Finite Group Databasebeta

← C3×#80480 #11878885

Subgroups — C3×#80480 #11878885

Order 1152.

822 conjugacy classes of subgroups.

The subgroup lattice has 583 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C4⋊Q8C211yesmaximal, characteristic
2C3×#5578C211yesmaximal, characteristic
3C32×#462C211yesmaximal, characteristic, complemented
4C3×#5186C212yesmaximal
5C3×#5183C212yesmaximal, complemented
6C3×#5090C211yesmaximal, characteristic, complemented
7C3×#5031C211yesmaximal, characteristic, complemented
8C3×#4849C211yesmaximal, characteristic, complemented
9C3×#4833C211yesmaximal, characteristic
10C3×#4809C212yesmaximal
11C3×#4792C212yesmaximal, complemented
12C3×#3209—31nomaximal
13#80480C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8C2212yes—
15C2×C32×Q16C2212yes—
16C32×C4⋊Q8C2211yescharacteristic
17C32×C4×Q8C2211yescharacteristic
18C3×#946C2211yescharacteristic
19C3×#944C2211yescharacteristic
20C3×#944C2212yes—
21C2×C3×#216C2212yes—
22C2×C3×#216C2212yes—
23C2×C3×Dic12C2212yes—
24C3×#897C2211yescharacteristic
25C3×#896—21no—
26C3×D3×C4⋊C4—21no—
27C3×D3×C4⋊C4—21no—
28C3×#889—21no—
29C3×#888—21no—
30C3×#888—21no—
31C3×#888C2211yescharacteristic
32C3×#872—21no—
33C3×C42×D3C2211yescharacteristic
34C3×#869C2211yescharacteristic
35C3×C4×Dic6—21no—
36C3×C4×Dic6C2211yescharacteristic
37C32×C4⋊C8C2211yescharacteristic
38C32×#103C2212yes—
39C3×#835C2212yes—
40C3×(C2×D3)⋊C8C2212yes—
41C3×#816C2212yes—
42C3×C8×Dic3C2212yes—
43C3×#810C2212yes—
44C3×C4⋊(C3⋊C8)C2211yescharacteristic
45C3×#533—31no—
46C2×C3×C4⋊Q8—31no—
47D3×C4⋊Q8C2×C311yescharacteristic
48#5578C2×C311yescharacteristic
49C3×#494—32no—
50C3×#487—32no—
51C3×#462—21no—
52C3×#462—31no—
53C3×#462—31no—
54C3×#462—31no—
55C3×#462D311yescharacteristic, complemented
56C3×#462C2×C311yescharacteristic, complemented
57C3×#451—32no—
58C3×#451—32no—
59C3×#431—31no—
60#5186C2×C312yes—
61#5183C2×C312yescomplemented
62#5090C2×C311yescharacteristic, complemented
63#5031C2×C311yescharacteristic, complemented
64#4849C2×C311yescharacteristic, complemented
65#4833C2×C311yescharacteristic
66#4809C2×C312yes—
67#4792C2×C312yescomplemented
68C2×C32×Q8C2311yescharacteristic
69C2×C32×Q8C2312yes—
70C3×D3×Q8—42no—
71C3×D3×Q8—42no—
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3D411yescharacteristic
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3C2311yescharacteristic
76C2×C3×Dic6—22no—
77C2×C3×Dic6—21no—
78C2×C3×Dic6C2311yescharacteristic
79C2×C3×Dic6C2312yes—
80C32×Q16—42no—
81C2×C32×C8C2312yes—
82C32×C4⋊C4—21no—
83C32×C4⋊C4—21no—
84C32×C4⋊C4—21no—
85C32×C4⋊C4C2311yescharacteristic
86C32×C42—21no—
87C32×C42C2311yescharacteristic
88C3×#216—42no—
89C3×#216—42no—
90C3×(C2×D3)⋊C4—21no—
91C3×(C2×D3)⋊C4—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×Dic3⋊C4—21no—
97C3×Dic3⋊C4—22no—
98C3×Dic3⋊C4—22no—
99C3×Dic3⋊C4—21no—
100C3×Dic3⋊C4—21no—
101C3×Dic3⋊C4—21no—
102C3×Dic3⋊C4—21no—
103C3×C4×Dic3—21no—
104C3×C4×Dic3D411yescharacteristic
105C3×C4×Dic3D411yescharacteristic
106C3×C4×Dic3C2311yescharacteristic
107C2×C3×C3⋊C8C2312yes—
108C3×Dic12—42no—
109#3209—31noSylow
110C22×C3×Q8—32no—
111C2×D3×Q8C22×C312yes—
112C2×C3×Q16—22no—
113C2×C3×Q16—32no—
114C2×C3×Q16—32no—
115C2×C3×Q16—32no—
116C2×C3×Q16C2×D312yes—
117C2×C3×Q16C22×C312yes—
118C3×C4⋊Q8—21no—
119C3×C4⋊Q8—31no—
120C3×C4⋊Q8—32no—
121C3×C4⋊Q8—31no—
122C3×C4⋊Q8—31no—
123C3×C4⋊Q8—61no—
124C3×C4⋊Q8—61no—
125C3×C4⋊Q8C2×D311yescharacteristic
126C3×C4⋊Q8C22×C311yescharacteristic
127C3×#125—61no—
128C3×C22⋊Q8—31no—
129C3×C22⋊Q8—31no—
130C3×C22⋊Q8—61no—
131C3×C4×Q8—21no—
132C3×C4×Q8—31no—
133C3×C4×Q8—61no—
134C3×C4×Q8C2×D311yescharacteristic
135C3×C4×Q8C22×C311yescharacteristic
136C3×#117—61no—
137C2×C3×C4⋊C4—61no—
138C2×C3×C4⋊C4—61no—
139C2×C3×C42—31no—
140#946C22×C311yescharacteristic
141#944C22×C311yescharacteristic
142#944C22×C312yes—
143C2×#216C22×C312yes—
144C2×#216C22×C312yes—
145C2×Dic12C22×C312yes—
146#897C22×C311yescharacteristic
147#896—21no—
148D3×C4⋊C4—21no—
149D3×C4⋊C4—21no—
150#889—21no—
151#888—21no—
152#888—21no—
153#888C22×C311yescharacteristic
154#872—21no—
155C42×D3C22×C311yescharacteristic
156#869C22×C311yescharacteristic
157C4×Dic6—21no—
158C4×Dic6C22×C311yescharacteristic
159C3×C4⋊C8—21no—
160C3×C4⋊C8—31no—
161C3×C4⋊C8C2×D311yescharacteristic
162C3×C4⋊C8C22×C311yescharacteristic
163C3×#103—22no—
164C3×#103—32no—
165C3×#103—32no—
166C3×#103—32no—
167C3×#103C2×D312yes—
168C3×#103C22×C312yes—
169C3×C22⋊C8—32no—
170C3×C4×C8—32no—
171#835C22×C312yes—
172(C2×D3)⋊C8C22×C312yes—
173#816C22×C312yes—
174C8×Dic3C22×C312yes—
175#810C22×C312yes—
176C4⋊(C3⋊C8)C22×C311yescharacteristic
177C22×C3×D3C2×D411yescharacteristic
178C32×Q8—21no—
179C32×Q8—21no—
180C32×Q8—22no—
181C32×Q8—22no—
182C2×C32×C4—21no—
183C2×C32×C4—22no—
184C2×C32×C4—21no—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2411yescharacteristic
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3C2×D411yescharacteristic
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C3×C4×D3—21no—
195C3×C4×D3—21no—
196C3×C4×D3—22no—
197C3×C4×D3—44no—
198C3×C4×D3Q1614yescomplemented
199C3×Dic6—21no—
200C3×Dic6—22no—
201C3×Dic6—21no—
202C3×Dic6—22no—
203C3×Dic6—44no—
204C3×Dic6—42no—
205C32×C8—22no—
206C3×C3⋊C8—22no—
207#533—31no—
208C2×C4⋊Q8—31no—
209#494—32no—
210#487—32no—
211#462—31no—
212#462—31no—
213#462—31no—
214#462C3×D311yescharacteristic, complemented
215#451—32no—
216#451—32no—
217#431—31no—
218C2×C3×Q8—21no—
219C2×C3×Q8—22no—
220C2×C3×Q8—32no—
221C2×C3×Q8—31no—
222C2×C3×Q8—61no—
223C2×C3×Q8—62no—
224C2×C3×Q8—122no—
225C2×C3×Q8—122no—
226C2×C3×Q8C22×D312yes—
227C2×C3×Q8C22×D311yescharacteristic
228C2×C3×Q8C23×C312yes—
229C2×C3×Q8C23×C311yescharacteristic
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—31no—
233C22×C3×C4—62no—
234D3×Q8—42no—
235D3×Q8—42no—
236C2×C4×D3—22no—
237C2×C4×D3C3×D411yescharacteristic
238C2×C4×D3C3×D411yescharacteristic
239C2×C4×D3C23×C311yescharacteristic
240C2×Dic6—21no—
241C2×Dic6—22no—
242C2×Dic6C23×C312yes—
243C2×Dic6C23×C311yescharacteristic
244C3×Q16—42no—
245C3×Q16—42no—
246C3×Q16—44no—
247C3×Q16—122no—
248C3×Q16—122no—
249C3×Q16—122no—
250C2×C3×C8—22no—
251C2×C3×C8—32no—
252C2×C3×C8C22×D312yes—
253C2×C3×C8C23×C312yes—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—31no—
262C3×C4⋊C4—41no—
263C3×C4⋊C4—41no—
264C3×C4⋊C4—41no—
265C3×C4⋊C4—62no—
266C3×C4⋊C4—62no—
267C3×C4⋊C4—61no—
268C3×C4⋊C4—61no—
269C3×C4⋊C4—61no—
270C3×C4⋊C4—61no—
271C3×C4⋊C4—61no—
272C3×C4⋊C4—61no—
273C3×C4⋊C4—61no—
274C3×C4⋊C4—61no—
275C3×C4⋊C4C22×D311yescharacteristic
276C3×C4⋊C4C23×C311yescharacteristic
277C3×C22⋊C4—61no—
278C3×C22⋊C4—61no—
279C3×C42—21no—
280C3×C42—21no—
281C3×C42—21no—
282C3×C42—31no—
283C3×C42—31no—
284C3×C42—31no—
285C3×C42—41no—
286C3×C42—61no—
287C3×C42C22×D311yescharacteristic
288C3×C42C23×C311yescharacteristic
289#216—42no—
290#216—42no—
291(C2×D3)⋊C4—21no—
292(C2×D3)⋊C4—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3C23×C311yescharacteristic
297Dic3⋊C4—21no—
298Dic3⋊C4—21no—
299Dic3⋊C4—21no—
300Dic3⋊C4—21no—
301Dic3⋊C4—21no—
302Dic3⋊C4—22no—
303Dic3⋊C4—22no—
304C4×Dic3—21no—
305C4×Dic3C3×D411yescharacteristic
306C4×Dic3C3×D411yescharacteristic
307C4×Dic3C23×C311yescharacteristic
308C2×C3⋊C8C23×C312yes—
309Dic12—42no—
310C22×C32C22×D411yescharacteristic
311C2×C3×D3—21no—
312C2×C3×D3—21no—
313C2×C3×D3C2×Q1612yes—
314C32×C4—21no—
315C32×C4—41no—
316C32×C4—42no—
317C32×C4—41no—
318C32×C4C2×Q1612yes—
319C32×C4H(5,𝔽2)11yescharacteristic
320C32×C4H(5,𝔽2)11yescharacteristic
321C3×Dic3—21no—
322C3×Dic3—42no—
323C3×Dic3—41no—
324C3×Dic3—41no—
325C3×Dic3C2×Q1612yes—
326C3×Dic3#13712yes—
327C22×Q8—32no—
328C2×Q16—32no—
329C2×Q16—32no—
330C2×Q16—32no—
331C2×Q16C2×C3×D312yes—
332C4⋊Q8—31no—
333C4⋊Q8—32no—
334C4⋊Q8—31no—
335C4⋊Q8—31no—
336C4⋊Q8—61no—
337C4⋊Q8—61no—
338C4⋊Q8C2×C3×D311yescharacteristic
339#125—61no—
340C22⋊Q8—31no—
341C22⋊Q8—31no—
342C22⋊Q8—61no—
343C4×Q8—31no—
344C4×Q8—61no—
345C4×Q8C2×C3×D311yescharacteristic
346#117—61no—
347C2×C4⋊C4—61no—
348C2×C4⋊C4—61no—
349C2×C42—31no—
350C4⋊C8—31no—
351C4⋊C8C2×C3×D311yescharacteristic
352#103—32no—
353#103—32no—
354#103—32no—
355#103C2×C3×D312yes—
356C22⋊C8—32no—
357C4×C8—32no—
358C23×C3—31no—
359C22×D3C2×C3×D411yescharacteristic
360C3×Q8—22no—
361C3×Q8—21no—
362C3×Q8—22no—
363C3×Q8—21no—
364C3×Q8—22no—
365C3×Q8—21no—
366C3×Q8—22no—
367C3×Q8—21no—
368C3×Q8—22no—
369C3×Q8—41no—
370C3×Q8—42no—
371C3×Q8—42no—
372C3×Q8—61no—
373C3×Q8—62no—
374C3×Q8—61no—
375C3×Q8—62no—
376C3×Q8—122no—
377C3×Q8—124no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—22no—
381C2×C3×C4—21no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—31no—
388C2×C3×C4—31no—
389C2×C3×C4—34no—
390C2×C3×C4—31no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—42no—
394C2×C3×C4—62no—
395C2×C3×C4—61no—
396C2×C3×C4—61no—
397C2×C3×C4—61no—
398C2×C3×C4—61no—
399C2×C3×C4—62no—
400C2×C3×C4—124no—
401C2×C3×C4D3×D411yescharacteristic
402C2×C3×C4D3×D411yescharacteristic
403C2×C3×C4C2×C3×D411yescharacteristic
404C2×C3×C4C2×C3×D411yescharacteristic
405C2×C3×C4C23×D311yescharacteristic
406C2×C3×C4C24×C311yescharacteristic
407C2×Dic3—21no—
408C2×Dic3—21no—
409C2×Dic3—22no—
410C2×Dic3C2×C3×D411yescharacteristic
411C2×Dic3C2×C3×D411yescharacteristic
412C2×Dic3C2×C3×D411yescharacteristic
413C4×D3—21no—
414C4×D3—21no—
415C4×D3—22no—
416C4×D3—44no—
417C4×D3C3×Q1614yescomplemented
418Dic6—21no—
419Dic6—22no—
420Dic6—21no—
421Dic6—22no—
422Dic6—44no—
423Dic6—42no—
424C3×C8—22no—
425C3×C8—22no—
426C3×C8—42no—
427C3×C8—62no—
428C3⋊C8—22no—
429C2×C32#53511yescharacteristic
430C2×C32C22×Q1611yescharacteristic
431C2×C32C2×#13711yescharacteristic
432C3×D3—22no—
433C2×Q8—32no—
434C2×Q8—31no—
435C2×Q8—61no—
436C2×Q8—62no—
437C2×Q8—122no—
438C2×Q8—122no—
439C2×Q8C22×C3×D312yes—
440C2×Q8C22×C3×D311yescharacteristic
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—31no—
444C22×C4—62no—
445Q16—42no—
446Q16—122no—
447Q16—122no—
448Q16—122no—
449C2×C8—32no—
450C2×C8C22×C3×D312yes—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—31no—
455C4⋊C4—62no—
456C4⋊C4—62no—
457C4⋊C4—61no—
458C4⋊C4—61no—
459C4⋊C4—61no—
460C4⋊C4—61no—
461C4⋊C4—61no—
462C4⋊C4—61no—
463C4⋊C4—61no—
464C4⋊C4—61no—
465C4⋊C4C22×C3×D311yescharacteristic
466C22⋊C4—61no—
467C22⋊C4—61no—
468C42—21no—
469C42—31no—
470C42—31no—
471C42—31no—
472C42—61no—
473C42C22×C3×D311yescharacteristic
474C22×C3—21no—
475C22×C3—32no—
476C22×C3—61no—
477C22×C3—61no—
478C22×C3C2×D3×D411yescharacteristic
479C22×C3C22×C3×D411yescharacteristic
480C2×D3—21no—
481C2×D3—21no—
482C2×D3C2×C3×Q1612yes—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—22no—
486C3×C4—21no—
487C3×C4—21no—
488C3×C4—32no—
489C3×C4—32no—
490C3×C4—41no—
491C3×C4—42no—
492C3×C4—41no—
493C3×C4—41no—
494C3×C4—42no—
495C3×C4—41no—
496C3×C4—42no—
497C3×C4—41no—
498C3×C4—61no—
499C3×C4—82no—
500C3×C4—81no—
501C3×C4—121no—
502C3×C4—122no—
503C3×C4—121no—
504C3×C4D3×Q1612yes—
505C3×C4C2×C3×Q1612yes—
506C3×C4#100411yescharacteristic
507C3×C4#100911yescharacteristic
508C3×C4C3×H(5,𝔽2)11yescharacteristic
509C3×C4C3×H(5,𝔽2)11yescharacteristic
510Dic3—21no—
511Dic3—41no—
512Dic3—42no—
513Dic3—41no—
514Dic3C2×C3×Q1612yes—
515Dic3C3×#13712yes—
516C32#320911yescharacteristic, complemented, Sylow
517C23—31no—
518Q8—21no—
519Q8—22no—
520Q8—21no—
521Q8—22no—
522Q8—61no—
523Q8—62no—
524Q8—61no—
525Q8—62no—
526Q8—122no—
527Q8—124no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—31no—
532C2×C4—31no—
533C2×C4—34no—
534C2×C4—31no—
535C2×C4—62no—
536C2×C4—61no—
537C2×C4—61no—
538C2×C4—61no—
539C2×C4—61no—
540C2×C4—62no—
541C2×C4—124no—
542C2×C4C3×D3×D411yescharacteristic
543C2×C4C3×D3×D411yescharacteristic
544C2×C4C23×C3×D311yescharacteristic
545C8—22no—
546C8—62no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—62no—
551C2×C3#560711yescharacteristic
552C2×C3C2×D3×Q1611yescharacteristic
553C2×C3D3×#13711yescharacteristic
554C2×C3C3×#53511yescharacteristic
555C2×C3C22×C3×Q1611yescharacteristic
556C2×C3C2×C3×#13711yescharacteristic
557D3—22no—
558C22—32no—
559C22—61no—
560C22—61no—
561C22C2×C3×D3×D411yescharacteristic
562C4—21no—
563C4—32no—
564C4—32no—
565C4—41no—
566C4—42no—
567C4—41no—
568C4—61no—
569C4—121no—
570C4—122no—
571C4—121no—
572C4C3×D3×Q1612yes—
573C4C3×#100411yescharacteristic
574C4C3×#100911yescharacteristic
575C3—21no—
576C3#8048011yescharacteristic, direct product factor
577C3C3×#320911yescharacteristic, complemented
578C2—62no—
579C2C3×#560711yescharacteristic
580C2C2×C3×D3×Q1611yescharacteristic
581C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#462C2
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC3×#462D3
hypocenterC3C3×#3209
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#462

Complements

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

NH ≅ G/Ntype
3. C32×#462C2semidirect
5. C3×#5183C2semidirect
6. C3×#5090C2semidirect
7. C3×#5031C2semidirect
8. C3×#4849C2semidirect
11. C3×#4792C2semidirect
13. #80480C3direct (N × H)
55. C3×#462D3semidirect
56. C3×#462C2×C3semidirect
61. #5183C2×C3semidirect
62. #5090C2×C3semidirect
63. #5031C2×C3semidirect
64. #4849C2×C3semidirect
67. #4792C2×C3semidirect
198. C3×C4×D3Q16semidirect
214. #462C3×D3semidirect
417. C4×D3C3×Q16semidirect
516. C32#3209semidirect
576. C3#80480direct (N × H)
577. C3C3×#3209semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
C3×#55782
C32×#4622
C3×#51862
C3×#51832
C3×#50902
C3×#50312
C3×#48492
C3×#48332
C3×#48092
C3×#47922
C3×#32093
#804803