Finite Group Databasebeta

← #31795879

Subgroups — #31795879

Order 17536.

158 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 38 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#22578390C211yesmaximal, characteristic
2#22578376C211yesmaximal, characteristic
3#22577384C211yesmaximal, characteristic
4C2×#14555519—21no—
5C2×#14555519C411yescharacteristic
6C22×#11764047C411yescharacteristic
7#17984149—21no—
8#17984148C412yes—
9#17984145—21no—
10C22⋊#11764047—21no—
11C2×#14555509C2211yescharacteristic
12M16×D137—21no—
13#17984006—21no—
14#17984005C411yescharacteristic
15#100×C137C411yescharacteristic
16#14555519—22no—
17#14555519—41no—
18#14555519—41no—
19C2×#11764047—21no—
20C2×#11764047—21no—
21C2×#11764047—41no—
22C2×#11764047—41no—
23#14555509—41no—
24#14555509—41no—
25C2×Dic274D411yescharacteristic
26C2×C22⋊D137C2×C411yescharacteristic
27C2×C22⋊D137Q811yescharacteristic
28C22×Dic137C2×C411yescharacteristic
29C22×Dic137D411yescharacteristic
30C2×C4×D137D411yescharacteristic
31#14555494—21no—
32#14555493—41no—
33C8×D137—41no—
34C2×D4×C137C2×C411yescharacteristic
35M16×C137—21no—
36#11764047—42no—
37#11764047—41no—
38#11764047—41no—
39C22×D137C4⋊C411yescharacteristic
40Dic274—41no—
41C22⋊D137—41no—
42C22⋊D137—41no—
43C2×Dic137—21no—
44C2×Dic137—21no—
45C2×Dic137—21no—
46C2×Dic137—21no—
47C2×Dic137C22⋊C411yescharacteristic
48C2×Dic137C22⋊C411yescharacteristic
49C2×Dic137C4⋊C411yescharacteristic
50C4×D137—21no—
51C4×D137—21no—
52#11764040—41no—
53C23×C137C4211yescharacteristic
54C23×C137C4⋊C411yescharacteristic
55D4×C137—41no—
56C2×C4×C137C22⋊C411yescharacteristic
57C8×C137—41no—
58C22×C137—21no—
59C22×C137—21no—
60C22×C137—41no—
61C22×C137—41no—
62C22×C137#9511yescharacteristic
63C2×D137—21no—
64C2×D137—41no—
65C4×C137—21no—
66Dic137—21no—
67Dic137—21no—
68Dic137#9911yescharacteristic
69Dic137#9911yescharacteristic
70C2×C137—21no—
71C2×C137—41no—
72C2×C137—41no—
73C2×C137#34211yescharacteristic
74D137—41no—
75C137#139211yescharacteristic, complemented, Sylow
76#1392—1371nomaximal, Sylow
77#413—1371no—
78#413—1371no—
79#408—1371no—
80C2×#41—1371no—
81C2×M16—2741no—
82C2×M16—2741no—
83C2×M16—1371no—
84C22×C8—1371no—
85#101—2741no—
86#101—2741no—
87#100—1372no—
88#100—1371no—
89#100#1058773911yescharacteristic
90C22⋊C8—2741no—
91C22⋊C8—2741no—
92#41—5481no—
93#41—5481no—
94C2×Q8—1371no—
95C2×D4—1371no—
96C2×D4—1371no—
97C2×D4C2×#1058773911yescharacteristic
98C22×C4—1371no—
99C22×C4—1371no—
100C22×C4—1371no—
101M16—21no—
102M16—2742no—
103M16—2741no—
104M16—5481no—
105M16—5481no—
106M16—5481no—
107C2×C8—2741no—
108C2×C8—2741no—
109C2×C8—5481no—
110C2×C8—5481no—
111C2×C8—5481no—
112C23—1371no—
113C23C4×#1058773911yescharacteristic
114C23C4⋊#1058773911yescharacteristic
115Q8—5481no—
116D4—41no—
117D4—5481no—
118D4—5481no—
119C2×C4—2741no—
120C2×C4—2741no—
121C2×C4—2741no—
122C2×C4—2741no—
123C2×C4—2741no—
124C2×C4—2741no—
125C2×C4—1371no—
126C2×C4—1371no—
127C2×C4—1371no—
128C2×C4C22⋊#1058773911yescharacteristic
129C8—41no—
130C8—5481no—
131C8—5482no—
132C8—5481no—
133C8—5481no—
134C22—21no—
135C22—21no—
136C22—41no—
137C22—41no—
138C22—2741no—
139C22—5481no—
140C22(C2×#10587739)⋊C411yescharacteristic
141C4—21no—
142C4—2741no—
143C4—2741no—
144C4—1371no—
145C4—1371no—
146C2—21no—
147C2—41no—
148C2—41no—
149C2—5481no—
150C2#2257828011yescharacteristic
subgroupG/H
centerC2#22578280
commutatorC23×C137C42
FrattiniC2×D4C2×#10587739
Fitting#100×C137C4
socleC2×C137#342
prime radical, cosocleC2×#14555509C22
hypercenter#100#10587739
hypocenterC137#1392
LCSG ▷ C23×C137 ▷ C22×C137 ▷ C2×C137 ▷ C137
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #100

Complements

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

NH ≅ G/Ntype
75. C137#1392semidirect

Maximal subgroups

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

subgroupindex
#225783902
#225783762
#225773842
#1392137