Finite Group Databasebeta

← #21447885

Subgroups — #21447885

Order 7808.

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

normal subgroups only

This group has 154 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#16840203C211yesmaximal, characteristic, complemented
2#16840198C211yesmaximal, characteristic
3#16839880C211yesmaximal, characteristic, complemented
4#16839583C211yesmaximal, characteristic, complemented
5#16839578C211yesmaximal, characteristic, complemented
6#16839575C211yesmaximal, characteristic, complemented
7C61×#495C211yesmaximal, characteristic, complemented
8#14519799C2211yescharacteristic
9#14519783—21no—
10#14519723—21no—
11#14519721—21no—
12#14519720—21no—
13#14519718—21no—
14#14519717C2211yescharacteristic
15#14519717C2211yescharacteristic
16#14519713C2211yescharacteristic
17#14519705—21no—
18C2×Q16×C61C2211yescharacteristic
19C2×SD16×C61—21no—
20C2×D8×C61C2211yescharacteristic
21#124×C61—21no—
22C4×C8×C61C2211yescharacteristic
23C2×Q8×C61—21no—
24C2×D4×C61—21no—
25#11758222—21no—
26Q16×C61—21no—
27Q16×C61—21no—
28SD16×C61—41no—
29SD16×C61—41no—
30D8×C61—21no—
31D8×C61—21no—
32C2×C8×C61D411yescharacteristic
33C2×C8×C61C2311yescharacteristic
34C22⋊C4×C61—42no—
35C42×C61D411yescharacteristic
36#11758194—21no—
37Dic244D411yescharacteristic
38D488D411yescharacteristic
39#11758190—21no—
40#11758189—41no—
41C8×D61—41no—
42#11758185—21no—
43#11758185—21no—
44C23×C61—41no—
45Q8×C61—41no—
46Q8×C61—41no—
47D4×C61—41no—
48D4×C61—41no—
49C2×C4×C61—21no—
50C2×C4×C61—41no—
51C2×C4×C61C2×D411yescharacteristic
52C22⋊D61—41no—
53D244—21no—
54C4×D61—41no—
55Dic122—21no—
56C8×C61D811yescharacteristic
57C8×C61D811yescharacteristic
58C8×C61C2×D411yescharacteristic
59C8×C61#4111yescharacteristic
60#92418—41no—
61C22×C61—82no—
62C22×C61—81no—
63C22×C61AGL(1,ℤ/8)11yescharacteristic
64C2×D61—41no—
65C4×C61—41no—
66C4×C61—81no—
67C4×C61#12111yescharacteristic
68C4×C61C2×D811yescharacteristic
69Dic61—41no—
70#2212—611nomaximal, Sylow
71C2×C61—21no—
72C2×C61—161no—
73C2×C61#45911yescharacteristic
74D61—81no—
75#510—611no—
76#509—611no—
77#495D6111yescharacteristic, complemented
78#443—611no—
79#364—611no—
80#362—611no—
81#361—611no—
82C61#221211yescharacteristic, complemented, Sylow
83#135—611no—
84C2×Q16C2×D6111yescharacteristic
85C2×SD16—21no—
86C2×D8C2×D6111yescharacteristic
87#131—1221no—
88#124—21no—
89Q32—1221no—
90SD32—1221no—
91SD32—1221no—
92D16—1221no—
93M32—611no—
94M32—611no—
95#108—611no—
96#104—1221no—
97C4×C8C2×D6111yescharacteristic
98#41—1221no—
99C2×Q8—21no—
100C2×D4—21no—
101Q16—21no—
102Q16—21no—
103Q16—611no—
104SD16—41no—
105SD16—41no—
106SD16—1221no—
107D8—21no—
108D8—21no—
109D8—611no—
110M16—1221no—
111M16—2441no—
112C2×C8—2441no—
113C2×C8C22⋊D6111yescharacteristic
114C2×C8C22×D6111yescharacteristic
115C22⋊C4—42no—
116C42C22⋊D6111yescharacteristic
117C16—1221no—
118C16—1221no—
119C23—41no—
120Q8—41no—
121Q8—41no—
122Q8—1221no—
123D4—41no—
124D4—41no—
125D4—1221no—
126D4—2441no—
127C2×C4—21no—
128C2×C4—41no—
129C2×C4—2441no—
130C2×C4C2×C22⋊D6111yescharacteristic
131C8—2441no—
132C8#1175819911yescharacteristic
133C8#1175819911yescharacteristic
134C8D4×D6111yescharacteristic
135C8#1175822411yescharacteristic
136C22—82no—
137C22—81no—
138C22—2441no—
139C22#1451980311yescharacteristic
140C4—41no—
141C4—81no—
142C4—2441no—
143C4#1451974811yescharacteristic
144C4C2×#1175819911yescharacteristic
145C2—21no—
146C2—161no—
147C2—4881no—
148C2#1683995411yescharacteristic
subgroupG/H
centerC2#16839954
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#495C2
socleC2×C61#459
hypercenter#495D61
hypocenterC61#2212
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #16840203C2semidirect
3. #16839880C2semidirect
4. #16839583C2semidirect
5. #16839578C2semidirect
6. #16839575C2semidirect
7. C61×#495C2semidirect
77. #495D61semidirect
82. C61#2212semidirect