Finite Group Databasebeta

← D8×SD32 #492521

Subgroups — D8×SD32 #492521

Order 512.

551 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 551 conjugacy classes of subgroups — too many to draw. Only its 134 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
1D4×SD32C212yesmaximal, complemented
2D8×Q16C211yesmaximal, characteristic, complemented
3D82C211yesmaximal, characteristic
4#12517C211yesmaximal, characteristic, complemented
5#12432C212yesmaximal, complemented
6#12426C211yesmaximal, characteristic, complemented
7#12425C211yesmaximal, characteristic, complemented
8#12320C212yesmaximal, complemented
9#12318C212yesmaximal, complemented
10C8×SD32C211yesmaximal, characteristic, complemented
11C16×D8C211yesmaximal, characteristic, complemented
12C22×SD32—22no—
13Q8×D8—21no—
14D4×Q16C2212yescomplemented
15D4×D8—21no—
16D4×D8C2212yes—
17#2248C2212yescomplemented
18#2248C2212yescomplemented
19#2217—22no—
20#2208C2212yes—
21#2207C2212yescomplemented
22#2187—22no—
23#2185—22no—
24C4×SD32C2211yescharacteristic
25D4×C16C2212yescomplemented
26#1713C2211yescharacteristic, complemented
27#1712C2211yescharacteristic
28#1674—21no—
29#1669C2212yescomplemented
30#1667—21no—
31#1667C2212yes—
32#1649—22no—
33#1619—22no—
34C8×Q16C2211yescharacteristic, complemented
35C8×D8C2211yescharacteristic
36C8×D8C2211yescharacteristic
37#1372C2211yescharacteristic, complemented
38#1370C2211yescharacteristic, complemented
39#1362C2212yescomplemented
40#1361C2212yescomplemented
41#1332C2211yescharacteristic, complemented
42#1331C2211yescharacteristic
43D4⋊C16C2212yescomplemented
44C8×C16C2211yescharacteristic, complemented
45C22×Q16—22no—
46C22×D8—22no—
47C22×D8—41no—
48D4×Q8—22no—
49D42—22no—
50C2×SD32—22no—
51C2×SD32—22no—
52C2×SD32—22no—
53C2×SD32—22no—
54C2×SD32—42no—
55C2×SD32—48no—
56C2×SD32D411yescharacteristic
57C22×C16—22no—
58#500—21no—
59#500—21no—
60#500—41no—
61#494C2312yes—
62#493—21no—
63#493—21no—
64#493C2312yes—
65#474—22no—
66#474—42no—
67#467—22no—
68#466—22no—
69#466—41no—
70#462—22no—
71#459—22no—
72#459—22no—
73#451—42no—
74#447—42no—
75#447—42no—
76C8×Q8—21no—
77C4×Q16C2311yescharacteristic
78C4×D8—41no—
79C4×D8D411yescharacteristic
80C4×D8C2311yescharacteristic
81C8×D4—21no—
82C8×D4C2312yes—
83#367D411yescharacteristic
84C4⋊C16C2312yes—
85#358—22no—
86#358D411yescharacteristic
87#357—22no—
88#357D411yescharacteristic
89C22⋊C16—22no—
90C4×C16C2311yescharacteristic
91C4×C16C2311yescharacteristic
92#335D411yescharacteristic
93#335C2311yescharacteristic
94#335C2311yescharacteristic
95#332—22no—
96#331—22no—
97Q8⋊C8—21no—
98D4⋊C8—21no—
99D4⋊C8D412yes—
100C82C2311yescharacteristic
101C22×Q8—42no—
102C22×D4—42no—
103C22×D4—42no—
104C2×Q16—22no—
105C2×Q16—22no—
106C2×Q16—42no—
107C2×Q16—44no—
108C2×Q16—82no—
109C2×Q16C2×D411yescharacteristic
110C2×D8—22no—
111C2×D8—22no—
112C2×D8—42no—
113C2×D8—44no—
114C2×D8—42no—
115C2×D8—41no—
116C2×D8—41no—
117C2×D8—81no—
118C2×D8—82no—
119C2×D8—84no—
120C2×D8D811yescharacteristic
121C2×D8C2×D411yescharacteristic
122C22×C8—22no—
123C22×C8—41no—
124C4⋊Q8—22no—
125C4⋊Q8—42no—
126#127—22no—
127C22⋊Q8—42no—
128C22⋊Q8—82no—
129#121—42no—
130#121—42no—
131#120—82no—
132C4×Q8—21no—
133C4×D4—21no—
134C4×D4—42no—
135C4×D4C2×D412yes—
136SD32—44no—
137SD32—44no—
138SD32—44no—
139SD32—82no—
140SD32—84no—
141SD32D814yesdirect product factor
142C2×C16—21no—
143C2×C16—22no—
144C2×C16—44no—
145C2×C16C2×D411yescharacteristic
146C2×C16C2×D411yescharacteristic
147#107—41no—
148#107—41no—
149#107—42no—
150#107—81no—
151#107D811yescharacteristic
152#107C2×D411yescharacteristic
153#107C2×D411yescharacteristic
154C4⋊C8—21no—
155C4⋊C8—21no—
156C4⋊C8—41no—
157C4⋊C8C2×D412yes—
158#103—21no—
159#103—42no—
160#102—21no—
161#102—42no—
162#102—42no—
163#102—42no—
164#102D812yes—
165C22⋊C8—22no—
166C22⋊C8—41no—
167C4×C8—41no—
168C4×C8C2×D411yescharacteristic
169C4×C8C2×D411yescharacteristic
170C4×C8C2411yescharacteristic
171C24—82no—
172C2×Q8—21no—
173C2×Q8—42no—
174C2×Q8—82no—
175C2×Q8—84no—
176C2×Q8—162no—
177C2×D4—21no—
178C2×D4—42no—
179C2×D4—42no—
180C2×D4—42no—
181C2×D4—82no—
182C2×D4—84no—
183C2×D4—82no—
184C2×D4—84no—
185C2×D4—162no—
186C2×D4—162no—
187C2×D4C2×D812yes—
188C22×C4—22no—
189C22×C4—41no—
190C22×C4—82no—
191Q16—21no—
192Q16—42no—
193Q16—42no—
194Q16—82no—
195Q16—84no—
196Q16C2×D812yescomplemented
197D8—21no—
198D8—42no—
199D8—42no—
200D8—82no—
201D8—84no—
202D8—84no—
203D8—82no—
204D8—161no—
205D8—162no—
206D8SD3214yesdirect product factor
207D8C2×D812yes—
208C2×C8—21no—
209C2×C8—22no—
210C2×C8—42no—
211C2×C8—42no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—82no—
215C2×C8C2×D811yescharacteristic
216C2×C8C2×D811yescharacteristic
217C2×C8C22×D411yescharacteristic
218C2×C8H(5,𝔽2)11yescharacteristic
219C4⋊C4—21no—
220C4⋊C4—21no—
221C4⋊C4—41no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—82no—
225C4⋊C4C2×D812yes—
226C22⋊C4—22no—
227C22⋊C4—41no—
228C22⋊C4—82no—
229C22⋊C4—82no—
230C42—41no—
231C42C22×D411yescharacteristic
232C16—22no—
233C16—21no—
234C16—42no—
235C16C2×D812yescomplemented
236C23—22no—
237C23—41no—
238C23—82no—
239C23—164no—
240C23—164no—
241C23—322no—
242Q8—22no—
243Q8—41no—
244Q8—82no—
245Q8—82no—
246Q8—164no—
247D4—22no—
248D4—22no—
249D4—41no—
250D4—82no—
251D4—82no—
252D4—82no—
253D4—82no—
254D4—162no—
255D4—164no—
256D4—164no—
257D4C2×SD3214yescomplemented
258C2×C4—22no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—82no—
267C2×C4—164no—
268C2×C4D4211yescharacteristic
269C2×C4C22×D811yescharacteristic
270C2×C4#57611yescharacteristic
271C8—22no—
272C8—21no—
273C8—21no—
274C8—42no—
275C8—81no—
276C8—81no—
277C8C2×SD3212yescomplemented
278C8C22×D811yescharacteristic
279C8#57611yescharacteristic
280C22—24no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—81no—
285C22—81no—
286C22—162no—
287C22—162no—
288C22—162no—
289C22—328no—
290C22D4×D811yescharacteristic
291C4—21no—
292C4—42no—
293C4—42no—
294C4—81no—
295C4—81no—
296C4—162no—
297C4D4×D811yescharacteristic
298C4#329211yescharacteristic
299C4C22×SD3211yescharacteristic
300C4#341611yescharacteristic
301C2—44no—
302C2—82no—
303C2—322no—
304C2D8211yescharacteristic
305C2D4×SD3211yescharacteristic
306C2#3385611yescharacteristic
subgroupG/H
center, socleC22D4×D8
commutator, Frattini, cosocleC4×C8C24
prime radicalD82C2
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C42 ◁ C8×D8 ◁ G
LECSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. D4×SD32C2semidirect
2. D8×Q16C2semidirect
4. #12517C2semidirect
5. #12432C2semidirect
6. #12426C2semidirect
7. #12425C2semidirect
8. #12320C2semidirect
9. #12318C2semidirect
10. C8×SD32C2semidirect
11. C16×D8C2semidirect
14. D4×Q16C22semidirect
17. #2248C22semidirect
18. #2248C22semidirect
21. #2207C22semidirect
25. D4×C16C22semidirect
26. #1713C22semidirect
29. #1669C22semidirect
34. C8×Q16C22semidirect
37. #1372C22semidirect
38. #1370C22semidirect
39. #1362C22semidirect
40. #1361C22semidirect
41. #1332C22semidirect
43. D4⋊C16C22semidirect
44. C8×C16C22semidirect
141. SD32D8direct (N × H)
196. Q16C2×D8semidirect
206. D8SD32direct (N × H)
235. C16C2×D8semidirect
257. D4C2×SD32semidirect
277. C8C2×SD32semidirect

Maximal subgroups

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

subgroupindex
D4×SD322
D8×Q162
D822
#125172
#124322
#124262
#124252
#123202
#123182
C8×SD322
C16×D82