Finite Group Databasebeta

← #72258841

Subgroups — #72258841

Order 1536.

785 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 785 conjugacy classes of subgroups — too many to draw. Only its 69 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
1#14711⋊C3C211yesmaximal, characteristic
2#14711⋊C3C211yesmaximal, characteristic
3#14711⋊C3C211yesmaximal, characteristic
4#14710⋊C3C211yesmaximal, characteristic, complemented
5C4⋊(#383⋊C3)C211yesmaximal, characteristic, complemented
6C4×#383⋊C3C211yesmaximal, characteristic, complemented
7C4⋊C4×C42⋊C3C211yesmaximal, characteristic, complemented
8#616837C311yesmaximal, characteristic, complemented, Sylow
9A4×#126—41nomaximal
10C22×#126⋊C3C2211yescharacteristic
11C2×#383⋊C3C2211yescharacteristic
12C2×#383⋊C3C2211yescharacteristic
13C2×#383⋊C3C2211yescharacteristic
14C2×C4×C42⋊C3C2211yescharacteristic
15C2×C4×C42⋊C3C2211yescharacteristic
16C2×C4×C42⋊C3C2211yescharacteristic
17#15038—31no—
18#15037—31no—
19#14857—31no—
20#14856—31no—
21#14711C2×C311yescharacteristic
22#14711C2×C311yescharacteristic
23#14711C2×C311yescharacteristic
24#14710C2×C311yescharacteristic, complemented
25#14688C2×C311yescharacteristic, complemented
26#14253—31no—
27#14251—31no—
28#14113—31no—
29#14101—31no—
30C4×#383C2×C311yescharacteristic, complemented
31C42×C4⋊C4C2×C311yescharacteristic, complemented
32C2×#126⋊C3—21no—
33C2×#126⋊C3—21no—
34C2×#126⋊C3—21no—
35A4×C4⋊C4—41no—
36A4×C4⋊C4—41no—
37A4×C4⋊C4—41no—
38A4×C22⋊C4—41no—
39A4×C22⋊C4—41no—
40A4×C22⋊C4—41no—
41C42×A4—41no—
42C22×C42⋊C3C2311yescharacteristic
43#383⋊C3—21no—
44#383⋊C3—21no—
45#383⋊C3—21no—
46C4×C42⋊C3—21no—
47C4×C42⋊C3—21no—
48C4×C42⋊C3—21no—
49C22×#126A411yescharacteristic
50C22×#126C22×C311yescharacteristic
51C2×#401—31no—
52C2×#397—31no—
53C2×#387—31no—
54C2×#383C22×C311yescharacteristic
55C2×#383C22×C311yescharacteristic
56C2×#383C22×C311yescharacteristic
57C2×C4×C4⋊C4—31no—
58C2×C4×C4⋊C4—31no—
59C2×C43C22×C311yescharacteristic
60C2×C43C22×C311yescharacteristic
61C2×C43C22×C311yescharacteristic
62#1445—31no—
63#1443—31no—
64#1443—31no—
65#1443—31no—
66#1443—31no—
67#1442—31no—
68#1442—31no—
69#1442—31no—
70#1442—31no—
71#1441—31no—
72#1441—31no—
73#1440—31no—
74#1439—31no—
75#1439—31no—
76#1437—31no—
77#1437—31no—
78#1437—31no—
79#1437—31no—
80#1437—31no—
81#1437—31no—
82#1437—31no—
83#1436—31no—
84#1436—31no—
85#1436—31no—
86#1436—31no—
87#1436—31no—
88#1436—31no—
89#1436—31no—
90#1436—31no—
91#1436—31no—
92#1436—31no—
93#1436—31no—
94C4⋊#95—31no—
95C4⋊#95—31no—
96#1434—31no—
97#1434—31no—
98#1434—31no—
99#1434—31no—
100#1434—31no—
101#1434—31no—
102C4×#95—31no—
103C4×#95—31no—
104C4×#95—31no—
105C4×#95—31no—
106C23×A4—41no—
107C2×C4×A4—41no—
108C2×C4×A4—41no—
109C2×C4×A4—41no—
110C2×C4×A4—41no—
111C2×C4×A4—41no—
112C2×C4×A4—41no—
113C3×#126—161no—
114#126⋊C3—41no—
115C2×C42⋊C3#4111yescharacteristic
116C2×C42⋊C3#4111yescharacteristic
117C2×C42⋊C3#4111yescharacteristic
118C2×#126—21no—
119C2×#126—21no—
120C2×#126—21no—
121C2×#126—61no—
122C2×#126—61no—
123C2×#126—61no—
124C2×#126—61no—
125C2×#126—61no—
126C2×#126—61no—
127C2×#126—61no—
128C22×C4⋊C4—31no—
129C22×C4⋊C4—31no—
130C22×C4⋊C4—31no—
131C22×C4⋊C4—31no—
132C22×C4⋊C4C2×A411yescharacteristic
133C22×C4⋊C4C2×A411yescharacteristic
134C22×C4⋊C4C2×A411yescharacteristic
135C22×C22⋊C4—31no—
136C22×C22⋊C4—31no—
137C22×C22⋊C4—31no—
138C22×C22⋊C4—31no—
139C22×C22⋊C4C2×A411yescharacteristic
140C22×C22⋊C4C2×A411yescharacteristic
141C22×C22⋊C4C2×A411yescharacteristic
142C22×C42—31no—
143C22×C42—31no—
144C22×C42—31no—
145C22×C42—31no—
146C22×C42—31no—
147C22×C42—31no—
148C22×C42—31no—
149C22×C42C2×A411yescharacteristic
150C22×C42C23×C311yescharacteristic
151#401—64no—
152#397—64no—
153#387—61no—
154#387—61no—
155#387—61no—
156#387—61no—
157#383—21no—
158#383—21no—
159#383—21no—
160#383—61no—
161#383—61no—
162#383—61no—
163C4×C4⋊C4—64no—
164C4×C4⋊C4—61no—
165C4×C4⋊C4—61no—
166C4×C4⋊C4—61no—
167C4×C4⋊C4—61no—
168C2×#95—31no—
169C2×#95—31no—
170C2×#95—31no—
171C2×#95—31no—
172C2×#95—31no—
173C2×#95—31no—
174C2×#95—31no—
175C2×#95—31no—
176C2×#95—31no—
177C2×#95—31no—
178C2×#95—31no—
179C2×#95—31no—
180C2×#95—31no—
181C2×#95—31no—
182C2×#95—31no—
183C2×#95—31no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C43—21no—
203C43—21no—
204C43—21no—
205C43—61no—
206C43—61no—
207C43—61no—
208C22×A4—41no—
209C22×A4—81no—
210C22×A4—81no—
211C22×A4—81no—
212C4×A4—81no—
213C4×A4—81no—
214C4×A4—81no—
215C4×A4—81no—
216C4×A4—81no—
217C4×A4—81no—
218C3×C4⋊C4—161no—
219C3×C4⋊C4—161no—
220C3×C4⋊C4—161no—
221C3×C22⋊C4—161no—
222C3×C22⋊C4—161no—
223C3×C22⋊C4—161no—
224C3×C42—161no—
225C42⋊C3#12611yescharacteristic, complemented
226C25C22×A411yescharacteristic
227C23×C4—31no—
228C23×C4—31no—
229C23×C4—31no—
230C23×C4—31no—
231C23×C4—31no—
232C23×C4—31no—
233C23×C4—31no—
234C23×C4—31no—
235C23×C4C22×A411yescharacteristic
236C23×C4C22×A411yescharacteristic
237C23×C4C22×A411yescharacteristic
238C23×C4C22×A411yescharacteristic
239C23×C4C22×A411yescharacteristic
240C23×C4C22×A411yescharacteristic
241#126—41no—
242#126—41no—
243#126—122no—
244#126—121no—
245#126—121no—
246#126—121no—
247#126—121no—
248#126—121no—
249#126—121no—
250#126—122no—
251C2×C4⋊C4—31no—
252C2×C4⋊C4—31no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4—61no—
256C2×C4⋊C4—61no—
257C2×C4⋊C4—61no—
258C2×C4⋊C4—61no—
259C2×C4⋊C4—62no—
260C2×C4⋊C4—62no—
261C2×C4⋊C4—61no—
262C2×C4⋊C4—61no—
263C2×C4⋊C4—61no—
264C2×C4⋊C4—61no—
265C2×C4⋊C4—61no—
266C2×C4⋊C4—61no—
267C2×C4⋊C4—61no—
268C2×C4⋊C4—61no—
269C2×C4⋊C4—61no—
270C2×C4⋊C4—61no—
271C2×C4⋊C4—62no—
272C2×C4⋊C4—121no—
273C2×C4⋊C4—121no—
274C2×C4⋊C4—121no—
275C2×C4⋊C4—121no—
276C2×C22⋊C4—61no—
277C2×C22⋊C4—61no—
278C2×C22⋊C4—61no—
279C2×C22⋊C4—61no—
280C2×C22⋊C4—61no—
281C2×C22⋊C4—61no—
282C2×C22⋊C4—61no—
283C2×C22⋊C4—61no—
284C2×C22⋊C4—61no—
285C2×C22⋊C4—61no—
286C2×C22⋊C4—61no—
287C2×C22⋊C4—61no—
288C2×C22⋊C4—62no—
289C2×C22⋊C4—62no—
290C2×C22⋊C4—62no—
291C2×C22⋊C4—121no—
292C2×C22⋊C4—121no—
293C2×C22⋊C4—121no—
294C2×C22⋊C4—121no—
295C2×C22⋊C4—121no—
296C2×C22⋊C4—121no—
297C2×C42—31no—
298C2×C42—31no—
299C2×C42—31no—
300C2×C42—61no—
301C2×C42—61no—
302C2×C42—61no—
303C2×C42—61no—
304C2×C42—61no—
305C2×C42—62no—
306C2×C42—61no—
307C2×C42—61no—
308C2×C42—61no—
309C2×C42—61no—
310C2×C42—61no—
311C2×C42—61no—
312C2×C42—61no—
313C2×C42—61no—
314C2×C42—61no—
315C2×C42—61no—
316C2×C42—61no—
317C2×C42—61no—
318C2×C42—61no—
319C2×C42—61no—
320C2×C42—62no—
321C2×C42—62no—
322C2×C42—61no—
323C2×C42—61no—
324C2×C42—61no—
325C2×C42—121no—
326C2×C42—121no—
327C2×C42—121no—
328C2×C42—121no—
329C2×C42—121no—
330C2×C42—121no—
331C2×C42—121no—
332C2×C42—121no—
333C2×C42C3×#4111yescharacteristic
334C2×C42C3×#4111yescharacteristic
335C2×C42C3×#4111yescharacteristic
336#95—34no—
337#95—61no—
338#95—61no—
339#95—61no—
340#95—61no—
341#95—61no—
342#95—61no—
343#95—61no—
344#95—61no—
345#95—61no—
346#95—61no—
347#95—61no—
348#95—61no—
349#95—61no—
350#95—61no—
351#95—61no—
352#95—61no—
353#95—62no—
354#95—61no—
355#95—61no—
356#95—61no—
357#95—61no—
358#95—61no—
359#95—61no—
360#95—61no—
361#95—61no—
362#95—62no—
363#95—62no—
364#95—62no—
365#95—62no—
366#95—62no—
367#95—62no—
368#95—62no—
369#95—62no—
370#95—121no—
371#95—121no—
372#95—121no—
373#95—121no—
374#95—121no—
375#95—121no—
376#95—121no—
377#95—121no—
378#95—121no—
379#95—121no—
380#95—121no—
381#95—121no—
382C23×C3—161no—
383C2×A4—41no—
384C2×A4—41no—
385C2×A4—41no—
386C2×A4—161no—
387C2×C3×C4—161no—
388C2×C3×C4—161no—
389C2×C3×C4—161no—
390C2×C3×C4—161no—
391C2×C3×C4—161no—
392C2×C3×C4—161no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—61no—
397C24—61no—
398C24—61no—
399C24—61no—
400C24C23×A411yescharacteristic
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—31no—
408C22×C4—31no—
409C22×C4—31no—
410C22×C4—31no—
411C22×C4—31no—
412C22×C4—31no—
413C22×C4—31no—
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—31no—
418C22×C4—31no—
419C22×C4—32no—
420C22×C4—32no—
421C22×C4—32no—
422C22×C4—61no—
423C22×C4—61no—
424C22×C4—61no—
425C22×C4—61no—
426C22×C4—61no—
427C22×C4—61no—
428C22×C4—61no—
429C22×C4—61no—
430C22×C4—61no—
431C22×C4—61no—
432C22×C4—61no—
433C22×C4—61no—
434C22×C4—61no—
435C22×C4—61no—
436C22×C4—61no—
437C22×C4—61no—
438C22×C4—61no—
439C22×C4—61no—
440C22×C4—61no—
441C22×C4—61no—
442C22×C4—61no—
443C22×C4—61no—
444C22×C4—61no—
445C22×C4—61no—
446C22×C4—61no—
447C22×C4—61no—
448C22×C4—61no—
449C22×C4—61no—
450C22×C4—61no—
451C22×C4—61no—
452C22×C4—61no—
453C22×C4—61no—
454C22×C4—61no—
455C22×C4—61no—
456C22×C4—61no—
457C22×C4—61no—
458C22×C4—61no—
459C22×C4—61no—
460C22×C4—61no—
461C22×C4—61no—
462C22×C4—61no—
463C22×C4—61no—
464C22×C4—61no—
465C22×C4—61no—
466C22×C4—61no—
467C22×C4—61no—
468C22×C4—61no—
469C22×C4—61no—
470C22×C4—61no—
471C22×C4—61no—
472C22×C4—61no—
473C22×C4—61no—
474C22×C4—61no—
475C22×C4—61no—
476C22×C4—61no—
477C22×C4—61no—
478C22×C4—61no—
479C22×C4—61no—
480C22×C4—61no—
481C4⋊C4—32no—
482C4⋊C4—31no—
483C4⋊C4—31no—
484C4⋊C4—31no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—64no—
488C4⋊C4—64no—
489C4⋊C4—121no—
490C4⋊C4—121no—
491C4⋊C4—121no—
492C4⋊C4—121no—
493C4⋊C4—121no—
494C4⋊C4—121no—
495C4⋊C4—241no—
496C4⋊C4—241no—
497C4⋊C4—242no—
498C4⋊C4#126⋊C311yescharacteristic, complemented
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—121no—
503C22⋊C4—121no—
504C22⋊C4—121no—
505C22⋊C4—121no—
506C22⋊C4—121no—
507C22⋊C4—121no—
508C22⋊C4—121no—
509C22⋊C4—242no—
510C22⋊C4—242no—
511C22⋊C4—242no—
512C42—31no—
513C42—31no—
514C42—31no—
515C42—32no—
516C42—41no—
517C42—62no—
518C42—62no—
519C42—62no—
520C42—62no—
521C42—121no—
522C42—121no—
523C42—121no—
524C42—121no—
525C42—121no—
526C42—121no—
527C42—121no—
528C42—121no—
529C42—121no—
530C42—122no—
531C42—122no—
532C42—122no—
533C42—122no—
534C42—122no—
535C42—122no—
536C42—241no—
537C42—241no—
538C42C3×#12611yescharacteristic, complemented
539C22×C3—161no—
540C22×C3—321no—
541C22×C3—321no—
542C22×C3—321no—
543A4—41no—
544C3×C4—321no—
545C3×C4—321no—
546C3×C4—321no—
547C3×C4—321no—
548C3×C4—321no—
549C3×C4—321no—
550C23—31no—
551C23—31no—
552C23—31no—
553C23—31no—
554C23—41no—
555C23—41no—
556C23—121no—
557C23—121no—
558C23—121no—
559C23—121no—
560C23—121no—
561C23—121no—
562C23—121no—
563C23—121no—
564C23—121no—
565C23—121no—
566C23—121no—
567C23A4×#4111yescharacteristic
568C23A4×#4111yescharacteristic
569C23A4×#4111yescharacteristic
570C2×C4—31no—
571C2×C4—31no—
572C2×C4—31no—
573C2×C4—31no—
574C2×C4—31no—
575C2×C4—31no—
576C2×C4—31no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—61no—
581C2×C4—61no—
582C2×C4—61no—
583C2×C4—61no—
584C2×C4—61no—
585C2×C4—61no—
586C2×C4—61no—
587C2×C4—61no—
588C2×C4—61no—
589C2×C4—61no—
590C2×C4—61no—
591C2×C4—61no—
592C2×C4—61no—
593C2×C4—61no—
594C2×C4—61no—
595C2×C4—61no—
596C2×C4—61no—
597C2×C4—61no—
598C2×C4—61no—
599C2×C4—61no—
600C2×C4—61no—
601C2×C4—61no—
602C2×C4—61no—
603C2×C4—61no—
604C2×C4—62no—
605C2×C4—62no—
606C2×C4—62no—
607C2×C4—62no—
608C2×C4—62no—
609C2×C4—62no—
610C2×C4—62no—
611C2×C4—62no—
612C2×C4—62no—
613C2×C4—121no—
614C2×C4—121no—
615C2×C4—121no—
616C2×C4—121no—
617C2×C4—121no—
618C2×C4—121no—
619C2×C4—121no—
620C2×C4—121no—
621C2×C4—121no—
622C2×C4—121no—
623C2×C4—121no—
624C2×C4—121no—
625C2×C4—121no—
626C2×C4—121no—
627C2×C4—121no—
628C2×C4—121no—
629C2×C4—121no—
630C2×C4—121no—
631C2×C4—121no—
632C2×C4—121no—
633C2×C4—121no—
634C2×C4—121no—
635C2×C4—121no—
636C2×C4—121no—
637C2×C4—121no—
638C2×C4—121no—
639C2×C4—121no—
640C2×C4—121no—
641C2×C4—121no—
642C2×C4—121no—
643C2×C4—121no—
644C2×C4—121no—
645C2×C4—121no—
646C2×C4—121no—
647C2×C4—121no—
648C2×C4—121no—
649C2×C4—121no—
650C2×C4—121no—
651C2×C4—121no—
652C2×C4—121no—
653C2×C4—121no—
654C2×C4—121no—
655C2×C4—121no—
656C2×C4—121no—
657C2×C4—121no—
658C2×C4—121no—
659C2×C4C2×#126⋊C311yescharacteristic
660C2×C4C2×#126⋊C311yescharacteristic
661C2×C4C2×#126⋊C311yescharacteristic
662C2×C3—161no—
663C2×C3—161no—
664C2×C3—161no—
665C2×C3—641no—
666C22—31no—
667C22—31no—
668C22—31no—
669C22—31no—
670C22—31no—
671C22—31no—
672C22—31no—
673C22—31no—
674C22—31no—
675C22—31no—
676C22—31no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—241no—
681C22—241no—
682C22—241no—
683C22—241no—
684C22C22×#126⋊C311yescharacteristic
685C22A4×#12611yescharacteristic
686C4—21no—
687C4—21no—
688C4—21no—
689C4—61no—
690C4—61no—
691C4—61no—
692C4—61no—
693C4—61no—
694C4—61no—
695C4—61no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4—122no—
700C4—122no—
701C4—122no—
702C4—241no—
703C4—241no—
704C4—241no—
705C4—241no—
706C3—161noSylow
707C2—31no—
708C2—31no—
709C2—31no—
710C2—31no—
711C2—161no—
712C2#36166⋊C311yescharacteristic
713C2#1171001011yescharacteristic
714C2#36641⋊C311yescharacteristic
subgroupG/H
centerC22C22×#126⋊C3
commutator, cosocleC22×C42C23×C3
Frattini, socleC24C23×A4
Fitting#616837C3
prime radicalC22×#126⋊C3C22
hypercenterC4⋊C4#126⋊C3
hypocenterC42C3×#126
LCSG ▷ C22×C42 ▷ C42
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #14710⋊C3C2semidirect
5. C4⋊(#383⋊C3)C2semidirect
6. C4×#383⋊C3C2semidirect
7. C4⋊C4×C42⋊C3C2semidirect
8. #616837C3semidirect
24. #14710C2×C3semidirect
25. #14688C2×C3semidirect
30. C4×#383C2×C3semidirect
31. C42×C4⋊C4C2×C3semidirect
225. C42⋊C3#126semidirect
498. C4⋊C4#126⋊C3semidirect
538. C42C3×#126semidirect

Maximal subgroups

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

subgroupindex
#14711⋊C32
#14710⋊C32
C4⋊(#383⋊C3)2
C4×#383⋊C32
C4⋊C4×C42⋊C32
#6168373
A4×#1264