Finite Group Databasebeta

← #49120402

Subgroups — #49120402

Order 36224.

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

normal subgroups only

This group has 206 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#31827195C211yesmaximal, characteristic
2#31826844C211yesmaximal, characteristic
3#31826761C212yesmaximal
4#31826195C212yesmaximal
5#333×C283C211yesmaximal, characteristic
6C2×#17985382—22no—
7#22583610C2211yescharacteristic
8#22583609—22no—
9#22583608—22no—
10C4×Dic566C2212yes—
11#22583575—22no—
12#22583544—22no—
13#22583535—22no—
14C4×C283⋊C8C2211yescharacteristic
15C4⋊Q8×C283C2211yescharacteristic
16C4⋊C8×C283C2212yes—
17C2×Dic566—22no—
18C2×Dic566—21no—
19C2×Dic566D412yes—
20#17985382—44no—
21C2×C283⋊C8—21no—
22C4⋊Dic283—22no—
23C4⋊Dic283D412yes—
24Dic283⋊C4—24no—
25Dic283⋊C4—22no—
26C4×Dic283—22no—
27C4×Dic283—22no—
28C2×Q8×C283D412yes—
29C2×C8×C283—22no—
30C4⋊C4×C283—22no—
31C42×C283C2311yescharacteristic
32Dic566—22no—
33Dic566—42no—
34Dic566—82no—
35Dic566Q1614yescomplemented
36C2×Dic283—22no—
37C2×Dic283—22no—
38C2×Dic283—41no—
39C283⋊C8—22no—
40Q8×C283—42no—
41C2×C4×C283—22no—
42C2×C4×C283C2×D412yes—
43C2×C4×C283C2×D411yescharacteristic
44C8×C283—42no—
45C22×C283#12011yescharacteristic
46C4×C283—21no—
47C4×C283—42no—
48C4×C283C2×Q1612yes—
49C4×C283#13712yes—
50Dic283—24no—
51Dic283—42no—
52Dic283—81no—
53C2×C283#45112yes—
54C2×C283#45311yescharacteristic
55C283#163311yescharacteristic, complemented, Sylow
56#1633—2831nomaximal, Sylow
57Q82—2831no—
58#494—2831no—
59#477—2832no—
60#333D28311yescharacteristic
61Q8⋊C8—2832no—
62C2×Q16—5662no—
63C4⋊Q8—2831no—
64C4⋊Q8—5662no—
65C4⋊Q8—5662no—
66C4⋊Q8C2×D28311yescharacteristic
67C4×Q8—2832no—
68C4×Q8—5662no—
69#107—5662no—
70C4⋊C8C2×D28312yes—
71#103—5662no—
72C4×C8—2831no—
73C2×Q8—2832no—
74C2×Q8—5662no—
75C2×Q8—5661no—
76C2×Q8D113212yes—
77Q16—11324no—
78C2×C8—22no—
79C2×C8—5661no—
80C4⋊C4—22no—
81C4⋊C4—2832no—
82C4⋊C4—5664no—
83C4⋊C4—5662no—
84C4⋊C4—5662no—
85C42—5662no—
86C42—5662no—
87C42C22×D28311yescharacteristic
88Q8—42no—
89Q8—2834no—
90Q8—5662no—
91Q8—11322no—
92Q8—22642no—
93C2×C4—22no—
94C2×C4—5662no—
95C2×C4—5662no—
96C2×C4—11321no—
97C2×C4D4×D28312yes—
98C2×C4C2×D113211yescharacteristic
99C8—42no—
100C8—5662no—
101C22#2258358011yescharacteristic
102C4—21no—
103C4—42no—
104C4—5664no—
105C4—11322no—
106C4—22641no—
107C4Q16×D28312yes—
108C4#2258363912yes—
109C2#3182662212yes—
110C2#3182663511yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#333×C283C2
socle, prime radicalC22×C283#120
hypercenter#333D283
hypocenterC283#1633
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
35. Dic566Q16semidirect
55. C283#1633semidirect

Maximal subgroups

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

subgroupindex
#318271952
#318268442
#318267612
#318261952
#333×C2832
#1633283