Finite Group Databasebeta

← #21448003

Subgroups — #21448003

Order 7808.

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

normal subgroups only

This group has 150 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#16839995C211yesmaximal, characteristic
2#107×D61C211yesmaximal, characteristic, complemented
3#16839590C211yesmaximal, characteristic, complemented
4#16839589C211yesmaximal, characteristic, complemented
5#16839563C211yesmaximal, characteristic, complemented
6#16839541C211yesmaximal, characteristic, complemented
7C61×#357C211yesmaximal, characteristic, complemented
8C2×C8×D61C2211yescharacteristic
9#14519748—21no—
10C4⋊C4×D61—21no—
11C2×#11758185C2211yescharacteristic
12#14519711C2211yescharacteristic
13#14519711C2211yescharacteristic
14#14519710—21no—
15#14519698—21no—
16C2×D8×C61C2211yescharacteristic
17C2×C16×C61C2211yescharacteristic
18#107×C61C2211yescharacteristic
19C2×D4×C61—21no—
20C2×C22⋊D61—41no—
21C2×C4×D61—41no—
22C2×C4×D61D411yescharacteristic
23D8×C61—21no—
24D8×C61—21no—
25C2×C8×C61C2311yescharacteristic
26C4⋊C4×C61—21no—
27C22⋊Dic61—41no—
28C4⋊Dic61—21no—
29C4⋊Dic61—21no—
30#11758196—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—
48C4×D61—82no—
49C8×C61#4111yescharacteristic
50C8×C61#4111yescharacteristic
51#92418—21no—
52C22×C61—81no—
53C22×C61—81no—
54C22×C61—81no—
55C22×C61C2×D811yescharacteristic
56C2×D61—21no—
57C2×D61—21no—
58C2×D61SD3212yes—
59C4×C61—81no—
60C4×C61#12311yescharacteristic
61C4×C61#13711yescharacteristic
62Dic61—21no—
63Dic61—81no—
64Dic61—81no—
65#2233—611nomaximal, Sylow
66C2×C61—161no—
67C2×C61#48011yescharacteristic
68C2×C61C2×SD3211yescharacteristic
69C2×C61#50911yescharacteristic
70D61—22no—
71#466—611no—
72C2×#107—611no—
73#367—611no—
74#367—611no—
75#357—611no—
76#357D6111yescharacteristic, complemented
77C22⋊C16—611no—
78C61#223311yescharacteristic, complemented, Sylow
79C2×D8C2×D6111yescharacteristic
80C22×C8—611no—
81#121—1221no—
82C2×C4⋊C4—1221no—
83C2×C16—611no—
84C2×C16C2×D6111yescharacteristic
85#107—611no—
86#107—611no—
87#107—1221no—
88#107C2×D6111yescharacteristic
89#102—1221no—
90C2×D4—21no—
91C2×D4—2441no—
92C22×C4—611no—
93C22×C4—2441no—
94D8—21no—
95D8—21no—
96C2×C8—611no—
97C2×C8—1221no—
98C2×C8—1221no—
99C2×C8C22×D6111yescharacteristic
100C4⋊C4—21no—
101C4⋊C4—1221no—
102C4⋊C4—1221no—
103C4⋊C4—2441no—
104C22⋊C4—2441no—
105C16—21no—
106C16—1221no—
107C23—41no—
108C23—611no—
109D4—41no—
110D4—41no—
111D4—4882no—
112C2×C4—41no—
113C2×C4—611no—
114C2×C4—1221no—
115C2×C4—1221no—
116C2×C4—4882no—
117C2×C4—2441no—
118C2×C4—2441no—
119C2×C4D4×D6111yescharacteristic
120C8—1221no—
121C8#1175822211yescharacteristic
122C8#1175822411yescharacteristic
123C22—81no—
124C22—81no—
125C22—81no—
126C22—612no—
127C22—1221no—
128C22—1221no—
129C22D8×D6111yescharacteristic
130C4—81no—
131C4—1221no—
132C4—4881no—
133C4—4881no—
134C4#1451975911yescharacteristic
135C4#1451980611yescharacteristic
136C2—161no—
137C2—1222no—
138C2#1684007411yescharacteristic
139C2SD32×D6111yescharacteristic
140C2#1684019611yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#357C2
socleC22×C61C2×D8
hypercenter#357D61
hypocenterC61#2233
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. #107×D61C2semidirect
3. #16839590C2semidirect
4. #16839589C2semidirect
5. #16839563C2semidirect
6. #16839541C2semidirect
7. C61×#357C2semidirect
76. #357D61semidirect
78. C61#2233semidirect