Finite Group Databasebeta

← #22612168

Subgroups — #22612168

Order 9344.

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

normal subgroups only

This group has 142 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
1#17988992C211yesmaximal, characteristic, complemented
2#17988971C211yesmaximal, characteristic
3#17988392C212yesmaximal, complemented
4#17988389C212yesmaximal
5#346×C73C211yesmaximal, characteristic, complemented
6C2×Dic292C2211yescharacteristic
7C2×#11924017—21no—
8C2×D584C2211yescharacteristic
9#14556591—21no—
10#14556579—21no—
11#14556525—21no—
12#14556525C2212yes—
13C2×C16×C73C2212yes—
14C4×C8×C73C2211yescharacteristic
15C2×Dic146—21no—
16C2×Dic146—41no—
17C2×D292—21no—
18Dic292—22no—
19#11924017—42no—
20D584—22no—
21C4⋊Dic73—22no—
22C4⋊Dic73—41no—
23#11924005—41no—
24#11924005—41no—
25C2×C8×C73D411yescharacteristic
26C2×C8×C73C2311yescharacteristic
27C42×C73D411yescharacteristic
28C16×C73—22no—
29C22×D73—41no—
30C2×C4×C73D811yescharacteristic
31C2×C4×C73D811yescharacteristic
32C2×C4×C73C2×D411yescharacteristic
33C2×Dic73—41no—
34C2×Dic73—42no—
35D292—41no—
36D292—41no—
37Dic146—41no—
38Dic146—41no—
39Dic146—82no—
40C8×C73SD1612yes—
41C8×C73#4112yes—
42C22×C73C2×D811yescharacteristic
43C2×D73—81no—
44C2×D73—81no—
45C2×D73—81no—
46C4×C73—21no—
47C4×C73—21no—
48C4×C73#12411yescharacteristic
49C4×C73C2×SD1611yescharacteristic
50Dic73—81no—
51Dic73—82no—
52C2×C73#48611yescharacteristic
53C2×C73#50911yescharacteristic
54C2×C73#51011yescharacteristic
55D73—161no—
56#2243—731nomaximal, Sylow
57C73#224311yescharacteristic, complemented, Sylow
58#500—731no—
59#495—731no—
60#358—732no—
61#357—732no—
62#346D7311yescharacteristic, complemented
63C2×Q16—731no—
64C2×SD16—1461no—
65C2×D8—731no—
66C4⋊Q8—1461no—
67#124—1461no—
68C2×C16C2×D7312yes—
69#107—732no—
70#107—1461no—
71C4×C8C2×D7311yescharacteristic
72C2×Q8—2921no—
73C2×Q8—1461no—
74C2×D4—1461no—
75Q16—1462no—
76SD16—2922no—
77D8—1462no—
78C2×C8D29211yescharacteristic
79C2×C8C22×D7311yescharacteristic
80C4⋊C4—2921no—
81C4⋊C4—1462no—
82C22⋊C4—2921no—
83C22⋊C4—2921no—
84C42D29211yescharacteristic
85C16—22no—
86C23—2921no—
87Q8—2921no—
88Q8—2921no—
89Q8—5842no—
90D4—2921no—
91D4—2921no—
92C2×C4—2921no—
93C2×C4—2922no—
94C2×C4D58411yescharacteristic
95C2×C4D58411yescharacteristic
96C2×C4C2×D29211yescharacteristic
97C8#1192401712yes—
98C8#1192402812yes—
99C22—5841no—
100C22—5841no—
101C22—5841no—
102C22C2×D58411yescharacteristic
103C4—21no—
104C4—21no—
105C4—5841no—
106C4—5842no—
107C4#1455657911yescharacteristic
108C4C2×#1192401711yescharacteristic
109C2—11681no—
110C2#1798893411yescharacteristic
111C2#1798902511yescharacteristic
112C2#1798903011yescharacteristic
subgroupG/H
centerC22C2×D584
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#346×C73C2
socleC22×C73C2×D8
hypercenter#346D73
hypocenterC73#2243
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #346

Complements

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

NH ≅ G/Ntype
1. #17988992C2semidirect
3. #17988392C2semidirect
5. #346×C73C2semidirect
57. C73#2243semidirect
62. #346D73semidirect