Finite Group Databasebeta

← #22612120

Subgroups — #22612120

Order 9344.

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

normal subgroups only

This group has 142 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#17988820C211yesmaximal, characteristic
2#17988624C211yesmaximal, characteristic, complemented
3#17988414C211yesmaximal, characteristic, complemented
4#17988413C211yesmaximal, characteristic, complemented
5#17988388C211yesmaximal, characteristic, complemented
6#17988366C211yesmaximal, characteristic, complemented
7#357×C73C211yesmaximal, characteristic, complemented
8C2×C8×D73C2211yescharacteristic
9#14556562—21no—
10#14556549—21no—
11C2×#11924003C2211yescharacteristic
12#14556525C2211yescharacteristic
13#14556525C2211yescharacteristic
14#14556522—21no—
15#14556512—21no—
16C2×D8×C73C2211yescharacteristic
17C2×C16×C73C2211yescharacteristic
18#107×C73C2211yescharacteristic
19C2×C22⋊D73—41no—
20C2×C4×D73D411yescharacteristic
21C2×#10596831D411yescharacteristic
22C8×D73—21no—
23C8×D73—21no—
24C4⋊Dic73—21no—
25C4⋊Dic73—21no—
26C22⋊Dic73—41no—
27#11924005—41no—
28C4×Dic73—41no—
29#11924003—21no—
30C2×D4×C73—21no—
31D8×C73—21no—
32D8×C73—21no—
33C2×C8×C73C2311yescharacteristic
34C4⋊C4×C73—21no—
35C16×C73—21no—
36C23×C73—41no—
37C22×D73D811yescharacteristic
38D4×C73—41no—
39D4×C73—41no—
40C2×C4×C73—41no—
41C2×C4×C73C2×D411yescharacteristic
42C22⋊D73—82no—
43C2×Dic73—41no—
44C2×Dic73—41no—
45C2×Dic73D811yescharacteristic
46C4×D73—21no—
47C4×D73—21no—
48C8×C73#4111yescharacteristic
49C8×C73#4111yescharacteristic
50#10596831—21no—
51C22×C73—81no—
52C22×C73—81no—
53C22×C73—81no—
54C22×C73C2×D811yescharacteristic
55C2×D73—21no—
56C2×D73—21no—
57C2×D73—21no—
58C4×C73—81no—
59C4×C73#12311yescharacteristic
60C4×C73#13711yescharacteristic
61Dic73—21no—
62Dic73—81no—
63Dic73—81no—
64C2×C73—161no—
65C2×C73#48011yescharacteristic
66C2×C73#50811yescharacteristic
67C2×C73#50911yescharacteristic
68D73—41no—
69#2234—731nomaximal, Sylow
70C73#223411yescharacteristic, complemented, Sylow
71#466—731no—
72#427—731no—
73#367—731no—
74#366—731no—
75#357—731no—
76#357D7311yescharacteristic, complemented
77C22⋊C16—731no—
78C2×D8C2×D7311yescharacteristic
79C22×C8—731no—
80#121—1461no—
81#117—1461no—
82C2×C16—731no—
83C2×C16C2×D7311yescharacteristic
84#107—731no—
85#107—731no—
86#107C2×D7311yescharacteristic
87#106—1461no—
88#102—1461no—
89C2×D4—21no—
90C2×D4—2921no—
91C22×C4—731no—
92D8—21no—
93D8—21no—
94C2×C8—731no—
95C2×C8—1461no—
96C2×C8—1461no—
97C2×C8C22×D7311yescharacteristic
98C4⋊C4—21no—
99C4⋊C4—1461no—
100C4⋊C4—1461no—
101C22⋊C4—2921no—
102C22⋊C4—2921no—
103C42—2921no—
104C16—21no—
105C16—1461no—
106C23—41no—
107C23—731no—
108D4—41no—
109D4—41no—
110D4—5842no—
111C2×C4—41no—
112C2×C4—2921no—
113C2×C4—2921no—
114C2×C4—731no—
115C2×C4—1461no—
116C2×C4—1461no—
117C2×C4D4×D7311yescharacteristic
118C8—1461no—
119C8#1192402711yescharacteristic
120C8#1192402811yescharacteristic
121C22—81no—
122C22—81no—
123C22—81no—
124C22—1461no—
125C22—1461no—
126C22—1461no—
127C22D8×D7311yescharacteristic
128C4—81no—
129C4—5841no—
130C4—5841no—
131C4—1461no—
132C4#1455657311yescharacteristic
133C4#1455662011yescharacteristic
134C2—161no—
135C2—2921no—
136C2#1798889911yescharacteristic
137C2#1798901611yescharacteristic
138C2#1798902411yescharacteristic
subgroupG/H
centerC22D8×D73
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#357×C73C2
socleC22×C73C2×D8
hypercenter#357D73
hypocenterC73#2234
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
2. #17988624C2semidirect
3. #17988414C2semidirect
4. #17988413C2semidirect
5. #17988388C2semidirect
6. #17988366C2semidirect
7. #357×C73C2semidirect
70. C73#2234semidirect
76. #357D73semidirect