Finite Group Databasebeta

← C3×#74059 #11805069

Subgroups — C3×#74059 #11805069

Order 1152.

1173 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#926C211yesmaximal, characteristic
2C32×#381C211yesmaximal, characteristic
3C2×C3×C3⋊#95C211yesmaximal, characteristic
4C3×#4946C212yesmaximal
5C3×Dic3×C22⋊C4C212yesmaximal
6C3×#4654C212yesmaximal, complemented
7C3×#4653C212yesmaximal, complemented
8C3×#4651C211yesmaximal, characteristic, complemented
9C3×#4650C211yesmaximal, characteristic, complemented
10C3×#4649C211yesmaximal, characteristic, complemented
11C3×#4648C211yesmaximal, characteristic, complemented
12C3×#2343—31nomaximal
13#74059C311yesmaximal, characteristic, direct product factor
14C23×C32×C4C2211yescharacteristic
15C23×C3×Dic3C2212yes—
16C2×C32×C22⋊C4C2212yes—
17C2×C3×#217C2211yescharacteristic
18C2×C3×#217C2211yescharacteristic
19C3×#926C418yescomplemented
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×Dic3⋊C4C2212yes—
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×C4×Dic3C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C32×#95C2211yescharacteristic
29C32×#95C2211yescharacteristic
30C32×#95C2212yes—
31C3×C3⋊#95C2211yescharacteristic
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C2×C3×#117—31no—
39C2×#926C2×C311yescharacteristic
40C3×#387—32no—
41C3×#387—32no—
42C3×#385—32no—
43C3×#383—31no—
44C3×#382—31no—
45C3×#381—21no—
46C3×#381D311yescharacteristic
47C3×#381C2×C311yescharacteristic
48C3×C4×C4⋊C4—31no—
49C3×C4×C22⋊C4—32no—
50C3×#376—31no—
51C2×C3×#95—31no—
52C2×C3⋊#95C2×C311yescharacteristic
53#4946C2×C312yes—
54Dic3×C22⋊C4C2×C312yes—
55#4654C2×C312yescomplemented
56#4653C2×C312yescomplemented
57#4651C2×C311yescharacteristic, complemented
58#4650C2×C311yescharacteristic, complemented
59#4649C2×C311yescharacteristic, complemented
60#4648C2×C311yescharacteristic, complemented
61C24×C32C2311yescharacteristic
62C22×C32×C4—24no—
63C22×C32×C4C2×C414yes—
64C22×C32×C4C2312yes—
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3×Dic3—24no—
69C22×C3×Dic3—24no—
70C22×C3×Dic3—42no—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2312yes—
77C32×C22⋊C4—24no—
78C3×#217C2×C414yes—
79C3×#217C2×C414yes—
80C3×C4⋊Dic3C2×C414yescomplemented
81C3×C4⋊Dic3C2×C414yescomplemented
82C3×Dic3⋊C4—24no—
83C3×Dic3⋊C4—42no—
84C3×C4×Dic3—24no—
85C3×C4×Dic3—42no—
86C3×C4×Dic3C2×C414yescomplemented
87C3×C4×Dic3C2×C414yescomplemented
88#2343—31noSylow
89C23×C3×C4—21no—
90C23×C3×C4—32no—
91C23×C3×C4C2×D311yescharacteristic
92C23×C3×C4C22×C311yescharacteristic
93C23×Dic3C22×C312yes—
94C3×#117—38no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—32no—
98C2×C3×C4⋊C4—32no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—31no—
101C2×C3×C22⋊C4—31no—
102C2×C3×C22⋊C4C2×D312yes—
103C2×C3×C22⋊C4C22×C312yes—
104C2×C3×C42—31no—
105C2×C3×C42—31no—
106C2×C3×C42—32no—
107C2×C3×C42—32no—
108C2×#217C22×C311yescharacteristic
109C2×#217C22×C311yescharacteristic
110#926C3×C418yescomplemented
111C2×C4⋊Dic3C22×C311yescharacteristic
112C2×C4⋊Dic3C22×C311yescharacteristic
113C2×Dic3⋊C4C22×C312yes—
114C2×Dic3⋊C4C22×C312yes—
115C2×C4×Dic3C22×C312yes—
116C2×C4×Dic3C22×C312yes—
117C2×C4×Dic3C22×C311yescharacteristic
118C2×C4×Dic3C22×C311yescharacteristic
119C3×#95—21no—
120C3×#95—21no—
121C3×#95—22no—
122C3×#95—31no—
123C3×#95—31no—
124C3×#95—32no—
125C3×#95—32no—
126C3×#95—32no—
127C3×#95—32no—
128C3×#95—32no—
129C3×#95C2×D311yescharacteristic
130C3×#95C2×D311yescharacteristic
131C3×#95C2×D312yes—
132C3×#95C22×C311yescharacteristic
133C3×#95C22×C311yescharacteristic
134C3×#95C22×C312yes—
135C3⋊#95C22×C311yescharacteristic
136C3⋊#95C22×C312yes—
137C3⋊#95C22×C311yescharacteristic
138C3⋊#95C22×C312yes—
139C3⋊#95C22×C312yes—
140C3⋊#95C22×C312yes—
141C3⋊#95C22×C312yes—
142C23×C32—22no—
143C23×C32—21no—
144C23×C32—21no—
145C23×C32C22×C412yes—
146C23×C32#4114yes—
147C23×C32C2411yescharacteristic
148C2×C32×C4—28no—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4—22no—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4C22×C412yes—
158C2×C32×C4C22×C412yes—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—48no—
171C2×C3×Dic3C22×C412yes—
172C2×C3×Dic3C22×C412yes—
173C2×C3×Dic3C22×C412yes—
174C2×C3×Dic3C22×C412yes—
175C2×C3×Dic3#4114yes—
176C2×#117—31no—
177#387—32no—
178#387—32no—
179#385—32no—
180#383—31no—
181#382—31no—
182#381C3×D311yescharacteristic
183C4×C4⋊C4—31no—
184C4×C22⋊C4—32no—
185#376—31no—
186C2×#95—31no—
187C24×C3—21no—
188C24×C3C22×D311yescharacteristic
189C24×C3C23×C311yescharacteristic
190C22×C3×C4—24no—
191C22×C3×C4—24no—
192C22×C3×C4—24no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—32no—
198C22×C3×C4—31no—
199C22×C3×C4—31no—
200C22×C3×C4—31no—
201C22×C3×C4—31no—
202C22×C3×C4—32no—
203C22×C3×C4—44no—
204C22×C3×C4—64no—
205C22×C3×C4—64no—
206C22×C3×C4—122no—
207C22×C3×C4C4×D314yes—
208C22×C3×C4C2×C3×C414yes—
209C22×C3×C4C22×D312yes—
210C22×C3×C4C22×D312yes—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C23×C312yes—
214C22×C3×C4C23×C312yes—
215C22×C3×C4C23×C311yescharacteristic
216C22×C3×C4C23×C311yescharacteristic
217C22×Dic3—24no—
218C22×Dic3—24no—
219C22×Dic3—42no—
220C22×Dic3C23×C312yes—
221C22×Dic3C23×C311yescharacteristic
222C22×Dic3C23×C311yescharacteristic
223C22×Dic3C23×C311yescharacteristic
224C22×Dic3C23×C311yescharacteristic
225C22×Dic3C23×C312yes—
226C3×C4⋊C4—34no—
227C3×C4⋊C4—34no—
228C3×C4⋊C4—64no—
229C3×C4⋊C4—122no—
230C3×C22⋊C4—24no—
231C3×C22⋊C4—24no—
232C3×C22⋊C4—34no—
233C3×C22⋊C4—34no—
234C3×C22⋊C4—44no—
235C3×C42—34no—
236C3×C42—34no—
237C3×C42—64no—
238C3×C42—122no—
239#217C2×C3×C414yes—
240#217C2×C3×C414yes—
241C4⋊Dic3C2×C3×C414yescomplemented
242C4⋊Dic3C2×C3×C414yescomplemented
243Dic3⋊C4—24no—
244Dic3⋊C4—42no—
245C4×Dic3—24no—
246C4×Dic3—42no—
247C4×Dic3C2×C3×C414yescomplemented
248C4×Dic3C2×C3×C414yescomplemented
249C22×C32—22no—
250C22×C32—22no—
251C22×C32—24no—
252C22×C32—24no—
253C22×C32#11714yes—
254C22×C32C23×C411yescharacteristic
255C22×C32C2×#4112yes—
256C22×C32C2×#4112yes—
257C22×C32H(5,𝔽2)11yescharacteristic
258C22×C322−1+411yescharacteristic
259C32×C4—22no—
260C32×C4—22no—
261C32×C4—42no—
262C32×C4—42no—
263C3×Dic3—22no—
264C3×Dic3—22no—
265C3×Dic3—22no—
266C3×Dic3—22no—
267C3×Dic3—24no—
268C3×Dic3—42no—
269C23×C4—32no—
270C23×C4C2×C3×D311yescharacteristic
271#117—38no—
272C2×C4⋊C4—31no—
273C2×C4⋊C4—31no—
274C2×C4⋊C4—32no—
275C2×C4⋊C4—32no—
276C2×C22⋊C4—31no—
277C2×C22⋊C4—31no—
278C2×C22⋊C4C2×C3×D312yes—
279C2×C42—31no—
280C2×C42—31no—
281C2×C42—32no—
282C2×C42—32no—
283#95—31no—
284#95—31no—
285#95—32no—
286#95—32no—
287#95—32no—
288#95—32no—
289#95—32no—
290#95C2×C3×D311yescharacteristic
291#95C2×C3×D311yescharacteristic
292#95C2×C3×D312yes—
293C23×C3—22no—
294C23×C3—21no—
295C23×C3—21no—
296C23×C3—22no—
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—22no—
301C23×C3—24no—
302C23×C3—42no—
303C23×C3—41no—
304C23×C3—41no—
305C23×C3C2×C4×D312yes—
306C23×C3#23714yes—
307C23×C3C22×C3×C412yes—
308C23×C3C3×#4114yes—
309C23×C3C23×D311yescharacteristic
310C23×C3C24×C311yescharacteristic
311C2×C3×C4—28no—
312C2×C3×C4—28no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—32no—
332C2×C3×C4—32no—
333C2×C3×C4—32no—
334C2×C3×C4—32no—
335C2×C3×C4—34no—
336C2×C3×C4—48no—
337C2×C3×C4—42no—
338C2×C3×C4—42no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—61no—
349C2×C3×C4—62no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—128no—
357C2×C3×C4C2×C4×D312yes—
358C2×C3×C4C2×C4×D312yes—
359C2×C3×C4C22×C3×C412yes—
360C2×C3×C4C22×C3×C412yes—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—21no—
365C2×Dic3—22no—
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—48no—
373C2×Dic3C22×C3×C412yes—
374C2×Dic3C22×C3×C412yes—
375C2×Dic3C22×C3×C412yes—
376C2×Dic3C22×C3×C412yes—
377C2×Dic3C3×#4114yes—
378C2×C32—24no—
379C2×C32C2×#11711yescharacteristic
380C2×C32C4×#4111yescharacteristic
381C2×C32#52011yescharacteristic
382C2×C32#55112yes—
383C2×C32#55212yes—
384C24C22×C3×D311yescharacteristic
385C22×C4—24no—
386C22×C4—32no—
387C22×C4—31no—
388C22×C4—31no—
389C22×C4—31no—
390C22×C4—31no—
391C22×C4—32no—
392C22×C4—64no—
393C22×C4—64no—
394C22×C4—122no—
395C22×C4C3×C4×D314yes—
396C22×C4C22×C3×D312yes—
397C22×C4C22×C3×D312yes—
398C22×C4C22×C3×D311yescharacteristic
399C22×C4C22×C3×D311yescharacteristic
400C4⋊C4—34no—
401C4⋊C4—34no—
402C4⋊C4—64no—
403C4⋊C4—122no—
404C22⋊C4—24no—
405C22⋊C4—34no—
406C22⋊C4—34no—
407C42—34no—
408C42—34no—
409C42—64no—
410C42—122no—
411C22×C3—24no—
412C22×C3—24no—
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—22no—
417C22×C3—24no—
418C22×C3—24no—
419C22×C3—24no—
420C22×C3—21no—
421C22×C3—22no—
422C22×C3—22no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—42no—
426C22×C3—42no—
427C22×C3—44no—
428C22×C3—44no—
429C22×C3#87714yes—
430C22×C3C3×#11714yes—
431C22×C3C22×C4×D311yescharacteristic
432C22×C3C2×#23712yes—
433C22×C3D3×#4112yes—
434C22×C3#100911yescharacteristic
435C22×C3#101011yescharacteristic
436C22×C3C23×C3×C411yescharacteristic
437C22×C3C2×C3×#4112yes—
438C22×C3C2×C3×#4112yes—
439C22×C3C3×H(5,𝔽2)11yescharacteristic
440C22×C3C3×2−1+411yescharacteristic
441C3×C4—22no—
442C3×C4—22no—
443C3×C4—22no—
444C3×C4—22no—
445C3×C4—42no—
446C3×C4—42no—
447C3×C4—42no—
448C3×C4—42no—
449C3×C4—42no—
450C3×C4—42no—
451C3×C4—64no—
452C3×C4—62no—
453C3×C4—62no—
454C3×C4—62no—
455C3×C4—62no—
456C3×C4—82no—
457C3×C4—82no—
458C3×C4—122no—
459Dic3—22no—
460Dic3—22no—
461Dic3—22no—
462Dic3—22no—
463Dic3—24no—
464Dic3—42no—
465C32#234311yescharacteristic, complemented, Sylow
466C23—22no—
467C23—21no—
468C23—21no—
469C23C2×C3×C4×D312yes—
470C23C3×#23714yes—
471C23C23×C3×D311yescharacteristic
472C2×C4—28no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—32no—
482C2×C4—32no—
483C2×C4—32no—
484C2×C4—32no—
485C2×C4—34no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—61no—
490C2×C4—62no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—61no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—128no—
498C2×C4C2×C3×C4×D312yes—
499C2×C4C2×C3×C4×D312yes—
500C2×C3—24no—
501C2×C3—24no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—22no—
505C2×C3—22no—
506C2×C3—21no—
507C2×C3—44no—
508C2×C3C2×#87711yescharacteristic
509C2×C3#552211yescharacteristic
510C2×C3#552311yescharacteristic
511C2×C3#565012yes—
512C2×C3#565812yes—
513C2×C3C2×C3×#11711yescharacteristic
514C2×C3C3×C4×#4111yescharacteristic
515C2×C3C3×#52011yescharacteristic
516C2×C3C3×#55112yes—
517C2×C3C3×#55212yes—
518C22—22no—
519C22—22no—
520C22—24no—
521C22—24no—
522C22C3×#87714yes—
523C22C22×C3×C4×D311yescharacteristic
524C22C2×C3×#23712yes—
525C22C3×D3×#4112yes—
526C22C3×#100911yescharacteristic
527C22C3×#101011yescharacteristic
528C4—22no—
529C4—22no—
530C4—42no—
531C4—42no—
532C4—62no—
533C4—62no—
534C4—62no—
535C4—62no—
536C4—64no—
537C4—122no—
538C3—21no—
539C3#7405911yescharacteristic, direct product factor
540C3C3×#234311yescharacteristic, complemented
541C2—24no—
542C2C2×C3×#87711yescharacteristic
543C2C3×#552211yescharacteristic
544C2C3×#552311yescharacteristic
545C2C3×#565012yes—
546C2C3×#565812yes—
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#381C2
socleC23×C32C24
prime radicalC24×C32C23
cosocleC23×C3C24×C3
hypercenterC3×#381D3
hypocenterC3C3×#2343
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#381

Complements

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

NH ≅ G/Ntype
6. C3×#4654C2semidirect
7. C3×#4653C2semidirect
8. C3×#4651C2semidirect
9. C3×#4650C2semidirect
10. C3×#4649C2semidirect
11. C3×#4648C2semidirect
13. #74059C3direct (N × H)
19. C3×#926C4semidirect
55. #4654C2×C3semidirect
56. #4653C2×C3semidirect
57. #4651C2×C3semidirect
58. #4650C2×C3semidirect
59. #4649C2×C3semidirect
60. #4648C2×C3semidirect
80. C3×C4⋊Dic3C2×C4semidirect
81. C3×C4⋊Dic3C2×C4semidirect
86. C3×C4×Dic3C2×C4semidirect
87. C3×C4×Dic3C2×C4semidirect
110. #926C3×C4semidirect
241. C4⋊Dic3C2×C3×C4semidirect
242. C4⋊Dic3C2×C3×C4semidirect
247. C4×Dic3C2×C3×C4semidirect
248. C4×Dic3C2×C3×C4semidirect
465. C32#2343semidirect
539. C3#74059direct (N × H)
540. C3C3×#2343semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9262
C32×#3812
C2×C3×C3⋊#952
C3×#49462
C3×Dic3×C22⋊C42
C3×#46542
C3×#46532
C3×#46512
C3×#46502
C3×#46492
C3×#46482
C3×#23433
#740593