Finite Group Databasebeta

← C3×#85495 #11922775

Subgroups — C3×#85495 #11922775

Order 1152.

1070 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 1070 conjugacy classes of subgroups — too many to draw. Only its 92 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×D4×A4C211yesmaximal, characteristic, complemented
2C2×C3×GL(2,ℤ/4)C211yesmaximal, characteristic, complemented
3C2×C3×GL(2,ℤ/4)C211yesmaximal, characteristic, complemented
4C22×C3×SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
5C3×#5432C211yesmaximal, characteristic, complemented
6C3×(C2×S4)⋊C4C211yesmaximal, characteristic, complemented
7C3×SL(2,ℤ/4)⋊C4C211yesmaximal, characteristic, complemented
8#85495C311yesmaximal, characteristic, direct product factor
9C3×#2410—31nomaximal
10C23×C3×A4C2211yescharacteristic
11C23×C3×A4C2211yescharacteristic
12C22×C3×S4C2211yescharacteristic
13C3×D4×A4—22no—
14C2×C3×C4×A4C2211yescharacteristic
15C3×GL(2,ℤ/4)—22no—
16C3×GL(2,ℤ/4)—22no—
17C2×C3×SL(2,ℤ/4)—22no—
18C2×C3×SL(2,ℤ/4)C2211yescharacteristic
19C2×C3×SL(2,ℤ/4)C2211yescharacteristic
20C2×C3×SL(2,ℤ/4)C2211yescharacteristic
21C3×#939—41nomaximal
22C23×C3×D4D311yescharacteristic, complemented
23C2×D4×A4—21no—
24C2×D4×A4C2×C311yescharacteristic, complemented
25C2×GL(2,ℤ/4)C2×C311yescharacteristic, complemented
26C2×GL(2,ℤ/4)C2×C311yescharacteristic, complemented
27C22×SL(2,ℤ/4)C2×C311yescharacteristic, complemented
28C2×C3×#121—31no—
29C2×C3×#121—31no—
30C2×C3×#120—31no—
31C2×C3×#120—31no—
32C22×C3×C22⋊C4—31no—
33#5432C2×C311yescharacteristic, complemented
34(C2×S4)⋊C4C2×C311yescharacteristic, complemented
35SL(2,ℤ/4)⋊C4C2×C311yescharacteristic, complemented
36C3×#394—31no—
37C3×#394—31no—
38C3×#392—31no—
39C3×#392—31no—
40C3×#386—31no—
41C3×#386—31no—
42C3×#386—31no—
43C3×#385—31no—
44C3×#379—31no—
45C22×C3×A4—21no—
46C22×C3×A4—21no—
47C22×C3×A4—21no—
48C22×C3×A4—21no—
49C22×C3×A4—21no—
50C22×C3×A4D412yescomplemented
51C22×C3×A4C2311yescharacteristic
52C2×C3×S4—21no—
53C2×C3×S4—21no—
54C2×C3×S4—21no—
55C2×C32×D4—41no—
56C2×C3×#67—41no—
57C2×C3×#67—41no—
58C22×C3×Dic3—41no—
59C3×C4×A4—21no—
60C3×SL(2,ℤ/4)—21no—
61C3×SL(2,ℤ/4)—21no—
62C3×SL(2,ℤ/4)D412yescomplemented
63C3×#217—41no—
64C3×(C2×D3)⋊C4—41no—
65C3×Dic3⋊C4—41no—
66#2410—31noSylow
67C25×C3C2×D311yescharacteristic
68C25×C3C2×D311yescharacteristic
69C23×A4—21no—
70C23×A4—21no—
71C23×A4C22×C311yescharacteristic
72C23×A4C22×C311yescharacteristic
73C22×S4C22×C311yescharacteristic
74C22×C3×D4—22no—
75C22×C3×D4—31no—
76C22×C3×D4—31no—
77C22×C3×D4—31no—
78C22×C3×D4—31no—
79C22×C3×D4—31no—
80C22×C3×D4—31no—
81C22×C3×D4—31no—
82C22×C3×D4—31no—
83C22×C3×D4—31no—
84C22×C3×D4—62no—
85C23×C3×C4—31no—
86C23×C3×C4—31no—
87C23×C3×C4C2×D311yescharacteristic
88D4×A4—24no—
89D4×A4—22no—
90C2×C4×A4—21no—
91C2×C4×A4C22×C311yescharacteristic
92GL(2,ℤ/4)—22no—
93GL(2,ℤ/4)—22no—
94C2×SL(2,ℤ/4)—22no—
95C2×SL(2,ℤ/4)C22×C311yescharacteristic
96C2×SL(2,ℤ/4)C22×C311yescharacteristic
97C2×SL(2,ℤ/4)C22×C311yescharacteristic
98C3×#121—64no—
99C3×#121—61no—
100C3×#121—61no—
101C3×#121—61no—
102C3×#121—61no—
103C3×#120—62no—
104C3×#120—62no—
105C3×#120—62no—
106C3×#120—62no—
107C2×C3×C4⋊C4—31no—
108C2×C3×C4⋊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×C22⋊C4—31no—
124C2×C3×C22⋊C4—62no—
125C2×C3×C22⋊C4—62no—
126#939—41no—
127C3×#95—31no—
128C3×#95—31no—
129C3×#95—31no—
130C3×#95—31no—
131C23×C32—41no—
132C23×C32—41no—
133C22×C3×D3—41no—
134C2×C3×A4—22no—
135C2×C3×A4—41no—
136C2×C3×A4C2×D411yescharacteristic
137C2×C3×A4C2×D411yescharacteristic
138C2×C3×A4#4111yescharacteristic
139C3×S4—41no—
140C32×D4—82no—
141C2×C32×C4—41no—
142C3×#67—82no—
143C3×#67—82no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—82no—
148C23×D4C3×D311yescharacteristic, complemented
149C2×#121—31no—
150C2×#121—31no—
151C2×#120—31no—
152C2×#120—31no—
153C22×C22⋊C4—31no—
154#394—31no—
155#394—31no—
156#392—31no—
157#392—31no—
158#386—31no—
159#386—31no—
160#386—31no—
161#385—31no—
162#379—31no—
163C24×C3—21no—
164C24×C3—21no—
165C24×C3—21no—
166C24×C3—21no—
167C24×C3—21no—
168C24×C3—31no—
169C24×C3—31no—
170C24×C3—31no—
171C24×C3—32no—
172C24×C3—31no—
173C24×C3—31no—
174C24×C3—61no—
175C24×C3—61no—
176C24×C3—61no—
177C24×C3—61no—
178C24×C3—61no—
179C24×C3#6712yescomplemented
180C24×C3C22×D311yescharacteristic
181C22×A4—21no—
182C22×A4—21no—
183C22×A4—22no—
184C22×A4—21no—
185C22×A4—21no—
186C22×A4—21no—
187C22×A4—22no—
188C22×A4—21no—
189C22×A4—41no—
190C22×A4—41no—
191C22×A4—41no—
192C22×A4—41no—
193C22×A4C3×D412yescomplemented
194C22×A4C23×C311yescharacteristic
195C2×S4—21no—
196C2×S4—21no—
197C2×S4—21no—
198C2×C3×D4—34no—
199C2×C3×D4—31no—
200C2×C3×D4—31no—
201C2×C3×D4—31no—
202C2×C3×D4—41no—
203C2×C3×D4—61no—
204C2×C3×D4—62no—
205C2×C3×D4—62no—
206C2×C3×D4—62no—
207C2×C3×D4—62no—
208C2×C3×D4—62no—
209C2×C3×D4—62no—
210C2×C3×D4—62no—
211C2×C3×D4—62no—
212C2×C3×D4—62no—
213C2×C3×D4—61no—
214C2×C3×D4—61no—
215C2×C3×D4—62no—
216C2×C3×D4—62no—
217C2×C3×D4—62no—
218C2×C3×D4—61no—
219C2×C3×D4—62no—
220C2×C3×D4—61no—
221C2×C3×D4—61no—
222C2×C3×D4—61no—
223C2×C3×D4—61no—
224C2×C3×D4—61no—
225C2×C3×D4—61no—
226C2×C3×D4—61no—
227C2×C3×D4—81no—
228C2×C3×D4—121no—
229C2×C3×D4—121no—
230C2×C3×D4—121no—
231C2×C3×D4—121no—
232C2×C3×D4S411yescharacteristic, complemented
233C22×C3×C4—21no—
234C22×C3×C4—31no—
235C22×C3×C4—31no—
236C22×C3×C4—31no—
237C22×C3×C4—31no—
238C22×C3×C4—31no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—31no—
242C22×C3×C4—31no—
243C22×C3×C4—61no—
244C22×C3×C4—62no—
245C22×C3×C4—62no—
246C22×C3×C4—62no—
247C22×C3×C4—61no—
248C22×C3×C4—61no—
249C22×C3×C4—121no—
250C22×C3×C4—121no—
251C2×#67—41no—
252C2×#67—41no—
253C22×Dic3—41no—
254C4×A4—22no—
255C4×A4—21no—
256SL(2,ℤ/4)—21no—
257SL(2,ℤ/4)—21no—
258SL(2,ℤ/4)C3×D412yescomplemented
259C3×C4⋊C4—62no—
260C3×C4⋊C4—61no—
261C3×C4⋊C4—61no—
262C3×C22⋊C4—32no—
263C3×C22⋊C4—32no—
264C3×C22⋊C4—62no—
265C3×C22⋊C4—62no—
266C3×C22⋊C4—62no—
267C3×C22⋊C4—62no—
268C3×C22⋊C4—62no—
269C3×C22⋊C4—61no—
270C3×C22⋊C4—61no—
271C3×C22⋊C4—61no—
272C3×C22⋊C4—62no—
273C3×C22⋊C4—62no—
274C3×C22⋊C4—62no—
275C3×C22⋊C4—61no—
276C3×C22⋊C4—61no—
277C3×C22⋊C4—61no—
278C3×C22⋊C4—61no—
279C3×C22⋊C4—61no—
280C3×C22⋊C4—121no—
281C3×C22⋊C4—121no—
282#217—41no—
283(C2×D3)⋊C4—41no—
284Dic3⋊C4—41no—
285C22×C32—42no—
286C22×C32—41no—
287C22×C32—81no—
288C22×C32—81no—
289C22×C32—81no—
290C22×C32—81no—
291C22×C32—81no—
292C2×C3×D3—81no—
293C2×C3×D3—81no—
294C2×C3×D3—81no—
295C3×A4#12111yescharacteristic, complemented
296C32×C4—81no—
297C3×Dic3—42no—
298C3×Dic3—81no—
299C3×Dic3—81no—
300C25C2×C3×D311yescharacteristic
301C25C2×C3×D311yescharacteristic
302C22×D4—22no—
303C22×D4—31no—
304C22×D4—31no—
305C22×D4—31no—
306C22×D4—31no—
307C22×D4—31no—
308C22×D4—31no—
309C22×D4—31no—
310C22×D4—31no—
311C22×D4—31no—
312C22×D4—62no—
313C23×C4—31no—
314C23×C4—31no—
315C23×C4C2×C3×D311yescharacteristic
316#121—64no—
317#121—61no—
318#121—61no—
319#121—61no—
320#121—61no—
321#120—62no—
322#120—62no—
323#120—62no—
324#120—62no—
325C2×C4⋊C4—31no—
326C2×C4⋊C4—31no—
327C2×C22⋊C4—31no—
328C2×C22⋊C4—31no—
329C2×C22⋊C4—31no—
330C2×C22⋊C4—31no—
331C2×C22⋊C4—31no—
332C2×C22⋊C4—31no—
333C2×C22⋊C4—31no—
334C2×C22⋊C4—31no—
335C2×C22⋊C4—31no—
336C2×C22⋊C4—31no—
337C2×C22⋊C4—31no—
338C2×C22⋊C4—31no—
339C2×C22⋊C4—31no—
340C2×C22⋊C4—31no—
341C2×C22⋊C4—31no—
342C2×C22⋊C4—62no—
343C2×C22⋊C4—62no—
344#95—31no—
345#95—31no—
346#95—31no—
347#95—31no—
348C23×C3—22no—
349C23×C3—31no—
350C23×C3—31no—
351C23×C3—31no—
352C23×C3—31no—
353C23×C3—32no—
354C23×C3—32no—
355C23×C3—32no—
356C23×C3—31no—
357C23×C3—32no—
358C23×C3—31no—
359C23×C3—41no—
360C23×C3—41no—
361C23×C3—41no—
362C23×C3—61no—
363C23×C3—61no—
364C23×C3—61no—
365C23×C3—61no—
366C23×C3—61no—
367C23×C3—61no—
368C23×C3—61no—
369C23×C3—61no—
370C23×C3—61no—
371C23×C3—61no—
372C23×C3—61no—
373C23×C3—62no—
374C23×C3—61no—
375C23×C3—61no—
376C23×C3—61no—
377C23×C3—61no—
378C23×C3—61no—
379C23×C3—61no—
380C23×C3—62no—
381C23×C3—62no—
382C23×C3—61no—
383C23×C3—61no—
384C23×C3—61no—
385C23×C3—61no—
386C23×C3—61no—
387C23×C3—61no—
388C23×C3—61no—
389C23×C3—61no—
390C23×C3—61no—
391C23×C3—61no—
392C23×C3—81no—
393C23×C3—81no—
394C23×C3—121no—
395C23×C3—121no—
396C23×C3—121no—
397C23×C3—122no—
398C23×C3—122no—
399C23×C3D3×D411yescharacteristic
400C23×C3#23711yescharacteristic
401C23×C3C2×#6711yescharacteristic
402C23×C3C2×S411yescharacteristic
403C23×C3C2×S411yescharacteristic
404C22×D3—41no—
405C2×A4—22no—
406C2×A4—21no—
407C2×A4—21no—
408C2×A4—21no—
409C2×A4—42no—
410C2×A4—42no—
411C2×A4—41no—
412C2×A4C2×C3×D411yescharacteristic
413C2×A4C2×C3×D411yescharacteristic
414C2×A4C3×#4111yescharacteristic
415S4—41no—
416C3×D4—22no—
417C3×D4—62no—
418C3×D4—62no—
419C3×D4—64no—
420C3×D4—62no—
421C3×D4—82no—
422C3×D4—84no—
423C3×D4—122no—
424C3×D4—124no—
425C3×D4—122no—
426C3×D4—121no—
427C3×D4—121no—
428C3×D4—121no—
429C3×D4—122no—
430C3×D4—124no—
431C3×D4—121no—
432C3×D4—122no—
433C2×C3×C4—32no—
434C2×C3×C4—32no—
435C2×C3×C4—32no—
436C2×C3×C4—31no—
437C2×C3×C4—41no—
438C2×C3×C4—61no—
439C2×C3×C4—61no—
440C2×C3×C4—61no—
441C2×C3×C4—61no—
442C2×C3×C4—61no—
443C2×C3×C4—61no—
444C2×C3×C4—61no—
445C2×C3×C4—61no—
446C2×C3×C4—61no—
447C2×C3×C4—61no—
448C2×C3×C4—61no—
449C2×C3×C4—61no—
450C2×C3×C4—61no—
451C2×C3×C4—61no—
452C2×C3×C4—61no—
453C2×C3×C4—61no—
454C2×C3×C4—61no—
455C2×C3×C4—61no—
456C2×C3×C4—61no—
457C2×C3×C4—61no—
458C2×C3×C4—61no—
459C2×C3×C4—61no—
460C2×C3×C4—81no—
461C2×C3×C4—122no—
462C2×C3×C4—124no—
463C2×C3×C4—122no—
464C2×C3×C4C2×S411yescharacteristic
465#67—82no—
466#67—82no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—82no—
471C2×C32—41no—
472C2×C32—41no—
473C2×C32—41no—
474C2×C32—82no—
475C2×C32—161no—
476C3×D3—161no—
477C24—21no—
478C24—21no—
479C24—21no—
480C24—21no—
481C24—21no—
482C24—31no—
483C24—31no—
484C24—31no—
485C24—32no—
486C24—31no—
487C24—31no—
488C24—61no—
489C24—61no—
490C24—61no—
491C24—61no—
492C24—61no—
493C24C3×#6712yescomplemented
494C24C22×C3×D311yescharacteristic
495C2×D4—34no—
496C2×D4—31no—
497C2×D4—31no—
498C2×D4—31no—
499C2×D4—61no—
500C2×D4—62no—
501C2×D4—62no—
502C2×D4—62no—
503C2×D4—62no—
504C2×D4—62no—
505C2×D4—62no—
506C2×D4—62no—
507C2×D4—62no—
508C2×D4—62no—
509C2×D4—61no—
510C2×D4—61no—
511C2×D4—62no—
512C2×D4—62no—
513C2×D4—62no—
514C2×D4—61no—
515C2×D4—62no—
516C2×D4—61no—
517C2×D4—61no—
518C2×D4—61no—
519C2×D4—61no—
520C2×D4—61no—
521C2×D4—61no—
522C2×D4—61no—
523C2×D4—121no—
524C2×D4—121no—
525C2×D4—121no—
526C2×D4—121no—
527C2×D4C3×S411yescharacteristic, complemented
528C22×C4—21no—
529C22×C4—31no—
530C22×C4—31no—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—31no—
534C22×C4—31no—
535C22×C4—31no—
536C22×C4—31no—
537C22×C4—31no—
538C22×C4—61no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—121no—
545C22×C4—121no—
546C4⋊C4—62no—
547C4⋊C4—61no—
548C4⋊C4—61no—
549C22⋊C4—32no—
550C22⋊C4—32no—
551C22⋊C4—62no—
552C22⋊C4—62no—
553C22⋊C4—62no—
554C22⋊C4—62no—
555C22⋊C4—62no—
556C22⋊C4—61no—
557C22⋊C4—61no—
558C22⋊C4—61no—
559C22⋊C4—62no—
560C22⋊C4—62no—
561C22⋊C4—62no—
562C22⋊C4—61no—
563C22⋊C4—61no—
564C22⋊C4—61no—
565C22⋊C4—61no—
566C22⋊C4—61no—
567C22⋊C4—121no—
568C22⋊C4—121no—
569C22×C3—21no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—21no—
574C22×C3—31no—
575C22×C3—31no—
576C22×C3—31no—
577C22×C3—31no—
578C22×C3—31no—
579C22×C3—31no—
580C22×C3—31no—
581C22×C3—31no—
582C22×C3—31no—
583C22×C3—32no—
584C22×C3—42no—
585C22×C3—41no—
586C22×C3—62no—
587C22×C3—62no—
588C22×C3—62no—
589C22×C3—62no—
590C22×C3—61no—
591C22×C3—62no—
592C22×C3—62no—
593C22×C3—62no—
594C22×C3—62no—
595C22×C3—61no—
596C22×C3—61no—
597C22×C3—61no—
598C22×C3—61no—
599C22×C3—61no—
600C22×C3—81no—
601C22×C3—81no—
602C22×C3—81no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3—82no—
606C22×C3—82no—
607C22×C3—81no—
608C22×C3—121no—
609C22×C3—121no—
610C22×C3—121no—
611C22×C3—121no—
612C22×C3—121no—
613C22×C3—121no—
614C22×C3—121no—
615C22×C3—121no—
616C22×C3—121no—
617C22×C3—121no—
618C22×C3—121no—
619C22×C3—121no—
620C22×C3—121no—
621C22×C3—121no—
622C22×C3—121no—
623C22×C3—161no—
624C22×C3—161no—
625C22×C3—161no—
626C22×C3—161no—
627C22×C3#93911yescharacteristic, complemented
628C22×C3GL(2,ℤ/4)12yescomplemented
629C22×C3C22×S411yescharacteristic
630C2×D3—81no—
631C2×D3—81no—
632C2×D3—81no—
633A4—21no—
634A4C3×#12111yescharacteristic, complemented
635C3×C4—21no—
636C3×C4—62no—
637C3×C4—62no—
638C3×C4—61no—
639C3×C4—81no—
640C3×C4—82no—
641C3×C4—121no—
642C3×C4—121no—
643C3×C4—121no—
644C3×C4—121no—
645C3×C4—121no—
646Dic3—42no—
647Dic3—81no—
648Dic3—81no—
649C32—41noSylow
650C23—22no—
651C23—31no—
652C23—31no—
653C23—31no—
654C23—31no—
655C23—32no—
656C23—32no—
657C23—32no—
658C23—31no—
659C23—32no—
660C23—31no—
661C23—41no—
662C23—61no—
663C23—61no—
664C23—61no—
665C23—61no—
666C23—61no—
667C23—61no—
668C23—61no—
669C23—61no—
670C23—61no—
671C23—61no—
672C23—61no—
673C23—62no—
674C23—61no—
675C23—61no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23—61no—
680C23—62no—
681C23—62no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—61no—
686C23—61no—
687C23—61no—
688C23—61no—
689C23—61no—
690C23—61no—
691C23—61no—
692C23—121no—
693C23—121no—
694C23—121no—
695C23—122no—
696C23—122no—
697C23C3×D3×D411yescharacteristic
698C23C3×#23711yescharacteristic
699C23C2×C3×#6711yescharacteristic
700C23C2×C3×S411yescharacteristic
701C23C2×C3×S411yescharacteristic
702D4—22no—
703D4—62no—
704D4—62no—
705D4—64no—
706D4—62no—
707D4—122no—
708D4—124no—
709D4—122no—
710D4—121no—
711D4—121no—
712D4—121no—
713D4—122no—
714D4—124no—
715D4—122no—
716D4—121no—
717C2×C4—32no—
718C2×C4—32no—
719C2×C4—32no—
720C2×C4—31no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—122no—
744C2×C4—124no—
745C2×C4—122no—
746C2×C4C2×C3×S411yescharacteristic
747C2×C3—22no—
748C2×C3—31no—
749C2×C3—31no—
750C2×C3—31no—
751C2×C3—31no—
752C2×C3—41no—
753C2×C3—41no—
754C2×C3—41no—
755C2×C3—41no—
756C2×C3—62no—
757C2×C3—82no—
758C2×C3—81no—
759C2×C3—81no—
760C2×C3—81no—
761C2×C3—121no—
762C2×C3—162no—
763C2×C3—161no—
764C2×C3—162no—
765C2×C3—241no—
766C2×C3D4×S411yescharacteristic
767C2×C3#591411yescharacteristic
768C2×C3C2×GL(2,ℤ/4)11yescharacteristic
769D3—161no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—31no—
776C22—31no—
777C22—31no—
778C22—31no—
779C22—31no—
780C22—31no—
781C22—31no—
782C22—31no—
783C22—31no—
784C22—32no—
785C22—62no—
786C22—62no—
787C22—62no—
788C22—62no—
789C22—61no—
790C22—62no—
791C22—62no—
792C22—62no—
793C22—62no—
794C22—61no—
795C22—61no—
796C22—61no—
797C22—61no—
798C22—61no—
799C22—121no—
800C22—121no—
801C22—121no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—121no—
806C22—121no—
807C22—121no—
808C22—121no—
809C22—121no—
810C22—121no—
811C22—121no—
812C22—121no—
813C22—121no—
814C22C3×#93911yescharacteristic, complemented
815C22C3×GL(2,ℤ/4)12yescomplemented
816C22C22×C3×S411yescharacteristic
817C4—21no—
818C4—62no—
819C4—62no—
820C4—61no—
821C4—121no—
822C4—121no—
823C4—121no—
824C4—121no—
825C4—121no—
826C3—41no—
827C3—81no—
828C3#8549511yescharacteristic, direct product factor
829C2—22no—
830C2—31no—
831C2—31no—
832C2—31no—
833C2—31no—
834C2—41no—
835C2—62no—
836C2—121no—
837C2—241no—
838C2C3×D4×S411yescharacteristic
839C2C3×#591411yescharacteristic
840C2C2×C3×GL(2,ℤ/4)11yescharacteristic
subgroupG/H
centerC22×C3C22×S4
commutator, cosocleC22×A4C23×C3
FrattiniC22C22×C3×S4
FittingC23×C3×D4D3
socleC24×C3C22×D3
hypercenterC2×C3×D4S4
hypocenterA4C3×#121
LCSG ▷ C22×A4 ▷ A4
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×A4C2semidirect
2. C2×C3×GL(2,ℤ/4)C2semidirect
3. C2×C3×GL(2,ℤ/4)C2semidirect
4. C22×C3×SL(2,ℤ/4)C2semidirect
5. C3×#5432C2semidirect
6. C3×(C2×S4)⋊C4C2semidirect
7. C3×SL(2,ℤ/4)⋊C4C2semidirect
8. #85495C3direct (N × H)
22. C23×C3×D4D3semidirect
24. C2×D4×A4C2×C3semidirect
25. C2×GL(2,ℤ/4)C2×C3semidirect
26. C2×GL(2,ℤ/4)C2×C3semidirect
27. C22×SL(2,ℤ/4)C2×C3semidirect
33. #5432C2×C3semidirect
34. (C2×S4)⋊C4C2×C3semidirect
35. SL(2,ℤ/4)⋊C4C2×C3semidirect
50. C22×C3×A4D4semidirect
62. C3×SL(2,ℤ/4)D4semidirect
148. C23×D4C3×D3semidirect
179. C24×C3#67semidirect
193. C22×A4C3×D4semidirect
232. C2×C3×D4S4semidirect
258. SL(2,ℤ/4)C3×D4semidirect
295. C3×A4#121semidirect
493. C24C3×#67semidirect
527. C2×D4C3×S4semidirect
627. C22×C3#939semidirect
628. C22×C3GL(2,ℤ/4)semidirect
634. A4C3×#121semidirect
814. C22C3×#939semidirect
815. C22C3×GL(2,ℤ/4)semidirect
828. C3#85495direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×A42
C2×C3×GL(2,ℤ/4)2
C22×C3×SL(2,ℤ/4)2
C3×#54322
C3×(C2×S4)⋊C42
C3×SL(2,ℤ/4)⋊C42
#854953
C3×#24103
C3×#9394