Finite Group Databasebeta

← C3×#85299 #11922584

Subgroups — C3×#85299 #11922584

Order 1152.

942 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 942 conjugacy classes of subgroups — too many to draw. Only its 84 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×GL(2,ℤ/4)C211yesmaximal, characteristic, complemented
2C2×C3×GL(2,ℤ/4)C211yesmaximal, characteristic, complemented
3C2×C3×C4⋊S4C211yesmaximal, characteristic, complemented
4C2×C3×C4×S4C211yesmaximal, characteristic, complemented
5C3×A4×C22⋊C4C211yesmaximal, characteristic, complemented
6C3×(C2×S4)⋊C4C211yesmaximal, characteristic, complemented
7C3×SL(2,ℤ/4)⋊C4C211yesmaximal, characteristic, complemented
8#85299C311yesmaximal, characteristic, direct product factor
9C3×#2424—31nomaximal
10C23×C3×A4C2211yescharacteristic
11C22×C3×S4C2211yescharacteristic
12C22×C3×S4C2211yescharacteristic
13C2×C3×C4×A4C2211yescharacteristic
14C2×C3×C4×A4C2211yescharacteristic
15C3×GL(2,ℤ/4)—22no—
16C3×GL(2,ℤ/4)—22no—
17C2×C3×SL(2,ℤ/4)C2211yescharacteristic
18C2×C3×SL(2,ℤ/4)C2211yescharacteristic
19C3×C4⋊S4—22no—
20C3×C4×S4—22no—
21C3×#884—41nomaximal
22C2×GL(2,ℤ/4)C2×C311yescharacteristic, complemented
23C2×GL(2,ℤ/4)C2×C311yescharacteristic, complemented
24C2×C4⋊S4C2×C311yescharacteristic, complemented
25C2×C4×S4C2×C311yescharacteristic, complemented
26C2×C3×#121—31no—
27C2×C3×#121—31no—
28C2×C3×#120—31no—
29C2×C3×#120—31no—
30C2×C3×C4×D4—31no—
31C22×C3×C22⋊C4D311yescharacteristic, complemented
32A4×C22⋊C4—21no—
33A4×C22⋊C4C2×C311yescharacteristic, complemented
34(C2×S4)⋊C4C2×C311yescharacteristic, complemented
35SL(2,ℤ/4)⋊C4C2×C311yescharacteristic, complemented
36C3×#396—31no—
37C3×#394—31no—
38C3×#394—31no—
39C3×#392—31no—
40C3×#390—31no—
41C3×#388—31no—
42C3×#386—31no—
43C3×#386—31no—
44C3×#385—31no—
45C22×C3×A4—21no—
46C22×C3×A4—21no—
47C22×C3×A4—21no—
48C22×C3×A4C2311yescharacteristic
49C2×C3×S4—21no—
50C2×C3×S4—21no—
51C2×C3×S4—21no—
52C2×C3×S4—21no—
53C2×C3×S4—21no—
54C2×C3×S4D412yescomplemented
55C2×C3×#67—41no—
56C2×C3×#67—41no—
57C2×C3×D12—41no—
58C2×C3×C4×D3—41no—
59C3×C4×A4—21no—
60C3×C4×A4—21no—
61C3×SL(2,ℤ/4)—21no—
62C3×SL(2,ℤ/4)D412yescomplemented
63C32×C22⋊C4—41no—
64C3×(C2×D3)⋊C4—41no—
65C3×Dic3⋊C4—41no—
66#2424—31noSylow
67C25×C3C2×D311yescharacteristic
68C23×A4—21no—
69C23×A4C22×C311yescharacteristic
70C22×S4C22×C311yescharacteristic
71C22×S4C22×C311yescharacteristic
72C22×C3×D4—31no—
73C22×C3×D4—31no—
74C22×C3×D4—31no—
75C22×C3×D4—31no—
76C22×C3×D4—31no—
77C22×C3×D4—31no—
78C22×C3×D4—31no—
79C23×C3×C4—31no—
80C23×C3×C4C2×D311yescharacteristic
81C23×C3×C4C2×D311yescharacteristic
82C2×C4×A4—21no—
83C2×C4×A4—21no—
84C2×C4×A4C22×C311yescharacteristic
85C2×C4×A4C22×C311yescharacteristic
86GL(2,ℤ/4)—22no—
87GL(2,ℤ/4)—22no—
88C2×SL(2,ℤ/4)C22×C311yescharacteristic
89C2×SL(2,ℤ/4)C22×C311yescharacteristic
90C4⋊S4—22no—
91C4×S4—22no—
92C3×#121—61no—
93C3×#121—61no—
94C3×#121—61no—
95C3×#121—62no—
96C3×#121—62no—
97C3×#121—61no—
98C3×#120—62no—
99C3×#120—62no—
100C3×#120—62no—
101C3×#120—62no—
102C3×C4×D4—62no—
103C3×C4×D4—62no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C4⋊C4—31no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C4⋊C4—31no—
108C2×C3×C22⋊C4—31no—
109C2×C3×C22⋊C4—31no—
110C2×C3×C22⋊C4—31no—
111C2×C3×C22⋊C4—31no—
112C2×C3×C22⋊C4—31no—
113C2×C3×C22⋊C4—31no—
114C2×C3×C22⋊C4—31no—
115C2×C3×C22⋊C4—31no—
116C2×C3×C22⋊C4—31no—
117C2×C3×C22⋊C4—31no—
118C2×C3×C22⋊C4—31no—
119C2×C3×C22⋊C4—31no—
120C2×C3×C22⋊C4—31no—
121C2×C3×C22⋊C4—31no—
122C2×C3×C22⋊C4—31no—
123C2×C3×C42—31no—
124#884—41no—
125C3×#95—31no—
126C3×#95—31no—
127C3×#95—31no—
128C3×#95—31no—
129C23×C32—41no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C2×C3×A4—41no—
133C2×C3×A4C2×D411yescharacteristic
134C2×C3×A4C2×D411yescharacteristic
135C2×C3×A4#4111yescharacteristic
136C3×S4—22no—
137C3×S4—41no—
138C2×C32×C4—41no—
139C2×C32×C4—41no—
140C3×#67—82no—
141C3×#67—82no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C3×D12—82no—
145C3×C4×D3—82no—
146C2×#121—31no—
147C2×#121—31no—
148C2×#120—31no—
149C2×#120—31no—
150C2×C4×D4—31no—
151C22×C22⋊C4C3×D311yescharacteristic, complemented
152#396—31no—
153#394—31no—
154#394—31no—
155#392—31no—
156#390—31no—
157#388—31no—
158#386—31no—
159#386—31no—
160#385—31no—
161C24×C3—21no—
162C24×C3—21no—
163C24×C3—21no—
164C24×C3—31no—
165C24×C3—31no—
166C24×C3—31no—
167C24×C3—31no—
168C24×C3—61no—
169C24×C3—61no—
170C24×C3—61no—
171C24×C3C22×D311yescharacteristic
172C22×A4—22no—
173C22×A4—21no—
174C22×A4—21no—
175C22×A4—21no—
176C22×A4—21no—
177C22×A4—41no—
178C22×A4—41no—
179C22×A4C23×C311yescharacteristic
180C2×S4—21no—
181C2×S4—21no—
182C2×S4—21no—
183C2×S4—21no—
184C2×S4—21no—
185C2×S4C3×D412yescomplemented
186C2×C3×D4—32no—
187C2×C3×D4—32no—
188C2×C3×D4—62no—
189C2×C3×D4—62no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C2×C3×D4—61no—
195C2×C3×D4—62no—
196C2×C3×D4—61no—
197C2×C3×D4—62no—
198C2×C3×D4—62no—
199C2×C3×D4—61no—
200C2×C3×D4—61no—
201C2×C3×D4—61no—
202C2×C3×D4—62no—
203C2×C3×D4—61no—
204C2×C3×D4—62no—
205C2×C3×D4—61no—
206C2×C3×D4—61no—
207C2×C3×D4—61no—
208C2×C3×D4—61no—
209C2×C3×D4—61no—
210C2×C3×D4—61no—
211C2×C3×D4—121no—
212C2×C3×D4—121no—
213C2×C3×D4—121no—
214C2×C3×D4—121no—
215C2×C3×D4—121no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—31no—
219C22×C3×C4—31no—
220C22×C3×C4—31no—
221C22×C3×C4—31no—
222C22×C3×C4—31no—
223C22×C3×C4—31no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—31no—
228C22×C3×C4—62no—
229C22×C3×C4—61no—
230C22×C3×C4—61no—
231C22×C3×C4—61no—
232C22×C3×C4—61no—
233C22×C3×C4—121no—
234C2×#67—41no—
235C2×#67—41no—
236C2×D12—41no—
237C2×C4×D3—41no—
238C4×A4—21no—
239C4×A4—21no—
240C4×A4—41no—
241C4×A4—41no—
242SL(2,ℤ/4)—21no—
243SL(2,ℤ/4)C3×D412yescomplemented
244C3×C4⋊C4—62no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4—121no—
249C3×C22⋊C4—32no—
250C3×C22⋊C4—32no—
251C3×C22⋊C4—31no—
252C3×C22⋊C4—31no—
253C3×C22⋊C4—31no—
254C3×C22⋊C4—41no—
255C3×C22⋊C4—61no—
256C3×C22⋊C4—62no—
257C3×C22⋊C4—62no—
258C3×C22⋊C4—62no—
259C3×C22⋊C4—62no—
260C3×C22⋊C4—62no—
261C3×C22⋊C4—62no—
262C3×C22⋊C4—61no—
263C3×C22⋊C4—61no—
264C3×C22⋊C4—62no—
265C3×C22⋊C4—61no—
266C3×C22⋊C4—61no—
267C3×C22⋊C4—81no—
268C3×C22⋊C4—121no—
269C3×C22⋊C4S411yescharacteristic, complemented
270C3×C42—62no—
271(C2×D3)⋊C4—41no—
272Dic3⋊C4—41no—
273C22×C32—41no—
274C22×C32—81no—
275C22×C32—81no—
276C22×C32—81no—
277C2×C3×D3—42no—
278C2×C3×D3—81no—
279C2×C3×D3—81no—
280C2×C3×D3—81no—
281C2×C3×D3—81no—
282C2×C3×D3—81no—
283C3×A4#12111yescharacteristic, complemented
284C32×C4—81no—
285C32×C4—81no—
286C3×Dic3—42no—
287C3×Dic3—81no—
288C25C2×C3×D311yescharacteristic
289C22×D4—31no—
290C22×D4—31no—
291C22×D4—31no—
292C22×D4—31no—
293C22×D4—31no—
294C22×D4—31no—
295C22×D4—31no—
296C23×C4—31no—
297C23×C4C2×C3×D311yescharacteristic
298C23×C4C2×C3×D311yescharacteristic
299#121—61no—
300#121—61no—
301#121—61no—
302#121—62no—
303#121—62no—
304#121—61no—
305#120—62no—
306#120—62no—
307#120—62no—
308#120—62no—
309C4×D4—62no—
310C4×D4—62no—
311C2×C4⋊C4—31no—
312C2×C4⋊C4—31no—
313C2×C4⋊C4—31no—
314C2×C4⋊C4—31no—
315C2×C22⋊C4—31no—
316C2×C22⋊C4—31no—
317C2×C22⋊C4—31no—
318C2×C22⋊C4—31no—
319C2×C22⋊C4—31no—
320C2×C22⋊C4—31no—
321C2×C22⋊C4—31no—
322C2×C22⋊C4—31no—
323C2×C22⋊C4—31no—
324C2×C22⋊C4—31no—
325C2×C22⋊C4—31no—
326C2×C22⋊C4—31no—
327C2×C22⋊C4—31no—
328C2×C22⋊C4—31no—
329C2×C22⋊C4—31no—
330C2×C42—31no—
331#95—31no—
332#95—31no—
333#95—31no—
334#95—31no—
335C23×C3—31no—
336C23×C3—31no—
337C23×C3—31no—
338C23×C3—31no—
339C23×C3—32no—
340C23×C3—32no—
341C23×C3—31no—
342C23×C3—41no—
343C23×C3—41no—
344C23×C3—61no—
345C23×C3—61no—
346C23×C3—61no—
347C23×C3—61no—
348C23×C3—61no—
349C23×C3—61no—
350C23×C3—61no—
351C23×C3—61no—
352C23×C3—61no—
353C23×C3—61no—
354C23×C3—61no—
355C23×C3—61no—
356C23×C3—61no—
357C23×C3—61no—
358C23×C3—61no—
359C23×C3—61no—
360C23×C3—61no—
361C23×C3—61no—
362C23×C3—61no—
363C23×C3—61no—
364C23×C3—61no—
365C23×C3—61no—
366C23×C3—61no—
367C23×C3—61no—
368C23×C3—81no—
369C23×C3—121no—
370C23×C3—121no—
371C23×C3—121no—
372C23×C3—122no—
373C23×C3#23511yescharacteristic
374C23×C3D3×D411yescharacteristic
375C23×C3D3×D411yescharacteristic
376C23×C3C2×S411yescharacteristic
377C22×D3—41no—
378C22×D3—41no—
379C2×A4—21no—
380C2×A4—21no—
381C2×A4—21no—
382C2×A4—42no—
383C2×A4—41no—
384C2×A4C2×C3×D411yescharacteristic
385C2×A4C2×C3×D411yescharacteristic
386C2×A4C3×#4111yescharacteristic
387S4—22no—
388S4—41no—
389C3×D4—62no—
390C3×D4—62no—
391C3×D4—62no—
392C3×D4—62no—
393C3×D4—122no—
394C3×D4—122no—
395C3×D4—124no—
396C3×D4—122no—
397C3×D4—122no—
398C3×D4—122no—
399C3×D4—121no—
400C3×D4—121no—
401C3×D4—121no—
402C3×D4—124no—
403C3×D4—122no—
404C3×D4—121no—
405C2×C3×C4—32no—
406C2×C3×C4—32no—
407C2×C3×C4—32no—
408C2×C3×C4—31no—
409C2×C3×C4—31no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—61no—
413C2×C3×C4—61no—
414C2×C3×C4—61no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4—61no—
418C2×C3×C4—61no—
419C2×C3×C4—61no—
420C2×C3×C4—61no—
421C2×C3×C4—61no—
422C2×C3×C4—61no—
423C2×C3×C4—61no—
424C2×C3×C4—61no—
425C2×C3×C4—61no—
426C2×C3×C4—61no—
427C2×C3×C4—61no—
428C2×C3×C4—61no—
429C2×C3×C4—61no—
430C2×C3×C4—61no—
431C2×C3×C4—61no—
432C2×C3×C4—61no—
433C2×C3×C4—61no—
434C2×C3×C4—61no—
435C2×C3×C4—81no—
436C2×C3×C4—81no—
437C2×C3×C4—122no—
438C2×C3×C4—122no—
439C2×C3×C4C2×S411yescharacteristic
440C2×C3×C4C2×S411yescharacteristic
441#67—82no—
442#67—82no—
443C2×Dic3—41no—
444C2×Dic3—41no—
445D12—82no—
446C4×D3—82no—
447C2×C32—41no—
448C2×C32—41no—
449C2×C32—41no—
450C2×C32—161no—
451C3×D3—82no—
452C3×D3—161no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—31no—
457C24—31no—
458C24—31no—
459C24—31no—
460C24—61no—
461C24—61no—
462C24—61no—
463C24C22×C3×D311yescharacteristic
464C2×D4—32no—
465C2×D4—32no—
466C2×D4—62no—
467C2×D4—62no—
468C2×D4—61no—
469C2×D4—61no—
470C2×D4—61no—
471C2×D4—61no—
472C2×D4—61no—
473C2×D4—62no—
474C2×D4—61no—
475C2×D4—62no—
476C2×D4—62no—
477C2×D4—61no—
478C2×D4—61no—
479C2×D4—61no—
480C2×D4—62no—
481C2×D4—61no—
482C2×D4—62no—
483C2×D4—61no—
484C2×D4—61no—
485C2×D4—61no—
486C2×D4—61no—
487C2×D4—61no—
488C2×D4—61no—
489C2×D4—121no—
490C2×D4—121no—
491C2×D4—121no—
492C2×D4—121no—
493C2×D4—121no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—31no—
497C22×C4—31no—
498C22×C4—31no—
499C22×C4—31no—
500C22×C4—31no—
501C22×C4—31no—
502C22×C4—31no—
503C22×C4—31no—
504C22×C4—31no—
505C22×C4—31no—
506C22×C4—62no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4—121no—
512C4⋊C4—62no—
513C4⋊C4—62no—
514C4⋊C4—61no—
515C4⋊C4—61no—
516C4⋊C4—121no—
517C22⋊C4—32no—
518C22⋊C4—31no—
519C22⋊C4—32no—
520C22⋊C4—31no—
521C22⋊C4—31no—
522C22⋊C4—61no—
523C22⋊C4—62no—
524C22⋊C4—62no—
525C22⋊C4—62no—
526C22⋊C4—62no—
527C22⋊C4—62no—
528C22⋊C4—62no—
529C22⋊C4—61no—
530C22⋊C4—61no—
531C22⋊C4—62no—
532C22⋊C4—61no—
533C22⋊C4—61no—
534C22⋊C4—121no—
535C22⋊C4C3×S411yescharacteristic, complemented
536C42—62no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—31no—
541C22×C3—31no—
542C22×C3—31no—
543C22×C3—31no—
544C22×C3—31no—
545C22×C3—31no—
546C22×C3—31no—
547C22×C3—31no—
548C22×C3—31no—
549C22×C3—41no—
550C22×C3—61no—
551C22×C3—62no—
552C22×C3—62no—
553C22×C3—62no—
554C22×C3—62no—
555C22×C3—61no—
556C22×C3—62no—
557C22×C3—61no—
558C22×C3—61no—
559C22×C3—81no—
560C22×C3—81no—
561C22×C3—81no—
562C22×C3—82no—
563C22×C3—81no—
564C22×C3—121no—
565C22×C3—121no—
566C22×C3—121no—
567C22×C3—121no—
568C22×C3—121no—
569C22×C3—121no—
570C22×C3—121no—
571C22×C3—121no—
572C22×C3—121no—
573C22×C3—121no—
574C22×C3—121no—
575C22×C3—121no—
576C22×C3—121no—
577C22×C3—121no—
578C22×C3—121no—
579C22×C3—121no—
580C22×C3—121no—
581C22×C3—161no—
582C22×C3—161no—
583C22×C3#88411yescharacteristic, complemented
584C22×C3C22×S411yescharacteristic
585C2×D3—42no—
586C2×D3—81no—
587C2×D3—81no—
588C2×D3—81no—
589C2×D3—81no—
590C2×D3—81no—
591A4—21no—
592A4C3×#12111yescharacteristic, complemented
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—62no—
596C3×C4—62no—
597C3×C4—61no—
598C3×C4—61no—
599C3×C4—62no—
600C3×C4—81no—
601C3×C4—81no—
602C3×C4—121no—
603C3×C4—121no—
604C3×C4—121no—
605C3×C4—161no—
606C3×C4—161no—
607Dic3—42no—
608Dic3—81no—
609C32—41noSylow
610C23—31no—
611C23—31no—
612C23—31no—
613C23—31no—
614C23—32no—
615C23—32no—
616C23—31no—
617C23—41no—
618C23—61no—
619C23—61no—
620C23—61no—
621C23—61no—
622C23—61no—
623C23—61no—
624C23—61no—
625C23—61no—
626C23—61no—
627C23—61no—
628C23—61no—
629C23—61no—
630C23—61no—
631C23—61no—
632C23—61no—
633C23—61no—
634C23—61no—
635C23—61no—
636C23—61no—
637C23—61no—
638C23—61no—
639C23—61no—
640C23—61no—
641C23—61no—
642C23—121no—
643C23—121no—
644C23—121no—
645C23—122no—
646C23C3×#23511yescharacteristic
647C23C3×D3×D411yescharacteristic
648C23C3×D3×D411yescharacteristic
649C23C2×C3×S411yescharacteristic
650D4—62no—
651D4—62no—
652D4—62no—
653D4—62no—
654D4—122no—
655D4—122no—
656D4—124no—
657D4—122no—
658D4—122no—
659D4—122no—
660D4—121no—
661D4—121no—
662D4—121no—
663D4—124no—
664D4—122no—
665D4—121no—
666C2×C4—32no—
667C2×C4—32no—
668C2×C4—32no—
669C2×C4—31no—
670C2×C4—31no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—122no—
695C2×C4—122no—
696C2×C4C2×C3×S411yescharacteristic
697C2×C4C2×C3×S411yescharacteristic
698C2×C3—31no—
699C2×C3—31no—
700C2×C3—31no—
701C2×C3—31no—
702C2×C3—41no—
703C2×C3—41no—
704C2×C3—41no—
705C2×C3—41no—
706C2×C3—81no—
707C2×C3—81no—
708C2×C3—81no—
709C2×C3—121no—
710C2×C3—122no—
711C2×C3—161no—
712C2×C3—162no—
713C2×C3—241no—
714C2×C3#591211yescharacteristic
715C2×C3D4×S411yescharacteristic
716C2×C3D4×S411yescharacteristic
717D3—82no—
718D3—161no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—31no—
723C22—31no—
724C22—31no—
725C22—31no—
726C22—31no—
727C22—31no—
728C22—31no—
729C22—31no—
730C22—31no—
731C22—61no—
732C22—62no—
733C22—62no—
734C22—62no—
735C22—62no—
736C22—61no—
737C22—62no—
738C22—61no—
739C22—61no—
740C22—121no—
741C22—121no—
742C22—121no—
743C22—121no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22—121no—
755C22—121no—
756C22—121no—
757C22C3×#88411yescharacteristic, complemented
758C22C22×C3×S411yescharacteristic
759C4—21no—
760C4—21no—
761C4—62no—
762C4—62no—
763C4—61no—
764C4—61no—
765C4—62no—
766C4—121no—
767C4—121no—
768C4—121no—
769C3—41no—
770C3—81no—
771C3#8529911yescharacteristic, direct product factor
772C2—31no—
773C2—31no—
774C2—31no—
775C2—31no—
776C2—41no—
777C2—121no—
778C2—122no—
779C2—241no—
780C2C3×#591211yescharacteristic
781C2C3×D4×S411yescharacteristic
782C2C3×D4×S411yescharacteristic
subgroupG/H
centerC22×C3C22×S4
commutator, cosocleC22×A4C23×C3
FrattiniC22C22×C3×S4
FittingC22×C3×C22⋊C4D3
socleC24×C3C22×D3
hypercenterC3×C22⋊C4S4
hypocenterA4C3×#121
LCSG ▷ C22×A4 ▷ A4
UCSC1 ◁ C22×C3 ◁ C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×GL(2,ℤ/4)C2semidirect
2. C2×C3×GL(2,ℤ/4)C2semidirect
3. C2×C3×C4⋊S4C2semidirect
4. C2×C3×C4×S4C2semidirect
5. C3×A4×C22⋊C4C2semidirect
6. C3×(C2×S4)⋊C4C2semidirect
7. C3×SL(2,ℤ/4)⋊C4C2semidirect
8. #85299C3direct (N × H)
22. C2×GL(2,ℤ/4)C2×C3semidirect
23. C2×GL(2,ℤ/4)C2×C3semidirect
24. C2×C4⋊S4C2×C3semidirect
25. C2×C4×S4C2×C3semidirect
31. C22×C3×C22⋊C4D3semidirect
33. A4×C22⋊C4C2×C3semidirect
34. (C2×S4)⋊C4C2×C3semidirect
35. SL(2,ℤ/4)⋊C4C2×C3semidirect
54. C2×C3×S4D4semidirect
62. C3×SL(2,ℤ/4)D4semidirect
151. C22×C22⋊C4C3×D3semidirect
185. C2×S4C3×D4semidirect
243. SL(2,ℤ/4)C3×D4semidirect
269. C3×C22⋊C4S4semidirect
283. C3×A4#121semidirect
535. C22⋊C4C3×S4semidirect
583. C22×C3#884semidirect
592. A4C3×#121semidirect
757. C22C3×#884semidirect
771. C3#85299direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×GL(2,ℤ/4)2
C2×C3×C4⋊S42
C2×C3×C4×S42
C3×A4×C22⋊C42
C3×(C2×S4)⋊C42
C3×SL(2,ℤ/4)⋊C42
#852993
C3×#24243
C3×#8844