Finite Group Databasebeta

← #22612149

Subgroups — #22612149

Order 9344.

124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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#17988842C211yesmaximal, characteristic
2#17988634C211yesmaximal, characteristic
3#17988411C211yesmaximal, characteristic, complemented
4#17988410C211yesmaximal, characteristic, complemented
5#17988403C211yesmaximal, characteristic, complemented
6#17988368C211yesmaximal, characteristic
7#362×C73C211yesmaximal, characteristic, complemented
8C2×#11924011C2211yescharacteristic
9M16×D73—21no—
10#14556567—21no—
11#14556531C2211yescharacteristic
12#14556527C2211yescharacteristic
13#14556526—21no—
14#14556523C2211yescharacteristic
15#14556515—21no—
16C2×Q16×C73C2211yescharacteristic
17M32×C73C2211yescharacteristic
18#108×C73C2211yescharacteristic
19C2×C4×D73D411yescharacteristic
20#11924012—21no—
21#11924011—21no—
22#11924011—21no—
23#11924011—41no—
24C2×#10596831D411yescharacteristic
25C8×D73—41no—
26C4⋊Dic73—21no—
27#11924007—41no—
28#11924005—41no—
29#11924003—21no—
30C2×Q8×C73—21no—
31Q16×C73—21no—
32Q16×C73—21no—
33M16×C73—21no—
34C2×C8×C73C2311yescharacteristic
35C16×C73—21no—
36C22×D73SD1611yescharacteristic
37Q8×C73—41no—
38Q8×C73—41no—
39C2×C4×C73—41no—
40C2×C4×C73C2×D411yescharacteristic
41C2×Dic73—41no—
42C2×Dic73SD1611yescharacteristic
43C4×D73—21no—
44C4×D73—21no—
45C8×C73—41no—
46C8×C73#4111yescharacteristic
47C8×C73#4111yescharacteristic
48#10596831—21no—
49#10596831—41no—
50C22×C73C2×SD1611yescharacteristic
51C2×D73—21no—
52C2×D73—41no—
53C4×C73—81no—
54C4×C73#12311yescharacteristic
55C4×C73AGL(1,ℤ/8)11yescharacteristic
56Dic73—21no—
57Dic73—81no—
58C2×C73—21no—
59C2×C73#48111yescharacteristic
60D73—41no—
61#2239—731nomaximal, Sylow
62C73#223911yescharacteristic, complemented, Sylow
63#470—731no—
64#430—731no—
65#365—731no—
66#365—731no—
67#362—731no—
68#362D7311yescharacteristic, complemented
69#349—731no—
70C2×Q16C2×D7311yescharacteristic
71C2×M16—731no—
72C2×M16—1461no—
73C22⋊Q8—1461no—
74M32—731no—
75M32C2×D7311yescharacteristic
76#108—731no—
77#108—1461no—
78#108C2×D7311yescharacteristic
79#106—731no—
80#103—1461no—
81C2×Q8—21no—
82C22×C4—731no—
83Q16—21no—
84Q16—21no—
85M16—21no—
86M16—2921no—
87M16—1461no—
88M16—1461no—
89M16—1461no—
90C2×C8—2921no—
91C2×C8—731no—
92C2×C8C22×D7311yescharacteristic
93C4⋊C4—2921no—
94C4⋊C4—1461no—
95C22⋊C4—2921no—
96C16—21no—
97C16—1461no—
98C23—731no—
99Q8—41no—
100Q8—41no—
101C2×C4—41no—
102C2×C4—2921no—
103C2×C4—731no—
104C2×C4—1461no—
105C2×C4—1461no—
106C2×C4D4×D7311yescharacteristic
107C8—41no—
108C8—2921no—
109C8—1461no—
110C8#1192402711yescharacteristic
111C8#1192402811yescharacteristic
112C22—2921no—
113C22—1461no—
114C22SD16×D7311yescharacteristic
115C4—81no—
116C4—5841no—
117C4—1461no—
118C4#1455657311yescharacteristic
119C4#1455661511yescharacteristic
120C2—21no—
121C2—2921no—
122C2#1798890411yescharacteristic
subgroupG/H
centerC2#17988904
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#362×C73C2
socleC2×C73#481
hypercenter#362D73
hypocenterC73#2239
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. #17988411C2semidirect
4. #17988410C2semidirect
5. #17988403C2semidirect
7. #362×C73C2semidirect
62. C73#2239semidirect
68. #362D73semidirect