Finite Group Databasebeta

← #34099341

Subgroups — #34099341

Order 20096.

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

normal subgroups only

This group has 208 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#23757980C211yesmaximal, characteristic
2#23757625C211yesmaximal, characteristic, complemented
3#23757555C211yesmaximal, characteristic, complemented
4#23757021C211yesmaximal, characteristic, complemented
5#23757003C211yesmaximal, characteristic, complemented
6D4⋊#11929434C211yesmaximal, characteristic
7#461×C157C211yesmaximal, characteristic
8#19097771C2211yescharacteristic
9#19097762—21no—
10#19097750—21no—
11#19097748—22no—
12C4×Dic314C2211yescharacteristic
13D4×Dic157—21no—
14C2×C4⋊Dic157—21no—
15#19097702—21no—
16C4⋊#11929434C2211yescharacteristic
17#19097694—22no—
18#19097694—21no—
19C4×#11929434C2211yescharacteristic
20C2×SD16×C157—21no—
21C4⋊Q8×C157C2211yescharacteristic
22C4×D4×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24#103×C157—21no—
25C2×Dic314D411yescharacteristic
26C2×Dic314D412yes—
27C22×Dic157—22no—
28C2×#11929434—21no—
29C2×#11929434—21no—
30C4⋊Dic157—22no—
31C4⋊Dic157—21no—
32C4⋊Dic157—21no—
33C4⋊Dic157D411yescharacteristic
34#14578933—22no—
35#14578933—21no—
36C22⋊Dic157—22no—
37C4×Dic157—21no—
38C2×Q8×C157—21no—
39C2×D4×C157D411yescharacteristic
40C22×C4×C157—21no—
41SD16×C157—42no—
42C2×C8×C157—21no—
43C4⋊C4×C157—21no—
44C4⋊C4×C157—21no—
45C4⋊C4×C157D411yescharacteristic
46C22⋊C4×C157—21no—
47C42×C157C2311yescharacteristic
48Dic314—21no—
49Dic314—21no—
50Dic314—42no—
51C2×Dic157—21no—
52C2×Dic157—22no—
53C2×Dic157—21no—
54C2×Dic157—82no—
55#11929434—41no—
56#11929434—41no—
57C23×C157—21no—
58Q8×C157—41no—
59Q8×C157—41no—
60D4×C157—21no—
61D4×C157SD1612yes—
62C2×C4×C157—21no—
63C2×C4×C157—41no—
64C2×C4×C157—41no—
65C2×C4×C157—41no—
66C2×C4×C157C2×D411yescharacteristic
67C2×C4×C157C2×D411yescharacteristic
68C2×C4×C157C2×D411yescharacteristic
69C8×C157—41no—
70C22×C157—22no—
71C22×C157—41no—
72C22×C157—41no—
73C22×C157#12011yescharacteristic
74C4×C157—21no—
75C4×C157—41no—
76C4×C157—81no—
77C4×C157C2×SD1611yescharacteristic
78C4×C157#13511yescharacteristic
79C4×C157#13711yescharacteristic
80C4×C157#13711yescharacteristic
81Dic157—41no—
82Dic157—41no—
83Dic157—42no—
84C2×C157—42no—
85C2×C157#44811yescharacteristic
86C2×C157#45211yescharacteristic
87C2×C157#45511yescharacteristic
88C157#164311yescharacteristic, complemented, Sylow
89#1643—1571nomaximal, Sylow
90#554—1571no—
91#487—1571no—
92#475—1571no—
93#461D15711yescharacteristic
94#333—1571no—
95Q8⋊C8—1571no—
96D4⋊C8—1571no—
97C2×SD16—21no—
98C4⋊Q8—1571no—
99C4⋊Q8C2×D15711yescharacteristic
100#125—3141no—
101C22⋊Q8—3142no—
102C22⋊Q8—3141no—
103C4×Q8—1571no—
104C4×D4—3141no—
105C4×D4C2×D15711yescharacteristic
106C2×C4⋊C4—3141no—
107#106—3141no—
108C4⋊C8—1571no—
109C4⋊C8C2×D15711yescharacteristic
110#103—21no—
111#103—3141no—
112#103—3142no—
113C4×C8—1571no—
114C2×Q8—21no—
115C2×Q8—1571no—
116C2×Q8—1572no—
117C2×D4C22⋊D15711yescharacteristic
118C22×C4—21no—
119C22×C4—3142no—
120SD16—42no—
121C2×C8—21no—
122C2×C8—3141no—
123C2×C8—3141no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—3142no—
127C4⋊C4—3142no—
128C4⋊C4—3141no—
129C4⋊C4—3141no—
130C4⋊C4—3141no—
131C4⋊C4—1571no—
132C4⋊C4C22⋊D15711yescharacteristic
133C22⋊C4—21no—
134C22⋊C4—3142no—
135C42—3141no—
136C42C22×D15711yescharacteristic
137C23—21no—
138Q8—41no—
139Q8—41no—
140Q8—3141no—
141Q8—3141no—
142Q8—6282no—
143D4—21no—
144D4#1457894212yes—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—3141no—
150C2×C4—3141no—
151C2×C4—3142no—
152C2×C4—12562no—
153C2×C4D4×D15711yescharacteristic
154C2×C4D4×D15711yescharacteristic
155C2×C4C2×C22⋊D15711yescharacteristic
156C8—41no—
157C8—6281no—
158C8—6281no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22#1909773911yescharacteristic
163C4—21no—
164C4—41no—
165C4—81no—
166C4—6281no—
167C4—6281no—
168C4—6282no—
169C4C2×#1457894211yescharacteristic
170C4#1909779211yescharacteristic
171C4#1909780011yescharacteristic
172C4#1909780111yescharacteristic
173C2—42no—
174C2#2375741111yescharacteristic
175C2#2375743211yescharacteristic
176C2#2375744911yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#461×C157C2
socleC22×C157#120
prime radicalC2×D4×C157D4
hypercenter#461D157
hypocenterC157#1643
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #23757625C2semidirect
3. #23757555C2semidirect
4. #23757021C2semidirect
5. #23757003C2semidirect
88. C157#1643semidirect

Maximal subgroups

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

subgroupindex
#237579802
#237576252
#237575552
#237570212
#237570032
D4⋊#119294342
#461×C1572
#1643157