Finite Group Databasebeta

← #22626542

Subgroups — #22626542

Order 9344.

756 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 198 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#17989667C212yesmaximal, complemented
2#17989573C216yesmaximal, complemented
3D73⋊#100C216yesmaximal, complemented
4C2×#14556637C211yesmaximal, characteristic
5#14556679—28no—
6D73⋊M16C22112yescomplemented
7#14556652C2214yescomplemented
8#14556651C22112yescomplemented
9#14556637—28no—
10C2×#11924029C411yescharacteristic
11C2×#11924029C2211yescharacteristic
12C2×#11924028C2213yes—
13C22×D292C413yes—
14C2×D4×D73C413yes—
15C2×D4×D73C2213yes—
16C2×#41×C73C411yescharacteristic
17#11924038—212no—
18#11924037C2318yes—
19#11924036—212no—
20C23×D73C2×C416yes—
21#11924029—24no—
22#11924029D418yes—
23#11924028—212no—
24C2×Dic146C2311yescharacteristic
25C2×D292—212no—
26C2×D292C2×C413yes—
27C2×D292C2×C413yes—
28C2×D292C2×C413yes—
29C2×C22⋊D73C2×C413yes—
30C2×C22⋊D73C2313yes—
31D4×D73—212no—
32D4×D73—212no—
33C2×C4×D73C2×C413yes—
34C2×C4×D73C2313yes—
35#41×C73—24no—
36C2×Q8×C73C2×C411yescharacteristic
37C2×D4×C73C2×C413yes—
38C22×C4×C73C2×C413yes—
39C23×C73C22×C413yes—
40C22×D73—212no—
41C22×D73—86no—
42C22×D73C22×C413yes—
43C22×D73C22×C413yes—
44Q8×C73C22⋊C414yes—
45D4×C73—26no—
46C2×C4×C73—26no—
47C2×C4×C73C22×C411yescharacteristic
48C2×C4×C73C22×C413yes—
49C22⋊D73—26no—
50C22⋊D73—26no—
51C2×Dic73C22×C411yescharacteristic
52C2×Dic73C2411yescharacteristic
53D292—26no—
54D292—26no—
55D292C22⋊C4112yes—
56C4×D73—26no—
57C4×D73C2×D4112yes—
58Dic146—22no—
59#10596833—28no—
60C22×C73—23no—
61C22×C73—43no—
62C22×C73C23×C411yescharacteristic
63C2×D73—23no—
64C2×D73—43no—
65C2×D73—43no—
66C2×D73—812no—
67C2×D73C2×C22⋊C416yes—
68C4×C73—21no—
69C4×C73C2×C22⋊C416yes—
70Dic73—21no—
71Dic73C22×D412yes—
72C2×C73—21no—
73C2×C73—43no—
74C2×C73C22×C22⋊C411yescharacteristic
75D73—26no—
76D73—43no—
77#2888—731nomaximal, Sylow
78C73#288811yescharacteristic, complemented, Sylow
79C2×H(5,𝔽2)—731no—
80#568—732no—
81#413—736no—
82C2×#100—736no—
83H(5,𝔽2)—1468no—
84C2×#41—731no—
85C2×#41—731no—
86C2×#41—733no—
87C2×#41#6440811yescharacteristic
88C22×D4—733no—
89C22×D4—733no—
90C22×D4—733no—
91#131—1468no—
92C2×M16—7312no—
93#101—734no—
94#100—7312no—
95C24—736no—
96#41—24no—
97#41—738no—
98#41—14612no—
99#41—1464no—
100C2×Q8—731no—
101C2×Q8C2×#6440811yescharacteristic
102C2×D4—733no—
103C2×D4—733no—
104C2×D4—733no—
105C2×D4—733no—
106C2×D4—733no—
107C2×D4—14612no—
108C2×D4—14612no—
109C2×D4—14612no—
110C2×D4C2×#6440813yes—
111C22×C4—733no—
112C22×C4—733no—
113C22×C4C2×#6440813yes—
114M16—738no—
115M16—14612no—
116C2×C8—14612no—
117C23—5846no—
118C23—733no—
119C23—733no—
120C23—14612no—
121C23C22×#6440813yes—
122Q8—1462no—
123Q8C22⋊#6440814yes—
124D4—26no—
125D4—7312no—
126D4—1466no—
127D4—1466no—
128D4—1466no—
129D4—1466no—
130C2×C4—26no—
131C2×C4—731no—
132C2×C4—7312no—
133C2×C4—731no—
134C2×C4—1466no—
135C2×C4C22×#6440811yescharacteristic
136C2×C4C22×#6440813yes—
137C8—1468no—
138C22—23no—
139C22—43no—
140C22—2923no—
141C22—2923no—
142C22—58412no—
143C22—736no—
144C22—1463no—
145C22C23×#6440811yescharacteristic
146C4—21no—
147C4—732no—
148C4—1461no—
149C4C2×C22⋊#6440816yes—
150C2—21no—
151C2—43no—
152C2—2923no—
153C2—1466no—
154C2C22×C22⋊#6440811yescharacteristic
subgroupG/H
centerC2C22×C22⋊#64408
commutatorC22×C73C23×C4
FrattiniC22C23×#64408
FittingC2×#41×C73C4
socleC2×C73C22×C22⋊C4
hypercenterC2×#41#64408
hypocenterC73#2888
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×Q8 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #17989667C2semidirect
2. #17989573C2semidirect
3. D73⋊#100C2semidirect
6. D73⋊M16C22semidirect
7. #14556652C22semidirect
8. #14556651C22semidirect
78. C73#2888semidirect