Finite Group Databasebeta

← C22×#16812661 #28376202

Subgroups — C22×#16812661 #28376202

Order 13952.

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×D436C211yesmaximal, characteristic
2C23×C4×D109C212yesmaximal, complemented
3C2×#16812661C2124yesmaximal, direct product factor
4C22×#13182006C212yesmaximal, complemented
5C22×C4×Dic109C211yesmaximal, characteristic, complemented
6C22×C4⋊C4×C109C211yesmaximal, characteristic, complemented
7C24×D109C2212yes—
8C22×D436C4116yescomplemented
9C22×D436C22112yes—
10C23×Dic109C2211yescharacteristic
11C23×Dic109C2211yescharacteristic
12C22×C4×D109—216no—
13C22×C4×D109C22124yescomplemented
14#16812661C22164yesdirect product factor
15C2×#13182006C22124yescomplemented
16C2×C4×Dic109C22112yescomplemented
17C23×C4×C109C2212yes—
18C23×C4×C109C2211yescharacteristic
19C2×C4⋊C4×C109C22112yescomplemented
20C23×D109—28no—
21C23×D109—28no—
22C23×D109C2×C4116yescomplemented
23C23×D109C23112yes—
24C2×D436C2×C4196yescomplemented
25C2×D436C23116yes—
26C22×Dic109—24no—
27C22×Dic109D418yescomplemented
28C22×Dic109C2316yes—
29C22×Dic109C2316yes—
30C2×C4×D109—296no—
31C2×C4×D109C23132yescomplemented
32#13182006C23132yescomplemented
33C4×Dic109C23116yescomplemented
34C24×C109C2311yescharacteristic
35C22×C4×C109—28no—
36C22×C4×C109C2×C418yescomplemented
37C22×C4×C109C23112yes—
38C22×C4×C109C2316yes—
39C4⋊C4×C109C23116yescomplemented
40C23×C109C22×C414yes—
41C23×C109C2×D414yes—
42C23×C109#4114yes—
43C23×C109C2413yes—
44C22×D109—264no—
45C22×D109—224no—
46C22×D109—224no—
47C22×D109C22×C4148yescomplemented
48C22×D109C2418yes—
49C2×C4×C109—224no—
50C2×C4×C109C22×C4124yescomplemented
51C2×C4×C109C2418yes—
52C2×C4×C109C2414yes—
53C2×Dic109—212no—
54C2×Dic109C2×D4124yescomplemented
55C2×Dic109C2414yes—
56C2×Dic109C2414yes—
57D436C22×C4164yescomplemented
58C4×D109—264no—
59C22×C109C4×D4116yescomplemented
60C22×C109C23×C416yes—
61C22×C109C22×D416yes—
62C22×C109C2×#4116yes—
63C22×C109C2511yescharacteristic
64C2×D109—296no—
65C2×D109—28no—
66C2×D109—28no—
67C2×D109C23×C4116yescomplemented
68C4×C109—28no—
69C4×C109C23×C418yescomplemented
70Dic109—24no—
71Dic109C22×D418yescomplemented
72C2×C109C2×C4×D4112yescomplemented
73C2×C109C24×C411yescharacteristic
74C2×C109C23×D411yescharacteristic
75C2×C109C22×#4111yescharacteristic
76D109—216no—
77C22×C4×D4—1091nomaximal, Sylow
78C109C22×C4×D411yescharacteristic, complemented, Sylow
79C23×D4—1091no—
80C24×C4—1092no—
81C2×C4×D4—10924no—
82C22×C4⋊C4D10911yescharacteristic, complemented
83C22×C22⋊C4—1092no—
84C22×C42—1091no—
85C25—1092no—
86C22×D4—10916no—
87C22×D4—10912no—
88C23×C4—1091no—
89C23×C4—1091no—
90C23×C4—10924no—
91C23×C4—21816no—
92C23×C4C2×D10912yes—
93C23×C4C2×D10911yescharacteristic
94C4×D4—10964no—
95C2×C4⋊C4C2×D109112yescomplemented
96C2×C22⋊C4—10924no—
97C2×C42—10912no—
98C24—10916no—
99C24—10912no—
100C24—2188no—
101C24—2188no—
102C24C22×D10911yescharacteristic
103C2×D4—10996no—
104C2×D4—10916no—
105C22×C4—28no—
106C22×C4—1098no—
107C22×C4—1096no—
108C22×C4—1096no—
109C22×C4—10932no—
110C22×C4—21896no—
111C22×C4—2184no—
112C22×C4C4×D10918yescomplemented
113C22×C4C22×D109112yes—
114C22×C4C22×D10916yes—
115C4⋊C4C22×D109116yescomplemented
116C22⋊C4—10932no—
117C42—10916no—
118C23—10948no—
119C23—1098no—
120C23—21864no—
121C23—21824no—
122C23—21824no—
123C23C2×C4×D10914yes—
124C23D4×D10914yes—
125C23#1318203014yes—
126C23C23×D10913yes—
127D4—10964no—
128C2×C4—224no—
129C2×C4—10924no—
130C2×C4—1094no—
131C2×C4—1094no—
132C2×C4—21864no—
133C2×C4—21812no—
134C2×C4C2×C4×D109124yescomplemented
135C2×C4C23×D10918yes—
136C2×C4C23×D10914yes—
137C22—10916no—
138C22—21896no—
139C22—2188no—
140C22—2188no—
141C22#16812661116yesdirect product factor
142C22C22×C4×D10916yes—
143C22C2×D4×D10916yes—
144C22C2×#1318203016yes—
145C22C24×D10911yescharacteristic
146C4—28no—
147C4—1098no—
148C4—2184no—
149C4C22×C4×D10918yescomplemented
150C2—21816no—
151C2C2×#16812661112yesdirect product factor
152C2C23×C4×D10911yescharacteristic
153C2C22×D4×D10911yescharacteristic
154C2C22×#1318203011yescharacteristic
subgroupG/H
centerC24C22×D109
commutatorC2×C109C24×C4
FrattiniC22C24×D109
FittingC22×C4⋊C4×C109C2
socleC24×C109C23
prime radicalC23×D436C2
cosocleC22×C109C25
hypercenterC22×C4⋊C4D109
hypocenterC109C22×C4×D4
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C23×C4×D109C2semidirect
3. C2×#16812661C2direct (N × H)
4. C22×#13182006C2semidirect
5. C22×C4×Dic109C2semidirect
6. C22×C4⋊C4×C109C2semidirect
8. C22×D436C4semidirect
13. C22×C4×D109C22semidirect
14. #16812661C22direct (N × H)
15. C2×#13182006C22semidirect
16. C2×C4×Dic109C22semidirect
19. C2×C4⋊C4×C109C22semidirect
22. C23×D109C2×C4semidirect
24. C2×D436C2×C4semidirect
27. C22×Dic109D4semidirect
31. C2×C4×D109C23semidirect
32. #13182006C23semidirect
33. C4×Dic109C23semidirect
36. C22×C4×C109C2×C4semidirect
39. C4⋊C4×C109C23semidirect
47. C22×D109C22×C4semidirect
50. C2×C4×C109C22×C4semidirect
54. C2×Dic109C2×D4semidirect
57. D436C22×C4semidirect
59. C22×C109C4×D4semidirect
67. C2×D109C23×C4semidirect
69. C4×C109C23×C4semidirect
71. Dic109C22×D4semidirect
72. C2×C109C2×C4×D4semidirect
78. C109C22×C4×D4semidirect
82. C22×C4⋊C4D109semidirect
95. C2×C4⋊C4C2×D109semidirect
112. C22×C4C4×D109semidirect
115. C4⋊C4C22×D109semidirect
134. C2×C4C2×C4×D109semidirect
141. C22#16812661direct (N × H)
149. C4C22×C4×D109semidirect
151. C2C2×#16812661direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D4362
C23×C4×D1092
C2×#168126612
C22×#131820062
C22×C4×Dic1092
C22×C4⋊C4×C1092
C22×C4×D4109