Finite Group Databasebeta

← C3×#85486 #11922770

Subgroups — C3×#85486 #11922770

Order 1152.

1048 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C22×C3×C4×A4C211yesmaximal, characteristic, complemented
2C2×C3×GL(2,ℤ/4)C212yesmaximal, complemented
3C2×C3×C4⋊S4C211yesmaximal, characteristic, complemented
4C3×(C2×S4)⋊C4C212yesmaximal, complemented
5C3×C4⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
6#85486C311yesmaximal, characteristic, direct product factor
7C3×#2847—31nomaximal
8C23×C3×A4C2211yescharacteristic
9C22×C3×S4C2212yes—
10C2×C3×C4×A4—22no—
11C2×C3×C4×A4C2211yescharacteristic
12C2×C3×C4×A4C2211yescharacteristic
13C3×GL(2,ℤ/4)—24no—
14C2×C3×SL(2,ℤ/4)C2212yes—
15C3×C4⋊S4—22no—
16C3×#930—41nomaximal
17C24×C3×C4D311yescharacteristic, complemented
18C22×C4×A4—21no—
19C22×C4×A4C2×C311yescharacteristic, complemented
20C2×GL(2,ℤ/4)C2×C312yescomplemented
21C2×C4⋊S4C2×C311yescharacteristic, complemented
22C2×C3×#121—31no—
23C2×C3×#121—31no—
24C2×C3×#121—31no—
25C2×C3×#120—32no—
26(C2×S4)⋊C4C2×C312yescomplemented
27C4⋊SL(2,ℤ/4)C2×C311yescharacteristic, complemented
28C3×#386—32no—
29C3×#386—32no—
30C3×#386—32no—
31C3×#380—31no—
32C3×#380—31no—
33C3×#380—31no—
34C22×C3×A4—21no—
35C22×C3×A4—21no—
36C22×C3×A4D412yescomplemented
37C22×C3×A4C2311yescharacteristic
38C2×C3×S4—22no—
39C2×C3×S4—22no—
40C2×C3×S4—22no—
41C22×C32×C4—41no—
42C2×C3×#67—42no—
43C2×C3×D12—41no—
44C3×C4×A4—21no—
45C3×C4×A4D412yescomplemented
46C3×SL(2,ℤ/4)—22no—
47C3×(C2×D3)⋊C4—42no—
48C3×C4⋊Dic3—41no—
49#2847—31noSylow
50C25×C3C2×D311yescharacteristic
51C23×A4—21no—
52C23×A4C22×C311yescharacteristic
53C22×S4C22×C312yes—
54C22×C3×D4—32no—
55C22×C3×D4—32no—
56C22×C3×D4—31no—
57C22×C3×D4—32no—
58C23×C3×C4—22no—
59C23×C3×C4—31no—
60C23×C3×C4—31no—
61C23×C3×C4—31no—
62C23×C3×C4—31no—
63C23×C3×C4—62no—
64C23×C3×C4C2×D311yescharacteristic
65C23×C3×C4C2×D311yescharacteristic
66C2×C4×A4—24no—
67C2×C4×A4—22no—
68C2×C4×A4—21no—
69C2×C4×A4—21no—
70C2×C4×A4C22×C311yescharacteristic
71C2×C4×A4C22×C311yescharacteristic
72GL(2,ℤ/4)—24no—
73C2×SL(2,ℤ/4)C22×C312yes—
74C4⋊S4—22no—
75C3×#121—62no—
76C3×#121—64no—
77C3×#121—61no—
78C3×#121—61no—
79C3×#121—61no—
80C3×#121—62no—
81C3×#121—61no—
82C3×#120—64no—
83C3×#120—64no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C4⋊C4—31no—
87C2×C3×C22⋊C4—32no—
88C2×C3×C22⋊C4—32no—
89C2×C3×C22⋊C4—32no—
90C2×C3×C22⋊C4—32no—
91C2×C3×C22⋊C4—32no—
92C2×C3×C22⋊C4—32no—
93#930—41no—
94C3×#95—32no—
95C3×#95—32no—
96C3×#95—32no—
97C23×C32—41no—
98C22×C3×D3—42no—
99C2×C3×A4—22no—
100C2×C3×A4C2×D411yescharacteristic
101C2×C3×A4C2×D411yescharacteristic
102C2×C3×A4#4111yescharacteristic
103C3×S4—42no—
104C2×C32×C4—41no—
105C2×C32×C4—41no—
106C2×C32×C4—82no—
107C3×#67—84no—
108C2×C3×Dic3—42no—
109C3×D12—82no—
110C24×C4C3×D311yescharacteristic, complemented
111C2×#121—31no—
112C2×#121—31no—
113C2×#121—31no—
114C2×#120—32no—
115#386—32no—
116#386—32no—
117#386—32no—
118#380—31no—
119#380—31no—
120#380—31no—
121C24×C3—21no—
122C24×C3—21no—
123C24×C3—31no—
124C24×C3—31no—
125C24×C3—32no—
126C24×C3—32no—
127C24×C3—61no—
128C24×C3—61no—
129C24×C3D1212yescomplemented
130C24×C3C22×D311yescharacteristic
131C22×A4—22no—
132C22×A4—22no—
133C22×A4—21no—
134C22×A4—21no—
135C22×A4—22no—
136C22×A4—21no—
137C22×A4C3×D412yescomplemented
138C22×A4C23×C311yescharacteristic
139C2×S4—22no—
140C2×S4—22no—
141C2×S4—22no—
142C2×C3×D4—61no—
143C2×C3×D4—62no—
144C2×C3×D4—62no—
145C2×C3×D4—64no—
146C2×C3×D4—62no—
147C2×C3×D4—64no—
148C2×C3×D4—62no—
149C2×C3×D4—64no—
150C2×C3×D4—62no—
151C2×C3×D4—62no—
152C2×C3×D4—64no—
153C2×C3×D4—64no—
154C2×C3×D4—62no—
155C2×C3×D4—62no—
156C2×C3×D4—62no—
157C2×C3×D4—62no—
158C2×C3×D4—61no—
159C22×C3×C4—21no—
160C22×C3×C4—31no—
161C22×C3×C4—31no—
162C22×C3×C4—31no—
163C22×C3×C4—32no—
164C22×C3×C4—34no—
165C22×C3×C4—31no—
166C22×C3×C4—31no—
167C22×C3×C4—31no—
168C22×C3×C4—31no—
169C22×C3×C4—32no—
170C22×C3×C4—32no—
171C22×C3×C4—32no—
172C22×C3×C4—41no—
173C22×C3×C4—62no—
174C22×C3×C4—62no—
175C22×C3×C4—61no—
176C22×C3×C4—61no—
177C22×C3×C4—62no—
178C22×C3×C4—62no—
179C22×C3×C4—62no—
180C22×C3×C4—62no—
181C22×C3×C4—62no—
182C22×C3×C4—81no—
183C22×C3×C4#6712yescomplemented
184C22×C3×C4S411yescharacteristic, complemented
185C2×#67—42no—
186C2×D12—41no—
187C4×A4—22no—
188C4×A4—21no—
189C4×A4—22no—
190C4×A4C3×D412yescomplemented
191SL(2,ℤ/4)—22no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—62no—
194C3×C4⋊C4—62no—
195C3×C4⋊C4—61no—
196C3×C22⋊C4—64no—
197C3×C22⋊C4—64no—
198C3×C22⋊C4—62no—
199C3×C22⋊C4—64no—
200C3×C22⋊C4—62no—
201C3×C22⋊C4—64no—
202C3×C22⋊C4—62no—
203C3×C22⋊C4—62no—
204(C2×D3)⋊C4—42no—
205C4⋊Dic3—41no—
206C22×C32—42no—
207C22×C32—41no—
208C22×C32—81no—
209C22×C32—81no—
210C2×C3×D3—82no—
211C2×C3×D3—82no—
212C2×C3×D3—82no—
213C3×A4#12111yescharacteristic, complemented
214C32×C4—42no—
215C32×C4—81no—
216C3×Dic3—82no—
217C25C2×C3×D311yescharacteristic
218C22×D4—32no—
219C22×D4—32no—
220C22×D4—31no—
221C22×D4—32no—
222C23×C4—22no—
223C23×C4—31no—
224C23×C4—31no—
225C23×C4—31no—
226C23×C4—31no—
227C23×C4—62no—
228C23×C4C2×C3×D311yescharacteristic
229C23×C4C2×C3×D311yescharacteristic
230#121—62no—
231#121—64no—
232#121—61no—
233#121—61no—
234#121—61no—
235#121—62no—
236#121—61no—
237#120—64no—
238#120—64no—
239C2×C4⋊C4—31no—
240C2×C4⋊C4—31no—
241C2×C4⋊C4—31no—
242C2×C22⋊C4—32no—
243C2×C22⋊C4—32no—
244C2×C22⋊C4—32no—
245C2×C22⋊C4—32no—
246C2×C22⋊C4—32no—
247C2×C22⋊C4—32no—
248#95—32no—
249#95—32no—
250#95—32no—
251C23×C3—22no—
252C23×C3—31no—
253C23×C3—32no—
254C23×C3—31no—
255C23×C3—31no—
256C23×C3—31no—
257C23×C3—32no—
258C23×C3—32no—
259C23×C3—32no—
260C23×C3—32no—
261C23×C3—31no—
262C23×C3—41no—
263C23×C3—61no—
264C23×C3—61no—
265C23×C3—61no—
266C23×C3—61no—
267C23×C3—62no—
268C23×C3—61no—
269C23×C3—61no—
270C23×C3—62no—
271C23×C3—62no—
272C23×C3—61no—
273C23×C3—64no—
274C23×C3—62no—
275C23×C3—62no—
276C23×C3—62no—
277C23×C3—62no—
278C23×C3—62no—
279C23×C3—62no—
280C23×C3—62no—
281C23×C3—81no—
282C23×C3C2×D1211yescharacteristic
283C23×C3#23511yescharacteristic
284C23×C3C2×#6711yescharacteristic
285C23×C3C2×S411yescharacteristic
286C22×D3—42no—
287C2×A4—24no—
288C2×A4—22no—
289C2×A4—21no—
290C2×A4—21no—
291C2×A4—21no—
292C2×A4C2×C3×D411yescharacteristic
293C2×A4C2×C3×D411yescharacteristic
294C2×A4C3×#4111yescharacteristic
295S4—42no—
296C3×D4—122no—
297C3×D4—122no—
298C3×D4—122no—
299C3×D4—122no—
300C3×D4—128no—
301C3×D4—124no—
302C3×D4—122no—
303C3×D4—124no—
304C3×D4—122no—
305C2×C3×C4—22no—
306C2×C3×C4—31no—
307C2×C3×C4—32no—
308C2×C3×C4—32no—
309C2×C3×C4—32no—
310C2×C3×C4—32no—
311C2×C3×C4—31no—
312C2×C3×C4—41no—
313C2×C3×C4—41no—
314C2×C3×C4—62no—
315C2×C3×C4—61no—
316C2×C3×C4—61no—
317C2×C3×C4—61no—
318C2×C3×C4—62no—
319C2×C3×C4—64no—
320C2×C3×C4—62no—
321C2×C3×C4—61no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—82no—
332C2×C3×C4—84no—
333C2×C3×C4—81no—
334C2×C3×C4—81no—
335C2×C3×C4C2×S411yescharacteristic
336C2×C3×C4C2×S411yescharacteristic
337#67—84no—
338C2×Dic3—42no—
339D12—82no—
340C2×C32—41no—
341C2×C32—41no—
342C2×C32—41no—
343C2×C32—82no—
344C3×D3—162no—
345C24—21no—
346C24—21no—
347C24—31no—
348C24—31no—
349C24—32no—
350C24—32no—
351C24—61no—
352C24—61no—
353C24C3×D1212yescomplemented
354C24C22×C3×D311yescharacteristic
355C2×D4—61no—
356C2×D4—62no—
357C2×D4—62no—
358C2×D4—64no—
359C2×D4—62no—
360C2×D4—64no—
361C2×D4—62no—
362C2×D4—64no—
363C2×D4—62no—
364C2×D4—62no—
365C2×D4—64no—
366C2×D4—64no—
367C2×D4—62no—
368C2×D4—62no—
369C2×D4—62no—
370C2×D4—62no—
371C2×D4—61no—
372C22×C4—21no—
373C22×C4—31no—
374C22×C4—31no—
375C22×C4—31no—
376C22×C4—32no—
377C22×C4—34no—
378C22×C4—31no—
379C22×C4—31no—
380C22×C4—31no—
381C22×C4—31no—
382C22×C4—32no—
383C22×C4—32no—
384C22×C4—32no—
385C22×C4—62no—
386C22×C4—62no—
387C22×C4—61no—
388C22×C4—61no—
389C22×C4—62no—
390C22×C4—62no—
391C22×C4—62no—
392C22×C4—62no—
393C22×C4—62no—
394C22×C4C3×#6712yescomplemented
395C22×C4C3×S411yescharacteristic, complemented
396C4⋊C4—61no—
397C4⋊C4—62no—
398C4⋊C4—62no—
399C4⋊C4—61no—
400C22⋊C4—64no—
401C22⋊C4—64no—
402C22⋊C4—62no—
403C22⋊C4—64no—
404C22⋊C4—62no—
405C22⋊C4—64no—
406C22⋊C4—62no—
407C22⋊C4—62no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—31no—
411C22×C3—31no—
412C22×C3—31no—
413C22×C3—31no—
414C22×C3—31no—
415C22×C3—31no—
416C22×C3—31no—
417C22×C3—31no—
418C22×C3—31no—
419C22×C3—34no—
420C22×C3—32no—
421C22×C3—41no—
422C22×C3—42no—
423C22×C3—62no—
424C22×C3—62no—
425C22×C3—62no—
426C22×C3—62no—
427C22×C3—61no—
428C22×C3—62no—
429C22×C3—62no—
430C22×C3—62no—
431C22×C3—61no—
432C22×C3—61no—
433C22×C3—81no—
434C22×C3—81no—
435C22×C3—82no—
436C22×C3—82no—
437C22×C3—81no—
438C22×C3—82no—
439C22×C3—122no—
440C22×C3—122no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3—122no—
444C22×C3—122no—
445C22×C3—122no—
446C22×C3#93011yescharacteristic, complemented
447C22×C3C4⋊S412yescomplemented
448C22×C3C22×S411yescharacteristic
449C2×D3—82no—
450C2×D3—82no—
451C2×D3—82no—
452A4—21no—
453A4C3×#12111yescharacteristic, complemented
454C3×C4—21no—
455C3×C4—32no—
456C3×C4—42no—
457C3×C4—61no—
458C3×C4—81no—
459C3×C4—82no—
460C3×C4—82no—
461C3×C4—122no—
462C3×C4—122no—
463C3×C4—122no—
464C3×C4GL(2,ℤ/4)12yescomplemented
465Dic3—82no—
466C32—41noSylow
467C23—22no—
468C23—31no—
469C23—32no—
470C23—31no—
471C23—31no—
472C23—31no—
473C23—32no—
474C23—32no—
475C23—31no—
476C23—32no—
477C23—32no—
478C23—61no—
479C23—61no—
480C23—61no—
481C23—61no—
482C23—62no—
483C23—61no—
484C23—61no—
485C23—62no—
486C23—62no—
487C23—61no—
488C23—64no—
489C23—62no—
490C23—62no—
491C23—62no—
492C23—62no—
493C23—62no—
494C23—62no—
495C23—62no—
496C23C2×C3×D1211yescharacteristic
497C23C3×#23511yescharacteristic
498C23C2×C3×#6711yescharacteristic
499C23C2×C3×S411yescharacteristic
500D4—122no—
501D4—122no—
502D4—122no—
503D4—122no—
504D4—128no—
505D4—124no—
506D4—122no—
507D4—124no—
508D4—122no—
509C2×C4—22no—
510C2×C4—31no—
511C2×C4—32no—
512C2×C4—32no—
513C2×C4—32no—
514C2×C4—32no—
515C2×C4—31no—
516C2×C4—62no—
517C2×C4—61no—
518C2×C4—61no—
519C2×C4—61no—
520C2×C4—62no—
521C2×C4—64no—
522C2×C4—62no—
523C2×C4—61no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4C2×C3×S411yescharacteristic
534C2×C4C2×C3×S411yescharacteristic
535C2×C3—22no—
536C2×C3—31no—
537C2×C3—31no—
538C2×C3—31no—
539C2×C3—31no—
540C2×C3—41no—
541C2×C3—41no—
542C2×C3—41no—
543C2×C3—62no—
544C2×C3—82no—
545C2×C3—84no—
546C2×C3—81no—
547C2×C3—81no—
548C2×C3—81no—
549C2×C3—242no—
550C2×C3C2×C4⋊S411yescharacteristic
551C2×C3#591211yescharacteristic
552C2×C3C2×GL(2,ℤ/4)11yescharacteristic
553D3—162no—
554C22—21no—
555C22—21no—
556C22—31no—
557C22—31no—
558C22—31no—
559C22—31no—
560C22—31no—
561C22—31no—
562C22—31no—
563C22—31no—
564C22—31no—
565C22—34no—
566C22—32no—
567C22—62no—
568C22—62no—
569C22—62no—
570C22—62no—
571C22—61no—
572C22—62no—
573C22—62no—
574C22—62no—
575C22—61no—
576C22—61no—
577C22—122no—
578C22—122no—
579C22—122no—
580C22—122no—
581C22—122no—
582C22—122no—
583C22—122no—
584C22C3×#93011yescharacteristic, complemented
585C22C3×C4⋊S412yescomplemented
586C22C22×C3×S411yescharacteristic
587C4—21no—
588C4—32no—
589C4—61no—
590C4—122no—
591C4—122no—
592C4—122no—
593C4C3×GL(2,ℤ/4)12yescomplemented
594C3—41no—
595C3—81no—
596C3#8548611yescharacteristic, direct product factor
597C2—22no—
598C2—31no—
599C2—31no—
600C2—31no—
601C2—31no—
602C2—62no—
603C2—242no—
604C2C2×C3×C4⋊S411yescharacteristic
605C2C3×#591211yescharacteristic
606C2C2×C3×GL(2,ℤ/4)11yescharacteristic
subgroupG/H
centerC22×C3C22×S4
commutator, cosocleC22×A4C23×C3
FrattiniC22C22×C3×S4
FittingC24×C3×C4D3
socleC24×C3C22×D3
hypercenterC22×C3×C4S4
hypocenterA4C3×#121
LCSG ▷ C22×A4 ▷ A4
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4×A4C2semidirect
2. C2×C3×GL(2,ℤ/4)C2semidirect
3. C2×C3×C4⋊S4C2semidirect
4. C3×(C2×S4)⋊C4C2semidirect
5. C3×C4⋊SL(2,ℤ/4)C2semidirect
6. #85486C3direct (N × H)
17. C24×C3×C4D3semidirect
19. C22×C4×A4C2×C3semidirect
20. C2×GL(2,ℤ/4)C2×C3semidirect
21. C2×C4⋊S4C2×C3semidirect
26. (C2×S4)⋊C4C2×C3semidirect
27. C4⋊SL(2,ℤ/4)C2×C3semidirect
36. C22×C3×A4D4semidirect
45. C3×C4×A4D4semidirect
110. C24×C4C3×D3semidirect
129. C24×C3D12semidirect
137. C22×A4C3×D4semidirect
183. C22×C3×C4#67semidirect
184. C22×C3×C4S4semidirect
190. C4×A4C3×D4semidirect
213. C3×A4#121semidirect
353. C24C3×D12semidirect
394. C22×C4C3×#67semidirect
395. C22×C4C3×S4semidirect
446. C22×C3#930semidirect
447. C22×C3C4⋊S4semidirect
453. A4C3×#121semidirect
464. C3×C4GL(2,ℤ/4)semidirect
584. C22C3×#930semidirect
585. C22C3×C4⋊S4semidirect
593. C4C3×GL(2,ℤ/4)semidirect
596. C3#85486direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×A42
C2×C3×GL(2,ℤ/4)2
C2×C3×C4⋊S42
C3×(C2×S4)⋊C42
C3×C4⋊SL(2,ℤ/4)2
#854863
C3×#28473
C3×#9304