Finite Group Databasebeta

← #34099343

Subgroups — #34099343

Order 20096.

208 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 61 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#23757623C211yesmaximal, characteristic, complemented
2#23757558C211yesmaximal, characteristic, complemented
3#23757478C211yesmaximal, characteristic
4#23757022C211yesmaximal, characteristic, complemented
5Q8⋊#11929434C211yesmaximal, characteristic, complemented
6D4⋊#11929434C211yesmaximal, characteristic
7#554×C157C211yesmaximal, characteristic
8C2×#14578942—21no—
9#19097771C2211yescharacteristic
10#19097702—21no—
11C4⋊#11929434C2211yescharacteristic
12C4⋊#11929434C2211yescharacteristic
13#19097695—22no—
14#19097695—21no—
15#19097694—21no—
16C4×#11929434C2211yescharacteristic
17C4⋊Q8×C157C2211yescharacteristic
18#125×C157—21no—
19C22⋊Q8×C157—21no—
20C22⋊Q8×C157—22no—
21C4×Q8×C157C2211yescharacteristic
22C4×D4×C157—21no—
23C4×D4×C157C2211yescharacteristic
24C2×C4⋊C4×C157—21no—
25C2×Dic314—21no—
26#14578942—42no—
27C2×#11929434—21no—
28C2×#11929434—21no—
29C2×#11929434—21no—
30C4⋊Dic157—21no—
31C4⋊Dic157—21no—
32C2×Q8×C157D411yescharacteristic
33C2×Q8×C157D412yes—
34C2×D4×C157D411yescharacteristic
35C22×C4×C157—22no—
36C22×C4×C157—21no—
37C4⋊C4×C157—22no—
38C4⋊C4×C157—22no—
39C4⋊C4×C157—21no—
40C4⋊C4×C157—21no—
41C4⋊C4×C157—21no—
42C4⋊C4×C157D411yescharacteristic
43C4⋊C4×C157D411yescharacteristic
44C22⋊C4×C157—22no—
45C22⋊C4×C157—21no—
46C42×C157—21no—
47C42×C157C2311yescharacteristic
48Dic314—41no—
49Dic314—41no—
50C2×Dic157—41no—
51#11929434—41no—
52#11929434—41no—
53#11929434—41no—
54C23×C157—21no—
55Q8×C157—21no—
56Q8×C157—21no—
57Q8×C157—42no—
58D4×C157—21no—
59D4×C157SD1612yes—
60C2×C4×C157—21no—
61C2×C4×C157—21no—
62C2×C4×C157—21no—
63C2×C4×C157—22no—
64C2×C4×C157—41no—
65C2×C4×C157—41no—
66C2×C4×C157—82no—
67C2×C4×C157C2×D411yescharacteristic
68C2×C4×C157C2×D411yescharacteristic
69C2×C4×C157C2×D411yescharacteristic
70C22×C157—22no—
71C22×C157—41no—
72C22×C157—41no—
73C22×C157#12011yescharacteristic
74C4×C157—21no—
75C4×C157—41no—
76C4×C157—41no—
77C4×C157—41no—
78C4×C157—42no—
79C4×C157C2×SD1611yescharacteristic
80C4×C157#13511yescharacteristic
81C4×C157#13711yescharacteristic
82C4×C157#13711yescharacteristic
83Dic157—81no—
84C2×C157—42no—
85C2×C157#44811yescharacteristic
86C2×C157#45211yescharacteristic
87C2×C157#45511yescharacteristic
88C157#164311yescharacteristic, complemented, Sylow
89#1643—1571nomaximal, Sylow
90#554D15711yescharacteristic
91#487—1571no—
92#475—1571no—
93#461—1571no—
94#333—1571no—
95Q8⋊C8—1571no—
96D4⋊C8—1571no—
97C2×SD16—3141no—
98C4⋊Q8—1571no—
99C4⋊Q8C2×D15711yescharacteristic
100#125—21no—
101C22⋊Q8—21no—
102C22⋊Q8—22no—
103C4×Q8C2×D15711yescharacteristic
104C4×D4—21no—
105C4×D4C2×D15711yescharacteristic
106C2×C4⋊C4—21no—
107#106—3141no—
108C4⋊C8—1571no—
109C4⋊C8—1571no—
110#103—3141no—
111#103—3142no—
112#103—3141no—
113C4×C8—1571no—
114C2×Q8—3141no—
115C2×Q8C22⋊D15711yescharacteristic
116C2×Q8C22⋊D15712yes—
117C2×D4C22⋊D15711yescharacteristic
118C22×C4—22no—
119C22×C4—21no—
120SD16—6282no—
121C2×C8—3141no—
122C2×C8—3141no—
123C2×C8—3141no—
124C4⋊C4—22no—
125C4⋊C4—22no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—3141no—
130C4⋊C4—3141no—
131C4⋊C4C22⋊D15711yescharacteristic
132C4⋊C4C22⋊D15711yescharacteristic
133C22⋊C4—22no—
134C22⋊C4—21no—
135C42—21no—
136C42C22×D15711yescharacteristic
137C23—21no—
138Q8—21no—
139Q8—21no—
140Q8—42no—
141Q8—6281no—
142Q8—6281no—
143D4—21no—
144D4#1457894112yes—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—82no—
152C2×C4—6281no—
153C2×C4C2×C22⋊D15711yescharacteristic
154C2×C4C2×C22⋊D15711yescharacteristic
155C2×C4C2×C22⋊D15711yescharacteristic
156C8—6281no—
157C8—6281no—
158C8—6281no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22#1909774011yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—41no—
167C4—42no—
168C4—12561no—
169C4C2×#1457894111yescharacteristic
170C4#1909779111yescharacteristic
171C4#1909780111yescharacteristic
172C4#1909780211yescharacteristic
173C2—42no—
174C2#2375741211yescharacteristic
175C2#2375743511yescharacteristic
176C2#2375745111yescharacteristic
subgroupG/H
centerC22#19097740
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#554×C157C2
socleC22×C157#120
prime radicalC2×D4×C157D4
hypercenter#554D157
hypocenterC157#1643
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #23757623C2semidirect
2. #23757558C2semidirect
4. #23757022C2semidirect
5. Q8⋊#11929434C2semidirect
88. C157#1643semidirect

Maximal subgroups

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

subgroupindex
#237576232
#237575582
#237574782
#237570222
Q8⋊#119294342
D4⋊#119294342
#554×C1572
#1643157