Finite Group Databasebeta

← #86357

Subgroups — #86357

Order 384.

1022 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#536C211yesmaximal, characteristic, complemented
2#5828C211yesmaximal, characteristic
3#5827C211yesmaximal, characteristic, complemented
4C2×#946C211yesmaximal, characteristic, complemented
5#5812C211yesmaximal, characteristic, complemented
6#5731C212yesmaximal, complemented
7#5728C212yesmaximal, complemented
8#5682C212yesmaximal, complemented
9#5680C212yesmaximal, complemented
10#5658C214yesmaximal, complemented
11#5650C214yesmaximal, complemented
12#5642C212yesmaximal, complemented
13#5641C212yesmaximal, complemented
14#5639C212yesmaximal, complemented
15#5635C212yesmaximal, complemented
16D3×#117C211yesmaximal, characteristic, complemented
17#5519C211yesmaximal, characteristic, complemented
18#3495—31nomaximal, Sylow
19C2×C3×#41C2211yescharacteristic
20C22×C3×Q8C2211yescharacteristic
21C22×C4×D3C2211yescharacteristic
22C3×C4⋊Q8C2212yescomplemented
23C3×#124C2212yescomplemented
24C3×#123C2214yes—
25C3×C22⋊Q8C2212yescomplemented
26C3×C22⋊Q8C2212yescomplemented
27C3×#117C2211yescharacteristic
28#946C2212yes—
29#946C2212yes—
30#946C2212yes—
31#946C2212yes—
32#946C2211yescharacteristic
33#946C2211yescharacteristic
34Q8×Dic3C2212yescomplemented
35Q8×Dic3C2212yescomplemented
36Q8×Dic3C2212yescomplemented
37Q8×Dic3C2212yescomplemented
38Q8×Dic3C2212yescomplemented
39#938C2211yescharacteristic
40#938C2211yescharacteristic
41#937C2212yes—
42#935C2212yes—
43D4×Dic3C2214yes—
44D4×Dic3C2212yescomplemented
45C4×#67C2212yes—
46C4×#67C2212yes—
47C2×(C2×D3)⋊C4C2212yes—
48#926C2214yes—
49#926C2211yescharacteristic
50#926C2211yescharacteristic
51#926C2212yescomplemented
52C2×C4⋊Dic3C2211yescharacteristic
53C2×C4⋊Dic3C2212yescomplemented
54C2×Dic3⋊C4C2212yes—
55#898C2214yes—
56#898C2214yes—
57#897C2214yes—
58#892C2214yes—
59#892C2211yescharacteristic
60#892C2211yescharacteristic
61D3×C4⋊C4C2211yescharacteristic
62D3×C4⋊C4C2211yescharacteristic
63#890C2212yescomplemented
64#890C2214yescomplemented
65#889C2214yescomplemented
66#889C2214yescomplemented
67#888C2212yescomplemented
68#887C2214yescomplemented
69#886C2214yes—
70#885C2214yes—
71#883C2214yes—
72#67⋊C4C2214yes—
73D3×C22⋊C4C2212yes—
74#879C2214yescomplemented
75#879C2214yescomplemented
76#878C2214yes—
77#878C2214yescomplemented
78#877C2212yes—
79#877C2214yescomplemented
80#872C2212yes—
81C42×D3C2212yes—
82#870C2212yescomplemented
83#869C2212yescomplemented
84#556—32no—
85#554—32no—
86#552—34no—
87#552—32no—
88#552—32no—
89#551—34no—
90#544—31no—
91#542—32no—
92#541—32no—
93#536D311yescharacteristic, complemented
94#533—32no—
95#529—32no—
96#525—31no—
97C2×C22⋊Q8—31no—
98#520—31no—
99#519—31no—
100C2×#117—31no—
101C23×D3C2311yescharacteristic
102C3×#41—24no—
103C2×C3×Q8—24no—
104C2×C3×Q8C2312yes—
105C2×C3×Q8C2312yes—
106C2×C3×Q8C2311yescharacteristic
107C2×C3×D4C2312yes—
108C2×C3×D4C2311yescharacteristic
109C22×C3×C4C2312yes—
110C22×C3×C4C2312yes—
111C22×C3×C4C2311yescharacteristic
112C2×#67C2312yes—
113C2×#67C2312yes—
114C22×Dic3C2311yescharacteristic
115C22×Dic3C2314yes—
116C22×Dic3C2312yes—
117C2×C4×D3—24no—
118C2×C4×D3C2311yescharacteristic
119C2×C4×D3C2312yes—
120C2×C4×D3C2311yescharacteristic
121C2×C4×D3C2311yescharacteristic
122C2×C4×D3C2311yescharacteristic
123C2×C4×D3C2312yes—
124C2×Dic6C2314yes—
125C3×C4⋊C4C2314yes—
126C3×C4⋊C4C2311yescharacteristic
127C3×C4⋊C4C2314yes—
128C3×C4⋊C4C2311yescharacteristic
129C3×C22⋊C4C2312yes—
130C3×C22⋊C4C2314yes—
131C3×C22⋊C4C2314yes—
132C3×C42C2312yes—
133#217C2312yes—
134#217C2312yes—
135#217C2312yes—
136#217C2312yes—
137#217C2314yes—
138(C2×D3)⋊C4C2312yes—
139(C2×D3)⋊C4C2312yes—
140(C2×D3)⋊C4C2314yes—
141(C2×D3)⋊C4C2314yes—
142(C2×D3)⋊C4C2312yes—
143(C2×D3)⋊C4C2312yes—
144C4⋊Dic3C2311yescharacteristic
145C4⋊Dic3C2312yes—
146C4⋊Dic3C2314yes—
147C4⋊Dic3C2311yescharacteristic
148C4⋊Dic3C2314yes—
149C4⋊Dic3C2314yes—
150C4⋊Dic3C2312yes—
151C4⋊Dic3C2314yes—
152C4⋊Dic3C2311yescharacteristic
153C4⋊Dic3C2311yescharacteristic
154Dic3⋊C4C2314yes—
155Dic3⋊C4C2314yes—
156Dic3⋊C4C2312yes—
157Dic3⋊C4C2312yes—
158Dic3⋊C4C2314yes—
159Dic3⋊C4C2314yes—
160Dic3⋊C4C2312yes—
161Dic3⋊C4C2312yes—
162C4×Dic3C2312yes—
163C4×Dic3C2312yes—
164C4×Dic3C2312yes—
165C4×Dic3C2314yes—
166C4×Dic3C2314yes—
167C4×Dic3C2314yes—
168C4×Dic3C2312yes—
169C2×#41C2×D311yescharacteristic
170C22×Q8C2×D311yescharacteristic
171C23×C4—31no—
172C4⋊Q8—32no—
173C4⋊Q8—32no—
174C4⋊Q8C2×D312yescomplemented
175#126—34no—
176#126—34no—
177#126—34no—
178#126—34no—
179#125—34no—
180#125—34no—
181#125—34no—
182#125—32no—
183#125—32no—
184#124—34no—
185#124C2×D312yescomplemented
186#123—32no—
187#123—34no—
188#123—34no—
189#123C2×D314yes—
190C22⋊Q8—32no—
191C22⋊Q8—32no—
192C22⋊Q8—32no—
193C22⋊Q8—32no—
194C22⋊Q8—31no—
195C22⋊Q8—31no—
196C22⋊Q8—34no—
197C22⋊Q8—34no—
198C22⋊Q8—34no—
199C22⋊Q8C2×D312yescomplemented
200C22⋊Q8C2×D312yescomplemented
201#121—31no—
202#121—31no—
203#120—32no—
204C4×Q8—32no—
205C4×Q8—32no—
206C4×Q8—32no—
207C4×Q8—32no—
208C4×Q8—32no—
209C4×Q8—34no—
210C4×D4—32no—
211C4×D4—34no—
212C4×D4—32no—
213C4×D4—32no—
214C4×D4—34no—
215#117—31no—
216#117—31no—
217#117—34no—
218#117—32no—
219#117—31no—
220#117—31no—
221#117—34no—
222#117—32no—
223#117—34no—
224#117—32no—
225#117C2×D311yescharacteristic
226C2×C4⋊C4—31no—
227C2×C4⋊C4—32no—
228C2×C4⋊C4—32no—
229C2×C4⋊C4—31no—
230C2×C4⋊C4—31no—
231C2×C22⋊C4—32no—
232C2×C22⋊C4—32no—
233C2×C42—32no—
234C23×C3C2412yes—
235C23×C3C2411yescharacteristic
236C22×D3—22no—
237C22×D3—22no—
238C22×D3—41no—
239C22×D3C2411yescharacteristic
240C22×D3C2411yescharacteristic
241C3×Q8—24no—
242C3×Q8—24no—
243C3×Q8—22no—
244C3×D4—24no—
245C3×D4—22no—
246C2×C3×C4—24no—
247C2×C3×C4—24no—
248C2×C3×C4#4114yes—
249C2×C3×C4C2414yes—
250C2×C3×C4C2412yes—
251C2×C3×C4C2412yes—
252C2×C3×C4C2412yes—
253C2×C3×C4C2411yescharacteristic
254C2×C3×C4C2411yescharacteristic
255#67—24no—
256#67—42no—
257C2×Dic3—22no—
258C2×Dic3—42no—
259C2×Dic3—44no—
260C2×Dic3C2412yes—
261C2×Dic3C2411yescharacteristic
262C2×Dic3C2412yes—
263C2×Dic3C2412yes—
264C2×Dic3C2412yes—
265C2×Dic3C2414yes—
266C2×Dic3C2411yescharacteristic
267C4×D3—24no—
268C4×D3—22no—
269C4×D3—22no—
270C4×D3—22no—
271C4×D3—22no—
272C4×D3—42no—
273Dic6—44no—
274C24—31no—
275#41—24no—
276C2×Q8—24no—
277C2×Q8—34no—
278C2×Q8C22×D312yes—
279C2×Q8C22×D312yes—
280C2×Q8C22×D311yescharacteristic
281C2×D4—32no—
282C2×D4—32no—
283C2×D4C22×D312yes—
284C2×D4C22×D311yescharacteristic
285C22×C4—31no—
286C22×C4—32no—
287C22×C4—34no—
288C22×C4—31no—
289C22×C4—32no—
290C22×C4—31no—
291C22×C4—31no—
292C22×C4—31no—
293C22×C4—32no—
294C22×C4—64no—
295C22×C4C22×D312yes—
296C22×C4C22×D312yes—
297C22×C4C22×D311yescharacteristic
298C4⋊C4—31no—
299C4⋊C4—32no—
300C4⋊C4—31no—
301C4⋊C4—32no—
302C4⋊C4—32no—
303C4⋊C4—34no—
304C4⋊C4—32no—
305C4⋊C4—34no—
306C4⋊C4—34no—
307C4⋊C4—31no—
308C4⋊C4—31no—
309C4⋊C4—34no—
310C4⋊C4—34no—
311C4⋊C4—34no—
312C4⋊C4—34no—
313C4⋊C4—32no—
314C4⋊C4—32no—
315C4⋊C4—34no—
316C4⋊C4C22×D311yescharacteristic
317C4⋊C4C22×D311yescharacteristic
318C4⋊C4C22×D314yes—
319C4⋊C4C22×D314yes—
320C22⋊C4—32no—
321C22⋊C4—32no—
322C22⋊C4—32no—
323C22⋊C4—34no—
324C22⋊C4—32no—
325C22⋊C4—32no—
326C22⋊C4—32no—
327C22⋊C4—34no—
328C22⋊C4—34no—
329C22⋊C4—32no—
330C22⋊C4—32no—
331C22⋊C4C22×D312yes—
332C22⋊C4C22×D314yes—
333C22⋊C4C22×D314yes—
334C42—32no—
335C42—32no—
336C42—32no—
337C42—34no—
338C42—34no—
339C42—34no—
340C42—32no—
341C42C22×D312yes—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—22no—
345C22×C3—22no—
346C22×C3—22no—
347C22×C3C2×#4112yes—
348C22×C3C2511yescharacteristic
349C2×D3—21no—
350C2×D3—21no—
351C2×D3—21no—
352C2×D3—21no—
353C2×D3—21no—
354C2×D3—44no—
355C2×D32−1+412yes—
356C3×C4—22no—
357C3×C4—24no—
358C3×C4—22no—
359C3×C4—22no—
360C3×C4C2×#4112yes—
361C3×C4C2×#4112yes—
362Dic3—21no—
363Dic3—21no—
364Dic3—22no—
365Dic3—22no—
366Dic3—22no—
367Dic3—24no—
368Dic3—22no—
369C23—31no—
370C23—31no—
371C23—62no—
372C23—62no—
373C23—121no—
374C23C23×D312yes—
375C23C23×D311yescharacteristic
376Q8—24no—
377Q8—24no—
378Q8—22no—
379Q8—124no—
380D4—24no—
381D4—22no—
382D4—64no—
383D4—122no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—32no—
387C2×C4—31no—
388C2×C4—32no—
389C2×C4—32no—
390C2×C4—32no—
391C2×C4—34no—
392C2×C4—31no—
393C2×C4—64no—
394C2×C4—62no—
395C2×C4—62no—
396C2×C4—62no—
397C2×C4—62no—
398C2×C4—62no—
399C2×C4—122no—
400C2×C4—124no—
401C2×C4—122no—
402C2×C4#23714yes—
403C2×C4C23×D314yes—
404C2×C4C23×D312yes—
405C2×C4C23×D312yes—
406C2×C4C23×D312yes—
407C2×C4C23×D311yescharacteristic
408C2×C4C23×D311yescharacteristic
409C2×C3—22no—
410C2×C3—42no—
411C2×C3C22×#4111yescharacteristic
412C2×C3C2×2−1+411yescharacteristic
413C2×C3#58511yescharacteristic
414D3—22no—
415D3—41no—
416C22—21no—
417C22—21no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—32no—
422C22—61no—
423C22—61no—
424C22—61no—
425C22—61no—
426C22—61no—
427C22—124no—
428C22C2×#23712yes—
429C22C24×D311yescharacteristic
430C4—22no—
431C4—24no—
432C4—22no—
433C4—22no—
434C4—61no—
435C4—61no—
436C4—62no—
437C4—62no—
438C4—62no—
439C4—64no—
440C4—62no—
441C4C2×#23712yes—
442C4C2×#23712yes—
443C3#349511yescharacteristic, complemented, Sylow
444C2—22no—
445C2—42no—
446C2—62no—
447C2—121no—
448C2C22×#23711yescharacteristic
449C2D3×2−1+411yescharacteristic
450C2#596811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D3
commutator, socle, cosocleC22×C3C25
FittingC3×#536C2
prime radical#5828C2
hypercenter#536D3
hypocenterC3#3495
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C3×#536C2semidirect
3. #5827C2semidirect
4. C2×#946C2semidirect
5. #5812C2semidirect
6. #5731C2semidirect
7. #5728C2semidirect
8. #5682C2semidirect
9. #5680C2semidirect
10. #5658C2semidirect
11. #5650C2semidirect
12. #5642C2semidirect
13. #5641C2semidirect
14. #5639C2semidirect
15. #5635C2semidirect
16. D3×#117C2semidirect
17. #5519C2semidirect
22. C3×C4⋊Q8C22semidirect
23. C3×#124C22semidirect
25. C3×C22⋊Q8C22semidirect
26. C3×C22⋊Q8C22semidirect
34. Q8×Dic3C22semidirect
35. Q8×Dic3C22semidirect
36. Q8×Dic3C22semidirect
37. Q8×Dic3C22semidirect
38. Q8×Dic3C22semidirect
44. D4×Dic3C22semidirect
51. #926C22semidirect
53. C2×C4⋊Dic3C22semidirect
63. #890C22semidirect
64. #890C22semidirect
65. #889C22semidirect
66. #889C22semidirect
67. #888C22semidirect
68. #887C22semidirect
74. #879C22semidirect
75. #879C22semidirect
77. #878C22semidirect
79. #877C22semidirect
82. #870C22semidirect
83. #869C22semidirect
93. #536D3semidirect
174. C4⋊Q8C2×D3semidirect
185. #124C2×D3semidirect
199. C22⋊Q8C2×D3semidirect
200. C22⋊Q8C2×D3semidirect
443. C3#3495semidirect

Maximal subgroups

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

subgroupindex
C3×#5362
#58282
#58272
C2×#9462
#58122
#57312
#57282
#56822
#56802
#56582
#56502
#56422
#56412
#56392
#56352
D3×#1172
#55192
#34953