Finite Group Databasebeta

← #22611997

Subgroups — #22611997

Order 9344.

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

normal subgroups only

This group has 154 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#17989028C211yesmaximal, characteristic, complemented
2#17989023C211yesmaximal, characteristic
3#17988705C211yesmaximal, characteristic, complemented
4#17988408C211yesmaximal, characteristic, complemented
5#17988403C211yesmaximal, characteristic, complemented
6#17988400C211yesmaximal, characteristic, complemented
7#495×C73C211yesmaximal, characteristic, complemented
8#14556613C2211yescharacteristic
9#14556597—21no—
10#14556537—21no—
11#14556535—21no—
12#14556534—21no—
13#14556532—21no—
14#14556531C2211yescharacteristic
15#14556531C2211yescharacteristic
16#14556527C2211yescharacteristic
17#14556519—21no—
18C2×Q16×C73C2211yescharacteristic
19C2×SD16×C73—21no—
20C2×D8×C73C2211yescharacteristic
21#124×C73—21no—
22C4×C8×C73C2211yescharacteristic
23#11924028—21no—
24Dic292D411yescharacteristic
25#11924017—21no—
26D584D411yescharacteristic
27#11924012—21no—
28#11924011—41no—
29C8×D73—41no—
30#11924003—21no—
31#11924003—21no—
32C2×Q8×C73—21no—
33C2×D4×C73—21no—
34Q16×C73—21no—
35Q16×C73—21no—
36SD16×C73—41no—
37SD16×C73—41no—
38D8×C73—21no—
39D8×C73—21no—
40C2×C8×C73D411yescharacteristic
41C2×C8×C73C2311yescharacteristic
42C22⋊C4×C73—42no—
43C42×C73D411yescharacteristic
44C23×C73—41no—
45Q8×C73—41no—
46Q8×C73—41no—
47D4×C73—41no—
48D4×C73—41no—
49C2×C4×C73—21no—
50C2×C4×C73—41no—
51C2×C4×C73C2×D411yescharacteristic
52C22⋊D73—41no—
53D292—21no—
54C4×D73—41no—
55Dic146—21no—
56C8×C73D811yescharacteristic
57C8×C73D811yescharacteristic
58C8×C73C2×D411yescharacteristic
59C8×C73#4111yescharacteristic
60#10596831—41no—
61C22×C73—82no—
62C22×C73—81no—
63C22×C73AGL(1,ℤ/8)11yescharacteristic
64C2×D73—41no—
65C4×C73—41no—
66C4×C73—81no—
67C4×C73#12111yescharacteristic
68C4×C73C2×D811yescharacteristic
69Dic73—41no—
70C2×C73—21no—
71C2×C73—161no—
72C2×C73#45911yescharacteristic
73D73—81no—
74#2212—731nomaximal, Sylow
75C73#221211yescharacteristic, complemented, Sylow
76#510—731no—
77#509—731no—
78#495D7311yescharacteristic, complemented
79#443—731no—
80#364—731no—
81#362—731no—
82#361—731no—
83#135—731no—
84C2×Q16C2×D7311yescharacteristic
85C2×SD16—21no—
86C2×D8C2×D7311yescharacteristic
87#131—1461no—
88#124—21no—
89Q32—1461no—
90SD32—1461no—
91SD32—1461no—
92D16—1461no—
93M32—731no—
94M32—731no—
95#108—731no—
96#104—1461no—
97C4×C8C2×D7311yescharacteristic
98#41—1461no—
99C2×Q8—21no—
100C2×D4—21no—
101Q16—21no—
102Q16—21no—
103Q16—731no—
104SD16—41no—
105SD16—41no—
106SD16—1461no—
107D8—21no—
108D8—21no—
109D8—731no—
110M16—2921no—
111M16—1461no—
112C2×C8—2921no—
113C2×C8C22⋊D7311yescharacteristic
114C2×C8C22×D7311yescharacteristic
115C22⋊C4—42no—
116C42C22⋊D7311yescharacteristic
117C16—1461no—
118C16—1461no—
119C23—41no—
120Q8—41no—
121Q8—41no—
122Q8—1461no—
123D4—41no—
124D4—41no—
125D4—2921no—
126D4—1461no—
127C2×C4—21no—
128C2×C4—41no—
129C2×C4—2921no—
130C2×C4C2×C22⋊D7311yescharacteristic
131C8—2921no—
132C8#1192401311yescharacteristic
133C8#1192401311yescharacteristic
134C8D4×D7311yescharacteristic
135C8#1192402711yescharacteristic
136C22—82no—
137C22—81no—
138C22—2921no—
139C22#1455661711yescharacteristic
140C4—41no—
141C4—81no—
142C4—2921no—
143C4#1455656211yescharacteristic
144C4C2×#1192401311yescharacteristic
145C2—21no—
146C2—161no—
147C2—5841no—
148C2#1798877911yescharacteristic
subgroupG/H
centerC2#17988779
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#495×C73C2
socleC2×C73#459
hypercenter#495D73
hypocenterC73#2212
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #17989028C2semidirect
3. #17988705C2semidirect
4. #17988408C2semidirect
5. #17988403C2semidirect
6. #17988400C2semidirect
7. #495×C73C2semidirect
75. C73#2212semidirect
78. #495D73semidirect