Finite Group Databasebeta

← C2×#14271303 #16828681

Subgroups — C2×#14271303 #16828681

Order 3712.

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

normal subgroups only

This group has 792 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×Q8×D29C211yesmaximal, characteristic, complemented
2C22×#90773C211yesmaximal, characteristic, complemented
3C22×#90784C211yesmaximal, characteristic, complemented
4C2×#11745257C211yesmaximal, characteristic
5#14271303C218yesmaximal, direct product factor
6C2×#11745158C211yesmaximal, characteristic, complemented
7C2×#11745168C211yesmaximal, characteristic, complemented
8C2×C29×#103C211yesmaximal, characteristic, complemented
9C22×Q8×C29C2211yescharacteristic
10C2×Q8×D29—24no—
11C2×Q8×D29—22no—
12C2×Q8×D29—24no—
13C2×Q8×D29C2214yescomplemented
14C22×D116—21no—
15C22×D116C2211yescharacteristic
16C22×C4×D29—21no—
17C22×C4×D29C2211yescharacteristic
18C22×Dic58—21no—
19C22×Dic58C2211yescharacteristic
20C22×C8×C29C2211yescharacteristic
21C2×C4⋊C4×C29C2211yescharacteristic
22C2×#90784—24no—
23C2×#90784C2214yescomplemented
24C2×#90781—21no—
25C22×#6597C2211yescharacteristic
26C2×#90773—24no—
27C2×#90773C2214yescomplemented
28#11745257—22no—
29#11745257C2214yes—
30C29×#103C2214yescomplemented
31#11745168C2214yescomplemented
32#11745158C2214yescomplemented
33C23×D29—21no—
34C23×D29D411yescharacteristic
35C2×Q8×C29—22no—
36C2×Q8×C29—21no—
37C2×Q8×C29D414yescomplemented
38C2×Q8×C29C2312yes—
39C22×C4×C29—21no—
40C22×C4×C29—21no—
41C22×C4×C29C2311yescharacteristic
42C22×Dic29—21no—
43C22×Dic29D411yescharacteristic
44Q8×D29—216no—
45Q8×D29—28no—
46Q8×D29—28no—
47C2×D116—22no—
48C2×D116—22no—
49C2×D116—24no—
50C2×D116—21no—
51C2×D116—44no—
52C2×D116C2312yes—
53C2×C4×D29—28no—
54C2×C4×D29—24no—
55C2×C4×D29—22no—
56C2×C4×D29—22no—
57C2×C4×D29D412yes—
58C2×C4×D29C2312yes—
59C2×Dic58—28no—
60C2×Dic58—22no—
61C2×Dic58—21no—
62C2×Dic58—24no—
63C2×Dic58D414yescomplemented
64C2×Dic58C2312yes—
65C2×C8×C29—22no—
66C2×C8×C29C2312yes—
67C4⋊C4×C29—21no—
68C4⋊C4×C29C2312yes—
69#90784—28no—
70#90781—24no—
71C2×#6597—22no—
72C2×#6597C2312yes—
73#90773—28no—
74C23×C29C2×D411yescharacteristic
75C22×D29—22no—
76C22×D29—22no—
77C22×D29—22no—
78C22×D29—42no—
79C22×D29—42no—
80C22×D29—42no—
81C22×D29SD1614yescomplemented
82C22×D29C2×D412yes—
83Q8×C29—24no—
84Q8×C29—22no—
85Q8×C29C2×D414yescomplemented
86C2×C4×C29—24no—
87C2×C4×C29—22no—
88C2×C4×C29—22no—
89C2×C4×C29—42no—
90C2×C4×C29C2×D412yes—
91C2×C4×C29C2×D411yescharacteristic
92C2×C4×C29C2×D412yes—
93C2×C4×C29C2411yescharacteristic
94C2×Dic29—22no—
95C2×Dic29—24no—
96C2×Dic29—22no—
97C2×Dic29C2×D412yes—
98D116—22no—
99D116—22no—
100D116—48no—
101D116—42no—
102C4×D29—216no—
103C4×D29—24no—
104C4×D29—22no—
105C4×D29—22no—
106Dic58—216no—
107Dic58—24no—
108Dic58—22no—
109Dic58C2×D414yescomplemented
110C8×C29—22no—
111#6597—22no—
112C2×#448—291nomaximal, Sylow
113C22×C29#12012yes—
114C22×C29C2×SD1612yes—
115C22×C29#13712yes—
116C22×C29C22×D411yescharacteristic
117C2×D29—22no—
118C2×D29—22no—
119C2×D29—28no—
120C2×D29—42no—
121C2×D29—42no—
122C2×D29—42no—
123C2×D29—84no—
124C2×D29C2×SD1614yescomplemented
125C4×C29—24no—
126C4×C29—42no—
127C4×C29#12012yes—
128C4×C29C22×D411yescharacteristic
129C4×C29C22×D411yescharacteristic
130Dic29—22no—
131Dic29—24no—
132C23×Q8—291no—
133C22×SD16—291no—
134C22×SD16—291no—
135C2×#121—291no—
136#448—298no—
137C2×#103—291no—
138C2×#103D2911yescharacteristic, complemented
139C2×C22⋊C8—291no—
140C2×C29#44814yescomplemented
141C2×C29C2×#12011yescharacteristic
142C2×C29C22×SD1611yescharacteristic
143C2×C29C2×#13711yescharacteristic
144D29—24no—
145D29—82no—
146C22×Q8—294no—
147C22×Q8—291no—
148C22×Q8—581no—
149C22×Q8—582no—
150C22×Q8—584no—
151C22×Q8—584no—
152C22×Q8C2×D2911yescharacteristic
153C22×D4—291no—
154C22×D4—581no—
155C23×C4—291no—
156C23×C4—581no—
157C2×SD16—294no—
158C2×SD16—294no—
159C2×SD16—584no—
160C2×SD16—584no—
161C22×C8—291no—
162C22×C8C2×D2911yescharacteristic
163#121—294no—
164#121—582no—
165C2×C4⋊C4C2×D2911yescharacteristic
166C2×C22⋊C4—581no—
167#103—294no—
168#103C2×D2914yescomplemented
169C22⋊C8—294no—
170C29C2×#44811yescharacteristic, complemented, Sylow
171C24—291no—
172C24—581no—
173C2×Q8—21no—
174C2×Q8—22no—
175C2×Q8—294no—
176C2×Q8—292no—
177C2×Q8—584no—
178C2×Q8—588no—
179C2×Q8—588no—
180C2×Q8—5816no—
181C2×Q8—588no—
182C2×Q8—582no—
183C2×Q8—581no—
184C2×Q8D11614yescomplemented
185C2×Q8C22×D2912yes—
186C2×D4—292no—
187C2×D4—584no—
188C2×D4—582no—
189C2×D4—582no—
190C2×D4—581no—
191C2×D4—1164no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—291no—
195C22×C4—292no—
196C22×C4—292no—
197C22×C4—584no—
198C22×C4—588no—
199C22×C4—581no—
200C22×C4—582no—
201C22×C4—582no—
202C22×C4C22×D2911yescharacteristic
203SD16—588no—
204SD16—588no—
205C2×C8—22no—
206C2×C8—292no—
207C2×C8—582no—
208C2×C8C22×D2912yes—
209C4⋊C4—21no—
210C4⋊C4C22×D2912yes—
211C22⋊C4—584no—
212C23—292no—
213C23—294no—
214C23—582no—
215C23—582no—
216C23—582no—
217C23—1162no—
218C23—1162no—
219C23—1162no—
220C23D4×D2911yescharacteristic
221Q8—22no—
222Q8—24no—
223Q8—294no—
224Q8—5816no—
225Q8—582no—
226Q8—584no—
227Q8C2×D11614yescomplemented
228D4—582no—
229D4—582no—
230D4—1168no—
231D4—1162no—
232C2×C4—22no—
233C2×C4—24no—
234C2×C4—22no—
235C2×C4—42no—
236C2×C4—292no—
237C2×C4—5816no—
238C2×C4—582no—
239C2×C4—582no—
240C2×C4—584no—
241C2×C4—582no—
242C2×C4—582no—
243C2×C4—584no—
244C2×C4C2×D11612yes—
245C2×C4D4×D2912yes—
246C2×C4D4×D2911yescharacteristic
247C2×C4C23×D2911yescharacteristic
248C8—22no—
249C8—582no—
250C22—294no—
251C22—588no—
252C22—582no—
253C22—582no—
254C22—1162no—
255C22—1162no—
256C22—1162no—
257C22—2324no—
258C22#1174524412yes—
259C22SD16×D2912yes—
260C22#1174528012yes—
261C22C2×D4×D2911yescharacteristic
262C4—24no—
263C4—42no—
264C4—582no—
265C4—584no—
266C4#1174524412yes—
267C4C22×D11611yescharacteristic
268C4C2×D4×D2911yescharacteristic
269C2—584no—
270C2—2322no—
271C2#1427130314yesdirect product factor
272C2C2×#1174524411yescharacteristic
273C2C2×SD16×D2911yescharacteristic
274C2C2×#1174528011yescharacteristic
subgroupG/H
centerC23D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×#103C2
socleC23×C29C2×D4
prime radicalC2×#11745257C2
hypercenterC2×#103D29
hypocenterC29C2×#448
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D29C2semidirect
2. C22×#90773C2semidirect
3. C22×#90784C2semidirect
5. #14271303C2direct (N × H)
6. C2×#11745158C2semidirect
7. C2×#11745168C2semidirect
8. C2×C29×#103C2semidirect
13. C2×Q8×D29C22semidirect
23. C2×#90784C22semidirect
27. C2×#90773C22semidirect
30. C29×#103C22semidirect
31. #11745168C22semidirect
32. #11745158C22semidirect
37. C2×Q8×C29D4semidirect
63. C2×Dic58D4semidirect
81. C22×D29SD16semidirect
85. Q8×C29C2×D4semidirect
109. Dic58C2×D4semidirect
124. C2×D29C2×SD16semidirect
138. C2×#103D29semidirect
140. C2×C29#448semidirect
168. #103C2×D29semidirect
170. C29C2×#448semidirect
184. C2×Q8D116semidirect
227. Q8C2×D116semidirect
271. C2#14271303direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D292
C22×#907732
C22×#907842
C2×#117452572
#142713032
C2×#117451582
C2×#117451682
C2×C29×#1032
C2×#44829