Finite Group Databasebeta

← #22612000

Subgroups — #22612000

Order 9344.

154 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 49 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#17989022C211yesmaximal, characteristic
3#17988971C211yesmaximal, characteristic, complemented
4#17988408C211yesmaximal, characteristic, complemented
5#17988402C211yesmaximal, characteristic, complemented
6#17988399C211yesmaximal, characteristic, complemented
7#443×C73C211yesmaximal, characteristic, complemented
8C2×Dic292C2211yescharacteristic
9C2×#11924017—21no—
10C2×D584C2211yescharacteristic
11#14556579—21no—
12#14556537—21no—
13#14556535—21no—
14#14556534—21no—
15#14556532—21no—
16#14556531C2211yescharacteristic
17#14556531C2211yescharacteristic
18#135×C73C2211yescharacteristic
19#131×C73—21no—
20#108×C73C2211yescharacteristic
21#104×C73—21no—
22C4×C8×C73C2211yescharacteristic
23C2×Dic146—21no—
24C2×D292—21no—
25Dic292—21no—
26Dic292—21no—
27#11924017—41no—
28#11924017—41no—
29D584—21no—
30D584—21no—
31#11924005—42no—
32#11924003—21no—
33#11924003—21no—
34#41×C73—21no—
35Q16×C73D411yescharacteristic
36SD16×C73—21no—
37D8×C73D411yescharacteristic
38M16×C73—21no—
39M16×C73—41no—
40C2×C8×C73—41no—
41C2×C8×C73D411yescharacteristic
42C2×C8×C73C2311yescharacteristic
43C42×C73D411yescharacteristic
44C22×D73—41no—
45Q8×C73—21no—
46D4×C73—21no—
47D4×C73—41no—
48C2×C4×C73—21no—
49C2×C4×C73—41no—
50C2×C4×C73C2×D411yescharacteristic
51C2×Dic73—41no—
52D292—41no—
53D292—41no—
54Dic146—41no—
55Dic146—41no—
56C8×C73—41no—
57C8×C73D811yescharacteristic
58C8×C73D811yescharacteristic
59C8×C73C2×D411yescharacteristic
60C8×C73#4111yescharacteristic
61C22×C73—41no—
62C22×C73AGL(1,ℤ/8)11yescharacteristic
63C2×D73—82no—
64C2×D73—81no—
65C4×C73—41no—
66C4×C73—41no—
67C4×C73#12111yescharacteristic
68C4×C73C2×D811yescharacteristic
69Dic73—81no—
70C2×C73—21no—
71C2×C73—81no—
72C2×C73#45911yescharacteristic
73D73—161no—
74#2212—731nomaximal, Sylow
75C73#221211yescharacteristic, complemented, Sylow
76#510—731no—
77#509—731no—
78#495—731no—
79#443D7311yescharacteristic, complemented
80#364—731no—
81#362—731no—
82#361—731no—
83#135C2×D7311yescharacteristic
84C2×Q16—731no—
85C2×SD16—1461no—
86C2×D8—731no—
87#131—21no—
88#124—1461no—
89Q32—1461no—
90SD32—1461no—
91SD32—1461no—
92D16—1461no—
93M32—731no—
94M32—731no—
95#108C2×D7311yescharacteristic
96#104—21no—
97C4×C8C2×D7311yescharacteristic
98#41—21no—
99C2×Q8—1461no—
100C2×D4—1461no—
101Q16—1461no—
102Q16—1461no—
103Q16D29211yescharacteristic
104SD16—21no—
105SD16—2921no—
106SD16—2921no—
107D8—1461no—
108D8—1461no—
109D8D29211yescharacteristic
110M16—21no—
111M16—41no—
112C2×C8—41no—
113C2×C8C22⋊D7311yescharacteristic
114C2×C8C22×D7311yescharacteristic
115C22⋊C4—2922no—
116C42C22⋊D7311yescharacteristic
117C16—1461no—
118C16—1461no—
119C23—2921no—
120Q8—21no—
121Q8—2921no—
122Q8—2921no—
123D4—21no—
124D4—41no—
125D4—2921no—
126D4—2921no—
127C2×C4—21no—
128C2×C4—41no—
129C2×C4—2921no—
130C2×C4C2×C22⋊D7311yescharacteristic
131C8—41no—
132C8#1192401311yescharacteristic
133C8#1192401311yescharacteristic
134C8C2×D29211yescharacteristic
135C8#1192402811yescharacteristic
136C22—41no—
137C22—5842no—
138C22—5841no—
139C22#1455661611yescharacteristic
140C4—41no—
141C4—41no—
142C4—5841no—
143C4#1455656511yescharacteristic
144C4C2×#1192401311yescharacteristic
145C2—21no—
146C2—81no—
147C2—11681no—
148C2#1798878211yescharacteristic
subgroupG/H
centerC2#17988782
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#443×C73C2
socleC2×C73#459
hypercenter#443D73
hypocenterC73#2212
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #17989027C2semidirect
3. #17988971C2semidirect
4. #17988408C2semidirect
5. #17988402C2semidirect
6. #17988399C2semidirect
7. #443×C73C2semidirect
75. C73#2212semidirect
79. #443D73semidirect