Finite Group Databasebeta

← #22612124

Subgroups — #22612124

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#17988824C211yesmaximal, characteristic
2#17988624C211yesmaximal, characteristic, complemented
3#17988412C211yesmaximal, characteristic, complemented
4#17988389C211yesmaximal, characteristic, complemented
5#17988387C211yesmaximal, characteristic, complemented
6#17988366C211yesmaximal, characteristic, complemented
7#367×C73C211yesmaximal, characteristic, complemented
8C2×D584C2211yescharacteristic
9C2×C8×D73C2211yescharacteristic
10#14556566—21no—
11#14556549—21no—
12C2×#11924003C2211yescharacteristic
13#14556525C2211yescharacteristic
14#14556522—21no—
15#14556511—21no—
16C2×C16×C73C2211yescharacteristic
17#107×C73C2211yescharacteristic
18#107×C73C2211yescharacteristic
19C2×D292—21no—
20C2×D292—41no—
21C2×C4×D73D411yescharacteristic
22D584—21no—
23D584—21no—
24C2×#10596831D411yescharacteristic
25C8×D73—21no—
26C8×D73—21no—
27C4⋊Dic73—21no—
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×D73—41no—
37C22×D73D811yescharacteristic
38C2×C4×C73—41no—
39C2×C4×C73—41no—
40C2×C4×C73C2×D411yescharacteristic
41C2×Dic73—41no—
42C2×Dic73D811yescharacteristic
43D292—41no—
44D292—41no—
45D292—82no—
46C4×D73—21no—
47C4×D73—21no—
48C8×C73#4111yescharacteristic
49C8×C73#4111yescharacteristic
50#10596831—21no—
51C22×C73C2×D811yescharacteristic
52C2×D73—21no—
53C2×D73—21no—
54C2×D73—21no—
55C2×D73—81no—
56C2×D73—81no—
57C2×D73—81no—
58C4×C73—81no—
59C4×C73—81no—
60C4×C73#12311yescharacteristic
61C4×C73#13711yescharacteristic
62Dic73—21no—
63Dic73—81no—
64C2×C73#48011yescharacteristic
65C2×C73#50811yescharacteristic
66C2×C73#50911yescharacteristic
67D73—41no—
68D73—161no—
69#2234—731nomaximal, Sylow
70C73#223411yescharacteristic, complemented, Sylow
71#466—731no—
72#427—731no—
73#367D7311yescharacteristic, complemented
74#366—731no—
75#357—731no—
76#357—731no—
77C22⋊C16—731no—
78C2×D8—731no—
79C22×C8—731no—
80#121—1461no—
81#117—1461no—
82C2×C16—731no—
83C2×C16C2×D7311yescharacteristic
84#107—731no—
85#107C2×D7311yescharacteristic
86#107C2×D7311yescharacteristic
87#106—1461no—
88#102—1461no—
89C2×D4—2921no—
90C2×D4—1461no—
91C22×C4—731no—
92D8—1461no—
93D8—1461no—
94C2×C8—731no—
95C2×C8—1461no—
96C2×C8—1461no—
97C2×C8C22×D7311yescharacteristic
98C4⋊C4—21no—
99C4⋊C4—21no—
100C4⋊C4—1461no—
101C22⋊C4—2921no—
102C22⋊C4—2921no—
103C42—2921no—
104C16—21no—
105C16—1461no—
106C23—2921no—
107C23—731no—
108D4—2921no—
109D4—2921no—
110D4—5842no—
111C2×C4—41no—
112C2×C4—41no—
113C2×C4—2921no—
114C2×C4—731no—
115C2×C4—1461no—
116C2×C4—1461no—
117C2×C4D4×D7311yescharacteristic
118C8—1461no—
119C8#1192402811yescharacteristic
120C8#1192402911yescharacteristic
121C22—5841no—
122C22—5841no—
123C22—5841no—
124C22—1461no—
125C22—1461no—
126C22—1461no—
127C22D8×D7311yescharacteristic
128C4—81no—
129C4—81no—
130C4—5841no—
131C4—1461no—
132C4#1455657611yescharacteristic
133C4#1455662311yescharacteristic
134C2—2921no—
135C2—11681no—
136C2#1798890211yescharacteristic
137C2#1798901811yescharacteristic
138C2#1798902411yescharacteristic
subgroupG/H
centerC22D8×D73
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#367×C73C2
socleC22×C73C2×D8
hypercenter#367D73
hypocenterC73#2234
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

Complements

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

NH ≅ G/Ntype
2. #17988624C2semidirect
3. #17988412C2semidirect
4. #17988389C2semidirect
5. #17988387C2semidirect
6. #17988366C2semidirect
7. #367×C73C2semidirect
70. C73#2234semidirect
73. #367D73semidirect