Finite Group Databasebeta

← #49120340

Subgroups — #49120340

Order 36224.

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

normal subgroups only

This group has 228 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, complemented
2#31826839C211yesmaximal, characteristic
3#31826666C212yesmaximal
4#31826195C212yesmaximal, complemented
5#333×C283C211yesmaximal, characteristic, complemented
6C2×#17985381—22no—
7C2×#17985379—22no—
8#22583609—22no—
9#22583608—22no—
10#22583607C2211yescharacteristic
11C4×Dic566C2212yes—
12#22583575—22no—
13#22583532—22no—
14C4×C283⋊C8C2211yescharacteristic
15C4⋊Q8×C283C2211yescharacteristic
16C4⋊C8×C283C2212yes—
17C2×Dic566—22no—
18C2×Dic566D412yes—
19C2×D1132—21no—
20C2×D1132—22no—
21#17985381—44no—
22#17985379—44no—
23C2×C283⋊C8—21no—
24C4⋊Dic283D412yes—
25Dic283⋊C4—24no—
26Dic283⋊C4—22no—
27C4×Dic283—22no—
28C4×Dic283—22no—
29C2×Q8×C283D412yes—
30C2×C8×C283—22no—
31C4⋊C4×C283—22no—
32C42×C283C2311yescharacteristic
33C22×D283—41no—
34Dic566—22no—
35Dic566—82no—
36Dic566SD1614yescomplemented
37D1132—42no—
38D1132—42no—
39D1132—42no—
40C2×Dic283—22no—
41C2×Dic283—22no—
42C283⋊C8—22no—
43Q8×C283—42no—
44C2×C4×C283—22no—
45C2×C4×C283C2×D412yes—
46C2×C4×C283C2×D411yescharacteristic
47C8×C283—42no—
48C22×C283#12011yescharacteristic
49C2×D283—82no—
50C2×D283—81no—
51C4×C283—21no—
52C4×C283—42no—
53C4×C283C2×SD1612yes—
54C4×C283#13712yes—
55Dic283—24no—
56Dic283—42no—
57C2×C283#44812yes—
58C2×C283#45311yescharacteristic
59D283—161no—
60C283#162311yescharacteristic, complemented, Sylow
61#1623—2831nomaximal, Sylow
62Q82—2831no—
63#492—2831no—
64#460—2832no—
65#333D28311yescharacteristic, complemented
66Q8⋊C8—2832no—
67C2×SD16—5662no—
68C2×SD16—5662no—
69C4⋊Q8—5662no—
70C4⋊Q8—5662no—
71C4⋊Q8C2×D28311yescharacteristic
72#127—2831no—
73C4×Q8—2832no—
74C4×Q8—5662no—
75C4⋊C8C2×D28312yes—
76#102—5662no—
77C4×C8—2831no—
78C2×Q8—2832no—
79C2×Q8—5662no—
80C2×Q8D113212yes—
81C2×D4—5662no—
82C2×D4—5661no—
83SD16—11324no—
84SD16—11324no—
85C2×C8—22no—
86C2×C8—5661no—
87C4⋊C4—22no—
88C4⋊C4—2832no—
89C4⋊C4—5664no—
90C4⋊C4—5662no—
91C42—5662no—
92C42—5662no—
93C42C22×D28311yescharacteristic
94C23—11321no—
95Q8—42no—
96Q8—2834no—
97Q8—5662no—
98Q8—22642no—
99D4—11322no—
100D4—11322no—
101D4—11322no—
102C2×C4—22no—
103C2×C4—5662no—
104C2×C4—5662no—
105C2×C4D4×D28312yes—
106C2×C4C2×D113211yescharacteristic
107C8—42no—
108C8—5662no—
109C22—22642no—
110C22—22641no—
111C22#2258358011yescharacteristic
112C4—21no—
113C4—42no—
114C4—5664no—
115C4—11322no—
116C4SD16×D28312yes—
117C4#2258364212yes—
118C2—45281no—
119C2#3182660512yes—
120C2#3182663511yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#333×C283C2
socleC22×C283#120
prime radical#22583607C22
hypercenter#333D283
hypocenterC283#1623
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #31827195C2semidirect
4. #31826195C2semidirect
5. #333×C283C2semidirect
36. Dic566SD16semidirect
60. C283#1623semidirect
65. #333D283semidirect

Maximal subgroups

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

subgroupindex
#318271952
#318268392
#318266662
#318261952
#333×C2832
#1623283