Finite Group Databasebeta

← #49094448

Subgroups — #49094448

Order 35968.

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

normal subgroups only

This group has 218 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#31823842C211yesmaximal, characteristic, complemented
2#31823753C212yesmaximal, complemented
3#31823212C211yesmaximal, characteristic, complemented
4D4⋊#14555886C212yesmaximal, complemented
5#555×C281C211yesmaximal, characteristic
6C2×#17985128—22no—
7#22582879C2211yescharacteristic
8#22582810—22no—
9C4⋊#14555886C2212yes—
10#22582800—22no—
11C4×#14555886C2211yescharacteristic
12C4⋊Q8×C281C2211yescharacteristic
13#124×C281—22no—
14#121×C281—22no—
15C4×D4×C281C2212yes—
16#117×C281—22no—
17C2×Dic562—21no—
18#17985128—44no—
19C2×#14555886—21no—
20C2×#14555886—22no—
21C4⋊Dic281—22no—
22C2×Q8×C281D412yes—
23C2×D4×C281—22no—
24C2×D4×C281D412yes—
25C22×C4×C281—22no—
26C4⋊C4×C281—22no—
27C4⋊C4×C281D412yes—
28C22⋊C4×C281—24no—
29C22⋊C4×C281—22no—
30C42×C281—22no—
31C42×C281C2311yescharacteristic
32Dic562—42no—
33C2×Dic281—41no—
34#14555886—22no—
35#14555886—42no—
36C23×C281—22no—
37Q8×C281—42no—
38D4×C281—22no—
39D4×C281—22no—
40D4×C281—82no—
41C2×C4×C281—22no—
42C2×C4×C281—22no—
43C2×C4×C281—42no—
44C2×C4×C281—42no—
45C2×C4×C281C2×D411yescharacteristic
46C2×C4×C281C2×D412yes—
47C22×C281—42no—
48C22×C281—42no—
49C22×C281—42no—
50C22×C281#12011yescharacteristic
51C4×C281—21no—
52C4×C281—42no—
53C4×C281—42no—
54C4×C281#13512yes—
55C4×C281#13712yes—
56Dic281—81no—
57C2×C281—82no—
58C2×C281#45212yes—
59C2×C281#45311yescharacteristic
60C281#163411yescharacteristic, complemented, Sylow
61#1634—2811nomaximal, Sylow
62#555D28111yescharacteristic
63#494—2811no—
64#476—2812no—
65#333—2811no—
66D4⋊C8—2812no—
67C2×Q16—5622no—
68C4⋊Q8—2811no—
69C4⋊Q8C2×D28111yescharacteristic
70#124—22no—
71#121—22no—
72C4×D4C2×D28112yes—
73#117—22no—
74#106—5622no—
75C4⋊C8—2812no—
76#102—5622no—
77C4×C8—2811no—
78C2×Q8—5621no—
79C2×Q8C22⋊D28112yes—
80C2×D4—22no—
81C2×D4C22⋊D28112yes—
82C22×C4—22no—
83Q16—11244no—
84C2×C8—5621no—
85C2×C8—5622no—
86C4⋊C4—22no—
87C4⋊C4—5622no—
88C4⋊C4C22⋊D28112yes—
89C22⋊C4—24no—
90C22⋊C4—22no—
91C42—22no—
92C42C22×D28111yescharacteristic
93C23—22no—
94Q8—42no—
95Q8—11242no—
96D4—22no—
97D4—22no—
98D4—82no—
99C2×C4—22no—
100C2×C4—22no—
101C2×C4—42no—
102C2×C4—42no—
103C2×C4—11241no—
104C2×C4C2×C22⋊D28111yescharacteristic
105C2×C4C2×C22⋊D28112yes—
106C8—5622no—
107C8—11242no—
108C22—42no—
109C22—42no—
110C22—42no—
111C22#2258284811yescharacteristic
112C4—21no—
113C4—42no—
114C4—42no—
115C4—22481no—
116C4#2258289912yes—
117C4#2258290912yes—
118C2—82no—
119C2#3182362512yes—
120C2#3182363111yescharacteristic
subgroupG/H
centerC22#22582848
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting, prime radical#555×C281C2
socleC22×C281#120
hypercenter#555D281
hypocenterC281#1634
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. #31823842C2semidirect
2. #31823753C2semidirect
3. #31823212C2semidirect
4. D4⋊#14555886C2semidirect
60. C281#1634semidirect

Maximal subgroups

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

subgroupindex
#318238422
#318237532
#318232122
D4⋊#145558862
#555×C2812
#1634281