Finite Group Databasebeta

← #11921979

Subgroups — #11921979

Order 1152.

734 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 63 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×C4⋊S4C211yesmaximal, characteristic
2C2×Dic3×S4C211yesmaximal, characteristic, complemented
3A4×Dic3⋊C4C211yesmaximal, characteristic, complemented
4#10593645C211yesmaximal, characteristic, complemented
5(C2×S4)⋊Dic3C211yesmaximal, characteristic, complemented
6(C2×S4)⋊Dic3C211yesmaximal, characteristic, complemented
7(C2×S4)⋊Dic3C211yesmaximal, characteristic, complemented
8#85309—31nomaximal
9#82655—31nomaximal
10C22×C3×S4C2211yescharacteristic
11C22×C3×S4C2211yescharacteristic
12C2×C3×C4×A4C2211yescharacteristic
13C2×Dic3×A4C2211yescharacteristic
14C2×Dic3×A4C2211yescharacteristic
15C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
16C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
17C3×C4⋊S4—22no—
18Dic3×S4—22no—
19#63884—41nomaximal
20C2×C4⋊S4D311yescharacteristic
21C2×C4×S4—31no—
22C2×C3×#121—31no—
23C2×#935—31no—
24C2×D4×Dic3—31no—
25C22×Dic3⋊C4D311yescharacteristic, complemented
26A4×C4⋊C4—31no—
27(C2×S4)⋊C4—31no—
28(C2×S4)⋊C4—31no—
29(C2×S4)⋊C4—31no—
30SL(2,ℤ/4)⋊C4—31no—
31SL(2,ℤ/4)⋊C4—61no—
32#5222—31no—
33#5220—31no—
34#5220—31no—
35#5220—31no—
36#5210—31no—
37#4981—31no—
38#4978—31no—
39#4952—31no—
40#4949—31no—
41#4946—31no—
42#4944—31no—
43C22×C3×A4C2311yescharacteristic
44C2×C3×S4—21no—
45C2×C3×S4—21no—
46C2×C3×S4—21no—
47C2×C3×S4—21no—
48C2×C3×S4—21no—
49C2×C3×S4D412yes—
50C2×C3×D12—41no—
51C3×C4×A4—21no—
52C2×D3×Dic3—41no—
53Dic3×A4—21no—
54Dic3×A4—21no—
55C3⋊SL(2,ℤ/4)—21no—
56C3⋊SL(2,ℤ/4)—21no—
57#3750—41no—
58C3×Dic3⋊C4—41no—
59(C2×D3)⋊Dic3—41no—
60(C2×D3)⋊Dic3—41no—
61(C2×D3)⋊Dic3—41no—
62#2443—91noSylow
63C22×S4C2×D311yescharacteristic
64C22×S4C2×D311yescharacteristic
65C22×C3×D4—31no—
66C22×C3×D4—31no—
67C22×C3×D4—31no—
68C23×C3×C4C2×D311yescharacteristic
69C23×Dic3—31no—
70C23×Dic3C2×D311yescharacteristic
71C23×Dic3C2×D311yescharacteristic
72C2×C4×A4—21no—
73C2×C4×A4—31no—
74C2×C4×A4—31no—
75C2×C4×A4C2×D311yescharacteristic
76C2×SL(2,ℤ/4)—31no—
77C2×SL(2,ℤ/4)—31no—
78C2×SL(2,ℤ/4)—61no—
79C2×SL(2,ℤ/4)—61no—
80C4⋊S4—22no—
81C4×S4—62no—
82C3×#121—62no—
83C3×#121—62no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C22⋊C4—31no—
86C2×C3×C22⋊C4—31no—
87C2×#217—31no—
88C2×#217—31no—
89C2×#217—31no—
90C2×#217—31no—
91C2×#217—31no—
92C2×#217—31no—
93C2×#217—31no—
94C2×#217—31no—
95C2×#217—31no—
96#935—61no—
97#935—61no—
98#935—61no—
99#935—61no—
100D4×Dic3—62no—
101D4×Dic3—62no—
102C2×C4⋊Dic3—31no—
103C2×Dic3⋊C4—31no—
104C2×Dic3⋊C4—31no—
105C2×Dic3⋊C4—31no—
106C2×Dic3⋊C4—31no—
107C2×Dic3⋊C4—31no—
108C2×Dic3⋊C4—31no—
109C2×C4×Dic3—31no—
110#894—121no—
111C3⋊#95—31no—
112C3⋊#95—31no—
113C3⋊#95—31no—
114C3⋊#95—31no—
115C3⋊#95—31no—
116C3⋊#95—31no—
117C3⋊#95—31no—
118C3⋊#95—31no—
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C2×C3×A4C2×D411yescharacteristic
122C2×C3×A4#4111yescharacteristic
123C2×C3×A4#4111yescharacteristic
124C3×S4—22no—
125C3×S4—41no—
126C2×C32×C4—41no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—41no—
131C3×D12—82no—
132D3×Dic3—82no—
133C2×#123—91no—
134C2×#121—31no—
135C2×C4×D4—91no—
136C22×C4⋊C4—31no—
137#399—91no—
138#398—91no—
139#397—91no—
140#394—91no—
141#388—91no—
142#387—91no—
143#386—91no—
144#386—91no—
145#386—91no—
146#385—91no—
147#385—91no—
148C24×C3—31no—
149C24×C3—31no—
150C24×C3C22×D311yescharacteristic
151C22×A4—21no—
152C22×A4C22×D311yescharacteristic
153C2×S4—21no—
154C2×S4—21no—
155C2×S4—21no—
156C2×S4—21no—
157C2×S4—21no—
158C2×S4#6712yes—
159C2×C3×D4—32no—
160C2×C3×D4—32no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4—61no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C2×C3×D4—62no—
167C2×C3×D4—61no—
168C2×C3×D4—61no—
169C2×C3×D4—61no—
170C2×C3×D4—61no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C2×C3×D4—121no—
175C22×C3×C4—21no—
176C22×C3×C4—31no—
177C22×C3×C4—31no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C22×C3×C4—61no—
181C22×Dic3—21no—
182C22×Dic3—21no—
183C22×Dic3—31no—
184C22×Dic3—31no—
185C22×Dic3—31no—
186C22×Dic3—31no—
187C22×Dic3—31no—
188C22×Dic3—31no—
189C22×Dic3—31no—
190C22×Dic3—31no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C22×Dic3—61no—
194C22×Dic3—62no—
195C22×Dic3—61no—
196C22×Dic3—121no—
197C2×D12—41no—
198C2×C4×D3—121no—
199C4×A4—21no—
200C4×A4—41no—
201C4×A4—61no—
202C4×A4—61no—
203SL(2,ℤ/4)—62no—
204SL(2,ℤ/4)—61no—
205SL(2,ℤ/4)—61no—
206SL(2,ℤ/4)—121no—
207C3×C4⋊C4—62no—
208C3×C4⋊C4—121no—
209C3×C22⋊C4—62no—
210C3×C22⋊C4—62no—
211#217—61no—
212#217—61no—
213#217—61no—
214#217—62no—
215#217—62no—
216#217—62no—
217#217—61no—
218#217—61no—
219#217—61no—
220#217—61no—
221#217—61no—
222#217—61no—
223#217—61no—
224#217—121no—
225(C2×D3)⋊C4—121no—
226(C2×D3)⋊C4—121no—
227(C2×D3)⋊C4—121no—
228C4⋊Dic3—62no—
229Dic3⋊C4—31no—
230Dic3⋊C4—31no—
231Dic3⋊C4—31no—
232Dic3⋊C4—61no—
233Dic3⋊C4—61no—
234Dic3⋊C4—61no—
235Dic3⋊C4—121no—
236Dic3⋊C4—121no—
237Dic3⋊C4—241no—
238Dic3⋊C4S411yescharacteristic, complemented
239C4×Dic3—62no—
240C22×C32—41no—
241C2×C3×D3—42no—
242C2×C3×D3—81no—
243C2×C3×D3—81no—
244C2×C3×D3—81no—
245C2×C3×D3—81no—
246C2×C3×D3—81no—
247C3×A4#12311yescharacteristic, complemented
248C32×C4—81no—
249C3⋊Dic3—81no—
250C3⋊Dic3—81no—
251C3×Dic3—81no—
252C3×Dic3—81no—
253C22×D4—31no—
254C22×D4—31no—
255C22×D4—31no—
256C23×C4—31no—
257C23×C4—31no—
258C23×C4—91no—
259C23×C4D3211yescharacteristic
260#123—181no—
261#123—181no—
262#123—181no—
263#123—181no—
264#121—62no—
265#121—62no—
266C4×D4—182no—
267C4×D4—182no—
268C2×C4⋊C4—31no—
269C2×C4⋊C4—91no—
270C2×C4⋊C4—91no—
271C2×C4⋊C4—91no—
272C2×C4⋊C4—91no—
273C2×C4⋊C4—91no—
274C2×C4⋊C4—91no—
275C2×C4⋊C4—91no—
276C2×C22⋊C4—31no—
277C2×C22⋊C4—31no—
278C2×C22⋊C4—91no—
279C2×C22⋊C4—91no—
280C2×C22⋊C4—91no—
281C2×C22⋊C4—91no—
282C2×C22⋊C4—91no—
283C2×C22⋊C4—91no—
284C2×C22⋊C4—91no—
285C2×C22⋊C4—91no—
286C2×C22⋊C4—91no—
287C2×C42—91no—
288#95—91no—
289#95—91no—
290#95—91no—
291#95—91no—
292#95—91no—
293#95—91no—
294#95—91no—
295#95—91no—
296C23×C3—31no—
297C23×C3—31no—
298C23×C3—31no—
299C23×C3—31no—
300C23×C3—32no—
301C23×C3—61no—
302C23×C3—61no—
303C23×C3—61no—
304C23×C3—61no—
305C23×C3—61no—
306C23×C3—61no—
307C23×C3—61no—
308C23×C3—61no—
309C23×C3—61no—
310C23×C3—61no—
311C23×C3—61no—
312C23×C3—61no—
313C23×C3—61no—
314C23×C3#23511yescharacteristic
315C23×C3D3×D411yescharacteristic
316C23×C3#23911yescharacteristic
317C22×D3—41no—
318C22×D3—41no—
319C2×A4—21no—
320C2×A4—21no—
321C2×A4—21no—
322C2×A4#23711yescharacteristic
323C2×A4#23711yescharacteristic
324C2×A4C2×#6711yescharacteristic
325S4—22no—
326S4—41no—
327C3×D4—62no—
328C3×D4—62no—
329C3×D4—62no—
330C3×D4—62no—
331C3×D4—122no—
332C3×D4—122no—
333C3×D4—121no—
334C3×D4—121no—
335C3×D4—121no—
336C3×D4—121no—
337C2×C3×C4—32no—
338C2×C3×C4—31no—
339C2×C3×C4—41no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—61no—
349C2×C3×C4—81no—
350C2×C3×C4—121no—
351C2×C3×C4—121no—
352C2×C3×C4C2×S411yescharacteristic
353C2×Dic3—32no—
354C2×Dic3—31no—
355C2×Dic3—31no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—121no—
376C2×Dic3—121no—
377C2×Dic3—122no—
378C2×Dic3—122no—
379C2×Dic3—241no—
380C2×Dic3—241no—
381C2×Dic3C2×S411yescharacteristic
382C2×Dic3C2×S411yescharacteristic
383D12—82no—
384C4×D3—242no—
385C2×C32—41no—
386C2×C32—41no—
387C2×C32—41no—
388C3×D3—82no—
389C3×D3—161no—
390C24—31no—
391C24—31no—
392C24C2×D3211yescharacteristic
393C2×D4—32no—
394C2×D4—32no—
395C2×D4—61no—
396C2×D4—61no—
397C2×D4—61no—
398C2×D4—61no—
399C2×D4—61no—
400C2×D4—62no—
401C2×D4—61no—
402C2×D4—61no—
403C2×D4—61no—
404C2×D4—61no—
405C2×D4—61no—
406C2×D4—61no—
407C2×D4—61no—
408C2×D4—121no—
409C22×C4—21no—
410C22×C4—31no—
411C22×C4—31no—
412C22×C4—31no—
413C22×C4—31no—
414C22×C4—61no—
415C22×C4—61no—
416C22×C4—61no—
417C22×C4—91no—
418C22×C4—91no—
419C22×C4—91no—
420C22×C4—91no—
421C22×C4—91no—
422C22×C4—91no—
423C22×C4—91no—
424C22×C4—91no—
425C22×C4—181no—
426C22×C4—181no—
427C22×C4—181no—
428C22×C4—181no—
429C22×C4—182no—
430C22×C4—361no—
431C4⋊C4—31no—
432C4⋊C4—62no—
433C4⋊C4—91no—
434C4⋊C4—91no—
435C4⋊C4—91no—
436C4⋊C4—181no—
437C4⋊C4—182no—
438C4⋊C4—181no—
439C4⋊C4—181no—
440C4⋊C4—361no—
441C22⋊C4—62no—
442C22⋊C4—62no—
443C22⋊C4—181no—
444C22⋊C4—181no—
445C22⋊C4—181no—
446C22⋊C4—181no—
447C22⋊C4—181no—
448C22⋊C4—181no—
449C22⋊C4—182no—
450C22⋊C4—182no—
451C22⋊C4—182no—
452C22⋊C4—181no—
453C22⋊C4—181no—
454C22⋊C4—181no—
455C22⋊C4—181no—
456C22⋊C4—361no—
457C42—182no—
458C22×C3—31no—
459C22×C3—31no—
460C22×C3—31no—
461C22×C3—31no—
462C22×C3—31no—
463C22×C3—31no—
464C22×C3—31no—
465C22×C3—31no—
466C22×C3—31no—
467C22×C3—41no—
468C22×C3—61no—
469C22×C3—62no—
470C22×C3—62no—
471C22×C3—62no—
472C22×C3—81no—
473C22×C3—121no—
474C22×C3—121no—
475C22×C3—121no—
476C22×C3—121no—
477C22×C3—121no—
478C22×C3—121no—
479C22×C3—121no—
480C22×C3—121no—
481C22×C3—121no—
482C22×C3—121no—
483C22×C3—121no—
484C22×C3#89411yescharacteristic, complemented
485C22×C3C22×S411yescharacteristic
486C2×D3—42no—
487C2×D3—81no—
488C2×D3—81no—
489C2×D3—81no—
490C2×D3—81no—
491C2×D3—81no—
492A4—21no—
493A4#93511yescharacteristic, complemented
494C3×C4—21no—
495C3×C4—62no—
496C3×C4—61no—
497C3×C4—81no—
498C3×C4—121no—
499C3×C4—161no—
500C3×C4—241no—
501C3×C4—241no—
502Dic3—21no—
503Dic3—21no—
504Dic3—61no—
505Dic3—61no—
506Dic3—121no—
507Dic3—121no—
508Dic3—121no—
509Dic3—121no—
510Dic3—241no—
511Dic3—241no—
512Dic3—242no—
513Dic3—481no—
514C32—41noSylow
515C23—31no—
516C23—31no—
517C23—31no—
518C23—31no—
519C23—32no—
520C23—61no—
521C23—61no—
522C23—61no—
523C23—61no—
524C23—61no—
525C23—61no—
526C23—61no—
527C23—61no—
528C23—61no—
529C23—61no—
530C23—61no—
531C23—61no—
532C23—61no—
533C23#379511yescharacteristic
534C23#379611yescharacteristic
535C23D3×#6711yescharacteristic
536D4—62no—
537D4—62no—
538D4—62no—
539D4—62no—
540D4—122no—
541D4—122no—
542D4—121no—
543D4—121no—
544D4—121no—
545D4—121no—
546C2×C4—32no—
547C2×C4—31no—
548C2×C4—31no—
549C2×C4—31no—
550C2×C4—61no—
551C2×C4—61no—
552C2×C4—61no—
553C2×C4—61no—
554C2×C4—61no—
555C2×C4—61no—
556C2×C4—61no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—92no—
560C2×C4—91no—
561C2×C4—91no—
562C2×C4—181no—
563C2×C4—181no—
564C2×C4—181no—
565C2×C4—181no—
566C2×C4—181no—
567C2×C4—181no—
568C2×C4—181no—
569C2×C4—181no—
570C2×C4—181no—
571C2×C4—181no—
572C2×C4—181no—
573C2×C4—181no—
574C2×C4—181no—
575C2×C4—181no—
576C2×C4—181no—
577C2×C4—181no—
578C2×C4—181no—
579C2×C4—181no—
580C2×C4—181no—
581C2×C4—362no—
582C2×C4—362no—
583C2×C4D3×S411yescharacteristic
584C2×C3—31no—
585C2×C3—31no—
586C2×C3—31no—
587C2×C3—31no—
588C2×C3—41no—
589C2×C3—41no—
590C2×C3—41no—
591C2×C3—81no—
592C2×C3—81no—
593C2×C3—81no—
594C2×C3—122no—
595C2×C3—241no—
596C2×C3#591211yescharacteristic
597C2×C3D4×S411yescharacteristic
598C2×C3#591911yescharacteristic
599D3—82no—
600D3—161no—
601C22—31no—
602C22—31no—
603C22—31no—
604C22—31no—
605C22—31no—
606C22—31no—
607C22—31no—
608C22—31no—
609C22—31no—
610C22—61no—
611C22—62no—
612C22—62no—
613C22—62no—
614C22—121no—
615C22—121no—
616C22—121no—
617C22—121no—
618C22—121no—
619C22—121no—
620C22—121no—
621C22—121no—
622C22—121no—
623C22—121no—
624C22—121no—
625C22#6388411yescharacteristic, complemented
626C22C2×D3×S411yescharacteristic
627C4—21no—
628C4—62no—
629C4—61no—
630C4—61no—
631C4—61no—
632C4—121no—
633C4—181no—
634C4—181no—
635C4—361no—
636C4—361no—
637C4—361no—
638C4—361no—
639C3—41no—
640C3—81no—
641C3#8530911yescharacteristic, complemented
642C2—31no—
643C2—31no—
644C2—31no—
645C2—31no—
646C2—122no—
647C2—241no—
648C2#1059642011yescharacteristic
649C2#1059642711yescharacteristic
650C2#67×S411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, cosocleC22×C3×A4C23
FittingC23×C3×C4C2×D3
socleC24×C3C22×D3
prime radicalC2×C3×C4⋊S4C2
hypercenterC2×C4D3×S4
hypocenterC3×A4#123
LCSG ▷ C22×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×S4C2semidirect
3. A4×Dic3⋊C4C2semidirect
4. #10593645C2semidirect
5. (C2×S4)⋊Dic3C2semidirect
6. (C2×S4)⋊Dic3C2semidirect
7. (C2×S4)⋊Dic3C2semidirect
25. C22×Dic3⋊C4D3semidirect
238. Dic3⋊C4S4semidirect
247. C3×A4#123semidirect
484. C22×C3#894semidirect
493. A4#935semidirect
625. C22#63884semidirect
641. C3#85309semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4⋊S42
C2×Dic3×S42
A4×Dic3⋊C42
#105936452
(C2×S4)⋊Dic32
#853093
#826553
#638844