Finite Group Databasebeta

← #10595469

Subgroups — #10595469

Order 576.

554 conjugacy classes of subgroups.

The subgroup lattice has 433 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#41C211yesmaximal, characteristic, complemented
2C2×#3795C211yesmaximal, characteristic, complemented
3#64160C211yesmaximal, characteristic, complemented
4C3×#949C211yesmaximal, characteristic, complemented
5#63947C212yesmaximal, complemented
6#63946C212yesmaximal, complemented
7#63933C212yesmaximal, complemented
8#63932C212yesmaximal, complemented
9#63831C211yesmaximal, characteristic, complemented
10#63823C211yesmaximal, characteristic, complemented
11D3×#208C211yesmaximal, characteristic, complemented
12#5822—31nomaximal
13#5773—31nomaximal
14C32×#41C2211yescharacteristic
15C2×#634C2211yescharacteristic, complemented
16C3×#239C2211yescharacteristic, complemented
17C3×D3×Q8C2211yescharacteristic, complemented
18C3×#237—21no—
19C3×#237C2211yescharacteristic, complemented
20C3×D3×D4—21no—
21C3×D3×D4C2211yescharacteristic, complemented
22C3×#235—21no—
23C3×#235C2211yescharacteristic
24C2×C3×D12C2211yescharacteristic, complemented
25C2×C3×C4×D3—21no—
26C2×C3×C4×D3C2211yescharacteristic
27C2×#625—21no—
28C2×D3×Dic3—21no—
29#3795—21no—
30#3795—21no—
31#3795C2212yes—
32#3795C2212yescomplemented
33#3756C2212yescomplemented
34#3754C2212yescomplemented
35#3748C2211yescharacteristic, complemented
36C3×#215C2212yescomplemented
37C3×#213C2212yescomplemented
38C3×#208C2211yescharacteristic, complemented
39#3719C2212yescomplemented
40#3716C2212yescomplemented
41#3715C2212yescomplemented
42#3713C2212yescomplemented
43#3711C2212yescomplemented
44D3×C3⋊C8C2212yescomplemented
45C2×C3×#41—31no—
46D3×#41D311yescharacteristic, complemented
47C2×#237—31no—
48C2×#235—31no—
49C3×AGL(1,ℤ/8)—31no—
50#951—31no—
51#951—31no—
52#951—31no—
53#951—61no—
54#950—32no—
55#950—32no—
56#949—31no—
57#949D311yescharacteristic, complemented
58#942—32no—
59#932—31no—
60#932—32no—
61C2×#208—31no—
62#916—32no—
63#915—32no—
64#912—32no—
65#911—32no—
66#909—31no—
67D3×M16—31no—
68C22×C3×D3—21no—
69C22×C3×D3—21no—
70C22×C3×D3D411yescharacteristic
71C32×Q8C2311yescharacteristic
72C32×D4—21no—
73C32×D4C2311yescharacteristic
74C2×C32×C4—21no—
75C2×C32×C4C2311yescharacteristic
76C2×C3⋊Dic3—21no—
77#634—21no—
78#634C2312yes—
79C3×#67—21no—
80C3×#67—21no—
81C3×#67—21no—
82C2×C3×Dic3—21no—
83C2×C3×Dic3D411yescharacteristic
84C3×D12—21no—
85C3×D12—21no—
86C3×D12C2311yescharacteristic
87C3×D12C2312yes—
88C3×C4×D3—21no—
89C3×C4×D3—21no—
90C3×C4×D3—21no—
91C3×C4×D3D411yescharacteristic
92C3×C4×D3D411yescharacteristic
93C3×C4×D3C2311yescharacteristic
94C3×C4×D3C2311yescharacteristic
95C3×Dic6—21no—
96C3×Dic6C2311yescharacteristic
97#625—22no—
98#625—22no—
99D3×Dic3—22no—
100D3×Dic3—22no—
101C3⋊(C3⋊C8)C2312yes—
102C3×C3⋊C8C2312yes—
103#575—91noSylow
104C3×#41—21no—
105C3×#41—31no—
106C3×#41—31no—
107C3×#41—31no—
108C3×#41—61no—
109C3×#41—61no—
110C3×#41C2×D311yescharacteristic
111C3×#41C2×D311yescharacteristic
112C2×C3×Q8—31no—
113C2×C3×D4—31no—
114C2×C3×D4—31no—
115C2×C3×D4—61no—
116C22×C3×C4—31no—
117C22×C3×C4—61no—
118C2×#67—61no—
119C2×#67—61no—
120C22×Dic3—61no—
121#239C2×D311yescharacteristic, complemented
122D3×Q8C2×D311yescharacteristic, complemented
123#237—21no—
124#237—32no—
125#237—32no—
126#237—61no—
127#237—61no—
128#237C2×D311yescharacteristic, complemented
129D3×D4—21no—
130D3×D4C2×D311yescharacteristic, complemented
131#235—21no—
132#235—32no—
133#235—32no—
134#235—61no—
135#235—61no—
136#235C2×D311yescharacteristic
137C2×D12C2×D311yescharacteristic, complemented
138C2×C4×D3—21no—
139C2×C4×D3—61no—
140C2×C4×D3C2×D311yescharacteristic
141C2×Dic6—31no—
142C2×Dic6—31no—
143C2×Dic6—61no—
144C3×SD16—32no—
145C3×D8—32no—
146C3×M16—31no—
147#216—32no—
148#216—32no—
149#216—32no—
150#216—62no—
151#215—32no—
152#215C2×D312yescomplemented
153#214—32no—
154#214—32no—
155#214—32no—
156#214—32no—
157#214—62no—
158#213—32no—
159#213—32no—
160#213C2×D312yescomplemented
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×C32—21no—
172C22×C32C2×D411yescharacteristic
173C2×C3×D3—22no—
174C2×C3×D3—21no—
175C2×C3×D3—41no—
176C2×C3×D3—42no—
177C2×C3×D3—42no—
178C2×C3×D3C2×D411yescharacteristic
179C2×C3×D3C2×D411yescharacteristic
180C32×C4—21no—
181C32×C4C2×D411yescharacteristic
182C32×C4C2411yescharacteristic
183C3⋊Dic3—22no—
184C3×Dic3—21no—
185C3×Dic3C2×D411yescharacteristic
186C3×Dic3C2×D411yescharacteristic
187C2×#41—31no—
188C2×#41—91no—
189#137—91no—
190#137—92no—
191#137—91no—
192AGL(1,ℤ/8)—31no—
193AGL(1,ℤ/8)—92no—
194AGL(1,ℤ/8)—91no—
195#135—92no—
196#135—92no—
197C2×M16—91no—
198C23×C3—31no—
199C23×C3—61no—
200C23×C3—61no—
201C22×D3—21no—
202C22×D3—21no—
203C22×D3#6711yescharacteristic
204C3×Q8—21no—
205C3×Q8—31no—
206C3×Q8—61no—
207C3×Q8C22×D311yescharacteristic
208C3×Q8C22×D311yescharacteristic
209C3×D4—21no—
210C3×D4—21no—
211C3×D4—21no—
212C3×D4—31no—
213C3×D4—32no—
214C3×D4—41no—
215C3×D4—61no—
216C3×D4—61no—
217C3×D4—61no—
218C3×D4—61no—
219C3×D4—61no—
220C3×D4C22×D311yescharacteristic
221C3×D4C22×D311yescharacteristic
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—31no—
226C2×C3×C4—31no—
227C2×C3×C4—31no—
228C2×C3×C4—31no—
229C2×C3×C4—31no—
230C2×C3×C4—41no—
231C2×C3×C4—61no—
232C2×C3×C4—61no—
233C2×C3×C4—61no—
234C2×C3×C4—61no—
235C2×C3×C4C22×D311yescharacteristic
236C2×C3×C4C22×D311yescharacteristic
237#67—21no—
238#67—21no—
239#67—21no—
240#67—62no—
241#67—62no—
242#67—62no—
243#67—62no—
244C2×Dic3—21no—
245C2×Dic3—61no—
246C2×Dic3—61no—
247C2×Dic3—62no—
248C2×Dic3—62no—
249C2×Dic3—121no—
250C2×Dic3#6711yescharacteristic
251D12—21no—
252D12—21no—
253D12C22×D311yescharacteristic
254D12C22×D312yes—
255C4×D3—21no—
256C4×D3—21no—
257C4×D3—21no—
258C4×D3—62no—
259C4×D3—62no—
260C4×D3#6711yescharacteristic
261C4×D3#6711yescharacteristic
262C4×D3C22×D311yescharacteristic
263C4×D3C22×D311yescharacteristic
264Dic6—21no—
265Dic6—32no—
266Dic6—32no—
267Dic6—62no—
268Dic6—61no—
269Dic6—61no—
270Dic6—121no—
271Dic6C22×D311yescharacteristic
272C3×C8—32no—
273C3⋊C8—32no—
274C3⋊C8—32no—
275C3⋊C8—62no—
276C3⋊C8C22×D312yes—
277C2×C32—21no—
278C2×C32—41no—
279C2×C32C22×D411yescharacteristic
280C3×D3—21no—
281C3×D3—21no—
282C3×D3—42no—
283C3×D3—41no—
284#41—31no—
285#41—31no—
286#41—31no—
287#41—61no—
288#41—61no—
289#41—92no—
290#41—92no—
291#41—181no—
292#41—181no—
293#41D3211yescharacteristic
294C2×Q8—31no—
295C2×Q8—91no—
296C2×D4—31no—
297C2×D4—31no—
298C2×D4—61no—
299C2×D4—181no—
300C22×C4—31no—
301C22×C4—61no—
302C22×C4—181no—
303Q16—92no—
304Q16—92no—
305SD16—32no—
306SD16—92no—
307SD16—92no—
308SD16—92no—
309D8—32no—
310D8—92no—
311M16—31no—
312M16—92no—
313M16—91no—
314C2×C8—92no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—31no—
319C22×C3—31no—
320C22×C3—41no—
321C22×C3—61no—
322C22×C3—62no—
323C22×C3—121no—
324C22×C3—122no—
325C22×C3—122no—
326C22×C3D3×D411yescharacteristic
327C22×C3C2×#6711yescharacteristic
328C2×D3—22no—
329C2×D3—21no—
330C2×D3—41no—
331C2×D3—42no—
332C2×D3—42no—
333C2×D3C2×#6711yescharacteristic
334C2×D3C2×#6711yescharacteristic
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—31no—
340C3×C4—31no—
341C3×C4—41no—
342C3×C4—61no—
343C3×C4D3×D411yescharacteristic
344C3×C4C2×#6711yescharacteristic
345C3×C4C23×D311yescharacteristic
346C3×C4C23×D311yescharacteristic
347Dic3—21no—
348Dic3—62no—
349Dic3—62no—
350Dic3—122no—
351Dic3C2×#6711yescharacteristic
352Dic3C2×#6711yescharacteristic
353C32#57511yescharacteristic, complemented, Sylow
354C23—31no—
355C23—61no—
356C23—61no—
357Q8—31no—
358Q8—61no—
359Q8—92no—
360Q8—181no—
361Q8C2×D3211yescharacteristic
362D4—21no—
363D4—32no—
364D4—31no—
365D4—61no—
366D4—61no—
367D4—61no—
368D4—61no—
369D4—61no—
370D4—182no—
371D4—182no—
372D4C2×D3211yescharacteristic
373C2×C4—21no—
374C2×C4—31no—
375C2×C4—31no—
376C2×C4—31no—
377C2×C4—31no—
378C2×C4—31no—
379C2×C4—61no—
380C2×C4—61no—
381C2×C4—61no—
382C2×C4—61no—
383C2×C4—182no—
384C2×C4—182no—
385C2×C4—181no—
386C2×C4C2×D3211yescharacteristic
387C8—32no—
388C8—92no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—41no—
393C2×C3—41no—
394C2×C3—41no—
395C2×C3—61no—
396C2×C3—61no—
397C2×C3—81no—
398C2×C3—121no—
399C2×C3—122no—
400C2×C3C2×D3×D411yescharacteristic
401C2×C3C22×#6711yescharacteristic
402D3—21no—
403D3—21no—
404D3—42no—
405D3—41no—
406C22—21no—
407C22—31no—
408C22—31no—
409C22—61no—
410C22—62no—
411C22—121no—
412C22—122no—
413C22—122no—
414C22D3×#6711yescharacteristic
415C4—21no—
416C4—31no—
417C4—31no—
418C4—61no—
419C4—182no—
420C4D3×#6711yescharacteristic
421C4C22×D3211yescharacteristic
422C3—21no—
423C3#577311yescharacteristic, complemented
424C3#582211yescharacteristic, complemented
425C2—21no—
426C2—41no—
427C2—61no—
428C2—61no—
429C2—121no—
430C2—122no—
431C2C2×D3×#6711yescharacteristic
subgroupG/H
centerC2C2×D3×#67
commutator, cosocleC32×C4C24
FrattiniC4C22×D32
FittingC32×#41C22
socleC2×C32C22×D4
hypercenter#41D32
hypocenterC32#575
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C3×D3×#41C2semidirect
2. C2×#3795C2semidirect
3. #64160C2semidirect
4. C3×#949C2semidirect
5. #63947C2semidirect
6. #63946C2semidirect
7. #63933C2semidirect
8. #63932C2semidirect
9. #63831C2semidirect
10. #63823C2semidirect
11. D3×#208C2semidirect
15. C2×#634C22semidirect
16. C3×#239C22semidirect
17. C3×D3×Q8C22semidirect
19. C3×#237C22semidirect
21. C3×D3×D4C22semidirect
24. C2×C3×D12C22semidirect
32. #3795C22semidirect
33. #3756C22semidirect
34. #3754C22semidirect
35. #3748C22semidirect
36. C3×#215C22semidirect
37. C3×#213C22semidirect
38. C3×#208C22semidirect
39. #3719C22semidirect
40. #3716C22semidirect
41. #3715C22semidirect
42. #3713C22semidirect
43. #3711C22semidirect
44. D3×C3⋊C8C22semidirect
46. D3×#41D3semidirect
57. #949D3semidirect
121. #239C2×D3semidirect
122. D3×Q8C2×D3semidirect
128. #237C2×D3semidirect
130. D3×D4C2×D3semidirect
137. C2×D12C2×D3semidirect
152. #215C2×D3semidirect
160. #213C2×D3semidirect
165. #208C2×D3semidirect
353. C32#575semidirect
423. C3#5773semidirect
424. C3#5822semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#412
C2×#37952
#641602
C3×#9492
#639472
#639462
#639332
#639322
#638312
#638232
D3×#2082
#58223
#57733