Finite Group Databasebeta

← D4×#16864387 #46822558

Subgroups — D4×#16864387 #46822558

Order 34432.

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
1C22×#16864387C212yesmaximal, complemented
2D4×D1076C211yesmaximal, characteristic, complemented
3#31770981C211yesmaximal, characteristic, complemented
4#31770839C212yesmaximal, complemented
5#31770800C211yesmaximal, characteristic, complemented
6#31770797C211yesmaximal, characteristic, complemented
7#31770739C212yesmaximal, complemented
8#31770738C212yesmaximal, complemented
9C4×#16864387C211yesmaximal, characteristic, complemented
10D4×#14524130C211yesmaximal, characteristic, complemented
11D42×C269C211yesmaximal, characteristic, complemented
12C22×D1076C2212yescomplemented
13C2×D4×D269—21no—
14C2×#16864387—28no—
15C2×#16864387C2211yescharacteristic
16C2×#16864387C2212yescomplemented
17C2×#16864387C2212yescomplemented
18C2×#16864387C2212yescomplemented
19C2×#16864387C2212yescomplemented
20C22×#14524130C2212yescomplemented
21#22575450C2211yescharacteristic, complemented
22#22575428—21no—
23#22575427C2212yescomplemented
24#22575423—22no—
25C4×D1076C2211yescharacteristic, complemented
26#22575386C2211yescharacteristic, complemented
27C4⋊#14524130C2211yescharacteristic, complemented
28#22575374C2211yescharacteristic, complemented
29#22575374C2212yescomplemented
30#22575373C2211yescharacteristic, complemented
31#22575373C2212yescomplemented
32C22⋊#14524130C2212yescomplemented
33C4×#14524130C2211yescharacteristic, complemented
34C22×D4×C269—21no—
35C22×D4×C269C2212yescomplemented
36#127×C269C2211yescharacteristic, complemented
37#121×C269—21no—
38#121×C269C2212yescomplemented
39#120×C269—22no—
40C4×D4×C269C2211yescharacteristic
41C4×D4×C269C2211yescharacteristic, complemented
42C23×D269—22no—
43C2×D1076—24no—
44C2×D1076—22no—
45C2×D1076—21no—
46C2×D1076—21no—
47C2×D1076—42no—
48C2×D1076C2312yes—
49C2×D1076C2311yescharacteristic
50C2×C22⋊D269—22no—
51D4×D269—44no—
52C2×C4×D269—21no—
53#16864387—24no—
54#16864387—24no—
55#16864387—24no—
56#16864387—42no—
57#16864387D414yesdirect product factor
58C2×#14524130—24no—
59C2×#14524130C2311yescharacteristic
60C2×#14524130C2312yes—
61C2×#14524130C2311yescharacteristic
62C4⋊Dic269C2311yescharacteristic
63#16864379—21no—
64#16864379—22no—
65C24×C269—22no—
66C2×D4×C269—24no—
67C2×D4×C269—22no—
68C2×D4×C269—22no—
69C2×D4×C269—21no—
70C2×D4×C269—21no—
71C2×D4×C269—42no—
72C2×D4×C269—44no—
73C2×D4×C269D411yescharacteristic
74C2×D4×C269C2312yes—
75C2×D4×C269C2311yescharacteristic
76C22×C4×C269—21no—
77C22×C4×C269C2312yes—
78C4⋊C4×C269D411yescharacteristic
79C4⋊C4×C269C2311yescharacteristic
80C22⋊C4×C269—21no—
81C22⋊C4×C269—22no—
82C22⋊C4×C269D412yes—
83C42×C269C2311yescharacteristic
84C22×D269—21no—
85C22×D269—22no—
86C22×D269—44no—
87C22×D269—44no—
88C22×D269—82no—
89D1076—22no—
90D1076—21no—
91D1076—22no—
92D1076—44no—
93D1076—42no—
94D1076—81no—
95D1076C2×D412yescomplemented
96C22⋊D269—44no—
97C2×Dic269—21no—
98C4×D269—42no—
99#14524130—22no—
100#14524130—21no—
101#14524130C2×D412yescomplemented
102C23×C269—21no—
103C23×C269—22no—
104C23×C269—44no—
105C23×C269—44no—
106C23×C269—82no—
107C23×C269C2×D412yes—
108D4×C269—22no—
109D4×C269—21no—
110D4×C269—22no—
111D4×C269—44no—
112D4×C269—44no—
113D4×C269—42no—
114D4×C269—81no—
115D4×C269D814yescomplemented
116D4×C269C2×D412yescomplemented
117C2×C4×C269—22no—
118C2×C4×C269—22no—
119C2×C4×C269—21no—
120C2×C4×C269—42no—
121C2×C4×C269C2×D411yescharacteristic
122C2×C4×C269C2×D412yes—
123C2×C4×C269C2×D411yescharacteristic
124C2×C4×C269C2411yescharacteristic
125C22×C269—22no—
126C22×C269—22no—
127C22×C269—22no—
128C22×C269—41no—
129C22×C269—41no—
130C22×C269—42no—
131C22×C269—42no—
132C22×C269—42no—
133C22×C269—88no—
134C22×C269C2×D814yescomplemented
135C22×C269C22×D411yescharacteristic
136C2×D269—22no—
137C2×D269—41no—
138C2×D269—41no—
139C2×D269—42no—
140C2×D269—42no—
141C2×D269—42no—
142C2×D269—88no—
143C4×C269—22no—
144C4×C269—21no—
145C4×C269—41no—
146C4×C269C2×D812yescomplemented
147C4×C269C22×D411yescharacteristic
148C4×C269H(5,𝔽2)11yescharacteristic
149Dic269—41no—
150C2×C269—24no—
151C2×C269—42no—
152C2×C269—82no—
153C2×C269D4211yescharacteristic
154C2×C269C22×D811yescharacteristic
155C2×C269#57611yescharacteristic
156D269—42no—
157D269—82no—
158C269D4×D811yescharacteristic, complemented, Sylow
159D4×D8—2691nomaximal, Sylow
160C22×D8—2692no—
161D42—2691no—
162D42D26911yescharacteristic, complemented
163#493—2691no—
164#466—2692no—
165#459—2691no—
166#459—2691no—
167#447—2692no—
168#447—2692no—
169C4×D8—2691no—
170C8×D4—2691no—
171C22×D4—21no—
172C22×D4—2692no—
173C22×D4—5381no—
174C22×D4C2×D26912yescomplemented
175C2×D8—2691no—
176C2×D8—2692no—
177C2×D8—2692no—
178C2×D8—2692no—
179C2×D8—2692no—
180C2×D8—5388no—
181C22×C8—2692no—
182#127—2691no—
183#127C2×D26911yescharacteristic, complemented
184#121—21no—
185#121—2692no—
186#121—5381no—
187#121C2×D26912yescomplemented
188#120—22no—
189#120—5382no—
190C4×D4—2691no—
191C4×D4C2×D26911yescharacteristic
192C4×D4C2×D26911yescharacteristic, complemented
193#107—2691no—
194C4⋊C8—2691no—
195#102—2691no—
196#102—2692no—
197#102—2691no—
198#102—2692no—
199C22⋊C8—2692no—
200C4×C8—2691no—
201C24—22no—
202C24—5382no—
203C2×D4—24no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—42no—
209C2×D4—44no—
210C2×D4—2691no—
211C2×D4—2692no—
212C2×D4—5384no—
213C2×D4—5382no—
214C2×D4—5382no—
215C2×D4—5381no—
216C2×D4—5381no—
217C2×D4—10762no—
218C2×D4—10764no—
219C2×D4C22⋊D26911yescharacteristic
220C2×D4C22×D26912yes—
221C2×D4C22×D26911yescharacteristic
222C22×C4—21no—
223C22×C4—5381no—
224C22×C4C22×D26912yes—
225D8—2694no—
226D8—5384no—
227D8—5384no—
228D8—5384no—
229D8—10762no—
230C2×C8—2691no—
231C2×C8—2691no—
232C2×C8—2692no—
233C2×C8—5384no—
234C4⋊C4—2691no—
235C4⋊C4C22⋊D26911yescharacteristic
236C4⋊C4C22×D26911yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—22no—
239C22⋊C4—5381no—
240C22⋊C4—5382no—
241C22⋊C4C22⋊D26912yes—
242C42C22×D26911yescharacteristic
243C23—21no—
244C23—22no—
245C23—44no—
246C23—44no—
247C23—82no—
248C23—5381no—
249C23—5382no—
250C23—10764no—
251C23—10764no—
252C23—21522no—
253C23C2×C22⋊D26912yes—
254D4—22no—
255D4—21no—
256D4—22no—
257D4—44no—
258D4—44no—
259D4—42no—
260D4—81no—
261D4—2692no—
262D4—5382no—
263D4—5381no—
264D4—5382no—
265D4—10764no—
266D4—10764no—
267D4—10762no—
268D4—21521no—
269D4#1686438714yesdirect product factor
270D4D4×D26912yescomplemented
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—42no—
275C2×C4—5381no—
276C2×C4—10762no—
277C2×C4C2×C22⋊D26911yescharacteristic
278C2×C4C2×C22⋊D26912yes—
279C2×C4C2×C22⋊D26911yescharacteristic
280C2×C4C23×D26911yescharacteristic
281C8—2692no—
282C8—5382no—
283C8—5381no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—88no—
293C22—5382no—
294C22—10761no—
295C22—10761no—
296C22—10762no—
297C22—10762no—
298C22—10762no—
299C22—21528no—
300C22C2×#1686438714yescomplemented
301C22C22×C22⋊D26911yescharacteristic
302C4—21no—
303C4—22no—
304C4—41no—
305C4—10761no—
306C4C2×#1686438712yescomplemented
307C4C2×D4×D26911yescharacteristic
308C4#2257549811yescharacteristic
309C2—24no—
310C2—42no—
311C2—82no—
312C2—10762no—
313C2—21522no—
314C2D4×C22⋊D26911yescharacteristic
315C2C22×#1686438711yescharacteristic
316C2#3177140811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingD42×C269C2
socleC22×C269C22×D4
hypercenterD42D269
hypocenterC269D4×D8
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C22×#16864387C2semidirect
2. D4×D1076C2semidirect
3. #31770981C2semidirect
4. #31770839C2semidirect
5. #31770800C2semidirect
6. #31770797C2semidirect
7. #31770739C2semidirect
8. #31770738C2semidirect
9. C4×#16864387C2semidirect
10. D4×#14524130C2semidirect
11. D42×C269C2semidirect
12. C22×D1076C22semidirect
16. C2×#16864387C22semidirect
17. C2×#16864387C22semidirect
18. C2×#16864387C22semidirect
19. C2×#16864387C22semidirect
20. C22×#14524130C22semidirect
21. #22575450C22semidirect
23. #22575427C22semidirect
25. C4×D1076C22semidirect
26. #22575386C22semidirect
27. C4⋊#14524130C22semidirect
28. #22575374C22semidirect
29. #22575374C22semidirect
30. #22575373C22semidirect
31. #22575373C22semidirect
32. C22⋊#14524130C22semidirect
33. C4×#14524130C22semidirect
35. C22×D4×C269C22semidirect
36. #127×C269C22semidirect
38. #121×C269C22semidirect
41. C4×D4×C269C22semidirect
57. #16864387D4direct (N × H)
95. D1076C2×D4semidirect
101. #14524130C2×D4semidirect
115. D4×C269D8semidirect
116. D4×C269C2×D4semidirect
134. C22×C269C2×D8semidirect
146. C4×C269C2×D8semidirect
158. C269D4×D8semidirect
162. D42D269semidirect
174. C22×D4C2×D269semidirect
183. #127C2×D269semidirect
187. #121C2×D269semidirect
192. C4×D4C2×D269semidirect
269. D4#16864387direct (N × H)
270. D4D4×D269semidirect
300. C22C2×#16864387semidirect
306. C4C2×#16864387semidirect

Maximal subgroups

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

subgroupindex
C22×#168643872
D4×D10762
#317709812
#317708392
#317708002
#317707972
#317707392
#317707382
C4×#168643872
D4×#145241302
D42×C2692
D4×D8269