Finite Group Databasebeta

← C2×#14271315 #16828675

Subgroups — C2×#14271315 #16828675

Order 3712.

996 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 173 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×D4×D29C211yesmaximal, characteristic
2C22×#90773C211yesmaximal, characteristic, complemented
3C22×#90783C211yesmaximal, characteristic, complemented
4C2×#11745259C211yesmaximal, characteristic, complemented
5#14271315C218yesmaximal, direct product factor
6C2×#11745157C211yesmaximal, characteristic, complemented
7C2×#11745168C211yesmaximal, characteristic, complemented
8C2×C29×#102C211yesmaximal, characteristic, complemented
9C24×D29—21no—
10C22×D4×C29C2211yescharacteristic
11C22×C22⋊D29—21no—
12C2×D4×D29—24no—
13C2×D4×D29—24no—
14C2×D4×D29—22no—
15C2×D4×D29C2214yes—
16C22×D116C2211yescharacteristic
17C22×C4×D29C2211yescharacteristic
18C22×Dic58C2211yescharacteristic, complemented
19C22×C8×C29C2211yescharacteristic, complemented
20C2×C4⋊C4×C29C2211yescharacteristic, complemented
21C2×#90783—24no—
22C2×#90783C2214yescomplemented
23C2×#90781—21no—
24C2×C4⋊Dic29—21no—
25C22×#6597C2211yescharacteristic, complemented
26C2×#90773—24no—
27C2×#90773C2214yescomplemented
28#11745259—22no—
29#11745259C2214yescomplemented
30C29×#102C2214yescomplemented
31#11745168C2214yescomplemented
32#11745157C2214yescomplemented
33C24×C29—21no—
34C23×D29—28no—
35C23×D29—21no—
36C23×D29—24no—
37C23×D29—44no—
38C23×D29—44no—
39C23×D29D411yescharacteristic
40C2×D4×C29—21no—
41C2×D4×C29—22no—
42C2×D4×C29D414yes—
43C2×D4×C29C2312yes—
44C22×C4×C29—21no—
45C22×C4×C29C2311yescharacteristic
46C2×C22⋊D29—28no—
47C2×C22⋊D29—24no—
48C22×Dic29—21no—
49C22×Dic29D411yescharacteristic
50D4×D29—216no—
51D4×D29—28no—
52D4×D29—28no—
53C2×D116—22no—
54C2×D116—21no—
55C2×D116D414yes—
56C2×D116C2312yes—
57C2×C4×D29—22no—
58C2×C4×D29—22no—
59C2×C4×D29D412yes—
60C2×C4×D29C2312yes—
61C2×Dic58—22no—
62C2×Dic58—22no—
63C2×Dic58—21no—
64C2×Dic58C2312yescomplemented
65C2×C8×C29—22no—
66C2×C8×C29C2312yescomplemented
67C4⋊C4×C29—21no—
68C4⋊C4×C29C2312yescomplemented
69#90783—28no—
70#90781—24no—
71C4⋊Dic29—24no—
72C2×#6597—22no—
73C2×#6597C2312yescomplemented
74#90773—28no—
75C23×C29—24no—
76C23×C29—22no—
77C23×C29—42no—
78C23×C29—42no—
79C23×C29C2×D411yescharacteristic
80C22×D29—22no—
81C22×D29—22no—
82C22×D29—216no—
83C22×D29—24no—
84C22×D29—22no—
85C22×D29—48no—
86C22×D29—432no—
87C22×D29—42no—
88C22×D29—42no—
89C22×D29—48no—
90C22×D29SD1614yescomplemented
91C22×D29C2×D412yes—
92D4×C29—24no—
93D4×C29—22no—
94D4×C29C2×D414yes—
95C2×C4×C29—22no—
96C2×C4×C29—42no—
97C2×C4×C29C2×D412yes—
98C2×C4×C29C2×D411yescharacteristic
99C2×C4×C29C2×D412yes—
100C2×C4×C29C2411yescharacteristic
101C22⋊D29—216no—
102C2×Dic29—22no—
103C2×Dic29—22no—
104C2×Dic29—42no—
105C2×Dic29C2×D412yes—
106D116—24no—
107D116—22no—
108D116C2×D414yes—
109C4×D29—24no—
110C4×D29—22no—
111C4×D29—22no—
112Dic58—22no—
113Dic58—22no—
114Dic58—42no—
115C8×C29—22no—
116#6597—22no—
117C2×#450—291nomaximal, Sylow
118C22×C29—24no—
119C22×C29—42no—
120C22×C29—42no—
121C22×C29—48no—
122C22×C29#12012yes—
123C22×C29C2×SD1612yes—
124C22×C29AGL(1,ℤ/8)12yes—
125C22×C29C22×D411yescharacteristic
126C2×D29—22no—
127C2×D29—22no—
128C2×D29—28no—
129C2×D29—24no—
130C2×D29—432no—
131C2×D29—42no—
132C2×D29—42no—
133C2×D29—48no—
134C2×D29C2×SD1614yescomplemented
135C4×C29—42no—
136C4×C29#12012yes—
137C4×C29C22×D411yescharacteristic
138C4×C29C22×D411yescharacteristic
139Dic29—22no—
140Dic29—42no—
141C23×D4—291no—
142C22×SD16—291no—
143C22×SD16—291no—
144C2×C22⋊Q8—291no—
145#450—298no—
146C2×#102—291no—
147C2×#102D2911yescharacteristic, complemented
148C2×C22⋊C8—291no—
149C2×C29—44no—
150C2×C29#45014yescomplemented
151C2×C29C2×#12011yescharacteristic
152C2×C29C22×SD1611yescharacteristic
153C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
154D29—24no—
155D29—44no—
156C25—581no—
157C22×Q8—291no—
158C22×D4—294no—
159C22×D4—291no—
160C22×D4—582no—
161C22×D4—581no—
162C22×D4—584no—
163C22×D4—584no—
164C22×D4C2×D2911yescharacteristic
165C23×C4—291no—
166C2×SD16—294no—
167C2×SD16—294no—
168C2×SD16—584no—
169C2×SD16—584no—
170C22×C8—291no—
171C22×C8C2×D2911yescharacteristic, complemented
172C22⋊Q8—294no—
173C22⋊Q8—582no—
174C2×C4⋊C4—581no—
175C2×C4⋊C4C2×D2911yescharacteristic, complemented
176C2×C22⋊C4—581no—
177#102—294no—
178#102C2×D2914yescomplemented
179C22⋊C8—294no—
180C29C2×#45011yescharacteristic, complemented, Sylow
181C24—21no—
182C24—291no—
183C24—584no—
184C24—588no—
185C24—581no—
186C24—1164no—
187C24—1164no—
188C2×Q8—292no—
189C2×Q8—581no—
190C2×Q8—582no—
191C2×Q8—582no—
192C2×D4—22no—
193C2×D4—21no—
194C2×D4—294no—
195C2×D4—292no—
196C2×D4—584no—
197C2×D4—588no—
198C2×D4—5816no—
199C2×D4—588no—
200C2×D4—588no—
201C2×D4—582no—
202C2×D4—581no—
203C2×D4D11614yes—
204C2×D4C22×D2912yes—
205C22×C4—21no—
206C22×C4—291no—
207C22×C4—292no—
208C22×C4—292no—
209C22×C4—582no—
210C22×C4—582no—
211C22×C4—581no—
212C22×C4C22×D2911yescharacteristic
213SD16—588no—
214SD16—588no—
215C2×C8—22no—
216C2×C8—292no—
217C2×C8—582no—
218C2×C8C22×D2912yescomplemented
219C4⋊C4—21no—
220C4⋊C4—584no—
221C4⋊C4C22×D2912yescomplemented
222C22⋊C4—584no—
223C23—22no—
224C23—24no—
225C23—42no—
226C23—42no—
227C23—292no—
228C23—294no—
229C23—5816no—
230C23—582no—
231C23—582no—
232C23—582no—
233C23—584no—
234C23—1168no—
235C23—11632no—
236C23—1168no—
237C23—1162no—
238C23—1162no—
239C23D4×D2911yescharacteristic
240Q8—582no—
241Q8—582no—
242Q8—1162no—
243D4—22no—
244D4—24no—
245D4—294no—
246D4—5816no—
247D4—582no—
248D4—584no—
249D4C2×D11614yes—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—292no—
253C2×C4—582no—
254C2×C4—582no—
255C2×C4—582no—
256C2×C4—584no—
257C2×C4—582no—
258C2×C4—1162no—
259C2×C4C2×D11612yes—
260C2×C4D4×D2912yes—
261C2×C4D4×D2911yescharacteristic
262C2×C4C23×D2911yescharacteristic
263C8—22no—
264C8—582no—
265C22—24no—
266C22—48no—
267C22—42no—
268C22—42no—
269C22—294no—
270C22—588no—
271C22—582no—
272C22—582no—
273C22—584no—
274C22—11632no—
275C22—1168no—
276C22—1162no—
277C22—1162no—
278C22#1174524412yes—
279C22#1174527312yes—
280C22SD16×D2912yes—
281C22C2×D4×D2911yescharacteristic
282C4—42no—
283C4—582no—
284C4—1162no—
285C4#1174524412yes—
286C4C22×D11611yescharacteristic
287C4C2×D4×D2911yescharacteristic
288C2—44no—
289C2—584no—
290C2—1164no—
291C2#1427131514yesdirect product factor
292C2C2×#1174524411yescharacteristic
293C2C2×SD16×D2911yescharacteristic
294C2C2×#1174527311yescharacteristic
subgroupG/H
centerC23D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×#102C2
socleC23×C29C2×D4
prime radicalC22×D4×D29C2
hypercenterC2×#102D29
hypocenterC29C2×#450
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C22×#90773C2semidirect
3. C22×#90783C2semidirect
4. C2×#11745259C2semidirect
5. #14271315C2direct (N × H)
6. C2×#11745157C2semidirect
7. C2×#11745168C2semidirect
8. C2×C29×#102C2semidirect
18. C22×Dic58C22semidirect
19. C22×C8×C29C22semidirect
20. C2×C4⋊C4×C29C22semidirect
22. C2×#90783C22semidirect
25. C22×#6597C22semidirect
27. C2×#90773C22semidirect
29. #11745259C22semidirect
30. C29×#102C22semidirect
31. #11745168C22semidirect
32. #11745157C22semidirect
64. C2×Dic58C23semidirect
66. C2×C8×C29C23semidirect
68. C4⋊C4×C29C23semidirect
73. C2×#6597C23semidirect
90. C22×D29SD16semidirect
134. C2×D29C2×SD16semidirect
147. C2×#102D29semidirect
150. C2×C29#450semidirect
171. C22×C8C2×D29semidirect
175. C2×C4⋊C4C2×D29semidirect
178. #102C2×D29semidirect
180. C29C2×#450semidirect
218. C2×C8C22×D29semidirect
221. C4⋊C4C22×D29semidirect
291. C2#14271315direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D292
C22×#907732
C22×#907832
C2×#117452592
#142713152
C2×#117451572
C2×#117451682
C2×C29×#1022
C2×#45029