Finite Group Databasebeta

← #21448009

Subgroups — #21448009

Order 7808.

142 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 142 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#16839995C211yesmaximal, characteristic
2#16839799C211yesmaximal, characteristic, complemented
3#16839590C211yesmaximal, characteristic, complemented
4#16839587C211yesmaximal, characteristic, complemented
5#16839563C211yesmaximal, characteristic, complemented
6#16839541C211yesmaximal, characteristic, complemented
7C61×#357C211yesmaximal, characteristic, complemented
8C2×C8×D61C2211yescharacteristic
9#14519748—21no—
10#14519735—21no—
11C2×#11758185C2211yescharacteristic
12#14519711C2211yescharacteristic
13#14519711C2211yescharacteristic
14#14519708—21no—
15#14519698—21no—
16C2×D8×C61C2211yescharacteristic
17C2×C16×C61C2211yescharacteristic
18#107×C61C2211yescharacteristic
19C2×D4×C61—21no—
20C2×C22⋊D61—41no—
21C2×C4×D61D411yescharacteristic
22D8×C61—21no—
23D8×C61—21no—
24C2×C8×C61C2311yescharacteristic
25C4⋊C4×C61—21no—
26C22⋊Dic61—41no—
27#11758198—41no—
28C4⋊Dic61—21no—
29C4⋊Dic61—21no—
30C4×Dic61—41no—
31C2×#92418D411yescharacteristic
32C8×D61—21no—
33C8×D61—21no—
34C16×C61—21no—
35#11758185—21no—
36C23×C61—41no—
37C22×D61D811yescharacteristic
38D4×C61—41no—
39D4×C61—41no—
40C2×C4×C61—41no—
41C2×C4×C61C2×D411yescharacteristic
42C22⋊D61—82no—
43C2×Dic61—41no—
44C2×Dic61—41no—
45C2×Dic61D811yescharacteristic
46C4×D61—21no—
47C4×D61—21no—
48C8×C61#4111yescharacteristic
49C8×C61#4111yescharacteristic
50#92418—21no—
51C22×C61—81no—
52C22×C61—81no—
53C22×C61—81no—
54C22×C61C2×D811yescharacteristic
55C2×D61—21no—
56C2×D61—21no—
57C2×D61—21no—
58C4×C61—81no—
59C4×C61#12311yescharacteristic
60C4×C61#13711yescharacteristic
61Dic61—21no—
62Dic61—81no—
63Dic61—81no—
64#2234—611nomaximal, Sylow
65C2×C61—161no—
66C2×C61#48011yescharacteristic
67C2×C61#50811yescharacteristic
68C2×C61#50911yescharacteristic
69D61—41no—
70#466—611no—
71#427—611no—
72#367—611no—
73#366—611no—
74#357—611no—
75#357D6111yescharacteristic, complemented
76C22⋊C16—611no—
77C61#223411yescharacteristic, complemented, Sylow
78C2×D8C2×D6111yescharacteristic
79C22×C8—611no—
80#121—1221no—
81#117—1221no—
82C2×C16—611no—
83C2×C16C2×D6111yescharacteristic
84#107—611no—
85#107—611no—
86#107C2×D6111yescharacteristic
87#106—1221no—
88#102—1221no—
89C2×D4—21no—
90C2×D4—2441no—
91C22×C4—611no—
92D8—21no—
93D8—21no—
94C2×C8—611no—
95C2×C8—1221no—
96C2×C8—1221no—
97C2×C8C22×D6111yescharacteristic
98C4⋊C4—21no—
99C4⋊C4—1221no—
100C4⋊C4—1221no—
101C22⋊C4—2441no—
102C22⋊C4—2441no—
103C42—2441no—
104C16—21no—
105C16—1221no—
106C23—41no—
107C23—611no—
108D4—41no—
109D4—41no—
110D4—4882no—
111C2×C4—41no—
112C2×C4—611no—
113C2×C4—1221no—
114C2×C4—1221no—
115C2×C4—2441no—
116C2×C4—2441no—
117C2×C4D4×D6111yescharacteristic
118C8—1221no—
119C8#1175822211yescharacteristic
120C8#1175822411yescharacteristic
121C22—81no—
122C22—81no—
123C22—81no—
124C22—1221no—
125C22—1221no—
126C22—1221no—
127C22D8×D6111yescharacteristic
128C4—81no—
129C4—1221no—
130C4—4881no—
131C4—4881no—
132C4#1451975911yescharacteristic
133C4#1451980611yescharacteristic
134C2—161no—
135C2—2441no—
136C2#1684007411yescharacteristic
137C2#1684019311yescharacteristic
138C2#1684019611yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#357C2
socleC22×C61C2×D8
hypercenter#357D61
hypocenterC61#2234
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
2. #16839799C2semidirect
3. #16839590C2semidirect
4. #16839587C2semidirect
5. #16839563C2semidirect
6. #16839541C2semidirect
7. C61×#357C2semidirect
75. #357D61semidirect
77. C61#2234semidirect