Finite Group Databasebeta

← #22612087

Subgroups — #22612087

Order 9344.

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

normal subgroups only

This group has 136 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#17988669C211yesmaximal, characteristic
3#17988412C211yesmaximal, characteristic, complemented
4#17988405C211yesmaximal, characteristic, complemented
5#17988389C211yesmaximal, characteristic
6#17988387C211yesmaximal, characteristic
7#367×C73C211yesmaximal, characteristic, complemented
8C2×D584C2211yescharacteristic
9#14556582—21no—
10#14556553—21no—
11C2×#11924003C2211yescharacteristic
12#14556525C2211yescharacteristic
13#14556522—21no—
14#14556511—21no—
15C8×Dic73C2211yescharacteristic
16C2×C16×C73C2211yescharacteristic
17#107×C73C2211yescharacteristic
18#107×C73C2211yescharacteristic
19C2×D292—21no—
20C2×C4×D73—41no—
21D584—21no—
22D584Q812yes—
23C2×#10596831D411yescharacteristic
24C4⋊Dic73—21no—
25C4⋊Dic73—41no—
26#11924007—41no—
27#11924005—41no—
28C4×Dic73D411yescharacteristic
29#11924003—21no—
30C2×C8×C73C2311yescharacteristic
31C4⋊C4×C73—21no—
32C4⋊C4×C73—21no—
33C16×C73—21no—
34C22×D73—41no—
35C2×C4×C73—41no—
36C2×C4×C73—41no—
37C2×C4×C73C2×D411yescharacteristic
38C2×Dic73—41no—
39C2×Dic73D811yescharacteristic
40C2×Dic73D811yescharacteristic
41D292—22no—
42D292—41no—
43C4×D73—82no—
44C8×C73C2×Q811yescharacteristic
45C8×C73#4111yescharacteristic
46#10596831—21no—
47C22×C73C2×D811yescharacteristic
48C2×D73—42no—
49C2×D73—81no—
50C2×D73—81no—
51C4×C73—81no—
52C4×C73—81no—
53C4×C73C22⋊Q811yescharacteristic
54C4×C73#13711yescharacteristic
55Dic73—21no—
56Dic73—21no—
57Dic73—81no—
58C2×C73#47411yescharacteristic
59C2×C73#50811yescharacteristic
60C2×C73#50911yescharacteristic
61D73—82no—
62#2228—731nomaximal, Sylow
63C73#222811yescharacteristic, complemented, Sylow
64#499—731no—
65C4×D8—731no—
66#367D7311yescharacteristic, complemented
67#366—731no—
68C4⋊C16—731no—
69#357—731no—
70#357—731no—
71C2×D8—731no—
72#125—1461no—
73C4×D4—1461no—
74C2×C16—731no—
75C2×C16C2×D7311yescharacteristic
76#107—731no—
77#107C2×D7311yescharacteristic
78#107C2×D7311yescharacteristic
79#106—1461no—
80#102—1461no—
81C4×C8—731no—
82C2×D4—1461no—
83C22×C4—2921no—
84D8—732no—
85D8—1461no—
86C2×C8—731no—
87C2×C8C22×D7311yescharacteristic
88C4⋊C4—21no—
89C4⋊C4—21no—
90C4⋊C4—2921no—
91C4⋊C4—2921no—
92C4⋊C4—1461no—
93C22⋊C4—2921no—
94C42—731no—
95C16—21no—
96C16—1461no—
97C23—2921no—
98D4—2921no—
99D4—1462no—
100C2×C4—41no—
101C2×C4—41no—
102C2×C4—2921no—
103C2×C4—5842no—
104C2×C4—731no—
105C2×C4—731no—
106C2×C4D4×D7311yescharacteristic
107C8—1461no—
108C8Q8×D7311yescharacteristic
109C8#1192402811yescharacteristic
110C22—2922no—
111C22—5841no—
112C22—5841no—
113C22D8×D7311yescharacteristic
114C4—81no—
115C4—81no—
116C4—5841no—
117C4—1461no—
118C4—1461no—
119C4#1455656911yescharacteristic
120C4#1455662311yescharacteristic
121C2—5842no—
122C2#1798886611yescharacteristic
123C2#1798901811yescharacteristic
124C2#1798902411yescharacteristic
subgroupG/H
centerC22D8×D73
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#367×C73C2
socleC22×C73C2×D8
hypercenter#367D73
hypocenterC73#2228
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
1. #17988988C2semidirect
3. #17988412C2semidirect
4. #17988405C2semidirect
7. #367×C73C2semidirect
63. C73#2228semidirect
66. #367D73semidirect