Finite Group Databasebeta

← #21447973

Subgroups — #21447973

Order 7808.

136 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C4×D488C211yesmaximal, characteristic
2#16839589C211yesmaximal, characteristic, complemented
3#16839587C211yesmaximal, characteristic, complemented
4C4⋊#11758185C211yesmaximal, characteristic, complemented
5#16839562C211yesmaximal, characteristic
6#16839562C211yesmaximal, characteristic
7C61×#499C211yesmaximal, characteristic, complemented
8C2×D488C2211yescharacteristic
9C4×D244—21no—
10C2×#11758185C2211yescharacteristic
11C2×#11758185C2211yescharacteristic
12#14519711C2211yescharacteristic
13#14519699—21no—
14#125×C61—21no—
15#107×C61C2211yescharacteristic
16#107×C61C2211yescharacteristic
17#106×C61—21no—
18C4×C8×C61C2211yescharacteristic
19C2×D244—21no—
20C2×C4×D61—41no—
21C2×C8×C61D411yescharacteristic
22C2×C8×C61C2311yescharacteristic
23C4⋊C4×C61—21no—
24C4⋊C4×C61—21no—
25C4⋊C4×C61—41no—
26C4⋊C4×C61—41no—
27C42×C61D411yescharacteristic
28#11758198—41no—
29C4⋊Dic61—21no—
30D488—21no—
31D488Q812yes—
32#11758185—21no—
33#11758185—21no—
34C22×D61—41no—
35C2×C4×C61—41no—
36C2×C4×C61—41no—
37C2×C4×C61D811yescharacteristic
38C2×C4×C61D811yescharacteristic
39C2×C4×C61C2×D411yescharacteristic
40C2×Dic61—41no—
41D244—22no—
42D244—41no—
43C4×D61—82no—
44C8×C61—21no—
45C8×C61C2×Q811yescharacteristic
46C8×C61#4111yescharacteristic
47C22×C61C2×D811yescharacteristic
48C2×D61—42no—
49C2×D61—81no—
50C2×D61—81no—
51C4×C61—21no—
52C4×C61—21no—
53C4×C61—81no—
54C4×C61—81no—
55C4×C61C22⋊Q811yescharacteristic
56C4×C61#13711yescharacteristic
57Dic61—81no—
58#2228—611nomaximal, Sylow
59C2×C61#47411yescharacteristic
60C2×C61#50811yescharacteristic
61C2×C61#50911yescharacteristic
62D61—82no—
63#499D6111yescharacteristic, complemented
64C4×D8—611no—
65#367—611no—
66#366—611no—
67C4⋊C16—611no—
68#357—611no—
69#357—611no—
70C61#222811yescharacteristic, complemented, Sylow
71C2×D8—611no—
72#125—21no—
73C4×D4—1221no—
74C2×C16—611no—
75C2×C16—611no—
76#107—611no—
77#107C2×D6111yescharacteristic
78#107C2×D6111yescharacteristic
79#106—21no—
80#102—1221no—
81C4×C8C2×D6111yescharacteristic
82C2×D4—1221no—
83C22×C4—2441no—
84D8—612no—
85D8—1221no—
86C2×C8C22⋊D6111yescharacteristic
87C2×C8C22×D6111yescharacteristic
88C4⋊C4—21no—
89C4⋊C4—21no—
90C4⋊C4—41no—
91C4⋊C4—41no—
92C4⋊C4—1221no—
93C22⋊C4—2441no—
94C42C22⋊D6111yescharacteristic
95C16—1221no—
96C16—1221no—
97C23—2441no—
98D4—1222no—
99D4—2441no—
100C2×C4—41no—
101C2×C4—41no—
102C2×C4—4882no—
103C2×C4—2441no—
104C2×C4#1175819911yescharacteristic
105C2×C4#1175819911yescharacteristic
106C2×C4C2×C22⋊D6111yescharacteristic
107C8—21no—
108C8Q8×D6111yescharacteristic
109C8#1175822611yescharacteristic
110C22—4881no—
111C22—4881no—
112C22—2442no—
113C22C2×#1175819911yescharacteristic
114C4—21no—
115C4—21no—
116C4—81no—
117C4—81no—
118C4—4881no—
119C4#1451975311yescharacteristic
120C4#1451980811yescharacteristic
121C2—4882no—
122C2#1684003911yescharacteristic
123C2#1684019211yescharacteristic
124C2#1684019711yescharacteristic
subgroupG/H
centerC22C2×#11758199
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#499C2
socleC22×C61C2×D8
hypercenter#499D61
hypocenterC61#2228
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #499

Complements

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

NH ≅ G/Ntype
2. #16839589C2semidirect
3. #16839587C2semidirect
4. C4⋊#11758185C2semidirect
7. C61×#499C2semidirect
63. #499D61semidirect
70. C61#2228semidirect