Finite Group Databasebeta

← C2×#14271312 #16828672

Subgroups — C2×#14271312 #16828672

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×#90784C211yesmaximal, characteristic, complemented
3C2×#11745308C211yesmaximal, characteristic, complemented
4#14271312C218yesmaximal, direct product factor
5C2×#11745169C211yesmaximal, characteristic, complemented
6C2×#11745180C211yesmaximal, characteristic, complemented
7C2×#11745168C211yesmaximal, characteristic, complemented
8C22×SD16×C29C211yesmaximal, characteristic, complemented
9C24×D29—21no—
10C22×Q8×C29C2211yescharacteristic, complemented
11C22×D4×C29C2211yescharacteristic
12C22×C22⋊D29—21no—
13C2×D4×D29—24no—
14C2×D4×D29—24no—
15C2×D4×D29—22no—
16C2×D4×D29C2214yes—
17C22×D116C2211yescharacteristic
18C22×C4×D29C2211yescharacteristic
19C2×SD16×C29—24no—
20C2×SD16×C29C2214yescomplemented
21C22×C8×C29C2211yescharacteristic, complemented
22#11745308—22no—
23#11745308C2214yescomplemented
24C2×#90784—24no—
25C2×#90784C2214yescomplemented
26C2×#90781—21no—
27C2×C4⋊Dic29C2211yescharacteristic, complemented
28C2×#90779—21no—
29C22×#6597C2211yescharacteristic, complemented
30#11745180C2214yescomplemented
31#11745169C2214yescomplemented
32#11745168C2214yescomplemented
33C24×C29—21no—
34C23×D29—28no—
35C23×D29—21no—
36C23×D29—24no—
37C23×D29—44no—
38C23×D29—44no—
39C23×D29D411yescharacteristic
40C2×Q8×C29—21no—
41C2×Q8×C29—22no—
42C2×Q8×C29—22no—
43C2×Q8×C29C2312yescomplemented
44C2×D4×C29—21no—
45C2×D4×C29—22no—
46C2×D4×C29D414yes—
47C2×D4×C29C2312yes—
48C22×C4×C29—21no—
49C22×C4×C29C2311yescharacteristic
50C2×C22⋊D29—28no—
51C2×C22⋊D29—24no—
52C22×Dic29—21no—
53C22×Dic29D411yescharacteristic
54D4×D29—216no—
55D4×D29—28no—
56D4×D29—28no—
57C2×D116—21no—
58C2×D116—22no—
59C2×D116D414yes—
60C2×D116C2312yes—
61C2×C4×D29—22no—
62C2×C4×D29—22no—
63C2×C4×D29D412yes—
64C2×C4×D29C2312yes—
65SD16×C29—28no—
66C2×C8×C29—22no—
67C2×C8×C29C2312yescomplemented
68#90784—28no—
69#90781—24no—
70C4⋊Dic29—21no—
71C4⋊Dic29C2312yescomplemented
72#90779—24no—
73C2×#6597—22no—
74C2×#6597C2312yescomplemented
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—
92Q8×C29—22no—
93Q8×C29—22no—
94Q8×C29—42no—
95D4×C29—24no—
96D4×C29—22no—
97D4×C29C2×D414yes—
98C2×C4×C29—22no—
99C2×C4×C29—42no—
100C2×C4×C29C2×D411yescharacteristic
101C2×C4×C29C2×D412yes—
102C2×C4×C29C2×D412yes—
103C2×C4×C29C2411yescharacteristic
104C22⋊D29—216no—
105C2×Dic29—22no—
106C2×Dic29—22no—
107C2×Dic29—42no—
108C2×Dic29C2×D412yes—
109D116—24no—
110D116—22no—
111D116C2×D414yes—
112C4×D29—24no—
113C4×D29—22no—
114C4×D29—22no—
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×SD16D2911yescharacteristic, complemented
144C2×C22⋊Q8—291no—
145#450—298no—
146C2×#102—291no—
147C2×#102—291no—
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×Q8C2×D2911yescharacteristic, complemented
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—24no—
167C2×SD16—294no—
168C2×SD16—584no—
169C2×SD16C2×D2914yescomplemented
170C22×C8—291no—
171C22×C8C2×D2911yescharacteristic, complemented
172C22⋊Q8—294no—
173C22⋊Q8—582no—
174C2×C4⋊C4—291no—
175C2×C4⋊C4—581no—
176C2×C22⋊C4—581no—
177#102—294no—
178#102—294no—
179C22⋊C8—294no—
180C29C2×#45011yescharacteristic, complemented, Sylow
181C24—21no—
182C24—291no—
183C24—584no—
184C24—588no—
185C24—581no—
186C24—1164no—
187C24—1164no—
188C2×Q8—21no—
189C2×Q8—22no—
190C2×Q8—22no—
191C2×Q8C22×D2912yescomplemented
192C2×D4—21no—
193C2×D4—22no—
194C2×D4—294no—
195C2×D4—292no—
196C2×D4—584no—
197C2×D4—588no—
198C2×D4—5816no—
199C2×D4—588no—
200C2×D4—588no—
201C2×D4—581no—
202C2×D4—582no—
203C2×D4C22⋊D2914yes—
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—28no—
214SD16—588no—
215C2×C8—22no—
216C2×C8—292no—
217C2×C8—582no—
218C2×C8C22×D2912yescomplemented
219C4⋊C4—292no—
220C4⋊C4—584no—
221C4⋊C4—581no—
222C22⋊C4—584no—
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—292no—
228C23—294no—
229C23—5816no—
230C23—582no—
231C23—582no—
232C23—584no—
233C23—582no—
234C23—1168no—
235C23—11632no—
236C23—1168no—
237C23—1162no—
238C23—1162no—
239C23D4×D2911yescharacteristic
240Q8—22no—
241Q8—22no—
242Q8—42no—
243D4—24no—
244D4—22no—
245D4—294no—
246D4—5816no—
247D4—584no—
248D4—582no—
249D4C2×C22⋊D2914yes—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—292no—
253C2×C4—582no—
254C2×C4—584no—
255C2×C4—582no—
256C2×C4—582no—
257C2×C4—582no—
258C2×C4—1162no—
259C2×C4D4×D2911yescharacteristic
260C2×C4D4×D2912yes—
261C2×C4C2×C22⋊D2912yes—
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—
278C22SD16×D2912yes—
279C22#1174527612yes—
280C22#1174529912yes—
281C22C2×D4×D2911yescharacteristic
282C4—42no—
283C4—582no—
284C4—1162no—
285C4#1174529912yes—
286C4C2×D4×D2911yescharacteristic
287C4C22×C22⋊D2911yescharacteristic
288C2—44no—
289C2—584no—
290C2—1164no—
291C2#1427131214yesdirect product factor
292C2C2×#1174529911yescharacteristic
293C2C2×SD16×D2911yescharacteristic
294C2C2×#1174527611yescharacteristic
subgroupG/H
centerC23D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC22×SD16×C29C2
socleC23×C29C2×D4
prime radicalC22×D4×D29C2
hypercenterC22×SD16D29
hypocenterC29C2×#450
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. C22×#90784C2semidirect
3. C2×#11745308C2semidirect
4. #14271312C2direct (N × H)
5. C2×#11745169C2semidirect
6. C2×#11745180C2semidirect
7. C2×#11745168C2semidirect
8. C22×SD16×C29C2semidirect
10. C22×Q8×C29C22semidirect
20. C2×SD16×C29C22semidirect
21. C22×C8×C29C22semidirect
23. #11745308C22semidirect
25. C2×#90784C22semidirect
27. C2×C4⋊Dic29C22semidirect
29. C22×#6597C22semidirect
30. #11745180C22semidirect
31. #11745169C22semidirect
32. #11745168C22semidirect
43. C2×Q8×C29C23semidirect
67. C2×C8×C29C23semidirect
71. C4⋊Dic29C23semidirect
74. C2×#6597C23semidirect
90. C22×D29SD16semidirect
134. C2×D29C2×SD16semidirect
143. C22×SD16D29semidirect
150. C2×C29#450semidirect
157. C22×Q8C2×D29semidirect
169. C2×SD16C2×D29semidirect
171. C22×C8C2×D29semidirect
180. C29C2×#450semidirect
191. C2×Q8C22×D29semidirect
218. C2×C8C22×D29semidirect
291. C2#14271312direct (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×#907842
C2×#117453082
#142713122
C2×#117451692
C2×#117451802
C2×#117451682
C22×SD16×C292
C2×#45029