Finite Group Databasebeta

← #21445142

Subgroups — #21445142

Order 7808.

196 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 49 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#16840132C211yesmaximal, characteristic, complemented
2#16840121C212yesmaximal, complemented
3#16839504C211yesmaximal, characteristic, complemented
4#16839502C212yesmaximal, complemented
5C61×#562C211yesmaximal, characteristic
6#14519777C2211yescharacteristic
7#14519701—22no—
8#14519700—22no—
9#14519698—22no—
10#14519688C2211yescharacteristic
11#14519688C2212yes—
12#125×C61C2211yescharacteristic
13#124×C61C2212yes—
14#123×C61—22no—
15C22⋊Q8×C61—22no—
16#121×C61—22no—
17C2×Q8×C61D412yes—
18C2×D4×C61—22no—
19C2×D4×C61D412yes—
20C22×C4×C61—22no—
21C2×Dic122—21no—
22C4⋊C4×C61—22no—
23C4⋊C4×C61—22no—
24C4⋊C4×C61D412yes—
25C22⋊C4×C61—22no—
26C22⋊C4×C61—22no—
27C22⋊C4×C61—22no—
28C42×C61C2311yescharacteristic
29C4⋊Dic61—22no—
30C2×#92418—22no—
31C2×#92418—21no—
32C23×C61—22no—
33Q8×C61—42no—
34D4×C61—42no—
35D4×C61—82no—
36C2×C4×C61—22no—
37C2×C4×C61—22no—
38C2×C4×C61—82no—
39C2×C4×C61C2×D412yes—
40C2×C4×C61C2×D411yescharacteristic
41C2×Dic61—41no—
42Dic122—42no—
43#92418—41no—
44#92418—42no—
45C22×C61—42no—
46C22×C61—42no—
47C22×C61—42no—
48C22×C61#12011yescharacteristic
49C4×C61—21no—
50C4×C61—22no—
51C4×C61—42no—
52C4×C61—42no—
53Dic61—81no—
54#1662—611nomaximal, Sylow
55C2×C61—82no—
56C2×C61#45411yescharacteristic
57C2×C61#45512yes—
58#562D6111yescharacteristic
59#491—611no—
60#489—612no—
61#330—611no—
62#329—612no—
63C61#166211yescharacteristic, complemented, Sylow
64C4⋊Q8—611no—
65#125C2×D6111yescharacteristic
66#124C2×D6112yes—
67#123—22no—
68C22⋊Q8—22no—
69#121—22no—
70#103—1222no—
71#103—1222no—
72#102—1222no—
73#97—611no—
74#97—612no—
75C2×Q8—1221no—
76C2×Q8C22⋊D6112yes—
77C2×D4—22no—
78C2×D4C22⋊D6112yes—
79C22×C4—22no—
80C2×C8—1222no—
81C2×C8—1221no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—1222no—
85C4⋊C4C22⋊D6112yes—
86C22⋊C4—22no—
87C22⋊C4—22no—
88C22⋊C4—22no—
89C42C22×D6111yescharacteristic
90C23—22no—
91Q8—42no—
92Q8—2442no—
93D4—42no—
94D4—82no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—82no—
98C2×C4—2441no—
99C2×C4C2×C22⋊D6111yescharacteristic
100C2×C4C2×C22⋊D6112yes—
101C8—2442no—
102C8—2441no—
103C22—42no—
104C22—42no—
105C22—42no—
106C22#1451974611yescharacteristic
107C4—22no—
108C4—21no—
109C4—42no—
110C4—42no—
111C4—4881no—
112C2—82no—
113C2#1683993511yescharacteristic
114C2#1683994012yes—
subgroupG/H
centerC22#14519746
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#562C2
socleC22×C61#120
hypercenter#562D61
hypocenterC61#1662
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #16840132C2semidirect
2. #16840121C2semidirect
3. #16839504C2semidirect
4. #16839502C2semidirect
63. C61#1662semidirect