Finite Group Databasebeta

← #21447975

Subgroups — #21447975

Order 7808.

136 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 47 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#16840163C211yesmaximal, characteristic, complemented
2#16839844C211yesmaximal, characteristic
3#16839587C211yesmaximal, characteristic, complemented
4#16839580C211yesmaximal, characteristic, complemented
5#16839564C211yesmaximal, characteristic
6#16839562C211yesmaximal, characteristic
7C61×#367C211yesmaximal, characteristic, complemented
8C2×D488C2211yescharacteristic
9#14519768—21no—
10#14519739—21no—
11C2×#11758185C2211yescharacteristic
12#14519711C2211yescharacteristic
13#14519708—21no—
14#14519697—21no—
15C8×Dic61C2211yescharacteristic
16C2×C16×C61C2211yescharacteristic
17#107×C61C2211yescharacteristic
18#107×C61C2211yescharacteristic
19C2×D244—21no—
20C2×C4×D61—41no—
21C2×C8×C61C2311yescharacteristic
22C4⋊C4×C61—21no—
23C4⋊C4×C61—21no—
24#11758198—41no—
25C4⋊Dic61—21no—
26C4⋊Dic61—41no—
27#11758196—41no—
28C4×Dic61D411yescharacteristic
29C2×#92418D411yescharacteristic
30D488—21no—
31D488Q812yes—
32C16×C61—21no—
33#11758185—21no—
34C22×D61—41no—
35C2×C4×C61—41no—
36C2×C4×C61—41no—
37C2×C4×C61C2×D411yescharacteristic
38C2×Dic61—41no—
39C2×Dic61D811yescharacteristic
40C2×Dic61D811yescharacteristic
41D244—22no—
42D244—41no—
43C4×D61—82no—
44C8×C61C2×Q811yescharacteristic
45C8×C61#4111yescharacteristic
46#92418—21no—
47C22×C61C2×D811yescharacteristic
48C2×D61—42no—
49C2×D61—81no—
50C2×D61—81no—
51C4×C61—81no—
52C4×C61—81no—
53C4×C61C22⋊Q811yescharacteristic
54C4×C61#13711yescharacteristic
55Dic61—21no—
56Dic61—21no—
57Dic61—81no—
58#2228—611nomaximal, Sylow
59C2×C61#47411yescharacteristic
60C2×C61#50811yescharacteristic
61C2×C61#50911yescharacteristic
62D61—82no—
63#499—611no—
64C4×D8—611no—
65#367D6111yescharacteristic, complemented
66#366—611no—
67C4⋊C16—611no—
68#357—611no—
69#357—611no—
70C61#222811yescharacteristic, complemented, Sylow
71C2×D8—611no—
72#125—1221no—
73C4×D4—1221no—
74C2×C16—611no—
75C2×C16C2×D6111yescharacteristic
76#107—611no—
77#107C2×D6111yescharacteristic
78#107C2×D6111yescharacteristic
79#106—1221no—
80#102—1221no—
81C4×C8—611no—
82C2×D4—1221no—
83C22×C4—2441no—
84D8—612no—
85D8—1221no—
86C2×C8—611no—
87C2×C8C22×D6111yescharacteristic
88C4⋊C4—21no—
89C4⋊C4—21no—
90C4⋊C4—1221no—
91C4⋊C4—2441no—
92C4⋊C4—2441no—
93C22⋊C4—2441no—
94C42—611no—
95C16—21no—
96C16—1221no—
97C23—2441no—
98D4—1222no—
99D4—2441no—
100C2×C4—41no—
101C2×C4—41no—
102C2×C4—611no—
103C2×C4—611no—
104C2×C4—4882no—
105C2×C4—2441no—
106C2×C4D4×D6111yescharacteristic
107C8—1221no—
108C8#1175822211yescharacteristic
109C8Q8×D6111yescharacteristic
110C22—4881no—
111C22—4881no—
112C22—2442no—
113C22D8×D6111yescharacteristic
114C4—81no—
115C4—81no—
116C4—1221no—
117C4—1221no—
118C4—4881no—
119C4#1451975511yescharacteristic
120C4#1451980911yescharacteristic
121C2—4882no—
122C2#1684004111yescharacteristic
123C2#1684019311yescharacteristic
124C2#1684019911yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#367C2
socleC22×C61C2×D8
hypercenter#367D61
hypocenterC61#2228
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

Complements

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

NH ≅ G/Ntype
1. #16840163C2semidirect
3. #16839587C2semidirect
4. #16839580C2semidirect
7. C61×#367C2semidirect
65. #367D61semidirect
70. C61#2228semidirect