Finite Group Databasebeta

← #86369

Subgroups — #86369

Order 384.

1032 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#537C211yesmaximal, characteristic, complemented
2#5833C211yesmaximal, characteristic, complemented
3#5832C211yesmaximal, characteristic, complemented
4#5827C211yesmaximal, characteristic, complemented
5Dic3×#41C211yesmaximal, characteristic, complemented
6#5642C212yesmaximal, complemented
7#5639C212yesmaximal, complemented
8#5625C212yesmaximal, complemented
9#5624C212yesmaximal, complemented
10#5619C212yesmaximal, complemented
11#5618C214yesmaximal, complemented
12#5618C212yesmaximal, complemented
13#5614C212yesmaximal, complemented
14#5601C214yesmaximal, complemented
15#5600C212yesmaximal, complemented
16#5504C211yesmaximal, characteristic, complemented
17C2×#890C211yesmaximal, characteristic, complemented
18#3512—31nomaximal, Sylow
19C2×C3×#41C2211yescharacteristic
20C2×C3×#41C2211yescharacteristic
21C2×#235C2211yescharacteristic
22C3×C22⋊Q8C2212yes—
23C3×C22⋊Q8C2212yes—
24C3×#121C2212yes—
25C3×#121C2214yes—
26C3×#121C2212yes—
27C2×C3×C4⋊C4C2211yescharacteristic
28#947C2211yescharacteristic
29#946C2212yes—
30Q8×Dic3C2211yescharacteristic
31Q8×Dic3C2211yescharacteristic
32Q8×Dic3C2212yes—
33#944C2211yescharacteristic
34#940C2211yescharacteristic
35#939C2212yes—
36#939C2212yes—
37#939C2214yes—
38#939C2214yes—
39#938C2212yes—
40#938C2214yes—
41#936C2211yescharacteristic
42#935C2214yes—
43D4×Dic3C2212yes—
44D4×Dic3C2211yescharacteristic
45D4×Dic3C2212yes—
46D4×Dic3C2211yescharacteristic
47D4×Dic3C2212yes—
48D4×Dic3C2214yes—
49D4×Dic3C2214yes—
50#930C2212yes—
51C4×#67C2212yes—
52C4×#67C2212yes—
53C4×#67C2214yes—
54#926C2212yes—
55#926C2211yescharacteristic
56#926C2212yes—
57C2×C4⋊Dic3C2212yes—
58C2×C4⋊Dic3C2211yescharacteristic
59C2×C4⋊Dic3C2212yes—
60#924C2212yes—
61C2×Dic3⋊C4C2212yes—
62C2×C4×Dic3C2211yescharacteristic
63C2×C4×Dic3C2212yes—
64#898C2214yes—
65#893C2212yes—
66#892C2214yes—
67#892C2212yes—
68D3×C4⋊C4C2212yes—
69#890C2212yes—
70#890C2212yes—
71#890C2214yes—
72#890C2212yes—
73#890C2212yes—
74#889C2214yes—
75#887C2212yes—
76#886C2214yes—
77#886C2214yes—
78#883C2214yes—
79#67⋊C4C2214yes—
80#879C2214yes—
81#879C2214yes—
82#879C2214yes—
83#877C2214yes—
84#553—34no—
85#553—32no—
86#553—32no—
87#553—34no—
88#552—32no—
89#552—32no—
90#541—32no—
91#540—32no—
92#537—31no—
93#537D311yescharacteristic, complemented
94#532—31no—
95#529—32no—
96#529—32no—
97C2×#125—31no—
98#520—31no—
99#520—31no—
100C4×#41—31no—
101C3×#41—24no—
102C3×#41—24no—
103C2×C3×Q8C2311yescharacteristic
104C2×C3×Q8C2311yescharacteristic
105C2×C3×D4C2311yescharacteristic
106C2×C3×D4C2311yescharacteristic
107C2×C3×D4C2312yes—
108C2×C3×D4C2312yes—
109C2×C3×D4C2314yes—
110C22×C3×C4C2312yes—
111C22×C3×C4C2312yes—
112C22×C3×C4C2312yes—
113C22×C3×C4C2311yescharacteristic
114C2×#67C2312yes—
115C2×#67C2314yes—
116C2×#67C2312yes—
117C2×#67C2312yes—
118C22×Dic3C2314yes—
119C22×Dic3C2312yes—
120C22×Dic3C2312yes—
121C22×Dic3C2311yescharacteristic
122C22×Dic3C2311yescharacteristic
123C22×Dic3C2312yes—
124#235—24no—
125C2×D12C2311yescharacteristic
126C2×C4×D3C2312yes—
127C2×C4×D3C2314yes—
128C2×Dic6C2311yescharacteristic
129C3×C4⋊C4C2312yes—
130C3×C4⋊C4C2314yes—
131C3×C4⋊C4C2312yes—
132C3×C22⋊C4C2314yes—
133C3×C22⋊C4C2314yes—
134#217C2312yes—
135#217C2314yes—
136#217C2312yes—
137#217C2312yes—
138#217C2312yes—
139#217C2314yes—
140#217C2312yes—
141(C2×D3)⋊C4C2312yes—
142(C2×D3)⋊C4C2314yes—
143(C2×D3)⋊C4C2312yes—
144(C2×D3)⋊C4C2314yes—
145C4⋊Dic3C2314yes—
146C4⋊Dic3C2314yes—
147C4⋊Dic3C2314yes—
148C4⋊Dic3C2312yes—
149C4⋊Dic3C2312yes—
150C4⋊Dic3C2312yes—
151C4⋊Dic3C2312yes—
152C4⋊Dic3C2311yescharacteristic
153C4⋊Dic3C2311yescharacteristic
154Dic3⋊C4C2314yes—
155Dic3⋊C4C2314yes—
156Dic3⋊C4C2314yes—
157Dic3⋊C4C2312yes—
158Dic3⋊C4C2312yes—
159Dic3⋊C4C2314yes—
160C4×Dic3C2312yes—
161C4×Dic3C2314yes—
162C4×Dic3C2312yes—
163C4×Dic3C2314yes—
164C4×Dic3C2312yes—
165C4×Dic3C2311yescharacteristic
166C4×Dic3C2311yescharacteristic
167C4×Dic3C2311yescharacteristic
168C4×Dic3C2311yescharacteristic
169C2×#41—31no—
170C2×#41C2×D311yescharacteristic
171C2×#41C2×D311yescharacteristic
172C4⋊Q8—31no—
173#127—31no—
174#126—34no—
175#126—34no—
176#126—34no—
177#126—34no—
178#125—32no—
179#125—32no—
180#125—32no—
181#125—32no—
182#125—34no—
183#125—34no—
184#124—31no—
185#124—31no—
186#123—34no—
187#123—34no—
188#123—34no—
189#123—34no—
190C22⋊Q8—32no—
191C22⋊Q8—32no—
192C22⋊Q8C2×D312yes—
193C22⋊Q8C2×D312yes—
194#121—32no—
195#121—32no—
196#121—32no—
197#121—34no—
198#121—34no—
199#121—34no—
200#121—32no—
201#121C2×D312yes—
202#121C2×D314yes—
203#121C2×D312yes—
204C4×Q8—31no—
205C4×Q8—31no—
206C4×Q8—32no—
207C4×Q8—32no—
208C4×D4—32no—
209C4×D4—32no—
210C4×D4—31no—
211C4×D4—31no—
212C4×D4—32no—
213C4×D4—34no—
214C4×D4—34no—
215C4×D4—34no—
216C4×D4—32no—
217C4×D4—32no—
218C4×D4—32no—
219C4×D4—34no—
220#117—31no—
221#117—32no—
222#117—32no—
223#117—32no—
224#117—34no—
225#117—34no—
226C2×C4⋊C4—31no—
227C2×C4⋊C4—32no—
228C2×C4⋊C4—32no—
229C2×C4⋊C4—32no—
230C2×C4⋊C4—32no—
231C2×C4⋊C4C2×D311yescharacteristic
232C2×C42—31no—
233C2×C42—32no—
234C23×C3C2412yes—
235C23×C3C2412yes—
236C23×C3C2411yescharacteristic
237C22×D3C2412yes—
238C3×Q8—22no—
239C3×Q8—22no—
240C3×D4—24no—
241C3×D4—24no—
242C3×D4—22no—
243C3×D4—22no—
244C3×D4—44no—
245C2×C3×C4—24no—
246C2×C3×C4—24no—
247C2×C3×C4—42no—
248C2×C3×C4#4114yes—
249C2×C3×C4C2412yes—
250C2×C3×C4C2412yes—
251C2×C3×C4C2414yes—
252C2×C3×C4C2411yescharacteristic
253C2×C3×C4C2411yescharacteristic
254#67—24no—
255#67—44no—
256#67—42no—
257#67—42no—
258C2×Dic3—42no—
259C2×Dic3—42no—
260C2×Dic3—44no—
261C2×Dic3—41no—
262C2×Dic3—41no—
263C2×Dic3—42no—
264C2×Dic3C2411yescharacteristic
265C2×Dic3C2412yes—
266C2×Dic3C2412yes—
267C2×Dic3C2411yescharacteristic
268C2×Dic3C2411yescharacteristic
269C2×Dic3C2412yes—
270C2×Dic3C2411yescharacteristic
271C2×Dic3C2414yes—
272D12—22no—
273C4×D3—24no—
274C4×D3—44no—
275Dic6—22no—
276#41—24no—
277#41—24no—
278#41—64no—
279C2×Q8—31no—
280C2×Q8C22×D311yescharacteristic
281C2×Q8C22×D311yescharacteristic
282C2×D4—32no—
283C2×D4—34no—
284C2×D4—32no—
285C2×D4—32no—
286C2×D4—31no—
287C2×D4C22×D312yes—
288C2×D4C22×D312yes—
289C2×D4C22×D311yescharacteristic
290C2×D4C22×D311yescharacteristic
291C2×D4C22×D314yes—
292C22×C4—31no—
293C22×C4—31no—
294C22×C4—32no—
295C22×C4—32no—
296C22×C4—32no—
297C22×C4—34no—
298C22×C4—32no—
299C22×C4—34no—
300C22×C4C22×D312yes—
301C22×C4C22×D312yes—
302C22×C4C22×D312yes—
303C22×C4C22×D311yescharacteristic
304C4⋊C4—31no—
305C4⋊C4—31no—
306C4⋊C4—32no—
307C4⋊C4—34no—
308C4⋊C4—34no—
309C4⋊C4—32no—
310C4⋊C4—34no—
311C4⋊C4—34no—
312C4⋊C4—34no—
313C4⋊C4—34no—
314C4⋊C4—32no—
315C4⋊C4—32no—
316C4⋊C4—34no—
317C4⋊C4—32no—
318C4⋊C4—32no—
319C4⋊C4C22×D312yes—
320C4⋊C4C22×D312yes—
321C4⋊C4C22×D314yes—
322C22⋊C4—32no—
323C22⋊C4—32no—
324C22⋊C4—32no—
325C22⋊C4—32no—
326C22⋊C4—34no—
327C22⋊C4—32no—
328C22⋊C4—34no—
329C22⋊C4—32no—
330C22⋊C4—34no—
331C22⋊C4—34no—
332C22⋊C4—32no—
333C22⋊C4C22×D314yes—
334C22⋊C4C22×D314yes—
335C42—31no—
336C42—32no—
337C42—32no—
338C42—32no—
339C42—31no—
340C42—31no—
341C42—31no—
342C42—34no—
343C42—34no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—22no—
347C22×C3—22no—
348C22×C3—22no—
349C22×C3—22no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3C2×#4112yes—
353C22×C3C2511yescharacteristic
354C2×D3—22no—
355C2×D3—22no—
356C2×D3—22no—
357C3×C4—22no—
358C3×C4—22no—
359C3×C4—24no—
360C3×C4C2×#4112yes—
361C3×C4C2×#4112yes—
362Dic3—22no—
363Dic3—22no—
364Dic3—21no—
365Dic3—21no—
366Dic3—22no—
367Dic3—24no—
368Dic3—21no—
369Dic3—21no—
370C23—32no—
371C23C23×D312yes—
372C23C23×D312yes—
373C23C23×D311yescharacteristic
374Q8—22no—
375Q8—22no—
376Q8—62no—
377D4—24no—
378D4—24no—
379D4—22no—
380D4—22no—
381D4—44no—
382D4—64no—
383D4—62no—
384D4—122no—
385D4—124no—
386D4—122no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—31no—
390C2×C4—32no—
391C2×C4—31no—
392C2×C4—32no—
393C2×C4—32no—
394C2×C4—31no—
395C2×C4—31no—
396C2×C4—34no—
397C2×C4—42no—
398C2×C4—64no—
399C2×C4—124no—
400C2×C4—122no—
401C2×C4—121no—
402C2×C4—122no—
403C2×C4—124no—
404C2×C4—121no—
405C2×C4—122no—
406C2×C4#23714yes—
407C2×C4C23×D312yes—
408C2×C4C23×D312yes—
409C2×C4C23×D314yes—
410C2×C4C23×D311yescharacteristic
411C2×C4C23×D311yescharacteristic
412C2×C3—22no—
413C2×C3—42no—
414C2×C3—42no—
415C2×C3C22×#4111yescharacteristic
416C2×C3#58511yescharacteristic
417C2×C3#58511yescharacteristic
418D3—42no—
419C22—21no—
420C22—21no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—62no—
428C22—62no—
429C22—62no—
430C22C2×#23712yes—
431C22C24×D311yescharacteristic
432C4—22no—
433C4—22no—
434C4—24no—
435C4—62no—
436C4—62no—
437C4—61no—
438C4—61no—
439C4—61no—
440C4—62no—
441C4—64no—
442C4—61no—
443C4C2×#23712yes—
444C4C2×#23712yes—
445C3#351211yescharacteristic, complemented, Sylow
446C2—22no—
447C2—42no—
448C2—42no—
449C2—122no—
450C2C22×#23711yescharacteristic
451C2#596611yescharacteristic
452C2#596811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D3
commutator, socle, cosocleC22×C3C25
FittingC3×#537C2
hypercenter#537D3
hypocenterC3#3512
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C3×#537C2semidirect
2. #5833C2semidirect
3. #5832C2semidirect
4. #5827C2semidirect
5. Dic3×#41C2semidirect
6. #5642C2semidirect
7. #5639C2semidirect
8. #5625C2semidirect
9. #5624C2semidirect
10. #5619C2semidirect
11. #5618C2semidirect
12. #5618C2semidirect
13. #5614C2semidirect
14. #5601C2semidirect
15. #5600C2semidirect
16. #5504C2semidirect
17. C2×#890C2semidirect
93. #537D3semidirect
445. C3#3512semidirect

Maximal subgroups

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

subgroupindex
C3×#5372
#58332
#58322
#58272
Dic3×#412
#56422
#56392
#56252
#56242
#56192
#56182
#56142
#56012
#56002
#55042
C2×#8902
#35123