Finite Group Databasebeta

← #22612113

Subgroups — #22612113

Order 9344.

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

normal subgroups only

This group has 150 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#17988824C211yesmaximal, characteristic
2#107×D73C211yesmaximal, characteristic, complemented
3#17988412C211yesmaximal, characteristic, complemented
4#17988389C211yesmaximal, characteristic, complemented
5#17988387C211yesmaximal, characteristic, complemented
6#17988366C211yesmaximal, characteristic, complemented
7#366×C73C211yesmaximal, characteristic, complemented
8C2×D584C2211yescharacteristic
9C2×C8×D73C2211yescharacteristic
10#14556566—21no—
11C4⋊C4×D73—21no—
12C2×#11924003C2211yescharacteristic
13#14556525C2211yescharacteristic
14#14556524—21no—
15#14556511—21no—
16C2×C16×C73C2211yescharacteristic
17#107×C73C2211yescharacteristic
18#107×C73C2211yescharacteristic
19C2×D292—21no—
20C2×D292—41no—
21C2×C4×D73—41no—
22C2×C4×D73D411yescharacteristic
23D584—21no—
24D584—21no—
25C2×#10596831D411yescharacteristic
26C8×D73—21no—
27C8×D73—21no—
28C4⋊Dic73—21no—
29#11924007—41no—
30#11924005—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—
48C4×D73—82no—
49C8×C73#4111yescharacteristic
50C8×C73#4111yescharacteristic
51#10596831—21no—
52C22×C73C2×D811yescharacteristic
53C2×D73—21no—
54C2×D73—21no—
55C2×D73—81no—
56C2×D73—81no—
57C2×D73—81no—
58C2×D73D1612yes—
59C4×C73—81no—
60C4×C73—81no—
61C4×C73#12311yescharacteristic
62C4×C73#13711yescharacteristic
63Dic73—21no—
64Dic73—81no—
65C2×C73#48011yescharacteristic
66C2×C73C2×D1611yescharacteristic
67C2×C73#51011yescharacteristic
68D73—22no—
69D73—161no—
70#2232—731nomaximal, Sylow
71C73#223211yescharacteristic, complemented, Sylow
72#466—731no—
73C2×#107—731no—
74#366—731no—
75#366D7311yescharacteristic, complemented
76#357—731no—
77#357—731no—
78C22⋊C16—731no—
79C2×D8—731no—
80C22×C8—731no—
81#121—1461no—
82C2×C4⋊C4—1461no—
83C2×C16—731no—
84C2×C16C2×D7311yescharacteristic
85#107—731no—
86#107—1461no—
87#107C2×D7311yescharacteristic
88#107C2×D7311yescharacteristic
89#102—1461no—
90C2×D4—2921no—
91C2×D4—1461no—
92C22×C4—2921no—
93C22×C4—731no—
94D8—1461no—
95D8—1461no—
96C2×C8—731no—
97C2×C8—1461no—
98C2×C8—1461no—
99C2×C8C22×D7311yescharacteristic
100C4⋊C4—21no—
101C4⋊C4—21no—
102C4⋊C4—2921no—
103C4⋊C4—1461no—
104C22⋊C4—2921no—
105C16—21no—
106C16—1461no—
107C23—2921no—
108C23—731no—
109D4—2921no—
110D4—2921no—
111D4—5842no—
112C2×C4—41no—
113C2×C4—41no—
114C2×C4—2921no—
115C2×C4—5842no—
116C2×C4—731no—
117C2×C4—1461no—
118C2×C4—1461no—
119C2×C4D4×D7311yescharacteristic
120C8—1461no—
121C8#1192402811yescharacteristic
122C8#1192402911yescharacteristic
123C22—5841no—
124C22—5841no—
125C22—5841no—
126C22—732no—
127C22—1461no—
128C22—1461no—
129C22D8×D7311yescharacteristic
130C4—81no—
131C4—81no—
132C4—5841no—
133C4—1461no—
134C4#1455657611yescharacteristic
135C4#1455662311yescharacteristic
136C2—11681no—
137C2—1462no—
138C2#1798890211yescharacteristic
139C2D16×D7311yescharacteristic
140C2#1798902911yescharacteristic
subgroupG/H
centerC22D8×D73
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#366×C73C2
socleC22×C73C2×D8
hypercenter#366D73
hypocenterC73#2232
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
2. #107×D73C2semidirect
3. #17988412C2semidirect
4. #17988389C2semidirect
5. #17988387C2semidirect
6. #17988366C2semidirect
7. #366×C73C2semidirect
71. C73#2232semidirect
75. #366D73semidirect