Finite Group Databasebeta

← D3×#942 #10595316

Subgroups — D3×#942 #10595316

Order 576.

546 conjugacy classes of subgroups.

The subgroup lattice has 425 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×Q8C211yesmaximal, characteristic, complemented
2D3×#235C211yesmaximal, characteristic
3#64151C211yesmaximal, characteristic, complemented
4C3×#942C211yesmaximal, characteristic, complemented
5#63948C212yesmaximal, complemented
6#63946C212yesmaximal, complemented
7D3×#216C212yesmaximal, complemented
8D3×#215C212yesmaximal, complemented
9#63833C211yesmaximal, characteristic, complemented
10#63827C211yesmaximal, characteristic, complemented
11D3×#208C211yesmaximal, characteristic, complemented
12C2×#942—31nomaximal
13D3×#137—31nomaximal
14C2×C32×Q8C2211yescharacteristic, complemented
15#3828C2211yescharacteristic
16C3×D3×Q8—21no—
17C3×D3×Q8—21no—
18C3×D3×Q8C2212yes—
19C3×D3×Q8C2212yescomplemented
20C3×#235C2211yescharacteristic
21C2×C3×C4×D3—21no—
22C2×C3×C4×D3C2211yescharacteristic
23C2×C3×Dic6—21no—
24C2×C3×Dic6C2211yescharacteristic, complemented
25D3×#67—21no—
26#3804—21no—
27D3×D12C2211yescharacteristic
28C4×D32—21no—
29#3799C2211yescharacteristic
30#3798—21no—
31#3795C2211yescharacteristic
32D3×Dic6C2211yescharacteristic
33#3756C2212yescomplemented
34#3755C2212yescomplemented
35#3748C2211yescharacteristic, complemented
36C3×#216C2212yescomplemented
37C3×#215C2212yescomplemented
38C3×#208C2211yescharacteristic, complemented
39#3719C2212yescomplemented
40#3718C2212yescomplemented
41#3717C2212yescomplemented
42#3715C2212yescomplemented
43#3711C2212yescomplemented
44D3×C3⋊C8C2212yes—
45C22×C3×Q8—31no—
46D3×#41—31no—
47C2×D3×Q8D311yescharacteristic, complemented
48C2×#235—31no—
49C3×#137—31no—
50#951—31no—
51C2×#216—32no—
52#942—31no—
53#942—31no—
54#942—31no—
55#942—32no—
56#942—32no—
57#942—31no—
58#942—61no—
59#942D311yescharacteristic, direct product factor
60C2×#215—32no—
61C2×#208—31no—
62#918—32no—
63D3×Q16—32no—
64#915—32no—
65D3×SD16—32no—
66#909—31no—
67D3×M16—31no—
68C22×C3×D3D411yescharacteristic
69C2×D32—21no—
70C32×Q8—21no—
71C32×Q8C2312yes—
72C2×C32×C4—21no—
73C2×C32×C4C2311yescharacteristic
74#638—21no—
75C4⋊(C3⋊D3)C2311yescharacteristic
76C4×C3⋊D3—21no—
77#634C2311yescharacteristic
78C3×#67—21no—
79C2×C3×Dic3—21no—
80C2×C3×Dic3D411yescharacteristic
81C3×D12C2311yescharacteristic
82C3×C4×D3—22no—
83C3×C4×D3—22no—
84C3×C4×D3—21no—
85C3×C4×D3D411yescharacteristic
86C3×C4×D3D411yescharacteristic
87C3×C4×D3C2311yescharacteristic
88C3×C4×D3C2311yescharacteristic
89C3×Dic6—21no—
90C3×Dic6—22no—
91C3×Dic6—22no—
92C3×Dic6C2312yes—
93C3×Dic6C2311yescharacteristic
94#627—21no—
95#626—21no—
96#626—21no—
97#625—21no—
98#624—21no—
99D3×Dic3—21no—
100D3×Dic3—21no—
101C3⋊(C3⋊C8)C2312yes—
102C3×C3⋊C8C2312yes—
103C2×#137—91noSylow
104C3×#41—31no—
105C2×C3×Q8—21no—
106C2×C3×Q8—32no—
107C2×C3×Q8—32no—
108C2×C3×Q8—31no—
109C2×C3×Q8—61no—
110C2×C3×Q8—61no—
111C2×C3×Q8—61no—
112C2×C3×Q8C2×D311yescharacteristic, complemented
113C2×C3×Q8C2×D311yescharacteristic, complemented
114C22×C3×C4—31no—
115C22×C3×C4—61no—
116C2×#67—61no—
117#239—31no—
118D3×Q8—21no—
119D3×Q8—21no—
120D3×Q8—31no—
121D3×Q8C2×D312yes—
122D3×Q8C2×D312yescomplemented
123#237—31no—
124#237—61no—
125D3×D4—31no—
126D3×D4—61no—
127#235—31no—
128#235—31no—
129#235—31no—
130#235—31no—
131#235—61no—
132#235—61no—
133#235—61no—
134#235—61no—
135#235C2×D311yescharacteristic
136C2×D12—31no—
137C2×C4×D3—21no—
138C2×C4×D3—61no—
139C2×C4×D3—61no—
140C2×C4×D3C2×D311yescharacteristic
141C2×Dic6—21no—
142C2×Dic6—31no—
143C2×Dic6C2×D311yescharacteristic, complemented
144C3×Q16—32no—
145C3×SD16—32no—
146C3×M16—31no—
147#216—32no—
148#216—32no—
149#216—32no—
150#216—32no—
151#216—32no—
152#216—62no—
153#216C2×D312yescomplemented
154#215—32no—
155#215—32no—
156#215—32no—
157#215—32no—
158#215—62no—
159#215C2×D312yescomplemented
160#214—32no—
161#208—31no—
162#208—31no—
163#208—32no—
164#208—61no—
165#208C2×D311yescharacteristic, complemented
166C2×C3⋊C8—32no—
167Dic12—32no—
168#204—32no—
169ΓL(1,𝔽25)—32no—
170D3×C8—32no—
171C22×C32C2×D411yescharacteristic
172C2×C3⋊D3—21no—
173C2×C3×D3—22no—
174C2×C3×D3—21no—
175C2×C3×D3C2×D411yescharacteristic
176C2×C3×D3C2×D411yescharacteristic
177D32—42no—
178C32×C4—22no—
179C32×C4C2×D411yescharacteristic
180C32×C4C2411yescharacteristic
181C3⋊Dic3—21no—
182C3×Dic3—21no—
183C3×Dic3—22no—
184C3×Dic3C2×D411yescharacteristic
185C3×Dic3C2×D411yescharacteristic
186C2×#41—91no—
187C22×Q8—31no—
188#137—31no—
189#137—91no—
190#137—92no—
191#137—92no—
192#137—91no—
193#137—91no—
194C2×Q16—92no—
195C2×SD16—92no—
196C2×M16—91no—
197C23×C3—31no—
198C22×D3—61no—
199C22×D3—61no—
200C22×D3#6711yescharacteristic
201C3×Q8—21no—
202C3×Q8—21no—
203C3×Q8—22no—
204C3×Q8—32no—
205C3×Q8—31no—
206C3×Q8—41no—
207C3×Q8—62no—
208C3×Q8—62no—
209C3×Q8—61no—
210C3×Q8C22×D312yes—
211C3×Q8C22×D312yes—
212C3×D4—31no—
213C3×D4—61no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—31no—
218C2×C3×C4—31no—
219C2×C3×C4—31no—
220C2×C3×C4—31no—
221C2×C3×C4—31no—
222C2×C3×C4—41no—
223C2×C3×C4—62no—
224C2×C3×C4—62no—
225C2×C3×C4—61no—
226C2×C3×C4—61no—
227C2×C3×C4C22×D311yescharacteristic
228C2×C3×C4C22×D311yescharacteristic
229#67—21no—
230#67—61no—
231#67—61no—
232#67—61no—
233#67—61no—
234#67—61no—
235#67—61no—
236#67—121no—
237C2×Dic3—21no—
238C2×Dic3—61no—
239C2×Dic3—61no—
240C2×Dic3#6711yescharacteristic
241D12—31no—
242D12—31no—
243D12—61no—
244D12—61no—
245D12—61no—
246D12C22×D311yescharacteristic
247C4×D3—22no—
248C4×D3—22no—
249C4×D3—21no—
250C4×D3—61no—
251C4×D3—61no—
252C4×D3—61no—
253C4×D3—61no—
254C4×D3—61no—
255C4×D3—61no—
256C4×D3—121no—
257C4×D3#6711yescharacteristic
258C4×D3#6711yescharacteristic
259C4×D3C22×D311yescharacteristic
260C4×D3C22×D311yescharacteristic
261Dic6—21no—
262Dic6—22no—
263Dic6—22no—
264Dic6—31no—
265Dic6—31no—
266Dic6—61no—
267Dic6—61no—
268Dic6—61no—
269Dic6C22×D312yes—
270Dic6C22×D311yescharacteristic
271C3×C8—32no—
272C3⋊C8—32no—
273C3⋊C8—32no—
274C3⋊C8—62no—
275C3⋊C8C22×D312yes—
276C2×C32—21no—
277C2×C32C22×D411yescharacteristic
278C3⋊D3—41no—
279C3×D3—21no—
280C3×D3—41no—
281C3×D3#13712yescomplemented
282#41—31no—
283#41—91no—
284#41—91no—
285#41—91no—
286#41—181no—
287#41—181no—
288C2×Q8—32no—
289C2×Q8—32no—
290C2×Q8—31no—
291C2×Q8—61no—
292C2×Q8—61no—
293C2×Q8—61no—
294C2×Q8—91no—
295C2×Q8D3211yescharacteristic, complemented
296C2×D4—91no—
297C2×D4—181no—
298C22×C4—31no—
299C22×C4—61no—
300C22×C4—181no—
301Q16—32no—
302Q16—92no—
303Q16—92no—
304Q16—92no—
305SD16—32no—
306SD16—92no—
307SD16—92no—
308SD16—92no—
309M16—31no—
310M16—92no—
311M16—91no—
312C2×C8—92no—
313C22×C3—21no—
314C22×C3—31no—
315C22×C3—31no—
316C22×C3—62no—
317C22×C3—61no—
318C22×C3D3×D411yescharacteristic
319C22×C3C2×#6711yescharacteristic
320C2×D3—22no—
321C2×D3—21no—
322C2×D3—61no—
323C2×D3—61no—
324C2×D3—121no—
325C2×D3—122no—
326C2×D3—122no—
327C2×D3C2×#6711yescharacteristic
328C2×D3C2×#6711yescharacteristic
329C3×C4—22no—
330C3×C4—22no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—31no—
334C3×C4—31no—
335C3×C4—42no—
336C3×C4—62no—
337C3×C4—61no—
338C3×C4D3×D411yescharacteristic
339C3×C4C2×#6711yescharacteristic
340C3×C4C23×D311yescharacteristic
341C3×C4C23×D311yescharacteristic
342Dic3—21no—
343Dic3—22no—
344Dic3—61no—
345Dic3—61no—
346Dic3—121no—
347Dic3C2×#6711yescharacteristic
348Dic3C2×#6711yescharacteristic
349C32C2×#13711yescharacteristic, complemented, Sylow
350C23—31no—
351C23—181no—
352Q8—21no—
353Q8—32no—
354Q8—31no—
355Q8—62no—
356Q8—62no—
357Q8—61no—
358Q8—91no—
359Q8—181no—
360Q8C2×D3212yes—
361D4—31no—
362D4—61no—
363D4—91no—
364D4—181no—
365D4—181no—
366D4—181no—
367D4—181no—
368C2×C4—21no—
369C2×C4—31no—
370C2×C4—31no—
371C2×C4—31no—
372C2×C4—31no—
373C2×C4—31no—
374C2×C4—62no—
375C2×C4—62no—
376C2×C4—61no—
377C2×C4—61no—
378C2×C4—181no—
379C2×C4—181no—
380C2×C4—181no—
381C2×C4—181no—
382C2×C4C2×D3211yescharacteristic
383C8—32no—
384C8—92no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—32no—
389C2×C3—41no—
390C2×C3—61no—
391C2×C3—121no—
392C2×C3C2×D3×D411yescharacteristic
393C2×C3C22×#6711yescharacteristic
394D3—21no—
395D3—41no—
396D3—121no—
397D3—121no—
398D3—241no—
399D3#94212yesdirect product factor
400C22—31no—
401C22—31no—
402C22—62no—
403C22—61no—
404C22—181no—
405C22—362no—
406C22D3×#6711yescharacteristic
407C4—22no—
408C4—31no—
409C4—31no—
410C4—62no—
411C4—61no—
412C4—181no—
413C4D3×#6711yescharacteristic
414C4C22×D3211yescharacteristic
415C3—21no—
416C3D3×#13711yescharacteristic, complemented
417C3C2×#94211yescharacteristic, complemented
418C2—21no—
419C2—32no—
420C2—61no—
421C2—121no—
422C2—361no—
423C2C2×D3×#6711yescharacteristic
subgroupG/H
centerC2C2×D3×#67
commutator, cosocleC32×C4C24
FrattiniC4C22×D32
FittingC2×C32×Q8C22
socleC2×C32C22×D4
prime radicalD3×#235C2
hypercenterC2×Q8D32
hypocenterC32C2×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×Q8C2semidirect
3. #64151C2semidirect
4. C3×#942C2semidirect
5. #63948C2semidirect
6. #63946C2semidirect
7. D3×#216C2semidirect
8. D3×#215C2semidirect
9. #63833C2semidirect
10. #63827C2semidirect
11. D3×#208C2semidirect
14. C2×C32×Q8C22semidirect
19. C3×D3×Q8C22semidirect
24. C2×C3×Dic6C22semidirect
33. #3756C22semidirect
34. #3755C22semidirect
35. #3748C22semidirect
36. C3×#216C22semidirect
37. C3×#215C22semidirect
38. C3×#208C22semidirect
39. #3719C22semidirect
40. #3718C22semidirect
41. #3717C22semidirect
42. #3715C22semidirect
43. #3711C22semidirect
47. C2×D3×Q8D3semidirect
59. #942D3direct (N × H)
112. C2×C3×Q8C2×D3semidirect
113. C2×C3×Q8C2×D3semidirect
122. D3×Q8C2×D3semidirect
143. C2×Dic6C2×D3semidirect
153. #216C2×D3semidirect
159. #215C2×D3semidirect
165. #208C2×D3semidirect
281. C3×D3#137semidirect
295. C2×Q8D32semidirect
349. C32C2×#137semidirect
399. D3#942direct (N × H)
416. C3D3×#137semidirect
417. C3C2×#942semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×Q82
D3×#2352
#641512
C3×#9422
#639482
#639462
D3×#2162
D3×#2152
#638332
#638272
D3×#2082
C2×#9423
D3×#1373