Finite Group Databasebeta

← #21445140

Subgroups — #21445140

Order 7808.

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#16840510C211yesmaximal, characteristic
2#16840124C212yesmaximal, complemented
3#16839504C211yesmaximal, characteristic, complemented
4#16839501C212yesmaximal, complemented
5C61×#491C211yesmaximal, characteristic, complemented
6#14519765C2212yes—
7#14519762—22no—
8#14519755—22no—
9#14519752—22no—
10#14519700—22no—
11#14519697—22no—
12#14519688C2212yes—
13C4⋊Q8×C61C2211yescharacteristic
14#125×C61C2211yescharacteristic
15#103×C61—22no—
16#97×C61C2211yescharacteristic
17C2×Q8×C61—21no—
18C2×D244—22no—
19C2×D244D412yes—
20C2×C4×D61—22no—
21C2×Dic122D412yes—
22C2×C8×C61—21no—
23C4⋊C4×C61—22no—
24C4⋊C4×C61—22no—
25C4⋊C4×C61D412yes—
26C42×C61C2311yescharacteristic
27#11758198—22no—
28#11758198—22no—
29#11758198—22no—
30#11758196—22no—
31C2×#92418—22no—
32C22×D61—22no—
33Q8×C61—42no—
34C2×C4×C61—22no—
35C2×C4×C61—41no—
36C2×C4×C61C2×D412yes—
37C2×C4×C61C2×D411yescharacteristic
38C2×Dic61—22no—
39D244—42no—
40D244—82no—
41C4×D61—82no—
42Dic122—42no—
43C8×C61—41no—
44#92418—42no—
45C22×C61#12011yescharacteristic
46C2×D61—42no—
47C2×D61—42no—
48C2×D61—42no—
49C4×C61—21no—
50C4×C61—22no—
51C4×C61—42no—
52C4×C61—81no—
53Dic61—42no—
54#1662—611nomaximal, Sylow
55C2×C61#45411yescharacteristic
56C2×C61#45512yes—
57D61—82no—
58#562—611no—
59#491D6111yescharacteristic, complemented
60#489—612no—
61#330—611no—
62#329—612no—
63C61#166211yescharacteristic, complemented, Sylow
64C4⋊Q8C2×D6111yescharacteristic
65#125C2×D6111yescharacteristic
66#124—612no—
67#123—1222no—
68C22⋊Q8—1222no—
69#121—1222no—
70#103—22no—
71#103—1222no—
72#102—1222no—
73#97—612no—
74#97C2×D6111yescharacteristic
75C2×Q8—21no—
76C2×Q8—612no—
77C2×D4—612no—
78C2×D4—1222no—
79C22×C4—1222no—
80C2×C8—21no—
81C2×C8—1222no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—1222no—
85C4⋊C4C22⋊D6112yes—
86C22⋊C4—1222no—
87C22⋊C4—1222no—
88C22⋊C4—1222no—
89C42C22×D6111yescharacteristic
90C23—1222no—
91Q8—42no—
92Q8—2442no—
93D4—4882no—
94D4—2442no—
95C2×C4—22no—
96C2×C4—41no—
97C2×C4—1222no—
98C2×C4—4882no—
99C2×C4D4×D6112yes—
100C2×C4C2×C22⋊D6111yescharacteristic
101C8—41no—
102C8—2442no—
103C22—2442no—
104C22—2442no—
105C22—2442no—
106C22#1451974511yescharacteristic
107C4—22no—
108C4—21no—
109C4—42no—
110C4—81no—
111C4—2442no—
112C2—4882no—
113C2#1683993411yescharacteristic
114C2#1683993812yes—
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#491C2
socleC22×C61#120
hypercenter#491D61
hypocenterC61#1662
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #16840124C2semidirect
3. #16839504C2semidirect
4. #16839501C2semidirect
5. C61×#491C2semidirect
59. #491D61semidirect
63. C61#1662semidirect