Finite Group Databasebeta

← #44549660

Subgroups — #44549660

Order 32128.

230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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#30632435C211yesmaximal, characteristic, complemented
2#30632076C212yesmaximal, complemented
3#30632053C211yesmaximal, characteristic, complemented
4#30631426C212yesmaximal, complemented
5#330×C251C211yesmaximal, characteristic, complemented
6C2×#16860799—22no—
7C2×D2008—22no—
8#22548712C2211yescharacteristic
9#22548703C2212yes—
10#22548700—22no—
11#22548693—22no—
12#22548690—22no—
13#22548635—22no—
14#22548626C2211yescharacteristic
15#125×C251C2211yescharacteristic
16#97×C251C2212yes—
17C2×Dic502D412yes—
18C2×D1004—22no—
19C2×D1004—21no—
20C2×D1004—22no—
21C2×D1004D412yes—
22C2×C4×D251—22no—
23#16860799—44no—
24D2008—44no—
25C2×C251⋊C8—21no—
26Dic251⋊C4—22no—
27(C2×D251)⋊C4—22no—
28(C2×D251)⋊C4—22no—
29(C2×D251)⋊C4—22no—
30C2×C8×C251—22no—
31C4⋊C4×C251—22no—
32C4⋊C4×C251D412yes—
33C42×C251C2311yescharacteristic
34C22×D251—22no—
35C22×D251—41no—
36Dic502—42no—
37D1004—42no—
38D1004—42no—
39D1004—42no—
40D1004—42no—
41D1004—82no—
42C2×Dic251—22no—
43C4×D251—82no—
44C251⋊C8—41no—
45C2×C4×C251—22no—
46C2×C4×C251C2×D412yes—
47C2×C4×C251C2×D411yescharacteristic
48C8×C251—24no—
49C22×C251#12011yescharacteristic
50C2×D251—42no—
51C2×D251—42no—
52C2×D251—42no—
53C2×D251—82no—
54C2×D251—81no—
55C4×C251—22no—
56C4×C251—21no—
57C4×C251—42no—
58Dic251—42no—
59C2×C251#45312yes—
60C2×C251#45411yescharacteristic
61D251—82no—
62D251—161no—
63C251#165611yescharacteristic, complemented, Sylow
64#1656—2511nomaximal, Sylow
65#562—2511no—
66#496—2512no—
67#490—2511no—
68#330D25111yescharacteristic, complemented
69#329—2512no—
70C2×SD16—5022no—
71C2×D8—5022no—
72#127—2511no—
73#125C2×D25111yescharacteristic
74#124—2512no—
75#123—5022no—
76C22⋊Q8—5022no—
77#121—5022no—
78#102—5022no—
79#97—2511no—
80#97C2×D25112yes—
81C2×Q8—2512no—
82C2×D4—5022no—
83C2×D4—5022no—
84C2×D4—5021no—
85C2×D4—2512no—
86C22×C4—5022no—
87SD16—10044no—
88D8—10044no—
89C2×C8—22no—
90C2×C8—5021no—
91C4⋊C4—22no—
92C4⋊C4—5022no—
93C4⋊C4D100412yes—
94C22⋊C4—5022no—
95C22⋊C4—5022no—
96C22⋊C4—5022no—
97C42C22×D25111yescharacteristic
98C23—10041no—
99C23—5022no—
100Q8—10042no—
101D4—20082no—
102D4—10042no—
103D4—10042no—
104D4—10042no—
105D4—10042no—
106C2×C4—22no—
107C2×C4—20082no—
108C2×C4—5022no—
109C2×C4D4×D25112yes—
110C2×C4C2×D100411yescharacteristic
111C8—24no—
112C8—10041no—
113C22—20082no—
114C22—20081no—
115C22—10042no—
116C22—10042no—
117C22—10042no—
118C22#2254868511yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—10042no—
123C2—40161no—
124C2—20082no—
125C2#3063185612yes—
126C2#3063186211yescharacteristic
subgroupG/H
centerC22#22548685
commutator, cosocleC42×C251C23
FrattiniC42C22×D251
Fitting#330×C251C2
socleC22×C251#120
hypercenter#330D251
hypocenterC251#1656
LCSG ▷ C42×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #30632435C2semidirect
2. #30632076C2semidirect
3. #30632053C2semidirect
4. #30631426C2semidirect
5. #330×C251C2semidirect
63. C251#1656semidirect
68. #330D251semidirect

Maximal subgroups

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

subgroupindex
#306324352
#306320762
#306320532
#306314262
#330×C2512
#1656251