Finite Group Databasebeta

← #46835656

Subgroups — #46835656

Order 34688.

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#31774645C211yesmaximal, characteristic, complemented
2#31774284C212yesmaximal, complemented
3#31773639C211yesmaximal, characteristic, complemented
4#31773636C212yesmaximal, complemented
5#490×C271C211yesmaximal, characteristic, complemented
6C2×#16864642—22no—
7C2×#16864639—22no—
8#22576148C2212yes—
9#22576145—22no—
10#22576138—22no—
11#22576135—22no—
12#22576071C2212yes—
13#127×C271C2211yescharacteristic
14#125×C271C2211yescharacteristic
15#102×C271—22no—
16#97×C271C2211yescharacteristic
17C2×Dic542D412yes—
18C2×D1084—22no—
19C2×D1084D412yes—
20C2×C4×D271—22no—
21#16864642—44no—
22#16864639—44no—
23C2×C271⋊C8—22no—
24Dic271⋊C4—22no—
25(C2×D271)⋊C4—22no—
26(C2×D271)⋊C4—22no—
27(C2×D271)⋊C4—22no—
28C2×D4×C271—22no—
29C2×D4×C271—21no—
30C2×C8×C271—21no—
31C4⋊C4×C271—22no—
32C4⋊C4×C271D412yes—
33C42×C271C2311yescharacteristic
34C22×D271—22no—
35Dic542—42no—
36D1084—42no—
37D1084—82no—
38C2×Dic271—22no—
39C4×D271—82no—
40C271⋊C8—24no—
41C23×C271—41no—
42D4×C271—42no—
43D4×C271—42no—
44D4×C271—42no—
45C2×C4×C271—22no—
46C2×C4×C271C2×D412yes—
47C2×C4×C271C2×D411yescharacteristic
48C8×C271—41no—
49C22×C271—82no—
50C22×C271—81no—
51C22×C271#12011yescharacteristic
52C2×D271—42no—
53C2×D271—42no—
54C2×D271—42no—
55C4×C271—22no—
56C4×C271—21no—
57C4×C271—42no—
58Dic271—42no—
59C2×C271—161no—
60C2×C271#45312yes—
61C2×C271#45411yescharacteristic
62D271—82no—
63C271#165611yescharacteristic, complemented, Sylow
64#1656—2711nomaximal, Sylow
65#562—2711no—
66#496—2712no—
67#490D27111yescharacteristic, complemented
68#330—2711no—
69#329—2712no—
70C2×SD16—5422no—
71C2×D8—5422no—
72#127C2×D27111yescharacteristic
73#125C2×D27111yescharacteristic
74#124—2712no—
75#123—5422no—
76C22⋊Q8—5422no—
77#121—5422no—
78#102—22no—
79#97—2712no—
80#97C2×D27111yescharacteristic
81C2×Q8—2712no—
82C2×D4—22no—
83C2×D4—21no—
84C2×D4—2712no—
85C2×D4—5422no—
86C22×C4—5422no—
87SD16—10844no—
88D8—10844no—
89C2×C8—21no—
90C2×C8—5422no—
91C4⋊C4—22no—
92C4⋊C4—5422no—
93C4⋊C4C22⋊D27112yes—
94C22⋊C4—5422no—
95C22⋊C4—5422no—
96C22⋊C4—5422no—
97C42C22×D27111yescharacteristic
98C23—41no—
99C23—5422no—
100Q8—10842no—
101D4—42no—
102D4—42no—
103D4—42no—
104D4—10842no—
105D4—21682no—
106C2×C4—22no—
107C2×C4—5422no—
108C2×C4—21682no—
109C2×C4D4×D27112yes—
110C2×C4C2×C22⋊D27111yescharacteristic
111C8—41no—
112C8—5424no—
113C22—82no—
114C22—81no—
115C22—10842no—
116C22—10842no—
117C22—10842no—
118C22#2257612811yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—10842no—
123C2—161no—
124C2—21682no—
125C2#3177406312yes—
126C2#3177406911yescharacteristic
subgroupG/H
centerC22#22576128
commutator, cosocleC42×C271C23
FrattiniC42C22×D271
Fitting#490×C271C2
socleC22×C271#120
hypercenter#490D271
hypocenterC271#1656
LCSG ▷ C42×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #31774645C2semidirect
2. #31774284C2semidirect
3. #31773639C2semidirect
4. #31773636C2semidirect
5. #490×C271C2semidirect
63. C271#1656semidirect
67. #490D271semidirect

Maximal subgroups

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

subgroupindex
#317746452
#317742842
#317736392
#317736362
#490×C2712
#1656271