Finite Group Databasebeta

← #49123334

Subgroups — #49123334

Order 36224.

170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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#31826901C212yesmaximal, complemented
2#31826583C211yesmaximal, characteristic, complemented
3#31826286C211yesmaximal, characteristic, complemented
4#31826278C212yesmaximal, complemented
5#493×C283C211yesmaximal, characteristic, complemented
6#22583632C2211yescharacteristic
7#22583616—21no—
8#22583554—22no—
9#22583551—22no—
10#22583550C2212yes—
11#22583546C2211yescharacteristic
12#22583538—21no—
13C2×D8×C283—21no—
14C2×D8×C283C2212yes—
15#127×C283—21no—
16C4×C8×C283C2211yescharacteristic
17#17985392—21no—
18Dic1132D411yescharacteristic, complemented
19#17985381—21no—
20D2264D411yescharacteristic, complemented
21#17985376—21no—
22#17985375—41no—
23C8×D283—41no—
24C283⋊C16—22no—
25C2×D4×C283—22no—
26C2×D4×C283—42no—
27D8×C283—22no—
28D8×C283—22no—
29D8×C283—41no—
30D8×C283—41no—
31C2×C8×C283D411yescharacteristic
32C2×C8×C283C2311yescharacteristic
33C42×C283D411yescharacteristic
34Dic566—21no—
35D1132—21no—
36C22⋊D283—41no—
37C4×D283—41no—
38C283⋊C8—41no—
39C23×C283—42no—
40D4×C283—42no—
41D4×C283—42no—
42D4×C283—84no—
43C2×C4×C283—21no—
44C2×C4×C283C2×D411yescharacteristic
45C8×C283D811yescharacteristic
46C8×C283D811yescharacteristic
47C8×C283C2×D411yescharacteristic
48C8×C283#4111yescharacteristic
49C22×C283—84no—
50C22×C283—82no—
51C22×C283AGL(1,ℤ/8)11yescharacteristic
52C2×D283—41no—
53C4×C283—22no—
54C4×C283#12111yescharacteristic
55C4×C283C2×D811yescharacteristic
56Dic283—41no—
57C2×C283—21no—
58C2×C283—162no—
59C2×C283#45911yescharacteristic
60D283—81no—
61C283#221311yescharacteristic, complemented, Sylow
62#2213—2831nomaximal, Sylow
63#509—2832no—
64#493D28311yescharacteristic, complemented
65#443—2831no—
66#364—2831no—
67#361—2832no—
68#135—2831no—
69C2×D8—21no—
70C2×D8C2×D28312yes—
71#131—5661no—
72#127—21no—
73SD32—5662no—
74D16—5662no—
75M32—2832no—
76#108—2831no—
77#104—5661no—
78C4×C8C2×D28311yescharacteristic
79#41—5661no—
80C2×D4—22no—
81C2×D4—42no—
82Q16—2831no—
83SD16—5661no—
84D8—22no—
85D8—22no—
86D8—41no—
87D8—41no—
88D8—2831no—
89M16—5661no—
90M16—11321no—
91C2×C8—11321no—
92C2×C8C22⋊D28311yescharacteristic
93C2×C8C22×D28311yescharacteristic
94C42C22⋊D28311yescharacteristic
95C16—5662no—
96C23—42no—
97Q8—5661no—
98D4—42no—
99D4—42no—
100D4—84no—
101D4—5661no—
102D4—11321no—
103C2×C4—21no—
104C2×C4—11321no—
105C2×C4C2×C22⋊D28311yescharacteristic
106C8—11321no—
107C8#1798537711yescharacteristic
108C8#1798537711yescharacteristic
109C8D4×D28311yescharacteristic
110C8#1798539111yescharacteristic
111C22—84no—
112C22—82no—
113C22—11321no—
114C22#2258363611yescharacteristic
115C4—22no—
116C4—11321no—
117C4#2258358111yescharacteristic
118C4C2×#1798537711yescharacteristic
119C2—21no—
120C2—162no—
121C2—22641no—
122C2#3182665711yescharacteristic
subgroupG/H
centerC2#31826657
commutator, cosocleC2×C8×C283C23
FrattiniC2×C8C22×D283
Fitting#493×C283C2
socleC2×C283#459
hypercenter#493D283
hypocenterC283#2213
LCSG ▷ C2×C8×C283 ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #31826901C2semidirect
2. #31826583C2semidirect
3. #31826286C2semidirect
4. #31826278C2semidirect
5. #493×C283C2semidirect
18. Dic1132D4semidirect
20. D2264D4semidirect
61. C283#2213semidirect
64. #493D283semidirect

Maximal subgroups

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

subgroupindex
#318269012
#318265832
#318262862
#318262782
#493×C2832
#2213283