Finite Group Databasebeta

← #86314

Subgroups — #86314

Order 384.

1140 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#535C211yesmaximal, characteristic, complemented
2#5833C211yesmaximal, characteristic, complemented
3Dic3×#41C211yesmaximal, characteristic, complemented
4#5805C211yesmaximal, characteristic, complemented
5C2×D4×Dic3C211yesmaximal, characteristic, complemented
6#5719C212yesmaximal, complemented
7#5716C212yesmaximal, complemented
8#5682C212yesmaximal, complemented
9#5680C212yesmaximal, complemented
10#5619C212yesmaximal, complemented
11#5603C212yesmaximal, complemented
12#5600C212yesmaximal, complemented
13#5596C212yesmaximal, complemented
14#5593C214yesmaximal, complemented
15#5586C214yesmaximal, complemented
16#5522C211yesmaximal, characteristic, complemented
17#5519C211yesmaximal, characteristic, complemented
18#3460—31nomaximal, Sylow
19C2×C3×#41C2211yescharacteristic
20C22×C3×D4C2211yescharacteristic
21C23×Dic3C2212yes—
22C2×#237C2214yescomplemented
23C2×#235C2211yescharacteristic
24C3×#127C2212yes—
25C3×#124C2212yes—
26C3×#121C2212yes—
27C3×#121C2212yes—
28C3×#120C2214yes—
29C3×#117C2211yescharacteristic
30#953C2214yes—
31C2×#217C2212yes—
32#946C2212yescomplemented
33Q8×Dic3C2211yescharacteristic, complemented
34Q8×Dic3C2211yescharacteristic, complemented
35#940C2212yes—
36#939C2214yes—
37#939C2214yescomplemented
38#939C2214yescomplemented
39#938C2212yes—
40#938C2212yes—
41#938C2212yescomplemented
42#938C2214yescomplemented
43#936C2212yes—
44#936C2214yescomplemented
45#935C2214yescomplemented
46#935C2214yescomplemented
47D4×Dic3C2212yes—
48D4×Dic3C2212yes—
49D4×Dic3C2212yes—
50D4×Dic3C2212yes—
51D4×Dic3C2212yes—
52D4×Dic3C2212yes—
53D4×Dic3C2211yescharacteristic, complemented
54D4×Dic3C2214yescomplemented
55D4×Dic3C2211yescharacteristic, complemented
56#930C2212yescomplemented
57#926C2211yescharacteristic
58#926C2212yescomplemented
59C2×C4⋊Dic3C2211yescharacteristic
60#924C2212yescomplemented
61C2×C4×Dic3C2211yescharacteristic
62C2×C4×Dic3C2212yescomplemented
63#893C2211yescharacteristic, complemented
64#893C2211yescharacteristic, complemented
65#890C2212yescomplemented
66#888C2212yescomplemented
67#887C2211yescharacteristic, complemented
68#887C2211yescharacteristic, complemented
69#886C2214yescomplemented
70#885C2214yescomplemented
71#883C2214yescomplemented
72#67⋊C4C2212yes—
73#67⋊C4C2212yes—
74#67⋊C4C2214yescomplemented
75#879C2214yescomplemented
76#879C2214yescomplemented
77#878C2214yes—
78#878C2214yescomplemented
79#877C2214yescomplemented
80#872C2212yescomplemented
81C42×D3C2212yescomplemented
82#870C2212yescomplemented
83#869C2212yescomplemented
84#544—31no—
85#542—32no—
86#542—32no—
87#540—32no—
88#540—32no—
89#538—34no—
90#537—31no—
91#535—31no—
92#535D311yescharacteristic, complemented
93#532—32no—
94#532—32no—
95#529—32no—
96#529—32no—
97#525—34no—
98C4×#41—31no—
99C4×#41—31no—
100C2×C4×D4—31no—
101C24×C3C2312yes—
102C3×#41—24no—
103C2×C3×Q8C2311yescharacteristic
104C2×C3×D4—24no—
105C2×C3×D4C2312yes—
106C2×C3×D4C2312yes—
107C2×C3×D4C2312yes—
108C2×C3×D4C2311yescharacteristic
109C2×C3×D4C2314yes—
110C2×C3×D4C2314yes—
111C22×C3×C4C2312yes—
112C22×C3×C4C2311yescharacteristic
113C2×#67C2312yes—
114C2×#67C2314yes—
115C2×#67C2314yes—
116C2×#67C2314yes—
117C22×Dic3—44no—
118C22×Dic3C2314yes—
119C22×Dic3C2311yescharacteristic
120C22×Dic3C2312yes—
121C22×Dic3C2312yes—
122C22×Dic3C2314yes—
123C22×Dic3C2311yescharacteristic
124C22×Dic3C2312yes—
125#237—48no—
126#235—24no—
127C2×D12C2311yescharacteristic
128C2×C4×D3C2312yes—
129C2×C4×D3C2312yes—
130C2×C4×D3C2312yes—
131C2×Dic6C2311yescharacteristic
132C2×Dic6C2314yes—
133C3×C4⋊C4C2311yescharacteristic
134C3×C4⋊C4C2311yescharacteristic
135C3×C22⋊C4C2314yes—
136C3×C22⋊C4C2312yes—
137C3×C22⋊C4C2314yes—
138C3×C42C2312yes—
139#217C2314yes—
140#217C2312yes—
141#217C2314yes—
142#217C2314yes—
143#217C2314yes—
144#217C2314yes—
145#217C2312yes—
146#217C2312yes—
147(C2×D3)⋊C4C2312yes—
148(C2×D3)⋊C4C2312yes—
149(C2×D3)⋊C4C2314yes—
150C4⋊Dic3C2311yescharacteristic
151C4⋊Dic3C2312yes—
152C4⋊Dic3C2314yes—
153C4⋊Dic3C2311yescharacteristic
154C4⋊Dic3C2312yes—
155C4⋊Dic3C2312yes—
156C4⋊Dic3C2312yes—
157Dic3⋊C4C2314yes—
158Dic3⋊C4C2314yes—
159Dic3⋊C4C2312yes—
160Dic3⋊C4C2312yes—
161Dic3⋊C4C2314yes—
162C4×Dic3C2311yescharacteristic
163C4×Dic3C2312yes—
164C4×Dic3C2312yes—
165C4×Dic3C2311yescharacteristic
166C4×Dic3C2312yes—
167C4×Dic3C2312yes—
168C4×Dic3C2311yescharacteristic
169C4×Dic3C2311yescharacteristic
170C4×Dic3C2312yes—
171C2×#41—34no—
172C2×#41—31no—
173C2×#41C2×D311yescharacteristic
174C22×D4C2×D311yescharacteristic
175C23×C4—32no—
176C4⋊Q8—32no—
177C4⋊Q8—32no—
178#127—32no—
179#127C2×D312yes—
180#126—34no—
181#126—34no—
182#125—32no—
183#125—32no—
184#124—32no—
185#124—34no—
186#124—34no—
187#124C2×D312yes—
188#123—34no—
189#123—34no—
190#123—34no—
191#123—34no—
192C22⋊Q8—32no—
193C22⋊Q8—32no—
194C22⋊Q8—34no—
195C22⋊Q8—34no—
196#121—34no—
197#121—34no—
198#121—32no—
199#121—32no—
200#121—32no—
201#121—34no—
202#121—34no—
203#121—32no—
204#121C2×D312yes—
205#121C2×D312yes—
206#120—34no—
207#120C2×D314yes—
208C4×Q8—31no—
209C4×Q8—31no—
210C4×Q8—31no—
211C4×Q8—31no—
212C4×D4—32no—
213C4×D4—32no—
214C4×D4—32no—
215C4×D4—32no—
216C4×D4—32no—
217C4×D4—31no—
218C4×D4—32no—
219C4×D4—31no—
220C4×D4—34no—
221C4×D4—31no—
222C4×D4—31no—
223C4×D4—32no—
224C4×D4—32no—
225C4×D4—34no—
226#117—31no—
227#117—32no—
228#117—34no—
229#117—32no—
230#117C2×D311yescharacteristic
231C2×C4⋊C4—31no—
232C2×C22⋊C4—32no—
233C2×C42—31no—
234C2×C42—32no—
235C2×C42—32no—
236C23×C3—24no—
237C23×C3—42no—
238C23×C3—42no—
239C23×C3C2414yes—
240C23×C3C2412yes—
241C23×C3C2411yescharacteristic
242C22×D3C2412yes—
243C3×Q8—22no—
244C3×D4—24no—
245C3×D4—24no—
246C3×D4—24no—
247C3×D4—22no—
248C3×D4—44no—
249C3×D4—44no—
250C2×C3×C4—24no—
251C2×C3×C4#4114yescomplemented
252C2×C3×C4C2412yes—
253C2×C3×C4C2412yes—
254C2×C3×C4C2412yes—
255C2×C3×C4C2411yescharacteristic
256C2×C3×C4C2411yescharacteristic
257#67—24no—
258#67—44no—
259#67—44no—
260#67—44no—
261C2×Dic3—24no—
262C2×Dic3—28no—
263C2×Dic3—22no—
264C2×Dic3—42no—
265C2×Dic3—44no—
266C2×Dic3—41no—
267C2×Dic3—42no—
268C2×Dic3C2411yescharacteristic
269C2×Dic3C2411yescharacteristic
270C2×Dic3C2412yes—
271C2×Dic3C2412yes—
272C2×Dic3C2411yescharacteristic
273C2×Dic3C2412yes—
274C2×Dic3C2414yes—
275C2×Dic3C2411yescharacteristic
276D12—22no—
277C4×D3—24no—
278C4×D3—24no—
279C4×D3—42no—
280Dic6—22no—
281Dic6—44no—
282C24C22×D312yes—
283#41—24no—
284#41—64no—
285#41—128no—
286C2×Q8—31no—
287C2×Q8—34no—
288C2×Q8C22×D311yescharacteristic
289C2×D4—24no—
290C2×D4—32no—
291C2×D4—34no—
292C2×D4—34no—
293C2×D4—34no—
294C2×D4—31no—
295C2×D4C22×D312yes—
296C2×D4C22×D312yes—
297C2×D4C22×D311yescharacteristic
298C2×D4C22×D312yes—
299C2×D4C22×D314yes—
300C2×D4C22×D314yes—
301C22×C4—31no—
302C22×C4—32no—
303C22×C4—34no—
304C22×C4—31no—
305C22×C4—32no—
306C22×C4—32no—
307C22×C4—34no—
308C22×C4—32no—
309C22×C4—32no—
310C22×C4—32no—
311C22×C4—124no—
312C22×C4C22×D312yes—
313C22×C4C22×D311yescharacteristic
314C4⋊C4—32no—
315C4⋊C4—32no—
316C4⋊C4—31no—
317C4⋊C4—31no—
318C4⋊C4—32no—
319C4⋊C4—32no—
320C4⋊C4—32no—
321C4⋊C4—32no—
322C4⋊C4—34no—
323C4⋊C4—34no—
324C4⋊C4—34no—
325C4⋊C4—34no—
326C4⋊C4C22×D311yescharacteristic
327C4⋊C4C22×D311yescharacteristic
328C22⋊C4—34no—
329C22⋊C4—34no—
330C22⋊C4—32no—
331C22⋊C4—32no—
332C22⋊C4—32no—
333C22⋊C4—34no—
334C22⋊C4—34no—
335C22⋊C4—34no—
336C22⋊C4—32no—
337C22⋊C4—32no—
338C22⋊C4—34no—
339C22⋊C4C22×D314yes—
340C22⋊C4C22×D312yes—
341C22⋊C4C22×D314yes—
342C42—31no—
343C42—31no—
344C42—32no—
345C42—32no—
346C42—31no—
347C42—31no—
348C42—32no—
349C42—32no—
350C42—32no—
351C42C22×D312yes—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—22no—
355C22×C3—24no—
356C22×C3—24no—
357C22×C3—22no—
358C22×C3—22no—
359C22×C3—24no—
360C22×C3—48no—
361C22×C3C2×#4112yes—
362C22×C3C2511yescharacteristic
363C2×D3—22no—
364C2×D3—22no—
365C2×D3—22no—
366C3×C4—22no—
367C3×C4—22no—
368C3×C4—22no—
369C3×C4C2×#4112yes—
370C3×C4C2×#4112yes—
371Dic3—22no—
372Dic3—22no—
373Dic3—24no—
374Dic3—21no—
375Dic3—21no—
376Dic3—21no—
377Dic3—22no—
378Dic3H(5,𝔽2)12yes—
379C23—24no—
380C23—32no—
381C23—42no—
382C23—42no—
383C23C23×D314yes—
384C23C23×D312yes—
385C23C23×D311yescharacteristic
386Q8—22no—
387Q8—62no—
388Q8—124no—
389D4—24no—
390D4—24no—
391D4—24no—
392D4—22no—
393D4—44no—
394D4—44no—
395D4—64no—
396D4—62no—
397D4—124no—
398D4—124no—
399D4—124no—
400C2×C4—24no—
401C2×C4—31no—
402C2×C4—31no—
403C2×C4—31no—
404C2×C4—32no—
405C2×C4—32no—
406C2×C4—31no—
407C2×C4—32no—
408C2×C4—34no—
409C2×C4—64no—
410C2×C4—62no—
411C2×C4—68no—
412C2×C4—64no—
413C2×C4—64no—
414C2×C4—122no—
415C2×C4—124no—
416C2×C4—122no—
417C2×C4—121no—
418C2×C4—122no—
419C2×C4#23714yescomplemented
420C2×C4C23×D312yes—
421C2×C4C23×D312yes—
422C2×C4C23×D312yes—
423C2×C4C23×D311yescharacteristic
424C2×C4C23×D311yescharacteristic
425C2×C3—22no—
426C2×C3—42no—
427C2×C3—44no—
428C2×C3C22×#4111yescharacteristic
429C2×C3C2×H(5,𝔽2)11yescharacteristic
430C2×C3#58511yescharacteristic
431D3—42no—
432C22—21no—
433C22—21no—
434C22—22no—
435C22—24no—
436C22—24no—
437C22—22no—
438C22—22no—
439C22—24no—
440C22—48no—
441C22—62no—
442C22—62no—
443C22—62no—
444C22C2×#23712yes—
445C22C24×D311yescharacteristic
446C4—22no—
447C4—22no—
448C4—22no—
449C4—32no—
450C4—62no—
451C4—61no—
452C4—64no—
453C4—62no—
454C4—61no—
455C4—61no—
456C4—62no—
457C4C2×#23712yes—
458C4C2×#23712yes—
459C3#346011yescharacteristic, complemented, Sylow
460C2—22no—
461C2—44no—
462C2—42no—
463C2—122no—
464C2C22×#23711yescharacteristic
465C2D3×H(5,𝔽2)11yescharacteristic
466C2#596611yescharacteristic
subgroupG/H
center, FrattiniC22C24×D3
commutator, socle, cosocleC22×C3C25
FittingC3×#535C2
hypercenter#535D3
hypocenterC3#3460
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C3×#535C2semidirect
2. #5833C2semidirect
3. Dic3×#41C2semidirect
4. #5805C2semidirect
5. C2×D4×Dic3C2semidirect
6. #5719C2semidirect
7. #5716C2semidirect
8. #5682C2semidirect
9. #5680C2semidirect
10. #5619C2semidirect
11. #5603C2semidirect
12. #5600C2semidirect
13. #5596C2semidirect
14. #5593C2semidirect
15. #5586C2semidirect
16. #5522C2semidirect
17. #5519C2semidirect
22. C2×#237C22semidirect
32. #946C22semidirect
33. Q8×Dic3C22semidirect
34. Q8×Dic3C22semidirect
37. #939C22semidirect
38. #939C22semidirect
41. #938C22semidirect
42. #938C22semidirect
44. #936C22semidirect
45. #935C22semidirect
46. #935C22semidirect
53. D4×Dic3C22semidirect
54. D4×Dic3C22semidirect
55. D4×Dic3C22semidirect
56. #930C22semidirect
58. #926C22semidirect
60. #924C22semidirect
62. C2×C4×Dic3C22semidirect
63. #893C22semidirect
64. #893C22semidirect
65. #890C22semidirect
66. #888C22semidirect
67. #887C22semidirect
68. #887C22semidirect
69. #886C22semidirect
70. #885C22semidirect
71. #883C22semidirect
74. #67⋊C4C22semidirect
75. #879C22semidirect
76. #879C22semidirect
78. #878C22semidirect
79. #877C22semidirect
80. #872C22semidirect
81. C42×D3C22semidirect
82. #870C22semidirect
83. #869C22semidirect
92. #535D3semidirect
251. C2×C3×C4#41semidirect
419. C2×C4#237semidirect
459. C3#3460semidirect

Maximal subgroups

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

subgroupindex
C3×#5352
#58332
Dic3×#412
#58052
C2×D4×Dic32
#57192
#57162
#56822
#56802
#56192
#56032
#56002
#55962
#55932
#55862
#55222
#55192
#34603