Finite Group Databasebeta

← C22×#19149641 #36366733

Subgroups — C22×#19149641 #36366733

Order 22144.

2528 conjugacy classes of subgroups; only the 941 normal subgroups are shown.

normal subgroups only

This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 941 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
1C23×D692C211yesmaximal, characteristic
2C23×C4×D173C212yesmaximal, complemented
3C2×#19149641C2124yesmaximal, direct product factor
4C22×#14583803C212yesmaximal, complemented
5C22×C4×Dic173C211yesmaximal, characteristic, complemented
6C22×C4⋊C4×C173C211yesmaximal, characteristic, complemented
7C24×D173C2212yes—
8C22×D692C4116yescomplemented
9C22×D692C22112yes—
10C23×Dic173C2211yescharacteristic
11C23×Dic173C2211yescharacteristic
12C22×C4×D173—216no—
13C22×C4×D173C22124yescomplemented
14#19149641C22164yesdirect product factor
15C2×#14583803C22124yescomplemented
16C2×C4×Dic173C22112yescomplemented
17C23×C4×C173C2212yes—
18C23×C4×C173C2211yescharacteristic
19C2×C4⋊C4×C173C22112yescomplemented
20C23×D173—28no—
21C23×D173—28no—
22C23×D173C2×C4116yescomplemented
23C23×D173C23112yes—
24C2×D692C2×C4196yescomplemented
25C2×D692C23116yes—
26C22×Dic173—24no—
27C22×Dic173D418yescomplemented
28C22×Dic173C2316yes—
29C22×Dic173C2316yes—
30C2×C4×D173—296no—
31C2×C4×D173C23132yescomplemented
32#14583803C23132yescomplemented
33C4×Dic173C23116yescomplemented
34C24×C173C2311yescharacteristic
35C22×C4×C173—28no—
36C22×C4×C173C2×C418yescomplemented
37C22×C4×C173C23112yes—
38C22×C4×C173C2316yes—
39C4⋊C4×C173C23116yescomplemented
40C22×D173—264no—
41C22×D173—224no—
42C22×D173—224no—
43C22×D173C22×C4148yescomplemented
44C22×D173C2418yes—
45D692C22×C4164yescomplemented
46C2×Dic173—212no—
47C2×Dic173C2×D4124yescomplemented
48C2×Dic173C2414yes—
49C2×Dic173C2414yes—
50C4×D173—264no—
51C23×C173C22×C414yes—
52C23×C173C2×D414yes—
53C23×C173#4114yes—
54C23×C173C2413yes—
55C2×C4×C173—224no—
56C2×C4×C173C22×C4124yescomplemented
57C2×C4×C173C2418yes—
58C2×C4×C173C2414yes—
59C22×C173C4×D4116yescomplemented
60C22×C173C23×C416yes—
61C22×C173C22×D416yes—
62C22×C173C2×#4116yes—
63C22×C173C2511yescharacteristic
64C2×D173—296no—
65C2×D173—28no—
66C2×D173—28no—
67C2×D173C23×C4116yescomplemented
68C4×C173—28no—
69C4×C173C23×C418yescomplemented
70Dic173—24no—
71Dic173C22×D418yescomplemented
72C2×C173C2×C4×D4112yescomplemented
73C2×C173C24×C411yescharacteristic
74C2×C173C23×D411yescharacteristic
75C2×C173C22×#4111yescharacteristic
76D173—216no—
77C173C22×C4×D411yescharacteristic, complemented, Sylow
78C22×C4×D4—1731nomaximal, Sylow
79C23×D4—1731no—
80C24×C4—1732no—
81C2×C4×D4—17324no—
82C22×C4⋊C4D17311yescharacteristic, complemented
83C22×C22⋊C4—1732no—
84C22×C42—1731no—
85C25—1732no—
86C22×D4—17316no—
87C22×D4—17312no—
88C23×C4—34616no—
89C23×C4—1731no—
90C23×C4—17324no—
91C23×C4—1731no—
92C23×C4C2×D17312yes—
93C23×C4C2×D17311yescharacteristic
94C4×D4—17364no—
95C2×C4⋊C4C2×D173112yescomplemented
96C2×C22⋊C4—17324no—
97C2×C42—17312no—
98C24—3468no—
99C24—3468no—
100C24—17316no—
101C24—17312no—
102C24C22×D17311yescharacteristic
103C2×D4—17396no—
104C2×D4—17316no—
105C22×C4—28no—
106C22×C4—34696no—
107C22×C4—3464no—
108C22×C4—1736no—
109C22×C4—17332no—
110C22×C4—1738no—
111C22×C4—1736no—
112C22×C4C4×D17318yescomplemented
113C22×C4C22×D173112yes—
114C22×C4C22×D17316yes—
115C4⋊C4C22×D173116yescomplemented
116C22⋊C4—17332no—
117C42—17316no—
118C23—34664no—
119C23—34624no—
120C23—34624no—
121C23—17348no—
122C23—1738no—
123C23C2×C4×D17314yes—
124C23D4×D17314yes—
125C23#1458382714yes—
126C23C23×D17313yes—
127D4—17364no—
128C2×C4—224no—
129C2×C4—34664no—
130C2×C4—34612no—
131C2×C4—1734no—
132C2×C4—17324no—
133C2×C4—1734no—
134C2×C4C2×C4×D173124yescomplemented
135C2×C4C23×D17318yes—
136C2×C4C23×D17314yes—
137C22—34696no—
138C22—3468no—
139C22—3468no—
140C22—17316no—
141C22#19149641116yesdirect product factor
142C22C22×C4×D17316yes—
143C22C2×D4×D17316yes—
144C22C2×#1458382716yes—
145C22C24×D17311yescharacteristic
146C4—28no—
147C4—3464no—
148C4—1738no—
149C4C22×C4×D17318yescomplemented
150C2—34616no—
151C2C2×#19149641112yesdirect product factor
152C2C23×C4×D17311yescharacteristic
153C2C22×D4×D17311yescharacteristic
154C2C22×#1458382711yescharacteristic
subgroupG/H
centerC24C22×D173
commutatorC2×C173C24×C4
FrattiniC22C24×D173
FittingC22×C4⋊C4×C173C2
socleC24×C173C23
prime radicalC23×D692C2
cosocleC22×C173C25
hypercenterC22×C4⋊C4D173
hypocenterC173C22×C4×D4
LCSG ▷ C2×C173 ▷ C173
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C23×C4×D173C2semidirect
3. C2×#19149641C2direct (N × H)
4. C22×#14583803C2semidirect
5. C22×C4×Dic173C2semidirect
6. C22×C4⋊C4×C173C2semidirect
8. C22×D692C4semidirect
13. C22×C4×D173C22semidirect
14. #19149641C22direct (N × H)
15. C2×#14583803C22semidirect
16. C2×C4×Dic173C22semidirect
19. C2×C4⋊C4×C173C22semidirect
22. C23×D173C2×C4semidirect
24. C2×D692C2×C4semidirect
27. C22×Dic173D4semidirect
31. C2×C4×D173C23semidirect
32. #14583803C23semidirect
33. C4×Dic173C23semidirect
36. C22×C4×C173C2×C4semidirect
39. C4⋊C4×C173C23semidirect
43. C22×D173C22×C4semidirect
45. D692C22×C4semidirect
47. C2×Dic173C2×D4semidirect
56. C2×C4×C173C22×C4semidirect
59. C22×C173C4×D4semidirect
67. C2×D173C23×C4semidirect
69. C4×C173C23×C4semidirect
71. Dic173C22×D4semidirect
72. C2×C173C2×C4×D4semidirect
77. C173C22×C4×D4semidirect
82. C22×C4⋊C4D173semidirect
95. C2×C4⋊C4C2×D173semidirect
112. C22×C4C4×D173semidirect
115. C4⋊C4C22×D173semidirect
134. C2×C4C2×C4×D173semidirect
141. C22#19149641direct (N × H)
149. C4C22×C4×D173semidirect
151. C2C2×#19149641direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×D6922
C23×C4×D1732
C2×#191496412
C22×#145838032
C22×C4×Dic1732
C22×C4⋊C4×C1732
C22×C4×D4173