Finite Group Databasebeta

← #21447891

Subgroups — #21447891

Order 7808.

154 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 43 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#16840203C211yesmaximal, characteristic, complemented
2#16840200C211yesmaximal, characteristic
3#16840147C211yesmaximal, characteristic, complemented
4#16839878C211yesmaximal, characteristic, complemented
5#16839582C211yesmaximal, characteristic, complemented
6#16839574C211yesmaximal, characteristic, complemented
7C61×#362C211yesmaximal, characteristic, complemented
8#14519799C2211yescharacteristic
9C2×#11758201—21no—
10C2×D488C2211yescharacteristic
11#14519785—21no—
12#14519766—21no—
13#14519723—21no—
14#14519722—21no—
15#14519720—21no—
16D976—21no—
17#14519717C2211yescharacteristic
18#14519703—21no—
19C8×Dic61C2211yescharacteristic
20C2×Q16×C61C2211yescharacteristic
21M32×C61C2211yescharacteristic
22#108×C61C2211yescharacteristic
23C2×Q8×C61—21no—
24#11758222—21no—
25C2×D244—21no—
26Q16×C61—21no—
27Q16×C61—21no—
28M16×C61—21no—
29C2×C8×C61C2311yescharacteristic
30#11758201—41no—
31#11758201—41no—
32#11758198—42no—
33C4×Dic61D411yescharacteristic
34C2×#92418D411yescharacteristic
35Dic244D411yescharacteristic
36D488—21no—
37D488—21no—
38D488D411yescharacteristic
39#11758190—21no—
40#11758189—41no—
41C8×D61—41no—
42C16×C61—21no—
43#11758185—21no—
44C22×D61—41no—
45Q8×C61—41no—
46Q8×C61—41no—
47C2×C4×C61—41no—
48C2×C4×C61C2×D411yescharacteristic
49C22⋊D61—41no—
50C2×Dic61—21no—
51D244—21no—
52D244—41no—
53D244—41no—
54C4×D61—41no—
55Dic122—21no—
56C8×C61—41no—
57C8×C61C2×D411yescharacteristic
58C8×C61#4111yescharacteristic
59#92418D811yescharacteristic
60#92418D811yescharacteristic
61C22×C61AGL(1,ℤ/8)11yescharacteristic
62C2×D61—41no—
63C2×D61—82no—
64C2×D61—81no—
65C4×C61—81no—
66C4×C61#12111yescharacteristic
67C4×C61C2×D811yescharacteristic
68Dic61—41no—
69Dic61—41no—
70#2212—611nomaximal, Sylow
71C2×C61—21no—
72C2×C61#45911yescharacteristic
73D61—81no—
74D61—161no—
75#510—611no—
76#509—611no—
77#495—611no—
78#443—611no—
79#364—611no—
80#362D6111yescharacteristic, complemented
81#361—611no—
82C61#221211yescharacteristic, complemented, Sylow
83#135—611no—
84C2×Q16C2×D6111yescharacteristic
85C2×SD16—1221no—
86C2×D8—611no—
87#131—1221no—
88#124—1221no—
89Q32—1221no—
90SD32—1221no—
91SD32—1221no—
92D16—1221no—
93M32—611no—
94M32C2×D6111yescharacteristic
95#108C2×D6111yescharacteristic
96#104—1221no—
97C4×C8—611no—
98#41—1221no—
99C2×Q8—21no—
100C2×D4—1221no—
101Q16—21no—
102Q16—21no—
103Q16—611no—
104SD16—1221no—
105SD16—2441no—
106SD16—2441no—
107D8—611no—
108D8—1221no—
109D8—1221no—
110M16—21no—
111M16—2441no—
112C2×C8—611no—
113C2×C8—2441no—
114C2×C8C22×D6111yescharacteristic
115C22⋊C4—2442no—
116C42—611no—
117C16—21no—
118C16—1221no—
119C23—2441no—
120Q8—41no—
121Q8—41no—
122Q8—1221no—
123D4—1221no—
124D4—2441no—
125D4—2441no—
126D4—2441no—
127C2×C4—41no—
128C2×C4—1221no—
129C2×C4—2441no—
130C2×C4D4×D6111yescharacteristic
131C8—41no—
132C8—611no—
133C8—611no—
134C8#1175822211yescharacteristic
135C8D4×D6111yescharacteristic
136C22—4882no—
137C22—4881no—
138C22—2441no—
139C22#1451980411yescharacteristic
140C4—81no—
141C4—2441no—
142C4—2441no—
143C4#1451975011yescharacteristic
144C4D8×D6111yescharacteristic
145C2—21no—
146C2—9761no—
147C2—4881no—
148C2#1683995611yescharacteristic
subgroupG/H
centerC2#16839956
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#362C2
socleC2×C61#459
hypercenter#362D61
hypocenterC61#2212
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
1. #16840203C2semidirect
3. #16840147C2semidirect
4. #16839878C2semidirect
5. #16839582C2semidirect
6. #16839574C2semidirect
7. C61×#362C2semidirect
80. #362D61semidirect
82. C61#2212semidirect