Finite Group Databasebeta

← #49122956

Subgroups — #49122956

Order 36224.

230 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 73 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#31826449C212yesmaximal
2#31826264C214yesmaximal, complemented
3#536×C283C211yesmaximal, characteristic
4C2×#17985376—22no—
5#22583529C2214yes—
6#22583527—22no—
7C2×#41×C283C2211yescharacteristic
8C22×Q8×C283C411yescharacteristic
9C4⋊Q8×C283C2212yes—
10#124×C283C412yes—
11#123×C283—22no—
12C22⋊Q8×C283—22no—
13#117×C283C411yescharacteristic
14#17985376—24no—
15#17985376—42no—
16C2×C283⋊C8—42no—
17#41×C283—42no—
18C2×Q8×C283—21no—
19C2×Q8×C283—42no—
20C2×Q8×C283C2×C412yes—
21C2×Q8×C283C2311yescharacteristic
22C2×D4×C283C2×C411yescharacteristic
23C2×D4×C283D412yes—
24C22×C4×C283—21no—
25C22×C4×C283C2×C411yescharacteristic
26C22×C4×C283D412yes—
27C4⋊C4×C283—21no—
28C4⋊C4×C283—24no—
29C22⋊C4×C283—21no—
30C22⋊C4×C283—24no—
31C42×C283C2×C412yes—
32C283⋊C8—44no—
33C23×C283C22⋊C412yes—
34C23×C283C22⋊C411yescharacteristic
35Q8×C283—41no—
36Q8×C283—42no—
37Q8×C283—42no—
38D4×C283—41no—
39D4×C283—42no—
40C2×C4×C283—22no—
41C2×C4×C283—22no—
42C2×C4×C283—22no—
43C2×C4×C283—22no—
44C2×C4×C283—22no—
45C2×C4×C283—42no—
46C2×C4×C283C22⋊C411yescharacteristic
47C2×C4×C283C22×C411yescharacteristic
48C2×C4×C283C2×D412yes—
49C22×C283—21no—
50C22×C283—22no—
51C22×C283—42no—
52C22×C283—41no—
53C22×C283C2×C22⋊C411yescharacteristic
54C4×C283—21no—
55C4×C283—22no—
56C4×C283—42no—
57C4×C283—42no—
58C4×C283#9912yes—
59C2×C283—21no—
60C2×C283—41no—
61C2×C283—42no—
62C2×C283C2×#9911yescharacteristic
63C283#213511yescharacteristic, complemented, Sylow
64#2135—2831nomaximal, Sylow
65#536D28311yescharacteristic
66#413—2832no—
67#356—2834no—
68C2×#41C2×D28311yescharacteristic
69C22×Q8Dic28311yescharacteristic
70C2×M16—5662no—
71C4⋊Q8C2×D28312yes—
72#124Dic28312yes—
73#123—22no—
74C22⋊Q8—22no—
75#117Dic28311yescharacteristic
76#101—2834no—
77#100—5662no—
78#41—42no—
79C2×Q8—21no—
80C2×Q8—42no—
81C2×Q8C2×Dic28312yes—
82C2×Q8C22×D28311yescharacteristic
83C2×D4C2×Dic28311yescharacteristic
84C2×D4C22⋊D28312yes—
85C22×C4—21no—
86C22×C4C2×Dic28311yescharacteristic
87C22×C4C22⋊D28312yes—
88M16—5664no—
89M16—11322no—
90C2×C8—11322no—
91C4⋊C4—21no—
92C4⋊C4—24no—
93C22⋊C4—21no—
94C22⋊C4—24no—
95C42C2×Dic28312yes—
96C23C22⋊Dic28312yes—
97C23C22⋊Dic28311yescharacteristic
98Q8—41no—
99Q8—42no—
100Q8—42no—
101D4—41no—
102D4—42no—
103C2×C4—22no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—42no—
109C2×C4C22⋊Dic28311yescharacteristic
110C2×C4C22×Dic28311yescharacteristic
111C2×C4C2×C22⋊D28312yes—
112C8—11324no—
113C22—21no—
114C22—22no—
115C22—42no—
116C22—41no—
117C22C2×C22⋊Dic28311yescharacteristic
118C4—22no—
119C4—21no—
120C4—42no—
121C4—42no—
122C4#2258352512yes—
123C2—21no—
124C2—41no—
125C2—42no—
126C2C2×#2258352511yescharacteristic
subgroupG/H
centerC2C2×#22583525
commutatorC2×C4×C283C22×C4
FrattiniC2×Q8C22×D283
Fitting#536×C283C2
socleC2×C283C2×#99
prime radicalC2×#41×C283C22
cosocleC2×Q8×C283C23
hypercenter#536D283
hypocenterC283#2135
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #31826264C2semidirect
63. C283#2135semidirect

Maximal subgroups

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

subgroupindex
#318264492
#318262642
#536×C2832
#2135283