Finite Group Databasebeta

← C3×#70276 #11787418

Subgroups — C3×#70276 #11787418

Order 1152.

885 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#215C211yesmaximal, characteristic
2C2×C3×#893C211yesmaximal, characteristic
3C2×C32×#103C211yesmaximal, characteristic, complemented
4C3×#5229C211yesmaximal, characteristic, complemented
5C2×C3×#821C211yesmaximal, characteristic
6C3×#4550C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8C3×#1877—31nomaximal
9#70276C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3—21no—
13C22×C32×C8C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C3×#215—22no—
16C2×C3×#215—22no—
17C2×C3×#215C414yescomplemented
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#893—22no—
23C3×#893—22no—
24C32×#103—22no—
25C3×C3⋊#95—21no—
26C3×C3⋊#95—21no—
27C3×#821—22no—
28C22×C3×SD16—31no—
29C2×C3×C4×D4—31no—
30C22×#215C2×C311yescharacteristic
31C2×#893C2×C311yescharacteristic
32C2×C3×#103—21no—
33C2×C3×#103D311yescharacteristic, complemented
34C2×C3×#103C2×C311yescharacteristic, complemented
35C2×C3×#102—31no—
36C3×#391—31no—
37#5229C2×C311yescharacteristic, complemented
38C2×#821C2×C311yescharacteristic
39C3×#340—31no—
40C3×#336—31no—
41#4550C2×C311yescharacteristic, complemented
42#4529C2×C311yescharacteristic, complemented
43C23×C3×D3—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8C2×C412yescomplemented
50C22×C32×C4—21no—
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12C2×C412yes—
60C2×C3×D12D412yes—
61C2×C3×D12D412yes—
62C2×C3×C4×D3—24no—
63C2×C3×C4×D3—42no—
64C2×C3×C4×D3—42no—
65C2×C32×C8—21no—
66C2×C32×C8—21no—
67C2×C32×C8—21no—
68C32×C4⋊C4—21no—
69C32×C4⋊C4D412yes—
70C3×#215—28no—
71C3×(C2×D3)⋊C4—24no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8C2×C412yescomplemented
79#1877—31noSylow
80C22×C3×Q8—21no—
81C22×C3×Q8C2×D311yescharacteristic
82C22×C3×Q8C22×C311yescharacteristic
83C22×C3×D4—31no—
84C23×C3×C4—61no—
85C22×D12C22×C311yescharacteristic
86C22×C4×D3—21no—
87C2×C3×SD16—34no—
88C2×C3×SD16—62no—
89C2×C3×SD16—62no—
90C22×C3×C8—21no—
91C22×C3×C8—31no—
92C22×C3×C8C2×D311yescharacteristic
93C22×C3×C8C22×C311yescharacteristic
94C3×C4×D4—62no—
95C3×C4×D4—62no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C4⋊C4C2×D311yescharacteristic
99C2×C3×C4⋊C4C22×C311yescharacteristic
100C2×C3×C22⋊C4—61no—
101C2×C3×C42—31no—
102C2×#215—22no—
103C2×#215—22no—
104C2×#215C3×C414yescomplemented
105C2×(C2×D3)⋊C4—21no—
106C2×C4⋊Dic3C22×C311yescharacteristic
107C2×C4×Dic3C22×C311yescharacteristic
108C22×C3⋊C8C22×C311yescharacteristic
109#893—22no—
110#893—22no—
111C3×#103—24no—
112C3×#103—22no—
113C3×#103—22no—
114C3×#102—62no—
115C3×#95—61no—
116C3×#95—61no—
117C3⋊#95—21no—
118C3⋊#95—21no—
119#821—22no—
120C23×C32C2×D411yescharacteristic
121C22×C3×D3—22no—
122C22×C3×D3—22no—
123C22×C3×D3—22no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C32×Q8—22no—
129C32×Q8—22no—
130C32×Q8—41no—
131C32×Q8—41no—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4—41no—
135C2×C32×C4—41no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4C22×C411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3SD1612yescomplemented
153C3×D12—22no—
154C3×D12—22no—
155C3×D12—22no—
156C3×D12C22⋊C414yes—
157C3×C4×D3—48no—
158C32×C8—41no—
159C3×C3⋊C8—22no—
160C22×SD16—31no—
161C2×C4×D4—31no—
162C2×#103C3×D311yescharacteristic, complemented
163C2×#102—31no—
164#391—31no—
165#340—31no—
166#336—31no—
167C24×C3—61no—
168C23×D3—21no—
169C2×C3×Q8—21no—
170C2×C3×Q8—21no—
171C2×C3×Q8—22no—
172C2×C3×Q8—22no—
173C2×C3×Q8—21no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×Q8—21no—
177C2×C3×Q8—21no—
178C2×C3×Q8—21no—
179C2×C3×Q8—21no—
180C2×C3×Q8—21no—
181C2×C3×Q8—22no—
182C2×C3×Q8—41no—
183C2×C3×Q8—41no—
184C2×C3×Q8—41no—
185C2×C3×Q8C4×D312yescomplemented
186C2×C3×Q8C2×C3×C412yescomplemented
187C2×C3×D4—32no—
188C2×C3×D4—32no—
189C2×C3×D4—32no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—31no—
199C22×C3×C4—31no—
200C22×C3×C4—41no—
201C22×C3×C4—41no—
202C22×C3×C4—64no—
203C22×C3×C4—61no—
204C22×C3×C4—122no—
205C22×C3×C4—122no—
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C23×C311yescharacteristic
208C22×Dic3—21no—
209C22×Dic3C3×D411yescharacteristic
210C22×Dic3C3×D411yescharacteristic
211C2×D12—21no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12C2×C3×C412yes—
215C2×D12C3×D412yes—
216C2×D12C3×D412yes—
217C2×C4×D3—24no—
218C2×C4×D3—42no—
219C2×C4×D3—42no—
220C3×SD16—68no—
221C2×C3×C8—22no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—21no—
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8—32no—
229C2×C3×C8—41no—
230C2×C3×C8—41no—
231C2×C3×C8—61no—
232C2×C3×C8—61no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—22no—
236C3×C4⋊C4—41no—
237C3×C4⋊C4—61no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4#6712yes—
240C3×C4⋊C4C3×D412yes—
241C3×C22⋊C4—64no—
242C3×C42—61no—
243C3×C42—61no—
244#215—28no—
245(C2×D3)⋊C4—24no—
246C4⋊Dic3—21no—
247C4⋊Dic3—21no—
248C4×Dic3—21no—
249C4×Dic3—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8C2×C3×C412yescomplemented
253C22×C32C4×D411yescharacteristic
254C22×C32#12011yescharacteristic
255C22×C32#12111yescharacteristic
256C22×C32C2×SD1611yescharacteristic
257C22×C32#13511yescharacteristic
258C22×C32AGL(1,ℤ/8)11yescharacteristic
259C22×C32#13711yescharacteristic
260C2×C3×D3—24no—
261C2×C3×D3—42no—
262C2×C3×D3—42no—
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C2×C3×D3—42no—
266C2×C3×D3—42no—
267C32×C4—42no—
268C32×C4—42no—
269C32×C4C2×C22⋊C411yescharacteristic
270C32×C4C4×D411yescharacteristic
271C32×C4#12111yescharacteristic
272C32×C4#12311yescharacteristic
273C3×Dic3—22no—
274C3×Dic3—41no—
275C3×Dic3—81no—
276C22×Q8C2×C3×D311yescharacteristic
277C22×D4—31no—
278C23×C4—61no—
279C2×SD16—34no—
280C2×SD16—62no—
281C2×SD16—62no—
282C22×C8—31no—
283C22×C8C2×C3×D311yescharacteristic
284C4×D4—62no—
285C4×D4—62no—
286C2×C4⋊C4—31no—
287C2×C4⋊C4C2×C3×D311yescharacteristic
288C2×C22⋊C4—61no—
289C2×C42—31no—
290#103—22no—
291#102—62no—
292#95—61no—
293#95—61no—
294C23×C3—21no—
295C23×C3—62no—
296C23×C3—62no—
297C23×C3—62no—
298C23×C3—121no—
299C23×C3—121no—
300C23×C3—121no—
301C23×C3—121no—
302C23×C3D3×D411yescharacteristic
303C23×C3C2×C3×D411yescharacteristic
304C22×D3—22no—
305C22×D3—22no—
306C22×D3—22no—
307C22×D3—41no—
308C22×D3—41no—
309C22×D3—41no—
310C22×D3—41no—
311C3×Q8—24no—
312C3×Q8—22no—
313C3×Q8—22no—
314C3×Q8—22no—
315C3×Q8—22no—
316C3×Q8—42no—
317C3×Q8—42no—
318C3×Q8—42no—
319C3×Q8—41no—
320C3×Q8—41no—
321C3×Q8—41no—
322C3×Q8—41no—
323C3×D4—34no—
324C3×D4—62no—
325C3×D4—62no—
326C3×D4—62no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—32no—
338C2×C3×C4—42no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4—42no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—61no—
355C2×C3×C4—81no—
356C2×C3×C4—81no—
357C2×C3×C4—128no—
358C2×C3×C4—121no—
359C2×C3×C4—121no—
360C2×C3×C4—121no—
361C2×C3×C4C2×C4×D311yescharacteristic
362C2×C3×C4#23511yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4#23711yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C22×C3×C411yescharacteristic
368C2×C3×C4C2×C3×D411yescharacteristic
369C2×C3×C4C2×C3×D411yescharacteristic
370C2×C3×C4C2×C3×D411yescharacteristic
371C2×C3×C4C3×#4111yescharacteristic
372C2×C3×C4C3×#4111yescharacteristic
373C2×Dic3—21no—
374C2×Dic3—21no—
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—21no—
378C2×Dic3—41no—
379C2×Dic3—41no—
380C2×Dic3—41no—
381C2×Dic3C3×SD1612yescomplemented
382D12—22no—
383D12—22no—
384D12—22no—
385D12C3×C22⋊C414yes—
386C4×D3—48no—
387C3×C8—42no—
388C3×C8—41no—
389C3×C8—41no—
390C3×C8—62no—
391C3⋊C8—22no—
392C2×C32#38611yescharacteristic
393C2×C32C4×SD1611yescharacteristic
394C2×C32#44011yescharacteristic
395C2×C32#45011yescharacteristic
396C2×C32#45211yescharacteristic
397C2×C32#46111yescharacteristic
398C2×C32#46311yescharacteristic
399C3×D3—44no—
400C24—61no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8C3×C4×D312yescomplemented
407C2×D4—32no—
408C2×D4—32no—
409C2×D4—32no—
410C2×D4—61no—
411C2×D4—61no—
412C2×D4—61no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—64no—
418C22×C4—61no—
419C22×C4—122no—
420C22×C4—122no—
421C22×C4C22×C3×D311yescharacteristic
422SD16—68no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—32no—
427C2×C8—61no—
428C2×C8—61no—
429C4⋊C4—21no—
430C4⋊C4—61no—
431C4⋊C4—61no—
432C4⋊C4C3×#6712yes—
433C22⋊C4—64no—
434C42—61no—
435C42—61no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—64no—
444C22×C3—122no—
445C22×C3—122no—
446C22×C3—122no—
447C22×C3—122no—
448C22×C3—122no—
449C22×C3—122no—
450C22×C3#67⋊C411yescharacteristic
451C22×C3#88411yescharacteristic
452C22×C3D3×SD1611yescharacteristic
453C22×C3#91411yescharacteristic
454C22×C3#91811yescharacteristic
455C22×C3#91911yescharacteristic
456C22×C3#93711yescharacteristic
457C22×C3C3×C4×D411yescharacteristic
458C22×C3C3×#12011yescharacteristic
459C22×C3C3×#12111yescharacteristic
460C22×C3C2×C3×SD1611yescharacteristic
461C22×C3C3×#13511yescharacteristic
462C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
463C22×C3C3×#13711yescharacteristic
464C2×D3—24no—
465C2×D3—42no—
466C2×D3—42no—
467C2×D3—42no—
468C2×D3—42no—
469C2×D3—42no—
470C2×D3—42no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—44no—
476C3×C4—42no—
477C3×C4—42no—
478C3×C4—42no—
479C3×C4—42no—
480C3×C4—62no—
481C3×C4—82no—
482C3×C4—121no—
483C3×C4—241no—
484C3×C4D3×C22⋊C411yescharacteristic
485C3×C4#88311yescharacteristic
486C3×C4C4×#6711yescharacteristic
487C3×C4#93811yescharacteristic
488C3×C4C2×C3×C22⋊C411yescharacteristic
489C3×C4C3×C4×D411yescharacteristic
490C3×C4C3×#12111yescharacteristic
491C3×C4C3×#12311yescharacteristic
492Dic3—22no—
493Dic3—41no—
494Dic3—81no—
495C32#187711yescharacteristic, complemented, Sylow
496C23—62no—
497C23—62no—
498C23—62no—
499C23—121no—
500C23—121no—
501C23—121no—
502C23—121no—
503C23C3×D3×D411yescharacteristic
504Q8—22no—
505Q8—22no—
506Q8—41no—
507Q8—41no—
508D4—34no—
509D4—62no—
510D4—62no—
511D4—62no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—32no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—61no—
520C2×C4—61no—
521C2×C4—61no—
522C2×C4—61no—
523C2×C4—61no—
524C2×C4—128no—
525C2×C4—121no—
526C2×C4—121no—
527C2×C4—121no—
528C2×C4C2×C3×C4×D311yescharacteristic
529C2×C4C3×#23511yescharacteristic
530C2×C4C3×D3×D411yescharacteristic
531C2×C4C3×D3×D411yescharacteristic
532C2×C4C3×#23711yescharacteristic
533C2×C4C2×C3×#6711yescharacteristic
534C8—41no—
535C8—62no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—124no—
544C2×C3#478811yescharacteristic
545C2×C3#481711yescharacteristic
546C2×C3#481811yescharacteristic
547C2×C3#481911yescharacteristic
548C2×C3#495611yescharacteristic
549C2×C3#516911yescharacteristic
550C2×C3#518711yescharacteristic
551C2×C3C3×#38611yescharacteristic
552C2×C3C3×C4×SD1611yescharacteristic
553C2×C3C3×#44011yescharacteristic
554C2×C3C3×#45011yescharacteristic
555C2×C3C3×#45211yescharacteristic
556C2×C3C3×#46111yescharacteristic
557C2×C3C3×#46311yescharacteristic
558D3—44no—
559C22—64no—
560C22—122no—
561C22—122no—
562C22—122no—
563C22—122no—
564C22—122no—
565C22—122no—
566C22C3×#67⋊C411yescharacteristic
567C22C3×#88411yescharacteristic
568C22C3×D3×SD1611yescharacteristic
569C22C3×#91411yescharacteristic
570C22C3×#91811yescharacteristic
571C22C3×#91911yescharacteristic
572C22C3×#93711yescharacteristic
573C4—42no—
574C4—42no—
575C4—62no—
576C4—121no—
577C4—241no—
578C4C3×D3×C22⋊C411yescharacteristic
579C4C3×#88311yescharacteristic
580C4C3×C4×#6711yescharacteristic
581C4C3×#93811yescharacteristic
582C3—21no—
583C3#7027611yescharacteristic, direct product factor
584C3C3×#187711yescharacteristic, complemented
585C2—124no—
586C2C3×#478811yescharacteristic
587C2C3×#481711yescharacteristic
588C2C3×#481811yescharacteristic
589C2C3×#481911yescharacteristic
590C2C3×#495611yescharacteristic
591C2C3×#516911yescharacteristic
592C2C3×#518711yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#103D3
hypocenterC3C3×#1877
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#103

Complements

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

NH ≅ G/Ntype
3. C2×C32×#103C2semidirect
4. C3×#5229C2semidirect
6. C3×#4550C2semidirect
7. C3×#4529C2semidirect
9. #70276C3direct (N × H)
17. C2×C3×#215C4semidirect
33. C2×C3×#103D3semidirect
34. C2×C3×#103C2×C3semidirect
37. #5229C2×C3semidirect
41. #4550C2×C3semidirect
42. #4529C2×C3semidirect
49. C2×C32×Q8C2×C4semidirect
78. C2×C3×C3⋊C8C2×C4semidirect
104. C2×#215C3×C4semidirect
152. C2×C3×Dic3SD16semidirect
162. C2×#103C3×D3semidirect
185. C2×C3×Q8C4×D3semidirect
186. C2×C3×Q8C2×C3×C4semidirect
252. C2×C3⋊C8C2×C3×C4semidirect
381. C2×Dic3C3×SD16semidirect
406. C2×Q8C3×C4×D3semidirect
495. C32#1877semidirect
583. C3#70276direct (N × H)
584. C3C3×#1877semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2152
C2×C3×#8932
C2×C32×#1032
C3×#52292
C2×C3×#8212
C3×#45502
C3×#45292
C3×#18773
#702763