Finite Group Databasebeta

← #22611999

Subgroups — #22611999

Order 9344.

154 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 43 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#17989030C211yesmaximal, characteristic, complemented
2#17989023C211yesmaximal, characteristic
3#17988970C211yesmaximal, characteristic, complemented
4#17988703C211yesmaximal, characteristic, complemented
5#17988407C211yesmaximal, characteristic, complemented
6#17988402C211yesmaximal, characteristic, complemented
7#361×C73C211yesmaximal, characteristic, complemented
8#14556613C2211yescharacteristic
9C2×Dic292C2211yescharacteristic
10C2×#11924016—21no—
11#14556599—21no—
12#14556578—21no—
13Dic584—21no—
14#14556536—21no—
15#14556535—21no—
16#14556532—21no—
17#14556531C2211yescharacteristic
18#14556517—21no—
19C8×Dic73C2211yescharacteristic
20C2×D8×C73C2211yescharacteristic
21M32×C73C2211yescharacteristic
22#108×C73C2211yescharacteristic
23#11924028—21no—
24C2×Dic146—21no—
25Dic292—21no—
26Dic292—21no—
27Dic292D411yescharacteristic
28#11924017—21no—
29#11924016—41no—
30#11924016—41no—
31D584D411yescharacteristic
32#11924011—41no—
33C2×#10596831D411yescharacteristic
34C8×D73—41no—
35C22⋊Dic73—42no—
36C4×Dic73D411yescharacteristic
37#11924003—21no—
38C2×D4×C73—21no—
39D8×C73—21no—
40D8×C73—21no—
41M16×C73—21no—
42C2×C8×C73C2311yescharacteristic
43C16×C73—21no—
44C23×C73—41no—
45D4×C73—41no—
46D4×C73—41no—
47C2×C4×C73C2×D411yescharacteristic
48C22⋊D73—41no—
49C2×Dic73—21no—
50C2×Dic73—41no—
51D292—21no—
52C4×D73—41no—
53Dic146—21no—
54Dic146—41no—
55Dic146—41no—
56C8×C73—41no—
57C8×C73C2×D411yescharacteristic
58C8×C73#4111yescharacteristic
59#10596831D811yescharacteristic
60#10596831D811yescharacteristic
61C22×C73—82no—
62C22×C73—81no—
63C22×C73AGL(1,ℤ/8)11yescharacteristic
64C2×D73—41no—
65C4×C73#12111yescharacteristic
66C4×C73C2×D811yescharacteristic
67Dic73—41no—
68Dic73—41no—
69Dic73—81no—
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#495—731no—
79#443—731no—
80#364—731no—
81#362—731no—
82#361D7311yescharacteristic, complemented
83#135—731no—
84C2×Q16—731no—
85C2×SD16—1461no—
86C2×D8C2×D7311yescharacteristic
87#131—1461no—
88#124—1461no—
89Q32—1461no—
90SD32—1461no—
91SD32—1461no—
92D16—1461no—
93M32—731no—
94M32C2×D7311yescharacteristic
95#108C2×D7311yescharacteristic
96#104—1461no—
97C4×C8—731no—
98#41—1461no—
99C2×Q8—1461no—
100C2×D4—21no—
101Q16—731no—
102Q16—1461no—
103Q16—1461no—
104SD16—2921no—
105SD16—2921no—
106SD16—1461no—
107D8—21no—
108D8—21no—
109D8—731no—
110M16—21no—
111M16—2921no—
112C2×C8—2921no—
113C2×C8—731no—
114C2×C8C22×D7311yescharacteristic
115C22⋊C4—2922no—
116C42—731no—
117C16—21no—
118C16—1461no—
119C23—41no—
120Q8—2921no—
121Q8—2921no—
122Q8—1461no—
123D4—41no—
124D4—41no—
125D4—2921no—
126D4—1461no—
127C2×C4—2921no—
128C2×C4—2921no—
129C2×C4—1461no—
130C2×C4D4×D7311yescharacteristic
131C8—41no—
132C8—731no—
133C8—731no—
134C8D4×D7311yescharacteristic
135C8#1192402811yescharacteristic
136C22—82no—
137C22—81no—
138C22—2921no—
139C22#1455661811yescharacteristic
140C4—2921no—
141C4—2921no—
142C4—5841no—
143C4#1455656411yescharacteristic
144C4D8×D7311yescharacteristic
145C2—21no—
146C2—161no—
147C2—5841no—
148C2#1798878111yescharacteristic
subgroupG/H
centerC2#17988781
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#361×C73C2
socleC2×C73#459
hypercenter#361D73
hypocenterC73#2212
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
1. #17989030C2semidirect
3. #17988970C2semidirect
4. #17988703C2semidirect
5. #17988407C2semidirect
6. #17988402C2semidirect
7. #361×C73C2semidirect
75. C73#2212semidirect
82. #361D73semidirect