Finite Group Databasebeta

← #21447974

Subgroups — #21447974

Order 7808.

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

normal subgroups only

This group has 136 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#16840163C211yesmaximal, characteristic, complemented
2D8×Dic61C211yesmaximal, characteristic
3#16839589C211yesmaximal, characteristic, complemented
4#16839588C211yesmaximal, characteristic, complemented
5#16839580C211yesmaximal, characteristic, complemented
6#16839563C211yesmaximal, characteristic
7C61×#357C211yesmaximal, characteristic
8#14519768—21no—
9D4×Dic61—21no—
10C2×#11758185C2211yescharacteristic
11#14519711C2211yescharacteristic
12#14519711C2211yescharacteristic
13#14519708—21no—
14#14519698—21no—
15C8×Dic61C2211yescharacteristic
16C2×D8×C61C2211yescharacteristic
17C2×C16×C61C2211yescharacteristic
18#107×C61C2211yescharacteristic
19C2×D4×C61—21no—
20C22×Dic61—41no—
21D8×C61—21no—
22D8×C61Q812yes—
23C2×C8×C61C2311yescharacteristic
24C4⋊C4×C61—21no—
25C22⋊Dic61—41no—
26C4⋊Dic61—21no—
27C4⋊Dic61—21no—
28C4⋊Dic61—41no—
29#11758196—41no—
30C4×Dic61D411yescharacteristic
31C2×#92418D411yescharacteristic
32C16×C61—21no—
33#11758185—21no—
34C23×C61—41no—
35D4×C61—22no—
36D4×C61—41no—
37C2×C4×C61—41no—
38C2×C4×C61C2×D411yescharacteristic
39C2×Dic61—41no—
40C2×Dic61—41no—
41C2×Dic61—82no—
42C2×Dic61D811yescharacteristic
43C2×Dic61D811yescharacteristic
44C8×C61C2×Q811yescharacteristic
45C8×C61#4111yescharacteristic
46#92418—21no—
47C22×C61—42no—
48C22×C61—81no—
49C22×C61—81no—
50C22×C61C2×D811yescharacteristic
51C4×C61—81no—
52C4×C61C22⋊Q811yescharacteristic
53C4×C61#13711yescharacteristic
54Dic61—21no—
55Dic61—21no—
56Dic61—81no—
57Dic61—81no—
58#2228—611nomaximal, Sylow
59C2×C61—82no—
60C2×C61#47411yescharacteristic
61C2×C61#50811yescharacteristic
62C2×C61#50911yescharacteristic
63#499—611no—
64C4×D8—611no—
65#367—611no—
66#366—611no—
67C4⋊C16—611no—
68#357—611no—
69#357D6111yescharacteristic
70C61#222811yescharacteristic, complemented, Sylow
71C2×D8C2×D6111yescharacteristic
72#125—1221no—
73C4×D4—1221no—
74C2×C16—611no—
75C2×C16C2×D6111yescharacteristic
76#107—611no—
77#107—611no—
78#107C2×D6111yescharacteristic
79#106—1221no—
80#102—1221no—
81C4×C8—611no—
82C2×D4—21no—
83C22×C4—2441no—
84D8—21no—
85D8Dic12212yes—
86C2×C8—611no—
87C2×C8C22×D6111yescharacteristic
88C4⋊C4—21no—
89C4⋊C4—1221no—
90C4⋊C4—1221no—
91C4⋊C4—2441no—
92C4⋊C4—2441no—
93C22⋊C4—2441no—
94C42—611no—
95C16—21no—
96C16—1221no—
97C23—41no—
98D4—22no—
99D4—41no—
100C2×C4—41no—
101C2×C4—611no—
102C2×C4—611no—
103C2×C4—4882no—
104C2×C4—2441no—
105C2×C4—2441no—
106C2×C4D4×D6111yescharacteristic
107C8—1221no—
108C8C2×Dic12211yescharacteristic
109C8#1175822411yescharacteristic
110C22—42no—
111C22—81no—
112C22—81no—
113C22D8×D6111yescharacteristic
114C4—81no—
115C4—1221no—
116C4—1221no—
117C4—4881no—
118C4—4881no—
119C4#1451975411yescharacteristic
120C4#1451980611yescharacteristic
121C2—82no—
122C2#1684004011yescharacteristic
123C2#1684019111yescharacteristic
124C2#1684019911yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#357C2
socleC22×C61C2×D8
hypercenter#357D61
hypocenterC61#2228
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
1. #16840163C2semidirect
3. #16839589C2semidirect
4. #16839588C2semidirect
5. #16839580C2semidirect
70. C61#2228semidirect