Finite Group Databasebeta

← #22612011

Subgroups — #22612011

Order 9344.

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

normal subgroups only

This group has 150 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
2#17989028C211yesmaximal, characteristic
3#17988965C211yesmaximal, characteristic, complemented
4#17988703C211yesmaximal, characteristic
5#17988407C211yesmaximal, characteristic, complemented
6#17988402C211yesmaximal, characteristic, complemented
7#362×C73C211yesmaximal, characteristic, complemented
8#14556613C2211yescharacteristic
9C2×Dic292C2211yescharacteristic
10C2×#11924018—21no—
11#14556599—21no—
12#14556589—21no—
13Dic584—21no—
14#14556537—21no—
15#14556536—21no—
16#14556534—21no—
17#14556531C2211yescharacteristic
18#14556517—21no—
19C8×Dic73C2211yescharacteristic
20C2×Q16×C73C2211yescharacteristic
21M32×C73C2211yescharacteristic
22#108×C73C2211yescharacteristic
23#11924028—21no—
24C2×Dic146—21no—
25Dic292—21no—
26Dic292—21no—
27Dic292D411yescharacteristic
28#11924018—41no—
29#11924018—41no—
30#11924017—21no—
31D584D411yescharacteristic
32#11924011—41no—
33C2×#10596831D411yescharacteristic
34C8×D73—41no—
35#11924007—42no—
36C4×Dic73D411yescharacteristic
37#11924003—21no—
38C2×Q8×C73—21no—
39Q16×C73—21no—
40Q16×C73—21no—
41M16×C73—21no—
42C2×C8×C73C2311yescharacteristic
43C16×C73—21no—
44Q8×C73—41no—
45Q8×C73—41no—
46C2×C4×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×C73AGL(1,ℤ/8)11yescharacteristic
62C2×D73—41no—
63C4×C73—81no—
64C4×C73#12111yescharacteristic
65C4×C73C2×D811yescharacteristic
66Dic73—22no—
67Dic73—41no—
68Dic73—81no—
69C2×C73—21no—
70C2×C73#45911yescharacteristic
71D73—81no—
72#2214—731nomaximal, Sylow
73C73#221411yescharacteristic, complemented, Sylow
74#510—731no—
75#510—731no—
76#494—731no—
77#443—731no—
78#364—731no—
79#362—731no—
80#362D7311yescharacteristic, complemented
81#135—731no—
82C2×Q16—731no—
83C2×Q16—1461no—
84C2×Q16C2×D7311yescharacteristic
85#131—1461no—
86C4⋊Q8—1461no—
87Q32—1461no—
88Q32—1461no—
89SD32—1461no—
90SD32—1461no—
91M32—731no—
92M32C2×D7311yescharacteristic
93#108C2×D7311yescharacteristic
94#104—1461no—
95C4×C8—731no—
96#41—1461no—
97C2×Q8—21no—
98C2×Q8—1461no—
99Q16—21no—
100Q16—21no—
101Q16—2921no—
102Q16—2921no—
103Q16—731no—
104Q16—1461no—
105Q16—1461no—
106SD16—1461no—
107D8—731no—
108M16—21no—
109M16—2921no—
110C2×C8—2921no—
111C2×C8—731no—
112C2×C8C22×D7311yescharacteristic
113C4⋊C4—2922no—
114C42—731no—
115C16—21no—
116C16—1461no—
117Q8—41no—
118Q8—41no—
119Q8—2921no—
120Q8—2921no—
121Q8—1461no—
122D4—2921no—
123D4—1461no—
124C2×C4—41no—
125C2×C4—2921no—
126C2×C4—2921no—
127C2×C4—1461no—
128C2×C4D4×D7311yescharacteristic
129C8—41no—
130C8—731no—
131C8—731no—
132C8D4×D7311yescharacteristic
133C8#1192402811yescharacteristic
134C22—2921no—
135C22#1455661811yescharacteristic
136C4—81no—
137C4—2921no—
138C4—5841no—
139C4—1462no—
140C4#1455656411yescharacteristic
141C4D8×D7311yescharacteristic
142C2—21no—
143C2—5841no—
144C2#1798878111yescharacteristic
subgroupG/H
centerC2#17988781
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#362×C73C2
socleC2×C73#459
hypercenter#362D73
hypocenterC73#2214
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
3. #17988965C2semidirect
5. #17988407C2semidirect
6. #17988402C2semidirect
7. #362×C73C2semidirect
73. C73#2214semidirect
80. #362D73semidirect