Finite Group Databasebeta

← #29708921

Subgroups — #29708921

Order 15616.

914 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839803C211yesmaximal, characteristic, complemented
2#21454335C211yesmaximal, characteristic
3#417×D61C211yesmaximal, characteristic
4#21454261C211yesmaximal, characteristic
5#21447268C211yesmaximal, characteristic, complemented
6#21447267C211yesmaximal, characteristic, complemented
7#21447266C211yesmaximal, characteristic, complemented
8#21447264C211yesmaximal, characteristic, complemented
9#21447263C211yesmaximal, characteristic, complemented
10#21447262C211yesmaximal, characteristic, complemented
11#21447260C211yesmaximal, characteristic, complemented
12#21445556C211yesmaximal, characteristic, complemented
13#343×D61C211yesmaximal, characteristic, complemented
14#21445544C211yesmaximal, characteristic, complemented
15C61×#2078C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic
19C2×M16×D61C2211yescharacteristic
20C2×M16×D61C2211yescharacteristic
21C2×#14519735C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23#16839803—22no—
24#16839803—22no—
25C2×#14519710C2211yescharacteristic, complemented
26C2×#14519709C2211yescharacteristic, complemented
27C2×#14519708C2211yescharacteristic, complemented
28#16839769—21no—
29#16839765—21no—
30#16839764C2211yescharacteristic
31#16839764C2211yescharacteristic
32#16839763C2211yescharacteristic
33#16839763C2211yescharacteristic
34#16839762—21no—
35#16839761C2211yescharacteristic
36#16839761C2211yescharacteristic
37#16839760—21no—
38#16839757—21no—
39#16839755—21no—
40#103×D61—21no—
41#102×D61—21no—
42#16839730C2211yescharacteristic
43#16839729C2211yescharacteristic
44#16839728C2211yescharacteristic
45#16839727—22no—
46#16839724—22no—
47#16839531C2211yescharacteristic, complemented
48#16839531C2211yescharacteristic, complemented
49#16839530C2211yescharacteristic, complemented
50#16839530C2211yescharacteristic, complemented
51#16839530C2211yescharacteristic, complemented
52#16839530C2211yescharacteristic, complemented
53#16839527C2211yescharacteristic, complemented
54#16839526C2211yescharacteristic, complemented
55#16839526C2211yescharacteristic, complemented
56C2×#107×C61C2211yescharacteristic, complemented
57C61×#417C2211yescharacteristic
58C61×#417C2211yescharacteristic
59C61×#408C2211yescharacteristic
60C61×#343C2211yescharacteristic, complemented
61C61×#343C2211yescharacteristic, complemented
62C61×#341C2211yescharacteristic, complemented
63C2×#11758226D411yescharacteristic
64C2×#11758222—21no—
65C2×#11758222C2311yescharacteristic
66C2×#11758224—21no—
67C2×#11758224D411yescharacteristic
68#41×D61—22no—
69#41×D61—22no—
70#41×D61—22no—
71#41×D61—22no—
72C2×Q8×D61D411yescharacteristic
73C2×D4×D61—21no—
74C2×D4×D61D411yescharacteristic
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61C2311yescharacteristic
78C2×#11758194C2311yescharacteristic
79C2×#11758194C2311yescharacteristic
80C2×#11758194C2311yescharacteristic
81C2×#11758189—22no—
82C2×#11758189—22no—
83C2×#11758189—21no—
84C2×#11758189—21no—
85C2×#11758189—21no—
86C2×#11758189D412yes—
87C2×#11758189D412yes—
88M16×D61—22no—
89M16×D61—22no—
90M16×D61—22no—
91M16×D61—22no—
92M16×D61—22no—
93M16×D61—22no—
94C22×#92418C2311yescharacteristic
95C2×C8×D61—21no—
96C2×C8×D61—21no—
97C2×C8×D61—21no—
98#14519735—21no—
99#14519735—21no—
100#14519735—21no—
101#14519735—21no—
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×#11758196—21no—
105C4⋊C4×D61—21no—
106C4⋊C4×D61—21no—
107C4⋊C4×D61—21no—
108C4⋊C4×D61—21no—
109C2×#11758198—21no—
110C2×C4×Dic61—21no—
111#14519710—22no—
112#14519709—22no—
113#14519708—22no—
114#14519702—21no—
115#14519702—21no—
116#14519701—21no—
117#14519701—21no—
118#14519700—21no—
119#14519700—21no—
120#14519699—21no—
121#14519699—21no—
122#14519698—21no—
123#14519698—21no—
124#14519697—21no—
125#14519697—21no—
126C22⋊#92418—22no—
127#14519689—22no—
128#14519689—22no—
129C2×#41×C61C2311yescharacteristic
130C2×M16×C61C2311yescharacteristic
131C2×M16×C61C2311yescharacteristic
132C2×M16×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136#107×C61—22no—
137#103×C61—21no—
138#103×C61—21no—
139#102×C61—21no—
140#102×C61—21no—
141C22⋊C8×C61—22no—
142C23×D61—21no—
143C23×D61#4111yescharacteristic
144#41×C61—21no—
145#41×C61—21no—
146#41×C61—21no—
147#41×C61—21no—
148C2×Q8×C61C2×D411yescharacteristic
149C2×D4×C61—21no—
150C2×D4×C61C2×D411yescharacteristic
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61C2411yescharacteristic
155C2×C22⋊D61—21no—
156C2×C22⋊D61—21no—
157C2×C22⋊D61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61#4111yescharacteristic
162#11758226—22no—
163#11758226—22no—
164Q8×D61—22no—
165Q8×D61—22no—
166#11758224—22no—
167#11758224—22no—
168#11758224—42no—
169#11758224—42no—
170D4×D61—22no—
171D4×D61—22no—
172D4×D61—42no—
173D4×D61—42no—
174#11758222—21no—
175#11758222—21no—
176#11758222—21no—
177#11758222—21no—
178#11758222—42no—
179#11758222—42no—
180C2×D244—21no—
181C2×D244C2×D411yescharacteristic
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—42no—
186C2×C4×D61—42no—
187C2×C4×D61—41no—
188C2×C4×D61—41no—
189C2×C4×D61—82no—
190C2×C4×D61C2×D411yescharacteristic
191C2×C4×D61C2×D411yescharacteristic
192C2×C4×D61C2×D411yescharacteristic
193C2×C4×D61C2×D411yescharacteristic
194C2×C4×D61#4112yes—
195C2×C4×D61#4112yes—
196C2×C4×D61#4112yes—
197C2×C4×D61#4112yes—
198C2×Dic122—21no—
199C2×Dic122C2×D411yescharacteristic
200M16×C61—21no—
201M16×C61—21no—
202M16×C61—21no—
203M16×C61—21no—
204M16×C61—21no—
205M16×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61C2×D412yes—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216#11758198—41no—
217#11758198—41no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222#11758196—41no—
223#11758196—41no—
224C4×Dic61—41no—
225C4×Dic61—41no—
226#11758194—21no—
227#11758194—21no—
228#11758194—21no—
229#11758194—21no—
230#11758194—21no—
231#11758194—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418C2×D412yes—
238#11758189—24no—
239#11758189—24no—
240#11758189—42no—
241#11758189—42no—
242#11758189—42no—
243C8×D61—42no—
244C8×D61—42no—
245C8×D61—42no—
246C23×C61—21no—
247C23×C61C2×#4111yescharacteristic
248C22×D61—21no—
249C22×D61—41no—
250C22×D61—41no—
251C22×D61—42no—
252C22×D61—81no—
253C22×D61—81no—
254C22×D61#12111yescharacteristic
255C22×D61#12111yescharacteristic
256C22×D61#12612yes—
257C22×D61#12612yes—
258Q8×C61—21no—
259Q8×C61—21no—
260D4×C61—21no—
261D4×C61—21no—
262D4×C61—41no—
263D4×C61—41no—
264C2×C4×C61—21no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—81no—
270C2×C4×C61—81no—
271C2×C4×C61C22×D411yescharacteristic
272C2×C4×C61C22×D411yescharacteristic
273C2×C4×C61C2×#4111yescharacteristic
274C2×C4×C61C2×#4111yescharacteristic
275C2×C4×C61C2×#4111yescharacteristic
276C2×C4×C61C2×#4111yescharacteristic
277C22⋊D61—41no—
278C22⋊D61—41no—
279C22⋊D61—42no—
280C22⋊D61—42no—
281C2×Dic61—21no—
282C2×Dic61—42no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—81no—
286C2×Dic61—81no—
287C2×Dic61#12111yescharacteristic
288C2×Dic61#12111yescharacteristic
289C2×Dic61#12612yes—
290C2×Dic61#12612yes—
291D244—21no—
292D244—21no—
293D244—42no—
294C4×D61—42no—
295C4×D61—41no—
296C4×D61—41no—
297C4×D61—42no—
298C4×D61—82no—
299C4×D61—82no—
300C4×D61#12312yes—
301C4×D61#12312yes—
302C4×D61#12312yes—
303C4×D61#12312yes—
304C4×D61#12312yes—
305C4×D61#12312yes—
306C4×D61#12412yes—
307C4×D61#12412yes—
308Dic122—21no—
309Dic122—21no—
310Dic122—42no—
311C8×C61—22no—
312C8×C61—41no—
313C8×C61—41no—
314C8×C61—41no—
315#92418—22no—
316#92418—41no—
317#92418—41no—
318#92418—41no—
319#23647—611nomaximal, Sylow
320C22×C61—21no—
321C22×C61—21no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61C2×#12111yescharacteristic
326C22×C61C2×#12611yescharacteristic
327C22×C61C2×#12611yescharacteristic
328C2×D61—21no—
329C2×D61—21no—
330C2×D61—21no—
331C2×D61—21no—
332C2×D61—42no—
333C2×D61—42no—
334C2×D61—41no—
335C2×D61—41no—
336C2×D61—41no—
337C2×D61—84no—
338C2×D61#39712yes—
339C2×D61#39712yes—
340C4×C61—41no—
341C4×C61—81no—
342C4×C61—81no—
343C4×C61C2×#12311yescharacteristic
344C4×C61C2×#12311yescharacteristic
345C4×C61C2×#12311yescharacteristic
346C4×C61C2×#12411yescharacteristic
347Dic61—41no—
348Dic61—81no—
349Dic61—81no—
350Dic61#39712yes—
351Dic61#39712yes—
352C2×#428—611no—
353#2896—611no—
354C2×#417—611no—
355#2879—611no—
356#2079—611no—
357#2079—611no—
358#2079—611no—
359#2079—611no—
360#2078—611no—
361#2078—611no—
362#2078—611no—
363#2078D6111yescharacteristic, complemented
364#1742—611no—
365C2×#343—611no—
366#1738—611no—
367C2×C61—21no—
368C2×C61—21no—
369C2×C61—81no—
370C2×C61C2×#39711yescharacteristic
371C2×C61#306811yescharacteristic
372C2×C61#306911yescharacteristic
373D61—22no—
374D61—22no—
375D61—81no—
376C22×#41—611no—
377C22×M16—611no—
378C22×M16—611no—
379C22×M16—611no—
380C22×M16—611no—
381C2×#117—611no—
382C22×C4⋊C4—611no—
383#428—1222no—
384#428—1222no—
385C2×#107—611no—
386C2×#107C2×D6111yescharacteristic, complemented
387C2×#106—611no—
388C2×#106—611no—
389#419—1221no—
390#418—1221no—
391#417—611no—
392#417—611no—
393#417—611no—
394#417—611no—
395#417—611no—
396#417—611no—
397#417—1221no—
398#417—1221no—
399#417C2×D6111yescharacteristic
400#417C2×D6111yescharacteristic
401#416—1221no—
402#416—1221no—
403C2×#103—1221no—
404C2×#102—1221no—
405#408—611no—
406#408—611no—
407#408—611no—
408#408—1222no—
409#408C2×D6111yescharacteristic
410#407—1222no—
411#343—611no—
412#343—611no—
413#343—611no—
414#343—611no—
415#343—611no—
416#343—611no—
417#343C2×D6111yescharacteristic, complemented
418#343C2×D6111yescharacteristic, complemented
419#341—611no—
420#341—611no—
421#341—611no—
422#341C2×D6111yescharacteristic, complemented
423C61#2364711yescharacteristic, complemented, Sylow
424C2×#41—611no—
425C2×#41—611no—
426C2×#41—611no—
427C2×#41—1221no—
428C2×#41—1221no—
429C2×#41—1222no—
430C2×#41—1222no—
431C2×#41—1222no—
432C2×#41—1222no—
433C2×#41C22×D6111yescharacteristic
434C22×Q8—611no—
435C22×D4—611no—
436C22×D4—1221no—
437C23×C4—611no—
438C23×C4—1221no—
439C23×C4—1221no—
440C2×M16—612no—
441C2×M16—612no—
442C2×M16—611no—
443C2×M16—611no—
444C2×M16—611no—
445C2×M16—1222no—
446C2×M16—1222no—
447C2×M16—1221no—
448C2×M16—1221no—
449C2×M16—1221no—
450C2×M16—1222no—
451C2×M16—1222no—
452C2×M16—1222no—
453C2×M16—1222no—
454C2×M16—1222no—
455C2×M16—1222no—
456C2×M16C22×D6111yescharacteristic
457C2×M16C22×D6111yescharacteristic
458C2×M16C22×D6111yescharacteristic
459C22×C8—611no—
460C22×C8—1221no—
461C22×C8—1221no—
462C22×C8—1221no—
463C22×C8C22×D6111yescharacteristic
464#117—1221no—
465#117—1221no—
466#117—1221no—
467#117—1221no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—1221no—
471C2×C4⋊C4—1221no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4C22×D6111yescharacteristic
476C2×C4⋊C4C22×D6111yescharacteristic
477C2×C22⋊C4—1221no—
478C2×C42—1221no—
479#107—22no—
480#107—1222no—
481#106—1222no—
482#106—1222no—
483#103—21no—
484#103—21no—
485#103—1221no—
486#103—1221no—
487#103—1221no—
488#103—1221no—
489#103—1221no—
490#103—1221no—
491#102—21no—
492#102—21no—
493#102—1221no—
494#102—1221no—
495#102—1221no—
496#102—1221no—
497#102—1221no—
498#102—1221no—
499C22⋊C8—22no—
500C22⋊C8—1222no—
501C22⋊C8—1222no—
502C22⋊C8—1222no—
503C24—611no—
504C24—1221no—
505#41—21no—
506#41—21no—
507#41—21no—
508#41—21no—
509#41—1222no—
510#41—1222no—
511#41—1222no—
512#41—1222no—
513#41—1221no—
514#41—1221no—
515#41—1221no—
516#41—1221no—
517#41—2442no—
518#41—2442no—
519#41—2442no—
520#41—2442no—
521C2×Q8—611no—
522C2×Q8—1221no—
523C2×Q8—1222no—
524C2×Q8—1222no—
525C2×Q8D4×D6111yescharacteristic
526C2×D4—21no—
527C2×D4—611no—
528C2×D4—1221no—
529C2×D4—1222no—
530C2×D4—1222no—
531C2×D4—1221no—
532C2×D4—1221no—
533C2×D4—1221no—
534C2×D4—2442no—
535C2×D4—2442no—
536C2×D4D4×D6111yescharacteristic
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—612no—
546C22×C4—612no—
547C22×C4—612no—
548C22×C4—612no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—4882no—
556C22×C4—2442no—
557C22×C4—2442no—
558C22×C4—2441no—
559C22×C4—2441no—
560C22×C4C23×D6111yescharacteristic
561M16—21no—
562M16—21no—
563M16—21no—
564M16—21no—
565M16—21no—
566M16—21no—
567M16—1224no—
568M16—1224no—
569M16—1221no—
570M16—1221no—
571M16—1221no—
572M16—1221no—
573M16—1221no—
574M16—1221no—
575M16—2442no—
576M16—2442no—
577M16—2442no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—612no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—2442no—
590C2×C8—2442no—
591C2×C8—2442no—
592C2×C8D4×D6112yes—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—2441no—
602C4⋊C4—2441no—
603C22⋊C4—2441no—
604C22⋊C4—2441no—
605C42—2441no—
606C42—2441no—
607C23—21no—
608C23—611no—
609C23—611no—
610C23—612no—
611C23—612no—
612C23—1221no—
613C23—4881no—
614C23—4881no—
615C23—2441no—
616C23—2441no—
617C23—2442no—
618C23#41×D6111yescharacteristic
619Q8—21no—
620Q8—21no—
621Q8—1221no—
622Q8—1221no—
623Q8—2442no—
624D4—21no—
625D4—21no—
626D4—41no—
627D4—41no—
628D4—1221no—
629D4—1221no—
630D4—2442no—
631D4—2442no—
632D4—2442no—
633D4—2441no—
634D4—2441no—
635C2×C4—21no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—81no—
641C2×C4—81no—
642C2×C4—611no—
643C2×C4—611no—
644C2×C4—612no—
645C2×C4—612no—
646C2×C4—612no—
647C2×C4—612no—
648C2×C4—612no—
649C2×C4—612no—
650C2×C4—612no—
651C2×C4—612no—
652C2×C4—612no—
653C2×C4—612no—
654C2×C4—1221no—
655C2×C4—4882no—
656C2×C4—4882no—
657C2×C4—4881no—
658C2×C4—4881no—
659C2×C4—2442no—
660C2×C4—2442no—
661C2×C4—2442no—
662C2×C4—2441no—
663C2×C4—2441no—
664C2×C4—2441no—
665C2×C4—2441no—
666C2×C4C2×D4×D6111yescharacteristic
667C2×C4C2×D4×D6111yescharacteristic
668C2×C4#41×D6111yescharacteristic
669C2×C4#41×D6111yescharacteristic
670C2×C4#41×D6111yescharacteristic
671C2×C4#41×D6111yescharacteristic
672C8—22no—
673C8—41no—
674C8—41no—
675C8—41no—
676C8—1222no—
677C8—2441no—
678C8—2441no—
679C8—2441no—
680C22—21no—
681C22—21no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—612no—
686C22—612no—
687C22—1221no—
688C22—1221no—
689C22—1221no—
690C22—1221no—
691C22—4884no—
692C22—2442no—
693C22—2442no—
694C22—2441no—
695C22—2441no—
696C22—2441no—
697C22#121×D6111yescharacteristic
698C22#126×D6111yescharacteristic
699C22#126×D6111yescharacteristic
700C4—41no—
701C4—81no—
702C4—81no—
703C4—612no—
704C4—612no—
705C4—4881no—
706C4—4881no—
707C4—2441no—
708C4#123×D6111yescharacteristic
709C4#123×D6111yescharacteristic
710C4#123×D6111yescharacteristic
711C4#124×D6111yescharacteristic
712C2—21no—
713C2—21no—
714C2—81no—
715C2—1222no—
716C2—1222no—
717C2—4881no—
718C2#397×D6111yescharacteristic
719C2#2145554511yescharacteristic
720C2#2145555411yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2078C2
socleC22×C61C2×#121
prime radicalC2×#41×D61C22
hypercenter#2078D61
hypocenterC61#23647
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2078

Complements

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

NH ≅ G/Ntype
1. C2×#16839803C2semidirect
5. #21447268C2semidirect
6. #21447267C2semidirect
7. #21447266C2semidirect
8. #21447264C2semidirect
9. #21447263C2semidirect
10. #21447262C2semidirect
11. #21447260C2semidirect
12. #21445556C2semidirect
13. #343×D61C2semidirect
14. #21445544C2semidirect
15. C61×#2078C2semidirect
25. C2×#14519710C22semidirect
26. C2×#14519709C22semidirect
27. C2×#14519708C22semidirect
47. #16839531C22semidirect
48. #16839531C22semidirect
49. #16839530C22semidirect
50. #16839530C22semidirect
51. #16839530C22semidirect
52. #16839530C22semidirect
53. #16839527C22semidirect
54. #16839526C22semidirect
55. #16839526C22semidirect
56. C2×#107×C61C22semidirect
60. C61×#343C22semidirect
61. C61×#343C22semidirect
62. C61×#341C22semidirect
363. #2078D61semidirect
386. C2×#107C2×D61semidirect
417. #343C2×D61semidirect
418. #343C2×D61semidirect
422. #341C2×D61semidirect
423. C61#23647semidirect

Maximal subgroups

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

subgroupindex
C2×#168398032
#214543352
#417×D612
#214542612
#214472682
#214472672
#214472662
#214472642
#214472632
#214472622
#214472602
#214455562
#343×D612
#214455442
C61×#20782
#2364761