Finite Group Databasebeta

← #22625002

Subgroups — #22625002

Order 9344.

140 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 52 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×#14556666C211yesmaximal, characteristic
2C2×#14556659C211yesmaximal, characteristic
3#17988624C211yesmaximal, characteristic
4C2×C4⋊#64408—21no—
5#14556666—21no—
6#14556666C412yescomplemented
7C2×#11924031—21no—
8#14556659—21no—
9#14556659C412yescomplemented
10C2×C8×D73C2211yescharacteristic
11#14556549—21no—
12#14556525C411yescharacteristic, complemented
13#14556522—21no—
14#107×C73C411yescharacteristic, complemented
15C22×#64408—41no—
16C4⋊#64408—22no—
17C4⋊#64408—41no—
18#11924031—22no—
19C2×C4×D73D411yescharacteristic
20C2×#10596831D411yescharacteristic
21C8×D73C2×C411yescharacteristic
22C8×D73C2×C411yescharacteristic
23C8×D73D411yescharacteristic
24C8×D73Q811yescharacteristic
25C4⋊Dic73—21no—
26#11924005—41no—
27C4×Dic73—41no—
28C2×C8×C73C2×C411yescharacteristic
29C4⋊C4×C73—21no—
30C22×D73D811yescharacteristic
31C2×#64408—42no—
32C2×#64408—81no—
33C2×#64408—81no—
34C2×C4×C73—41no—
35C2×C4×C73C22⋊C411yescharacteristic
36C2×Dic73—41no—
37C2×Dic73SD1611yescharacteristic
38C4×D73C22⋊C411yescharacteristic
39C4×D73C4⋊C411yescharacteristic
40C4×D73SD1611yescharacteristic
41C4×D73Q1611yescharacteristic
42C8×C73C4211yescharacteristic
43C8×C73C4⋊C411yescharacteristic
44#10596831C22⋊C411yescharacteristic
45#10596831C4⋊C411yescharacteristic
46C22×C73#10211yescharacteristic
47C2×D73—21no—
48C2×D73—21no—
49C2×D73#10211yescharacteristic
50C2×D73#10711yescharacteristic
51#64408—82no—
52C4×C73—81no—
53C4×C73#9511yescharacteristic
54C4×C73#10311yescharacteristic
55Dic73—81no—
56Dic73#10311yescharacteristic
57Dic73#10611yescharacteristic
58C2×C73#34011yescharacteristic
59C2×C73#36011yescharacteristic
60C2×C73#36011yescharacteristic
61D73—21no—
62D73—21no—
63#1386—731nomaximal, Sylow
64C73#138611yescharacteristic, complemented, Sylow
65C2×M32—731no—
66#427—731no—
67C2×#106—731no—
68C22×C8—731no—
69#117—1461no—
70C2×C4⋊C4—1461no—
71M32—732no—
72M32—1461no—
73C2×C16—1461no—
74#107—731no—
75#107#6440811yescharacteristic, complemented
76#106—732no—
77#106—1461no—
78#106—1461no—
79C22×C4—2921no—
80C22×C4—731no—
81C2×C8—731no—
82C2×C8—731no—
83C2×C8—731no—
84C2×C8—731no—
85C2×C8—731no—
86C2×C8C2×#6440811yescharacteristic
87C4⋊C4—21no—
88C4⋊C4—2921no—
89C4⋊C4—1462no—
90C4⋊C4—1461no—
91C22⋊C4—2921no—
92C42—2921no—
93C16—1462no—
94C23—731no—
95C2×C4—41no—
96C2×C4—2922no—
97C2×C4—2921no—
98C2×C4—5841no—
99C2×C4—5841no—
100C2×C4—731no—
101C2×C4—731no—
102C2×C4—731no—
103C2×C4—731no—
104C2×C4—731no—
105C2×C4C22⋊#6440811yescharacteristic
106C8—731no—
107C8—731no—
108C8C4×#6440811yescharacteristic
109C8C4⋊#6440811yescharacteristic
110C22—731no—
111C22—731no—
112C22—1461no—
113C22—1461no—
114C22#1455665311yescharacteristic
115C4—81no—
116C4—5842no—
117C4—5841no—
118C4—731no—
119C4—731no—
120C4(C2×#64408)⋊C411yescharacteristic
121C4#1455665411yescharacteristic
122C2—1461no—
123C2—1461no—
124C2#1798946011yescharacteristic
125C2#1798950311yescharacteristic
126C2#1798950411yescharacteristic
subgroupG/H
centerC22#14556653
commutatorC8×C73C42
FrattiniC2×C8C2×#64408
Fitting#107×C73C4
socleC22×C73#102
hypercenter#107#64408
hypocenterC73#1386
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
6. #14556666C4semidirect
9. #14556659C4semidirect
12. #14556525C4semidirect
14. #107×C73C4semidirect
64. C73#1386semidirect
75. #107#64408semidirect