Finite Group Databasebeta

← #22612166

Subgroups — #22612166

Order 9344.

142 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 47 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#17988991C211yesmaximal, characteristic, complemented
2#17988970C211yesmaximal, characteristic
3#17988392C211yesmaximal, characteristic, complemented
4#17988390C211yesmaximal, characteristic, complemented
5#17988388C211yesmaximal, characteristic
6#17988362C211yesmaximal, characteristic, complemented
7#357×C73C211yesmaximal, characteristic
8C2×Dic292C2211yescharacteristic
9C2×#11924016—21no—
10#14556590—21no—
11#14556578—21no—
12C2×#11924003C2211yescharacteristic
13#14556525C2211yescharacteristic
14#14556524—21no—
15C8×Dic73C2211yescharacteristic
16C2×D8×C73C2211yescharacteristic
17C2×C16×C73C2211yescharacteristic
18#107×C73C2211yescharacteristic
19C2×Dic146—21no—
20C2×Dic146—41no—
21Dic292—21no—
22Dic292—21no—
23#11924016—42no—
24C2×#10596831D411yescharacteristic
25C4⋊Dic73—21no—
26#11924007—41no—
27C22⋊Dic73—41no—
28C22⋊Dic73—41no—
29C4×Dic73D411yescharacteristic
30#11924003—21no—
31C2×D4×C73—21no—
32D8×C73—21no—
33D8×C73—21no—
34C2×C8×C73C2311yescharacteristic
35C4⋊C4×C73—21no—
36C16×C73—21no—
37C23×C73—41no—
38D4×C73—41no—
39D4×C73—41no—
40C2×C4×C73—41no—
41C2×C4×C73C2×D411yescharacteristic
42C2×Dic73—41no—
43C2×Dic73—41no—
44C2×Dic73D811yescharacteristic
45C2×Dic73D811yescharacteristic
46Dic146—41no—
47Dic146—41no—
48Dic146—82no—
49C8×C73#4111yescharacteristic
50C8×C73#4111yescharacteristic
51#10596831SD1612yes—
52C22×C73—81no—
53C22×C73—81no—
54C22×C73—81no—
55C22×C73C2×D811yescharacteristic
56C4×C73—81no—
57C4×C73#12411yescharacteristic
58C4×C73C2×SD1611yescharacteristic
59Dic73—21no—
60Dic73—21no—
61Dic73—81no—
62Dic73—81no—
63C2×C73—161no—
64C2×C73#48611yescharacteristic
65C2×C73#50911yescharacteristic
66C2×C73#51011yescharacteristic
67#2243—731nomaximal, Sylow
68C73#224311yescharacteristic, complemented, Sylow
69#500—731no—
70#495—731no—
71#358—731no—
72#358—731no—
73#357—731no—
74#357D7311yescharacteristic
75#346—731no—
76C2×Q16—731no—
77C2×SD16—1461no—
78C2×D8C2×D7311yescharacteristic
79C4⋊Q8—1461no—
80#124—1461no—
81C2×C16—731no—
82C2×C16C2×D7311yescharacteristic
83#107—731no—
84#107—1461no—
85#107C2×D7311yescharacteristic
86C4×C8—731no—
87C2×Q8—2921no—
88C2×Q8—1461no—
89C2×D4—21no—
90Q16—1461no—
91Q16—1461no—
92SD16—2922no—
93D8—21no—
94D8—21no—
95C2×C8—731no—
96C2×C8C22×D7311yescharacteristic
97C4⋊C4—21no—
98C4⋊C4—2921no—
99C4⋊C4—1461no—
100C22⋊C4—2921no—
101C22⋊C4—2921no—
102C42—731no—
103C16—21no—
104C16—1461no—
105C23—41no—
106Q8—2921no—
107Q8—2921no—
108Q8—5842no—
109D4—41no—
110D4—41no—
111C2×C4—41no—
112C2×C4—2921no—
113C2×C4—2921no—
114C2×C4—731no—
115C2×C4—731no—
116C2×C4D4×D7311yescharacteristic
117C8—732no—
118C8#1192402711yescharacteristic
119C8#1192402811yescharacteristic
120C22—81no—
121C22—81no—
122C22—81no—
123C22D8×D7311yescharacteristic
124C4—81no—
125C4—5841no—
126C4—5841no—
127C4—1461no—
128C4—1461no—
129C4#1455657711yescharacteristic
130C4SD16×D7311yescharacteristic
131C2—161no—
132C2#1798893211yescharacteristic
133C2#1798902111yescharacteristic
134C2#1798902611yescharacteristic
subgroupG/H
centerC22D8×D73
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#357×C73C2
socleC22×C73C2×D8
hypercenter#357D73
hypocenterC73#2243
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
1. #17988991C2semidirect
3. #17988392C2semidirect
4. #17988390C2semidirect
6. #17988362C2semidirect
68. C73#2243semidirect