Finite Group Databasebeta

← #22612002

Subgroups — #22612002

Order 9344.

154 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 45 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#17989022C211yesmaximal, characteristic
2#17988972C211yesmaximal, characteristic, complemented
3#17988704C211yesmaximal, characteristic, complemented
4#17988407C211yesmaximal, characteristic, complemented
5#17988403C211yesmaximal, characteristic, complemented
6#17988401C211yesmaximal, characteristic, complemented
7#510×C73C211yesmaximal, characteristic, complemented
8C2×#11924015—21no—
9C2×D584C2211yescharacteristic
10#14556598—21no—
11#14556580—21no—
12#14556534—21no—
13#14556532—21no—
14#14556531C2211yescharacteristic
15#14556527C2211yescharacteristic
16#14556518—21no—
17C8×Dic73C2211yescharacteristic
18#135×C73C2211yescharacteristic
19C2×Q16×C73C2211yescharacteristic
20Q32×C73—21no—
21SD32×C73—21no—
22M32×C73C2211yescharacteristic
23C2×D292—21no—
24#11924015—41no—
25#11924015—41no—
26D584—21no—
27D584—21no—
28#11924012—21no—
29#11924012—41no—
30C2×#10596831—41no—
31C2×#10596831D411yescharacteristic
32#11924005—42no—
33C4×Dic73D411yescharacteristic
34#11924003—21no—
35#41×C73—21no—
36C2×Q8×C73—21no—
37Q16×C73—21no—
38Q16×C73—21no—
39Q16×C73D411yescharacteristic
40SD16×C73—21no—
41D8×C73D411yescharacteristic
42C2×C8×C73C2311yescharacteristic
43C16×C73—21no—
44C22×D73—41no—
45Q8×C73—21no—
46Q8×C73—41no—
47Q8×C73—41no—
48D4×C73—21no—
49D4×C73—41no—
50C2×C4×C73—41no—
51C2×C4×C73—41no—
52C2×C4×C73C2×D411yescharacteristic
53C2×Dic73—21no—
54D292—41no—
55D292—41no—
56C8×C73C2×D411yescharacteristic
57C8×C73#4111yescharacteristic
58#10596831—41no—
59#10596831D811yescharacteristic
60#10596831D811yescharacteristic
61C22×C73—41no—
62C22×C73AGL(1,ℤ/8)11yescharacteristic
63C2×D73—82no—
64C2×D73—81no—
65C4×C73—41no—
66C4×C73—81no—
67C4×C73#12111yescharacteristic
68C4×C73C2×D811yescharacteristic
69Dic73—41no—
70C2×C73—21no—
71C2×C73—81no—
72C2×C73#45911yescharacteristic
73D73—161no—
74#2212—731nomaximal, Sylow
75C73#221211yescharacteristic, complemented, Sylow
76#510D7311yescharacteristic, complemented
77#509—731no—
78#495—731no—
79#443—731no—
80#364—731no—
81#362—731no—
82#361—731no—
83#135C2×D7311yescharacteristic
84C2×Q16C2×D7311yescharacteristic
85C2×SD16—1461no—
86C2×D8—731no—
87#131—1461no—
88#124—1461no—
89Q32—21no—
90SD32—21no—
91SD32—1461no—
92D16—1461no—
93M32—731no—
94M32C2×D7311yescharacteristic
95#108—731no—
96#104—1461no—
97C4×C8—731no—
98#41—21no—
99C2×Q8—21no—
100C2×D4—1461no—
101Q16—21no—
102Q16—21no—
103Q16C22⋊D7311yescharacteristic
104SD16—21no—
105SD16—2921no—
106SD16—2921no—
107D8—1461no—
108D8—1461no—
109D8C22⋊D7311yescharacteristic
110M16—2921no—
111M16—1461no—
112C2×C8—2921no—
113C2×C8—731no—
114C2×C8C22×D7311yescharacteristic
115C22⋊C4—2922no—
116C42—731no—
117C16—21no—
118C16—1461no—
119C23—2921no—
120Q8—21no—
121Q8—41no—
122Q8—41no—
123D4—21no—
124D4—41no—
125D4—2921no—
126D4—2921no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—1461no—
130C2×C4D4×D7311yescharacteristic
131C8—2921no—
132C8—731no—
133C8—731no—
134C8C2×C22⋊D7311yescharacteristic
135C8#1192402711yescharacteristic
136C22—41no—
137C22—5842no—
138C22—5841no—
139C22#1455661511yescharacteristic
140C4—41no—
141C4—81no—
142C4—2921no—
143C4#1455656311yescharacteristic
144C4D8×D7311yescharacteristic
145C2—21no—
146C2—81no—
147C2—11681no—
148C2#1798878011yescharacteristic
subgroupG/H
centerC2#17988780
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#510×C73C2
socleC2×C73#459
hypercenter#510D73
hypocenterC73#2212
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. #17988972C2semidirect
3. #17988704C2semidirect
4. #17988407C2semidirect
5. #17988403C2semidirect
6. #17988401C2semidirect
7. #510×C73C2semidirect
75. C73#2212semidirect
76. #510D73semidirect