Finite Group Databasebeta

← #22625419

Subgroups — #22625419

Order 9344.

238 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 58 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#17989608C212yesmaximal, complemented
2#17989443C212yesmaximal, complemented
3#17989442C212yesmaximal, complemented
4#17989133C211yesmaximal, characteristic
5C4⋊#10596833—22no—
6C22⋊#10596833—22no—
7#14556646C2214yes—
8C2×#11924028C411yescharacteristic
9#14556589C411yescharacteristic
10#14556587C411yescharacteristic
11#14556580C2211yescharacteristic
12#14556578C2211yescharacteristic
13#14556563—22no—
14C4×C22⋊D73—22no—
15C2×C4×Dic73C2211yescharacteristic
16C2×#41×C73C411yescharacteristic
17C2×#10596833—24no—
18#11924028—42no—
19C2×Dic146C2×C411yescharacteristic
20C2×D292C2×C411yescharacteristic
21C2×C22⋊D73—21no—
22C2×C22⋊D73—22no—
23C22×Dic73D412yes—
24C2×C4×D73—21no—
25#11924007—22no—
26C22⋊Dic73—22no—
27#11924005—22no—
28C4×Dic73C2×C411yescharacteristic
29C4×Dic73D412yes—
30C4×Dic73C2311yescharacteristic
31#41×C73—42no—
32C2×Q8×C73C2×C411yescharacteristic
33C2×D4×C73—21no—
34C2×D4×C73C2×C411yescharacteristic
35C22×C4×C73—21no—
36C22×C4×C73C2×C411yescharacteristic
37C23×C73—21no—
38C23×C73C22⋊C411yescharacteristic
39C22×D73—21no—
40Q8×C73—41no—
41D4×C73—41no—
42D4×C73—42no—
43C2×C4×C73—22no—
44C2×C4×C73—21no—
45C2×C4×C73—42no—
46C2×C4×C73C22⋊C411yescharacteristic
47C2×C4×C73C22×C411yescharacteristic
48C22⋊D73—44no—
49C22⋊D73—42no—
50C2×Dic73—21no—
51C2×Dic73—42no—
52C2×Dic73C22⋊C412yes—
53C2×Dic73C2×D412yes—
54D292—41no—
55C4×D73—42no—
56Dic146—41no—
57#10596833—44no—
58C22×C73—21no—
59C22×C73—22no—
60C22×C73—41no—
61C22×C73—42no—
62C22×C73C2×C22⋊C411yescharacteristic
63C2×D73—41no—
64C2×D73—42no—
65C4×C73—21no—
66C4×C73—41no—
67C4×C73#10012yes—
68Dic73—22no—
69Dic73—22no—
70Dic73—41no—
71C2×C73—41no—
72C2×C73—81no—
73C2×C73C2×#10011yescharacteristic
74C2×C73#42112yes—
75D73—81no—
76#1536—731nomaximal, Sylow
77C73#153611yescharacteristic, complemented, Sylow
78#532—731no—
79#432—732no—
80#329—732no—
81#329—732no—
82C2×#41—731no—
83C2×#41#6440811yescharacteristic
84C4⋊Q8—731no—
85#127—731no—
86#124—731no—
87#124—731no—
88#121—1462no—
89C4×D4—1462no—
90C2×C42—731no—
91C4⋊C8—1462no—
92C22⋊C8—1462no—
93#97—734no—
94#41—42no—
95#41—2922no—
96C2×Q8—731no—
97C2×Q8C2×#6440811yescharacteristic
98C2×D4—21no—
99C2×D4—731no—
100C2×D4—1462no—
101C2×D4—1461no—
102C2×D4C2×#6440811yescharacteristic
103C22×C4—21no—
104C22×C4—732no—
105C22×C4—1461no—
106C22×C4C2×#6440811yescharacteristic
107C2×C8—1464no—
108C4⋊C4—1462no—
109C22⋊C4—1462no—
110C22⋊C4—1462no—
111C42—732no—
112C42—731no—
113C42—731no—
114C23—21no—
115C23—1461no—
116C23C22⋊#6440811yescharacteristic
117Q8—41no—
118Q8—2921no—
119D4—41no—
120D4—42no—
121D4—2921no—
122D4—2922no—
123D4—2924no—
124C2×C4—22no—
125C2×C4—21no—
126C2×C4—42no—
127C2×C4—2922no—
128C2×C4—2922no—
129C2×C4—732no—
130C2×C4—732no—
131C2×C4—1461no—
132C2×C4C22⋊#6440811yescharacteristic
133C2×C4C22×#6440811yescharacteristic
134C8—2924no—
135C22—21no—
136C22—22no—
137C22—41no—
138C22—42no—
139C22—2921no—
140C22—2922no—
141C22C2×C22⋊#6440811yescharacteristic
142C4—21no—
143C4—41no—
144C4—2921no—
145C4—1462no—
146C4—1462no—
147C4#1455665112yes—
148C2—41no—
149C2—81no—
150C2—5841no—
151C2C2×#1455665111yescharacteristic
152C2#1798958412yes—
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC2×#41×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×#41#64408
hypocenterC73#1536
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #17989608C2semidirect
2. #17989443C2semidirect
3. #17989442C2semidirect
77. C73#1536semidirect