Finite Group Databasebeta

← #72258852

Subgroups — #72258852

Order 1536.

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

normal subgroups only

This group has 828 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#14710⋊C3C211yesmaximal, characteristic, complemented
2#14710⋊C3C211yesmaximal, characteristic, complemented
3C4⋊(#383⋊C3)C211yesmaximal, characteristic, complemented
4#14683⋊C3C211yesmaximal, characteristic
5#14683⋊C3C211yesmaximal, characteristic
6C4×#383⋊C3C211yesmaximal, characteristic, complemented
7C22⋊C4×C42⋊C3C211yesmaximal, characteristic
8#616832C311yesmaximal, characteristic, complemented, Sylow
9A4×#126—41nomaximal
10C23×C42⋊C3C2211yescharacteristic
11C2×#383⋊C3C2211yescharacteristic
12C2×#383⋊C3C2211yescharacteristic
13C2×#383⋊C3C2211yescharacteristic
14C2×#383⋊C3C2211yescharacteristic
15C2×C4×C42⋊C3C2211yescharacteristic
16C2×C4×C42⋊C3C2211yescharacteristic
17#15049—31no—
18#15044—31no—
19#14835—31no—
20#14834—31no—
21#14710C2×C311yescharacteristic, complemented
22#14710C2×C311yescharacteristic, complemented
23#14688C2×C311yescharacteristic, complemented
24#14683C2×C311yescharacteristic
25#14683C2×C311yescharacteristic
26#14252—31no—
27#14251—31no—
28#14114—31no—
29#14102—31no—
30C4×#383C2×C311yescharacteristic, complemented
31C42×C22⋊C4C2×C311yescharacteristic
32A4×C4⋊C4—41no—
33A4×C4⋊C4—41no—
34A4×C4⋊C4—41no—
35A4×C22⋊C4—41no—
36A4×C22⋊C4—41no—
37A4×C22⋊C4—41no—
38C42×A4—41no—
39C22×C42⋊C3—21no—
40C22×C42⋊C3—21no—
41C22×C42⋊C3—21no—
42C22×C42⋊C3C2311yescharacteristic
43#383⋊C3—21no—
44#383⋊C3—21no—
45#383⋊C3—21no—
46#383⋊C3—21no—
47C4×C42⋊C3—21no—
48C4×C42⋊C3—21no—
49C22×#126A411yescharacteristic
50C23×C42C22×C311yescharacteristic
51C2×#401—31no—
52C2×#400—31no—
53C2×#388—31no—
54C2×#383C22×C311yescharacteristic
55C2×#383C22×C311yescharacteristic
56C2×#383C22×C311yescharacteristic
57C2×#383C22×C311yescharacteristic
58C2×C4×C22⋊C4—31no—
59C2×C4×C22⋊C4—31no—
60C2×C43C22×C311yescharacteristic
61C2×C43C22×C311yescharacteristic
62#1445—31no—
63#1445—31no—
64#1443—31no—
65#1443—31no—
66#1443—31no—
67#1443—31no—
68#1442—31no—
69#1442—31no—
70#1441—31no—
71#1441—31no—
72#1440—31no—
73#1440—31no—
74#1439—31no—
75#1439—31no—
76#1436—31no—
77#1436—31no—
78#1436—31no—
79#1436—31no—
80#1436—31no—
81#1436—31no—
82#1436—31no—
83#1436—31no—
84#1436—31no—
85#1436—31no—
86C4⋊#95—31no—
87C4⋊#95—31no—
88#1434—31no—
89#1434—31no—
90#1434—31no—
91#1434—31no—
92#1434—31no—
93#1434—31no—
94#1434—31no—
95#1434—31no—
96#1434—31no—
97#1434—31no—
98C22⋊#95—31no—
99C22⋊#95—31no—
100C22⋊#95—31no—
101C22⋊#95—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—
114C2×C42⋊C3—41no—
115C2×C42⋊C3#4111yescharacteristic
116C2×C42⋊C3#4111yescharacteristic
117C2×C42⋊C3#4111yescharacteristic
118C24×C4—31no—
119C2×#126—61no—
120C2×#126—61no—
121C2×#126—61no—
122C2×#126—61no—
123C22×C4⋊C4—31no—
124C22×C4⋊C4—31no—
125C22×C4⋊C4—31no—
126C22×C4⋊C4C2×A411yescharacteristic
127C22×C4⋊C4C2×A411yescharacteristic
128C22×C4⋊C4C2×A411yescharacteristic
129C22×C22⋊C4—31no—
130C22×C22⋊C4—31no—
131C22×C22⋊C4—31no—
132C22×C22⋊C4C2×A411yescharacteristic
133C22×C22⋊C4C2×A411yescharacteristic
134C22×C22⋊C4C2×A411yescharacteristic
135C22×C42—21no—
136C22×C42—21no—
137C22×C42—21no—
138C22×C42—31no—
139C22×C42—31no—
140C22×C42—31no—
141C22×C42—31no—
142C22×C42—31no—
143C22×C42—31no—
144C22×C42—61no—
145C22×C42—61no—
146C22×C42—61no—
147C22×C42C2×A411yescharacteristic
148C22×C42C23×C311yescharacteristic
149#401—64no—
150#400—64no—
151#388—61no—
152#388—61no—
153#388—61no—
154#388—61no—
155#383—21no—
156#383—21no—
157#383—21no—
158#383—21no—
159#383—61no—
160#383—61no—
161#383—61no—
162#383—61no—
163C4×C22⋊C4—64no—
164C4×C22⋊C4—61no—
165C4×C22⋊C4—61no—
166C4×C22⋊C4—61no—
167C4×C22⋊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—
202C2×#95—31no—
203C2×#95—31no—
204C43—21no—
205C43—21no—
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×C4—61no—
236C23×C4—61no—
237C23×C4—62no—
238C23×C4—61no—
239C23×C4—61no—
240C23×C4—61no—
241C23×C4—61no—
242C23×C4—61no—
243C23×C4—61no—
244C23×C4—121no—
245C23×C4—121no—
246C23×C4C22×A411yescharacteristic
247C23×C4C22×A411yescharacteristic
248C23×C4C22×A411yescharacteristic
249C23×C4C22×A411yescharacteristic
250C23×C4C22×A411yescharacteristic
251C23×C4C22×A411yescharacteristic
252#126—41no—
253#126—121no—
254#126—121no—
255#126—121no—
256#126—122no—
257C2×C4⋊C4—61no—
258C2×C4⋊C4—61no—
259C2×C4⋊C4—61no—
260C2×C4⋊C4—61no—
261C2×C4⋊C4—61no—
262C2×C4⋊C4—61no—
263C2×C4⋊C4—61no—
264C2×C4⋊C4—61no—
265C2×C4⋊C4—62no—
266C2×C4⋊C4—62no—
267C2×C4⋊C4—121no—
268C2×C4⋊C4—121no—
269C2×C4⋊C4—121no—
270C2×C4⋊C4—121no—
271C2×C4⋊C4—121no—
272C2×C4⋊C4—121no—
273C2×C22⋊C4—31no—
274C2×C22⋊C4—31no—
275C2×C22⋊C4—31no—
276C2×C22⋊C4—31no—
277C2×C22⋊C4—61no—
278C2×C22⋊C4—61no—
279C2×C22⋊C4—62no—
280C2×C22⋊C4—62no—
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—61no—
289C2×C22⋊C4—121no—
290C2×C22⋊C4—121no—
291C2×C22⋊C4—121no—
292C2×C22⋊C4—121no—
293C2×C42—31no—
294C2×C42—31no—
295C2×C42—31no—
296C2×C42—41no—
297C2×C42—61no—
298C2×C42—61no—
299C2×C42—61no—
300C2×C42—61no—
301C2×C42—61no—
302C2×C42—61no—
303C2×C42—61no—
304C2×C42—61no—
305C2×C42—61no—
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—62no—
317C2×C42—62no—
318C2×C42—61no—
319C2×C42—61no—
320C2×C42—61no—
321C2×C42—122no—
322C2×C42—121no—
323C2×C42—121no—
324C2×C42—121no—
325C2×C42—121no—
326C2×C42—121no—
327C2×C42—121no—
328C2×C42—121no—
329C2×C42—121no—
330C2×C42—121no—
331C2×C42C3×#4111yescharacteristic
332C2×C42C3×#4111yescharacteristic
333C2×C42C3×#4111yescharacteristic
334#95—34no—
335#95—61no—
336#95—61no—
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—61no—
354#95—61no—
355#95—62no—
356#95—61no—
357#95—61no—
358#95—61no—
359#95—61no—
360#95—62no—
361#95—62no—
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—31no—
397C24—31no—
398C24—61no—
399C24—61no—
400C24—61no—
401C24C23×A411yescharacteristic
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
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—32no—
419C22×C4—32no—
420C22×C4—32no—
421C22×C4—61no—
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—62no—
445C22×C4—62no—
446C22×C4—62no—
447C22×C4—62no—
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—
481C22×C4—61no—
482C22×C4—61no—
483C22×C4—61no—
484C22×C4—61no—
485C22×C4—121no—
486C22×C4—121no—
487C22×C4—121no—
488C22×C4—121no—
489C22×C4—122no—
490C22×C4—122no—
491C22×C4—122no—
492C22×C4—122no—
493C22×C4—121no—
494C22×C4—121no—
495C22×C4—121no—
496C22×C4—121no—
497C22×C4—121no—
498C22×C4—121no—
499C22×C4—121no—
500C22×C4—121no—
501C22×C4—122no—
502C22×C4—122no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—121no—
507C4⋊C4—121no—
508C4⋊C4—121no—
509C4⋊C4—241no—
510C4⋊C4—241no—
511C4⋊C4—242no—
512C4⋊C4—242no—
513C22⋊C4—32no—
514C22⋊C4—31no—
515C22⋊C4—31no—
516C22⋊C4—31no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—64no—
520C22⋊C4—64no—
521C22⋊C4—121no—
522C22⋊C4—121no—
523C22⋊C4—241no—
524C22⋊C4—241no—
525C22⋊C4—241no—
526C22⋊C4—241no—
527C22⋊C4#126⋊C311yescharacteristic
528C42—31no—
529C42—31no—
530C42—31no—
531C42—32no—
532C42—41no—
533C42—121no—
534C42—121no—
535C42—121no—
536C42—121no—
537C42—121no—
538C42—121no—
539C42—121no—
540C42—121no—
541C42—121no—
542C42—121no—
543C42—121no—
544C42—121no—
545C42—121no—
546C42—122no—
547C42—122no—
548C42—122no—
549C42—122no—
550C42—241no—
551C42—241no—
552C42C3×#12611yescharacteristic, complemented
553C22×C3—161no—
554C22×C3—321no—
555C22×C3—321no—
556C22×C3—321no—
557A4—41no—
558C3×C4—321no—
559C3×C4—321no—
560C3×C4—321no—
561C3×C4—321no—
562C3×C4—321no—
563C3×C4—321no—
564C23—31no—
565C23—31no—
566C23—31no—
567C23—31no—
568C23—31no—
569C23—41no—
570C23—61no—
571C23—61no—
572C23—61no—
573C23—61no—
574C23—61no—
575C23—61no—
576C23—61no—
577C23—61no—
578C23—61no—
579C23—61no—
580C23—61no—
581C23—61no—
582C23—121no—
583C23—121no—
584C23—121no—
585C23—121no—
586C23—121no—
587C23C2×#126⋊C311yescharacteristic
588C23A4×#4111yescharacteristic
589C23A4×#4111yescharacteristic
590C23A4×#4111yescharacteristic
591C2×C4—31no—
592C2×C4—31no—
593C2×C4—31no—
594C2×C4—31no—
595C2×C4—31no—
596C2×C4—31no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—61no—
602C2×C4—61no—
603C2×C4—61no—
604C2×C4—61no—
605C2×C4—61no—
606C2×C4—61no—
607C2×C4—61no—
608C2×C4—61no—
609C2×C4—61no—
610C2×C4—61no—
611C2×C4—61no—
612C2×C4—61no—
613C2×C4—61no—
614C2×C4—61no—
615C2×C4—61no—
616C2×C4—61no—
617C2×C4—61no—
618C2×C4—61no—
619C2×C4—61no—
620C2×C4—61no—
621C2×C4—62no—
622C2×C4—62no—
623C2×C4—62no—
624C2×C4—62no—
625C2×C4—62no—
626C2×C4—62no—
627C2×C4—62no—
628C2×C4—62no—
629C2×C4—62no—
630C2×C4—122no—
631C2×C4—122no—
632C2×C4—122no—
633C2×C4—122no—
634C2×C4—122no—
635C2×C4—122no—
636C2×C4—122no—
637C2×C4—122no—
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×C4—121no—
660C2×C4—121no—
661C2×C4—121no—
662C2×C4—121no—
663C2×C4—121no—
664C2×C4—121no—
665C2×C4—121no—
666C2×C4—121no—
667C2×C4—121no—
668C2×C4—121no—
669C2×C4—121no—
670C2×C4—121no—
671C2×C4—121no—
672C2×C4—121no—
673C2×C4—121no—
674C2×C4—121no—
675C2×C4—121no—
676C2×C4—121no—
677C2×C4—121no—
678C2×C4—121no—
679C2×C4—121no—
680C2×C4—121no—
681C2×C4—121no—
682C2×C4—121no—
683C2×C4—121no—
684C2×C4—121no—
685C2×C4—121no—
686C2×C4C2×#126⋊C311yescharacteristic
687C2×C4C2×#126⋊C311yescharacteristic
688C2×C3—161no—
689C2×C3—161no—
690C2×C3—161no—
691C2×C3—641no—
692C22—21no—
693C22—21no—
694C22—21no—
695C22—31no—
696C22—31no—
697C22—31no—
698C22—31no—
699C22—31no—
700C22—31no—
701C22—31no—
702C22—31no—
703C22—31no—
704C22—31no—
705C22—31no—
706C22—61no—
707C22—61no—
708C22—61no—
709C22—121no—
710C22—121no—
711C22—121no—
712C22—121no—
713C22—121no—
714C22—121no—
715C22—121no—
716C22—121no—
717C22C22×#126⋊C311yescharacteristic
718C22A4×#12611yescharacteristic
719C4—21no—
720C4—21no—
721C4—61no—
722C4—61no—
723C4—61no—
724C4—61no—
725C4—61no—
726C4—61no—
727C4—81no—
728C4—81no—
729C4—81no—
730C4—81no—
731C4—122no—
732C4—122no—
733C4—122no—
734C4—241no—
735C4—241no—
736C4—241no—
737C4—241no—
738C3—161noSylow
739C2—31no—
740C2—31no—
741C2—31no—
742C2—31no—
743C2—41no—
744C2—121no—
745C2#36166⋊C311yescharacteristic
746C2#36166⋊C311yescharacteristic
747C2#36641⋊C311yescharacteristic
subgroupG/H
centerC22C22×#126⋊C3
commutator, cosocleC22×C42C23×C3
Frattini, socleC24C23×A4
Fitting#616832C3
prime radicalC23×C42⋊C3C22
hypercenterC22⋊C4#126⋊C3
hypocenterC42C3×#126
LCSG ▷ C22×C42 ▷ C42
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #14710⋊C3C2semidirect
2. #14710⋊C3C2semidirect
3. C4⋊(#383⋊C3)C2semidirect
6. C4×#383⋊C3C2semidirect
8. #616832C3semidirect
21. #14710C2×C3semidirect
22. #14710C2×C3semidirect
23. #14688C2×C3semidirect
30. C4×#383C2×C3semidirect
225. C42⋊C3#126semidirect
552. C42C3×#126semidirect

Maximal subgroups

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

subgroupindex
#14710⋊C32
C4⋊(#383⋊C3)2
#14683⋊C32
C4×#383⋊C32
C22⋊C4×C42⋊C32
#6168323
A4×#1264