Finite Group Databasebeta

← #21447966

Subgroups — #21447966

Order 7808.

142 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 57 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#16840167C211yesmaximal, characteristic, complemented
2#16839589C212yesmaximal, complemented
3C4⋊#11758185C211yesmaximal, characteristic, complemented
4#16839563C212yesmaximal
5C4×D8×C61C211yesmaximal, characteristic
6#14519777—21no—
7C2×#11758185C2212yes—
8#14519711—21no—
9#14519711C2212yes—
10C2×D8×C61C2211yescharacteristic
11C4×D4×C61—21no—
12#107×C61C2211yescharacteristic
13#102×C61—21no—
14C4×C8×C61C2211yescharacteristic
15C2×D4×C61—21no—
16C22×C4×C61—41no—
17C2×Dic122—41no—
18D8×C61—21no—
19D8×C61Q812yescomplemented
20C2×C8×C61D411yescharacteristic
21C2×C8×C61C2311yescharacteristic
22C4⋊C4×C61—21no—
23C22⋊C4×C61—41no—
24C42×C61D411yescharacteristic
25C4⋊Dic61—22no—
26C4⋊Dic61—41no—
27#11758185—22no—
28C23×C61—41no—
29D4×C61—22no—
30D4×C61—41no—
31C2×C4×C61—41no—
32C2×C4×C61—82no—
33C2×C4×C61D811yescharacteristic
34C2×C4×C61D811yescharacteristic
35C2×C4×C61C2×D411yescharacteristic
36C2×Dic61—42no—
37Dic122—82no—
38C8×C61—21no—
39C8×C61C2×Q811yescharacteristic
40C8×C61#4111yescharacteristic
41C22×C61—42no—
42C22×C61—81no—
43C22×C61—81no—
44C22×C61C2×D811yescharacteristic
45C4×C61—21no—
46C4×C61—81no—
47C4×C61SD3212yes—
48C4×C61C22⋊Q811yescharacteristic
49C4×C61#13711yescharacteristic
50Dic61—82no—
51#2226—611nomaximal, Sylow
52C2×C61—82no—
53C2×C61#47411yescharacteristic
54C2×C61C2×SD3211yescharacteristic
55C2×C61#50911yescharacteristic
56#500—611no—
57C4×D8D6111yescharacteristic
58#367—612no—
59C4⋊C16—611no—
60#357—612no—
61C61#222611yescharacteristic, complemented, Sylow
62C2×D8C2×D6111yescharacteristic
63C4⋊Q8—1221no—
64C4×D4—21no—
65C2×C16—612no—
66#107—612no—
67#107—1221no—
68#107C2×D6111yescharacteristic
69#102—21no—
70C4×C8C2×D6111yescharacteristic
71C2×Q8—2441no—
72C2×D4—21no—
73C22×C4—41no—
74D8—21no—
75D8Dic12212yescomplemented
76C2×C8C22⋊D6111yescharacteristic
77C2×C8C22×D6111yescharacteristic
78C4⋊C4—21no—
79C4⋊C4—1222no—
80C4⋊C4—2441no—
81C22⋊C4—41no—
82C42C22⋊D6111yescharacteristic
83C16—1222no—
84C23—41no—
85Q8—4882no—
86D4—22no—
87D4—41no—
88C2×C4—41no—
89C2×C4—82no—
90C2×C4—2442no—
91C2×C4#1175819911yescharacteristic
92C2×C4#1175819911yescharacteristic
93C2×C4C2×C22⋊D6111yescharacteristic
94C8—21no—
95C8C2×Dic12211yescharacteristic
96C8#1175822211yescharacteristic
97C22—42no—
98C22—81no—
99C22—81no—
100C22C2×#1175819911yescharacteristic
101C4—21no—
102C4—81no—
103C4—4882no—
104C4#1451972112yes—
105C4#1451975611yescharacteristic
106C4#1451980711yescharacteristic
107C2—82no—
108C2#1684004211yescharacteristic
109C2C2×#1451972111yescharacteristic
110C2#1684019711yescharacteristic
subgroupG/H
centerC22C2×#11758199
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC4×D8×C61C2
socleC22×C61C2×D8
hypercenterC4×D8D61
hypocenterC61#2226
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #16840167C2semidirect
2. #16839589C2semidirect
3. C4⋊#11758185C2semidirect
19. D8×C61Q8semidirect
61. C61#2226semidirect
75. D8Dic122semidirect