Finite Group Databasebeta

← #22612106

Subgroups — #22612106

Order 9344.

120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 43 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#17988987C211yesmaximal, characteristic, complemented
2#17988703C211yesmaximal, characteristic
3#17988411C211yesmaximal, characteristic, complemented
4#17988407C211yesmaximal, characteristic, complemented
5#17988398C211yesmaximal, characteristic
6#17988396C211yesmaximal, characteristic
7#365×C73C211yesmaximal, characteristic, complemented
8#14556613C2211yescharacteristic
9#14556599—21no—
10#14556582—21no—
11#14556531C2211yescharacteristic
12#14556524—21no—
13#14556523C2211yescharacteristic
14#14556517—21no—
15C8×Dic73C2211yescharacteristic
16M32×C73C2211yescharacteristic
17#108×C73C2211yescharacteristic
18#106×C73C2211yescharacteristic
19#11924028—21no—
20Dic292Q811yescharacteristic
21#11924017—21no—
22D584Q811yescharacteristic
23#11924011—41no—
24C2×#10596831D411yescharacteristic
25C8×D73—41no—
26C4⋊Dic73—21no—
27C4⋊Dic73—41no—
28#11924007—41no—
29C4×Dic73D411yescharacteristic
30#11924003—21no—
31M16×C73—21no—
32C2×C8×C73C2311yescharacteristic
33C4⋊C4×C73—21no—
34C16×C73—21no—
35C2×C4×C73—41no—
36C2×C4×C73C2×D411yescharacteristic
37C22⋊D73—41no—
38C2×Dic73—21no—
39C2×Dic73—41no—
40D292—21no—
41C4×D73—41no—
42Dic146—21no—
43C8×C73—41no—
44C8×C73C2×Q811yescharacteristic
45C8×C73#4111yescharacteristic
46#10596831SD1611yescharacteristic
47#10596831SD1611yescharacteristic
48C22×C73AGL(1,ℤ/8)11yescharacteristic
49C2×D73—41no—
50C4×C73—81no—
51C4×C73C22⋊Q811yescharacteristic
52C4×C73C2×SD1611yescharacteristic
53Dic73—41no—
54Dic73—41no—
55Dic73—81no—
56C2×C73—21no—
57C2×C73#47611yescharacteristic
58D73—81no—
59#2231—731nomaximal, Sylow
60C73#223111yescharacteristic, complemented, Sylow
61#499—731no—
62#443—731no—
63#365—731no—
64#365D7311yescharacteristic, complemented
65#364—731no—
66#360—731no—
67#360—731no—
68#135—731no—
69#131—1461no—
70#125—1461no—
71M32—731no—
72M32C2×D7311yescharacteristic
73#108C2×D7311yescharacteristic
74#107—1461no—
75#106—731no—
76#106C2×D7311yescharacteristic
77#104—1461no—
78C4×C8—731no—
79#41—1461no—
80Q16—731no—
81SD16—1461no—
82D8—731no—
83M16—21no—
84M16—2921no—
85C2×C8—2921no—
86C2×C8—731no—
87C2×C8C22×D7311yescharacteristic
88C4⋊C4—21no—
89C4⋊C4—2921no—
90C4⋊C4—2921no—
91C4⋊C4—1461no—
92C42—731no—
93C16—21no—
94C16—1461no—
95Q8—1461no—
96D4—2921no—
97D4—1461no—
98C2×C4—41no—
99C2×C4—2921no—
100C2×C4—2921no—
101C2×C4—1461no—
102C2×C4D4×D7311yescharacteristic
103C8—41no—
104C8—731no—
105C8—731no—
106C8Q8×D7311yescharacteristic
107C8#1192402811yescharacteristic
108C22—2921no—
109C22#1455661811yescharacteristic
110C4—81no—
111C4—2921no—
112C4—2921no—
113C4—5841no—
114C4#1455656911yescharacteristic
115C4SD16×D7311yescharacteristic
116C2—21no—
117C2—5841no—
118C2#1798887611yescharacteristic
subgroupG/H
centerC2#17988876
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#365×C73C2
socleC2×C73#476
hypercenter#365D73
hypocenterC73#2231
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #365

Complements

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

NH ≅ G/Ntype
1. #17988987C2semidirect
3. #17988411C2semidirect
4. #17988407C2semidirect
7. #365×C73C2semidirect
60. C73#2231semidirect
64. #365D73semidirect