Finite Group Databasebeta

← #34099342

Subgroups — #34099342

Order 20096.

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

normal subgroups only

This group has 208 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#23757625C211yesmaximal, characteristic, complemented
3#23757475C211yesmaximal, characteristic
4#23757021C211yesmaximal, characteristic, complemented
5Q8⋊#11929434C211yesmaximal, characteristic, complemented
6#23757000C211yesmaximal, characteristic
7#475×C157C211yesmaximal, characteristic, complemented
8C2×#14578941—21no—
9#19097771C2211yescharacteristic
10#19097763—21no—
11#19097749—22no—
12#19097747—21no—
13C4×D628—21no—
14C4×D628C2211yescharacteristic
15C4⋊C4×D157—21no—
16C4⋊#11929434C2211yescharacteristic
17#19097695—21no—
18#19097694—22no—
19C4×#11929434C2211yescharacteristic
20C4⋊Q8×C157C2211yescharacteristic
21C4×Q8×C157C2211yescharacteristic
22#106×C157—21no—
23C4⋊C8×C157C2211yescharacteristic
24#103×C157—21no—
25C2×Dic314D412yes—
26C2×D628D411yescharacteristic
27C2×C4×D157—22no—
28C2×C4×D157—21no—
29#14578941—42no—
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—
51D628SD1612yes—
52C2×Dic157—22no—
53C2×Dic157—21no—
54C4×D157—41no—
55C4×D157—41no—
56C4×D157—82no—
57#11929434—41no—
58#11929434—41no—
59Q8×C157—21no—
60Q8×C157—21no—
61Q8×C157—41no—
62Q8×C157—41no—
63C2×C4×C157—21no—
64C2×C4×C157—21no—
65C2×C4×C157—41no—
66C2×C4×C157C2×D411yescharacteristic
67C2×C4×C157C2×D411yescharacteristic
68C2×C4×C157C2×D411yescharacteristic
69C8×C157—41no—
70C22×C157#12011yescharacteristic
71C2×D157—22no—
72C2×D157—41no—
73C2×D157—41no—
74C4×C157—21no—
75C4×C157—41no—
76C4×C157—41no—
77C4×C157—81no—
78C4×C157C2×SD1611yescharacteristic
79C4×C157#13511yescharacteristic
80C4×C157#13711yescharacteristic
81C4×C157#13711yescharacteristic
82Dic157—41no—
83Dic157—42no—
84C2×C157#44811yescharacteristic
85C2×C157#45211yescharacteristic
86C2×C157#45511yescharacteristic
87D157—42no—
88C157#164311yescharacteristic, complemented, Sylow
89#1643—1571nomaximal, Sylow
90#554—1571no—
91#487—1571no—
92#475D15711yescharacteristic, complemented
93#461—1571no—
94#333—1571no—
95Q8⋊C8—1571no—
96D4⋊C8—1571no—
97C2×SD16—3141no—
98C4⋊Q8—1571no—
99C4⋊Q8C2×D15711yescharacteristic
100#125—3141no—
101C22⋊Q8—3142no—
102C22⋊Q8—3141no—
103C4×Q8C2×D15711yescharacteristic
104C4×D4—3141no—
105C4×D4—1571no—
106C2×C4⋊C4—3141no—
107#106—21no—
108C4⋊C8—1571no—
109C4⋊C8C2×D15711yescharacteristic
110#103—21no—
111#103—3142no—
112#103—3141no—
113C4×C8—1571no—
114C2×Q8—21no—
115C2×Q8—1572no—
116C2×Q8C22⋊D15711yescharacteristic
117C2×D4—1571no—
118C22×C4—3142no—
119C22×C4—3141no—
120SD16—6282no—
121C2×C8—21no—
122C2×C8—3141no—
123C2×C8—3141no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—3142no—
128C4⋊C4—3142no—
129C4⋊C4—3141no—
130C4⋊C4—3141no—
131C4⋊C4—1571no—
132C4⋊C4C22⋊D15711yescharacteristic
133C22⋊C4—3142no—
134C22⋊C4—3141no—
135C42—21no—
136C42C22×D15711yescharacteristic
137C23—3141no—
138Q8—21no—
139Q8—21no—
140Q8—41no—
141Q8—41no—
142Q8—6282no—
143D4—3141no—
144D4—1572no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—3141no—
149C2×C4—3142no—
150C2×C4—6281no—
151C2×C4—6281no—
152C2×C4—12562no—
153C2×C4D4×D15711yescharacteristic
154C2×C4D4×D15711yescharacteristic
155C2×C4C2×C22⋊D15711yescharacteristic
156C8—41no—
157C8—6281no—
158C8—6281no—
159C22—3142no—
160C22—6281no—
161C22—6281no—
162C22#1909773911yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—81no—
167C4—6281no—
168C4—6282no—
169C4SD16×D15711yescharacteristic
170C4#1909779111yescharacteristic
171C4#1909780011yescharacteristic
172C4#1909780211yescharacteristic
173C2—6282no—
174C2#2375741011yescharacteristic
175C2#2375743311yescharacteristic
176C2#2375744911yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#475×C157C2
socleC22×C157#120
prime radicalC2×D628D4
hypercenter#475D157
hypocenterC157#1643
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #23757625C2semidirect
4. #23757021C2semidirect
5. Q8⋊#11929434C2semidirect
7. #475×C157C2semidirect
88. C157#1643semidirect
92. #475D157semidirect

Maximal subgroups

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

subgroupindex
#237579832
#237576252
#237574752
#237570212
Q8⋊#119294342
#237570002
#475×C1572
#1643157