Finite Group Databasebeta

← C4×D3×C3⋊S4 #13180798

Subgroups — C4×D3×C3⋊S4 #13180798

Order 1728.

1300 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 1300 conjugacy classes of subgroups — too many to draw. Only its 112 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×D3×C3⋊S4C211yesmaximal, characteristic
2C3×C4×D3×A4C211yesmaximal, characteristic, complemented
3C4×C3⋊(C3⋊S4)C211yesmaximal, characteristic, complemented
4C3×C4×C3⋊S4C211yesmaximal, characteristic, complemented
5D3×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
6#11724201C211yesmaximal, characteristic, complemented
7Dic3×C3⋊S4C211yesmaximal, characteristic, complemented
8C2×C4×C3⋊S4—31nomaximal
9C4×D3×S4—33nomaximal
10C4×D3×#67—31nomaximal
11C2×C3×D3×A4C2211yescharacteristic
12C2×C3⋊(C3⋊S4)C2211yescharacteristic
13C2×C3×C3⋊S4C2211yescharacteristic
14D3×C3⋊S4C414yesdirect product factor
15C32×C4×A4C2211yescharacteristic, complemented
16C4×D3×C3⋊D3—41nomaximal
17C3×Dic3×A4C2211yescharacteristic, complemented
18C3⋊(C3⋊SL(2,ℤ/4))C2211yescharacteristic, complemented
19C3×C3⋊SL(2,ℤ/4)C2211yescharacteristic, complemented
20C22×C3⋊S4—31no—
21C2×D3×S4—33no—
22C22×C3×C4×D3D311yescharacteristic, complemented
23C2×C3×C4×A4—31no—
24C2×D3×#67—31no—
25C2×C4×D32—31no—
26C4×D3×A4D313yescomplemented
27C2×C3⋊SL(2,ℤ/4)—31no—
28C4×C3⋊S4—31no—
29C4×C3⋊S4—33no—
30C4×C3⋊S4—31no—
31C4×C3⋊S4—31no—
32C4×C3⋊S4—61no—
33C4×C3⋊S4—63no—
34C4×C3⋊S4D311yescharacteristic, direct product factor
35C3×C4×S4—33no—
36D3×SL(2,ℤ/4)—33no—
37(C3⋊S4)⋊C4—33no—
38Dic3×S4—33no—
39C4×#638—31no—
40C3×C4×#67—31no—
41Dic3×#67—31no—
42D3×#217—31no—
43#63952—31no—
44D3×(C2×D3)⋊C4—31no—
45#63904—31no—
46C4×#626—31no—
47C4×#625—31no—
48#63879—31no—
49D3×Dic3⋊C4—31no—
50C4×D3×Dic3—31no—
51C2×C32×A4C2311yescharacteristic
52C2×D3×C3⋊D3—41no—
53C3×D3×A4C2×C412yescomplemented
54C3⋊(C3⋊S4)C2×C412yescomplemented
55C3×C3⋊S4C2×C412yescomplemented
56C4×C3⋊(C3⋊D3)—41no—
57C3×C4×C3⋊D3—41no—
58C32×C4×D3—41no—
59#6289—41no—
60Dic3×C3⋊D3—41no—
61D3×C3⋊Dic3—41no—
62C2×C4×S4—93no—
63C2×C4×#67—91no—
64C4×D3×D4—91no—
65C23×C3×D3C2×D311yescharacteristic
66C22×C3×A4—31no—
67C22×D32—31no—
68C2×D3×A4C2×D313yes—
69C2×C3⋊S4—31no—
70C2×C3⋊S4—33no—
71C2×C3⋊S4—34no—
72C2×C3⋊S4—61no—
73C2×C3⋊S4—63no—
74C2×C3⋊S4C2×D311yescharacteristic
75C2×C3×S4—33no—
76D3×S4—312no—
77C22×C32×C4C2×D311yescharacteristic, complemented
78C2×#638—31no—
79C2×C4×C3⋊D3—31no—
80C2×C4×C3⋊D3—121no—
81C2×C3×#67—31no—
82C22×C3×Dic3C2×D311yescharacteristic, complemented
83C2×C3×C4×D3—31no—
84C2×C3×C4×D3—31no—
85C2×C3×C4×D3—31no—
86C2×C3×C4×D3—31no—
87C2×C3×C4×D3—31no—
88C3×C4×A4—21no—
89C3×C4×A4—23no—
90C3×C4×A4—31no—
91C3×C4×A4C2×D313yescomplemented
92C3×C4×A4C2×D311yescharacteristic, complemented
93D3×#67—34no—
94D3×#67—34no—
95C2×#626—31no—
96C2×#625—31no—
97C2×#624—31no—
98C2×D3×Dic3—31no—
99C2×D3×Dic3—31no—
100C2×D3×Dic3—31no—
101C2×D3×Dic3—31no—
102C4×D32—61no—
103C4×D32—61no—
104C4×D32—61no—
105C4×D32—61no—
106C4×D32—123no—
107Dic3×A4C2×D313yescomplemented
108C3⋊SL(2,ℤ/4)—31no—
109C3⋊SL(2,ℤ/4)—33no—
110C3⋊SL(2,ℤ/4)—61no—
111C3⋊SL(2,ℤ/4)—63no—
112C3⋊SL(2,ℤ/4)C2×D311yescharacteristic, complemented
113C3×SL(2,ℤ/4)—33no—
114#3757—31no—
115#3752—31no—
116#3750—31no—
117C4×C3⋊Dic3—31no—
118C3×#217—31no—
119C3×(C2×D3)⋊C4—31no—
120C3×Dic3⋊C4—31no—
121C3×C4×Dic3—31no—
122#3724—31no—
123Dic3⋊Dic3—31no—
124#3722—31no—
125(C2×D3)⋊Dic3—31no—
126(C2×D3)⋊Dic3—31no—
127(C2×D3)⋊Dic3—31no—
128Dic32—31no—
129Dic32—31no—
130C2×C3⋊(C3⋊D3)—41no—
131C2×C3×C3⋊D3—41no—
132C2×C32×D3—41no—
133C32×A4C22×C411yescharacteristic, complemented
134D3×C3⋊D3—44no—
135C33×C4—41no—
136C3⋊(C3⋊Dic3)—41no—
137C3×C3⋊Dic3—41no—
138C32×Dic3—41no—
139C22×S4—93no—
140C23×C3×C4—31no—
141C22×#67—91no—
142C2×D3×D4—91no—
143C22×C4×D3—91no—
144C22×C4×D3—91no—
145C22×C4×D3C3⋊D311yescharacteristic, complemented
146C2×C4×A4—33no—
147C2×SL(2,ℤ/4)—93no—
148C4×S4—33no—
149C4×S4—93no—
150C4×S4—93no—
151C4×S4—93no—
152C4×S4—183no—
153C3×C4×D4—91no—
154C2×#217—91no—
155D4×Dic3—91no—
156C4×#67—31no—
157C4×#67—91no—
158C4×#67—91no—
159C4×#67—91no—
160C4×#67—91no—
161C4×#67—91no—
162C4×#67—91no—
163C4×#67—91no—
164C4×#67—91no—
165C4×#67—91no—
166C4×#67—181no—
167C2×(C2×D3)⋊C4—91no—
168C2×Dic3⋊C4—91no—
169C2×C4×Dic3—91no—
170#893—91no—
171D3×C4⋊C4—91no—
172#67⋊C4—91no—
173#67⋊C4—91no—
174D3×C22⋊C4—91no—
175D3×C22⋊C4—91no—
176C4×D12—91no—
177C42×D3—91no—
178C23×C32C22×D311yescharacteristic
179C22×C3⋊D3—31no—
180C22×C3⋊D3—121no—
181C22×C3×D3—31no—
182C22×C3×D3—31no—
183C22×C3×D3—32no—
184C22×C3×D3—31no—
185C22×C3×D3C4×D312yescomplemented
186C2×C3×A4—21no—
187C2×C3×A4—23no—
188C2×C3×A4—32no—
189C2×C3×A4C22×D313yes—
190C2×C3×A4C22×D311yescharacteristic
191C2×D32—34no—
192C2×D32—62no—
193C2×D32—61no—
194C2×D32—61no—
195C2×D32—123no—
196D3×A4C4×D316yescomplemented
197C3⋊S4—32no—
198C3⋊S4—36no—
199C3⋊S4—62no—
200C3⋊S4—66no—
201C3⋊S4C4×D312yesdirect product factor
202C3×S4—36no—
203C2×C32×C4—31no—
204C2×C32×C4—31no—
205C2×C32×C4—121no—
206#638—32no—
207#638—32no—
208C2×C3⋊Dic3—31no—
209C2×C3⋊Dic3—31no—
210C2×C3⋊Dic3—31no—
211C2×C3⋊Dic3—121no—
212C4×C3⋊D3—41no—
213C4×C3⋊D3—61no—
214C4×C3⋊D3—61no—
215C4×C3⋊D3—121no—
216C4×C3⋊D3—121no—
217C4×C3⋊D3—121no—
218C4×C3⋊D3—123no—
219C4×C3⋊D3—241no—
220C4×C3⋊D3—243no—
221C3×#67—32no—
222C3×#67—32no—
223C2×C3×Dic3—31no—
224C2×C3×Dic3—31no—
225C2×C3×Dic3—31no—
226C2×C3×Dic3—31no—
227C2×C3×Dic3—31no—
228C3×C4×D3—31no—
229C3×C4×D3—31no—
230C3×C4×D3—31no—
231C3×C4×D3—43no—
232C3×C4×D3—61no—
233C3×C4×D3—61no—
234C3×C4×D3—61no—
235C3×C4×D3—123no—
236C3×C4×D3S411yescharacteristic, complemented
237#626—34no—
238#625—34no—
239#624—61no—
240#624—61no—
241#624—123no—
242D3×Dic3—34no—
243D3×Dic3—61no—
244D3×Dic3—61no—
245D3×Dic3—62no—
246D3×Dic3—61no—
247D3×Dic3—61no—
248D3×Dic3—123no—
249D3×Dic3—123no—
250C2×C4×D4—271noSylow
251C2×C33—41no—
252C3⋊(C3⋊D3)—42no—
253C3×C3⋊D3—42no—
254C32×D3—42no—
255C24×C3—31no—
256C23×D3—91no—
257C23×D3—91no—
258C23×D3C2×C3⋊D311yescharacteristic
259C22×A4—33no—
260C2×S4—33no—
261C2×S4—912no—
262C2×S4—93no—
263C2×S4—183no—
264C2×C3×D4—91no—
265C22×C3×C4—21no—
266C22×C3×C4—31no—
267C22×C3×C4—91no—
268C22×C3×C4—91no—
269C22×C3×C4—91no—
270C22×C3×C4—91no—
271C22×C3×C4—91no—
272C22×C3×C4D3211yescharacteristic, complemented
273C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
274C2×#67—31no—
275C2×#67—91no—
276C2×#67—94no—
277C2×#67—94no—
278C2×#67—91no—
279C2×#67—91no—
280C2×#67—91no—
281C2×#67—91no—
282C2×#67—181no—
283C22×Dic3—91no—
284C22×Dic3—91no—
285C22×Dic3—91no—
286C22×Dic3—91no—
287C22×Dic3C2×C3⋊D311yescharacteristic, complemented
288D3×D4—94no—
289D3×D4—94no—
290C2×D12—91no—
291C2×C4×D3—31no—
292C2×C4×D3—31no—
293C2×C4×D3—31no—
294C2×C4×D3—31no—
295C2×C4×D3—31no—
296C2×C4×D3—91no—
297C2×C4×D3—91no—
298C2×C4×D3—91no—
299C2×C4×D3—91no—
300C2×C4×D3—91no—
301C2×C4×D3—91no—
302C2×C4×D3—91no—
303C2×C4×D3—91no—
304C2×C4×D3—181no—
305C2×C4×D3—181no—
306C2×C4×D3—181no—
307C2×C4×D3—181no—
308C2×C4×D3—181no—
309C2×C4×D3—181no—
310C2×C4×D3—181no—
311C2×C4×D3—181no—
312C2×C4×D3—181no—
313C2×C4×D3—363no—
314C4×A4—23no—
315C4×A4—33no—
316C4×A4D3213yescomplemented
317SL(2,ℤ/4)—33no—
318SL(2,ℤ/4)—93no—
319SL(2,ℤ/4)—183no—
320C3×C4⋊C4—91no—
321C3×C22⋊C4—91no—
322C3×C22⋊C4—91no—
323C3×C42—91no—
324#217—31no—
325#217—91no—
326#217—91no—
327#217—91no—
328#217—91no—
329#217—91no—
330#217—181no—
331(C2×D3)⋊C4—31no—
332(C2×D3)⋊C4—91no—
333(C2×D3)⋊C4—91no—
334(C2×D3)⋊C4—91no—
335(C2×D3)⋊C4—91no—
336(C2×D3)⋊C4—91no—
337(C2×D3)⋊C4—91no—
338(C2×D3)⋊C4—91no—
339(C2×D3)⋊C4—181no—
340C4⋊Dic3—91no—
341Dic3⋊C4—31no—
342Dic3⋊C4—91no—
343Dic3⋊C4—91no—
344Dic3⋊C4—91no—
345Dic3⋊C4—91no—
346Dic3⋊C4—91no—
347Dic3⋊C4—181no—
348C4×Dic3—31no—
349C4×Dic3—91no—
350C4×Dic3—91no—
351C4×Dic3—91no—
352C4×Dic3—91no—
353C4×Dic3—91no—
354C4×Dic3—91no—
355C4×Dic3—181no—
356C22×C32—31no—
357C22×C32—31no—
358C22×C32—121no—
359C22×C32C2×C4×D311yescharacteristic, complemented
360C2×C3⋊D3—32no—
361C2×C3⋊D3—41no—
362C2×C3⋊D3—61no—
363C2×C3⋊D3—61no—
364C2×C3⋊D3—124no—
365C2×C3⋊D3—121no—
366C2×C3⋊D3—123no—
367C2×C3⋊D3—241no—
368C2×C3⋊D3—243no—
369C2×C3×D3—31no—
370C2×C3×D3—32no—
371C2×C3×D3—32no—
372C2×C3×D3—32no—
373C2×C3×D3—32no—
374C2×C3×D3—43no—
375C2×C3×D3—61no—
376C2×C3×D3—61no—
377C2×C3×D3—61no—
378C2×C3×D3—123no—
379C2×C3×D3C2×S411yescharacteristic
380C3×A4—21no—
381C3×A4—23no—
382C3×A4C2×C4×D313yescomplemented
383C3×A4C2×C4×D311yescharacteristic, complemented
384D32—64no—
385D32—64no—
386D32—1212no—
387C32×C4—31no—
388C32×C4—41no—
389C32×C4—43no—
390C32×C4—83no—
391C32×C4—81no—
392C32×C4—121no—
393C32×C4C2×S411yescharacteristic, complemented
394C3⋊Dic3—32no—
395C3⋊Dic3—41no—
396C3⋊Dic3—61no—
397C3⋊Dic3—61no—
398C3⋊Dic3—121no—
399C3⋊Dic3—123no—
400C3⋊Dic3—241no—
401C3⋊Dic3—243no—
402C3×Dic3—32no—
403C3×Dic3—31no—
404C3×Dic3—43no—
405C3×Dic3—61no—
406C3×Dic3—61no—
407C3×Dic3—123no—
408C3×Dic3C2×S411yescharacteristic, complemented
409C22×D4—271no—
410C23×C4—31no—
411C23×C4—271no—
412C4×D4—91no—
413C4×D4—271no—
414C4×D4—271no—
415C4×D4—271no—
416C4×D4—271no—
417C4×D4—271no—
418C4×D4—271no—
419C4×D4—271no—
420C2×C4⋊C4—271no—
421C2×C22⋊C4—271no—
422C2×C22⋊C4—271no—
423C2×C42—271no—
424C33—41noSylow
425C23×C3—21no—
426C23×C3—32no—
427C23×C3—91no—
428C23×C3—91no—
429C23×C3—92no—
430C23×C3—91no—
431C23×C3C2×D3211yescharacteristic
432C23×C3C22×C3⋊D311yescharacteristic
433C22×D3—31no—
434C22×D3—31no—
435C22×D3—32no—
436C22×D3—31no—
437C22×D3—94no—
438C22×D3—94no—
439C22×D3—91no—
440C22×D3—91no—
441C22×D3—181no—
442C22×D3—181no—
443C22×D3—182no—
444C22×D3—181no—
445C22×D3—181no—
446C22×D3—182no—
447C22×D3—181no—
448C22×D3—363no—
449C22×D3C4×C3⋊D312yescomplemented
450C2×A4—23no—
451C2×A4—36no—
452C2×A4C2×D3213yes—
453S4—36no—
454S4—96no—
455S4—186no—
456C3×D4—92no—
457C3×D4—92no—
458C2×C3×C4—31no—
459C2×C3×C4—31no—
460C2×C3×C4—31no—
461C2×C3×C4—31no—
462C2×C3×C4—31no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—91no—
466C2×C3×C4—91no—
467C2×C3×C4—91no—
468C2×C3×C4—91no—
469C2×C3×C4—91no—
470C2×C3×C4—91no—
471C2×C3×C4—91no—
472C2×C3×C4—91no—
473C2×C3×C4—123no—
474C2×C3×C4—181no—
475C2×C3×C4—181no—
476C2×C3×C4—181no—
477#67—32no—
478#67—32no—
479#67—94no—
480#67—94no—
481#67—94no—
482#67—92no—
483#67—92no—
484#67—92no—
485#67—92no—
486#67—182no—
487#67—182no—
488C2×Dic3—31no—
489C2×Dic3—31no—
490C2×Dic3—31no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493C2×Dic3—94no—
494C2×Dic3—91no—
495C2×Dic3—91no—
496C2×Dic3—91no—
497C2×Dic3—91no—
498C2×Dic3—91no—
499C2×Dic3—91no—
500C2×Dic3—181no—
501C2×Dic3—181no—
502C2×Dic3—181no—
503C2×Dic3—181no—
504C2×Dic3—181no—
505C2×Dic3—181no—
506C2×Dic3—182no—
507C2×Dic3—181no—
508C2×Dic3—363no—
509D12—94no—
510C4×D3—31no—
511C4×D3—31no—
512C4×D3—31no—
513C4×D3—61no—
514C4×D3—61no—
515C4×D3—61no—
516C4×D3—94no—
517C4×D3—123no—
518C4×D3—181no—
519C4×D3—181no—
520C4×D3—181no—
521C4×D3—181no—
522C4×D3—181no—
523C4×D3—181no—
524C4×D3—181no—
525C4×D3—182no—
526C4×D3—181no—
527C4×D3—181no—
528C4×D3—181no—
529C4×D3—181no—
530C4×D3—181no—
531C4×D3—363no—
532C4×D3—361no—
533C4×D3—363no—
534C4×D3—361no—
535C4×D3—363no—
536C4×D3—723no—
537C4×D3C3⋊S411yescharacteristic, direct product factor
538C2×C32—31no—
539C2×C32—31no—
540C2×C32—41no—
541C2×C32—43no—
542C2×C32—83no—
543C2×C32—81no—
544C2×C32—122no—
545C2×C32C22×S411yescharacteristic
546C3⋊D3—42no—
547C3⋊D3—62no—
548C3⋊D3—122no—
549C3⋊D3—126no—
550C3⋊D3—242no—
551C3⋊D3—246no—
552C3×D3—32no—
553C3×D3—46no—
554C3×D3—62no—
555C3×D3—126no—
556C3×D3C4×S412yescomplemented
557C24—31no—
558C24—271no—
559C2×D4—91no—
560C2×D4—271no—
561C2×D4—274no—
562C2×D4—274no—
563C2×D4—271no—
564C2×D4—271no—
565C22×C4—31no—
566C22×C4—91no—
567C22×C4—91no—
568C22×C4—91no—
569C22×C4—91no—
570C22×C4—91no—
571C22×C4—271no—
572C22×C4—271no—
573C22×C4—271no—
574C22×C4—271no—
575C22×C4—271no—
576C22×C4—271no—
577C22×C4—541no—
578C22×C4—541no—
579C22×C4—541no—
580C22×C4—541no—
581C22×C4D3×C3⋊D311yescharacteristic, complemented
582C4⋊C4—91no—
583C4⋊C4—271no—
584C4⋊C4—271no—
585C4⋊C4—271no—
586C22⋊C4—91no—
587C22⋊C4—91no—
588C22⋊C4—271no—
589C22⋊C4—271no—
590C22⋊C4—271no—
591C22⋊C4—271no—
592C22⋊C4—271no—
593C22⋊C4—271no—
594C42—91no—
595C42—271no—
596C42—271no—
597C42—271no—
598C22×C3—21no—
599C22×C3—31no—
600C22×C3—31no—
601C22×C3—31no—
602C22×C3—31no—
603C22×C3—31no—
604C22×C3—61no—
605C22×C3—61no—
606C22×C3—92no—
607C22×C3—92no—
608C22×C3—92no—
609C22×C3—92no—
610C22×C3—91no—
611C22×C3—123no—
612C22×C3—181no—
613C22×C3—181no—
614C22×C3—181no—
615C22×C3C4×D3211yescharacteristic, complemented
616C22×C3C2×C4×C3⋊D311yescharacteristic, complemented
617C2×D3—31no—
618C2×D3—32no—
619C2×D3—32no—
620C2×D3—32no—
621C2×D3—32no—
622C2×D3—61no—
623C2×D3—61no—
624C2×D3—61no—
625C2×D3—92no—
626C2×D3—92no—
627C2×D3—123no—
628C2×D3—182no—
629C2×D3—184no—
630C2×D3—184no—
631C2×D3—184no—
632C2×D3—181no—
633C2×D3—181no—
634C2×D3—181no—
635C2×D3—181no—
636C2×D3—184no—
637C2×D3—3612no—
638C2×D3—361no—
639C2×D3—363no—
640C2×D3—361no—
641C2×D3—723no—
642C2×D3C2×C3⋊S411yescharacteristic
643A4—23no—
644A4C4×D3213yescomplemented
645C3×C4—21no—
646C3×C4—31no—
647C3×C4—31no—
648C3×C4—31no—
649C3×C4—43no—
650C3×C4—61no—
651C3×C4—83no—
652C3×C4—92no—
653C3×C4—91no—
654C3×C4—123no—
655C3×C4—181no—
656C3×C4—181no—
657C3×C4D3×S411yescharacteristic, complemented
658C3×C4C2×C3⋊S411yescharacteristic, complemented
659Dic3—32no—
660Dic3—31no—
661Dic3—61no—
662Dic3—61no—
663Dic3—92no—
664Dic3—92no—
665Dic3—123no—
666Dic3—182no—
667Dic3—181no—
668Dic3—181no—
669Dic3—181no—
670Dic3—181no—
671Dic3—361no—
672Dic3—363no—
673Dic3—361no—
674Dic3—723no—
675Dic3C2×C3⋊S411yescharacteristic, complemented
676C32—41no—
677C32—43no—
678C32—83no—
679C32—81no—
680C32C2×C4×S411yescharacteristic, complemented
681C23—32no—
682C23—91no—
683C23—91no—
684C23—92no—
685C23—91no—
686C23—271no—
687C23—274no—
688C23—541no—
689C23—541no—
690C23—542no—
691C23C2×D3×C3⋊D311yescharacteristic
692D4—92no—
693D4—92no—
694D4—274no—
695D4—272no—
696D4—274no—
697D4—272no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—91no—
702C2×C4—91no—
703C2×C4—91no—
704C2×C4—91no—
705C2×C4—91no—
706C2×C4—91no—
707C2×C4—91no—
708C2×C4—91no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4—274no—
713C2×C4—271no—
714C2×C4—271no—
715C2×C4—271no—
716C2×C4—541no—
717C2×C4—541no—
718C2×C4—541no—
719C2×C4—541no—
720C2×C4—541no—
721C2×C4—541no—
722C2×C4—541no—
723C2×C4—542no—
724C2×C4—541no—
725C2×C3—21no—
726C2×C3—31no—
727C2×C3—31no—
728C2×C3—32no—
729C2×C3—31no—
730C2×C3—31no—
731C2×C3—43no—
732C2×C3—61no—
733C2×C3—61no—
734C2×C3—83no—
735C2×C3—92no—
736C2×C3—126no—
737C2×C3—182no—
738C2×C3C2×D3×S411yescharacteristic
739C2×C3C22×C3⋊S411yescharacteristic
740D3—32no—
741D3—62no—
742D3—126no—
743D3—182no—
744D3—182no—
745D3—362no—
746D3—366no—
747D3—726no—
748D3C4×C3⋊S412yesdirect product factor
749C22—31no—
750C22—31no—
751C22—31no—
752C22—92no—
753C22—92no—
754C22—92no—
755C22—92no—
756C22—91no—
757C22—181no—
758C22—181no—
759C22—181no—
760C22—272no—
761C22—544no—
762C22—541no—
763C22—544no—
764C22—541no—
765C22C4×D3×C3⋊D311yescharacteristic, complemented
766C4—31no—
767C4—31no—
768C4—92no—
769C4—91no—
770C4—181no—
771C4—181no—
772C4—272no—
773C4—541no—
774C4—541no—
775C4D3×C3⋊S411yescharacteristic, direct product factor
776C3—21no—
777C3—43no—
778C3—83no—
779C3C4×D3×S411yescharacteristic, complemented
780C3C2×C4×C3⋊S411yescharacteristic, complemented
781C2—31no—
782C2—31no—
783C2—32no—
784C2—92no—
785C2—182no—
786C2—542no—
787C2C2×D3×C3⋊S411yescharacteristic
subgroupG/H
center, hypercenterC4D3×C3⋊S4
commutator, hypocenterC32×A4C22×C4
FrattiniC2C2×D3×C3⋊S4
FittingC22×C32×C4C2×D3
socleC23×C32C22×D3
prime radicalC2×D3×C3⋊S4C2
cosocleC2×C32×A4C23
LCSG ▷ C32×A4
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×D3×A4C2semidirect
3. C4×C3⋊(C3⋊S4)C2semidirect
4. C3×C4×C3⋊S4C2semidirect
5. D3×C3⋊SL(2,ℤ/4)C2semidirect
6. #11724201C2semidirect
7. Dic3×C3⋊S4C2semidirect
14. D3×C3⋊S4C4direct (N × H)
15. C32×C4×A4C22semidirect
17. C3×Dic3×A4C22semidirect
18. C3⋊(C3⋊SL(2,ℤ/4))C22semidirect
19. C3×C3⋊SL(2,ℤ/4)C22semidirect
22. C22×C3×C4×D3D3semidirect
26. C4×D3×A4D3semidirect
34. C4×C3⋊S4D3direct (N × H)
53. C3×D3×A4C2×C4semidirect
54. C3⋊(C3⋊S4)C2×C4semidirect
55. C3×C3⋊S4C2×C4semidirect
77. C22×C32×C4C2×D3semidirect
82. C22×C3×Dic3C2×D3semidirect
91. C3×C4×A4C2×D3semidirect
92. C3×C4×A4C2×D3semidirect
107. Dic3×A4C2×D3semidirect
112. C3⋊SL(2,ℤ/4)C2×D3semidirect
133. C32×A4C22×C4semidirect
145. C22×C4×D3C3⋊D3semidirect
185. C22×C3×D3C4×D3semidirect
196. D3×A4C4×D3semidirect
201. C3⋊S4C4×D3direct (N × H)
236. C3×C4×D3S4semidirect
272. C22×C3×C4D32semidirect
273. C22×C3×C4C2×C3⋊D3semidirect
287. C22×Dic3C2×C3⋊D3semidirect
316. C4×A4D32semidirect
359. C22×C32C2×C4×D3semidirect
382. C3×A4C2×C4×D3semidirect
383. C3×A4C2×C4×D3semidirect
393. C32×C4C2×S4semidirect
408. C3×Dic3C2×S4semidirect
449. C22×D3C4×C3⋊D3semidirect
537. C4×D3C3⋊S4direct (N × H)
556. C3×D3C4×S4semidirect
581. C22×C4D3×C3⋊D3semidirect
615. C22×C3C4×D32semidirect
616. C22×C3C2×C4×C3⋊D3semidirect
644. A4C4×D32semidirect
657. C3×C4D3×S4semidirect
658. C3×C4C2×C3⋊S4semidirect
675. Dic3C2×C3⋊S4semidirect
680. C32C2×C4×S4semidirect
748. D3C4×C3⋊S4direct (N × H)
765. C22C4×D3×C3⋊D3semidirect
775. C4D3×C3⋊S4direct (N × H)
779. C3C4×D3×S4semidirect
780. C3C2×C4×C3⋊S4semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C3⋊S42
C3×C4×D3×A42
C4×C3⋊(C3⋊S4)2
C3×C4×C3⋊S42
D3×C3⋊SL(2,ℤ/4)2
#117242012
Dic3×C3⋊S42
C2×C4×C3⋊S43
C4×D3×S43
C4×D3×#673
C4×D3×C3⋊D34