Finite Group Databasebeta

← #22612013

Subgroups — #22612013

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#17989030C212yesmaximal
2#17988967C211yesmaximal, characteristic, complemented
3#17988705C211yesmaximal, characteristic
4#17988404C212yesmaximal, complemented
5#364×C73C211yesmaximal, characteristic, complemented
6#14556613C2211yescharacteristic
7C2×Dic292—21no—
8C2×Dic292C2212yes—
9#14556597—21no—
10#14556591—21no—
11Dic584—22no—
12#14556536—22no—
13#14556527C2211yescharacteristic
14#14556519—21no—
15M32×C73C2212yes—
16C4×C8×C73C2211yescharacteristic
17#11924028—21no—
18C2×Dic146—22no—
19Dic292—22no—
20Dic292—22no—
21Dic292—41no—
22Dic292—41no—
23Dic292D411yescharacteristic
24#11924017—21no—
25D584D411yescharacteristic
26#11924012—21no—
27#11924011—41no—
28C8×D73—41no—
29C4⋊Dic73—42no—
30C2×C8×C73D411yescharacteristic
31C2×C8×C73C2311yescharacteristic
32C42×C73D411yescharacteristic
33C16×C73—22no—
34C2×C4×C73—21no—
35C2×C4×C73C2×D411yescharacteristic
36C22⋊D73—41no—
37C2×Dic73—42no—
38D292—21no—
39C4×D73—41no—
40Dic146—21no—
41Dic146—42no—
42Dic146—42no—
43C8×C73D811yescharacteristic
44C8×C73D811yescharacteristic
45C8×C73C2×D411yescharacteristic
46C8×C73#4111yescharacteristic
47#10596831—41no—
48C22×C73AGL(1,ℤ/8)11yescharacteristic
49C2×D73—41no—
50C4×C73—22no—
51C4×C73#12111yescharacteristic
52C4×C73C2×D811yescharacteristic
53Dic73—41no—
54Dic73—82no—
55C2×C73—21no—
56C2×C73#45911yescharacteristic
57D73—81no—
58#2214—731nomaximal, Sylow
59C73#221411yescharacteristic, complemented, Sylow
60#510—732no—
61#494—731no—
62#443—731no—
63#364D7311yescharacteristic, complemented
64#362—732no—
65#135—731no—
66C2×Q16—732no—
67C2×Q16—1461no—
68#131—1461no—
69C4⋊Q8—1461no—
70Q32—1462no—
71SD32—1462no—
72M32C2×D7312yes—
73#108—731no—
74#104—1461no—
75C4×C8C2×D7311yescharacteristic
76#41—1461no—
77C2×Q8—1462no—
78Q16—2921no—
79Q16—2921no—
80Q16—731no—
81Q16—1462no—
82Q16—1462no—
83SD16—1461no—
84D8—731no—
85M16—2921no—
86M16—1461no—
87C2×C8—2921no—
88C2×C8D29211yescharacteristic
89C2×C8C22×D7311yescharacteristic
90C4⋊C4—2922no—
91C42D29211yescharacteristic
92C16—22no—
93Q8—2922no—
94Q8—2922no—
95Q8—1461no—
96D4—2921no—
97D4—1461no—
98C2×C4—21no—
99C2×C4—2921no—
100C2×C4—2922no—
101C2×C4C2×D29211yescharacteristic
102C8—2921no—
103C8D58411yescharacteristic
104C8D58411yescharacteristic
105C8D4×D7311yescharacteristic
106C8#1192402911yescharacteristic
107C22—2921no—
108C22#1455661911yescharacteristic
109C4—22no—
110C4—2921no—
111C4—5842no—
112C4#1455656611yescharacteristic
113C4C2×D58411yescharacteristic
114C2—21no—
115C2—5841no—
116C2#1798878311yescharacteristic
subgroupG/H
centerC2#17988783
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#364×C73C2
socleC2×C73#459
hypercenter#364D73
hypocenterC73#2214
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
2. #17988967C2semidirect
4. #17988404C2semidirect
5. #364×C73C2semidirect
59. C73#2214semidirect
63. #364D73semidirect