Finite Group Databasebeta

← C22×C4⋊C4×D271 #46849523

Subgroups — C22×C4⋊C4×D271 #46849523

Order 34688.

2488 conjugacy classes of subgroups; only the 1157 normal subgroups are shown.

normal subgroups only

This group has 2488 conjugacy classes of subgroups — too many to draw. Only its 1157 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×C4×D271C212yesmaximal
2C23×C4×D271C211yesmaximal, characteristic
3C22×C4⋊Dic271C211yesmaximal, characteristic, complemented
4C22×Dic271⋊C4C212yesmaximal, complemented
5C2×C4⋊C4×D271C2124yesmaximal, direct product factor
6C22×C4⋊C4×C271C211yesmaximal, characteristic, complemented
7C24×D271C2211yescharacteristic
8C23×Dic271C2212yes—
9C23×Dic271C2211yescharacteristic
10C22×C4×D271—216no—
11C22×C4×D271C4116yescomplemented
12C22×C4×D271C22124yes—
13C22×C4×D271C22112yes—
14C2×C4⋊Dic271C22112yescomplemented
15C2×Dic271⋊C4C22124yescomplemented
16C4⋊C4×D271C22164yesdirect product factor
17C23×C4×C271C2212yes—
18C23×C4×C271C2211yescharacteristic
19C2×C4⋊C4×C271C22112yescomplemented
20C23×D271C2×C418yes—
21C23×D271D418yes—
22C23×D271Q818yes—
23C23×D271C2316yes—
24C22×Dic271—28no—
25C22×Dic271C2×C418yescomplemented
26C22×Dic271C23112yes—
27C22×Dic271C2316yes—
28C2×C4×D271—296no—
29C2×C4×D271C2×C4196yescomplemented
30C2×C4×D271C23132yes—
31C2×C4×D271C23116yes—
32C4⋊Dic271C23116yescomplemented
33Dic271⋊C4C23132yescomplemented
34C24×C271C2311yescharacteristic
35C22×C4×C271—28no—
36C22×C4×C271C2×C418yescomplemented
37C22×C4×C271C23112yes—
38C22×C4×C271C2316yes—
39C4⋊C4×C271C23116yescomplemented
40C22×D271C4⋊C4164yesdirect product factor
41C22×D271C22×C4124yes—
42C22×D271C2×D4124yes—
43C22×D271C2×Q8124yes—
44C22×D271C2414yes—
45C2×Dic271—224no—
46C2×Dic271C22×C4124yescomplemented
47C2×Dic271C2418yes—
48C2×Dic271C2414yes—
49C4×D271—264no—
50C4×D271C22×C4164yescomplemented
51C23×C271C22×C414yes—
52C23×C271C2×D414yes—
53C23×C271C2×Q814yes—
54C23×C271C2413yes—
55C2×C4×C271—224no—
56C2×C4×C271C22×C4124yescomplemented
57C2×C4×C271C2418yes—
58C2×C4×C271C2414yes—
59C22×C271C2×C4⋊C4116yescomplemented
60C22×C271C23×C416yes—
61C22×C271C22×D416yes—
62C22×C271C22×Q816yes—
63C22×C271C2511yescharacteristic
64C2×D271C2×C4⋊C4196yesdirect product factor
65C2×D271C23×C418yes—
66C2×D271C22×D418yes—
67C2×D271C22×Q818yes—
68C4×C271—28no—
69C4×C271C23×C418yescomplemented
70Dic271—28no—
71Dic271C23×C418yescomplemented
72C2×C271C22×C4⋊C4112yescomplemented
73C2×C271C24×C411yescharacteristic
74C2×C271C23×D411yescharacteristic
75C2×C271C23×Q811yescharacteristic
76D271C22×C4⋊C4116yesdirect product factor
77C271C23×C4⋊C411yescharacteristic, complemented, Sylow
78C23×C4⋊C4—2711nomaximal, Sylow
79C24×C4—2711no—
80C24×C4—2712no—
81C22×C4⋊C4—2712no—
82C22×C4⋊C4—2711no—
83C22×C4⋊C4—27124no—
84C22×C4⋊C4D27111yescharacteristic, direct product factor
85C25—2711no—
86C23×C4—2711no—
87C23×C4—27116no—
88C23×C4—27112no—
89C23×C4—2712no—
90C23×C4—27124no—
91C23×C4—54216no—
92C23×C4C2×D27112yes—
93C23×C4C2×D27111yescharacteristic
94C2×C4⋊C4—27124no—
95C2×C4⋊C4—27112no—
96C2×C4⋊C4—27164no—
97C2×C4⋊C4C2×D271112yesdirect product factor
98C24—2718no—
99C24—2718no—
100C24—2718no—
101C24—2716no—
102C24C22×D27111yescharacteristic
103C22×C4—28no—
104C22×C4—2718no—
105C22×C4—2716no—
106C22×C4—27196no—
107C22×C4—27116no—
108C22×C4—27112no—
109C22×C4—27132no—
110C22×C4—54296no—
111C22×C4—5428no—
112C22×C4C4×D27118yescomplemented
113C22×C4C22×D271112yes—
114C22×C4C22×D27116yes—
115C4⋊C4—27132no—
116C4⋊C4—27116no—
117C4⋊C4C22×D271116yesdirect product factor
118C23—27124no—
119C23—27124no—
120C23—27124no—
121C23—2714no—
122C23—27164no—
123C23C2×C4×D27114yes—
124C23D4×D27114yes—
125C23Q8×D27114yes—
126C23C23×D27113yes—
127C2×C4—224no—
128C2×C4—27124no—
129C2×C4—2714no—
130C2×C4—27164no—
131C2×C4—2718no—
132C2×C4—54264no—
133C2×C4—54224no—
134C2×C4C2×C4×D271124yescomplemented
135C2×C4C23×D27118yes—
136C2×C4C23×D27114yes—
137C22—2718no—
138C22—27196no—
139C22—2718no—
140C22—2718no—
141C22C4⋊C4×D271116yesdirect product factor
142C22C22×C4×D27116yes—
143C22C2×D4×D27116yes—
144C22C2×Q8×D27116yes—
145C22C24×D27111yescharacteristic
146C4—28no—
147C4—2718no—
148C4—5428no—
149C4C22×C4×D27118yescomplemented
150C2—27116no—
151C2C2×C4⋊C4×D271112yesdirect product factor
152C2C23×C4×D27111yescharacteristic
153C2C22×D4×D27111yescharacteristic
154C2C22×Q8×D27111yescharacteristic
subgroupG/H
centerC24C22×D271
commutatorC2×C271C24×C4
FrattiniC22C24×D271
FittingC22×C4⋊C4×C271C2
socleC24×C271C23
prime radicalC24×D271C22
cosocleC22×C271C25
hypercenterC22×C4⋊C4D271
hypocenterC271C23×C4⋊C4
LCSG ▷ C2×C271 ▷ C271
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊Dic271C2semidirect
4. C22×Dic271⋊C4C2semidirect
5. C2×C4⋊C4×D271C2direct (N × H)
6. C22×C4⋊C4×C271C2semidirect
11. C22×C4×D271C4semidirect
14. C2×C4⋊Dic271C22semidirect
15. C2×Dic271⋊C4C22semidirect
16. C4⋊C4×D271C22direct (N × H)
19. C2×C4⋊C4×C271C22semidirect
25. C22×Dic271C2×C4semidirect
29. C2×C4×D271C2×C4semidirect
32. C4⋊Dic271C23semidirect
33. Dic271⋊C4C23semidirect
36. C22×C4×C271C2×C4semidirect
39. C4⋊C4×C271C23semidirect
40. C22×D271C4⋊C4direct (N × H)
46. C2×Dic271C22×C4semidirect
50. C4×D271C22×C4semidirect
56. C2×C4×C271C22×C4semidirect
59. C22×C271C2×C4⋊C4semidirect
64. C2×D271C2×C4⋊C4direct (N × H)
69. C4×C271C23×C4semidirect
71. Dic271C23×C4semidirect
72. C2×C271C22×C4⋊C4semidirect
76. D271C22×C4⋊C4direct (N × H)
77. C271C23×C4⋊C4semidirect
84. C22×C4⋊C4D271direct (N × H)
97. C2×C4⋊C4C2×D271direct (N × H)
112. C22×C4C4×D271semidirect
117. C4⋊C4C22×D271direct (N × H)
134. C2×C4C2×C4×D271semidirect
141. C22C4⋊C4×D271direct (N × H)
149. C4C22×C4×D271semidirect
151. C2C2×C4⋊C4×D271direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×D2712
C22×C4⋊Dic2712
C22×Dic271⋊C42
C2×C4⋊C4×D2712
C22×C4⋊C4×C2712
C23×C4⋊C4271