Finite Group Databasebeta

← C22×#16812667 #28376247

Subgroups — C22×#16812667 #28376247

Order 13952.

4544 conjugacy classes of subgroups; only the 725 normal subgroups are shown.

normal subgroups only

This group has 4544 conjugacy classes of subgroups — too many to draw. Only its 725 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
1C25×D109C211yesmaximal, characteristic, complemented
2C23×C22⋊D109C212yesmaximal, complemented
3C2×#16812667C2124yesmaximal, direct product factor
4C22×C22⋊Dic109C211yesmaximal, characteristic, complemented
5C22×#13182006C212yesmaximal, complemented
6C23×D4×C109C211yesmaximal, characteristic, complemented
7C24×D109—216no—
8C24×D109—28no—
9C24×D109C2212yes—
10C24×D109C22112yescomplemented
11C22×C22⋊D109—216no—
12C22×C22⋊D109C22124yescomplemented
13C23×Dic109C2212yescomplemented
14#16812667C22164yesdirect product factor
15C2×C22⋊Dic109C22112yescomplemented
16C2×#13182006C22124yescomplemented
17C25×C109C2211yescharacteristic
18C25×C109C2211yescharacteristic, complemented
19C22×D4×C109—28no—
20C22×D4×C109C22112yescomplemented
21C23×C4×C109C2211yescharacteristic, complemented
22C23×D109—2128no—
23C23×D109—28no—
24C23×D109—28no—
25C23×D109—248no—
26C23×D109—296no—
27C23×D109D4116yescomplemented
28C23×D109C23112yes—
29C23×D109C23116yescomplemented
30C2×C22⋊D109—296no—
31C2×C22⋊D109C23132yescomplemented
32C22×Dic109—28no—
33C22×Dic109C23112yescomplemented
34C22⋊Dic109C23116yescomplemented
35#13182006C23132yescomplemented
36C24×C109—28no—
37C24×C109—24no—
38C24×C109—28no—
39C24×C109D418yescomplemented
40C24×C109C2316yes—
41C24×C109C2311yescharacteristic
42C24×C109C2316yescomplemented
43C2×D4×C109—248no—
44C2×D4×C109C23116yescomplemented
45C22×C4×C109—24no—
46C22×C4×C109C2316yescomplemented
47C23×C109—232no—
48C23×C109—224no—
49C23×C109—212no—
50C23×C109—224no—
51C23×C109—416no—
52C23×C109C2×D418yes—
53C23×C109C2×D414yes—
54C23×C109C2×D4124yescomplemented
55C23×C109C2414yes—
56C23×C109C2413yes—
57C23×C109C2414yescomplemented
58C22×D109—2384no—
59C22×D109—264no—
60C22×D109—224no—
61C22×D109—224no—
62C22×D109—232no—
63C22×D109—264no—
64C22×D109C2×D4148yescomplemented
65C22×D109C2418yes—
66D4×C109—232no—
67C2×C4×C109—212no—
68C2×C4×C109C2414yescomplemented
69C22⋊D109—264no—
70C2×Dic109—224no—
71C2×Dic109C2418yescomplemented
72C22×C109—248no—
73C22×C109—28no—
74C22×C109—28no—
75C22×C109—24no—
76C22×C109—424no—
77C22×C109#120116yescomplemented
78C22×C109C22×D4112yes—
79C22×C109C22×D416yes—
80C22×C109C22×D418yescomplemented
81C22×C109C2511yescharacteristic
82C2×D109—2128no—
83C2×D109—296no—
84C2×D109—28no—
85C2×D109—28no—
86C2×D109C22×D4116yescomplemented
87C4×C109—24no—
88Dic109—28no—
89C2×C109—28no—
90C2×C109—44no—
91C2×C109C2×#120112yescomplemented
92C2×C109C23×D412yes—
93C2×C109C23×D411yescharacteristic
94D109—216no—
95C22×#120—1091nomaximal, Sylow
96C109C22×#12011yescharacteristic, complemented, Sylow
97C26—1091no—
98C23×D4—1092no—
99C23×D4D10911yescharacteristic, complemented
100C2×#120—10924no—
101C22×C22⋊C4—1091no—
102C22×C22⋊C4—1092no—
103C25—1092no—
104C25—10912no—
105C25—21816no—
106C25—2188no—
107C25C2×D10911yescharacteristic
108C25C2×D10911yescharacteristic, complemented
109C22×D4—28no—
110C22×D4—10924no—
111C22×D4—21816no—
112C22×D4C2×D109112yescomplemented
113C23×C4—1092no—
114C23×C4C2×D10911yescharacteristic, complemented
115#120—10964no—
116C2×C22⋊C4—10912no—
117C2×C22⋊C4—10924no—
118C24—28no—
119C24—28no—
120C24—24no—
121C24—10916no—
122C24—10912no—
123C24—10916no—
124C24—21896no—
125C24—218128no—
126C24—2188no—
127C24—2188no—
128C24—21848no—
129C24C22⋊D10918yescomplemented
130C24C22×D10916yes—
131C24C22×D10911yescharacteristic
132C24C22×D10916yescomplemented
133C2×D4—248no—
134C2×D4—10932no—
135C2×D4—21896no—
136C2×D4C22×D109116yescomplemented
137C22×C4—24no—
138C22×C4—10912no—
139C22×C4—2188no—
140C22×C4C22×D10916yescomplemented
141C22⋊C4—10916no—
142C22⋊C4—10932no—
143C23—232no—
144C23—224no—
145C23—224no—
146C23—212no—
147C23—416no—
148C23—10948no—
149C23—1098no—
150C23—21864no—
151C23—218384no—
152C23—21864no—
153C23—21824no—
154C23—21824no—
155C23—21832no—
156C23D4×D10918yes—
157C23C2×C22⋊D10914yes—
158C23C2×C22⋊D109124yescomplemented
159C23C23×D10914yes—
160C23C23×D10913yes—
161C23C23×D10914yescomplemented
162D4—232no—
163D4—21864no—
164C2×C4—212no—
165C2×C4—1098no—
166C2×C4—21824no—
167C2×C4C23×D10914yescomplemented
168C22—248no—
169C22—28no—
170C22—28no—
171C22—24no—
172C22—424no—
173C22—10916no—
174C22—218128no—
175C22—21896no—
176C22—2188no—
177C22—2188no—
178C22#16812667116yesdirect product factor
179C22C2×D4×D109112yes—
180C22C22×C22⋊D10916yes—
181C22C22×C22⋊D10918yescomplemented
182C22C24×D10911yescharacteristic
183C4—24no—
184C4—2188no—
185C2—28no—
186C2—44no—
187C2—21816no—
188C2C2×#16812667112yesdirect product factor
189C2C22×D4×D10912yes—
190C2C23×C22⋊D10911yescharacteristic
subgroupG/H
centerC24C22×D109
commutator, cosocleC22×C109C25
FrattiniC22C24×D109
FittingC23×D4×C109C2
socleC24×C109C23
hypercenterC23×D4D109
hypocenterC109C22×#120
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C25×D109C2semidirect
2. C23×C22⋊D109C2semidirect
3. C2×#16812667C2direct (N × H)
4. C22×C22⋊Dic109C2semidirect
5. C22×#13182006C2semidirect
6. C23×D4×C109C2semidirect
10. C24×D109C22semidirect
12. C22×C22⋊D109C22semidirect
13. C23×Dic109C22semidirect
14. #16812667C22direct (N × H)
15. C2×C22⋊Dic109C22semidirect
16. C2×#13182006C22semidirect
18. C25×C109C22semidirect
20. C22×D4×C109C22semidirect
21. C23×C4×C109C22semidirect
27. C23×D109D4semidirect
29. C23×D109C23semidirect
31. C2×C22⋊D109C23semidirect
33. C22×Dic109C23semidirect
34. C22⋊Dic109C23semidirect
35. #13182006C23semidirect
39. C24×C109D4semidirect
42. C24×C109C23semidirect
44. C2×D4×C109C23semidirect
46. C22×C4×C109C23semidirect
54. C23×C109C2×D4semidirect
57. C23×C109C24semidirect
64. C22×D109C2×D4semidirect
68. C2×C4×C109C24semidirect
71. C2×Dic109C24semidirect
77. C22×C109#120semidirect
80. C22×C109C22×D4semidirect
86. C2×D109C22×D4semidirect
91. C2×C109C2×#120semidirect
96. C109C22×#120semidirect
99. C23×D4D109semidirect
108. C25C2×D109semidirect
112. C22×D4C2×D109semidirect
114. C23×C4C2×D109semidirect
129. C24C22⋊D109semidirect
132. C24C22×D109semidirect
136. C2×D4C22×D109semidirect
140. C22×C4C22×D109semidirect
158. C23C2×C22⋊D109semidirect
161. C23C23×D109semidirect
167. C2×C4C23×D109semidirect
178. C22#16812667direct (N × H)
181. C22C22×C22⋊D109semidirect
188. C2C2×#16812667direct (N × H)

Maximal subgroups

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

subgroupindex
C25×D1092
C23×C22⋊D1092
C2×#168126672
C22×C22⋊Dic1092
C22×#131820062
C23×D4×C1092
C22×#120109