Finite Group Databasebeta

← #49097464

Subgroups — #49097464

Order 35968.

124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C4×Dic1124C211yesmaximal, characteristic
2#31823290C211yesmaximal, characteristic
3#31823288C211yesmaximal, characteristic
4C4⋊#17985113C211yesmaximal, characteristic
5#31823266C211yesmaximal, characteristic
6#31823266C211yesmaximal, characteristic
7#499×C281C211yesmaximal, characteristic
8C2×Dic1124C2211yescharacteristic
9C4×Dic562—21no—
10C2×#17985113C2211yescharacteristic
11C2×#17985113C2211yescharacteristic
12#22582813C2211yescharacteristic
13#22582804—21no—
14#125×C281—21no—
15#107×C281C2211yescharacteristic
16#107×C281C2211yescharacteristic
17#106×C281—21no—
18C4×C8×C281C2211yescharacteristic
19C2×Dic562—21no—
20Dic1124—21no—
21Dic1124Q812yes—
22C4⋊Dic281—21no—
23#17985117—41no—
24C4×Dic281—41no—
25#17985113—21no—
26#17985113—21no—
27C2×C8×C281D411yescharacteristic
28C2×C8×C281C2311yescharacteristic
29C4⋊C4×C281—21no—
30C4⋊C4×C281—21no—
31C4⋊C4×C281—41no—
32C4⋊C4×C281—41no—
33C42×C281D411yescharacteristic
34Dic562—22no—
35Dic562—41no—
36C2×Dic281—41no—
37C2×Dic281—41no—
38C2×C4×C281—41no—
39C2×C4×C281—41no—
40C2×C4×C281D811yescharacteristic
41C2×C4×C281D811yescharacteristic
42C2×C4×C281C2×D411yescharacteristic
43C8×C281—21no—
44C8×C281C2×Q811yescharacteristic
45C8×C281#4111yescharacteristic
46C22×C281C2×D811yescharacteristic
47C4×C281—21no—
48C4×C281—21no—
49C4×C281—81no—
50C4×C281—81no—
51C4×C281C22⋊Q811yescharacteristic
52C4×C281#13711yescharacteristic
53Dic281—42no—
54Dic281—81no—
55C2×C281#47411yescharacteristic
56C2×C281#50811yescharacteristic
57C2×C281#51011yescharacteristic
58C281#222911yescharacteristic, complemented, Sylow
59#2229—2811nomaximal, Sylow
60#499D28111yescharacteristic
61C4×Q16—2811no—
62#367—2811no—
63#366—2811no—
64C4⋊C16—2811no—
65#358—2811no—
66#358—2811no—
67C2×Q16—2811no—
68#125—21no—
69C4×Q8—5621no—
70C2×C16—2811no—
71C2×C16—2811no—
72#107—2811no—
73#107C2×D28111yescharacteristic
74#107C2×D28111yescharacteristic
75#106—21no—
76#103—5621no—
77C4×C8C2×D28111yescharacteristic
78C2×Q8—5621no—
79Q16—2812no—
80Q16—5621no—
81C2×C8C22⋊D28111yescharacteristic
82C2×C8C22×D28111yescharacteristic
83C4⋊C4—21no—
84C4⋊C4—21no—
85C4⋊C4—41no—
86C4⋊C4—41no—
87C4⋊C4—5621no—
88C4⋊C4—11241no—
89C42—11241no—
90C42C22⋊D28111yescharacteristic
91C16—5621no—
92C16—5621no—
93Q8—5622no—
94Q8—11241no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—11241no—
98C2×C4—11241no—
99C2×C4#1798512311yescharacteristic
100C2×C4#1798512311yescharacteristic
101C2×C4C2×C22⋊D28111yescharacteristic
102C8—21no—
103C8Q8×D28111yescharacteristic
104C8#1798513911yescharacteristic
105C22C2×#1798512311yescharacteristic
106C4—21no—
107C4—21no—
108C4—81no—
109C4—81no—
110C4—11242no—
111C4—22481no—
112C4#2258285511yescharacteristic
113C4#2258291011yescharacteristic
114C2#3182374011yescharacteristic
115C2#3182389311yescharacteristic
116C2#3182390311yescharacteristic
subgroupG/H
centerC22C2×#17985123
commutator, cosocleC2×C8×C281C23
FrattiniC2×C8C22×D281
Fitting#499×C281C2
socle, prime radicalC22×C281C2×D8
hypercenter#499D281
hypocenterC281#2229
LCSG ▷ C2×C8×C281 ▷ C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #499

Complements

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

NH ≅ G/Ntype
58. C281#2229semidirect

Maximal subgroups

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

subgroupindex
C4×Dic11242
#318232902
#318232882
C4⋊#179851132
#318232662
#499×C2812
#2229281