Finite Group Databasebeta

← #22626156

Subgroups — #22626156

Order 9344.

272 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 94 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×#14556664C212yesmaximal, complemented
2#17989482C212yesmaximal, complemented
3C22⋊#11924031C212yesmaximal, complemented
4C22×C8×D73C211yesmaximal, characteristic
5#14556664—24no—
6C2×#11924031C2214yescomplemented
7C22×C4×D73C411yescharacteristic
8C22×#10596831C2211yescharacteristic
9C2×C8×D73—24no—
10C2×C8×D73C411yescharacteristic
11C2×C8×D73C411yescharacteristic
12C2×C8×D73C2211yescharacteristic
13C2×C8×D73C2211yescharacteristic
14C22×C8×C73C411yescharacteristic
15#11924031—24no—
16C23×D73C811yescharacteristic
17C22×Dic73C811yescharacteristic
18C2×C4×D73—22no—
19C2×C4×D73—22no—
20C2×C4×D73C811yescharacteristic
21C2×C4×D73C811yescharacteristic
22C2×C4×D73C2×C411yescharacteristic
23C2×C4×D73C2×C411yescharacteristic
24C2×#10596831—22no—
25C2×#10596831C2×C411yescharacteristic
26C2×#10596831C2311yescharacteristic
27C8×D73—22no—
28C8×D73—22no—
29C8×D73—22no—
30C8×D73D414yes—
31C22×C4×C73C2×C411yescharacteristic
32C2×C8×C73—22no—
33C2×C8×C73C2×C411yescharacteristic
34C2×C8×C73C2×C411yescharacteristic
35C23×C73C2×C811yescharacteristic
36C22×D73—22no—
37C22×D73—22no—
38C22×D73C1614yescomplemented
39C22×D73C2×C811yescharacteristic
40C22×D73C2×C811yescharacteristic
41C2×C4×C73—21no—
42C2×C4×C73—21no—
43C2×C4×C73C2×C811yescharacteristic
44C2×C4×C73C22×C411yescharacteristic
45C2×Dic73—22no—
46C2×Dic73C2×C811yescharacteristic
47C2×Dic73C2×C811yescharacteristic
48C4×D73—22no—
49C4×D73—21no—
50C4×D73—21no—
51C4×D73—22no—
52C4×D73C22⋊C412yes—
53C4×D73M1612yes—
54C8×C73—21no—
55C8×C73C22⋊C412yes—
56#10596831—21no—
57#10596831C2×D412yes—
58C22×C73—21no—
59C22×C73—21no—
60C22×C73C2×C1612yescomplemented
61C22×C73C22×C811yescharacteristic
62C2×D73—21no—
63C2×D73—21no—
64C2×D73—28no—
65C2×D73C22⋊C812yes—
66C2×D73C2×C1612yes—
67C2×D73C2×C1612yescomplemented
68C2×D73M3212yes—
69C4×C73—21no—
70C4×C73C2×C22⋊C411yescharacteristic
71C4×C73C2×M1611yescharacteristic
72Dic73—21no—
73Dic73C22⋊C812yes—
74C2×C73—22no—
75C2×C73C2×C22⋊C811yescharacteristic
76C2×C73C22×C1611yescharacteristic
77C2×C73C2×M3211yescharacteristic
78D73—22no—
79D73C22⋊C1614yescomplemented
80C2×C22⋊C16—731nomaximal, Sylow
81C73C2×C22⋊C1611yescharacteristic, complemented, Sylow
82C23×C8—731no—
83C22×C16—732no—
84C22⋊C16—732no—
85C22⋊C16—732no—
86C23×C4—731no—
87C22×C8—731no—
88C22×C8—731no—
89C22×C8—731no—
90C22×C8—731no—
91C22×C8—731no—
92C22×C8—1464no—
93C22×C8#6440811yescharacteristic
94C2×C16—734no—
95C2×C16—1464no—
96C24—731no—
97C22×C4—731no—
98C22×C4—731no—
99C22×C4—731no—
100C22×C4—731no—
101C22×C4—731no—
102C22×C4—1462no—
103C22×C4—1462no—
104C22×C4C2×#6440811yescharacteristic
105C2×C8—22no—
106C2×C8—731no—
107C2×C8—734no—
108C2×C8—731no—
109C2×C8—1462no—
110C2×C8—1462no—
111C2×C8—1462no—
112C2×C8—1462no—
113C2×C8C2×#6440811yescharacteristic
114C2×C8C2×#6440811yescharacteristic
115C16—1464no—
116C23—731no—
117C23—731no—
118C23—734no—
119C23—1462no—
120C23—1462no—
121C23#1192403611yescharacteristic
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—731no—
125C2×C4—732no—
126C2×C4—732no—
127C2×C4—731no—
128C2×C4—1462no—
129C2×C4—1462no—
130C2×C4—1462no—
131C2×C4—1461no—
132C2×C4—1461no—
133C2×C4#1192403611yescharacteristic
134C2×C4C22×#6440811yescharacteristic
135C8—21no—
136C8—732no—
137C8—1461no—
138C8C22⋊#6440812yes—
139C22—21no—
140C22—21no—
141C22—732no—
142C22—732no—
143C22—732no—
144C22—732no—
145C22—1468no—
146C22—1461no—
147C22—1461no—
148C22#1455666412yescomplemented
149C22C2×#1192403611yescharacteristic
150C4—21no—
151C4—732no—
152C4—1461no—
153C4C2×C22⋊#6440811yescharacteristic
154C4D73⋊M1611yescharacteristic
155C2—22no—
156C2—734no—
157C2—1462no—
158C2#1798955511yescharacteristic
159C2C2×#1455666411yescharacteristic
160C2#1798964311yescharacteristic
subgroupG/H
centerC2×C8C2×#64408
commutatorC2×C73C22×C16
FrattiniC2×C4C22×#64408
FittingC22×C8×C73C4
socleC22×C73C22×C8
hypercenterC22×C8#64408
hypocenterC73C2×C22⋊C16
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#14556664C2semidirect
2. #17989482C2semidirect
3. C22⋊#11924031C2semidirect
6. C2×#11924031C22semidirect
38. C22×D73C16semidirect
60. C22×C73C2×C16semidirect
67. C2×D73C2×C16semidirect
79. D73C22⋊C16semidirect
81. C73C2×C22⋊C16semidirect
148. C22#14556664semidirect