Finite Group Databasebeta

← C2×#14271427 #16829192

Subgroups — C2×#14271427 #16829192

Order 3712.

468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#11745271C211yesmaximal, characteristic, complemented
2C2×#11745270C211yesmaximal, characteristic
3C22×#90773C211yesmaximal, characteristic, complemented
4C2×#11745263C211yesmaximal, characteristic, complemented
5#14271427C218yesmaximal, direct product factor
6C2×#11745172C211yesmaximal, characteristic, complemented
7C2×#11745171C211yesmaximal, characteristic, complemented
8C2×C29×#108C211yesmaximal, characteristic, complemented
9C2×#90805C2211yescharacteristic
10C22×D116C2211yescharacteristic
11C22×Dic58C2211yescharacteristic
12C2×M16×C29C2211yescharacteristic
13C2×M16×C29C2211yescharacteristic
14C22×C8×C29C2211yescharacteristic
15C2×#90777C2211yescharacteristic
16#11745271—22no—
17#11745271C2214yescomplemented
18#11745270—22no—
19#11745270C2214yes—
20C2×Dic116—21no—
21C2×D232—21no—
22C2×#90773—21no—
23C2×#90773—21no—
24C2×#90773—21no—
25C2×#90773—21no—
26C2×#90773—22no—
27C2×#90773C2214yescomplemented
28#11745263—22no—
29#11745263C2214yescomplemented
30C2×#90772—21no—
31C2×C8×D29—21no—
32C29×#108C2214yescomplemented
33#11745172C2214yescomplemented
34#11745171C2214yescomplemented
35C23×D29—21no—
36C22×C4×C29C2311yescharacteristic
37C2×C22⋊D29—21no—
38C22×Dic29—21no—
39#90805—21no—
40#90805—21no—
41#90805D412yes—
42#90805C2312yes—
43C2×D116—21no—
44C2×D116—21no—
45C2×D116—21no—
46C2×D116—21no—
47C2×D116—21no—
48C2×D116D411yescharacteristic
49C2×D116C2312yes—
50C2×C4×D29—21no—
51C2×Dic58—21no—
52C2×Dic58—21no—
53C2×Dic58—21no—
54C2×Dic58—21no—
55C2×Dic58—21no—
56C2×Dic58D411yescharacteristic
57C2×Dic58C2312yes—
58M16×C29—21no—
59M16×C29—21no—
60M16×C29C2312yes—
61M16×C29C2312yes—
62C2×C8×C29—21no—
63C2×C8×C29—21no—
64C2×C8×C29D411yescharacteristic
65C2×C8×C29D411yescharacteristic
66C2×C8×C29D412yes—
67C2×C8×C29C2312yes—
68#90777—21no—
69#90777C2312yes—
70C2×#6597—21no—
71Dic116—24no—
72D232—24no—
73#90773—24no—
74#90773—24no—
75#90773—24no—
76#90773—24no—
77#90772—24no—
78C8×D29—24no—
79C23×C29#4111yescharacteristic
80C22×D29—21no—
81C22×D29—22no—
82C22×D29—41no—
83C22×D29—41no—
84C22×D29—82no—
85C2×C4×C29C2×D411yescharacteristic
86C2×C4×C29C2×D411yescharacteristic
87C2×C4×C29C2×D411yescharacteristic
88C2×C4×C29C2×D411yescharacteristic
89C2×C4×C29#4111yescharacteristic
90C2×C4×C29C2411yescharacteristic
91C22⋊D29—22no—
92C22⋊D29—22no—
93C2×Dic29—21no—
94C2×Dic29—22no—
95C2×Dic29—41no—
96C2×Dic29—41no—
97D116—21no—
98D116—22no—
99D116—22no—
100D116—41no—
101D116—41no—
102D116C2×D412yes—
103C4×D29—22no—
104C4×D29—22no—
105Dic58—21no—
106Dic58—22no—
107Dic58—22no—
108Dic58—41no—
109Dic58—41no—
110Dic58C2×D412yes—
111C8×C29—22no—
112C8×C29—22no—
113C8×C29C2×D412yes—
114C8×C29C2×D412yes—
115#6597—22no—
116C2×#471—291nomaximal, Sylow
117C22×C29—22no—
118C22×C29#12111yescharacteristic
119C22×C29#12111yescharacteristic
120C22×C29C2×#4111yescharacteristic
121C2×D29—22no—
122C2×D29—42no—
123C2×D29—42no—
124C2×D29—82no—
125C2×D29—82no—
126C2×D29—82no—
127C4×C29#12111yescharacteristic
128C4×C29#12111yescharacteristic
129C4×C29C22×D411yescharacteristic
130C4×C29C22×D411yescharacteristic
131Dic29—22no—
132Dic29—42no—
133C2×#137—291no—
134C2×AGL(1,ℤ/8)—291no—
135C22×SD16—291no—
136C2×#131—291no—
137#471—298no—
138C2×#108D2911yescharacteristic, complemented
139C2×#101—291no—
140C2×#100—291no—
141C2×C29—21no—
142C2×C29—21no—
143C2×C29#47112yescomplemented
144C2×C29C2×#12111yescharacteristic
145D29—42no—
146D29—82no—
147C2×#41—291no—
148C22×Q8—291no—
149C22×D4—291no—
150#137—294no—
151#137—582no—
152AGL(1,ℤ/8)—294no—
153AGL(1,ℤ/8)—582no—
154C2×Q16—581no—
155C2×SD16—294no—
156C2×SD16—581no—
157C2×SD16—581no—
158C2×SD16—581no—
159C2×SD16—581no—
160C2×SD16—582no—
161C2×D8—581no—
162#131—294no—
163#131—582no—
164C2×M16—291no—
165C2×M16—581no—
166C2×M16C2×D2911yescharacteristic
167C2×M16C2×D2911yescharacteristic
168C22×C8—581no—
169C22×C8C2×D2911yescharacteristic
170#108C2×D2914yescomplemented
171#101—294no—
172#100—294no—
173C29C2×#47111yescharacteristic, complemented, Sylow
174C24—581no—
175#41—292no—
176#41—292no—
177#41—581no—
178#41—581no—
179C2×Q8—291no—
180C2×Q8—292no—
181C2×Q8—581no—
182C2×Q8—581no—
183C2×Q8—581no—
184C2×Q8—581no—
185C2×Q8—581no—
186C2×D4—291no—
187C2×D4—292no—
188C2×D4—581no—
189C2×D4—581no—
190C2×D4—581no—
191C2×D4—581no—
192C2×D4—581no—
193C2×D4—581no—
194C22×C4—581no—
195C22×C4—581no—
196C22×C4C22×D2911yescharacteristic
197Q16—584no—
198SD16—584no—
199SD16—584no—
200SD16—584no—
201SD16—584no—
202D8—584no—
203M16—21no—
204M16—21no—
205M16—292no—
206M16—581no—
207M16—584no—
208M16C22×D2912yes—
209M16C22×D2912yes—
210C2×C8—21no—
211C2×C8—21no—
212C2×C8—581no—
213C2×C8—584no—
214C2×C8D11611yescharacteristic
215C2×C8D11611yescharacteristic
216C2×C8D11612yes—
217C2×C8C22×D2912yes—
218C23—581no—
219C23—582no—
220C23—1161no—
221C23—1161no—
222C23—2322no—
223C23#9080911yescharacteristic
224Q8—292no—
225Q8—581no—
226Q8—582no—
227Q8—582no—
228Q8—1161no—
229Q8—1161no—
230D4—292no—
231D4—582no—
232D4—582no—
233D4—582no—
234D4—582no—
235D4—581no—
236D4—1161no—
237D4—1161no—
238C2×C4—581no—
239C2×C4—582no—
240C2×C4—582no—
241C2×C4—582no—
242C2×C4—1161no—
243C2×C4—1161no—
244C2×C4C2×D11611yescharacteristic
245C2×C4C2×D11611yescharacteristic
246C2×C4D4×D2911yescharacteristic
247C2×C4D4×D2911yescharacteristic
248C2×C4#9080911yescharacteristic
249C2×C4C23×D2911yescharacteristic
250C8—22no—
251C8—22no—
252C8—582no—
253C8C2×D11612yes—
254C8C2×D11612yes—
255C22—22no—
256C22—582no—
257C22—1162no—
258C22—1162no—
259C22—2322no—
260C22—2322no—
261C22—2322no—
262C22#1174525711yescharacteristic
263C22#1174525711yescharacteristic
264C22C2×#9080911yescharacteristic
265C4—582no—
266C4—1162no—
267C4#1174525711yescharacteristic
268C4#1174525711yescharacteristic
269C4C22×D11611yescharacteristic
270C4C2×D4×D2911yescharacteristic
271C2—21no—
272C2—21no—
273C2—1162no—
274C2—2322no—
275C2#1427142712yesdirect product factor
276C2C2×#1174525711yescharacteristic
subgroupG/H
centerC22#11745257
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×#108C2
socleC22×C29#121
prime radicalC2×#11745270C2
hypercenterC2×#108D29
hypocenterC29C2×#471
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
1. C2×#11745271C2semidirect
3. C22×#90773C2semidirect
4. C2×#11745263C2semidirect
5. #14271427C2direct (N × H)
6. C2×#11745172C2semidirect
7. C2×#11745171C2semidirect
8. C2×C29×#108C2semidirect
17. #11745271C22semidirect
27. C2×#90773C22semidirect
29. #11745263C22semidirect
32. C29×#108C22semidirect
33. #11745172C22semidirect
34. #11745171C22semidirect
138. C2×#108D29semidirect
143. C2×C29#471semidirect
170. #108C2×D29semidirect
173. C29C2×#471semidirect
275. C2#14271427direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117452712
C2×#117452702
C22×#907732
C2×#117452632
#142714272
C2×#117451722
C2×#117451712
C2×C29×#1082
C2×#47129