Finite Group Databasebeta

← #22612132

Subgroups — #22612132

Order 9344.

140 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 47 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#17988825C211yesmaximal, characteristic
2#107×D73C211yesmaximal, characteristic
3#17988413C211yesmaximal, characteristic, complemented
4#17988412C211yesmaximal, characteristic, complemented
5#17988391C211yesmaximal, characteristic, complemented
6#17988366C211yesmaximal, characteristic
7#358×C73C211yesmaximal, characteristic, complemented
8C2×C8×D73C2211yescharacteristic
9#14556567—21no—
10C4⋊C4×D73—21no—
11C2×#11924003C2211yescharacteristic
12#14556525C2211yescharacteristic
13#14556525C2211yescharacteristic
14#14556524—21no—
15#14556515—21no—
16C2×Q16×C73C2211yescharacteristic
17C2×C16×C73C2211yescharacteristic
18#107×C73C2211yescharacteristic
19C2×C4×D73—41no—
20C2×C4×D73D411yescharacteristic
21C2×#10596831D411yescharacteristic
22C8×D73—21no—
23C8×D73—21no—
24C4⋊Dic73—21no—
25C4⋊Dic73—21no—
26#11924007—41no—
27#11924007—41no—
28#11924005—41no—
29#11924003—21no—
30C2×Q8×C73—21no—
31Q16×C73—21no—
32Q16×C73—21no—
33C2×C8×C73C2311yescharacteristic
34C4⋊C4×C73—21no—
35C16×C73—21no—
36C22×D73D811yescharacteristic
37Q8×C73—41no—
38Q8×C73—41no—
39C2×C4×C73—41no—
40C2×C4×C73—41no—
41C2×C4×C73C2×D411yescharacteristic
42C2×Dic73—41no—
43C2×Dic73—41no—
44C2×Dic73D811yescharacteristic
45C4×D73—21no—
46C4×D73—21no—
47C4×D73—82no—
48C8×C73#4111yescharacteristic
49C8×C73#4111yescharacteristic
50#10596831—21no—
51C22×C73C2×D811yescharacteristic
52C2×D73—21no—
53C2×D73—21no—
54C2×D73Q3212yes—
55C4×C73—81no—
56C4×C73—81no—
57C4×C73#12311yescharacteristic
58C4×C73#13711yescharacteristic
59Dic73—21no—
60Dic73—81no—
61Dic73—81no—
62C2×C73#48011yescharacteristic
63C2×C73C2×Q3211yescharacteristic
64C2×C73#50911yescharacteristic
65D73—22no—
66#2236—731nomaximal, Sylow
67C73#223611yescharacteristic, complemented, Sylow
68#467—731no—
69C2×#107—731no—
70#366—731no—
71#366—731no—
72#358—731no—
73#358D7311yescharacteristic, complemented
74C22⋊C16—731no—
75C2×Q16C2×D7311yescharacteristic
76C22×C8—731no—
77C22⋊Q8—1461no—
78C2×C4⋊C4—1461no—
79C2×C16—731no—
80C2×C16C2×D7311yescharacteristic
81#107—731no—
82#107—731no—
83#107—1461no—
84#107C2×D7311yescharacteristic
85#103—1461no—
86C2×Q8—21no—
87C22×C4—2921no—
88C22×C4—731no—
89Q16—21no—
90Q16—21no—
91C2×C8—731no—
92C2×C8—1461no—
93C2×C8—1461no—
94C2×C8C22×D7311yescharacteristic
95C4⋊C4—21no—
96C4⋊C4—2921no—
97C4⋊C4—2921no—
98C4⋊C4—1461no—
99C4⋊C4—1461no—
100C22⋊C4—2921no—
101C16—21no—
102C16—1461no—
103C23—731no—
104Q8—41no—
105Q8—41no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—2921no—
109C2×C4—2921no—
110C2×C4—5842no—
111C2×C4—731no—
112C2×C4—1461no—
113C2×C4—1461no—
114C2×C4D4×D7311yescharacteristic
115C8—1461no—
116C8#1192402711yescharacteristic
117C8#1192402811yescharacteristic
118C22—732no—
119C22—1461no—
120C22—1461no—
121C22D8×D7311yescharacteristic
122C4—81no—
123C4—81no—
124C4—5841no—
125C4—5841no—
126C4—1461no—
127C4#1455657311yescharacteristic
128C4#1455662011yescharacteristic
129C2—1462no—
130C2#1798889911yescharacteristic
131C2Q32×D7311yescharacteristic
132C2#1798902411yescharacteristic
subgroupG/H
centerC22D8×D73
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#358×C73C2
socleC22×C73C2×D8
hypercenter#358D73
hypocenterC73#2236
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
3. #17988413C2semidirect
4. #17988412C2semidirect
5. #17988391C2semidirect
7. #358×C73C2semidirect
67. C73#2236semidirect
73. #358D73semidirect