Finite Group Databasebeta

← #22612099

Subgroups — #22612099

Order 9344.

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

normal subgroups only

This group has 126 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#17988705C211yesmaximal, characteristic
2#17988409C212yesmaximal, complemented
3#17988408C211yesmaximal, characteristic, complemented
4#17988396C212yesmaximal
5#498×C73C211yesmaximal, characteristic, complemented
6#14556613C2211yescharacteristic
7#14556597—21no—
8#14556531C2212yes—
9#14556527C2211yescharacteristic
10#14556519—21no—
11C4⋊Q8×C73—21no—
12#106×C73—21no—
13#106×C73C2212yes—
14C4×C8×C73C2211yescharacteristic
15#11924028—21no—
16Dic292Q811yescharacteristic, complemented
17#11924017—21no—
18D584Q811yescharacteristic, complemented
19#11924012—21no—
20#11924011—41no—
21C8×D73—41no—
22#11924003—22no—
23C2×Q8×C73—41no—
24C2×C8×C73D411yescharacteristic
25C2×C8×C73C2311yescharacteristic
26C4⋊C4×C73—22no—
27C4⋊C4×C73—41no—
28C42×C73D411yescharacteristic
29Q8×C73—82no—
30C2×C4×C73—21no—
31C2×C4×C73—42no—
32C2×C4×C73C2×D411yescharacteristic
33C22⋊D73—41no—
34D292—21no—
35C4×D73—41no—
36Dic146—21no—
37C8×C73SD1611yescharacteristic
38C8×C73SD1611yescharacteristic
39C8×C73C2×Q811yescharacteristic
40C8×C73#4111yescharacteristic
41#10596831—41no—
42C22×C73AGL(1,ℤ/8)11yescharacteristic
43C2×D73—41no—
44C4×C73—22no—
45C4×C73—82no—
46C4×C73C22⋊Q811yescharacteristic
47C4×C73C2×SD1611yescharacteristic
48Dic73—41no—
49C2×C73—21no—
50C2×C73#47611yescharacteristic
51D73—81no—
52#2230—731nomaximal, Sylow
53C73#223011yescharacteristic, complemented, Sylow
54#498D7311yescharacteristic, complemented
55#443—731no—
56#365—732no—
57#364—731no—
58#360—732no—
59#135—731no—
60#131—1461no—
61C4⋊Q8—21no—
62M32—732no—
63#108—731no—
64#106—21no—
65#106C2×D7312yes—
66#104—1461no—
67C4×C8C2×D7311yescharacteristic
68#41—1461no—
69C2×Q8—41no—
70Q16—731no—
71SD16—1461no—
72D8—731no—
73M16—2921no—
74M16—1461no—
75C2×C8—2921no—
76C2×C8C22⋊D7311yescharacteristic
77C2×C8C22×D7311yescharacteristic
78C4⋊C4—22no—
79C4⋊C4—41no—
80C42C22⋊D7311yescharacteristic
81C16—1462no—
82Q8—82no—
83Q8—1461no—
84D4—2921no—
85D4—1461no—
86C2×C4—21no—
87C2×C4—42no—
88C2×C4—2921no—
89C2×C4C2×C22⋊D7311yescharacteristic
90C8—2921no—
91C8#1192401511yescharacteristic
92C8#1192401511yescharacteristic
93C8Q8×D7311yescharacteristic
94C8#1192402911yescharacteristic
95C22—2921no—
96C22#1455661711yescharacteristic
97C4—22no—
98C4—82no—
99C4—2921no—
100C4#1455656711yescharacteristic
101C4C2×#1192401511yescharacteristic
102C2—21no—
103C2—5841no—
104C2#1798887411yescharacteristic
subgroupG/H
centerC2#17988874
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#498×C73C2
socleC2×C73#476
hypercenter#498D73
hypocenterC73#2230
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #498

Complements

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

NH ≅ G/Ntype
2. #17988409C2semidirect
3. #17988408C2semidirect
5. #498×C73C2semidirect
16. Dic292Q8semidirect
18. D584Q8semidirect
53. C73#2230semidirect
54. #498D73semidirect