Finite Group Databasebeta

← C22×SD16×D113 #28405291

Subgroups — C22×SD16×D113 #28405291

Order 14464.

1720 conjugacy classes of subgroups; only the 565 normal subgroups are shown.

normal subgroups only

This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 565 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
1C22×Q8×D113C211yesmaximal, characteristic, complemented
2C22×D4×D113C211yesmaximal, characteristic
3C22×#14268636C211yesmaximal, characteristic, complemented
4C22×#14268635C211yesmaximal, characteristic, complemented
5C22×#14268634C211yesmaximal, characteristic, complemented
6C2×SD16×D113C2124yesmaximal, direct product factor
7C22×C8×D113C211yesmaximal, characteristic, complemented
8C22×SD16×C113C211yesmaximal, characteristic, complemented
9C24×D113—21no—
10C22×Dic226—21no—
11C22×Dic226C2211yescharacteristic, complemented
12C2×Q8×D113—26no—
13C2×Q8×D113C22112yescomplemented
14C22×D452C2211yescharacteristic
15C22×C22⋊D113—21no—
16C2×D4×D113—26no—
17C2×D4×D113C22112yes—
18C22×C4×D113—21no—
19C22×C4×D113C2211yescharacteristic
20C2×#14268636C22112yescomplemented
21C2×#14268635C22112yescomplemented
22C2×#14268634C22112yescomplemented
23SD16×D113C22164yesdirect product factor
24C22×#11744751C2211yescharacteristic, complemented
25C2×C8×D113C22112yescomplemented
26C22×Q8×C113C2211yescharacteristic, complemented
27C22×D4×C113C2211yescharacteristic
28C2×SD16×C113C22112yescomplemented
29C22×C8×C113C2211yescharacteristic, complemented
30C23×D113—21no—
31C23×D113—212no—
32C23×D113—48no—
33C23×D113D411yescharacteristic
34C2×Dic226—23no—
35C2×Dic226—212no—
36C2×Dic226C2316yescomplemented
37Q8×D113—224no—
38Q8×D113C23116yescomplemented
39C2×D452—23no—
40C2×D452C2316yes—
41C2×C22⋊D113—212no—
42D4×D113—224no—
43D4×D113C23116yes—
44C22×Dic113—21no—
45C22×Dic113D411yescharacteristic
46C2×C4×D113—212no—
47C2×C4×D113D416yes—
48C2×C4×D113C2316yes—
49#14268636C23116yescomplemented
50#14268635C23116yescomplemented
51#14268634C23116yescomplemented
52C2×#11744751C2316yescomplemented
53C8×D113C23116yescomplemented
54C24×C113—21no—
55C2×Q8×C113—23no—
56C2×Q8×C113C2316yescomplemented
57C2×D4×C113—23no—
58C2×D4×C113C2316yes—
59C22×C4×C113—21no—
60C22×C4×C113C2311yescharacteristic
61SD16×C113C23116yescomplemented
62C2×C8×C113C2316yescomplemented
63C23×C113—26no—
64C23×C113—44no—
65C23×C113C2×D411yescharacteristic
66C22×D113—26no—
67C22×D113—216no—
68C22×D113—44no—
69C22×D113—448no—
70C22×D113SD1618yesdirect product factor
71C22×D113C2×D416yes—
72Q8×C113—26no—
73Q8×C113C2414yescomplemented
74D4×C113—26no—
75D4×C113C2414yes—
76C2×C4×C113—26no—
77C2×C4×C113C2×D413yes—
78C2×C4×C113C2413yes—
79C22⋊D113—216no—
80C2×Dic113—26no—
81C2×Dic113C2×D416yes—
82D452—26no—
83D452C2414yes—
84C4×D113—216no—
85C4×D113C2×D4112yes—
86C4×D113C2414yes—
87Dic226—26no—
88Dic226—216no—
89Dic226C2414yescomplemented
90C8×C113C2414yescomplemented
91#11744751C2414yescomplemented
92C22×C113—24no—
93C22×C113—412no—
94C22×C113C2×SD1614yescomplemented
95C22×C113C22×D413yes—
96C2×D113—24no—
97C2×D113—412no—
98C2×D113—432no—
99C2×D113C2×SD16124yesdirect product factor
100C2×D113C22×D414yes—
101C4×C113—24no—
102C4×C113C22×D413yes—
103C4×C113C2511yescharacteristic
104Dic113—24no—
105Dic113C22×D414yes—
106C2×C113—44no—
107C2×C113C22×SD1616yescomplemented
108C2×C113C23×D411yescharacteristic
109D113—44no—
110D113C22×SD1618yesdirect product factor
111C23×SD16—1131nomaximal, Sylow
112C113C23×SD1611yescharacteristic, complemented, Sylow
113C23×Q8—1131no—
114C23×D4—1131no—
115C22×SD16—1131no—
116C22×SD16—1131no—
117C22×SD16—11324no—
118C22×SD16—1131no—
119C22×SD16D11311yescharacteristic, direct product factor
120C23×C8—1131no—
121C25—2261no—
122C22×Q8—11312no—
123C22×Q8—1131no—
124C22×Q8—2261no—
125C22×Q8—2266no—
126C22×Q8C2×D11311yescharacteristic, complemented
127C22×D4—11312no—
128C22×D4—1131no—
129C22×D4—2266no—
130C22×D4—2261no—
131C22×D4C2×D11311yescharacteristic
132C23×C4—1131no—
133C23×C4—2261no—
134C2×SD16—11312no—
135C2×SD16—11312no—
136C2×SD16—11364no—
137C2×SD16—11312no—
138C2×SD16C2×D113112yesdirect product factor
139C22×C8—1131no—
140C22×C8—11312no—
141C22×C8C2×D11311yescharacteristic, complemented
142C24—21no—
143C24—1131no—
144C24—4528no—
145C24—22612no—
146C24—2261no—
147C2×Q8—23no—
148C2×Q8—11316no—
149C2×Q8—1136no—
150C2×Q8—22612no—
151C2×Q8—22624no—
152C2×Q8—2263no—
153C2×Q8C22×D11316yescomplemented
154C2×D4—23no—
155C2×D4—11316no—
156C2×D4—1136no—
157C2×D4—22624no—
158C2×D4—22612no—
159C2×D4—2263no—
160C2×D4C22×D11316yes—
161C22×C4—21no—
162C22×C4—1131no—
163C22×C4—1136no—
164C22×C4—1136no—
165C22×C4—22612no—
166C22×C4—2261no—
167C22×C4C22×D11311yescharacteristic
168SD16—11316no—
169SD16—11316no—
170SD16—11316no—
171SD16C22×D113116yesdirect product factor
172C2×C8—1136no—
173C2×C8—11316no—
174C2×C8C22×D11316yescomplemented
175C23—26no—
176C23—44no—
177C23—1138no—
178C23—1136no—
179C23—45248no—
180C23—4524no—
181C23—22616no—
182C23—2266no—
183C23D4×D11311yescharacteristic
184Q8—26no—
185Q8—1134no—
186Q8—22616no—
187Q8—2266no—
188Q8C23×D11314yescomplemented
189D4—26no—
190D4—1134no—
191D4—22616no—
192D4—2266no—
193D4C23×D11314yes—
194C2×C4—26no—
195C2×C4—1136no—
196C2×C4—11312no—
197C2×C4—1134no—
198C2×C4—22616no—
199C2×C4—2266no—
200C2×C4D4×D11313yes—
201C2×C4C23×D11313yes—
202C8—1134no—
203C8C23×D11314yescomplemented
204C22—24no—
205C22—412no—
206C22—11324no—
207C22—1134no—
208C22—45232no—
209C22—45212no—
210C22—2264no—
211C22SD16×D11314yesdirect product factor
212C22C2×D4×D11313yes—
213C4—24no—
214C4—1134no—
215C4—2264no—
216C4C2×D4×D11313yes—
217C4C24×D11311yescharacteristic
218C2—44no—
219C2—1138no—
220C2—4524no—
221C2C2×SD16×D11316yesdirect product factor
222C2C22×D4×D11311yescharacteristic
subgroupG/H
centerC23D4×D113
commutator, cosocleC4×C113C25
FrattiniC4C24×D113
FittingC22×SD16×C113C2
socleC23×C113C2×D4
prime radicalC22×D4×D113C2
hypercenterC22×SD16D113
hypocenterC113C23×SD16
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D113C2semidirect
3. C22×#14268636C2semidirect
4. C22×#14268635C2semidirect
5. C22×#14268634C2semidirect
6. C2×SD16×D113C2direct (N × H)
7. C22×C8×D113C2semidirect
8. C22×SD16×C113C2semidirect
11. C22×Dic226C22semidirect
13. C2×Q8×D113C22semidirect
20. C2×#14268636C22semidirect
21. C2×#14268635C22semidirect
22. C2×#14268634C22semidirect
23. SD16×D113C22direct (N × H)
24. C22×#11744751C22semidirect
25. C2×C8×D113C22semidirect
26. C22×Q8×C113C22semidirect
28. C2×SD16×C113C22semidirect
29. C22×C8×C113C22semidirect
36. C2×Dic226C23semidirect
38. Q8×D113C23semidirect
49. #14268636C23semidirect
50. #14268635C23semidirect
51. #14268634C23semidirect
52. C2×#11744751C23semidirect
53. C8×D113C23semidirect
56. C2×Q8×C113C23semidirect
61. SD16×C113C23semidirect
62. C2×C8×C113C23semidirect
70. C22×D113SD16direct (N × H)
73. Q8×C113C24semidirect
89. Dic226C24semidirect
90. C8×C113C24semidirect
91. #11744751C24semidirect
94. C22×C113C2×SD16semidirect
99. C2×D113C2×SD16direct (N × H)
107. C2×C113C22×SD16semidirect
110. D113C22×SD16direct (N × H)
112. C113C23×SD16semidirect
119. C22×SD16D113direct (N × H)
126. C22×Q8C2×D113semidirect
138. C2×SD16C2×D113direct (N × H)
141. C22×C8C2×D113semidirect
153. C2×Q8C22×D113semidirect
171. SD16C22×D113direct (N × H)
174. C2×C8C22×D113semidirect
188. Q8C23×D113semidirect
203. C8C23×D113semidirect
211. C22SD16×D113direct (N × H)
221. C2C2×SD16×D113direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D1132
C22×D4×D1132
C22×#142686362
C22×#142686352
C22×#142686342
C2×SD16×D1132
C22×C8×D1132
C22×SD16×C1132
C23×SD16113