Finite Group Databasebeta

← C3×#85745 #11904959

Subgroups — C3×#85745 #11904959

Order 1152.

2269 conjugacy classes of subgroups.

The subgroup lattice has 535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#117C211yesmaximal, characteristic, complemented
2C2×C3×#929C212yesmaximal, complemented
3C3×#5531C218yesmaximal, complemented
4C3×#5527C218yesmaximal, complemented
5C3×#5515C214yesmaximal, complemented
6C3×#5493C211yesmaximal, characteristic
7C3×#5486C212yesmaximal, complemented
8C3×#5483C211yesmaximal, characteristic, complemented
9C3×#5479C214yesmaximal, complemented
10C3×#3491—31nomaximal
11#85745C311yesmaximal, characteristic, direct product factor
12C23×C32×C4C2211yescharacteristic
13C22×C3×#67C2212yes—
14C32×#117C2218yescomplemented
15C2×C32×C4⋊C4C2212yescomplemented
16C2×C32×C22⋊C4C2211yescharacteristic
17C2×C32×C22⋊C4C2211yescharacteristic
18C2×C32×C42C2212yescomplemented
19C2×C3×#217C2212yes—
20C3×#930C2214yes—
21C3×#929C2218yes—
22C3×#929C2214yescomplemented
23C3×#929C2214yescomplemented
24C3×C4×#67C2218yescomplemented
25C2×C3×(C2×D3)⋊C4C2214yescomplemented
26C3×#924C2214yescomplemented
27C2×C3×Dic3⋊C4C2214yescomplemented
28C3×#898C2218yescomplemented
29C3×#896C2218yescomplemented
30C3×#894C2218yescomplemented
31C3×#889C2218yescomplemented
32C3×#886C2214yes—
33C3×#882C2214yes—
34C3×#67⋊C4C2218yes—
35C3×D3×C22⋊C4C2214yescomplemented
36C3×#878C2218yescomplemented
37C3×#877C2214yescomplemented
38C3×#876C2218yescomplemented
39C3×#875C2214yescomplemented
40C3×C4×D12C2214yescomplemented
41C3×#872C2218yescomplemented
42C3×#870C2214yescomplemented
43C3×C4×Dic6C2214yescomplemented
44C3×#552—38no—
45C3×#551—38no—
46C3×#543—31no—
47C3×#539—34no—
48C3×#534—31no—
49C3×#529—34no—
50C2×C3×#123—32no—
51C3×#518—32no—
52C2×C3×#117—21no—
53C2×C3×#117D311yescharacteristic, complemented
54C2×C3×#117C2×C311yescharacteristic, complemented
55C2×#929C2×C312yescomplemented
56#5531C2×C318yescomplemented
57#5527C2×C318yescomplemented
58#5515C2×C314yescomplemented
59#5493C2×C311yescharacteristic
60#5486C2×C312yescomplemented
61#5483C2×C311yescharacteristic, complemented
62#5479C2×C314yescomplemented
63C24×C32C2311yescharacteristic
64C23×C3×D3C2312yes—
65C22×C32×C4—24no—
66C22×C32×C4C2314yes—
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2312yes—
70C22×C32×C4C2312yes—
71C2×C3×#67—28no—
72C2×C3×#67C2314yes—
73C2×C3×#67C2314yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2314yes—
76C2×C3×D12C2314yes—
77C2×C3×C4×D3C2318yes—
78C2×C3×Dic6C2314yes—
79C32×C4⋊C4C2318yes—
80C32×C22⋊C4C2314yes—
81C32×C22⋊C4C2314yes—
82C32×C42C2314yes—
83C32×C42C2314yes—
84C3×#217C2314yes—
85C3×#217C2314yes—
86C3×(C2×D3)⋊C4C2318yes—
87C3×(C2×D3)⋊C4C2318yes—
88C3×(C2×D3)⋊C4C2318yes—
89C3×(C2×D3)⋊C4C2318yes—
90C3×C4⋊Dic3C2314yes—
91C3×C4⋊Dic3C2314yes—
92C3×Dic3⋊C4C2318yes—
93C3×Dic3⋊C4C2318yes—
94C3×Dic3⋊C4C2318yes—
95C3×Dic3⋊C4C2318yes—
96C3×C4×Dic3C2318yes—
97#3491—31noSylow
98C22×C3×D4—32no—
99C23×C3×C4—21no—
100C23×C3×C4C2×D311yescharacteristic
101C23×C3×C4C22×C311yescharacteristic
102C22×#67C22×C312yes—
103C3×#126—38no—
104C3×#126—38no—
105C3×#125—38no—
106C3×#125—34no—
107C3×#124—34no—
108C3×#123—38no—
109C3×#123—34no—
110C3×#123—34no—
111C3×#123—38no—
112C3×#123—34no—
113C3×C22⋊Q8—34no—
114C3×C22⋊Q8—38no—
115C3×C22⋊Q8—38no—
116C3×#121—34no—
117C3×#120—34no—
118C3×C4×Q8—34no—
119C3×C4×D4—38no—
120C3×C4×D4—38no—
121C3×C4×D4—34no—
122C3×#117—28no—
123C3×#117—34no—
124C3×#117—38no—
125C3×#117C2×D318yescomplemented
126C3×#117C22×C318yescomplemented
127C2×C3×C4⋊C4—22no—
128C2×C3×C4⋊C4—34no—
129C2×C3×C4⋊C4C2×D312yescomplemented
130C2×C3×C4⋊C4C22×C312yescomplemented
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—32no—
134C2×C3×C22⋊C4—34no—
135C2×C3×C22⋊C4—34no—
136C2×C3×C22⋊C4C2×D311yescharacteristic
137C2×C3×C22⋊C4C2×D311yescharacteristic
138C2×C3×C22⋊C4C22×C311yescharacteristic
139C2×C3×C22⋊C4C22×C311yescharacteristic
140C2×C3×C42—22no—
141C2×C3×C42C2×D312yescomplemented
142C2×C3×C42C22×C312yescomplemented
143C2×#217C22×C312yes—
144#930C22×C314yes—
145#929C22×C318yes—
146#929C22×C314yescomplemented
147#929C22×C314yescomplemented
148C4×#67C22×C318yescomplemented
149C2×(C2×D3)⋊C4C22×C314yescomplemented
150#924C22×C314yescomplemented
151C2×Dic3⋊C4C22×C314yescomplemented
152#898C22×C318yescomplemented
153#896C22×C318yescomplemented
154#894C22×C318yescomplemented
155#889C22×C318yescomplemented
156#886C22×C314yes—
157#882C22×C314yes—
158#67⋊C4C22×C318yes—
159D3×C22⋊C4C22×C314yescomplemented
160#878C22×C318yescomplemented
161#877C22×C314yescomplemented
162#876C22×C318yescomplemented
163#875C22×C314yescomplemented
164C4×D12C22×C314yescomplemented
165#872C22×C318yescomplemented
166#870C22×C314yescomplemented
167C4×Dic6C22×C314yescomplemented
168C23×C32—42no—
169C23×C32#4114yes—
170C23×C32C2412yes—
171C23×C32C2411yescharacteristic
172C22×C3×D3—24no—
173C22×C3×D3—44no—
174C22×C3×D3C2414yes—
175C2×C32×C4—28no—
176C2×C32×C4—22no—
177C2×C32×C4—22no—
178C2×C32×C4—42no—
179C2×C32×C4—42no—
180C2×C32×C4C2414yes—
181C2×C32×C4C2412yes—
182C2×C32×C4C2412yes—
183C2×C32×C4C2414yes—
184C3×#67—28no—
185C3×#67—28no—
186C2×C3×Dic3—24no—
187C2×C3×Dic3—44no—
188C2×C3×Dic3C2414yes—
189C2×C3×Dic3C2418yes—
190C3×D12—44no—
191C3×C4×D3—48no—
192C3×Dic6—44no—
193#552—38no—
194#551—38no—
195#543—31no—
196#539—34no—
197#534—31no—
198#529—34no—
199C2×#123—32no—
200#518—32no—
201C2×#117C3×D311yescharacteristic, complemented
202C24×C3—21no—
203C24×C3—32no—
204C24×C3C22×D311yescharacteristic
205C24×C3C23×C311yescharacteristic
206C23×D3C23×C312yes—
207C2×C3×Q8—34no—
208C2×C3×D4—34no—
209C2×C3×D4—34no—
210C2×C3×D4—34no—
211C2×C3×D4—68no—
212C22×C3×C4—28no—
213C22×C3×C4—24no—
214C22×C3×C4—24no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—24no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—32no—
221C22×C3×C4—34no—
222C22×C3×C4—38no—
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D314yes—
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D312yes—
227C22×C3×C4C22×D312yes—
228C22×C3×C4C23×C314yes—
229C22×C3×C4C23×C311yescharacteristic
230C22×C3×C4C23×C311yescharacteristic
231C22×C3×C4C23×C312yes—
232C22×C3×C4C23×C312yes—
233C2×#67—28no—
234C2×#67C23×C314yes—
235C2×#67C23×C314yes—
236C22×Dic3C23×C312yes—
237C22×Dic3C23×C314yes—
238C2×D12C23×C314yes—
239C2×C4×D3C23×C318yes—
240C2×Dic6C23×C314yes—
241C3×C4⋊C4—28no—
242C3×C4⋊C4—38no—
243C3×C4⋊C4—38no—
244C3×C4⋊C4—38no—
245C3×C4⋊C4—38no—
246C3×C4⋊C4—34no—
247C3×C4⋊C4—34no—
248C3×C4⋊C4C22×D318yes—
249C3×C4⋊C4C23×C318yes—
250C3×C22⋊C4—24no—
251C3×C22⋊C4—24no—
252C3×C22⋊C4—34no—
253C3×C22⋊C4—34no—
254C3×C22⋊C4—38no—
255C3×C22⋊C4—38no—
256C3×C22⋊C4—38no—
257C3×C22⋊C4—38no—
258C3×C22⋊C4C22×D314yes—
259C3×C22⋊C4C22×D314yes—
260C3×C22⋊C4C23×C314yes—
261C3×C22⋊C4C23×C314yes—
262C3×C42—24no—
263C3×C42—24no—
264C3×C42—38no—
265C3×C42C22×D314yes—
266C3×C42C22×D314yes—
267C3×C42C23×C314yes—
268C3×C42C23×C314yes—
269#217C23×C314yes—
270#217C23×C314yes—
271(C2×D3)⋊C4C23×C318yes—
272(C2×D3)⋊C4C23×C318yes—
273(C2×D3)⋊C4C23×C318yes—
274(C2×D3)⋊C4C23×C318yes—
275C4⋊Dic3C23×C314yes—
276C4⋊Dic3C23×C314yes—
277Dic3⋊C4C23×C318yes—
278Dic3⋊C4C23×C318yes—
279Dic3⋊C4C23×C318yes—
280Dic3⋊C4C23×C318yes—
281C4×Dic3C23×C318yes—
282C22×C32—22no—
283C22×C32—24no—
284C22×C32—44no—
285C22×C32C2×#4114yes—
286C22×C32C2×#4112yes—
287C22×C32C2511yescharacteristic
288C2×C3×D3—24no—
289C2×C3×D3—28no—
290C2×C3×D3—84no—
291C32×C4—22no—
292C32×C4—22no—
293C32×C4—24no—
294C32×C4—24no—
295C3×Dic3—24no—
296C3×Dic3—28no—
297C22×D4—32no—
298C23×C4C2×C3×D311yescharacteristic
299#126—38no—
300#126—38no—
301#125—38no—
302#125—34no—
303#124—34no—
304#123—34no—
305#123—34no—
306#123—38no—
307#123—38no—
308#123—34no—
309C22⋊Q8—34no—
310C22⋊Q8—38no—
311C22⋊Q8—38no—
312#121—34no—
313#120—34no—
314C4×Q8—34no—
315C4×D4—38no—
316C4×D4—38no—
317C4×D4—34no—
318#117—34no—
319#117—38no—
320#117C2×C3×D318yescomplemented
321C2×C4⋊C4—34no—
322C2×C4⋊C4C2×C3×D312yescomplemented
323C2×C22⋊C4—32no—
324C2×C22⋊C4—34no—
325C2×C22⋊C4—34no—
326C2×C22⋊C4C2×C3×D311yescharacteristic
327C2×C22⋊C4C2×C3×D311yescharacteristic
328C2×C42C2×C3×D312yescomplemented
329C23×C3—21no—
330C23×C3—22no—
331C23×C3—24no—
332C23×C3—34no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—44no—
336C23×C3—64no—
337C23×C3—124no—
338C23×C3#23514yes—
339C23×C3C3×#4114yes—
340C23×C3C23×D311yescharacteristic
341C23×C3C23×D312yes—
342C23×C3C24×C311yescharacteristic
343C23×C3C24×C312yes—
344C22×D3—24no—
345C22×D3—44no—
346C22×D3C24×C314yes—
347C3×Q8—124no—
348C3×D4—68no—
349C3×D4—68no—
350C3×D4—124no—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4—216no—
354C2×C3×C4—28no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—28no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—24no—
363C2×C3×C4—24no—
364C2×C3×C4—34no—
365C2×C3×C4—38no—
366C2×C3×C4—42no—
367C2×C3×C4—42no—
368C2×C3×C4—42no—
369C2×C3×C4—42no—
370C2×C3×C4—44no—
371C2×C3×C4—44no—
372C2×C3×C4—64no—
373C2×C3×C4—128no—
374C2×C3×C4—124no—
375C2×C3×C4C23×D314yes—
376C2×C3×C4C23×D312yes—
377C2×C3×C4C23×D314yes—
378C2×C3×C4C23×D312yes—
379C2×C3×C4C24×C314yes—
380C2×C3×C4C24×C312yes—
381C2×C3×C4C24×C312yes—
382C2×C3×C4C24×C314yes—
383#67—28no—
384#67—28no—
385C2×Dic3—24no—
386C2×Dic3—44no—
387C2×Dic3C24×C314yes—
388C2×Dic3C24×C318yes—
389D12—44no—
390C4×D3—48no—
391Dic6—44no—
392C2×C32—22no—
393C2×C32—24no—
394C2×C32C22×#4111yescharacteristic
395C2×C32#58512yes—
396C3×D3—44no—
397C24—32no—
398C24C22×C3×D311yescharacteristic
399C2×Q8—34no—
400C2×D4—34no—
401C2×D4—34no—
402C2×D4—34no—
403C2×D4—68no—
404C22×C4—24no—
405C22×C4—32no—
406C22×C4—34no—
407C22×C4—38no—
408C22×C4C22×C3×D311yescharacteristic
409C22×C4C22×C3×D314yes—
410C22×C4C22×C3×D311yescharacteristic
411C22×C4C22×C3×D312yes—
412C22×C4C22×C3×D312yes—
413C4⋊C4—38no—
414C4⋊C4—38no—
415C4⋊C4—38no—
416C4⋊C4—38no—
417C4⋊C4—34no—
418C4⋊C4—34no—
419C4⋊C4C22×C3×D318yes—
420C22⋊C4—34no—
421C22⋊C4—34no—
422C22⋊C4—38no—
423C22⋊C4—38no—
424C22⋊C4—38no—
425C22⋊C4—38no—
426C22⋊C4C22×C3×D314yes—
427C22⋊C4C22×C3×D314yes—
428C42—38no—
429C42C22×C3×D314yes—
430C42C22×C3×D314yes—
431C22×C3—24no—
432C22×C3—22no—
433C22×C3—24no—
434C22×C3—24no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—24no—
438C22×C3—21no—
439C22×C3—44no—
440C22×C3—44no—
441C22×C3—44no—
442C22×C3—48no—
443C22×C3—64no—
444C22×C3—68no—
445C22×C3—244no—
446C22×C3C2×#23514yes—
447C22×C3C2×#23512yes—
448C22×C3C2×C3×#4114yes—
449C22×C3C2×C3×#4112yes—
450C22×C3C24×D311yescharacteristic
451C22×C3C25×C311yescharacteristic
452C2×D3—24no—
453C2×D3—28no—
454C2×D3—84no—
455C3×C4—24no—
456C3×C4—24no—
457C3×C4—22no—
458C3×C4—22no—
459C3×C4—24no—
460C3×C4—24no—
461C3×C4—22no—
462C3×C4—22no—
463C3×C4—24no—
464C3×C4—24no—
465C3×C4—44no—
466C3×C4—44no—
467C3×C4—64no—
468C3×C4—68no—
469Dic3—24no—
470Dic3—28no—
471C32#349111yescharacteristic, complemented, Sylow
472C23—34no—
473C23—42no—
474C23—64no—
475C23—124no—
476C23C3×#23514yes—
477C23C23×C3×D311yescharacteristic
478C23C23×C3×D312yes—
479Q8—124no—
480D4—68no—
481D4—68no—
482D4—124no—
483C2×C4—28no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—34no—
487C2×C4—38no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—64no—
491C2×C4—128no—
492C2×C4—124no—
493C2×C4C23×C3×D314yes—
494C2×C4C23×C3×D312yes—
495C2×C4C23×C3×D314yes—
496C2×C4C23×C3×D312yes—
497C2×C3—24no—
498C2×C3—24no—
499C2×C3—22no—
500C2×C3—24no—
501C2×C3—22no—
502C2×C3—21no—
503C2×C3—22no—
504C2×C3—44no—
505C2×C3—124no—
506C2×C3C22×#23511yescharacteristic
507C2×C3#596412yes—
508C2×C3C22×C3×#4111yescharacteristic
509C2×C3C3×#58512yes—
510D3—44no—
511C22—22no—
512C22—24no—
513C22—44no—
514C22—64no—
515C22—68no—
516C22—244no—
517C22C2×C3×#23514yes—
518C22C2×C3×#23512yes—
519C22C24×C3×D311yescharacteristic
520C4—22no—
521C4—22no—
522C4—24no—
523C4—24no—
524C4—64no—
525C4—68no—
526C3—21no—
527C3#8574511yescharacteristic, direct product factor
528C3C3×#349111yescharacteristic, complemented
529C2—24no—
530C2—22no—
531C2—124no—
532C2C22×C3×#23511yescharacteristic
533C2C3×#596412yes—
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#117C2
socleC22×C32C25
prime radicalC3×#5493C2
hypercenterC2×C3×#117D3
hypocenterC3C3×#3491
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×#117

Complements

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

NH ≅ G/Ntype
1. C2×C32×#117C2semidirect
2. C2×C3×#929C2semidirect
3. C3×#5531C2semidirect
4. C3×#5527C2semidirect
5. C3×#5515C2semidirect
7. C3×#5486C2semidirect
8. C3×#5483C2semidirect
9. C3×#5479C2semidirect
11. #85745C3direct (N × H)
14. C32×#117C22semidirect
15. C2×C32×C4⋊C4C22semidirect
18. C2×C32×C42C22semidirect
22. C3×#929C22semidirect
23. C3×#929C22semidirect
24. C3×C4×#67C22semidirect
25. C2×C3×(C2×D3)⋊C4C22semidirect
26. C3×#924C22semidirect
27. C2×C3×Dic3⋊C4C22semidirect
28. C3×#898C22semidirect
29. C3×#896C22semidirect
30. C3×#894C22semidirect
31. C3×#889C22semidirect
35. C3×D3×C22⋊C4C22semidirect
36. C3×#878C22semidirect
37. C3×#877C22semidirect
38. C3×#876C22semidirect
39. C3×#875C22semidirect
40. C3×C4×D12C22semidirect
41. C3×#872C22semidirect
42. C3×#870C22semidirect
43. C3×C4×Dic6C22semidirect
53. C2×C3×#117D3semidirect
54. C2×C3×#117C2×C3semidirect
55. C2×#929C2×C3semidirect
56. #5531C2×C3semidirect
57. #5527C2×C3semidirect
58. #5515C2×C3semidirect
60. #5486C2×C3semidirect
61. #5483C2×C3semidirect
62. #5479C2×C3semidirect
125. C3×#117C2×D3semidirect
126. C3×#117C22×C3semidirect
129. C2×C3×C4⋊C4C2×D3semidirect
130. C2×C3×C4⋊C4C22×C3semidirect
141. C2×C3×C42C2×D3semidirect
142. C2×C3×C42C22×C3semidirect
146. #929C22×C3semidirect
147. #929C22×C3semidirect
148. C4×#67C22×C3semidirect
149. C2×(C2×D3)⋊C4C22×C3semidirect
150. #924C22×C3semidirect
151. C2×Dic3⋊C4C22×C3semidirect
152. #898C22×C3semidirect
153. #896C22×C3semidirect
154. #894C22×C3semidirect
155. #889C22×C3semidirect
159. D3×C22⋊C4C22×C3semidirect
160. #878C22×C3semidirect
161. #877C22×C3semidirect
162. #876C22×C3semidirect
163. #875C22×C3semidirect
164. C4×D12C22×C3semidirect
165. #872C22×C3semidirect
166. #870C22×C3semidirect
167. C4×Dic6C22×C3semidirect
201. C2×#117C3×D3semidirect
320. #117C2×C3×D3semidirect
322. C2×C4⋊C4C2×C3×D3semidirect
328. C2×C42C2×C3×D3semidirect
471. C32#3491semidirect
527. C3#85745direct (N × H)
528. C3C3×#3491semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1172
C2×C3×#9292
C3×#55312
C3×#55272
C3×#55152
C3×#54932
C3×#54862
C3×#54832
C3×#54792
C3×#34913
#857453