Finite Group Databasebeta

← C2×#14271071 #16822687

Subgroups — C2×#14271071 #16822687

Order 3712.

1812 conjugacy classes of subgroups; only the 285 normal subgroups are shown.

normal subgroups only

This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 285 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×C22⋊D29C212yesmaximal, complemented
2C22×C22⋊Dic29C212yesmaximal, complemented
3C22×#90781C211yesmaximal, characteristic, complemented
4#14271071C218yesmaximal, direct product factor
5C2×#11745179C211yesmaximal, characteristic, complemented
6C23×D4×C29C211yesmaximal, characteristic, complemented
7C25×C29C2212yes—
8C24×D29C2211yescharacteristic
9C22×D4×C29—28no—
10C22×D4×C29—24no—
11C22×D4×C29C2214yescomplemented
12C23×C4×C29C2211yescharacteristic
13C22×C22⋊D29—28no—
14C22×C22⋊D29—28no—
15C22×C22⋊D29—28no—
16C22×C22⋊D29C2218yescomplemented
17C23×Dic29C2211yescharacteristic
18C23×Dic29C2212yes—
19C2×C22⋊Dic29—28no—
20C2×C22⋊Dic29C2218yescomplemented
21C2×#90781—24no—
22C2×#90781C2214yescomplemented
23#11745179C2214yescomplemented
24C24×C29—24no—
25C24×C29—24no—
26C24×C29—24no—
27C24×C29—24no—
28C24×C29—24no—
29C24×C29—24no—
30C24×C29D418yescomplemented
31C24×C29C2314yes—
32C24×C29C2311yescharacteristic
33C23×D29—22no—
34C23×D29—24no—
35C23×D29—24no—
36C23×D29—22no—
37C23×D29D414yescomplemented
38C23×D29C2312yes—
39C2×D4×C29—232no—
40C2×D4×C29—216no—
41C2×D4×C29—28no—
42C22×C4×C29—24no—
43C22×C4×C29D414yescomplemented
44C22×C4×C29C2312yes—
45C2×C22⋊D29—264no—
46C2×C22⋊D29—216no—
47C2×C22⋊D29—216no—
48C2×C22⋊D29—216no—
49C22×Dic29—24no—
50C22×Dic29—24no—
51C22×Dic29—22no—
52C22×Dic29—24no—
53C22×Dic29D418yescomplemented
54C22×Dic29C2312yes—
55C22×Dic29C2314yes—
56C22⋊Dic29—216no—
57#90781—28no—
58C23×C29—216no—
59C23×C29—216no—
60C23×C29—216no—
61C23×C29—24no—
62C23×C29—24no—
63C23×C29—24no—
64C23×C29—24no—
65C23×C29—24no—
66C23×C29—24no—
67C23×C29—48no—
68C23×C29—48no—
69C23×C29—48no—
70C23×C29—48no—
71C23×C29C2×D412yes—
72C23×C29C2×D414yes—
73C23×C29C2×D414yes—
74C23×C29C2×D412yes—
75C23×C29C2×D418yescomplemented
76C23×C29#4112yes—
77C23×C29C2411yescharacteristic
78C22×D29—216no—
79C22×D29—28no—
80C22×D29—22no—
81C22×D29—24no—
82C22×D29—24no—
83C22×D29—22no—
84C22×D29—44no—
85C22×D29—48no—
86C22×D29—44no—
87C22×D29C2×D414yescomplemented
88D4×C29—232no—
89C2×C4×C29—28no—
90C2×C4×C29—24no—
91C2×C4×C29C2×D414yescomplemented
92C22⋊D29—264no—
93C2×Dic29—216no—
94C2×Dic29—24no—
95C2×Dic29—24no—
96C2×Dic29—22no—
97C2×Dic29—24no—
98C2×Dic29—44no—
99C2×Dic29C2×D418yescomplemented
100C2×#392—291nomaximal, Sylow
101C22×C29—28no—
102C22×C29—28no—
103C22×C29—28no—
104C22×C29—44no—
105C22×C29—44no—
106C22×C29—44no—
107C22×C29—44no—
108C22×C29—432no—
109C22×C29#12018yes—
110C22×C29#12014yes—
111C22×C29#12114yes—
112C22×C29#12118yes—
113C22×C29#12714yes—
114C22×C29C22×D411yescharacteristic
115C22×C29C22×D412yes—
116C22×C29C22×D412yes—
117C22×C29C22×D411yescharacteristic
118C22×C29C2×#4111yescharacteristic
119C2×D29—28no—
120C2×D29—24no—
121C2×D29—42no—
122C2×D29—44no—
123C2×D29—42no—
124C2×D29—416no—
125C4×C29—24no—
126Dic29—28no—
127Dic29—42no—
128C23×D4—292no—
129C23×D4D2911yescharacteristic, complemented
130C22×C22⋊C4—292no—
131C22×C22⋊C4—291no—
132#392—298no—
133C2×#95—291no—
134C2×C29—48no—
135C2×C29#39218yescomplemented
136C2×C29C2×#12012yes—
137C2×C29C2×#12011yescharacteristic
138C2×C29C2×#12111yescharacteristic
139C2×C29C2×#12112yes—
140C2×C29C2×#12711yescharacteristic
141D29—44no—
142C25—291no—
143C25C2×D2912yes—
144C22×D4—28no—
145C22×D4—24no—
146C22×D4—298no—
147C22×D4—588no—
148C22×D4—588no—
149C22×D4—588no—
150C22×D4C2×D2914yescomplemented
151C23×C4—292no—
152C23×C4—291no—
153C23×C4C2×D2911yescharacteristic
154C2×C22⋊C4—298no—
155C2×C22⋊C4—294no—
156C2×C22⋊C4—588no—
157C2×C22⋊C4—584no—
158#95—294no—
159C29C2×#39211yescharacteristic, complemented, Sylow
160C24—24no—
161C24—24no—
162C24—24no—
163C24—24no—
164C24—24no—
165C24—24no—
166C24—294no—
167C24—292no—
168C24—584no—
169C24—582no—
170C24—582no—
171C24—584no—
172C24C22⋊D2918yescomplemented
173C24C22×D2914yes—
174C24C22×D2911yescharacteristic
175C2×D4—232no—
176C2×D4—216no—
177C2×D4—28no—
178C2×D4—5816no—
179C2×D4—5816no—
180C2×D4—5864no—
181C2×D4—5816no—
182C22×C4—24no—
183C22×C4—298no—
184C22×C4—294no—
185C22×C4—292no—
186C22×C4—584no—
187C22×C4—584no—
188C22×C4—584no—
189C22×C4—582no—
190C22×C4C22⋊D2914yescomplemented
191C22×C4C22×D2912yes—
192C22⋊C4—5816no—
193C22⋊C4—588no—
194C23—216no—
195C23—216no—
196C23—216no—
197C23—24no—
198C23—24no—
199C23—24no—
200C23—24no—
201C23—24no—
202C23—24no—
203C23—48no—
204C23—48no—
205C23—48no—
206C23—48no—
207C23—294no—
208C23—5816no—
209C23—588no—
210C23—584no—
211C23—582no—
212C23—582no—
213C23—584no—
214C23—1168no—
215C23—1164no—
216C23—1164no—
217C23D4×D2912yes—
218C23D4×D2914yes—
219C23#9080712yes—
220C23C2×C22⋊D2914yes—
221C23C2×C22⋊D2912yes—
222C23C2×C22⋊D2918yescomplemented
223C23C23×D2911yescharacteristic
224D4—232no—
225D4—5864no—
226C2×C4—28no—
227C2×C4—24no—
228C2×C4—298no—
229C2×C4—5816no—
230C2×C4—584no—
231C2×C4—584no—
232C2×C4—584no—
233C2×C4—582no—
234C2×C4—1164no—
235C2×C4C2×C22⋊D2914yescomplemented
236C22—28no—
237C22—28no—
238C22—28no—
239C22—432no—
240C22—44no—
241C22—44no—
242C22—44no—
243C22—44no—
244C22—588no—
245C22—584no—
246C22—11616no—
247C22—1162no—
248C22—1164no—
249C22—1162no—
250C22#1174529918yes—
251C22#1174530014yes—
252C22#1174530118yes—
253C22#1174530214yes—
254C22#1174531514yes—
255C22C2×D4×D2911yescharacteristic
256C22C2×D4×D2912yes—
257C22C2×#9080711yescharacteristic
258C22C22×C22⋊D2912yes—
259C22C22×C22⋊D2911yescharacteristic
260C4—24no—
261C4—588no—
262C4—1162no—
263C2—48no—
264C2—1164no—
265C2#1427107118yesdirect product factor
266C2C2×#1174529912yes—
267C2C2×#1174531511yescharacteristic
268C2C2×#1174530011yescharacteristic
269C2C2×#1174530112yes—
270C2C2×#1174530211yescharacteristic
subgroupG/H
centerC24C22×D29
commutator, cosocleC23×C29C24
FrattiniC23C23×D29
FittingC23×D4×C29C2
socleC24×C29C23
hypercenterC23×D4D29
hypocenterC29C2×#392
LCSG ▷ C23×C29 ▷ C29
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D29C2semidirect
2. C22×C22⋊Dic29C2semidirect
3. C22×#90781C2semidirect
4. #14271071C2direct (N × H)
5. C2×#11745179C2semidirect
6. C23×D4×C29C2semidirect
11. C22×D4×C29C22semidirect
16. C22×C22⋊D29C22semidirect
20. C2×C22⋊Dic29C22semidirect
22. C2×#90781C22semidirect
23. #11745179C22semidirect
30. C24×C29D4semidirect
37. C23×D29D4semidirect
43. C22×C4×C29D4semidirect
53. C22×Dic29D4semidirect
75. C23×C29C2×D4semidirect
87. C22×D29C2×D4semidirect
91. C2×C4×C29C2×D4semidirect
99. C2×Dic29C2×D4semidirect
129. C23×D4D29semidirect
135. C2×C29#392semidirect
150. C22×D4C2×D29semidirect
159. C29C2×#392semidirect
172. C24C22⋊D29semidirect
190. C22×C4C22⋊D29semidirect
222. C23C2×C22⋊D29semidirect
235. C2×C4C2×C22⋊D29semidirect
265. C2#14271071direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D292
C22×C22⋊Dic292
C22×#907812
#142710712
C2×#117451792
C23×D4×C292
C2×#39229