Finite Group Databasebeta

← #22611824

Subgroups — #22611824

Order 9344.

142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 53 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
2#17988710C211yesmaximal, characteristic
3#17988695C211yesmaximal, characteristic, complemented
4#17988410C211yesmaximal, characteristic, complemented
5#17988404C211yesmaximal, characteristic, complemented
6#17988398C211yesmaximal, characteristic
7#347×C73C211yesmaximal, characteristic, complemented
8#14556613C2211yescharacteristic
9C2×Dic292C2211yescharacteristic
10#14556597—21no—
11C4×Dic146—21no—
12Dic584C412yescomplemented
13#14556536C412yescomplemented
14#14556527C2211yescharacteristic
15#14556523C2211yescharacteristic
16#14556519—21no—
17#14556516—21no—
18M32×C73C2211yescharacteristic
19M32×C73C2211yescharacteristic
20#97×C73C2211yescharacteristic
21#11924028—21no—
22C2×Dic146—21no—
23Dic292—21no—
24Dic292C2×C412yes—
25Dic292C2×C411yescharacteristic
26#11924017—21no—
27D584C2×C411yescharacteristic
28#11924012—21no—
29#11924011—41no—
30C8×D73—41no—
31C4⋊Dic73—21no—
32#11924007—41no—
33C4×Dic73—41no—
34C2×C8×C73D411yescharacteristic
35C2×C8×C73C2311yescharacteristic
36C42×C73D411yescharacteristic
37C16×C73—21no—
38C16×C73C2×C412yes—
39C2×C4×C73—21no—
40C2×C4×C73C2×D411yescharacteristic
41C22⋊D73—41no—
42C2×Dic73—41no—
43C2×Dic73—41no—
44D292—21no—
45C4×D73—41no—
46Dic146—21no—
47Dic146—22no—
48Dic146—41no—
49C8×C73—21no—
50C8×C73C22×C411yescharacteristic
51C8×C73#4111yescharacteristic
52#10596831—41no—
53C22×C73AGL(1,ℤ/8)11yescharacteristic
54C2×D73—41no—
55C4×C73—41no—
56C4×C73C4×D411yescharacteristic
57C4×C73AGL(1,ℤ/8)11yescharacteristic
58Dic73—42no—
59Dic73—41no—
60Dic73—81no—
61C2×C73—21no—
62C2×C73#44211yescharacteristic
63D73—81no—
64#2180—731nomaximal, Sylow
65C73#218011yescharacteristic, complemented, Sylow
66#510—731no—
67#444—731no—
68#441—731no—
69#365—731no—
70#362—731no—
71#360—731no—
72#347D7311yescharacteristic, complemented
73#135—731no—
74C2×Q16—731no—
75#131—1461no—
76C4×Q8—1461no—
77Q32—732no—
78SD32—732no—
79M32C2×D7311yescharacteristic
80M32C2×D7311yescharacteristic
81#108—731no—
82#106—731no—
83#104—1461no—
84#103—1461no—
85#97C2×D7311yescharacteristic
86#41—1461no—
87C2×Q8—1461no—
88Q16—732no—
89Q16—731no—
90Q16—1461no—
91SD16—1461no—
92D8—731no—
93M16—2921no—
94M16—1461no—
95C2×C8—2921no—
96C2×C8D29211yescharacteristic
97C2×C8C22×D7311yescharacteristic
98C4⋊C4—2921no—
99C4⋊C4—1461no—
100C42—2921no—
101C42D29211yescharacteristic
102C16—21no—
103C16C4×D7312yes—
104Q8—2921no—
105Q8—1461no—
106Q8—1462no—
107D4—2921no—
108D4—1461no—
109C2×C4—21no—
110C2×C4—2921no—
111C2×C4—2921no—
112C2×C4—2921no—
113C2×C4C2×D29211yescharacteristic
114C8—21no—
115C8—2921no—
116C8C2×C4×D7311yescharacteristic
117C8#1192402811yescharacteristic
118C22—2921no—
119C22#1455661911yescharacteristic
120C4—41no—
121C4—2921no—
122C4—2922no—
123C4—5841no—
124C4C4×D29211yescharacteristic
125C4#1455661911yescharacteristic
126C2—21no—
127C2—5841no—
128C2#1798870011yescharacteristic
subgroupG/H
centerC2#17988700
commutatorC8×C73C22×C4
FrattiniC2×C8C22×D73
Fitting#347×C73C2
socleC2×C73#442
hypercenter#347D73
hypocenterC73#2180
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #347

Complements

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

NH ≅ G/Ntype
3. #17988695C2semidirect
4. #17988410C2semidirect
5. #17988404C2semidirect
7. #347×C73C2semidirect
12. Dic584C4semidirect
13. #14556536C4semidirect
65. C73#2180semidirect
72. #347D73semidirect