Finite Group Databasebeta

← #44549689

Subgroups — #44549689

Order 32128.

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

normal subgroups only

This group has 196 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
2#30632057C211yesmaximal, characteristic, complemented
3#30632047C212yesmaximal, complemented
4#30631426C212yesmaximal, complemented
5#330×C251C211yesmaximal, characteristic, complemented
6#22548715C2211yescharacteristic
7#22548703C2212yes—
8#22548700—22no—
9#22548693—22no—
10#22548690—22no—
11#22548640—22no—
12#22548638—22no—
13#22548637—22no—
14#22548626C2211yescharacteristic
15#125×C251C2211yescharacteristic
16#97×C251C2212yes—
17C2×Dic502—21no—
18C2×Dic502D412yes—
19C2×D1004—22no—
20C2×D1004D412yes—
21C2×C4×D251—22no—
22C2×C251⋊C8—21no—
23C4⋊Dic251—22no—
24Dic251⋊C4—22no—
25(C2×D251)⋊C4—22no—
26(C2×D251)⋊C4—22no—
27(C2×D251)⋊C4—22no—
28C2×C8×C251—22no—
29C4⋊C4×C251—22no—
30C4⋊C4×C251D412yes—
31C42×C251C2311yescharacteristic
32C22×D251—22no—
33Dic502—42no—
34Dic502—42no—
35D1004—42no—
36D1004—82no—
37C2×Dic251—22no—
38C2×Dic251—41no—
39C4×D251—82no—
40C251⋊C8—41no—
41C2×C4×C251—22no—
42C2×C4×C251C2×D412yes—
43C2×C4×C251C2×D411yescharacteristic
44C8×C251—42no—
45C22×C251#12011yescharacteristic
46C2×D251—42no—
47C2×D251—42no—
48C2×D251—42no—
49C4×C251—21no—
50C4×C251—22no—
51C4×C251—42no—
52Dic251—42no—
53Dic251—81no—
54C2×C251#45411yescharacteristic
55C2×C251#45512yes—
56D251—82no—
57C251#166211yescharacteristic, complemented, Sylow
58#1662—2511nomaximal, Sylow
59#562—2511no—
60#491—2511no—
61#489—2512no—
62#330D25111yescharacteristic, complemented
63#329—2512no—
64C4⋊Q8—2511no—
65#125C2×D25111yescharacteristic
66#124—2512no—
67#123—5022no—
68C22⋊Q8—5022no—
69#121—5022no—
70#103—5022no—
71#103—5022no—
72#102—5022no—
73#97—2511no—
74#97C2×D25112yes—
75C2×Q8—5021no—
76C2×Q8—2512no—
77C2×D4—5022no—
78C2×D4—2512no—
79C22×C4—5022no—
80C2×C8—22no—
81C2×C8—5021no—
82C4⋊C4—22no—
83C4⋊C4—5022no—
84C4⋊C4—5022no—
85C4⋊C4D100412yes—
86C22⋊C4—5022no—
87C22⋊C4—5022no—
88C22⋊C4—5022no—
89C42C22×D25111yescharacteristic
90C23—5022no—
91Q8—10042no—
92Q8—10042no—
93D4—20082no—
94D4—10042no—
95C2×C4—22no—
96C2×C4—20082no—
97C2×C4—10041no—
98C2×C4—5022no—
99C2×C4D4×D25112yes—
100C2×C4C2×D100411yescharacteristic
101C8—42no—
102C8—10041no—
103C22—10042no—
104C22—10042no—
105C22—10042no—
106C22#2254868511yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—20081no—
111C4—10042no—
112C2—20082no—
113C2#3063186211yescharacteristic
114C2#3063186612yes—
subgroupG/H
centerC22#22548685
commutator, cosocleC42×C251C23
FrattiniC42C22×D251
Fitting#330×C251C2
socleC22×C251#120
prime radical#30632435C2
hypercenter#330D251
hypocenterC251#1662
LCSG ▷ C42×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #30632057C2semidirect
3. #30632047C2semidirect
4. #30631426C2semidirect
5. #330×C251C2semidirect
57. C251#1662semidirect
62. #330D251semidirect

Maximal subgroups

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

subgroupindex
#306324352
#306320572
#306320472
#306314262
#330×C2512
#1662251