Finite Group Databasebeta

← #21462227

Subgroups — #21462227

Order 7808.

142 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 44 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#16840808C211yesmaximal, characteristic
2#16840802C211yesmaximal, characteristic, complemented
3#16840687C211yesmaximal, characteristic, complemented
4#16840681C211yesmaximal, characteristic, complemented
5#16840679C211yesmaximal, characteristic
6#16840653C211yesmaximal, characteristic, complemented
7#16840204C211yesmaximal, characteristic
8#14519865—21no—
9Q8×#6923—21no—
10#14519852C2211yescharacteristic
11#14519847C2211yescharacteristic
12#14519845C2211yescharacteristic
13#14519842—21no—
14#14519840—21no—
15#14519831C2211yescharacteristic
16#14519800C2211yescharacteristic
17Q16×D61C2211yescharacteristic
18#14519723C411yescharacteristic, complemented
19#14519722C411yescharacteristic, complemented
20#14519720C411yescharacteristic, complemented
21#14519716C2211yescharacteristic
22Q32×C61C411yescharacteristic, complemented
23#11758226—21no—
24Q8×D61—21no—
25C4⋊#6923—21no—
26C4⋊#6923—41no—
27C4×#6923—41no—
28C4×#6923D411yescharacteristic
29#11758213—21no—
30#11758213—41no—
31D61⋊C8—41no—
32D61⋊C8D411yescharacteristic
33Q16×C61C2×C411yescharacteristic
34Q16×C61C2×C411yescharacteristic
35#11758202—21no—
36#11758201—21no—
37Dic244C2×C411yescharacteristic
38D488C2×C411yescharacteristic
39C8×D61C2311yescharacteristic
40#11758187—21no—
41C16×C61C2×C411yescharacteristic
42#11758185C2×C411yescharacteristic
43C2×#6923—21no—
44C2×#6923—41no—
45Q8×C61—21no—
46Q8×C61—21no—
47D244—21no—
48D244—41no—
49C4×D61—41no—
50C4×D61—41no—
51C4×D61C2×D411yescharacteristic
52Dic122—21no—
53Dic122—41no—
54#92420—21no—
55#92420—41no—
56C8×C61C22×C411yescharacteristic
57#92418#4111yescharacteristic
58C2×D61—41no—
59C2×D61AGL(1,ℤ/8)11yescharacteristic
60#6923—41no—
61#6923—81no—
62C4×C61—41no—
63C4×C61—41no—
64C4×C61C4×D411yescharacteristic
65Dic61—41no—
66Dic61AGL(1,ℤ/8)11yescharacteristic
67#2180—611nomaximal, Sylow
68C2×C61#44211yescharacteristic
69D61—21no—
70D61—81no—
71#510—611no—
72#444—611no—
73#441—611no—
74#365—611no—
75#362—611no—
76#360—611no—
77#347—611no—
78C61#218011yescharacteristic, complemented, Sylow
79#135—611no—
80C2×Q16—611no—
81#131—1221no—
82C4×Q8—1221no—
83Q32—611no—
84Q32#692311yescharacteristic, complemented
85SD32—611no—
86SD32—611no—
87M32—611no—
88M32—611no—
89#108—611no—
90#106—611no—
91#104—1221no—
92#103—1221no—
93#97—611no—
94#41—1221no—
95C2×Q8—1221no—
96Q16—611no—
97Q16—1221no—
98Q16C2×#692311yescharacteristic
99Q16C2×#692311yescharacteristic
100SD16—1221no—
101D8—611no—
102M16—1221no—
103M16—2441no—
104C2×C8—611no—
105C2×C8—611no—
106C2×C8—2441no—
107C4⋊C4—1221no—
108C4⋊C4—2441no—
109C42—611no—
110C42—2441no—
111C16—611no—
112C16—1221no—
113C16C2×#692311yescharacteristic
114Q8—21no—
115Q8—21no—
116Q8—1221no—
117Q8—2441no—
118D4—1221no—
119D4—2441no—
120C2×C4—611no—
121C2×C4—1221no—
122C2×C4—2441no—
123C2×C4—2441no—
124C2×C4—2441no—
125C8—611no—
126C8—1221no—
127C8—2441no—
128C8C22×#692311yescharacteristic
129C22—611no—
130C22—2441no—
131C4—41no—
132C4—41no—
133C4—611no—
134C4—4881no—
135C4—2441no—
136C4—2441no—
137C4D4×#692311yescharacteristic
138C2—1221no—
139C2—4881no—
140C2#1684080311yescharacteristic
subgroupG/H
centerC2#16840803
commutatorC8×C61C22×C4
FrattiniC8C22×#6923
FittingQ32×C61C4
socleC2×C61#442
hypercenterQ32#6923
hypocenterC61#2180
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32

Complements

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

NH ≅ G/Ntype
2. #16840802C2semidirect
3. #16840687C2semidirect
4. #16840681C2semidirect
6. #16840653C2semidirect
18. #14519723C4semidirect
19. #14519722C4semidirect
20. #14519720C4semidirect
22. Q32×C61C4semidirect
78. C61#2180semidirect
84. Q32#6923semidirect