Finite Group Databasebeta

← #22612141

Subgroups — #22612141

Order 9344.

132 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 45 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#17988829C211yesmaximal, characteristic
2#17988624C211yesmaximal, characteristic
3#17988414C211yesmaximal, characteristic, complemented
4#17988392C211yesmaximal, characteristic, complemented
5#17988390C211yesmaximal, characteristic, complemented
6#17988366C211yesmaximal, characteristic
7#366×C73C211yesmaximal, characteristic, complemented
8C2×Dic292C2211yescharacteristic
9C2×C8×D73C2211yescharacteristic
10#14556571—21no—
11#14556549—21no—
12C2×#11924003C2211yescharacteristic
13#14556525C2211yescharacteristic
14#14556522—21no—
15#14556514—21no—
16C2×C16×C73C2211yescharacteristic
17#107×C73C2211yescharacteristic
18#107×C73C2211yescharacteristic
19C2×Dic146—21no—
20C2×C4×D73D411yescharacteristic
21Dic292—21no—
22Dic292—21no—
23C2×#10596831D411yescharacteristic
24C8×D73—21no—
25C8×D73—21no—
26C4⋊Dic73—21no—
27C4⋊Dic73—41no—
28#11924005—41no—
29#11924005—41no—
30C4×Dic73—41no—
31#11924003—21no—
32C2×C8×C73C2311yescharacteristic
33C4⋊C4×C73—21no—
34C4⋊C4×C73—21no—
35C16×C73—21no—
36C22×D73D811yescharacteristic
37C2×C4×C73—41no—
38C2×C4×C73—41no—
39C2×C4×C73C2×D411yescharacteristic
40C2×Dic73—41no—
41C2×Dic73—41no—
42C2×Dic73D811yescharacteristic
43C4×D73—21no—
44C4×D73—21no—
45Dic146—41no—
46Dic146—41no—
47C8×C73#4111yescharacteristic
48C8×C73#4111yescharacteristic
49#10596831—21no—
50C22×C73C2×D811yescharacteristic
51C2×D73—21no—
52C2×D73—21no—
53C2×D73—21no—
54C4×C73—81no—
55C4×C73—81no—
56C4×C73#12311yescharacteristic
57C4×C73#13711yescharacteristic
58Dic73—21no—
59Dic73—81no—
60Dic73—81no—
61C2×C73#48011yescharacteristic
62C2×C73#50811yescharacteristic
63C2×C73#51011yescharacteristic
64D73—41no—
65#2237—731nomaximal, Sylow
66C73#223711yescharacteristic, complemented, Sylow
67#467—731no—
68#427—731no—
69#367—731no—
70#366D7311yescharacteristic, complemented
71#358—731no—
72#358—731no—
73C22⋊C16—731no—
74C2×Q16—731no—
75C22×C8—731no—
76C22⋊Q8—1461no—
77#117—1461no—
78C2×C16—731no—
79C2×C16C2×D7311yescharacteristic
80#107—731no—
81#107C2×D7311yescharacteristic
82#107C2×D7311yescharacteristic
83#106—1461no—
84#103—1461no—
85C2×Q8—1461no—
86C22×C4—731no—
87Q16—1461no—
88Q16—1461no—
89C2×C8—731no—
90C2×C8—1461no—
91C2×C8—1461no—
92C2×C8C22×D7311yescharacteristic
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—2921no—
96C4⋊C4—1461no—
97C22⋊C4—2921no—
98C22⋊C4—2921no—
99C42—2921no—
100C16—21no—
101C16—1461no—
102C23—731no—
103Q8—2921no—
104Q8—2921no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—2921no—
108C2×C4—2921no—
109C2×C4—731no—
110C2×C4—1461no—
111C2×C4—1461no—
112C2×C4D4×D7311yescharacteristic
113C8—1461no—
114C8#1192402811yescharacteristic
115C8#1192402911yescharacteristic
116C22—1461no—
117C22—1461no—
118C22—1461no—
119C22D8×D7311yescharacteristic
120C4—81no—
121C4—81no—
122C4—5841no—
123C4—5841no—
124C4—1461no—
125C4#1455657611yescharacteristic
126C4#1455662311yescharacteristic
127C2—2921no—
128C2#1798890211yescharacteristic
129C2#1798901611yescharacteristic
130C2#1798902911yescharacteristic
subgroupG/H
centerC22D8×D73
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#366×C73C2
socleC22×C73C2×D8
hypercenter#366D73
hypocenterC73#2237
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #366

Complements

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

NH ≅ G/Ntype
3. #17988414C2semidirect
4. #17988392C2semidirect
5. #17988390C2semidirect
7. #366×C73C2semidirect
66. C73#2237semidirect
70. #366D73semidirect