Finite Group Databasebeta

← #49094386

Subgroups — #49094386

Order 35968.

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

normal subgroups only

This group has 240 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#31823837C211yesmaximal, characteristic, complemented
2#31823658C212yesmaximal, complemented
3#31823212C211yesmaximal, characteristic, complemented
4D4⋊#14555886C212yesmaximal, complemented
5#555×C281C211yesmaximal, characteristic, complemented
6C2×#17985125—22no—
7C2×#17985123—22no—
8#22582876C2211yescharacteristic
9C4⋊#14555886C2212yes—
10#22582799—22no—
11C4×#14555886C2211yescharacteristic
12C4⋊Q8×C281C2211yescharacteristic
13#124×C281—22no—
14#121×C281—22no—
15C4×D4×C281C2212yes—
16#117×C281—22no—
17C2×D1124—22no—
18C2×D1124—21no—
19#17985125—44no—
20#17985123—44no—
21C2×#14555886—21no—
22C2×#14555886—22no—
23C2×Q8×C281D412yes—
24C2×D4×C281—22no—
25C2×D4×C281D412yes—
26C22×C4×C281—22no—
27C4⋊C4×C281—22no—
28C4⋊C4×C281D412yes—
29C22⋊C4×C281—24no—
30C22⋊C4×C281—22no—
31C42×C281—22no—
32C42×C281C2311yescharacteristic
33C22×D281—41no—
34D1124—42no—
35D1124—42no—
36D1124—42no—
37#14555886—22no—
38#14555886—42no—
39C23×C281—22no—
40Q8×C281—42no—
41D4×C281—22no—
42D4×C281—22no—
43D4×C281—82no—
44C2×C4×C281—22no—
45C2×C4×C281—22no—
46C2×C4×C281—42no—
47C2×C4×C281—42no—
48C2×C4×C281C2×D411yescharacteristic
49C2×C4×C281C2×D412yes—
50C22×C281—42no—
51C22×C281—42no—
52C22×C281—42no—
53C22×C281#12011yescharacteristic
54C2×D281—82no—
55C2×D281—81no—
56C4×C281—21no—
57C4×C281—42no—
58C4×C281—42no—
59C4×C281#13512yes—
60C4×C281AGL(1,ℤ/8)12yes—
61C2×C281—82no—
62C2×C281#44912yes—
63C2×C281#45311yescharacteristic
64D281—161no—
65C281#162411yescharacteristic, complemented, Sylow
66#1624—2811nomaximal, Sylow
67#555D28111yescharacteristic, complemented
68#492—2811no—
69#459—2812no—
70#333—2811no—
71D4⋊C8—2812no—
72C2×SD16—5622no—
73C2×D8—5622no—
74C4⋊Q8C2×D28111yescharacteristic
75#127—2811no—
76#124—22no—
77#121—22no—
78C4×D4C2×D28112yes—
79#117—22no—
80C4⋊C8—2812no—
81#102—5622no—
82C4×C8—2811no—
83C2×Q8C22⋊D28112yes—
84C2×D4—22no—
85C2×D4—5622no—
86C2×D4—5621no—
87C2×D4C22⋊D28112yes—
88C22×C4—22no—
89SD16—11244no—
90D8—11244no—
91C2×C8—5621no—
92C2×C8—5622no—
93C4⋊C4—22no—
94C4⋊C4C22⋊D28112yes—
95C22⋊C4—24no—
96C22⋊C4—22no—
97C42—22no—
98C42C22×D28111yescharacteristic
99C23—22no—
100C23—11241no—
101Q8—42no—
102D4—22no—
103D4—22no—
104D4—82no—
105D4—11242no—
106D4—11242no—
107D4—11242no—
108C2×C4—22no—
109C2×C4—22no—
110C2×C4—42no—
111C2×C4—42no—
112C2×C4C2×C22⋊D28111yescharacteristic
113C2×C4C2×C22⋊D28112yes—
114C8—5622no—
115C8—11242no—
116C22—42no—
117C22—42no—
118C22—42no—
119C22—22481no—
120C22—22482no—
121C22#2258284811yescharacteristic
122C4—21no—
123C4—42no—
124C4—42no—
125C4#2258289912yes—
126C4#2258290412yes—
127C2—82no—
128C2—44961no—
129C2#3182360812yes—
130C2#3182363111yescharacteristic
subgroupG/H
centerC22#22582848
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#555×C281C2
socleC22×C281#120
hypercenter#555D281
hypocenterC281#1624
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #31823837C2semidirect
2. #31823658C2semidirect
3. #31823212C2semidirect
4. D4⋊#14555886C2semidirect
5. #555×C281C2semidirect
65. C281#1624semidirect
67. #555D281semidirect

Maximal subgroups

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

subgroupindex
#318238372
#318236582
#318232122
D4⋊#145558862
#555×C2812
#1624281