Finite Group Databasebeta

← #49094596

Subgroups — #49094596

Order 35968.

230 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 49 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#31823853C212yesmaximal, complemented
2#31823829C211yesmaximal, characteristic, complemented
3#31823205C211yesmaximal, characteristic, complemented
4#31823203C212yesmaximal, complemented
5#562×C281C211yesmaximal, characteristic, complemented
6C2×#17985125—22no—
7C2×#17985123—22no—
8#22582876C2211yescharacteristic
9#22582799—22no—
10#22582790C2211yescharacteristic
11#22582790C2212yes—
12#125×C281C2211yescharacteristic
13#124×C281C2212yes—
14#123×C281—22no—
15C22⋊Q8×C281—22no—
16#121×C281—22no—
17C2×D1124—21no—
18C2×D1124—22no—
19#17985125—44no—
20#17985123—44no—
21C2×#14555886—22no—
22C2×#14555886—21no—
23C2×Q8×C281D412yes—
24C2×D4×C281—22no—
25C2×D4×C281D412yes—
26C22×C4×C281—22no—
27C4⋊C4×C281—22no—
28C4⋊C4×C281—22no—
29C4⋊C4×C281D412yes—
30C22⋊C4×C281—22no—
31C22⋊C4×C281—22no—
32C22⋊C4×C281—22no—
33C42×C281C2311yescharacteristic
34C22×D281—41no—
35D1124—42no—
36D1124—42no—
37D1124—42no—
38#14555886—24no—
39#14555886—41no—
40C23×C281—22no—
41Q8×C281—42no—
42D4×C281—42no—
43D4×C281—82no—
44C2×C4×C281—22no—
45C2×C4×C281—22no—
46C2×C4×C281—82no—
47C2×C4×C281C2×D411yescharacteristic
48C2×C4×C281C2×D412yes—
49C22×C281—42no—
50C22×C281—42no—
51C22×C281—42no—
52C22×C281#12011yescharacteristic
53C2×D281—82no—
54C2×D281—81no—
55C4×C281—22no—
56C4×C281—21no—
57C4×C281—42no—
58C4×C281—42no—
59C2×C281—82no—
60C2×C281#45312yes—
61C2×C281#45411yescharacteristic
62D281—161no—
63C281#165611yescharacteristic, complemented, Sylow
64#1656—2811nomaximal, Sylow
65#562D28111yescharacteristic, complemented
66#496—2812no—
67#490—2811no—
68#330—2811no—
69#329—2812no—
70C2×SD16—5622no—
71C2×D8—5622no—
72#127—2811no—
73#125C2×D28111yescharacteristic
74#124C2×D28112yes—
75#123—22no—
76C22⋊Q8—22no—
77#121—22no—
78#102—5622no—
79#97—2811no—
80#97—2812no—
81C2×Q8C22⋊D28112yes—
82C2×D4—22no—
83C2×D4—5621no—
84C2×D4—5622no—
85C2×D4C22⋊D28112yes—
86C22×C4—22no—
87SD16—11244no—
88D8—11244no—
89C2×C8—5622no—
90C2×C8—5621no—
91C4⋊C4—22no—
92C4⋊C4—22no—
93C4⋊C4C22⋊D28112yes—
94C22⋊C4—22no—
95C22⋊C4—22no—
96C22⋊C4—22no—
97C42C22×D28111yescharacteristic
98C23—22no—
99C23—11241no—
100Q8—42no—
101D4—42no—
102D4—82no—
103D4—11242no—
104D4—11242no—
105D4—11242no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—82no—
109C2×C4C2×C22⋊D28111yescharacteristic
110C2×C4C2×C22⋊D28112yes—
111C8—5624no—
112C8—11241no—
113C22—42no—
114C22—42no—
115C22—42no—
116C22—22482no—
117C22—22481no—
118C22#2258284811yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C2—82no—
124C2—44961no—
125C2#3182363112yes—
126C2#3182363611yescharacteristic
subgroupG/H
centerC22#22582848
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#562×C281C2
socleC22×C281#120
hypercenter#562D281
hypocenterC281#1656
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #31823853C2semidirect
2. #31823829C2semidirect
3. #31823205C2semidirect
4. #31823203C2semidirect
5. #562×C281C2semidirect
63. C281#1656semidirect
65. #562D281semidirect

Maximal subgroups

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

subgroupindex
#318238532
#318238292
#318232052
#318232032
#562×C2812
#1656281