Finite Group Databasebeta

← #21447899

Subgroups — #21447899

Order 7808.

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

normal subgroups only

This group has 150 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#16840205C211yesmaximal, characteristic
2#16840203C211yesmaximal, characteristic
3#16840140C211yesmaximal, characteristic, complemented
4#16839878C211yesmaximal, characteristic
5#16839582C211yesmaximal, characteristic, complemented
6#16839577C211yesmaximal, characteristic, complemented
7C61×#362C211yesmaximal, characteristic, complemented
8#14519799C2211yescharacteristic
9C2×Dic244C2211yescharacteristic
10C2×#11758202—21no—
11#14519785—21no—
12#14519775—21no—
13Dic488—21no—
14#14519723—21no—
15#14519722—21no—
16#14519720—21no—
17#14519717C2211yescharacteristic
18#14519703—21no—
19C8×Dic61C2211yescharacteristic
20C2×Q16×C61C2211yescharacteristic
21M32×C61C2211yescharacteristic
22#108×C61C2211yescharacteristic
23C2×Q8×C61—21no—
24#11758222—21no—
25C2×Dic122—21no—
26Q16×C61—21no—
27Q16×C61—21no—
28M16×C61—21no—
29C2×C8×C61C2311yescharacteristic
30#11758202—41no—
31#11758202—41no—
32#11758196—42no—
33C4×Dic61D411yescharacteristic
34C2×#92418D411yescharacteristic
35Dic244—21no—
36Dic244—21no—
37Dic244D411yescharacteristic
38D488D411yescharacteristic
39#11758190—21no—
40#11758189—41no—
41C8×D61—41no—
42C16×C61—21no—
43#11758185—21no—
44Q8×C61—41no—
45Q8×C61—41no—
46C2×C4×C61—41no—
47C2×C4×C61C2×D411yescharacteristic
48C22⋊D61—41no—
49C2×Dic61—21no—
50C2×Dic61—41no—
51D244—21no—
52C4×D61—41no—
53Dic122—21no—
54Dic122—41no—
55Dic122—41no—
56C8×C61—41no—
57C8×C61C2×D411yescharacteristic
58C8×C61#4111yescharacteristic
59#92418D811yescharacteristic
60#92418D811yescharacteristic
61C22×C61AGL(1,ℤ/8)11yescharacteristic
62C2×D61—41no—
63C4×C61—81no—
64C4×C61#12111yescharacteristic
65C4×C61C2×D811yescharacteristic
66Dic61—22no—
67Dic61—41no—
68Dic61—81no—
69#2214—611nomaximal, Sylow
70C2×C61—21no—
71C2×C61#45911yescharacteristic
72D61—81no—
73#510—611no—
74#510—611no—
75#494—611no—
76#443—611no—
77#364—611no—
78#362—611no—
79#362D6111yescharacteristic, complemented
80C61#221411yescharacteristic, complemented, Sylow
81#135—611no—
82C2×Q16—611no—
83C2×Q16—1221no—
84C2×Q16C2×D6111yescharacteristic
85#131—1221no—
86C4⋊Q8—1221no—
87Q32—1221no—
88Q32—1221no—
89SD32—1221no—
90SD32—1221no—
91M32—611no—
92M32C2×D6111yescharacteristic
93#108C2×D6111yescharacteristic
94#104—1221no—
95C4×C8—611no—
96#41—1221no—
97C2×Q8—21no—
98C2×Q8—1221no—
99Q16—21no—
100Q16—21no—
101Q16—611no—
102Q16—1221no—
103Q16—1221no—
104Q16—2441no—
105Q16—2441no—
106SD16—1221no—
107D8—611no—
108M16—21no—
109M16—2441no—
110C2×C8—611no—
111C2×C8—2441no—
112C2×C8C22×D6111yescharacteristic
113C4⋊C4—2442no—
114C42—611no—
115C16—21no—
116C16—1221no—
117Q8—41no—
118Q8—41no—
119Q8—1221no—
120Q8—2441no—
121Q8—2441no—
122D4—1221no—
123D4—2441no—
124C2×C4—41no—
125C2×C4—1221no—
126C2×C4—2441no—
127C2×C4—2441no—
128C2×C4D4×D6111yescharacteristic
129C8—41no—
130C8—611no—
131C8—611no—
132C8#1175822211yescharacteristic
133C8D4×D6111yescharacteristic
134C22—2441no—
135C22#1451980411yescharacteristic
136C4—81no—
137C4—1222no—
138C4—4881no—
139C4—2441no—
140C4#1451975011yescharacteristic
141C4D8×D6111yescharacteristic
142C2—21no—
143C2—4881no—
144C2#1683995611yescharacteristic
subgroupG/H
centerC2#16839956
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#362C2
socleC2×C61#459
hypercenter#362D61
hypocenterC61#2214
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
3. #16840140C2semidirect
5. #16839582C2semidirect
6. #16839577C2semidirect
7. C61×#362C2semidirect
79. #362D61semidirect
80. C61#2214semidirect