteristic
70C2×D157—22no—
71C2×D157—41no—
72C2×D157—41no—
73C4×C157—21no—
74C4×C157—41no—
75C4×C157—41no—
76C4×C157—81no—
77C4×C157C2×Q1611yescharacteristic
78C4×C157#13511yescharacteristic
79C4×C157#13711yescharacteristic
80C4×C157#13711yescharacteristic
81Dic157—41no—
82Dic157—42no—
83C2×C157#45111yescharacteristic
84C2×C157#45211yescharacteristic
85C2×C157#45311yescharacteristic
86D157—42no—
87C157#163211yescharacteristic, complemented, Sylow
88#1632—1571nomaximal, Sylow
89#554—1571no—
90#494—1571no—
91#477D15711yescharacteristic, complemented
92#476—1571no—
93#333—1571no—
94Q8⋊C8—1571no—
95D4⋊C8—1571no—
96C2×Q16—3142no—
97C4⋊Q8—1571no—
98C4⋊Q8C2×D15711yescharacteristic
99#125—3141no—
100C22⋊Q8—3142no—
101C22⋊Q8—3141no—
102C4×Q8C2×D15711yescharacteristic
103C4×D4—3141no—
104C4×D4—1571no—
105C2×C4⋊C4—3141no—
106#107—21no—
107#106—3141no—
108C4⋊C8—1571no—
109C4⋊C8C2×D15711yescharacteristic
110#103—21no—
111#102—3141no—
112C4×C8—1571no—
113C2×Q8—21no—
114C2×Q8—1572no—
115C2×Q8C22⋊D15711yescharacteristic
116C2×D4—1571no—
117C22×C4—3142no—
118C22×C4—3141no—
119Q16—6284no—
120C2×C8—21no—
121C2×C8—3141no—
122C2×C8—3141no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—3142no—
127C4⋊C4—3142no—
128C4⋊C4—3141no—
129C4⋊C4—3141no—
130C4⋊C4—1571no—
131C4⋊C4C22⋊D15711yescharacteristic
132C22⋊C4—3142no—
133C22⋊C4—3141no—
134C42—21no—
135C42C22×D15711yescharacteristic
136C23—3141no—
137Q8—21no—
138Q8—21no—
139Q8—42no—
140Q8—6282no—
141D4—3141no—
142D4—1572no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—3141no—
147C2×C4—3142no—
148C2×C4—6281no—
149C2×C4—6281no—
150C2×C4—12562no—
151C2×C4D4×D15711yescharacteristic
152C2×C4D4×D15711yescharacteristic
153C2×C4C2×C22⋊D15711yescharacteristic
154C8—41no—
155C8—3142no—
156C8—6281no—
157C22—3142no—
158C22—6281no—
159C22—6281no—
160C22#1909773911yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—6281no—
166C4—6282no—
167C4Q16×D15711yescharacteristic
168C4#1909779111yescharacteristic
169C4#1909780211yescharacteristic
170C4#1909780311yescharacteristic
171C2—6282no—
172C2#2375742711yescharacteristic
173C2#2375743311yescharacteristic
174C2#2375743911yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#477×C157C2
socleC22×C157#120
prime radicalC2×D628D4
hypercenter#477D157
hypocenterC157#1632
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #23757652C2semidirect
4. #23757021C2semidirect
5. Q8⋊#11929434C2semidirect
7. #477×C157C2semidirect
51. D628Q16semidirect
87. C157#1632semidirect
91. #477D157semidirect

Maximal subgroups

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

subgroupindex
#237579832
#237576522
#237575602
#237570212
Q8⋊#119294342
#237570002
#477×C1572
#1632157