Finite Group Databasebeta

← #49120905

Subgroups — #49120905

Order 36224.

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

normal subgroups only

This group has 164 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#31826868C211yesmaximal, characteristic
2#31826817C211yesmaximal, characteristic
3#31826816C211yesmaximal, characteristic
4#31826815C211yesmaximal, characteristic
5#31826815C211yesmaximal, characteristic
6#31826187C211yesmaximal, characteristic
7#498×C283C211yesmaximal, characteristic
8#22583610C2211yescharacteristic
9#22583610C2211yescharacteristic
10#22583543—22no—
11#22583535—22no—
12#22583534—22no—
13#22583534—22no—
14#22583533—22no—
15C4×C283⋊C8C2211yescharacteristic
16C4×C283⋊C8C2211yescharacteristic
17C4⋊Q8×C283C2211yescharacteristic
18C4⋊Q8×C283C2211yescharacteristic
19#106×C283—22no—
20C4×C8×C283C2211yescharacteristic
21C2×Dic566—21no—
22C2×Dic566—21no—
23C2×C283⋊C8D412yes—
24C2×C283⋊C8D412yes—
25C4⋊Dic283—21no—
26C4⋊Dic283—21no—
27C4⋊Dic283—21no—
28C4⋊Dic283—21no—
29C2×Q8×C283—21no—
30C2×Q8×C283—21no—
31C2×C8×C283D412yes—
32C4⋊C4×C283—21no—
33C4⋊C4×C283—21no—
34C4⋊C4×C283—21no—
35C4⋊C4×C283—21no—
36C42×C283C2311yescharacteristic
37Dic566—42no—
38Dic566—42no—
39C2×Dic283—41no—
40C2×Dic283—41no—
41C283⋊C8—22no—
42C283⋊C8—22no—
43Q8×C283—42no—
44Q8×C283—42no—
45C2×C4×C283—41no—
46C2×C4×C283—41no—
47C2×C4×C283C2×D411yescharacteristic
48C2×C4×C283C2×D411yescharacteristic
49C2×C4×C283C2×D411yescharacteristic
50C8×C283—22no—
51C22×C283#12711yescharacteristic
52C4×C283—81no—
53C4×C283—81no—
54C4×C283#13512yes—
55C4×C283#13712yes—
56C4×C283#13712yes—
57Dic283—81no—
58Dic283—81no—
59C2×C283#49511yescharacteristic
60C2×C283#49711yescharacteristic
61C2×C283#49711yescharacteristic
62C283#171811yescharacteristic, complemented, Sylow
63#1718—2831nomaximal, Sylow
64#500—2831no—
65#498D28311yescharacteristic
66#487—2831no—
67#487—2831no—
68#487—2831no—
69#487—2831no—
70#322—2831no—
71C4⋊Q8—2831no—
72C4⋊Q8—2831no—
73C4⋊Q8C2×D28311yescharacteristic
74C4⋊Q8C2×D28311yescharacteristic
75#107—5662no—
76#106—22no—
77#103—5662no—
78#103—5662no—
79#103—5662no—
80#103—5662no—
81C4×C8—2831no—
82C4×C8—2831no—
83C4×C8C2×D28311yescharacteristic
84C2×Q8—21no—
85C2×Q8—21no—
86C2×Q8—5661no—
87C2×Q8—5661no—
88C2×C8—2832no—
89C2×C8—2832no—
90C2×C8C22⋊D28312yes—
91C4⋊C4—21no—
92C4⋊C4—21no—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—5661no—
96C4⋊C4—5661no—
97C4⋊C4—5661no—
98C4⋊C4—5661no—
99C42C22×D28311yescharacteristic
100Q8—42no—
101Q8—42no—
102Q8—11322no—
103Q8—11322no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—11321no—
107C2×C4—11321no—
108C2×C4D4×D28311yescharacteristic
109C2×C4D4×D28311yescharacteristic
110C2×C4C2×C22⋊D28311yescharacteristic
111C8—22no—
112C8—5662no—
113C8—5662no—
114C22#2258360611yescharacteristic
115C4—81no—
116C4—81no—
117C4—22641no—
118C4—22641no—
119C4#2258363112yes—
120C4#2258363912yes—
121C4#2258364112yes—
122C2#3182684611yescharacteristic
123C2#3182685611yescharacteristic
124C2#3182685711yescharacteristic
subgroupG/H
centerC22#22583606
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#498×C283C2
socle, prime radicalC22×C283#127
hypercenter#498D283
hypocenterC283#1718
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
62. C283#1718semidirect

Maximal subgroups

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

subgroupindex
#318268682
#318268172
#318268162
#318268152
#318261872
#498×C2832
#1718283