Finite Group Databasebeta

← C3×#10596426 #13180685

Subgroups — C3×#10596426 #13180685

Order 1728.

816 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 82 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
1C3×C4×D3×A4C211yesmaximal, characteristic, complemented
2C3×C4×C3⋊S4C211yesmaximal, characteristic, complemented
3C32×C4×S4C211yesmaximal, characteristic, complemented
4C3×#64210C211yesmaximal, characteristic, complemented
5C3×#64209C211yesmaximal, characteristic, complemented
6C3×#64207C211yesmaximal, characteristic, complemented
7C3×#64204C211yesmaximal, characteristic, complemented
8C3×#5912—31nomaximal
9#10596426C311yesmaximal, characteristic, direct product factor
10C3×#5547—31nomaximal
11C2×C3×D3×A4C2211yescharacteristic
12C2×C3×C3⋊S4C2211yescharacteristic
13C2×C32×S4C2211yescharacteristic
14C32×C4×A4C2211yescharacteristic
15C3×#3798—41nomaximal
16C3×Dic3×A4C2211yescharacteristic
17C3×C3⋊SL(2,ℤ/4)C2211yescharacteristic
18C32×SL(2,ℤ/4)C2211yescharacteristic
19C2×C3×#235—31no—
20C22×C3×C4×D3D311yescharacteristic, complemented
21C2×C3×C4×A4—31no—
22C4×D3×A4—21no—
23C4×D3×A4C2×C311yescharacteristic, complemented
24C4×C3⋊S4C2×C311yescharacteristic, complemented
25C3×GL(2,ℤ/4)—31no—
26C3×GL(2,ℤ/4)—31no—
27C3×C4⋊S4—31no—
28C3×C4×S4—21no—
29C3×C4×S4—31no—
30C3×C4×S4—61no—
31C3×C4×S4D311yescharacteristic, complemented
32C3×C4×S4C2×C311yescharacteristic, complemented
33C3×A4⋊Q8—31no—
34#64210C2×C311yescharacteristic, complemented
35#64209C2×C311yescharacteristic, complemented
36#64207C2×C311yescharacteristic, complemented
37#64204C2×C311yescharacteristic, complemented
38C32×C4×D4—31no—
39C3×#939—31no—
40C3×#937—31no—
41C3×C4×#67—31no—
42C3×C4×#67—31no—
43C3×#896—31no—
44C3×#894—31no—
45C3×#884—31no—
46C3×#883—31no—
47C3×#882—31no—
48C3×#878—31no—
49C3×C4×D12—31no—
50C3×#872—31no—
51C2×C32×A4C2311yescharacteristic
52C3×D3×A4—21no—
53C3×C3⋊S4—21no—
54C32×S4—21no—
55C3×C4×C3⋊D3—41no—
56C32×C4×D3—41no—
57C32×C4×D3—41no—
58C3×#627—41no—
59C3×#626—41no—
60C3×#626—41no—
61C3×#625—41no—
62#5912—31no—
63C3×#525—91no—
64#5547—31no—
65C23×C3×D3C2×D311yescharacteristic
66C22×C3×A4—31no—
67C2×D3×A4—21no—
68C2×D3×A4C22×C311yescharacteristic
69C2×C3⋊S4C22×C311yescharacteristic
70C2×C3×S4—21no—
71C2×C3×S4—31no—
72C2×C3×S4—61no—
73C2×C3×S4C2×D311yescharacteristic
74C2×C3×S4C22×C311yescharacteristic
75C2×C32×D4—31no—
76C22×C32×C4—31no—
77C22×C32×C4C2×D311yescharacteristic
78C2×C3×#67—31no—
79C2×C3×#67—31no—
80C2×C3×#67—31no—
81C2×C3×#67—31no—
82C22×C3×Dic3C2×D311yescharacteristic
83C3×#235—61no—
84C3×#235—61no—
85C3×#235—61no—
86C3×#235—61no—
87C3×#235—121no—
88C2×C3×D12—31no—
89C2×C3×D12—31no—
90C2×C3×C4×D3—31no—
91C2×C3×C4×D3—31no—
92C2×C3×C4×D3—31no—
93C2×C3×C4×D3—31no—
94C2×C3×C4×D3—31no—
95C2×C3×Dic6—31no—
96C3×C4×A4—21no—
97C3×C4×A4—21no—
98C3×C4×A4—21no—
99C3×C4×A4—31no—
100C3×C4×A4—41no—
101C3×C4×A4C2×D311yescharacteristic
102C3×C4×A4C22×C311yescharacteristic
103#3798—41no—
104Dic3×A4—21no—
105Dic3×A4C22×C311yescharacteristic
106C3⋊SL(2,ℤ/4)C22×C311yescharacteristic
107C3×SL(2,ℤ/4)—21no—
108C3×SL(2,ℤ/4)—31no—
109C3×SL(2,ℤ/4)—61no—
110C3×SL(2,ℤ/4)C2×D311yescharacteristic
111C3×SL(2,ℤ/4)C22×C311yescharacteristic
112C32×C4⋊C4—31no—
113C32×C22⋊C4—31no—
114C32×C22⋊C4—31no—
115C32×C42—31no—
116C3×#217—31no—
117C3×#217—31no—
118C3×(C2×D3)⋊C4—31no—
119C3×(C2×D3)⋊C4—31no—
120C3×(C2×D3)⋊C4—31no—
121C3×(C2×D3)⋊C4—31no—
122C3×(C2×D3)⋊C4—31no—
123C3×(C2×D3)⋊C4—31no—
124C3×C4⋊Dic3—31no—
125C3×Dic3⋊C4—31no—
126C3×Dic3⋊C4—31no—
127C3×Dic3⋊C4—31no—
128C3×Dic3⋊C4—31no—
129C3×C4×Dic3—31no—
130C2×C3×C3⋊D3—41no—
131C2×C32×D3—41no—
132C2×C32×D3—41no—
133C32×A4#4111yescharacteristic, complemented
134C33×C4—41no—
135C3×C3⋊Dic3—41no—
136C32×Dic3—41no—
137C32×Dic3—41no—
138C2×C3×#41—91no—
139C23×C3×C4—31no—
140C2×#235—31no—
141C22×C4×D3C3×D311yescharacteristic, complemented
142C2×C4×A4—31no—
143C2×C4×A4—61no—
144GL(2,ℤ/4)—31no—
145GL(2,ℤ/4)—31no—
146C4⋊S4—31no—
147C4×S4—31no—
148C4×S4—61no—
149C4×S4C3×D311yescharacteristic, complemented
150A4⋊Q8—31no—
151C3×#123—91no—
152C3×#123—91no—
153C3×C22⋊Q8—91no—
154C3×C22⋊Q8—91no—
155C3×#121—91no—
156C3×#121—91no—
157C3×#120—91no—
158C3×#120—91no—
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C3×C4×D4—61no—
162C3×C4×D4—91no—
163C3×C4×D4—91no—
164C3×C4×D4—91no—
165C3×#117—91no—
166#939—31no—
167#937—31no—
168C4×#67—31no—
169C4×#67—31no—
170#896—31no—
171#894—31no—
172#884—31no—
173#883—31no—
174#882—31no—
175#878—31no—
176C4×D12—31no—
177#872—31no—
178C23×C32—31no—
179C23×C32C22×D311yescharacteristic
180C22×C3×D3—21no—
181C22×C3×D3—31no—
182C22×C3×D3—31no—
183C22×C3×D3—31no—
184C22×C3×D3—61no—
185C2×C3×A4—21no—
186C2×C3×A4—21no—
187C2×C3×A4—21no—
188C2×C3×A4—41no—
189C2×C3×A4—61no—
190C2×C3×A4C22×D311yescharacteristic
191C2×C3×A4C23×C311yescharacteristic
192D3×A4—22no—
193D3×A4—21no—
194C3⋊S4—21no—
195C3×S4—22no—
196C3×S4—21no—
197C3×S4—21no—
198C3×S4—62no—
199C3×S4—61no—
200C32×D4—61no—
201C32×D4—61no—
202C2×C32×C4—31no—
203C2×C32×C4—31no—
204C2×C32×C4—31no—
205C2×C32×C4—31no—
206C2×C32×C4—31no—
207C2×C32×C4—61no—
208C2×C32×C4—61no—
209C2×C32×C4—121no—
210C4×C3⋊D3—41no—
211C3×#67—61no—
212C3×#67—61no—
213C3×#67—62no—
214C3×#67—61no—
215C3×#67—61no—
216C3×#67—61no—
217C3×#67—61no—
218C3×#67—121no—
219C3×#67—121no—
220C2×C3×Dic3—31no—
221C2×C3×Dic3—31no—
222C2×C3×Dic3—31no—
223C2×C3×Dic3—31no—
224C2×C3×Dic3—31no—
225C3×D12—62no—
226C3×D12—61no—
227C3×D12—61no—
228C3×D12—121no—
229C3×C4×D3—31no—
230C3×C4×D3—31no—
231C3×C4×D3—31no—
232C3×C4×D3—41no—
233C3×C4×D3—41no—
234C3×C4×D3—41no—
235C3×C4×D3—61no—
236C3×C4×D3—61no—
237C3×C4×D3—61no—
238C3×C4×D3—81no—
239C3×C4×D3—81no—
240C3×C4×D3—121no—
241C3×C4×D3—241no—
242C3×C4×D3S411yescharacteristic, complemented
243C3×Dic6—61no—
244C3×Dic6—61no—
245C3×Dic6—121no—
246#627—41no—
247#626—41no—
248#626—41no—
249#625—41no—
250#525—91noSylow
251C2×C33—41no—
252C3×C3⋊D3—81no—
253C32×D3—81no—
254C32×D3—81no—
255C24×C3—31no—
256C23×D3C2×C3×D311yescharacteristic
257C22×A4—31no—
258C22×A4—61no—
259C2×S4—31no—
260C2×S4—61no—
261C2×S4C2×C3×D311yescharacteristic
262C3×#41—181no—
263C3×#41—181no—
264C3×#41—181no—
265C3×#41—181no—
266C2×C3×Q8—91no—
267C2×C3×D4—31no—
268C2×C3×D4—31no—
269C2×C3×D4—61no—
270C2×C3×D4—91no—
271C2×C3×D4—91no—
272C2×C3×D4—91no—
273C2×C3×D4—91no—
274C2×C3×D4—91no—
275C2×C3×D4—91no—
276C22×C3×C4—21no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4—61no—
281C22×C3×C4—91no—
282C22×C3×C4—91no—
283C22×C3×C4—91no—
284C22×C3×C4—91no—
285C22×C3×C4—91no—
286C22×C3×C4D3211yescharacteristic
287C22×C3×C4C2×C3×D311yescharacteristic
288C2×#67—31no—
289C2×#67—31no—
290C2×#67—31no—
291C2×#67—31no—
292C22×Dic3C2×C3×D311yescharacteristic
293#235—61no—
294#235—61no—
295#235—61no—
296#235—61no—
297#235—121no—
298C2×D12—31no—
299C2×D12—31no—
300C2×C4×D3—31no—
301C2×C4×D3—31no—
302C2×C4×D3—31no—
303C2×C4×D3—31no—
304C2×C4×D3—31no—
305C2×Dic6—31no—
306C4×A4—21no—
307C4×A4—21no—
308C4×A4—31no—
309C4×A4—41no—
310C4×A4—61no—
311C4×A4C2×C3×D311yescharacteristic
312SL(2,ℤ/4)—31no—
313SL(2,ℤ/4)—61no—
314SL(2,ℤ/4)C2×C3×D311yescharacteristic
315C3×C4⋊C4—31no—
316C3×C4⋊C4—31no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4—91no—
319C3×C4⋊C4—91no—
320C3×C4⋊C4—91no—
321C3×C4⋊C4—91no—
322C3×C4⋊C4—91no—
323C3×C22⋊C4—31no—
324C3×C22⋊C4—31no—
325C3×C22⋊C4—31no—
326C3×C22⋊C4—31no—
327C3×C22⋊C4—61no—
328C3×C22⋊C4—61no—
329C3×C22⋊C4—91no—
330C3×C22⋊C4—91no—
331C3×C22⋊C4—91no—
332C3×C22⋊C4—91no—
333C3×C22⋊C4—91no—
334C3×C22⋊C4—91no—
335C3×C22⋊C4—91no—
336C3×C22⋊C4—91no—
337C3×C42—31no—
338C3×C42—31no—
339C3×C42—61no—
340C3×C42—91no—
341#217—31no—
342#217—31no—
343(C2×D3)⋊C4—31no—
344(C2×D3)⋊C4—31no—
345(C2×D3)⋊C4—31no—
346(C2×D3)⋊C4—31no—
347(C2×D3)⋊C4—31no—
348(C2×D3)⋊C4—31no—
349C4⋊Dic3—31no—
350Dic3⋊C4—31no—
351Dic3⋊C4—31no—
352Dic3⋊C4—31no—
353Dic3⋊C4—31no—
354C4×Dic3—31no—
355C22×C32—31no—
356C22×C32—31no—
357C22×C32—61no—
358C22×C32—61no—
359C22×C32—61no—
360C22×C32—121no—
361C22×C32#23511yescharacteristic, complemented
362C2×C3⋊D3—41no—
363C2×C3×D3—32no—
364C2×C3×D3—31no—
365C2×C3×D3—41no—
366C2×C3×D3—41no—
367C2×C3×D3—41no—
368C2×C3×D3—61no—
369C2×C3×D3—61no—
370C2×C3×D3—61no—
371C2×C3×D3—61no—
372C2×C3×D3—61no—
373C2×C3×D3—61no—
374C2×C3×D3—81no—
375C2×C3×D3—81no—
376C2×C3×D3—121no—
377C2×C3×D3—241no—
378C2×C3×D3C2×S411yescharacteristic
379C3×A4—21no—
380C3×A4—21no—
381C3×A4—21no—
382C3×A4—41no—
383C3×A4#23511yescharacteristic, complemented
384C3×A4C3×#4111yescharacteristic, complemented
385C32×C4—31no—
386C32×C4—41no—
387C32×C4—41no—
388C32×C4—61no—
389C32×C4—61no—
390C32×C4—61no—
391C32×C4—81no—
392C32×C4—81no—
393C32×C4—81no—
394C32×C4—121no—
395C32×C4—161no—
396C32×C4C2×S411yescharacteristic
397C3⋊Dic3—41no—
398C3×Dic3—31no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3—41no—
402C3×Dic3—61no—
403C3×Dic3—61no—
404C3×Dic3—61no—
405C3×Dic3—81no—
406C3×Dic3—81no—
407C3×Dic3—121no—
408C3×Dic3—241no—
409C3×Dic3C2×S411yescharacteristic
410C2×#41—91no—
411C23×C4—31no—
412#123—91no—
413#123—91no—
414C22⋊Q8—91no—
415C22⋊Q8—91no—
416#121—91no—
417#121—91no—
418#120—91no—
419#120—91no—
420C4×D4—31no—
421C4×D4—91no—
422C4×D4—91no—
423C4×D4—91no—
424#117—91no—
425C33—41noSylow
426C23×C3—21no—
427C23×C3—31no—
428C23×C3—31no—
429C23×C3—61no—
430C23×C3—61no—
431C23×C3—91no—
432C23×C3—91no—
433C23×C3—91no—
434C23×C3—181no—
435C23×C3C2×D3211yescharacteristic
436C23×C3C22×C3×D311yescharacteristic
437C22×D3—21no—
438C22×D3—31no—
439C22×D3—31no—
440C22×D3—31no—
441C22×D3—61no—
442C2×A4—21no—
443C2×A4—21no—
444C2×A4—41no—
445C2×A4—62no—
446C2×A4—61no—
447C2×A4C22×C3×D311yescharacteristic
448S4—21no—
449S4—62no—
450S4—61no—
451C3×Q8—181no—
452C3×Q8—181no—
453C3×D4—62no—
454C3×D4—61no—
455C3×D4—61no—
456C3×D4—62no—
457C3×D4—61no—
458C3×D4—61no—
459C3×D4—181no—
460C3×D4—181no—
461C3×D4—182no—
462C3×D4—181no—
463C3×D4—181no—
464C3×D4—181no—
465C3×D4—181no—
466C3×D4—182no—
467C3×D4—181no—
468C3×D4—181no—
469C2×C3×C4—31no—
470C2×C3×C4—31no—
471C2×C3×C4—31no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—91no—
490C2×C3×C4—91no—
491C2×C3×C4—91no—
492C2×C3×C4—91no—
493C2×C3×C4—91no—
494C2×C3×C4—91no—
495C2×C3×C4—91no—
496C2×C3×C4—91no—
497C2×C3×C4—121no—
498C2×C3×C4—121no—
499C2×C3×C4—121no—
500C2×C3×C4—181no—
501C2×C3×C4—181no—
502C2×C3×C4—181no—
503C2×C3×C4—241no—
504#67—61no—
505#67—61no—
506#67—62no—
507#67—61no—
508#67—61no—
509#67—61no—
510#67—61no—
511#67—121no—
512#67—121no—
513C2×Dic3—31no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518D12—62no—
519D12—61no—
520D12—61no—
521D12—121no—
522C4×D3—31no—
523C4×D3—31no—
524C4×D3—31no—
525C4×D3—41no—
526C4×D3—61no—
527C4×D3—61no—
528C4×D3—61no—
529C4×D3—121no—
530C4×D3—241no—
531C4×D3C3×S411yescharacteristic, complemented
532Dic6—61no—
533Dic6—61no—
534Dic6—121no—
535C2×C32—31no—
536C2×C32—31no—
537C2×C32—41no—
538C2×C32—41no—
539C2×C32—81no—
540C2×C32—81no—
541C2×C32—81no—
542C2×C32—121no—
543C2×C32—161no—
544C2×C32—241no—
545C2×C32C22×S411yescharacteristic
546C3⋊D3—81no—
547C3×D3—21no—
548C3×D3—61no—
549C3×D3—81no—
550C3×D3—82no—
551C3×D3—81no—
552C3×D3—81no—
553C3×D3—82no—
554C3×D3—121no—
555C3×D3—241no—
556C3×D3—242no—
557C24—31no—
558#41—181no—
559#41—181no—
560#41—181no—
561#41—181no—
562C2×Q8—91no—
563C2×D4—31no—
564C2×D4—91no—
565C2×D4—91no—
566C2×D4—91no—
567C2×D4—91no—
568C2×D4—91no—
569C2×D4—91no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—91no—
573C22×C4—91no—
574C22×C4—91no—
575C22×C4—91no—
576C22×C4—91no—
577C22×C4C3×D3211yescharacteristic
578C4⋊C4—31no—
579C4⋊C4—91no—
580C4⋊C4—91no—
581C4⋊C4—91no—
582C4⋊C4—91no—
583C4⋊C4—91no—
584C22⋊C4—31no—
585C22⋊C4—31no—
586C22⋊C4—91no—
587C22⋊C4—91no—
588C22⋊C4—91no—
589C22⋊C4—91no—
590C22⋊C4—91no—
591C22⋊C4—91no—
592C22⋊C4—91no—
593C22⋊C4—91no—
594C42—31no—
595C42—91no—
596C22×C3—21no—
597C22×C3—31no—
598C22×C3—31no—
599C22×C3—31no—
600C22×C3—31no—
601C22×C3—31no—
602C22×C3—61no—
603C22×C3—61no—
604C22×C3—61no—
605C22×C3—61no—
606C22×C3—61no—
607C22×C3—61no—
608C22×C3—62no—
609C22×C3—61no—
610C22×C3—61no—
611C22×C3—92no—
612C22×C3—91no—
613C22×C3—121no—
614C22×C3—121no—
615C22×C3—121no—
616C22×C3—181no—
617C22×C3—181no—
618C22×C3—181no—
619C22×C3—181no—
620C22×C3—181no—
621C22×C3—181no—
622C22×C3—241no—
623C22×C3#379811yescharacteristic, complemented
624C22×C3C3×#23511yescharacteristic, complemented
625C2×D3—32no—
626C2×D3—31no—
627C2×D3—41no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—121no—
635C2×D3—241no—
636C2×D3C2×C3×S411yescharacteristic
637A4—21no—
638A4—21no—
639A4—41no—
640A4C3×#23511yescharacteristic, complemented
641C3×C4—21no—
642C3×C4—31no—
643C3×C4—31no—
644C3×C4—31no—
645C3×C4—41no—
646C3×C4—61no—
647C3×C4—61no—
648C3×C4—61no—
649C3×C4—61no—
650C3×C4—61no—
651C3×C4—62no—
652C3×C4—61no—
653C3×C4—61no—
654C3×C4—81no—
655C3×C4—81no—
656C3×C4—91no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4—161no—
661C3×C4—181no—
662C3×C4—181no—
663C3×C4—181no—
664C3×C4—241no—
665C3×C4D3×S411yescharacteristic
666C3×C4C2×C3×S411yescharacteristic
667Dic3—31no—
668Dic3—41no—
669Dic3—61no—
670Dic3—61no—
671Dic3—61no—
672Dic3—121no—
673Dic3—241no—
674Dic3C2×C3×S411yescharacteristic
675C32—41no—
676C32—41no—
677C32—81no—
678C32—81no—
679C32—81no—
680C32—161no—
681C32#591211yescharacteristic, complemented
682C23—31no—
683C23—61no—
684C23—91no—
685C23—91no—
686C23—91no—
687C23—181no—
688C23C2×C3×D3211yescharacteristic
689Q8—181no—
690Q8—181no—
691D4—61no—
692D4—61no—
693D4—181no—
694D4—181no—
695D4—181no—
696D4—182no—
697D4—181no—
698D4—181no—
699D4—181no—
700D4—181no—
701D4—182no—
702D4—181no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—91no—
712C2×C4—91no—
713C2×C4—91no—
714C2×C4—91no—
715C2×C4—91no—
716C2×C4—91no—
717C2×C4—91no—
718C2×C4—91no—
719C2×C4—181no—
720C2×C4—181no—
721C2×C4—181no—
722C2×C3—21no—
723C2×C3—31no—
724C2×C3—31no—
725C2×C3—31no—
726C2×C3—31no—
727C2×C3—41no—
728C2×C3—61no—
729C2×C3—61no—
730C2×C3—61no—
731C2×C3—81no—
732C2×C3—81no—
733C2×C3—122no—
734C2×C3—121no—
735C2×C3—121no—
736C2×C3—161no—
737C2×C3—181no—
738C2×C3—241no—
739C2×C3—242no—
740C2×C3—361no—
741C2×C3C2×D3×S411yescharacteristic
742C2×C3C22×C3×S411yescharacteristic
743D3—21no—
744D3—61no—
745D3—81no—
746D3—121no—
747D3—241no—
748D3—242no—
749C22—31no—
750C22—31no—
751C22—31no—
752C22—61no—
753C22—61no—
754C22—61no—
755C22—92no—
756C22—91no—
757C22—181no—
758C22—181no—
759C22—181no—
760C22—181no—
761C22—181no—
762C22—181no—
763C22C3×#379811yescharacteristic, complemented
764C4—31no—
765C4—31no—
766C4—61no—
767C4—61no—
768C4—61no—
769C4—91no—
770C4—181no—
771C4—181no—
772C4—181no—
773C4C3×D3×S411yescharacteristic
774C3—21no—
775C3—41no—
776C3—81no—
777C3—81no—
778C3—161no—
779C3#1059642611yescharacteristic, direct product factor
780C3C3×#591211yescharacteristic, complemented
781C2—31no—
782C2—31no—
783C2—61no—
784C2—121no—
785C2—181no—
786C2—361no—
787C2C2×C3×D3×S411yescharacteristic
subgroupG/H
center, hypercenterC3×C4D3×S4
commutator, cosocleC2×C3×A4C23×C3
FrattiniC2C2×C3×D3×S4
FittingC22×C32×C4C2×D3
socleC23×C32C22×D3
hypocenterC3×A4C3×#41
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
1. C3×C4×D3×A4C2semidirect
2. C3×C4×C3⋊S4C2semidirect
3. C32×C4×S4C2semidirect
4. C3×#64210C2semidirect
5. C3×#64209C2semidirect
6. C3×#64207C2semidirect
7. C3×#64204C2semidirect
9. #10596426C3direct (N × H)
20. C22×C3×C4×D3D3semidirect
23. C4×D3×A4C2×C3semidirect
24. C4×C3⋊S4C2×C3semidirect
31. C3×C4×S4D3semidirect
32. C3×C4×S4C2×C3semidirect
34. #64210C2×C3semidirect
35. #64209C2×C3semidirect
36. #64207C2×C3semidirect
37. #64204C2×C3semidirect
133. C32×A4#41semidirect
141. C22×C4×D3C3×D3semidirect
149. C4×S4C3×D3semidirect
242. C3×C4×D3S4semidirect
361. C22×C32#235semidirect
383. C3×A4#235semidirect
384. C3×A4C3×#41semidirect
531. C4×D3C3×S4semidirect
623. C22×C3#3798semidirect
624. C22×C3C3×#235semidirect
640. A4C3×#235semidirect
681. C32#5912semidirect
763. C22C3×#3798semidirect
779. C3#10596426direct (N × H)
780. C3C3×#5912semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×A42
C3×C4×C3⋊S42
C32×C4×S42
C3×#642102
C3×#642092
C3×#642072
C3×#642042
C3×#59123
#105964263
C3×#55473
C3×#37984