Finite Group Databasebeta

← #31795889

Subgroups — #31795889

Order 17536.

162 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 40 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#22578389C211yesmaximal, characteristic
2#22578382C211yesmaximal, characteristic
3#22577369C211yesmaximal, characteristic
4D137⋊M16—21no—
5#17984167—21no—
6#17984149C412yescomplemented
7#17984148—21no—
8#17984147C412yes—
9#17984146—21no—
10C2×#14555510C2211yescharacteristic
11C2×#14555494C411yescharacteristic, complemented
12#17984000—21no—
13#17984000—21no—
14C22×C8×C137C411yescharacteristic, complemented
15#14555520—41no—
16#14555519—22no—
17#14555518—41no—
18C4⋊#10587739—41no—
19C22⋊#10587739—22no—
20C4×#10587739—41no—
21#14555510—41no—
22#14555510—41no—
23C2×Dic274C2×C411yescharacteristic
24C2×D548C2×C411yescharacteristic
25C2×C22⋊D137D411yescharacteristic
26C2×C22⋊D137Q811yescharacteristic
27C2×C4×D137D411yescharacteristic
28C2×C4×D137D411yescharacteristic
29#14555494—41no—
30C2×#11764040—21no—
31C22×C4×C137C2×C411yescharacteristic
32C2×C8×C137—21no—
33C2×C8×C137—41no—
34C2×#10587739—42no—
35#11764047—42no—
36C22×D137C22⋊C411yescharacteristic
37C22×D137C4⋊C411yescharacteristic
38Dic274—41no—
39D548—41no—
40C22⋊D137—41no—
41C22⋊D137—41no—
42C2×Dic137C22⋊C411yescharacteristic
43C2×Dic137C4⋊C411yescharacteristic
44C4×D137—21no—
45C4×D137—21no—
46C4×D137—21no—
47C4×D137—21no—
48#11764040—41no—
49C23×C137C4⋊C411yescharacteristic
50C2×C4×C137—21no—
51C2×C4×C137—21no—
52C2×C4×C137C4211yescharacteristic
53C2×C4×C137C22⋊C411yescharacteristic
54C8×C137—41no—
55C22×C137—21no—
56C22×C137—41no—
57C22×C137#9511yescharacteristic
58C2×D137—21no—
59C2×D137—21no—
60C2×D137—41no—
61C2×D137—41no—
62#10587739—82no—
63C4×C137—21no—
64C4×C137#9911yescharacteristic
65C4×C137#9911yescharacteristic
66Dic137—21no—
67Dic137—21no—
68C2×C137—21no—
69C2×C137—41no—
70C2×C137#34211yescharacteristic
71D137—41no—
72D137—41no—
73C137#139511yescharacteristic, complemented, Sylow
74#1395—1371nomaximal, Sylow
75#413—1371no—
76#410—1371no—
77#408—1371no—
78C2×#41—1371no—
79C2×M16—2741no—
80C2×M16—1371no—
81C22×C8#1058773911yescharacteristic, complemented
82#117—2741no—
83#101—1372no—
84#100—2741no—
85#99—2741no—
86#99—1372no—
87C22⋊C8—2741no—
88C22⋊C8—2741no—
89#41—5481no—
90#41—5481no—
91C2×Q8—1371no—
92C2×D4—1371no—
93C2×D4—1371no—
94C2×D4—1371no—
95C22×C4—1371no—
96C22×C4—1371no—
97C22×C4C2×#1058773911yescharacteristic
98M16—2742no—
99M16—5481no—
100M16—5481no—
101C2×C8—21no—
102C2×C8—41no—
103C2×C8—2741no—
104C2×C8—5481no—
105C4⋊C4—5481no—
106C22⋊C4—2742no—
107C42—5481no—
108C23—1371no—
109C23—1371no—
110C23C4⋊#1058773911yescharacteristic
111Q8—5481no—
112D4—5481no—
113D4—5481no—
114D4—5481no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—2741no—
118C2×C4—2741no—
119C2×C4—2741no—
120C2×C4—2741no—
121C2×C4—5482no—
122C2×C4—1371no—
123C2×C4—1371no—
124C2×C4C4×#1058773911yescharacteristic
125C2×C4C22⋊#1058773911yescharacteristic
126C8—41no—
127C8—5482no—
128C8—5481no—
129C22—21no—
130C22—41no—
131C22—2741no—
132C22—2741no—
133C22—5481no—
134C22—5481no—
135C22(C2×#10587739)⋊C411yescharacteristic
136C4—21no—
137C4—2741no—
138C4—2741no—
139C4—10962no—
140C4#1798414611yescharacteristic
141C4#1798414711yescharacteristic
142C2—21no—
143C2—41no—
144C2—5481no—
145C2—5481no—
146C2#2257828111yescharacteristic
subgroupG/H
centerC4#17984147
commutatorC2×C4×C137C42
FrattiniC22×C4C2×#10587739
FittingC22×C8×C137C4
socleC2×C137#342
prime radical, cosocleC2×#14555510C22
hypercenterC22×C8#10587739
hypocenterC137#1395
LCSG ▷ C2×C4×C137 ▷ C22×C137 ▷ C2×C137 ▷ C137
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
6. #17984149C4semidirect
11. C2×#14555494C4semidirect
14. C22×C8×C137C4semidirect
73. C137#1395semidirect
81. C22×C8#10587739semidirect

Maximal subgroups

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

subgroupindex
#225783892
#225783822
#225773692
#1395137