Finite Group Databasebeta

← #22612108

Subgroups — #22612108

Order 9344.

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

normal subgroups only

This group has 120 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#17988989C211yesmaximal, characteristic, complemented
2#17988705C211yesmaximal, characteristic
3#17988410C212yesmaximal, complemented
4#17988398C212yesmaximal
5#364×C73C211yesmaximal, characteristic, complemented
6#14556613C2211yescharacteristic
7#14556597—21no—
8#14556583—21no—
9#14556527C2211yescharacteristic
10#14556525—21no—
11#14556523C2212yes—
12#14556519—21no—
13M32×C73C2212yes—
14C4×C8×C73C2211yescharacteristic
15#11924028—21no—
16Dic292Q811yescharacteristic
17#11924017—21no—
18D584Q811yescharacteristic
19#11924012—21no—
20#11924011—41no—
21C8×D73—41no—
22C4⋊Dic73—22no—
23#11924007—42no—
24C2×C8×C73D411yescharacteristic
25C2×C8×C73C2311yescharacteristic
26C42×C73D411yescharacteristic
27C16×C73—22no—
28C2×C4×C73—21no—
29C2×C4×C73C2×D411yescharacteristic
30C22⋊D73—41no—
31C2×Dic73—42no—
32D292—21no—
33C4×D73—41no—
34Dic146—21no—
35C8×C73SD1611yescharacteristic
36C8×C73SD1611yescharacteristic
37C8×C73C2×Q811yescharacteristic
38C8×C73#4111yescharacteristic
39#10596831—41no—
40C22×C73AGL(1,ℤ/8)11yescharacteristic
41C2×D73—41no—
42C4×C73—41no—
43C4×C73C22⋊Q811yescharacteristic
44C4×C73C2×SD1611yescharacteristic
45Dic73—41no—
46Dic73—82no—
47C2×C73—21no—
48C2×C73#47611yescharacteristic
49D73—81no—
50#2231—731nomaximal, Sylow
51C73#223111yescharacteristic, complemented, Sylow
52#499—731no—
53#443—731no—
54#365—732no—
55#364D7311yescharacteristic, complemented
56#360—732no—
57#135—731no—
58#131—1461no—
59#125—1461no—
60M32C2×D7312yes—
61#108—731no—
62#107—1461no—
63#106—732no—
64#104—1461no—
65C4×C8C2×D7311yescharacteristic
66#41—1461no—
67Q16—731no—
68SD16—1461no—
69D8—731no—
70M16—2921no—
71M16—1461no—
72C2×C8—2921no—
73C2×C8D29211yescharacteristic
74C2×C8C22×D7311yescharacteristic
75C4⋊C4—2922no—
76C4⋊C4—1462no—
77C42D29211yescharacteristic
78C16—22no—
79Q8—1461no—
80D4—2921no—
81D4—1461no—
82C2×C4—21no—
83C2×C4—2921no—
84C2×C4—2922no—
85C2×C4C2×D29211yescharacteristic
86C8—2921no—
87C8#1192401711yescharacteristic
88C8#1192401711yescharacteristic
89C8Q8×D7311yescharacteristic
90C8#1192402711yescharacteristic
91C22—2921no—
92C22#1455661911yescharacteristic
93C4—41no—
94C4—2921no—
95C4—5842no—
96C4#1455657111yescharacteristic
97C4C2×#1192401711yescharacteristic
98C2—21no—
99C2—5841no—
100C2#1798887811yescharacteristic
subgroupG/H
centerC2#17988878
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#364×C73C2
socleC2×C73#476
hypercenter#364D73
hypocenterC73#2231
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #364

Complements

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

NH ≅ G/Ntype
1. #17988989C2semidirect
3. #17988410C2semidirect
5. #364×C73C2semidirect
51. C73#2231semidirect
55. #364D73semidirect