Finite Group Databasebeta

← #86295

Subgroups — #86295

Order 384.

1160 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#534C211yesmaximal, characteristic, complemented
2#5804C212yesmaximal, complemented
3C2×D4×Dic3C212yesmaximal, complemented
4#5665C214yesmaximal, complemented
5#5649C214yesmaximal, complemented
6#5617C212yesmaximal, complemented
7#5606C212yesmaximal, complemented
8#5602C212yesmaximal, complemented
9#5600C212yesmaximal, complemented
10#5593C214yesmaximal, complemented
11#5586C214yesmaximal, complemented
12C2×#67⋊C4C211yesmaximal, characteristic, complemented
13#5483C211yesmaximal, characteristic, complemented
14#3459—31nomaximal, Sylow
15C22×C3×D4C2212yes—
16C22×#67C2211yescharacteristic
17C23×Dic3C2211yescharacteristic
18C23×Dic3C2212yescomplemented
19C2×#237C2212yescomplemented
20C22×C4×D3C2211yescharacteristic, complemented
21C3×#123C2214yescomplemented
22C3×#121C2212yes—
23C3×#121C2212yes—
24C3×#120C2214yescomplemented
25C2×C3×C22⋊C4C2211yescharacteristic
26#953C2214yescomplemented
27C2×#217C2212yes—
28C2×#217C2212yescomplemented
29#939C2214yes—
30#939C2214yes—
31#939C2214yescomplemented
32#938C2212yescomplemented
33#937C2214yescomplemented
34#936C2212yescomplemented
35#935C2214yescomplemented
36#935C2214yescomplemented
37D4×Dic3C2214yescomplemented
38D4×Dic3C2214yescomplemented
39D4×Dic3C2214yescomplemented
40D4×Dic3C2214yescomplemented
41D4×Dic3C2212yescomplemented
42#929C2214yescomplemented
43C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C2×C4⋊Dic3C2212yescomplemented
45#924C2212yescomplemented
46#924C2212yescomplemented
47C2×Dic3⋊C4C2211yescharacteristic, complemented
48C2×C4×Dic3C2212yescomplemented
49C2×C4×Dic3C2211yescharacteristic, complemented
50#898C2214yescomplemented
51#897C2212yescomplemented
52#892C2212yescomplemented
53#890C2212yescomplemented
54#889C2214yescomplemented
55#887C2212yescomplemented
56#886C2214yescomplemented
57#885C2214yescomplemented
58#883C2214yescomplemented
59#67⋊C4C2214yescomplemented
60#67⋊C4C2214yescomplemented
61#67⋊C4C2214yescomplemented
62#879C2214yescomplemented
63#879C2214yescomplemented
64#878C2214yescomplemented
65#878C2214yescomplemented
66#878C2214yescomplemented
67#877C2214yescomplemented
68#543—31no—
69#539—34no—
70#539—32no—
71#538—32no—
72#538—34no—
73#534—32no—
74#534D311yescharacteristic, complemented
75#529—34no—
76#529—32no—
77#525—32no—
78#525—34no—
79C2×C4×D4—32no—
80C2×C4×D4—31no—
81C24×C3C2312yes—
82C24×C3C2311yescharacteristic
83C23×D3C2311yescharacteristic
84C2×C3×D4—28no—
85C2×C3×D4C2314yes—
86C2×C3×D4C2314yes—
87C2×C3×D4C2312yes—
88C2×C3×D4C2312yes—
89C22×C3×C4C2312yes—
90C22×C3×C4C2311yescharacteristic
91C22×C3×C4C2311yescharacteristic
92C2×#67—24no—
93C2×#67C2314yes—
94C2×#67C2314yes—
95C2×#67C2314yes—
96C22×Dic3—42no—
97C22×Dic3—44no—
98C22×Dic3C2314yes—
99C22×Dic3C2312yes—
100C22×Dic3C2311yescharacteristic
101C22×Dic3C2311yescharacteristic
102C22×Dic3C2312yes—
103C22×Dic3C2312yes—
104C22×Dic3C2314yes—
105C22×Dic3C2312yes—
106C22×Dic3C2311yescharacteristic
107#237—44no—
108C2×C4×D3—42no—
109C2×C4×D3C2312yes—
110C2×C4×D3C2312yes—
111C2×Dic6C2312yes—
112C2×Dic6C2312yes—
113C3×C4⋊C4C2312yes—
114C3×C4⋊C4C2312yes—
115C3×C22⋊C4C2314yes—
116C3×C22⋊C4C2314yes—
117C3×C22⋊C4C2314yes—
118#217C2314yes—
119#217C2314yes—
120#217C2314yes—
121#217C2314yes—
122#217C2314yes—
123#217C2314yes—
124(C2×D3)⋊C4C2314yes—
125(C2×D3)⋊C4C2314yes—
126(C2×D3)⋊C4C2314yes—
127C4⋊Dic3C2312yes—
128C4⋊Dic3C2312yes—
129C4⋊Dic3C2314yes—
130C4⋊Dic3C2314yes—
131Dic3⋊C4C2314yes—
132Dic3⋊C4C2314yes—
133Dic3⋊C4C2314yes—
134Dic3⋊C4C2314yes—
135Dic3⋊C4C2314yes—
136C4×Dic3C2312yes—
137C4×Dic3C2314yes—
138C4×Dic3C2312yes—
139C4×Dic3C2314yes—
140C2×#41—32no—
141C22×D4—31no—
142C22×D4C2×D312yes—
143C23×C4—31no—
144C23×C4—32no—
145C23×C4—31no—
146#126—34no—
147#126—34no—
148#126—34no—
149#125—34no—
150#125—32no—
151#124—32no—
152#124—34no—
153#123—34no—
154#123—34no—
155#123—34no—
156#123—34no—
157#123—34no—
158#123C2×D314yescomplemented
159C22⋊Q8—32no—
160C22⋊Q8—32no—
161C22⋊Q8—32no—
162C22⋊Q8—34no—
163C22⋊Q8—34no—
164C22⋊Q8—34no—
165#121—34no—
166#121—32no—
167#121—34no—
168#121—34no—
169#121C2×D312yes—
170#121C2×D312yes—
171#120—34no—
172#120—34no—
173#120C2×D314yescomplemented
174C4×Q8—32no—
175C4×D4—34no—
176C4×D4—34no—
177C4×D4—34no—
178C4×D4—34no—
179C4×D4—32no—
180C4×D4—34no—
181C4×D4—34no—
182C4×D4—34no—
183#117—32no—
184#117—34no—
185C2×C4⋊C4—31no—
186C2×C4⋊C4—32no—
187C2×C22⋊C4—32no—
188C2×C22⋊C4—32no—
189C2×C22⋊C4—31no—
190C2×C22⋊C4C2×D311yescharacteristic
191C2×C42—31no—
192C2×C42—32no—
193C23×C3—24no—
194C23×C3—41no—
195C23×C3—42no—
196C23×C3—41no—
197C23×C3—42no—
198C23×C3#4114yescomplemented
199C23×C3C2414yes—
200C23×C3C2411yescharacteristic
201C23×C3C2412yes—
202C22×D3—22no—
203C22×D3—41no—
204C22×D3—41no—
205C22×D3C2412yes—
206C3×D4—28no—
207C3×D4—28no—
208C3×D4—42no—
209C3×D4—42no—
210C2×C3×C4—24no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4C2414yes—
214C2×C3×C4C2412yes—
215C2×C3×C4C2412yes—
216#67—28no—
217#67—44no—
218#67—44no—
219C2×Dic3—22no—
220C2×Dic3—22no—
221C2×Dic3—28no—
222C2×Dic3—24no—
223C2×Dic3—42no—
224C2×Dic3—44no—
225C2×Dic3—42no—
226C2×Dic3—41no—
227C2×Dic3—42no—
228C2×Dic3C2412yes—
229C2×Dic3C2414yes—
230C2×Dic3C2412yes—
231C2×Dic3C2411yescharacteristic
232C2×Dic3C2414yes—
233C2×Dic3C2411yescharacteristic
234C4×D3—24no—
235C4×D3—42no—
236Dic6—42no—
237Dic6—42no—
238C24—31no—
239C24C22×D312yes—
240C24C22×D311yescharacteristic
241#41—124no—
242C2×Q8—32no—
243C2×Q8—32no—
244C2×D4—28no—
245C2×D4—34no—
246C2×D4—34no—
247C2×D4—34no—
248C2×D4—64no—
249C2×D4C22×D314yes—
250C2×D4C22×D314yes—
251C2×D4C22×D312yes—
252C2×D4C22×D312yes—
253C22×C4—31no—
254C22×C4—31no—
255C22×C4—32no—
256C22×C4—34no—
257C22×C4—32no—
258C22×C4—31no—
259C22×C4—32no—
260C22×C4—32no—
261C22×C4—34no—
262C22×C4—32no—
263C22×C4—32no—
264C22×C4—122no—
265C22×C4—122no—
266C22×C4—124no—
267C22×C4C22×D312yes—
268C22×C4C22×D311yescharacteristic
269C22×C4C22×D311yescharacteristic
270C4⋊C4—34no—
271C4⋊C4—34no—
272C4⋊C4—34no—
273C4⋊C4—34no—
274C4⋊C4—32no—
275C4⋊C4—34no—
276C4⋊C4—34no—
277C4⋊C4—32no—
278C4⋊C4—34no—
279C4⋊C4C22×D312yes—
280C4⋊C4C22×D312yes—
281C22⋊C4—34no—
282C22⋊C4—34no—
283C22⋊C4—34no—
284C22⋊C4—34no—
285C22⋊C4—34no—
286C22⋊C4—34no—
287C22⋊C4—34no—
288C22⋊C4—34no—
289C22⋊C4—34no—
290C22⋊C4C22×D314yes—
291C22⋊C4C22×D314yes—
292C22⋊C4C22×D314yes—
293C42—34no—
294C42—32no—
295C42—34no—
296C42—32no—
297C22×C3—22no—
298C22×C3—21no—
299C22×C3—22no—
300C22×C3—21no—
301C22×C3—24no—
302C22×C3—24no—
303C22×C3—24no—
304C22×C3—44no—
305C22×C3—48no—
306C22×C3C2×#4112yes—
307C22×C3C2×#4114yes—
308C22×C3C2511yescharacteristic
309C2×D3—22no—
310C2×D3—22no—
311C2×D3—22no—
312C2×D3—44no—
313C3×C4—24no—
314C3×C4—22no—
315C3×C4—22no—
316Dic3—22no—
317Dic3—24no—
318Dic3—21no—
319Dic3—22no—
320Dic3—24no—
321Dic3H(5,𝔽2)12yes—
322C23—24no—
323C23—32no—
324C23—41no—
325C23—42no—
326C23—41no—
327C23—42no—
328C23—62no—
329C23—121no—
330C23—121no—
331C23#23714yescomplemented
332C23C23×D314yes—
333C23C23×D311yescharacteristic
334C23C23×D312yes—
335Q8—122no—
336Q8—122no—
337D4—28no—
338D4—28no—
339D4—42no—
340D4—42no—
341D4—68no—
342D4—124no—
343D4—124no—
344C2×C4—24no—
345C2×C4—31no—
346C2×C4—34no—
347C2×C4—32no—
348C2×C4—31no—
349C2×C4—32no—
350C2×C4—34no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—64no—
354C2×C4—62no—
355C2×C4—64no—
356C2×C4—68no—
357C2×C4—62no—
358C2×C4—122no—
359C2×C4—121no—
360C2×C4—122no—
361C2×C4—124no—
362C2×C4—122no—
363C2×C4—122no—
364C2×C4C23×D312yes—
365C2×C4C23×D314yes—
366C2×C4C23×D312yes—
367C2×C3—22no—
368C2×C3—24no—
369C2×C3—44no—
370C2×C3C22×#4111yescharacteristic
371C2×C3C2×H(5,𝔽2)11yescharacteristic
372C2×C3#58511yescharacteristic
373D3—42no—
374C22—21no—
375C22—22no—
376C22—21no—
377C22—22no—
378C22—24no—
379C22—24no—
380C22—24no—
381C22—44no—
382C22—48no—
383C22—62no—
384C22—62no—
385C22—62no—
386C22—124no—
387C22C2×#23714yes—
388C22C2×#23712yes—
389C22C24×D311yescharacteristic
390C4—24no—
391C4—22no—
392C4—22no—
393C4—32no—
394C4—62no—
395C4—61no—
396C4—62no—
397C4—64no—
398C4—64no—
399C3#345911yescharacteristic, complemented, Sylow
400C2—24no—
401C2—22no—
402C2—44no—
403C2—122no—
404C2C22×#23711yescharacteristic
405C2D3×H(5,𝔽2)11yescharacteristic
406C2#596611yescharacteristic
subgroupG/H
center, FrattiniC22C24×D3
commutator, socle, cosocleC22×C3C25
FittingC3×#534C2
hypercenter#534D3
hypocenterC3#3459
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #534

Complements

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

NH ≅ G/Ntype
1. C3×#534C2semidirect
2. #5804C2semidirect
3. C2×D4×Dic3C2semidirect
4. #5665C2semidirect
5. #5649C2semidirect
6. #5617C2semidirect
7. #5606C2semidirect
8. #5602C2semidirect
9. #5600C2semidirect
10. #5593C2semidirect
11. #5586C2semidirect
12. C2×#67⋊C4C2semidirect
13. #5483C2semidirect
18. C23×Dic3C22semidirect
19. C2×#237C22semidirect
20. C22×C4×D3C22semidirect
21. C3×#123C22semidirect
24. C3×#120C22semidirect
26. #953C22semidirect
28. C2×#217C22semidirect
31. #939C22semidirect
32. #938C22semidirect
33. #937C22semidirect
34. #936C22semidirect
35. #935C22semidirect
36. #935C22semidirect
37. D4×Dic3C22semidirect
38. D4×Dic3C22semidirect
39. D4×Dic3C22semidirect
40. D4×Dic3C22semidirect
41. D4×Dic3C22semidirect
42. #929C22semidirect
43. C2×(C2×D3)⋊C4C22semidirect
44. C2×C4⋊Dic3C22semidirect
45. #924C22semidirect
46. #924C22semidirect
47. C2×Dic3⋊C4C22semidirect
48. C2×C4×Dic3C22semidirect
49. C2×C4×Dic3C22semidirect
50. #898C22semidirect
51. #897C22semidirect
52. #892C22semidirect
53. #890C22semidirect
54. #889C22semidirect
55. #887C22semidirect
56. #886C22semidirect
57. #885C22semidirect
58. #883C22semidirect
59. #67⋊C4C22semidirect
60. #67⋊C4C22semidirect
61. #67⋊C4C22semidirect
62. #879C22semidirect
63. #879C22semidirect
64. #878C22semidirect
65. #878C22semidirect
66. #878C22semidirect
67. #877C22semidirect
74. #534D3semidirect
158. #123C2×D3semidirect
173. #120C2×D3semidirect
198. C23×C3#41semidirect
331. C23#237semidirect
399. C3#3459semidirect

Maximal subgroups

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

subgroupindex
C3×#5342
#58042
C2×D4×Dic32
#56652
#56492
#56172
#56062
#56022
#56002
#55932
#55862
C2×#67⋊C42
#54832
#34593