Finite Group Databasebeta

← C22×#22575415 #46824055

Subgroups — C22×#22575415 #46824055

Order 34432.

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×D1076C211yesmaximal, characteristic
2C23×C4×D269C212yesmaximal, complemented
3C2×#22575415C2124yesmaximal, direct product factor
4C22×#16864379C212yesmaximal, complemented
5C22×C4×Dic269C211yesmaximal, characteristic, complemented
6C22×C4⋊C4×C269C211yesmaximal, characteristic, complemented
7C24×D269C2212yes—
8C22×D1076C4116yescomplemented
9C22×D1076C22112yes—
10C23×Dic269C2211yescharacteristic
11C23×Dic269C2211yescharacteristic
12C22×C4×D269—216no—
13C22×C4×D269C22124yescomplemented
14#22575415C22164yesdirect product factor
15C2×#16864379C22124yescomplemented
16C2×C4×Dic269C22112yescomplemented
17C23×C4×C269C2212yes—
18C23×C4×C269C2211yescharacteristic
19C2×C4⋊C4×C269C22112yescomplemented
20C23×D269—28no—
21C23×D269—28no—
22C23×D269C2×C4116yescomplemented
23C23×D269C23112yes—
24C2×D1076C2×C4196yescomplemented
25C2×D1076C23116yes—
26C22×Dic269—24no—
27C22×Dic269D418yescomplemented
28C22×Dic269C2316yes—
29C22×Dic269C2316yes—
30C2×C4×D269—296no—
31C2×C4×D269C23132yescomplemented
32#16864379C23132yescomplemented
33C4×Dic269C23116yescomplemented
34C24×C269C2311yescharacteristic
35C22×C4×C269—28no—
36C22×C4×C269C2×C418yescomplemented
37C22×C4×C269C23112yes—
38C22×C4×C269C2316yes—
39C4⋊C4×C269C23116yescomplemented
40C22×D269—264no—
41C22×D269—224no—
42C22×D269—224no—
43C22×D269C22×C4148yescomplemented
44C22×D269C2418yes—
45D1076C22×C4164yescomplemented
46C2×Dic269—212no—
47C2×Dic269C2×D4124yescomplemented
48C2×Dic269C2414yes—
49C2×Dic269C2414yes—
50C4×D269—264no—
51C23×C269C22×C414yes—
52C23×C269C2×D414yes—
53C23×C269#4114yes—
54C23×C269C2413yes—
55C2×C4×C269—224no—
56C2×C4×C269C22×C4124yescomplemented
57C2×C4×C269C2418yes—
58C2×C4×C269C2414yes—
59C22×C269C4×D4116yescomplemented
60C22×C269C23×C416yes—
61C22×C269C22×D416yes—
62C22×C269C2×#4116yes—
63C22×C269C2511yescharacteristic
64C2×D269—296no—
65C2×D269—28no—
66C2×D269—28no—
67C2×D269C23×C4116yescomplemented
68C4×C269—28no—
69C4×C269C23×C418yescomplemented
70Dic269—24no—
71Dic269C22×D418yescomplemented
72C2×C269C2×C4×D4112yescomplemented
73C2×C269C24×C411yescharacteristic
74C2×C269C23×D411yescharacteristic
75C2×C269C22×#4111yescharacteristic
76D269—216no—
77C269C22×C4×D411yescharacteristic, complemented, Sylow
78C22×C4×D4—2691nomaximal, Sylow
79C23×D4—2691no—
80C24×C4—2692no—
81C2×C4×D4—26924no—
82C22×C4⋊C4D26911yescharacteristic, complemented
83C22×C22⋊C4—2692no—
84C22×C42—2691no—
85C25—2692no—
86C22×D4—26916no—
87C22×D4—26912no—
88C23×C4—2691no—
89C23×C4—2691no—
90C23×C4—26924no—
91C23×C4—53816no—
92C23×C4C2×D26912yes—
93C23×C4C2×D26911yescharacteristic
94C4×D4—26964no—
95C2×C4⋊C4C2×D269112yescomplemented
96C2×C22⋊C4—26924no—
97C2×C42—26912no—
98C24—26916no—
99C24—26912no—
100C24—5388no—
101C24—5388no—
102C24C22×D26911yescharacteristic
103C2×D4—26996no—
104C2×D4—26916no—
105C22×C4—28no—
106C22×C4—2698no—
107C22×C4—2696no—
108C22×C4—2696no—
109C22×C4—26932no—
110C22×C4—53896no—
111C22×C4—5384no—
112C22×C4C4×D26918yescomplemented
113C22×C4C22×D269112yes—
114C22×C4C22×D26916yes—
115C4⋊C4C22×D269116yescomplemented
116C22⋊C4—26932no—
117C42—26916no—
118C23—26948no—
119C23—2698no—
120C23—53864no—
121C23—53824no—
122C23—53824no—
123C23C2×C4×D26914yes—
124C23D4×D26914yes—
125C23#1686440314yes—
126C23C23×D26913yes—
127D4—26964no—
128C2×C4—224no—
129C2×C4—26924no—
130C2×C4—2694no—
131C2×C4—2694no—
132C2×C4—53864no—
133C2×C4—53812no—
134C2×C4C2×C4×D269124yescomplemented
135C2×C4C23×D26918yes—
136C2×C4C23×D26914yes—
137C22—26916no—
138C22—5388no—
139C22—5388no—
140C22—53896no—
141C22#22575415116yesdirect product factor
142C22C22×C4×D26916yes—
143C22C2×D4×D26916yes—
144C22C2×#1686440316yes—
145C22C24×D26911yescharacteristic
146C4—28no—
147C4—2698no—
148C4—5384no—
149C4C22×C4×D26918yescomplemented
150C2—53816no—
151C2C2×#22575415112yesdirect product factor
152C2C23×C4×D26911yescharacteristic
153C2C22×D4×D26911yescharacteristic
154C2C22×#1686440311yescharacteristic
subgroupG/H
centerC24C22×D269
commutatorC2×C269C24×C4
FrattiniC22C24×D269
FittingC22×C4⋊C4×C269C2
socleC24×C269C23
prime radicalC23×D1076C2
cosocleC22×C269C25
hypercenterC22×C4⋊C4D269
hypocenterC269C22×C4×D4
LCSG ▷ C2×C269 ▷ C269
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C23×C4×D269C2semidirect
3. C2×#22575415C2direct (N × H)
4. C22×#16864379C2semidirect
5. C22×C4×Dic269C2semidirect
6. C22×C4⋊C4×C269C2semidirect
8. C22×D1076C4semidirect
13. C22×C4×D269C22semidirect
14. #22575415C22direct (N × H)
15. C2×#16864379C22semidirect
16. C2×C4×Dic269C22semidirect
19. C2×C4⋊C4×C269C22semidirect
22. C23×D269C2×C4semidirect
24. C2×D1076C2×C4semidirect
27. C22×Dic269D4semidirect
31. C2×C4×D269C23semidirect
32. #16864379C23semidirect
33. C4×Dic269C23semidirect
36. C22×C4×C269C2×C4semidirect
39. C4⋊C4×C269C23semidirect
43. C22×D269C22×C4semidirect
45. D1076C22×C4semidirect
47. C2×Dic269C2×D4semidirect
56. C2×C4×C269C22×C4semidirect
59. C22×C269C4×D4semidirect
67. C2×D269C23×C4semidirect
69. C4×C269C23×C4semidirect
71. Dic269C22×D4semidirect
72. C2×C269C2×C4×D4semidirect
77. C269C22×C4×D4semidirect
82. C22×C4⋊C4D269semidirect
95. C2×C4⋊C4C2×D269semidirect
112. C22×C4C4×D269semidirect
115. C4⋊C4C22×D269semidirect
134. C2×C4C2×C4×D269semidirect
141. C22#22575415direct (N × H)
149. C4C22×C4×D269semidirect
151. C2C2×#22575415direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D10762
C23×C4×D2692
C2×#225754152
C22×#168643792
C22×C4×Dic2692
C22×C4⋊C4×C2692
C22×C4×D4269