Finite Group Databasebeta

← #22612164

Subgroups — #22612164

Order 9344.

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

normal subgroups only

This group has 138 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#17988988C211yesmaximal, characteristic, complemented
2#17988972C211yesmaximal, characteristic
3#17988391C211yesmaximal, characteristic, complemented
4#17988389C211yesmaximal, characteristic
5#17988387C211yesmaximal, characteristic
6C16×Dic73C211yesmaximal, characteristic, complemented
7#358×C73C211yesmaximal, characteristic, complemented
8C2×#11924015—21no—
9C2×D584C2211yescharacteristic
10#14556582—21no—
11#14556580—21no—
12C2×#11924003C2211yescharacteristic
13#14556525C2211yescharacteristic
14#14556522—21no—
15C8×Dic73C2211yescharacteristic
16C2×Q16×C73C2211yescharacteristic
17C2×C16×C73C2211yescharacteristic
18#107×C73C2211yescharacteristic
19C2×D292—21no—
20#11924015—42no—
21D584—21no—
22D584—21no—
23C2×#10596831D411yescharacteristic
24C4⋊Dic73—21no—
25C4⋊Dic73—41no—
26#11924007—41no—
27#11924005—41no—
28#11924005—41no—
29C4×Dic73D411yescharacteristic
30#11924003—21no—
31C2×Q8×C73—21no—
32Q16×C73—21no—
33Q16×C73—21no—
34C2×C8×C73C2311yescharacteristic
35C4⋊C4×C73—21no—
36C16×C73—21no—
37C22×D73—41no—
38Q8×C73—41no—
39Q8×C73—41no—
40C2×C4×C73—41no—
41C2×C4×C73—41no—
42C2×C4×C73C2×D411yescharacteristic
43C2×Dic73—41no—
44C2×Dic73D811yescharacteristic
45C2×Dic73D811yescharacteristic
46D292—41no—
47D292—41no—
48C8×C73#4111yescharacteristic
49C8×C73#4111yescharacteristic
50#10596831SD1612yes—
51C22×C73C2×D811yescharacteristic
52C2×D73—81no—
53C2×D73—81no—
54C2×D73—81no—
55C4×C73—81no—
56C4×C73—81no—
57C4×C73#12411yescharacteristic
58C4×C73C2×SD1611yescharacteristic
59Dic73—21no—
60Dic73—21no—
61Dic73—81no—
62C2×C73#48611yescharacteristic
63C2×C73#50811yescharacteristic
64C2×C73#50811yescharacteristic
65D73—161no—
66#2242—731nomaximal, Sylow
67C73#224211yescharacteristic, complemented, Sylow
68#499—731no—
69#495—731no—
70#358—731no—
71#358D7311yescharacteristic, complemented
72#357—731no—
73#357—731no—
74C4×C16—731no—
75C2×Q16C2×D7311yescharacteristic
76C2×SD16—1461no—
77C2×D8—731no—
78#125—1461no—
79#124—1461no—
80C2×C16—731no—
81C2×C16C2×D7311yescharacteristic
82#107—731no—
83#107C2×D7311yescharacteristic
84#106—1461no—
85C4×C8—731no—
86C2×Q8—21no—
87C2×D4—1461no—
88Q16—21no—
89Q16—21no—
90SD16—2922no—
91D8—1461no—
92D8—1461no—
93C2×C8—731no—
94C2×C8C22×D7311yescharacteristic
95C4⋊C4—21no—
96C4⋊C4—2921no—
97C4⋊C4—2921no—
98C4⋊C4—1461no—
99C22⋊C4—2921no—
100C22⋊C4—2921no—
101C42—731no—
102C16—21no—
103C16—1461no—
104C23—2921no—
105Q8—41no—
106Q8—41no—
107D4—2921no—
108D4—2921no—
109C2×C4—41no—
110C2×C4—41no—
111C2×C4—2921no—
112C2×C4—731no—
113C2×C4—731no—
114C2×C4D4×D7311yescharacteristic
115C8—732no—
116C8#1192402711yescharacteristic
117C8#1192402811yescharacteristic
118C22—5841no—
119C22—5841no—
120C22—5841no—
121C22D8×D7311yescharacteristic
122C4—81no—
123C4—81no—
124C4—5841no—
125C4—1461no—
126C4—1461no—
127C4#1455657711yescharacteristic
128C4SD16×D7311yescharacteristic
129C2—11681no—
130C2#1798893211yescharacteristic
131C2#1798901811yescharacteristic
132C2#1798902011yescharacteristic
subgroupG/H
centerC22D8×D73
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#358×C73C2
socleC22×C73C2×D8
hypercenter#358D73
hypocenterC73#2242
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
1. #17988988C2semidirect
3. #17988391C2semidirect
6. C16×Dic73C2semidirect
7. #358×C73C2semidirect
67. C73#2242semidirect
71. #358D73semidirect