Finite Group Databasebeta

← #49119995

Subgroups — #49119995

Order 36224.

254 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 67 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#31827016C211yesmaximal, characteristic
2#31826487C212yesmaximal, complemented
3#31826214C211yesmaximal, characteristic, complemented
4#31826208C212yesmaximal, complemented
5#333×C283C211yesmaximal, characteristic, complemented
6C2×#17985393C412yes—
7C2×#17985375—22no—
8#22583607C2211yescharacteristic
9#22583599C412yes—
10#22583585—22no—
11#22583572—22no—
12C42×D283C2211yescharacteristic
13C4⋊(C283⋊C8)C2212yes—
14Dic283⋊C8—22no—
15C4⋊Q8×C283C2211yescharacteristic
16C4⋊C8×C283C2212yes—
17#17985393—44no—
18C2×D1132—22no—
19C2×D1132—22no—
20C2×D1132C2×C412yes—
21C2×C4×D283—22no—
22C2×C4×D283C2×C411yescharacteristic
23C2×C4×D283D412yes—
24#17985375—44no—
25C2×C283⋊C8—22no—
26(C2×D283)⋊C4—24no—
27C4×Dic283C2×C411yescharacteristic
28C4×Dic283D412yes—
29C2×Q8×C283C2×C412yes—
30C2×C8×C283—22no—
31C4⋊C4×C283—22no—
32C42×C283C2311yescharacteristic
33C22×D283—22no—
34C22×D283C22⋊C411yescharacteristic
35D1132—42no—
36D1132—44no—
37D1132—42no—
38D1132—42no—
39C2×Dic283C22⋊C412yes—
40C2×Dic283C22⋊C411yescharacteristic
41C4×D283—22no—
42C4×D283—22no—
43C4×D283—22no—
44C4×D283—44no—
45C283⋊C8—42no—
46Q8×C283—42no—
47C2×C4×C283—22no—
48C2×C4×C283C22×C411yescharacteristic
49C2×C4×C283C2×D412yes—
50C8×C283—42no—
51C22×C283C2×C22⋊C411yescharacteristic
52C2×D283—21no—
53C2×D283—22no—
54C2×D283—42no—
55C2×D283—44no—
56C4×C283—21no—
57C4×C283—42no—
58C4×C283AGL(1,ℤ/8)12yes—
59C4×C283#13712yes—
60Dic283—22no—
61Dic283#10012yes—
62C2×C283C2×#10011yescharacteristic
63C2×C283#41712yes—
64D283—41no—
65D283—82no—
66C283#156011yescharacteristic, complemented, Sylow
67#1560—2831nomaximal, Sylow
68#532—2831no—
69#423—2832no—
70#333—2831no—
71#333D28311yescharacteristic, complemented
72#331—2832no—
73C2×#41—2832no—
74C2×M16—5662no—
75C4⋊Q8C2×D28311yescharacteristic
76#127—2831no—
77#124—2832no—
78#121—5662no—
79C4×D4—5662no—
80C2×C42—2831no—
81C4⋊C8—2832no—
82C4⋊C8—5662no—
83C4⋊C8C2×D28312yes—
84#41—11324no—
85C2×Q8C4×D28312yes—
86C2×D4—2832no—
87C2×D4—5662no—
88C2×D4—5662no—
89C22×C4—2831no—
90C22×C4—2832no—
91C22×C4—5662no—
92M16—11324no—
93C2×C8—22no—
94C2×C8—5662no—
95C4⋊C4—22no—
96C22⋊C4—5664no—
97C42—2831no—
98C42—2832no—
99C42C22×D28311yescharacteristic
100C23—2831no—
101C23—5662no—
102Q8—42no—
103D4—11322no—
104D4—11324no—
105D4—11322no—
106D4—11322no—
107C2×C4—22no—
108C2×C4—2831no—
109C2×C4—2832no—
110C2×C4—5662no—
111C2×C4—5662no—
112C2×C4—5662no—
113C2×C4—11324no—
114C2×C4C2×C4×D28311yescharacteristic
115C2×C4D4×D28312yes—
116C8—42no—
117C8—11322no—
118C22—5661no—
119C22—5662no—
120C22—11322no—
121C22—11324no—
122C22C22⋊C4×D28311yescharacteristic
123C4—21no—
124C4—42no—
125C4—2832no—
126C4—5662no—
127C4#2258363712yes—
128C4#2258364212yes—
129C2—11321no—
130C2—22642no—
131C2#100×D28311yescharacteristic
132C2#3182646512yes—
subgroupG/H
centerC22C22⋊C4×D283
commutatorC2×C4×C283C22×C4
FrattiniC42C22×D283
Fitting#333×C283C2
socleC22×C283C2×C22⋊C4
prime radical#31827016C2
cosocleC42×C283C23
hypercenter#333D283
hypocenterC283#1560
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #31826487C2semidirect
3. #31826214C2semidirect
4. #31826208C2semidirect
5. #333×C283C2semidirect
66. C283#1560semidirect
71. #333D283semidirect

Maximal subgroups

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

subgroupindex
#318270162
#318264872
#318262142
#318262082
#333×C2832
#1560283