Finite Group Databasebeta

← #22612096

Subgroups — #22612096

Order 9344.

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

normal subgroups only

This group has 124 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
1#17988989C211yesmaximal, characteristic
2C4×Dic292C211yesmaximal, characteristic
3#17988415C211yesmaximal, characteristic
4#17988413C211yesmaximal, characteristic
5#17988392C211yesmaximal, characteristic
6#17988392C211yesmaximal, characteristic
7C4⋊C16×C73C211yesmaximal, characteristic
8C2×Dic292C2211yescharacteristic
9#14556583—21no—
10C4×Dic146—21no—
11#14556525C2211yescharacteristic
12#14556525C2211yescharacteristic
13#14556525C2211yescharacteristic
14#14556523—21no—
15#14556516—21no—
16C2×C16×C73C2211yescharacteristic
17C2×C16×C73C2211yescharacteristic
18C4×C8×C73C2211yescharacteristic
19C2×Dic146—21no—
20Dic292—21no—
21Dic292Q812yes—
22C4⋊Dic73—21no—
23C4⋊Dic73—21no—
24C4⋊Dic73—21no—
25#11924007—41no—
26#11924007—41no—
27#11924007—41no—
28C4×Dic73—41no—
29C2×C8×C73D411yescharacteristic
30C2×C8×C73C2311yescharacteristic
31C42×C73D411yescharacteristic
32C16×C73—21no—
33C16×C73—21no—
34C2×C4×C73D811yescharacteristic
35C2×C4×C73D811yescharacteristic
36C2×C4×C73C2×D411yescharacteristic
37C2×Dic73—41no—
38C2×Dic73—41no—
39C2×Dic73—41no—
40C2×Dic73—41no—
41Dic146—22no—
42Dic146—41no—
43C8×C73—21no—
44C8×C73C2×Q811yescharacteristic
45C8×C73#4111yescharacteristic
46C22×C73C2×D811yescharacteristic
47C4×C73—21no—
48C4×C73—21no—
49C4×C73C22⋊Q811yescharacteristic
50C4×C73#13711yescharacteristic
51Dic73—42no—
52Dic73—81no—
53Dic73—81no—
54Dic73—81no—
55C2×C73#47411yescharacteristic
56C2×C73#50811yescharacteristic
57C2×C73#51011yescharacteristic
58#2229—731nomaximal, Sylow
59C73#222911yescharacteristic, complemented, Sylow
60#499—731no—
61C4×Q16—731no—
62#367—731no—
63#366—731no—
64C4⋊C16D7311yescharacteristic
65#358—731no—
66#358—731no—
67C2×Q16—731no—
68#125—1461no—
69C4×Q8—1461no—
70C2×C16C2×D7311yescharacteristic
71C2×C16C2×D7311yescharacteristic
72#107—731no—
73#107—731no—
74#107—731no—
75#106—1461no—
76#103—1461no—
77C4×C8C2×D7311yescharacteristic
78C2×Q8—1461no—
79Q16—732no—
80Q16—1461no—
81C2×C8D29211yescharacteristic
82C2×C8C22×D7311yescharacteristic
83C4⋊C4—2921no—
84C4⋊C4—2921no—
85C4⋊C4—2921no—
86C4⋊C4—1461no—
87C4⋊C4—1461no—
88C4⋊C4—1461no—
89C42—2921no—
90C42D29211yescharacteristic
91C16—21no—
92C16—21no—
93Q8—2921no—
94Q8—1462no—
95C2×C4—2921no—
96C2×C4—2921no—
97C2×C4—2921no—
98C2×C4—2921no—
99C2×C4D58411yescharacteristic
100C2×C4D58411yescharacteristic
101C2×C4C2×D29211yescharacteristic
102C8—21no—
103C8Q8×D7311yescharacteristic
104C8#1192402711yescharacteristic
105C22C2×D58411yescharacteristic
106C4—21no—
107C4—21no—
108C4—2922no—
109C4—5841no—
110C4—5841no—
111C4—5841no—
112C4#1455657111yescharacteristic
113C4#1455662411yescharacteristic
114C2#1798886811yescharacteristic
115C2#1798901911yescharacteristic
116C2#1798903011yescharacteristic
subgroupG/H
centerC22C2×D584
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
FittingC4⋊C16×C73C2
socleC22×C73C2×D8
hypercenterC4⋊C16D73
hypocenterC73#2229
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4⋊C16

Complements

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

NH ≅ G/Ntype
59. C73#2229semidirect