Finite Group Databasebeta

← #22612191

Subgroups — #22612191

Order 9344.

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

normal subgroups only

This group has 184 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
1C2×#14556537C211yesmaximal, characteristic, complemented
2C2×#14556536C211yesmaximal, characteristic, complemented
3C2×#14556532C211yesmaximal, characteristic
4#17988972C211yesmaximal, characteristic, complemented
5#17988970C211yesmaximal, characteristic, complemented
6C16×Dic73C211yesmaximal, characteristic, complemented
7C2×SD32×C73C211yesmaximal, characteristic, complemented
8C2×Dic292C2211yescharacteristic
9C2×#11924016—21no—
10C2×#11924015—21no—
11C2×D584C2211yescharacteristic
12#14556580—21no—
13#14556578—21no—
14#14556537—22no—
15#14556536—22no—
16#14556532—22no—
17C2×#11924003C2211yescharacteristic
18C8×Dic73C2211yescharacteristic
19C2×Q16×C73C2211yescharacteristic
20C2×D8×C73C2211yescharacteristic
21SD32×C73—22no—
22C2×C16×C73C2211yescharacteristic
23C2×Dic146—21no—
24C2×D292—21no—
25Dic292—21no—
26Dic292—21no—
27#11924016—42no—
28#11924015—42no—
29D584—21no—
30D584—21no—
31C2×#10596831D411yescharacteristic
32C22⋊Dic73—42no—
33#11924005—42no—
34C4×Dic73D411yescharacteristic
35#11924003D412yes—
36C2×Q8×C73—21no—
37C2×D4×C73—21no—
38Q16×C73—21no—
39Q16×C73—21no—
40D8×C73—21no—
41D8×C73—21no—
42C2×C8×C73C2311yescharacteristic
43C16×C73D412yes—
44C23×C73—41no—
45C22×D73—41no—
46Q8×C73—41no—
47Q8×C73—41no—
48D4×C73—41no—
49D4×C73—41no—
50C2×C4×C73—41no—
51C2×C4×C73C2×D411yescharacteristic
52C2×Dic73—41no—
53C2×Dic73D812yes—
54D292—41no—
55D292—41no—
56Dic146—41no—
57Dic146—41no—
58C8×C73C2×D411yescharacteristic
59C8×C73C2×D411yescharacteristic
60#10596831D812yes—
61C22×C73—81no—
62C22×C73—82no—
63C22×C73C2×D811yescharacteristic
64C2×D73—81no—
65C2×D73—82no—
66C4×C73—81no—
67C4×C73#12711yescharacteristic
68C4×C73C2×D811yescharacteristic
69Dic73—22no—
70Dic73—81no—
71C2×C73—161no—
72C2×C73#49311yescharacteristic
73C2×C73#50812yes—
74D73—161no—
75#2249—731nomaximal, Sylow
76C73#224911yescharacteristic, complemented, Sylow
77C2×Q32—731no—
78C2×SD32—731no—
79C2×SD32D7311yescharacteristic, complemented
80C2×D16—731no—
81#495—731no—
82#495—731no—
83C4×C16—731no—
84C2×Q16—731no—
85C2×Q16C2×D7311yescharacteristic
86C2×SD16—1461no—
87C2×SD16—1461no—
88C2×D8—731no—
89C2×D8C2×D7311yescharacteristic
90#124—1461no—
91#124—1461no—
92Q32—1462no—
93SD32—22no—
94SD32—1462no—
95D16—1462no—
96C2×C16—731no—
97C2×C16C2×D7311yescharacteristic
98C4×C8—731no—
99C2×Q8—21no—
100C2×Q8—1461no—
101C2×D4—21no—
102C2×D4—1461no—
103Q16—21no—
104Q16—21no—
105Q16—1461no—
106Q16—1461no—
107SD16—2922no—
108SD16—2922no—
109D8—21no—
110D8—21no—
111D8—1461no—
112D8—1461no—
113C2×C8—731no—
114C2×C8C22×D7311yescharacteristic
115C22⋊C4—2922no—
116C22⋊C4—2922no—
117C42—731no—
118C16—732no—
119C16C22⋊D7312yes—
120C23—41no—
121C23—2921no—
122Q8—41no—
123Q8—41no—
124Q8—2921no—
125Q8—2921no—
126D4—41no—
127D4—41no—
128D4—2921no—
129D4—2921no—
130C2×C4—41no—
131C2×C4—2921no—
132C2×C4—732no—
133C2×C4D4×D7311yescharacteristic
134C8—732no—
135C8D4×D7311yescharacteristic
136C8C2×C22⋊D7311yescharacteristic
137C22—81no—
138C22—82no—
139C22—5841no—
140C22—5842no—
141C22D8×D7311yescharacteristic
142C4—81no—
143C4—5841no—
144C4—1462no—
145C4#1455658711yescharacteristic
146C4D8×D7311yescharacteristic
147C2—161no—
148C2—11681no—
149C2#1798896211yescharacteristic
150C2#1798901812yes—
subgroupG/H
centerC22D8×D73
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
FittingC2×SD32×C73C2
socleC22×C73C2×D8
hypercenterC2×SD32D73
hypocenterC73#2249
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#14556537C2semidirect
2. C2×#14556536C2semidirect
4. #17988972C2semidirect
5. #17988970C2semidirect
6. C16×Dic73C2semidirect
7. C2×SD32×C73C2semidirect
76. C73#2249semidirect
79. C2×SD32D73semidirect