Finite Group Databasebeta

← #21447934

Subgroups — #21447934

Order 7808.

160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 51 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×#14519720C211yesmaximal, characteristic, complemented
2C2×#14519717C211yesmaximal, characteristic, complemented
3#16839998C211yesmaximal, characteristic
4#16839587C211yesmaximal, characteristic, complemented
5#16839566C211yesmaximal, characteristic, complemented
6#16839562C211yesmaximal, characteristic, complemented
7C61×#467C211yesmaximal, characteristic, complemented
8C2×D488C2211yescharacteristic
9#14519751—21no—
10#14519720—22no—
11#14519717—22no—
12C2×#11758185C2211yescharacteristic
13C2×#11758185C2211yescharacteristic
14#14519711C2211yescharacteristic
15#14519699—21no—
16C2×Q16×C61C2211yescharacteristic
17C22×C8×C61C2211yescharacteristic
18C22⋊Q8×C61—21no—
19#107×C61C2211yescharacteristic
20#103×C61—21no—
21C2×Q8×C61—21no—
22C22×C4×C61D411yescharacteristic
23C2×C22⋊D61—41no—
24C2×D244—21no—
25Q16×C61—21no—
26Q16×C61—21no—
27C2×C8×C61—21no—
28C2×C8×C61—21no—
29C2×C8×C61D411yescharacteristic
30C2×C8×C61C2311yescharacteristic
31C4⋊C4×C61—21no—
32C4⋊C4×C61—41no—
33C22⋊C4×C61—41no—
34#11758198—41no—
35C4⋊Dic61—21no—
36D488—21no—
37D488—21no—
38#11758185—21no—
39#11758185D412yescomplemented
40C23×C61D811yescharacteristic
41C22×D61—41no—
42Q8×C61—41no—
43Q8×C61—41no—
44C2×C4×C61—21no—
45C2×C4×C61—21no—
46C2×C4×C61—41no—
47C2×C4×C61—41no—
48C2×C4×C61D811yescharacteristic
49C2×C4×C61C2×D411yescharacteristic
50C22⋊D61—82no—
51C2×Dic61—41no—
52D244—41no—
53D244—41no—
54C8×C61—21no—
55C8×C61C2×D411yescharacteristic
56C8×C61#4111yescharacteristic
57C22×C61—21no—
58C22×C61—21no—
59C22×C61—21no—
60C22×C61C2×D811yescharacteristic
61C2×D61—81no—
62C2×D61—81no—
63C2×D61—81no—
64C4×C61—21no—
65C4×C61—81no—
66C4×C61—81no—
67C4×C61#12111yescharacteristic
68C4×C61#13511yescharacteristic
69Dic61—81no—
70#2220—611nomaximal, Sylow
71C2×C61—41no—
72C2×C61#46611yescharacteristic
73C2×C61#50911yescharacteristic
74C2×C61#51011yescharacteristic
75D61—161no—
76C2×SD32—611no—
77C2×M32—611no—
78#467D6111yescharacteristic, complemented
79#466—611no—
80#366—611no—
81#358—611no—
82#357—611no—
83C61#222011yescharacteristic, complemented, Sylow
84C2×Q16C2×D6111yescharacteristic
85C2×D8—611no—
86C22×C8C2×D6111yescharacteristic
87C22⋊Q8—21no—
88#121—1221no—
89SD32—1222no—
90M32—1222no—
91C2×C16—611no—
92C2×C16—611no—
93#107—611no—
94#107C2×D6111yescharacteristic
95#103—21no—
96#102—1221no—
97C2×Q8—21no—
98C2×D4—1221no—
99C2×D4—2441no—
100C22×C4C22⋊D6111yescharacteristic
101Q16—21no—
102Q16—21no—
103D8—1221no—
104D8—1221no—
105C2×C8—21no—
106C2×C8—21no—
107C2×C8C22⋊D6111yescharacteristic
108C2×C8C22×D6111yescharacteristic
109C4⋊C4—21no—
110C4⋊C4—41no—
111C4⋊C4—1221no—
112C22⋊C4—41no—
113C22⋊C4—2441no—
114C16—612no—
115C16—1221no—
116C23—2441no—
117C23#1175819911yescharacteristic
118Q8—41no—
119Q8—41no—
120D4—4882no—
121D4—2441no—
122D4—2441no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—2441no—
128C2×C4#1175819911yescharacteristic
129C2×C4C2×C22⋊D6111yescharacteristic
130C8—21no—
131C8D4×D6111yescharacteristic
132C8#1175822411yescharacteristic
133C22—21no—
134C22—21no—
135C22—21no—
136C22—4881no—
137C22—4881no—
138C22—4881no—
139C22C2×#1175819911yescharacteristic
140C4—21no—
141C4—81no—
142C4—81no—
143C4—4881no—
144C4#1451974911yescharacteristic
145C4#1451979711yescharacteristic
146C2—41no—
147C2—9761no—
148C2#1683999611yescharacteristic
149C2#1684019711yescharacteristic
150C2#1684020311yescharacteristic
subgroupG/H
centerC22C2×#11758199
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#467C2
socleC22×C61C2×D8
hypercenter#467D61
hypocenterC61#2220
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#14519720C2semidirect
2. C2×#14519717C2semidirect
4. #16839587C2semidirect
5. #16839566C2semidirect
6. #16839562C2semidirect
7. C61×#467C2semidirect
39. #11758185D4semidirect
78. #467D61semidirect
83. C61#2220semidirect