Finite Group Databasebeta

← C2×#14271306 #16828691

Subgroups — C2×#14271306 #16828691

Order 3712.

812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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×#90805C211yesmaximal, characteristic, complemented
2C22×#90783C211yesmaximal, characteristic, complemented
3C22×#90782C211yesmaximal, characteristic, complemented
4#14271306C218yesmaximal, direct product factor
5C2×#11745158C211yesmaximal, characteristic, complemented
6C2×#11745157C211yesmaximal, characteristic, complemented
7C2×C22⋊#6597C211yesmaximal, characteristic, complemented
8C2×C29×#121C211yesmaximal, characteristic, complemented
9C22×D4×C29—21no—
10C22×D4×C29C2211yescharacteristic
11C23×C4×C29C2211yescharacteristic
12C22×C22⋊D29—21no—
13C2×#90805—22no—
14C2×#90805—24no—
15C2×#90805—24no—
16C2×#90805C2214yescomplemented
17C22×D116C2211yescharacteristic
18C22×C4×D29—21no—
19C22×Dic58C2211yescharacteristic
20C29×#121—22no—
21C29×#121C2214yescomplemented
22C2×C4⋊C4×C29C2211yescharacteristic
23C2×C22⋊C4×C29—21no—
24C2×#90783—24no—
25C2×#90783C2214yescomplemented
26C2×#90782—24no—
27C2×#90782C2214yescomplemented
28C22×#6597C2211yescharacteristic
29C22×#6597C2211yescharacteristic
30C22⋊#6597C2214yescomplemented
31#11745158C2214yescomplemented
32#11745157C2214yescomplemented
33C24×C29—21no—
34C24×C29D411yescharacteristic
35C23×D29—21no—
36C2×D4×C29—24no—
37C2×D4×C29—22no—
38C2×D4×C29—22no—
39C2×D4×C29—21no—
40C2×D4×C29—44no—
41C2×D4×C29C2312yes—
42C22×C4×C29—22no—
43C22×C4×C29—22no—
44C22×C4×C29—21no—
45C22×C4×C29D411yescharacteristic
46C22×C4×C29D412yes—
47C22×C4×C29C2312yes—
48C22×C4×C29C2311yescharacteristic
49C2×C22⋊D29—28no—
50C2×C22⋊D29—24no—
51C22×Dic29—21no—
52#90805—216no—
53#90805—28no—
54#90805—28no—
55C2×D116—22no—
56C2×D116—21no—
57C2×D116D414yescomplemented
58C2×D116C2312yes—
59C2×C4×D29—28no—
60C2×C4×D29—24no—
61C2×Dic58—22no—
62C2×Dic58—21no—
63C2×Dic58D414yescomplemented
64C2×Dic58C2312yes—
65C4⋊C4×C29—21no—
66C4⋊C4×C29C2312yes—
67C22⋊C4×C29—24no—
68#90783—28no—
69#90782—28no—
70C2×#6597—22no—
71C2×#6597—22no—
72C2×#6597C2312yes—
73C2×#6597C2312yes—
74C23×C29—22no—
75C23×C29—22no—
76C23×C29—22no—
77C23×C29—22no—
78C23×C29—42no—
79C23×C29—42no—
80C23×C29—42no—
81C23×C29C2×D412yes—
82C23×C29C2×D411yescharacteristic
83C22×D29—24no—
84C22×D29—22no—
85C22×D29—42no—
86C22×D29—42no—
87D4×C29—22no—
88D4×C29—22no—
89D4×C29—48no—
90D4×C29—42no—
91C2×C4×C29—22no—
92C2×C4×C29—24no—
93C2×C4×C29—22no—
94C2×C4×C29—22no—
95C2×C4×C29—22no—
96C2×C4×C29—42no—
97C2×C4×C29C2×D412yes—
98C2×C4×C29C2×D412yes—
99C2×C4×C29C2×D412yes—
100C2×C4×C29C2×D411yescharacteristic
101C2×C4×C29C2411yescharacteristic
102C22⋊D29—216no—
103C2×Dic29—24no—
104C2×Dic29—22no—
105D116—24no—
106D116—22no—
107D116C2×D414yescomplemented
108C4×D29—216no—
109Dic58—24no—
110Dic58—22no—
111Dic58C2×D414yescomplemented
112#6597—22no—
113#6597—22no—
114C2×#449—291nomaximal, Sylow
115C22×C29—22no—
116C22×C29—22no—
117C22×C29—22no—
118C22×C29—44no—
119C22×C29—42no—
120C22×C29—42no—
121C22×C29—42no—
122C22×C29—84no—
123C22×C29#12012yes—
124C22×C29#13512yes—
125C22×C29AGL(1,ℤ/8)12yes—
126C22×C29C22×D411yescharacteristic
127C2×D29—24no—
128C2×D29—42no—
129C2×D29—42no—
130C2×D29—48no—
131C4×C29—22no—
132C4×C29—42no—
133C4×C29#12012yes—
134C4×C29C22×D411yescharacteristic
135C4×C29C22×D411yescharacteristic
136Dic29—24no—
137C22×#41—291no—
138C22×SD16—291no—
139C22×D8—291no—
140C2×#121D2911yescharacteristic, complemented
141#449—298no—
142C2×#103—291no—
143C2×#102—291no—
144C2×C22⋊C8—291no—
145C2×C29—42no—
146C2×C29—82no—
147C2×C29#44914yescomplemented
148C2×C29C2×#12011yescharacteristic
149C2×C29C2×#13511yescharacteristic
150C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
151D29—44no—
152C2×#41—294no—
153C2×#41—584no—
154C2×#41—584no—
155C2×#41—582no—
156C22×Q8—291no—
157C22×D4—21no—
158C22×D4—291no—
159C22×D4—581no—
160C22×D4C2×D2911yescharacteristic
161C23×C4—581no—
162C23×C4C2×D2911yescharacteristic
163C2×SD16—294no—
164C2×SD16—584no—
165C2×D8—294no—
166C2×D8—584no—
167C22×C8—291no—
168C22×C8—291no—
169#121—22no—
170#121C2×D2914yescomplemented
171C2×C4⋊C4C2×D2911yescharacteristic
172C2×C22⋊C4—21no—
173#103—294no—
174#102—294no—
175C22⋊C8—294no—
176C29C2×#44911yescharacteristic, complemented, Sylow
177C24—21no—
178C24—581no—
179C24C22⋊D2911yescharacteristic
180#41—588no—
181#41—588no—
182#41—5816no—
183C2×Q8—294no—
184C2×Q8—292no—
185C2×Q8—582no—
186C2×Q8—581no—
187C2×D4—24no—
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—21no—
191C2×D4—44no—
192C2×D4—294no—
193C2×D4—292no—
194C2×D4—588no—
195C2×D4—584no—
196C2×D4—582no—
197C2×D4—581no—
198C2×D4C22×D2912yes—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—21no—
202C22×C4—588no—
203C22×C4—581no—
204C22×C4—584no—
205C22×C4C22⋊D2912yes—
206C22×C4C22⋊D2911yescharacteristic
207C22×C4C22×D2912yes—
208C22×C4C22×D2911yescharacteristic
209SD16—588no—
210D8—588no—
211C2×C8—292no—
212C2×C8—292no—
213C2×C8—582no—
214C2×C8—582no—
215C4⋊C4—21no—
216C4⋊C4C22×D2912yes—
217C22⋊C4—24no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—42no—
223C23—42no—
224C23—42no—
225C23—584no—
226C23—582no—
227C23—1162no—
228C23—1162no—
229C23C2×C22⋊D2912yes—
230C23C2×C22⋊D2911yescharacteristic
231Q8—294no—
232Q8—584no—
233Q8—582no—
234D4—22no—
235D4—22no—
236D4—48no—
237D4—42no—
238D4—294no—
239D4—5816no—
240D4—584no—
241D4—582no—
242C2×C4—22no—
243C2×C4—24no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—42no—
248C2×C4—5816no—
249C2×C4—584no—
250C2×C4—582no—
251C2×C4D4×D2912yes—
252C2×C4D4×D2912yes—
253C2×C4C2×C22⋊D2912yes—
254C2×C4C2×C22⋊D2911yescharacteristic
255C2×C4C23×D2911yescharacteristic
256C8—582no—
257C8—582no—
258C22—22no—
259C22—22no—
260C22—22no—
261C22—44no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—84no—
266C22—584no—
267C22—1168no—
268C22—1162no—
269C22—1162no—
270C22#1174529412yes—
271C22#1174529912yes—
272C22#1174531212yes—
273C22C22×C22⋊D2911yescharacteristic
274C4—22no—
275C4—42no—
276C4—584no—
277C4#1174529912yes—
278C4C2×D4×D2911yescharacteristic
279C4C2×D4×D2911yescharacteristic
280C2—42no—
281C2—82no—
282C2—1164no—
283C2#1427130614yesdirect product factor
284C2C2×#1174529911yescharacteristic
285C2C2×#1174531211yescharacteristic
286C2C2×#1174529411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×#121C2
socleC23×C29C2×D4
hypercenterC2×#121D29
hypocenterC29C2×#449
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#90805C2semidirect
2. C22×#90783C2semidirect
3. C22×#90782C2semidirect
4. #14271306C2direct (N × H)
5. C2×#11745158C2semidirect
6. C2×#11745157C2semidirect
7. C2×C22⋊#6597C2semidirect
8. C2×C29×#121C2semidirect
16. C2×#90805C22semidirect
21. C29×#121C22semidirect
25. C2×#90783C22semidirect
27. C2×#90782C22semidirect
30. C22⋊#6597C22semidirect
31. #11745158C22semidirect
32. #11745157C22semidirect
57. C2×D116D4semidirect
63. C2×Dic58D4semidirect
107. D116C2×D4semidirect
111. Dic58C2×D4semidirect
140. C2×#121D29semidirect
147. C2×C29#449semidirect
170. #121C2×D29semidirect
176. C29C2×#449semidirect
283. C2#14271306direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#908052
C22×#907832
C22×#907822
#142713062
C2×#117451582
C2×#117451572
C2×C22⋊#65972
C2×C29×#1212
C2×#44929