Finite Group Databasebeta

← C3×#86274 #11901935

Subgroups — C3×#86274 #11901935

Order 1152.

2103 conjugacy classes of subgroups.

The subgroup lattice has 539 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#533C211yesmaximal, characteristic, complemented
2C3×#5729C214yesmaximal, complemented
3C3×#5689C214yesmaximal, complemented
4C3×#5634C214yesmaximal
5C3×#5623C214yesmaximal, complemented
6C3×#5578C218yesmaximal, complemented
7C3×D3×#117C212yesmaximal
8C3×#5517C212yesmaximal, complemented
9C2×C3×#872C211yesmaximal, characteristic
10C3×#5470C211yesmaximal, characteristic, complemented
11C3×#3458—31nomaximal
12#86274C311yesmaximal, characteristic, direct product factor
13C22×C3×C4×D3C2211yescharacteristic
14C32×C4⋊Q8C2212yescomplemented
15C32×#125C2212yescomplemented
16C32×C22⋊Q8C2214yes—
17C32×C4×Q8C2214yescomplemented
18C32×#117C2212yes—
19C2×C32×C42C2211yescharacteristic
20C3×#946C2218yes—
21C3×#944C2218yescomplemented
22C2×C3×(C2×D3)⋊C4C2212yes—
23C3×#926C2212yes—
24C3×#924C2214yes—
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C3×#897C2218yes—
28C3×#896C2218yes—
29C3×#896C2218yes—
30C3×#892C2214yes—
31C3×D3×C4⋊C4C2214yes—
32C3×#890C2214yescomplemented
33C3×#889C2218yescomplemented
34C3×#889C2218yescomplemented
35C3×#888C2214yescomplemented
36C3×#888C2218yescomplemented
37C3×D3×C22⋊C4C2214yes—
38C3×#878C2218yes—
39C3×#877C2214yes—
40C3×#872C2214yes—
41C3×#872C2214yes—
42C3×#872C2212yes—
43C3×#872C2212yes—
44C3×C42×D3C2214yes—
45C3×#870C2212yescomplemented
46C3×#869C2212yescomplemented
47C3×C4×Dic6C2218yescomplemented
48C3×C4×Dic6C2214yescomplemented
49C3×#544—34no—
50C3×#544—34no—
51C3×#544—34no—
52C3×#543—34no—
53C3×#533—21no—
54C3×#533—38no—
55C3×#533—32no—
56C3×#533—31no—
57C3×#533D311yescharacteristic, complemented
58C3×#533C2×C311yescharacteristic, complemented
59C2×C3×#117—32no—
60C2×C3×#117—31no—
61#5729C2×C314yescomplemented
62#5689C2×C314yescomplemented
63#5634C2×C314yes—
64#5623C2×C314yescomplemented
65#5578C2×C318yescomplemented
66D3×#117C2×C312yes—
67#5517C2×C312yescomplemented
68C2×#872C2×C311yescharacteristic
69#5470C2×C311yescharacteristic, complemented
70C23×C3×D3C2311yescharacteristic
71C2×C32×Q8C2314yes—
72C22×C32×C4C2312yes—
73C22×C32×C4C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2311yescharacteristic
76C2×C3×C4×D3Q818yescomplemented
77C2×C3×C4×D3C2318yes—
78C2×C3×C4×D3C2312yes—
79C2×C3×C4×D3C2312yes—
80C2×C3×Dic6C2318yes—
81C2×C3×Dic6C2314yes—
82C32×C4⋊C4C2318yes—
83C32×C4⋊C4C2314yes—
84C32×C4⋊C4C2314yes—
85C32×C22⋊C4C2314yes—
86C32×C42C2312yes—
87C32×C42C2311yescharacteristic
88C32×C42C2311yescharacteristic
89C32×C42C2314yes—
90C3×#217C2314yes—
91C3×(C2×D3)⋊C4C2318yes—
92C3×(C2×D3)⋊C4C2314yes—
93C3×(C2×D3)⋊C4C2314yes—
94C3×C4⋊Dic3C2318yes—
95C3×C4⋊Dic3C2314yes—
96C3×C4⋊Dic3C2314yes—
97C3×Dic3⋊C4C2318yes—
98C3×Dic3⋊C4C2318yes—
99C3×Dic3⋊C4C2318yes—
100C3×Dic3⋊C4C2314yes—
101C3×Dic3⋊C4C2314yes—
102C3×Dic3⋊C4C2318yes—
103C3×C4×Dic3C2318yes—
104C3×C4×Dic3C2312yes—
105C3×C4×Dic3C2312yes—
106C3×C4×Dic3C2314yes—
107#3458—31noSylow
108C23×C3×C4—31no—
109C22×C4×D3C22×C311yescharacteristic
110C3×C4⋊Q8—22no—
111C3×C4⋊Q8—38no—
112C3×C4⋊Q8—38no—
113C3×C4⋊Q8—34no—
114C3×C4⋊Q8—32no—
115C3×C4⋊Q8C2×D312yescomplemented
116C3×C4⋊Q8C22×C312yescomplemented
117C3×#125—22no—
118C3×#125—38no—
119C3×#125—38no—
120C3×#125—34no—
121C3×#125—32no—
122C3×#125C2×D312yescomplemented
123C3×#125C22×C312yescomplemented
124C3×C22⋊Q8—24no—
125C3×C22⋊Q8—38no—
126C3×C22⋊Q8—34no—
127C3×C22⋊Q8—38no—
128C3×C22⋊Q8—38no—
129C3×C22⋊Q8—38no—
130C3×C22⋊Q8—38no—
131C3×C22⋊Q8C2×D314yes—
132C3×C22⋊Q8C22×C314yes—
133C3×C4×Q8—24no—
134C3×C4×Q8—38no—
135C3×C4×Q8—34no—
136C3×C4×Q8C2×D314yescomplemented
137C3×C4×Q8C22×C314yescomplemented
138C3×#117—22no—
139C3×#117—32no—
140C3×#117—34no—
141C3×#117—34no—
142C3×#117—34no—
143C3×#117—34no—
144C3×#117—32no—
145C3×#117—32no—
146C3×#117C2×D312yes—
147C3×#117C22×C312yes—
148C2×C3×C4⋊C4—32no—
149C2×C3×C4⋊C4—34no—
150C2×C3×C22⋊C4—32no—
151C2×C3×C22⋊C4—34no—
152C2×C3×C42—21no—
153C2×C3×C42—31no—
154C2×C3×C42—34no—
155C2×C3×C42C2×D311yescharacteristic
156C2×C3×C42C22×C311yescharacteristic
157#946C22×C318yes—
158#944C22×C318yescomplemented
159C2×(C2×D3)⋊C4C22×C312yes—
160#926C22×C312yes—
161#924C22×C314yes—
162C2×Dic3⋊C4C22×C312yes—
163C2×C4×Dic3C22×C311yescharacteristic
164#897C22×C318yes—
165#896C22×C318yes—
166#896C22×C318yes—
167#892C22×C314yes—
168D3×C4⋊C4C22×C314yes—
169#890C22×C314yescomplemented
170#889C22×C318yescomplemented
171#889C22×C318yescomplemented
172#888C22×C314yescomplemented
173#888C22×C318yescomplemented
174D3×C22⋊C4C22×C314yes—
175#878C22×C318yes—
176#877C22×C314yes—
177#872C22×C312yes—
178#872C22×C312yes—
179#872C22×C314yes—
180#872C22×C314yes—
181C42×D3C22×C314yes—
182#870C22×C312yescomplemented
183#869C22×C312yescomplemented
184C4×Dic6C22×C314yescomplemented
185C4×Dic6C22×C318yescomplemented
186C23×C32C2411yescharacteristic
187C22×C3×D3—42no—
188C22×C3×D3C2×Q814yes—
189C22×C3×D3C2412yes—
190C32×Q8—44no—
191C2×C32×C4—42no—
192C2×C32×C4C2×Q814yes—
193C2×C32×C4C2418yes—
194C2×C32×C4C2412yes—
195C2×C32×C4C2412yes—
196C2×C32×C4C2411yescharacteristic
197C2×C32×C4C2411yescharacteristic
198C2×C3×Dic3—42no—
199C2×C3×Dic3C2×Q814yes—
200C2×C3×Dic3C2414yes—
201C2×C3×Dic3C2418yes—
202C2×C3×Dic3C2412yes—
203C3×C4×D3—48no—
204C3×C4×D3C2×Q818yes—
205C3×C4×D3C2×Q818yes—
206C3×Dic6—44no—
207C3×Dic6—48no—
208#544—34no—
209#544—34no—
210#544—34no—
211#543—34no—
212#533—38no—
213#533—32no—
214#533—31no—
215#533C3×D311yescharacteristic, complemented
216C2×#117—32no—
217C2×#117—31no—
218C24×C3—31no—
219C23×D3C23×C311yescharacteristic
220C2×C3×Q8—24no—
221C2×C3×Q8—38no—
222C2×C3×Q8—34no—
223C2×C3×Q8C22×D314yes—
224C2×C3×Q8C23×C314yes—
225C22×C3×C4—21no—
226C22×C3×C4—22no—
227C22×C3×C4—31no—
228C22×C3×C4—38no—
229C22×C3×C4—32no—
230C22×C3×C4—32no—
231C22×C3×C4—32no—
232C22×C3×C4—38no—
233C22×C3×C4C22×D312yes—
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C23×C312yes—
236C22×C3×C4C23×C311yescharacteristic
237C22×Dic3C23×C312yes—
238C22×Dic3C23×C311yescharacteristic
239C2×C4×D3C3×Q818yescomplemented
240C2×C4×D3C23×C318yes—
241C2×C4×D3C23×C312yes—
242C2×C4×D3C23×C312yes—
243C2×Dic6C23×C314yes—
244C2×Dic6C23×C318yes—
245C3×C4⋊C4—24no—
246C3×C4⋊C4—28no—
247C3×C4⋊C4—24no—
248C3×C4⋊C4—38no—
249C3×C4⋊C4—34no—
250C3×C4⋊C4—34no—
251C3×C4⋊C4—38no—
252C3×C4⋊C4—38no—
253C3×C4⋊C4—38no—
254C3×C4⋊C4—34no—
255C3×C4⋊C4—38no—
256C3×C4⋊C4—34no—
257C3×C4⋊C4C22×D314yes—
258C3×C4⋊C4C22×D314yes—
259C3×C4⋊C4C22×D318yes—
260C3×C4⋊C4C23×C318yes—
261C3×C4⋊C4C23×C314yes—
262C3×C4⋊C4C23×C314yes—
263C3×C22⋊C4—24no—
264C3×C22⋊C4—34no—
265C3×C22⋊C4—38no—
266C3×C22⋊C4—34no—
267C3×C22⋊C4—34no—
268C3×C22⋊C4C22×D314yes—
269C3×C22⋊C4C23×C314yes—
270C3×C42—22no—
271C3×C42—21no—
272C3×C42—21no—
273C3×C42—24no—
274C3×C42—38no—
275C3×C42—32no—
276C3×C42—32no—
277C3×C42—34no—
278C3×C42C22×D311yescharacteristic
279C3×C42C22×D311yescharacteristic
280C3×C42C22×D314yes—
281C3×C42C22×D312yes—
282C3×C42C23×C314yes—
283C3×C42C23×C312yes—
284C3×C42C23×C311yescharacteristic
285C3×C42C23×C311yescharacteristic
286#217C23×C314yes—
287(C2×D3)⋊C4C23×C314yes—
288(C2×D3)⋊C4C23×C314yes—
289(C2×D3)⋊C4C23×C318yes—
290C4⋊Dic3C23×C314yes—
291C4⋊Dic3C23×C318yes—
292C4⋊Dic3C23×C314yes—
293Dic3⋊C4C23×C318yes—
294Dic3⋊C4C23×C318yes—
295Dic3⋊C4C23×C318yes—
296Dic3⋊C4C23×C314yes—
297Dic3⋊C4C23×C314yes—
298Dic3⋊C4C23×C318yes—
299C4×Dic3C23×C314yes—
300C4×Dic3C23×C312yes—
301C4×Dic3C23×C318yes—
302C4×Dic3C23×C312yes—
303C22×C32—22no—
304C22×C32C22×Q812yes—
305C22×C32C2511yescharacteristic
306C2×C3×D3—24no—
307C2×C3×D3—44no—
308C2×C3×D3C22×Q814yes—
309C32×C4—22no—
310C32×C4—22no—
311C32×C4—28no—
312C32×C4C22×Q812yes—
313C32×C4C22×Q812yes—
314C3×Dic3—28no—
315C3×Dic3—24no—
316C3×Dic3C22×Q814yes—
317C23×C4—31no—
318C4⋊Q8—38no—
319C4⋊Q8—38no—
320C4⋊Q8—34no—
321C4⋊Q8—32no—
322C4⋊Q8C2×C3×D312yescomplemented
323#125—38no—
324#125—38no—
325#125—34no—
326#125—32no—
327#125C2×C3×D312yescomplemented
328C22⋊Q8—38no—
329C22⋊Q8—34no—
330C22⋊Q8—38no—
331C22⋊Q8—38no—
332C22⋊Q8—38no—
333C22⋊Q8—38no—
334C22⋊Q8C2×C3×D314yes—
335C4×Q8—38no—
336C4×Q8—34no—
337C4×Q8C2×C3×D314yescomplemented
338#117—32no—
339#117—34no—
340#117—34no—
341#117—34no—
342#117—34no—
343#117—32no—
344#117—32no—
345#117C2×C3×D312yes—
346C2×C4⋊C4—32no—
347C2×C4⋊C4—34no—
348C2×C22⋊C4—32no—
349C2×C22⋊C4—34no—
350C2×C42—31no—
351C2×C42—34no—
352C2×C42C2×C3×D311yescharacteristic
353C23×C3—21no—
354C23×C3—32no—
355C23×C3—34no—
356C23×C3—122no—
357C23×C3C23×D311yescharacteristic
358C23×C3C24×C311yescharacteristic
359C22×D3—42no—
360C22×D3C2×C3×Q814yes—
361C22×D3C24×C312yes—
362C3×Q8—44no—
363C3×Q8—44no—
364C3×Q8—48no—
365C3×Q8—124no—
366C3×Q8—128no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—28no—
372C2×C3×C4—24no—
373C2×C3×C4—34no—
374C2×C3×C4—32no—
375C2×C3×C4—38no—
376C2×C3×C4—38no—
377C2×C3×C4—34no—
378C2×C3×C4—38no—
379C2×C3×C4—42no—
380C2×C3×C4—42no—
381C2×C3×C4—44no—
382C2×C3×C4—128no—
383C2×C3×C4—122no—
384C2×C3×C4D3×Q814yes—
385C2×C3×C4C2×C3×Q814yes—
386C2×C3×C4C23×D318yes—
387C2×C3×C4C23×D312yes—
388C2×C3×C4C23×D312yes—
389C2×C3×C4C23×D311yescharacteristic
390C2×C3×C4C23×D311yescharacteristic
391C2×C3×C4C24×C318yes—
392C2×C3×C4C24×C312yes—
393C2×C3×C4C24×C312yes—
394C2×C3×C4C24×C311yescharacteristic
395C2×C3×C4C24×C311yescharacteristic
396C2×Dic3—42no—
397C2×Dic3C2×C3×Q814yes—
398C2×Dic3C24×C314yes—
399C2×Dic3C24×C318yes—
400C2×Dic3C24×C312yes—
401C4×D3—48no—
402C4×D3C2×C3×Q818yes—
403C4×D3C2×C3×Q818yes—
404Dic6—44no—
405Dic6—48no—
406C2×C32—22no—
407C2×C32C23×Q811yescharacteristic
408C2×C32#58512yes—
409C3×D3—24no—
410C24—31no—
411C2×Q8—38no—
412C2×Q8—34no—
413C2×Q8C22×C3×D314yes—
414C22×C4—31no—
415C22×C4—32no—
416C22×C4—32no—
417C22×C4—38no—
418C22×C4—32no—
419C22×C4—38no—
420C22×C4C22×C3×D312yes—
421C22×C4C22×C3×D311yescharacteristic
422C4⋊C4—38no—
423C4⋊C4—34no—
424C4⋊C4—34no—
425C4⋊C4—34no—
426C4⋊C4—38no—
427C4⋊C4—38no—
428C4⋊C4—38no—
429C4⋊C4—38no—
430C4⋊C4—34no—
431C4⋊C4C22×C3×D314yes—
432C4⋊C4C22×C3×D314yes—
433C4⋊C4C22×C3×D318yes—
434C22⋊C4—34no—
435C22⋊C4—38no—
436C22⋊C4—34no—
437C22⋊C4—34no—
438C22⋊C4C22×C3×D314yes—
439C42—32no—
440C42—34no—
441C42—38no—
442C42—32no—
443C42C22×C3×D314yes—
444C42C22×C3×D312yes—
445C42C22×C3×D311yescharacteristic
446C42C22×C3×D311yescharacteristic
447C22×C3—22no—
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—21no—
451C22×C3—34no—
452C22×C3—42no—
453C22×C3—64no—
454C22×C3—124no—
455C22×C3C2×D3×Q812yes—
456C22×C3C22×C3×Q812yes—
457C22×C3C24×D311yescharacteristic
458C22×C3C25×C311yescharacteristic
459C2×D3—24no—
460C2×D3—44no—
461C2×D3C22×C3×Q814yes—
462C3×C4—24no—
463C3×C4—22no—
464C3×C4—22no—
465C3×C4—28no—
466C3×C4—22no—
467C3×C4—28no—
468C3×C4—22no—
469C3×C4—22no—
470C3×C4—22no—
471C3×C4—34no—
472C3×C4—42no—
473C3×C4—48no—
474C3×C4—68no—
475C3×C4—64no—
476C3×C4C2×D3×Q812yes—
477C3×C4C2×D3×Q812yes—
478C3×C4C22×C3×Q812yes—
479C3×C4C22×C3×Q812yes—
480Dic3—28no—
481Dic3—24no—
482Dic3C22×C3×Q814yes—
483C32#345811yescharacteristic, complemented, Sylow
484C23—32no—
485C23—34no—
486C23—122no—
487C23C23×C3×D311yescharacteristic
488Q8—44no—
489Q8—124no—
490Q8—128no—
491C2×C4—34no—
492C2×C4—32no—
493C2×C4—38no—
494C2×C4—38no—
495C2×C4—38no—
496C2×C4—34no—
497C2×C4—42no—
498C2×C4—128no—
499C2×C4—122no—
500C2×C4C3×D3×Q814yes—
501C2×C4C23×C3×D318yes—
502C2×C4C23×C3×D312yes—
503C2×C4C23×C3×D312yes—
504C2×C4C23×C3×D311yescharacteristic
505C2×C4C23×C3×D311yescharacteristic
506C2×C3—22no—
507C2×C3—22no—
508C2×C3—21no—
509C2×C3—22no—
510C2×C3—42no—
511C2×C3—64no—
512C2×C3C22×D3×Q811yescharacteristic
513C2×C3#596412yes—
514C2×C3C23×C3×Q811yescharacteristic
515C2×C3C3×#58512yes—
516D3—24no—
517C22—22no—
518C22—34no—
519C22—64no—
520C22—124no—
521C22C2×C3×D3×Q812yes—
522C22C24×C3×D311yescharacteristic
523C4—22no—
524C4—22no—
525C4—28no—
526C4—34no—
527C4—68no—
528C4—64no—
529C4C2×C3×D3×Q812yes—
530C4C2×C3×D3×Q812yes—
531C3—21no—
532C3#8627411yescharacteristic, direct product factor
533C3C3×#345811yescharacteristic, complemented
534C2—22no—
535C2—64no—
536C2C22×C3×D3×Q811yescharacteristic
537C2C3×#596412yes—
subgroupG/H
centerC2×C3×C4C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#533C2
socleC22×C32C25
prime radicalC23×C3×D3C23
hypercenterC3×#533D3
hypocenterC3C3×#3458
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×#533

Complements

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

NH ≅ G/Ntype
1. C32×#533C2semidirect
2. C3×#5729C2semidirect
3. C3×#5689C2semidirect
5. C3×#5623C2semidirect
6. C3×#5578C2semidirect
8. C3×#5517C2semidirect
10. C3×#5470C2semidirect
12. #86274C3direct (N × H)
14. C32×C4⋊Q8C22semidirect
15. C32×#125C22semidirect
17. C32×C4×Q8C22semidirect
21. C3×#944C22semidirect
32. C3×#890C22semidirect
33. C3×#889C22semidirect
34. C3×#889C22semidirect
35. C3×#888C22semidirect
36. C3×#888C22semidirect
45. C3×#870C22semidirect
46. C3×#869C22semidirect
47. C3×C4×Dic6C22semidirect
48. C3×C4×Dic6C22semidirect
57. C3×#533D3semidirect
58. C3×#533C2×C3semidirect
61. #5729C2×C3semidirect
62. #5689C2×C3semidirect
64. #5623C2×C3semidirect
65. #5578C2×C3semidirect
67. #5517C2×C3semidirect
69. #5470C2×C3semidirect
76. C2×C3×C4×D3Q8semidirect
115. C3×C4⋊Q8C2×D3semidirect
116. C3×C4⋊Q8C22×C3semidirect
122. C3×#125C2×D3semidirect
123. C3×#125C22×C3semidirect
136. C3×C4×Q8C2×D3semidirect
137. C3×C4×Q8C22×C3semidirect
158. #944C22×C3semidirect
169. #890C22×C3semidirect
170. #889C22×C3semidirect
171. #889C22×C3semidirect
172. #888C22×C3semidirect
173. #888C22×C3semidirect
182. #870C22×C3semidirect
183. #869C22×C3semidirect
184. C4×Dic6C22×C3semidirect
185. C4×Dic6C22×C3semidirect
215. #533C3×D3semidirect
239. C2×C4×D3C3×Q8semidirect
322. C4⋊Q8C2×C3×D3semidirect
327. #125C2×C3×D3semidirect
337. C4×Q8C2×C3×D3semidirect
483. C32#3458semidirect
532. C3#86274direct (N × H)
533. C3C3×#3458semidirect

Maximal subgroups

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

subgroupindex
C32×#5332
C3×#57292
C3×#56892
C3×#56342
C3×#56232
C3×#55782
C3×D3×#1172
C3×#55172
C2×C3×#8722
C3×#54702
C3×#34583
#862743