Finite Group Databasebeta

← #22611998

Subgroups — #22611998

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#17989027C211yesmaximal, characteristic, complemented
2#17988970C211yesmaximal, characteristic, complemented
3#17988704C211yesmaximal, characteristic, complemented
4#17988407C211yesmaximal, characteristic, complemented
5#17988404C211yesmaximal, characteristic, complemented
6#17988400C211yesmaximal, characteristic, complemented
7#509×C73C211yesmaximal, characteristic
8C2×Dic292C2211yescharacteristic
9C2×#11924016—21no—
10#14556598—21no—
11#14556578—21no—
12#14556537—21no—
13#14556535—21no—
14#14556531C2211yescharacteristic
15#14556527C2211yescharacteristic
16#14556518—21no—
17C8×Dic73C2211yescharacteristic
18#135×C73C2211yescharacteristic
19C2×D8×C73C2211yescharacteristic
20SD32×C73—21no—
21D16×C73—21no—
22M32×C73C2211yescharacteristic
23C2×Dic146—21no—
24Dic292—21no—
25Dic292—21no—
26#11924016—41no—
27#11924016—41no—
28#11924012—21no—
29#11924012—41no—
30C2×#10596831—41no—
31C2×#10596831D411yescharacteristic
32C22⋊Dic73—42no—
33C4×Dic73D411yescharacteristic
34#11924003—21no—
35#41×C73—21no—
36C2×D4×C73—21no—
37Q16×C73D411yescharacteristic
38SD16×C73—21no—
39D8×C73—21no—
40D8×C73—21no—
41D8×C73D411yescharacteristic
42C2×C8×C73C2311yescharacteristic
43C16×C73—21no—
44C23×C73—41no—
45Q8×C73—21no—
46D4×C73—21no—
47D4×C73—41no—
48D4×C73—41no—
49D4×C73—41no—
50C2×C4×C73—41no—
51C2×C4×C73C2×D411yescharacteristic
52C2×Dic73—21no—
53C2×Dic73—41no—
54Dic146—41no—
55Dic146—41no—
56C8×C73C2×D411yescharacteristic
57C8×C73#4111yescharacteristic
58#10596831—41no—
59#10596831D811yescharacteristic
60#10596831D811yescharacteristic
61C22×C73—41no—
62C22×C73—82no—
63C22×C73—81no—
64C22×C73AGL(1,ℤ/8)11yescharacteristic
65C4×C73—41no—
66C4×C73#12111yescharacteristic
67C4×C73C2×D811yescharacteristic
68Dic73—41no—
69Dic73—81no—
70C2×C73—21no—
71C2×C73—81no—
72C2×C73—161no—
73C2×C73#45911yescharacteristic
74#2212—731nomaximal, Sylow
75C73#221211yescharacteristic, complemented, Sylow
76#510—731no—
77#509D7311yescharacteristic
78#495—731no—
79#443—731no—
80#364—731no—
81#362—731no—
82#361—731no—
83#135C2×D7311yescharacteristic
84C2×Q16—731no—
85C2×SD16—1461no—
86C2×D8C2×D7311yescharacteristic
87#131—1461no—
88#124—1461no—
89Q32—1461no—
90SD32—21no—
91SD32—1461no—
92D16—21no—
93M32—731no—
94M32C2×D7311yescharacteristic
95#108—731no—
96#104—1461no—
97C4×C8—731no—
98#41—21no—
99C2×Q8—1461no—
100C2×D4—21no—
101Q16—1461no—
102Q16—1461no—
103Q16C22⋊D7311yescharacteristic
104SD16—21no—
105SD16—2921no—
106SD16—2921no—
107D8—21no—
108D8—21no—
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—41no—
120Q8—21no—
121Q8—2921no—
122Q8—2921no—
123D4—21no—
124D4—41no—
125D4—41no—
126D4—41no—
127C2×C4—41no—
128C2×C4—2921no—
129C2×C4—1461no—
130C2×C4D4×D7311yescharacteristic
131C8—2921no—
132C8—731no—
133C8—731no—
134C8C2×C22⋊D7311yescharacteristic
135C8#1192402711yescharacteristic
136C22—41no—
137C22—82no—
138C22—81no—
139C22#1455661511yescharacteristic
140C4—41no—
141C4—2921no—
142C4—5841no—
143C4#1455656311yescharacteristic
144C4D8×D7311yescharacteristic
145C2—21no—
146C2—81no—
147C2—161no—
148C2#1798878011yescharacteristic
subgroupG/H
centerC2#17988780
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#509×C73C2
socleC2×C73#459
hypercenter#509D73
hypocenterC73#2212
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #17989027C2semidirect
2. #17988970C2semidirect
3. #17988704C2semidirect
4. #17988407C2semidirect
5. #17988404C2semidirect
6. #17988400C2semidirect
75. C73#2212semidirect