Finite Group Databasebeta

← #31795770

Subgroups — #31795770

Order 17536.

146 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 30 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#22578281C211yesmaximal, characteristic
2#22578247C211yesmaximal, characteristic
3#22577330C211yesmaximal, characteristic
4C2×C22⋊#10587739—21no—
5C22⋊#11764047—21no—
6C2×C4⋊Dic137C411yescharacteristic, complemented
7C2×#14555487—21no—
8C2×#14555487C2211yescharacteristic
9#17983995—21no—
10#95×C137C411yescharacteristic, complemented
11C22×#10587739—41no—
12C2×#11764047—41no—
13C22⋊#10587739—22no—
14C22⋊#10587739—41no—
15C23×D137D411yescharacteristic
16C22×Dic137—21no—
17C22×Dic137D411yescharacteristic
18C4⋊Dic137—41no—
19#14555487—41no—
20#14555487—41no—
21#14555487—41no—
22C22×C4×C137—21no—
23C22×C4×C137C2×C411yescharacteristic
24C2×#10587739—42no—
25C2×#10587739—81no—
26C2×#10587739—81no—
27#11764047—81no—
28C22×D137—21no—
29C22×D137—21no—
30C22×D137—41no—
31C22×D137—41no—
32C22×D137D811yescharacteristic
33C22×D137SD1611yescharacteristic
34C2×Dic137—21no—
35C2×Dic137—41no—
36C2×Dic137—41no—
37C2×Dic137—41no—
38C2×Dic137—41no—
39C23×C137C22⋊C411yescharacteristic
40C2×C4×C137—21no—
41C2×C4×C137—41no—
42C2×C4×C137—41no—
43C2×C4×C137—41no—
44C2×C4×C137—41no—
45C22×C137—21no—
46C22×C137—21no—
47C22×C137#9911yescharacteristic
48C22×C137#10211yescharacteristic
49C22×C137#10411yescharacteristic
50C2×D137—21no—
51C2×D137—21no—
52C2×D137—41no—
53C2×D137—41no—
54C2×D137—41no—
55C2×D137—41no—
56C2×D137—81no—
57#10587739—82no—
58C4×C137—41no—
59C4×C137—81no—
60Dic137—41no—
61Dic137—81no—
62C2×C137—21no—
63C2×C137—21no—
64C2×C137#32711yescharacteristic
65C2×C137#35211yescharacteristic
66C2×C137#35411yescharacteristic
67D137—41no—
68D137—41no—
69C137#134411yescharacteristic, complemented, Sylow
70#1344—1371nomaximal, Sylow
71#397—1371no—
72#342—1371no—
73#323—1371no—
74C2×C4⋊C4—1371no—
75C2×C22⋊C4—2741no—
76C2×C22⋊C4—2741no—
77C2×C22⋊C4—1371no—
78C22⋊C8—2741no—
79#95—2741no—
80#95#1058773911yescharacteristic, complemented
81C24—1371no—
82C22×C4—21no—
83C22×C4—2741no—
84C22×C4—5481no—
85C22×C4—1371no—
86C22×C4C2×#1058773911yescharacteristic
87C2×C8—5481no—
88C4⋊C4—5481no—
89C22⋊C4—2742no—
90C22⋊C4—5481no—
91C22⋊C4—5481no—
92C22⋊C4—5481no—
93C22⋊C4—5481no—
94C23—2741no—
95C23—2741no—
96C23—5481no—
97C23—5481no—
98C23—1371no—
99C23—1371no—
100C23C22⋊#1058773911yescharacteristic
101C2×C4—21no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—2741no—
107C2×C4—5481no—
108C2×C4—5482no—
109C2×C4—5481no—
110C2×C4—5481no—
111C2×C4—5481no—
112C2×C4—10961no—
113C2×C4—10961no—
114C8—10961no—
115C22—21no—
116C22—21no—
117C22—2741no—
118C22—2741no—
119C22—5481no—
120C22—5481no—
121C22—5481no—
122C22—5481no—
123C22—10961no—
124C22#1798414711yescharacteristic
125C22#1798415011yescharacteristic
126C22#1798415311yescharacteristic
127C4—41no—
128C4—81no—
129C4—5481no—
130C4—10962no—
131C4—10961no—
132C2—21no—
133C2—21no—
134C2—5481no—
135C2—5481no—
136C2#2257825511yescharacteristic
137C2#2257830611yescharacteristic
138C2#2257831011yescharacteristic
subgroupG/H
centerC22#17984147
commutatorC22×C4×C137C2×C4
FrattiniC22×C4C2×#10587739
Fitting#95×C137C4
socleC22×C137#99
prime radicalC23×D137D4
cosocleC2×#14555487C22
hypercenter#95#10587739
hypocenterC137#1344
LCSG ▷ C22×C4×C137 ▷ C23×C137 ▷ C2×C137 ▷ C137
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
6. C2×C4⋊Dic137C4semidirect
10. #95×C137C4semidirect
69. C137#1344semidirect
80. #95#10587739semidirect

Maximal subgroups

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

subgroupindex
#225782812
#225782472
#225773302
#1344137