Finite Group Databasebeta

← #21448079

Subgroups — #21448079

Order 7808.

184 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 53 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
1C2×#14519723C211yesmaximal, characteristic, complemented
2C2×#14519722C211yesmaximal, characteristic, complemented
3C2×#14519718C211yesmaximal, characteristic
4#16840147C211yesmaximal, characteristic, complemented
5#16840145C211yesmaximal, characteristic, complemented
6C16×Dic61C211yesmaximal, characteristic, complemented
7C2×SD32×C61C211yesmaximal, characteristic, complemented
8C2×Dic244C2211yescharacteristic
9C2×#11758200—21no—
10C2×#11758201—21no—
11C2×D488C2211yescharacteristic
12#14519766—21no—
13#14519764—21no—
14#14519723—22no—
15#14519722—22no—
16#14519718—22no—
17C2×#11758185C2211yescharacteristic
18C8×Dic61C2211yescharacteristic
19C2×Q16×C61C2211yescharacteristic
20C2×D8×C61C2211yescharacteristic
21SD32×C61—22no—
22C2×C16×C61C2211yescharacteristic
23C2×Q8×C61—21no—
24C2×D4×C61—21no—
25C2×D244—21no—
26C2×Dic122—21no—
27Q16×C61—21no—
28Q16×C61—21no—
29D8×C61—21no—
30D8×C61—21no—
31C2×C8×C61C2311yescharacteristic
32C22⋊Dic61—42no—
33#11758201—42no—
34#11758200—42no—
35#11758198—42no—
36C4×Dic61D411yescharacteristic
37C2×#92418D411yescharacteristic
38Dic244—21no—
39Dic244—21no—
40D488—21no—
41D488—21no—
42C16×C61D412yes—
43#11758185D412yes—
44C23×C61—41no—
45C22×D61—41no—
46Q8×C61—41no—
47Q8×C61—41no—
48D4×C61—41no—
49D4×C61—41no—
50C2×C4×C61—41no—
51C2×C4×C61C2×D411yescharacteristic
52C2×Dic61—41no—
53C2×Dic61D812yes—
54D244—41no—
55D244—41no—
56Dic122—41no—
57Dic122—41no—
58C8×C61C2×D411yescharacteristic
59C8×C61C2×D411yescharacteristic
60#92418D812yes—
61C22×C61—81no—
62C22×C61—82no—
63C22×C61C2×D811yescharacteristic
64C2×D61—81no—
65C2×D61—82no—
66C4×C61—81no—
67C4×C61#12711yescharacteristic
68C4×C61C2×D811yescharacteristic
69Dic61—22no—
70Dic61—81no—
71#2249—611nomaximal, Sylow
72C2×C61—161no—
73C2×C61#49311yescharacteristic
74C2×C61#50812yes—
75D61—161no—
76C2×Q32—611no—
77C2×SD32—611no—
78C2×SD32D6111yescharacteristic, complemented
79C2×D16—611no—
80#495—611no—
81#495—611no—
82C4×C16—611no—
83C61#224911yescharacteristic, complemented, Sylow
84C2×Q16—611no—
85C2×Q16C2×D6111yescharacteristic
86C2×SD16—1221no—
87C2×SD16—1221no—
88C2×D8—611no—
89C2×D8C2×D6111yescharacteristic
90#124—1221no—
91#124—1221no—
92Q32—1222no—
93SD32—22no—
94SD32—1222no—
95D16—1222no—
96C2×C16—611no—
97C2×C16C2×D6111yescharacteristic
98C4×C8—611no—
99C2×Q8—21no—
100C2×Q8—1221no—
101C2×D4—21no—
102C2×D4—1221no—
103Q16—21no—
104Q16—21no—
105Q16—1221no—
106Q16—1221no—
107SD16—2442no—
108SD16—2442no—
109D8—21no—
110D8—21no—
111D8—1221no—
112D8—1221no—
113C2×C8—611no—
114C2×C8C22×D6111yescharacteristic
115C22⋊C4—2442no—
116C22⋊C4—2442no—
117C42—611no—
118C16—612no—
119C16C22⋊D6112yes—
120C23—41no—
121C23—2441no—
122Q8—41no—
123Q8—41no—
124Q8—2441no—
125Q8—2441no—
126D4—41no—
127D4—41no—
128D4—2441no—
129D4—2441no—
130C2×C4—41no—
131C2×C4—612no—
132C2×C4—2441no—
133C2×C4D4×D6111yescharacteristic
134C8—612no—
135C8D4×D6111yescharacteristic
136C8C2×C22⋊D6111yescharacteristic
137C22—82no—
138C22—81no—
139C22—4882no—
140C22—4881no—
141C22D8×D6111yescharacteristic
142C4—81no—
143C4—1222no—
144C4—4881no—
145C4#1451977311yescharacteristic
146C4D8×D6111yescharacteristic
147C2—161no—
148C2—9761no—
149C2#1684013711yescharacteristic
150C2#1684019312yes—
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC2×SD32×C61C2
socleC22×C61C2×D8
hypercenterC2×SD32D61
hypocenterC61#2249
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#14519723C2semidirect
2. C2×#14519722C2semidirect
4. #16840147C2semidirect
5. #16840145C2semidirect
6. C16×Dic61C2semidirect
7. C2×SD32×C61C2semidirect
78. C2×SD32D61semidirect
83. C61#2249semidirect