Finite Group Databasebeta

← D32×Q32 #11899479

Subgroups — D32×Q32 #11899479

Order 1152.

761 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 761 conjugacy classes of subgroups — too many to draw. Only its 158 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
1D32×Q16C212yesmaximal
2C3⋊D3×Q32C211yesmaximal, characteristic, complemented
3C3×D3×Q32C212yesmaximal, complemented
4#10591043C212yesmaximal, complemented
5D3×#829C214yesmaximal, complemented
6#10590240C211yesmaximal, characteristic, complemented
7D3×Dic24C212yesmaximal, complemented
8D32×C16C211yesmaximal, characteristic
9C2×D3×Q32—32nomaximal
10D32×Q8—22no—
11Q16×C3⋊D3C2212yes—
12C3×D3×Q16C2214yes—
13#63944—22no—
14D3×#216—24no—
15#63802C2212yes—
16D3×Dic12C2214yes—
17D32×C8C2211yescharacteristic
18C32×Q32C2211yescharacteristic, complemented
19#63656C2212yescomplemented
20#63628C2211yescharacteristic, complemented
21C16×C3⋊D3C2211yescharacteristic
22C3×#829C2214yescomplemented
23C3×Dic24C2212yescomplemented
24C3×D3×C16C2212yes—
25#63551C2214yescomplemented
26#63550C2212yescomplemented
27#63542C2211yescharacteristic
28D3×C3⋊C16C2212yes—
29C2×D3×Q16—34no—
30C2×C3×Q32—32no—
31C2×#829—34no—
32D3×Q32—34no—
33D3×Q32—32no—
34D3×Q32—34no—
35D3×Q32—32no—
36D3×Q32—32no—
37D3×Q32—61no—
38D3×Q32D312yesdirect product factor
39C2×Dic24—32no—
40C2×D3×C16—32no—
41Q8×C3⋊D3—22no—
42C3×D3×Q8—24no—
43C4×D32—42no—
44C4×D32D411yescharacteristic
45#3797—22no—
46#3797—42no—
47D3×Dic6—24no—
48D3×Dic6—44no—
49C32×Q16C2312yes—
50#3756—22no—
51#3746C2312yes—
52C8×C3⋊D3C2311yescharacteristic
53C3×#216—24no—
54C3×Dic12C2314yes—
55C3×D3×C8C2312yes—
56#3719—24no—
57#3718—22no—
58#3710D411yescharacteristic
59D3×C3⋊C8D412yes—
60C32×C16C2311yescharacteristic
61C3⋊(C3⋊C16)C2311yescharacteristic
62C3×C3⋊C16C2312yes—
63C22×Q32—91noSylow
64C2×D3×Q8—64no—
65C2×C3×Q16—34no—
66C2×#216—64no—
67D3×Q16—34no—
68D3×Q16—34no—
69D3×Q16—34no—
70D3×Q16—62no—
71D3×Q16—64no—
72D3×Q16—64no—
73D3×Q16C2×D314yes—
74C2×Dic12—34no—
75C2×D3×C8—32no—
76C3×Q32—21no—
77C3×Q32—34no—
78C3×Q32—32no—
79C3×Q32C2×D312yescomplemented
80C2×C3×C16—32no—
81#829—34no—
82#829—34no—
83#829—34no—
84#829—62no—
85#829C2×D314yescomplemented
86C2×C3⋊C16—32no—
87Dic24—34no—
88Dic24—32no—
89Dic24—61no—
90Dic24C2×D312yescomplemented
91D3×C16—32no—
92D3×C16—32no—
93D3×C16—32no—
94D3×C16—61no—
95D3×C16C2×D312yes—
96C2×D32D811yescharacteristic
97C32×Q8—22no—
98C4×C3⋊D3—42no—
99C4×C3⋊D3C2×D411yescharacteristic
100#634—22no—
101#634—42no—
102C3×C4×D3—44no—
103C3×C4×D3C2×D412yes—
104C3×Dic6—24no—
105C3×Dic6—44no—
106#627—42no—
107#627—44no—
108#624—42no—
109#624D811yescharacteristic
110D3×Dic3—44no—
111D3×Dic3D812yes—
112C32×C8C2411yescharacteristic
113C3⋊(C3⋊C8)C2×D411yescharacteristic
114C3×C3⋊C8C2×D412yes—
115C22×Q16—92no—
116C2×Q32—32no—
117C2×Q32—92no—
118C2×Q32—92no—
119C2×Q32—91no—
120C2×Q32—94no—
121C2×Q32—91no—
122C22×C16—91no—
123C2×C3×Q8—64no—
124D3×Q8—24no—
125D3×Q8—64no—
126D3×Q8—64no—
127D3×Q8—64no—
128D3×Q8—122no—
129D3×Q8—124no—
130D3×Q8—124no—
131C2×C4×D3—32no—
132C2×C4×D3—124no—
133C2×Dic6—64no—
134C2×Dic6—124no—
135C3×Q16—22no—
136C3×Q16—34no—
137C3×Q16—64no—
138C3×Q16C22×D314yes—
139C2×C3×C8—32no—
140#216—24no—
141#216—64no—
142#216—64no—
143#216—64no—
144#216—122no—
145C2×C3⋊C8—32no—
146Dic12—34no—
147Dic12—62no—
148Dic12—64no—
149Dic12C22×D314yes—
150D3×C8—32no—
151D3×C8—32no—
152D3×C8—32no—
153D3×C8—61no—
154D3×C8C22×D312yes—
155C3×C16—21no—
156C3×C16—32no—
157C3×C16C22×D312yes—
158C3⋊C16—32no—
159C3⋊C16—61no—
160C3⋊C16C22×D312yes—
161C2×C3⋊D3C2×D811yescharacteristic
162C2×C3×D3C2×D812yes—
163D32Q3214yesdirect product factor
164C32×C4—42no—
165C32×C4C22×D411yescharacteristic
166C3⋊Dic3—42no—
167C3⋊Dic3C2×D811yescharacteristic
168C3×Dic3—44no—
169C3×Dic3C2×D812yes—
170C22×Q8—182no—
171C2×Q16—34no—
172C2×Q16—94no—
173C2×Q16—92no—
174C2×Q16—92no—
175C2×Q16—182no—
176C2×Q16—184no—
177C22×C8—91no—
178Q32—34no—
179Q32—32no—
180Q32—94no—
181Q32—92no—
182Q32—92no—
183Q32—91no—
184Q32D3211yescharacteristic, direct product factor
185C2×C16—32no—
186C2×C16—91no—
187C2×C16—92no—
188C2×C16—91no—
189C22×D3—32no—
190C3×Q8—24no—
191C3×Q8—42no—
192C3×Q8—64no—
193C3×Q8—124no—
194C2×C3×C4—32no—
195C2×C3×C4—124no—
196C2×Dic3—32no—
197C2×Dic3—124no—
198C4×D3—32no—
199C4×D3—32no—
200C4×D3—32no—
201C4×D3—44no—
202C4×D3—61no—
203C4×D3—124no—
204C4×D3—124no—
205C4×D3—124no—
206C4×D3—242no—
207C4×D3D3×D412yes—
208Dic6—24no—
209Dic6—44no—
210Dic6—64no—
211Dic6—122no—
212Dic6—124no—
213Dic6—124no—
214Dic6—124no—
215Dic6—124no—
216Dic6—242no—
217C3×C8—21no—
218C3×C8—32no—
219C3×C8C23×D312yes—
220C3⋊C8—32no—
221C3⋊C8—61no—
222C3⋊C8D3×D412yes—
223C2×C32C22×D811yescharacteristic
224C3⋊D3C2×Q3212yescomplemented
225C3×D3C2×Q3214yescomplemented
226C2×Q8—64no—
227C2×Q8—184no—
228C2×Q8—182no—
229C2×Q8—182no—
230C2×Q8—364no—
231C2×Q8—362no—
232C22×C4—91no—
233C22×C4—362no—
234Q16—34no—
235Q16—64no—
236Q16—92no—
237Q16—184no—
238Q16—182no—
239Q16—182no—
240Q16C2×D3212yes—
241C2×C8—32no—
242C2×C8—91no—
243C2×C8—92no—
244C2×C8—91no—
245C16—32no—
246C16—91no—
247C16C2×D3211yescharacteristic
248C22×C3—32no—
249C2×D3—32no—
250C2×D3—38no—
251C2×D3—61no—
252C2×D3D3×D812yes—
253C3×C4—21no—
254C3×C4—32no—
255C3×C4—44no—
256C3×C4—82no—
257C3×C4—124no—
258C3×C4C2×D3×D412yes—
259Dic3—32no—
260Dic3—44no—
261Dic3—61no—
262Dic3—124no—
263Dic3—242no—
264Dic3D3×D812yes—
265C32C22×Q3211yescharacteristic, complemented, Sylow
266C23—91no—
267Q8—22no—
268Q8—64no—
269Q8—124no—
270Q8—182no—
271Q8—364no—
272Q8—362no—
273Q8—362no—
274C2×C4—32no—
275C2×C4—91no—
276C2×C4—92no—
277C2×C4—91no—
278C2×C4—124no—
279C2×C4—362no—
280C2×C4—362no—
281C2×C4—364no—
282C8—32no—
283C8—91no—
284C8C22×D3211yescharacteristic
285C2×C3—21no—
286C2×C3—34no—
287C2×C3C2×D3×D812yes—
288D3—34no—
289D3—62no—
290D3D3×Q3214yesdirect product factor
291C22—32no—
292C22—94no—
293C22—91no—
294C4—32no—
295C4—42no—
296C4—91no—
297C4—124no—
298C4—362no—
299C4D32×D411yescharacteristic
300C3—21no—
301C3C2×D3×Q3212yescomplemented
302C2—34no—
303C2—92no—
304C2D32×D811yescharacteristic
subgroupG/H
centerC2D32×D8
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC32×Q32C22
socleC2×C32C22×D8
prime radicalC2×D32D8
hypercenterQ32D32
hypocenterC32C22×Q32
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×Q32C2semidirect
3. C3×D3×Q32C2semidirect
4. #10591043C2semidirect
5. D3×#829C2semidirect
6. #10590240C2semidirect
7. D3×Dic24C2semidirect
18. C32×Q32C22semidirect
19. #63656C22semidirect
20. #63628C22semidirect
22. C3×#829C22semidirect
23. C3×Dic24C22semidirect
25. #63551C22semidirect
26. #63550C22semidirect
38. D3×Q32D3direct (N × H)
79. C3×Q32C2×D3semidirect
85. #829C2×D3semidirect
90. Dic24C2×D3semidirect
163. D32Q32direct (N × H)
184. Q32D32direct (N × H)
224. C3⋊D3C2×Q32semidirect
225. C3×D3C2×Q32semidirect
265. C32C22×Q32semidirect
290. D3D3×Q32direct (N × H)
301. C3C2×D3×Q32semidirect

Maximal subgroups

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

subgroupindex
D32×Q162
C3⋊D3×Q322
C3×D3×Q322
#105910432
D3×#8292
#105902402
D3×Dic242
D32×C162
C2×D3×Q323