Finite Group Databasebeta

← D4×#4323 #13080289

Subgroups — D4×#4323 #13080289

Order 1408.

620 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 149 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
1D42×C11C211yesmaximal, characteristic, complemented
2C22×#4323C212yesmaximal, complemented
3D4×D44C211yesmaximal, characteristic, complemented
4#10622830C212yesmaximal, complemented
5#10622686C211yesmaximal, characteristic, complemented
6#10622685C211yesmaximal, characteristic, complemented
7#10622651C212yesmaximal, complemented
8#10622649C212yesmaximal, complemented
9#10622628C211yesmaximal, characteristic, complemented
10C4×#4323C211yesmaximal, characteristic, complemented
11D4×C11⋊C8C211yesmaximal, characteristic, complemented
12C22×D4×C11—21no—
13C22×D4×C11C2212yescomplemented
14C2×D4×D11—21no—
15C22×D44C2212yescomplemented
16C11×#127C2211yescharacteristic, complemented
17C11×#121—21no—
18C11×#121C2212yescomplemented
19C11×#120—22no—
20C4×D4×C11C2211yescharacteristic
21C4×D4×C11C2211yescharacteristic, complemented
22C2×#4323—28no—
23C2×#4323C2211yescharacteristic
24C2×#4323C2212yescomplemented
25C2×#4323C2212yescomplemented
26C2×#4323C2212yescomplemented
27C2×#4323C2212yescomplemented
28#66983C2212yescomplemented
29C22×C11⋊C8C2212yescomplemented
30#66948—21no—
31#66935—22no—
32#66927C2211yescharacteristic, complemented
33C4×D44C2211yescharacteristic, complemented
34#66896C2211yescharacteristic, complemented
35#66896C2212yescomplemented
36C22⋊(C11⋊C8)C2212yescomplemented
37#66873C2211yescharacteristic, complemented
38#66873C2212yescomplemented
39#66871C2211yescharacteristic, complemented
40C4⋊(C11⋊C8)C2211yescharacteristic, complemented
41C4×C11⋊C8C2211yescharacteristic, complemented
42C24×C11—22no—
43C23×D11—22no—
44C2×D4×C11—24no—
45C2×D4×C11—22no—
46C2×D4×C11—22no—
47C2×D4×C11—21no—
48C2×D4×C11—21no—
49C2×D4×C11—42no—
50C2×D4×C11—44no—
51C2×D4×C11D411yescharacteristic
52C2×D4×C11C2312yes—
53C2×D4×C11C2311yescharacteristic
54C22×C4×C11—21no—
55C22×C4×C11C2312yes—
56C2×C22⋊D11—22no—
57D4×D11—44no—
58C2×D44—24no—
59C2×D44—21no—
60C2×D44—22no—
61C2×D44—21no—
62C2×D44—42no—
63C2×D44C2312yes—
64C2×D44C2311yescharacteristic
65C2×C4×D11—21no—
66C11×C4⋊C4D411yescharacteristic
67C11×C4⋊C4C2311yescharacteristic
68C11×C22⋊C4—21no—
69C11×C22⋊C4—22no—
70C11×C22⋊C4D412yes—
71C42×C11C2311yescharacteristic
72#4323—24no—
73#4323—24no—
74#4323—24no—
75#4323—42no—
76#4323D414yesdirect product factor
77(C2×D11)⋊C4—21no—
78(C2×D11)⋊C4—22no—
79C4⋊Dic11C2311yescharacteristic
80C2×C11⋊C8—24no—
81C2×C11⋊C8C2311yescharacteristic
82C2×C11⋊C8C2312yes—
83C2×C11⋊C8C2311yescharacteristic
84D4×D8—111nomaximal, Sylow
85C23×C11—21no—
86C23×C11—22no—
87C23×C11—44no—
88C23×C11—44no—
89C23×C11—82no—
90C23×C11C2×D412yes—
91C22×D11—21no—
92C22×D11—22no—
93C22×D11—44no—
94C22×D11—44no—
95C22×D11—82no—
96D4×C11—22no—
97D4×C11—21no—
98D4×C11—22no—
99D4×C11—44no—
100D4×C11—44no—
101D4×C11—42no—
102D4×C11—81no—
103D4×C11D814yescomplemented
104D4×C11C2×D412yescomplemented
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—21no—
108C2×C4×C11—42no—
109C2×C4×C11C2×D411yescharacteristic
110C2×C4×C11C2×D412yes—
111C2×C4×C11C2×D411yescharacteristic
112C2×C4×C11C2411yescharacteristic
113C22⋊D11—44no—
114C2×Dic11—21no—
115D44—22no—
116D44—21no—
117D44—22no—
118D44—44no—
119D44—42no—
120D44—81no—
121D44C2×D412yescomplemented
122C4×D11—42no—
123C11⋊C8—22no—
124C11⋊C8—21no—
125C11⋊C8C2×D412yescomplemented
126C22×D8—112no—
127D42—111no—
128D42D1111yescharacteristic, complemented
129#493—111no—
130#466—112no—
131#459—111no—
132#459—111no—
133#447—112no—
134#447—112no—
135C4×D8—111no—
136C8×D4—111no—
137C22×C11—22no—
138C22×C11—22no—
139C22×C11—22no—
140C22×C11—41no—
141C22×C11—41no—
142C22×C11—42no—
143C22×C11—42no—
144C22×C11—42no—
145C22×C11—88no—
146C22×C11C2×D814yescomplemented
147C22×C11C22×D411yescharacteristic
148C2×D11—22no—
149C2×D11—41no—
150C2×D11—41no—
151C2×D11—42no—
152C2×D11—42no—
153C2×D11—42no—
154C2×D11—88no—
155C4×C11—22no—
156C4×C11—21no—
157C4×C11—41no—
158C4×C11C2×D812yescomplemented
159C4×C11C22×D411yescharacteristic
160C4×C11H(5,𝔽2)11yescharacteristic
161Dic11—41no—
162C22×D4—21no—
163C22×D4—112no—
164C22×D4—221no—
165C22×D4C2×D1112yescomplemented
166C2×D8—111no—
167C2×D8—112no—
168C2×D8—112no—
169C2×D8—112no—
170C2×D8—112no—
171C2×D8—228no—
172C22×C8—112no—
173#127—111no—
174#127C2×D1111yescharacteristic, complemented
175#121—21no—
176#121—112no—
177#121—221no—
178#121C2×D1112yescomplemented
179#120—22no—
180#120—222no—
181C4×D4—111no—
182C4×D4C2×D1111yescharacteristic
183C4×D4C2×D1111yescharacteristic, complemented
184#107—111no—
185C4⋊C8—111no—
186#102—111no—
187#102—112no—
188#102—111no—
189#102—112no—
190C22⋊C8—112no—
191C4×C8—111no—
192C2×C11—24no—
193C2×C11—42no—
194C2×C11—82no—
195C2×C11D4211yescharacteristic
196C2×C11C22×D811yescharacteristic
197C2×C11#57611yescharacteristic
198D11—42no—
199D11—82no—
200C24—22no—
201C24—222no—
202C2×D4—24no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—21no—
206C2×D4—21no—
207C2×D4—42no—
208C2×D4—44no—
209C2×D4—111no—
210C2×D4—112no—
211C2×D4—224no—
212C2×D4—222no—
213C2×D4—222no—
214C2×D4—221no—
215C2×D4—221no—
216C2×D4—442no—
217C2×D4—444no—
218C2×D4C22⋊D1111yescharacteristic
219C2×D4C22×D1112yes—
220C2×D4C22×D1111yescharacteristic
221C22×C4—21no—
222C22×C4—221no—
223C22×C4C22×D1112yes—
224D8—114no—
225D8—224no—
226D8—224no—
227D8—224no—
228D8—442no—
229C2×C8—111no—
230C2×C8—111no—
231C2×C8—112no—
232C2×C8—224no—
233C4⋊C4—111no—
234C4⋊C4C22⋊D1111yescharacteristic
235C4⋊C4C22×D1111yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—22no—
238C22⋊C4—221no—
239C22⋊C4—222no—
240C22⋊C4C22⋊D1112yes—
241C42C22×D1111yescharacteristic
242C11D4×D811yescharacteristic, complemented, Sylow
243C23—21no—
244C23—22no—
245C23—44no—
246C23—44no—
247C23—82no—
248C23—221no—
249C23—222no—
250C23—444no—
251C23—444no—
252C23—882no—
253C23C2×C22⋊D1112yes—
254D4—22no—
255D4—21no—
256D4—22no—
257D4—44no—
258D4—44no—
259D4—42no—
260D4—81no—
261D4—112no—
262D4—222no—
263D4—221no—
264D4—222no—
265D4—444no—
266D4—444no—
267D4—442no—
268D4—881no—
269D4#432314yesdirect product factor
270D4D4×D1112yescomplemented
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—42no—
275C2×C4—221no—
276C2×C4—442no—
277C2×C4C2×C22⋊D1111yescharacteristic
278C2×C4C2×C22⋊D1112yes—
279C2×C4C2×C22⋊D1111yescharacteristic
280C2×C4C23×D1111yescharacteristic
281C8—112no—
282C8—222no—
283C8—221no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—88no—
293C22—222no—
294C22—441no—
295C22—441no—
296C22—442no—
297C22—442no—
298C22—442no—
299C22—888no—
300C22C2×#432314yescomplemented
301C22C22×C22⋊D1111yescharacteristic
302C4—22no—
303C4—21no—
304C4—41no—
305C4—441no—
306C4C2×#432312yescomplemented
307C4C2×D4×D1111yescharacteristic
308C4#6703711yescharacteristic
309C2—24no—
310C2—42no—
311C2—82no—
312C2—442no—
313C2—882no—
314C2C22×#432311yescharacteristic
315C2D4×C22⋊D1111yescharacteristic
316C2#1062336611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingD42×C11C2
socleC22×C11C22×D4
hypercenterD42D11
hypocenterC11D4×D8
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. D42×C11C2semidirect
2. C22×#4323C2semidirect
3. D4×D44C2semidirect
4. #10622830C2semidirect
5. #10622686C2semidirect
6. #10622685C2semidirect
7. #10622651C2semidirect
8. #10622649C2semidirect
9. #10622628C2semidirect
10. C4×#4323C2semidirect
11. D4×C11⋊C8C2semidirect
13. C22×D4×C11C22semidirect
15. C22×D44C22semidirect
16. C11×#127C22semidirect
18. C11×#121C22semidirect
21. C4×D4×C11C22semidirect
24. C2×#4323C22semidirect
25. C2×#4323C22semidirect
26. C2×#4323C22semidirect
27. C2×#4323C22semidirect
28. #66983C22semidirect
29. C22×C11⋊C8C22semidirect
32. #66927C22semidirect
33. C4×D44C22semidirect
34. #66896C22semidirect
35. #66896C22semidirect
36. C22⋊(C11⋊C8)C22semidirect
37. #66873C22semidirect
38. #66873C22semidirect
39. #66871C22semidirect
40. C4⋊(C11⋊C8)C22semidirect
41. C4×C11⋊C8C22semidirect
76. #4323D4direct (N × H)
103. D4×C11D8semidirect
104. D4×C11C2×D4semidirect
121. D44C2×D4semidirect
125. C11⋊C8C2×D4semidirect
128. D42D11semidirect
146. C22×C11C2×D8semidirect
158. C4×C11C2×D8semidirect
165. C22×D4C2×D11semidirect
174. #127C2×D11semidirect
178. #121C2×D11semidirect
183. C4×D4C2×D11semidirect
242. C11D4×D8semidirect
269. D4#4323direct (N × H)
270. D4D4×D11semidirect
300. C22C2×#4323semidirect
306. C4C2×#4323semidirect

Maximal subgroups

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

subgroupindex
D42×C112
C22×#43232
D4×D442
#106228302
#106226862
#106226852
#106226512
#106226492
#106226282
C4×#43232
D4×C11⋊C82
D4×D811