Finite Group Databasebeta

← C2×#14271308 #16828693

Subgroups — C2×#14271308 #16828693

Order 3712.

812 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 181 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×#90784C211yesmaximal, characteristic, complemented
2C22×#90782C211yesmaximal, characteristic, complemented
3C2×#11745292C211yesmaximal, characteristic, complemented
4#14271308C218yesmaximal, direct product factor
5C2×#11745183C211yesmaximal, characteristic, complemented
6C2×#11745180C211yesmaximal, characteristic, complemented
7C2×C22⋊#6597C211yesmaximal, characteristic, complemented
8C22×#41×C29C211yesmaximal, characteristic, complemented
9C2×#41×C29—24no—
10C2×#41×C29—24no—
11C2×#41×C29—22no—
12C2×#41×C29C2214yescomplemented
13C22×Q8×C29C2211yescharacteristic
14C22×D4×C29—21no—
15C22×D4×C29C2211yescharacteristic
16C23×C4×C29—21no—
17C23×C4×C29C2211yescharacteristic
18C22×C22⋊D29—21no—
19C22×D116C2211yescharacteristic
20C2×#90784—24no—
21C2×#90784C2214yescomplemented
22C2×#90782—24no—
23C2×#90782C2214yescomplemented
24#11745292—22no—
25#11745292C2214yescomplemented
26C2×#90781—21no—
27C2×C4⋊Dic29C2211yescharacteristic
28C22×#6597C2211yescharacteristic
29C22×#6597C2211yescharacteristic
30#11745183C2214yescomplemented
31#11745180C2214yescomplemented
32C22⋊#6597C2214yescomplemented
33C24×C29—21no—
34C24×C29D411yescharacteristic
35C23×D29—21no—
36#41×C29—216no—
37#41×C29—28no—
38#41×C29—28no—
39C2×Q8×C29—22no—
40C2×Q8×C29—21no—
41C2×Q8×C29D414yescomplemented
42C2×Q8×C29C2312yes—
43C2×D4×C29—28no—
44C2×D4×C29—24no—
45C2×D4×C29—21no—
46C2×D4×C29—22no—
47C2×D4×C29D414yescomplemented
48C2×D4×C29C2312yes—
49C22×C4×C29—28no—
50C22×C4×C29—21no—
51C22×C4×C29—24no—
52C22×C4×C29—22no—
53C22×C4×C29—22no—
54C22×C4×C29D411yescharacteristic
55C22×C4×C29D412yes—
56C22×C4×C29C2312yes—
57C22×C4×C29C2311yescharacteristic
58C2×C22⋊D29—24no—
59C2×C22⋊D29—44no—
60C22×Dic29—21no—
61C2×D116—22no—
62C2×D116—22no—
63C2×D116—21no—
64C2×D116C2312yes—
65#90784—28no—
66#90782—28no—
67#90781—24no—
68C4⋊Dic29—21no—
69C4⋊Dic29C2312yes—
70C2×#6597—22no—
71C2×#6597—22no—
72C2×#6597C2312yes—
73C2×#6597C2312yes—
74C23×C29—22no—
75C23×C29—24no—
76C23×C29—22no—
77C23×C29—22no—
78C23×C29—22no—
79C23×C29—42no—
80C23×C29—42no—
81C23×C29C2×D412yes—
82C23×C29C2×D411yescharacteristic
83C22×D29—22no—
84C22×D29—42no—
85C22×D29—42no—
86C22×D29—42no—
87Q8×C29—24no—
88Q8×C29—22no—
89Q8×C29C2×D414yescomplemented
90D4×C29—216no—
91D4×C29—24no—
92D4×C29—22no—
93D4×C29C2×D414yescomplemented
94C2×C4×C29—216no—
95C2×C4×C29—22no—
96C2×C4×C29—24no—
97C2×C4×C29—22no—
98C2×C4×C29—24no—
99C2×C4×C29—22no—
100C2×C4×C29—22no—
101C2×C4×C29C2×D412yes—
102C2×C4×C29C2×D411yescharacteristic
103C2×C4×C29C2×D412yes—
104C2×C4×C29C2×D412yes—
105C2×C4×C29C2411yescharacteristic
106C22⋊D29—48no—
107C2×Dic29—22no—
108C2×Dic29—42no—
109D116—22no—
110D116—22no—
111D116—42no—
112#6597—22no—
113#6597—22no—
114C2×#449—291nomaximal, Sylow
115C22×C29—22no—
116C22×C29—24no—
117C22×C29—22no—
118C22×C29—22no—
119C22×C29—42no—
120C22×C29—42no—
121C22×C29—44no—
122C22×C29—48no—
123C22×C29#12012yes—
124C22×C29#13512yes—
125C22×C29AGL(1,ℤ/8)12yes—
126C22×C29C22×D411yescharacteristic
127C2×D29—42no—
128C2×D29—42no—
129C2×D29—42no—
130C2×D29—84no—
131C4×C29—22no—
132C4×C29—24no—
133C4×C29#12012yes—
134C4×C29C22×D411yescharacteristic
135C4×C29C22×D411yescharacteristic
136Dic29—42no—
137C22×#41D2911yescharacteristic, complemented
138C22×SD16—291no—
139C22×D8—291no—
140C2×#121—291no—
141#449—298no—
142C2×#103—291no—
143C2×#102—291no—
144C2×C22⋊C8—291no—
145C2×C29—42no—
146C2×C29—44no—
147C2×C29#44914yescomplemented
148C2×C29C2×#12011yescharacteristic
149C2×C29C2×#13511yescharacteristic
150C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
151D29—82no—
152C2×#41—24no—
153C2×#41—24no—
154C2×#41—22no—
155C2×#41C2×D2914yescomplemented
156C22×Q8C2×D2911yescharacteristic
157C22×D4—21no—
158C22×D4—291no—
159C22×D4—581no—
160C22×D4C2×D2911yescharacteristic
161C23×C4—21no—
162C23×C4C2×D2911yescharacteristic
163C2×SD16—294no—
164C2×SD16—584no—
165C2×D8—294no—
166C2×D8—584no—
167C22×C8—291no—
168C22×C8—291no—
169#121—294no—
170#121—582no—
171C2×C4⋊C4—291no—
172C2×C22⋊C4—581no—
173#103—294no—
174#102—294no—
175C22⋊C8—294no—
176C29C2×#44911yescharacteristic, complemented, Sylow
177C24—21no—
178C24—581no—
179C24C22⋊D2911yescharacteristic
180#41—216no—
181#41—28no—
182#41—28no—
183C2×Q8—22no—
184C2×Q8—21no—
185C2×Q8C22⋊D2914yescomplemented
186C2×Q8C22×D2912yes—
187C2×D4—28no—
188C2×D4—24no—
189C2×D4—21no—
190C2×D4—22no—
191C2×D4—292no—
192C2×D4—584no—
193C2×D4—582no—
194C2×D4—582no—
195C2×D4—581no—
196C2×D4—1164no—
197C2×D4C22⋊D2914yescomplemented
198C2×D4C22×D2912yes—
199C22×C4—28no—
200C22×C4—21no—
201C22×C4—24no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—581no—
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—292no—
216C4⋊C4—581no—
217C22⋊C4—584no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—24no—
222C23—22no—
223C23—42no—
224C23—42no—
225C23—582no—
226C23—1162no—
227C23—1162no—
228C23—1162no—
229C23C2×C22⋊D2912yes—
230C23C2×C22⋊D2911yescharacteristic
231Q8—24no—
232Q8—22no—
233Q8C2×C22⋊D2914yescomplemented
234D4—216no—
235D4—24no—
236D4—22no—
237D4—582no—
238D4—582no—
239D4—1168no—
240D4—1162no—
241D4C2×C22⋊D2914yescomplemented
242C2×C4—216no—
243C2×C4—22no—
244C2×C4—24no—
245C2×C4—22no—
246C2×C4—24no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—582no—
250C2×C4—1162no—
251C2×C4C2×C22⋊D2912yes—
252C2×C4C2×C22⋊D2911yescharacteristic
253C2×C4C2×C22⋊D2912yes—
254C2×C4C2×C22⋊D2912yes—
255C2×C4C23×D2911yescharacteristic
256C8—582no—
257C8—582no—
258C22—22no—
259C22—24no—
260C22—22no—
261C22—22no—
262C22—44no—
263C22—48no—
264C22—42no—
265C22—42no—
266C22—1162no—
267C22—1162no—
268C22—1162no—
269C22—2324no—
270C22#1174531112yes—
271C22#1174531212yes—
272C22#1174531512yes—
273C22C22×C22⋊D2911yescharacteristic
274C4—22no—
275C4—24no—
276C4—1162no—
277C4#1174531512yes—
278C4C22×C22⋊D2911yescharacteristic
279C4C22×C22⋊D2911yescharacteristic
280C2—42no—
281C2—44no—
282C2—2322no—
283C2#1427130814yesdirect product factor
284C2C2×#1174531511yescharacteristic
285C2C2×#1174531211yescharacteristic
286C2C2×#1174531111yescharacteristic
subgroupG/H
centerC23C2×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC22×#41×C29C2
socleC23×C29C2×D4
hypercenterC22×#41D29
hypocenterC29C2×#449
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×#90784C2semidirect
2. C22×#90782C2semidirect
3. C2×#11745292C2semidirect
4. #14271308C2direct (N × H)
5. C2×#11745183C2semidirect
6. C2×#11745180C2semidirect
7. C2×C22⋊#6597C2semidirect
8. C22×#41×C29C2semidirect
12. C2×#41×C29C22semidirect
21. C2×#90784C22semidirect
23. C2×#90782C22semidirect
25. #11745292C22semidirect
30. #11745183C22semidirect
31. #11745180C22semidirect
32. C22⋊#6597C22semidirect
41. C2×Q8×C29D4semidirect
47. C2×D4×C29D4semidirect
89. Q8×C29C2×D4semidirect
93. D4×C29C2×D4semidirect
137. C22×#41D29semidirect
147. C2×C29#449semidirect
155. C2×#41C2×D29semidirect
176. C29C2×#449semidirect
185. C2×Q8C22⋊D29semidirect
197. C2×D4C22⋊D29semidirect
233. Q8C2×C22⋊D29semidirect
241. D4C2×C22⋊D29semidirect
283. C2#14271308direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#907842
C22×#907822
C2×#117452922
#142713082
C2×#117451832
C2×#117451802
C2×C22⋊#65972
C22×#41×C292
C2×#44929