Finite Group Databasebeta

← #21448006

Subgroups — #21448006

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#16839999C211yesmaximal, characteristic
2#107×D61C211yesmaximal, characteristic, complemented
3#16839589C211yesmaximal, characteristic, complemented
4#16839564C211yesmaximal, characteristic, complemented
5#16839562C211yesmaximal, characteristic, complemented
6#16839541C211yesmaximal, characteristic, complemented
7C61×#367C211yesmaximal, characteristic, complemented
8C2×D488C2211yescharacteristic
9C2×C8×D61C2211yescharacteristic
10#14519752—21no—
11C4⋊C4×D61—21no—
12C2×#11758185C2211yescharacteristic
13#14519711C2211yescharacteristic
14#14519710—21no—
15#14519697—21no—
16C2×C16×C61C2211yescharacteristic
17#107×C61C2211yescharacteristic
18#107×C61C2211yescharacteristic
19C2×D244—21no—
20C2×D244—41no—
21C2×C4×D61—41no—
22C2×C4×D61D411yescharacteristic
23C2×C8×C61C2311yescharacteristic
24C4⋊C4×C61—21no—
25C4⋊C4×C61—21no—
26#11758198—41no—
27C4⋊Dic61—21no—
28#11758196—41no—
29C2×#92418D411yescharacteristic
30D488—21no—
31D488—21no—
32C8×D61—21no—
33C8×D61—21no—
34C16×C61—21no—
35#11758185—21no—
36C22×D61—41no—
37C22×D61D811yescharacteristic
38C2×C4×C61—41no—
39C2×C4×C61—41no—
40C2×C4×C61C2×D411yescharacteristic
41C2×Dic61—41no—
42C2×Dic61D811yescharacteristic
43D244—41no—
44D244—41no—
45D244—82no—
46C4×D61—21no—
47C4×D61—21no—
48C4×D61—82no—
49C8×C61#4111yescharacteristic
50C8×C61#4111yescharacteristic
51#92418—21no—
52C22×C61C2×D811yescharacteristic
53C2×D61—21no—
54C2×D61—21no—
55C2×D61—81no—
56C2×D61—81no—
57C2×D61—81no—
58C2×D61SD3212yes—
59C4×C61—81no—
60C4×C61—81no—
61C4×C61#12311yescharacteristic
62C4×C61#13711yescharacteristic
63Dic61—21no—
64Dic61—81no—
65#2233—611nomaximal, Sylow
66C2×C61#48011yescharacteristic
67C2×C61C2×SD3211yescharacteristic
68C2×C61#50911yescharacteristic
69D61—22no—
70D61—161no—
71#466—611no—
72C2×#107—611no—
73#367—611no—
74#367D6111yescharacteristic, complemented
75#357—611no—
76#357—611no—
77C22⋊C16—611no—
78C61#223311yescharacteristic, complemented, Sylow
79C2×D8—611no—
80C22×C8—611no—
81#121—1221no—
82C2×C4⋊C4—1221no—
83C2×C16—611no—
84C2×C16C2×D6111yescharacteristic
85#107—611no—
86#107—1221no—
87#107C2×D6111yescharacteristic
88#107C2×D6111yescharacteristic
89#102—1221no—
90C2×D4—1221no—
91C2×D4—2441no—
92C22×C4—611no—
93C22×C4—2441no—
94D8—1221no—
95D8—1221no—
96C2×C8—611no—
97C2×C8—1221no—
98C2×C8—1221no—
99C2×C8C22×D6111yescharacteristic
100C4⋊C4—21no—
101C4⋊C4—21no—
102C4⋊C4—1221no—
103C4⋊C4—2441no—
104C22⋊C4—2441no—
105C16—21no—
106C16—1221no—
107C23—611no—
108C23—2441no—
109D4—4882no—
110D4—2441no—
111D4—2441no—
112C2×C4—41no—
113C2×C4—41no—
114C2×C4—611no—
115C2×C4—1221no—
116C2×C4—1221no—
117C2×C4—4882no—
118C2×C4—2441no—
119C2×C4D4×D6111yescharacteristic
120C8—1221no—
121C8#1175822211yescharacteristic
122C8#1175822611yescharacteristic
123C22—612no—
124C22—1221no—
125C22—1221no—
126C22—4881no—
127C22—4881no—
128C22—4881no—
129C22D8×D6111yescharacteristic
130C4—81no—
131C4—81no—
132C4—1221no—
133C4—4881no—
134C4#1451976211yescharacteristic
135C4#1451980911yescharacteristic
136C2—1222no—
137C2—9761no—
138C2#1684007711yescharacteristic
139C2SD32×D6111yescharacteristic
140C2#1684019911yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#367C2
socleC22×C61C2×D8
hypercenter#367D61
hypocenterC61#2233
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

Complements

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

NH ≅ G/Ntype
2. #107×D61C2semidirect
3. #16839589C2semidirect
4. #16839564C2semidirect
5. #16839562C2semidirect
6. #16839541C2semidirect
7. C61×#367C2semidirect
74. #367D61semidirect
78. C61#2233semidirect