Finite Group Databasebeta

← C3×#85309 #11922594

Subgroups — C3×#85309 #11922594

Order 1152.

734 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4⋊S4C211yesmaximal, characteristic
2C2×C3×C4×S4C211yesmaximal, characteristic, complemented
3C3×A4×C4⋊C4C211yesmaximal, characteristic, complemented
4C3×(C2×S4)⋊C4C211yesmaximal, characteristic, complemented
5C3×(C2×S4)⋊C4C211yesmaximal, characteristic, complemented
6C3×(C2×S4)⋊C4C211yesmaximal, characteristic, complemented
7C3×SL(2,ℤ/4)⋊C4C211yesmaximal, characteristic, complemented
8#85309C311yesmaximal, characteristic, direct product factor
9C3×#2443—31nomaximal
10C22×C3×S4C2211yescharacteristic
11C22×C3×S4C2211yescharacteristic
12C2×C3×C4×A4C2211yescharacteristic
13C2×C3×C4×A4C2211yescharacteristic
14C2×C3×C4×A4C2211yescharacteristic
15C2×C3×SL(2,ℤ/4)C2211yescharacteristic
16C2×C3×SL(2,ℤ/4)C2211yescharacteristic
17C3×C4⋊S4—22no—
18C3×C4×S4—22no—
19C3×#894—41nomaximal
20C2×C4⋊S4C2×C311yescharacteristic
21C2×C4×S4C2×C311yescharacteristic, complemented
22C2×C3×#123—31no—
23C2×C3×#121—31no—
24C2×C3×C4×D4—31no—
25C22×C3×C4⋊C4D311yescharacteristic, complemented
26A4×C4⋊C4—21no—
27A4×C4⋊C4C2×C311yescharacteristic, complemented
28(C2×S4)⋊C4C2×C311yescharacteristic, complemented
29(C2×S4)⋊C4C2×C311yescharacteristic, complemented
30(C2×S4)⋊C4C2×C311yescharacteristic, complemented
31SL(2,ℤ/4)⋊C4C2×C311yescharacteristic, complemented
32C3×#399—31no—
33C3×#398—31no—
34C3×#397—31no—
35C3×#394—31no—
36C3×#388—31no—
37C3×#387—31no—
38C3×#386—31no—
39C3×#386—31no—
40C3×#386—31no—
41C3×#385—31no—
42C3×#385—31no—
43C22×C3×A4C2311yescharacteristic
44C2×C3×S4—21no—
45C2×C3×S4—21no—
46C2×C3×S4—21no—
47C2×C3×S4—21no—
48C2×C3×S4—21no—
49C2×C3×S4D412yes—
50C2×C3×D12—41no—
51C2×C3×C4×D3—41no—
52C3×C4×A4—21no—
53C3×C4×A4—21no—
54C3×C4×A4—21no—
55C3×SL(2,ℤ/4)—21no—
56C3×SL(2,ℤ/4)—21no—
57C32×C4⋊C4—41no—
58C3×(C2×D3)⋊C4—41no—
59C3×(C2×D3)⋊C4—41no—
60C3×(C2×D3)⋊C4—41no—
61C3×Dic3⋊C4—41no—
62#2443—31noSylow
63C22×S4C22×C311yescharacteristic
64C22×S4C22×C311yescharacteristic
65C22×C3×D4—31no—
66C22×C3×D4—31no—
67C22×C3×D4—31no—
68C23×C3×C4—31no—
69C23×C3×C4C2×D311yescharacteristic
70C23×C3×C4C2×D311yescharacteristic
71C23×C3×C4C2×D311yescharacteristic
72C2×C4×A4—21no—
73C2×C4×A4—21no—
74C2×C4×A4—21no—
75C2×C4×A4C22×C311yescharacteristic
76C2×C4×A4C22×C311yescharacteristic
77C2×C4×A4C22×C311yescharacteristic
78C2×SL(2,ℤ/4)C22×C311yescharacteristic
79C2×SL(2,ℤ/4)C22×C311yescharacteristic
80C4⋊S4—22no—
81C4×S4—22no—
82C3×#123—61no—
83C3×#123—61no—
84C3×#123—61no—
85C3×#123—61no—
86C3×#121—62no—
87C3×#121—62no—
88C3×C4×D4—62no—
89C3×C4×D4—62no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C22⋊C4—31no—
99C2×C3×C22⋊C4—31no—
100C2×C3×C22⋊C4—31no—
101C2×C3×C22⋊C4—31no—
102C2×C3×C22⋊C4—31no—
103C2×C3×C22⋊C4—31no—
104C2×C3×C22⋊C4—31no—
105C2×C3×C22⋊C4—31no—
106C2×C3×C22⋊C4—31no—
107C2×C3×C22⋊C4—31no—
108C2×C3×C22⋊C4—31no—
109C2×C3×C42—31no—
110#894—41no—
111C3×#95—31no—
112C3×#95—31no—
113C3×#95—31no—
114C3×#95—31no—
115C3×#95—31no—
116C3×#95—31no—
117C3×#95—31no—
118C3×#95—31no—
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C2×C3×A4C2×D411yescharacteristic
122C2×C3×A4#4111yescharacteristic
123C2×C3×A4#4111yescharacteristic
124C3×S4—22no—
125C3×S4—41no—
126C2×C32×C4—41no—
127C2×C32×C4—41no—
128C2×C32×C4—41no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—41no—
131C3×D12—82no—
132C3×C4×D3—82no—
133C2×#123—31no—
134C2×#121—31no—
135C2×C4×D4—31no—
136C22×C4⋊C4C3×D311yescharacteristic, complemented
137#399—31no—
138#398—31no—
139#397—31no—
140#394—31no—
141#388—31no—
142#387—31no—
143#386—31no—
144#386—31no—
145#386—31no—
146#385—31no—
147#385—31no—
148C24×C3—31no—
149C24×C3—31no—
150C24×C3C22×D311yescharacteristic
151C22×A4—21no—
152C22×A4C23×C311yescharacteristic
153C2×S4—21no—
154C2×S4—21no—
155C2×S4—21no—
156C2×S4—21no—
157C2×S4—21no—
158C2×S4C3×D412yes—
159C2×C3×D4—32no—
160C2×C3×D4—32no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4—61no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C2×C3×D4—62no—
167C2×C3×D4—61no—
168C2×C3×D4—61no—
169C2×C3×D4—61no—
170C2×C3×D4—61no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C2×C3×D4—121no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C22×C3×C4—31no—
181C22×C3×C4—31no—
182C22×C3×C4—31no—
183C22×C3×C4—31no—
184C22×C3×C4—31no—
185C22×C3×C4—31no—
186C22×C3×C4—31no—
187C22×C3×C4—31no—
188C22×C3×C4—31no—
189C22×C3×C4—31no—
190C22×C3×C4—61no—
191C22×C3×C4—61no—
192C22×C3×C4—61no—
193C22×C3×C4—61no—
194C22×C3×C4—62no—
195C22×C3×C4—61no—
196C22×C3×C4—121no—
197C2×D12—41no—
198C2×C4×D3—41no—
199C4×A4—22no—
200C4×A4—21no—
201C4×A4—21no—
202C4×A4—21no—
203C4×A4—41no—
204C4×A4—41no—
205SL(2,ℤ/4)—21no—
206SL(2,ℤ/4)—21no—
207C3×C4⋊C4—31no—
208C3×C4⋊C4—31no—
209C3×C4⋊C4—31no—
210C3×C4⋊C4—41no—
211C3×C4⋊C4—61no—
212C3×C4⋊C4—62no—
213C3×C4⋊C4—62no—
214C3×C4⋊C4—61no—
215C3×C4⋊C4—61no—
216C3×C4⋊C4—81no—
217C3×C4⋊C4—121no—
218C3×C4⋊C4S411yescharacteristic, complemented
219C3×C22⋊C4—62no—
220C3×C22⋊C4—62no—
221C3×C22⋊C4—62no—
222C3×C22⋊C4—61no—
223C3×C22⋊C4—61no—
224C3×C22⋊C4—61no—
225C3×C22⋊C4—61no—
226C3×C22⋊C4—62no—
227C3×C22⋊C4—61no—
228C3×C22⋊C4—62no—
229C3×C22⋊C4—61no—
230C3×C22⋊C4—61no—
231C3×C22⋊C4—61no—
232C3×C22⋊C4—61no—
233C3×C22⋊C4—61no—
234C3×C22⋊C4—121no—
235C3×C42—62no—
236(C2×D3)⋊C4—41no—
237(C2×D3)⋊C4—41no—
238(C2×D3)⋊C4—41no—
239Dic3⋊C4—41no—
240C22×C32—41no—
241C2×C3×D3—42no—
242C2×C3×D3—81no—
243C2×C3×D3—81no—
244C2×C3×D3—81no—
245C2×C3×D3—81no—
246C2×C3×D3—81no—
247C3×A4#12311yescharacteristic, complemented
248C32×C4—81no—
249C32×C4—81no—
250C32×C4—81no—
251C3×Dic3—81no—
252C3×Dic3—81no—
253C22×D4—31no—
254C22×D4—31no—
255C22×D4—31no—
256C23×C4—31no—
257C23×C4C2×C3×D311yescharacteristic
258C23×C4C2×C3×D311yescharacteristic
259C23×C4C2×C3×D311yescharacteristic
260#123—61no—
261#123—61no—
262#123—61no—
263#123—61no—
264#121—62no—
265#121—62no—
266C4×D4—62no—
267C4×D4—62no—
268C2×C4⋊C4—31no—
269C2×C4⋊C4—31no—
270C2×C4⋊C4—31no—
271C2×C4⋊C4—31no—
272C2×C4⋊C4—31no—
273C2×C4⋊C4—31no—
274C2×C4⋊C4—31no—
275C2×C4⋊C4—31no—
276C2×C22⋊C4—31no—
277C2×C22⋊C4—31no—
278C2×C22⋊C4—31no—
279C2×C22⋊C4—31no—
280C2×C22⋊C4—31no—
281C2×C22⋊C4—31no—
282C2×C22⋊C4—31no—
283C2×C22⋊C4—31no—
284C2×C22⋊C4—31no—
285C2×C22⋊C4—31no—
286C2×C22⋊C4—31no—
287C2×C42—31no—
288#95—31no—
289#95—31no—
290#95—31no—
291#95—31no—
292#95—31no—
293#95—31no—
294#95—31no—
295#95—31no—
296C23×C3—31no—
297C23×C3—31no—
298C23×C3—31no—
299C23×C3—31no—
300C23×C3—32no—
301C23×C3—61no—
302C23×C3—61no—
303C23×C3—61no—
304C23×C3—61no—
305C23×C3—61no—
306C23×C3—61no—
307C23×C3—61no—
308C23×C3—61no—
309C23×C3—61no—
310C23×C3—61no—
311C23×C3—61no—
312C23×C3—61no—
313C23×C3—61no—
314C23×C3#23511yescharacteristic
315C23×C3D3×D411yescharacteristic
316C23×C3#23911yescharacteristic
317C22×D3—41no—
318C22×D3—41no—
319C2×A4—21no—
320C2×A4—21no—
321C2×A4—21no—
322C2×A4C2×C3×D411yescharacteristic
323C2×A4C3×#4111yescharacteristic
324C2×A4C3×#4111yescharacteristic
325S4—22no—
326S4—41no—
327C3×D4—62no—
328C3×D4—62no—
329C3×D4—62no—
330C3×D4—62no—
331C3×D4—122no—
332C3×D4—122no—
333C3×D4—121no—
334C3×D4—121no—
335C3×D4—121no—
336C3×D4—121no—
337C2×C3×C4—32no—
338C2×C3×C4—32no—
339C2×C3×C4—31no—
340C2×C3×C4—31no—
341C2×C3×C4—31no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—61no—
349C2×C3×C4—61no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—61no—
355C2×C3×C4—61no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—61no—
364C2×C3×C4—61no—
365C2×C3×C4—61no—
366C2×C3×C4—61no—
367C2×C3×C4—61no—
368C2×C3×C4—61no—
369C2×C3×C4—61no—
370C2×C3×C4—61no—
371C2×C3×C4—61no—
372C2×C3×C4—61no—
373C2×C3×C4—81no—
374C2×C3×C4—81no—
375C2×C3×C4—81no—
376C2×C3×C4—122no—
377C2×C3×C4—122no—
378C2×C3×C4C2×S411yescharacteristic
379C2×C3×C4C2×S411yescharacteristic
380C2×C3×C4C2×S411yescharacteristic
381C2×Dic3—41no—
382C2×Dic3—41no—
383D12—82no—
384C4×D3—82no—
385C2×C32—41no—
386C2×C32—41no—
387C2×C32—41no—
388C3×D3—82no—
389C3×D3—161no—
390C24—31no—
391C24—31no—
392C24C22×C3×D311yescharacteristic
393C2×D4—32no—
394C2×D4—32no—
395C2×D4—61no—
396C2×D4—61no—
397C2×D4—61no—
398C2×D4—61no—
399C2×D4—61no—
400C2×D4—62no—
401C2×D4—61no—
402C2×D4—61no—
403C2×D4—61no—
404C2×D4—61no—
405C2×D4—61no—
406C2×D4—61no—
407C2×D4—61no—
408C2×D4—121no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—31no—
413C22×C4—31no—
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—31no—
418C22×C4—31no—
419C22×C4—31no—
420C22×C4—31no—
421C22×C4—31no—
422C22×C4—31no—
423C22×C4—31no—
424C22×C4—61no—
425C22×C4—61no—
426C22×C4—61no—
427C22×C4—61no—
428C22×C4—62no—
429C22×C4—61no—
430C22×C4—121no—
431C4⋊C4—31no—
432C4⋊C4—31no—
433C4⋊C4—31no—
434C4⋊C4—61no—
435C4⋊C4—62no—
436C4⋊C4—62no—
437C4⋊C4—61no—
438C4⋊C4—61no—
439C4⋊C4—121no—
440C4⋊C4C3×S411yescharacteristic, complemented
441C22⋊C4—62no—
442C22⋊C4—61no—
443C22⋊C4—61no—
444C22⋊C4—61no—
445C22⋊C4—62no—
446C22⋊C4—62no—
447C22⋊C4—62no—
448C22⋊C4—61no—
449C22⋊C4—62no—
450C22⋊C4—61no—
451C22⋊C4—61no—
452C22⋊C4—61no—
453C22⋊C4—61no—
454C22⋊C4—61no—
455C22⋊C4—61no—
456C22⋊C4—121no—
457C42—62no—
458C22×C3—31no—
459C22×C3—31no—
460C22×C3—31no—
461C22×C3—31no—
462C22×C3—31no—
463C22×C3—31no—
464C22×C3—31no—
465C22×C3—31no—
466C22×C3—31no—
467C22×C3—41no—
468C22×C3—61no—
469C22×C3—62no—
470C22×C3—62no—
471C22×C3—62no—
472C22×C3—81no—
473C22×C3—121no—
474C22×C3—121no—
475C22×C3—121no—
476C22×C3—121no—
477C22×C3—121no—
478C22×C3—121no—
479C22×C3—121no—
480C22×C3—121no—
481C22×C3—121no—
482C22×C3—121no—
483C22×C3—121no—
484C22×C3#89411yescharacteristic, complemented
485C22×C3C22×S411yescharacteristic
486C2×D3—42no—
487C2×D3—81no—
488C2×D3—81no—
489C2×D3—81no—
490C2×D3—81no—
491C2×D3—81no—
492A4—21no—
493A4C3×#12311yescharacteristic, complemented
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—21no—
497C3×C4—62no—
498C3×C4—61no—
499C3×C4—61no—
500C3×C4—61no—
501C3×C4—81no—
502C3×C4—81no—
503C3×C4—81no—
504C3×C4—82no—
505C3×C4—121no—
506C3×C4—121no—
507C3×C4—121no—
508C3×C4—121no—
509C3×C4—121no—
510C3×C4—161no—
511C3×C4—161no—
512Dic3—81no—
513Dic3—81no—
514C32—41noSylow
515C23—31no—
516C23—31no—
517C23—31no—
518C23—31no—
519C23—32no—
520C23—61no—
521C23—61no—
522C23—61no—
523C23—61no—
524C23—61no—
525C23—61no—
526C23—61no—
527C23—61no—
528C23—61no—
529C23—61no—
530C23—61no—
531C23—61no—
532C23—61no—
533C23C3×#23511yescharacteristic
534C23C3×D3×D411yescharacteristic
535C23C3×#23911yescharacteristic
536D4—62no—
537D4—62no—
538D4—62no—
539D4—62no—
540D4—122no—
541D4—122no—
542D4—121no—
543D4—121no—
544D4—121no—
545D4—121no—
546C2×C4—32no—
547C2×C4—32no—
548C2×C4—31no—
549C2×C4—31no—
550C2×C4—31no—
551C2×C4—61no—
552C2×C4—61no—
553C2×C4—61no—
554C2×C4—61no—
555C2×C4—61no—
556C2×C4—61no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—61no—
560C2×C4—61no—
561C2×C4—61no—
562C2×C4—61no—
563C2×C4—61no—
564C2×C4—61no—
565C2×C4—61no—
566C2×C4—61no—
567C2×C4—61no—
568C2×C4—61no—
569C2×C4—61no—
570C2×C4—61no—
571C2×C4—61no—
572C2×C4—61no—
573C2×C4—61no—
574C2×C4—61no—
575C2×C4—61no—
576C2×C4—61no—
577C2×C4—61no—
578C2×C4—61no—
579C2×C4—122no—
580C2×C4—122no—
581C2×C4C2×C3×S411yescharacteristic
582C2×C4C2×C3×S411yescharacteristic
583C2×C4C2×C3×S411yescharacteristic
584C2×C3—31no—
585C2×C3—31no—
586C2×C3—31no—
587C2×C3—31no—
588C2×C3—41no—
589C2×C3—41no—
590C2×C3—41no—
591C2×C3—81no—
592C2×C3—81no—
593C2×C3—81no—
594C2×C3—122no—
595C2×C3—241no—
596C2×C3#591211yescharacteristic
597C2×C3D4×S411yescharacteristic
598C2×C3#591911yescharacteristic
599D3—82no—
600D3—161no—
601C22—31no—
602C22—31no—
603C22—31no—
604C22—31no—
605C22—31no—
606C22—31no—
607C22—31no—
608C22—31no—
609C22—31no—
610C22—61no—
611C22—62no—
612C22—62no—
613C22—62no—
614C22—121no—
615C22—121no—
616C22—121no—
617C22—121no—
618C22—121no—
619C22—121no—
620C22—121no—
621C22—121no—
622C22—121no—
623C22—121no—
624C22—121no—
625C22C3×#89411yescharacteristic, complemented
626C22C22×C3×S411yescharacteristic
627C4—21no—
628C4—21no—
629C4—21no—
630C4—62no—
631C4—61no—
632C4—61no—
633C4—61no—
634C4—121no—
635C4—121no—
636C4—121no—
637C4—121no—
638C4—121no—
639C3—41no—
640C3—81no—
641C3#8530911yescharacteristic, direct product factor
642C2—31no—
643C2—31no—
644C2—31no—
645C2—31no—
646C2—122no—
647C2—241no—
648C2C3×#591211yescharacteristic
649C2C3×D4×S411yescharacteristic
650C2C3×#591911yescharacteristic
subgroupG/H
centerC22×C3C22×S4
commutator, cosocleC22×A4C23×C3
FrattiniC22C22×C3×S4
FittingC22×C3×C4⋊C4D3
socleC24×C3C22×D3
prime radicalC2×C3×C4⋊S4C2
hypercenterC3×C4⋊C4S4
hypocenterA4C3×#123
LCSG ▷ C22×A4 ▷ A4
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×S4C2semidirect
3. C3×A4×C4⋊C4C2semidirect
4. C3×(C2×S4)⋊C4C2semidirect
5. C3×(C2×S4)⋊C4C2semidirect
6. C3×(C2×S4)⋊C4C2semidirect
7. C3×SL(2,ℤ/4)⋊C4C2semidirect
8. #85309C3direct (N × H)
21. C2×C4×S4C2×C3semidirect
25. C22×C3×C4⋊C4D3semidirect
27. A4×C4⋊C4C2×C3semidirect
28. (C2×S4)⋊C4C2×C3semidirect
29. (C2×S4)⋊C4C2×C3semidirect
30. (C2×S4)⋊C4C2×C3semidirect
31. SL(2,ℤ/4)⋊C4C2×C3semidirect
136. C22×C4⋊C4C3×D3semidirect
218. C3×C4⋊C4S4semidirect
247. C3×A4#123semidirect
440. C4⋊C4C3×S4semidirect
484. C22×C3#894semidirect
493. A4C3×#123semidirect
625. C22C3×#894semidirect
641. C3#85309direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4⋊S42
C2×C3×C4×S42
C3×A4×C4⋊C42
C3×(C2×S4)⋊C42
C3×SL(2,ℤ/4)⋊C42
#853093
C3×#24433
C3×#8944