Finite Group Databasebeta

← #29737546

Subgroups — #29737546

Order 15616.

884 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455666C211yesmaximal, characteristic, complemented
2#21454342C211yesmaximal, characteristic
3#21454341C211yesmaximal, characteristic
4#21447344C211yesmaximal, characteristic, complemented
5#21447178C211yesmaximal, characteristic, complemented
6#21447176C211yesmaximal, characteristic, complemented
7#21446972C211yesmaximal, characteristic, complemented
8#21446096C211yesmaximal, characteristic, complemented
9#21446093C211yesmaximal, characteristic, complemented
10#21446045C211yesmaximal, characteristic, complemented
11#21446042C211yesmaximal, characteristic, complemented
12#21445884C211yesmaximal, characteristic, complemented
13#21445881C211yesmaximal, characteristic, complemented
14#21445771C211yesmaximal, characteristic
15C61×#3083C211yesmaximal, characteristic, complemented
16C2×#14519823C2211yescharacteristic
17C2×#14519784C2211yescharacteristic
18C2×#14519783C2211yescharacteristic
19#16840242C2211yescharacteristic
20#16840066—21no—
21#16840059—21no—
22#16840054—21no—
23#16840039—21no—
24C2×#14519713C2211yescharacteristic, complemented
25C2×#14519712C2211yescharacteristic, complemented
26#16839805C2211yescharacteristic, complemented
27C2×#14519710C2211yescharacteristic, complemented
28#16839789C2211yescharacteristic, complemented
29C2×#14519704C2211yescharacteristic
30C2×#14519703C2211yescharacteristic
31#16839766—21no—
32#16839766C2211yescharacteristic
33#16839766C2211yescharacteristic
34#16839765—21no—
35#16839763C2211yescharacteristic
36#16839762—21no—
37#16839761—21no—
38#16839761C2211yescharacteristic
39#16839761C2211yescharacteristic
40#16839757—21no—
41#16839756—21no—
42#16839756C2211yescharacteristic
43C2×#14519699C2211yescharacteristic
44C2×#14519697—21no—
45C2×#14519697C2211yescharacteristic
46#102×D61—21no—
47C2×#14519693C2211yescharacteristic
48#16839663C2211yescharacteristic
49#16839631C2211yescharacteristic, complemented
50#16839531C2211yescharacteristic, complemented
51#16839531C2211yescharacteristic, complemented
52#16839530C2211yescharacteristic, complemented
53#16839521C2211yescharacteristic, complemented
54#16839521C2211yescharacteristic, complemented
55#16839516C2211yescharacteristic, complemented
56C61×#544C2211yescharacteristic, complemented
57C61×#520C2211yescharacteristic
58C61×#479—21no—
59C61×#478—21no—
60C61×#477—21no—
61C61×#474—21no—
62C61×#428C2211yescharacteristic, complemented
63C2×#107×C61C2211yescharacteristic, complemented
64C61×#424C2211yescharacteristic, complemented
65C61×#417C2211yescharacteristic
66C61×#416C2211yescharacteristic
67#14519823—22no—
68#14519823—22no—
69#14519823—41no—
70#14519823Q814yescomplemented
71C2×#11758226—21no—
72C2×#11758222—21no—
73C2×#11758222C2311yescharacteristic
74C22×D244—21no—
75C22×D244C2311yescharacteristic
76C2×D4×D61—21no—
77C2×D4×D61—41no—
78#14519784—22no—
79#14519784—41no—
80#14519783—22no—
81#14519783—41no—
82C2×#11758194—21no—
83C2×#11758194C2311yescharacteristic
84C2×#11758194C2311yescharacteristic
85C2×#11758194C2311yescharacteristic
86C2×#11758189—21no—
87C22×#92418—21no—
88C22×#92418C2311yescharacteristic
89C2×C8×D61—21no—
90C4×Dic122—21no—
91C4×D244—21no—
92#14519737—41no—
93#14519735—21no—
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—41no—
96C4⋊C4×D61—21no—
97C2×#11758198—41no—
98C2×C4×Dic61C2311yescharacteristic
99#14519713—41no—
100#14519712—41no—
101#14519710—21no—
102#14519710—21no—
103#14519710—21no—
104#14519708—21no—
105C4⋊#92418—21no—
106C4⋊#92418—21no—
107#14519704—22no—
108#14519703—22no—
109#14519701—21no—
110#14519700—21no—
111#14519700—21no—
112#14519700D411yescharacteristic
113#14519700D411yescharacteristic
114#14519699—21no—
115#14519699—21no—
116#14519698—21no—
117#14519697—21no—
118#14519697—21no—
119#14519697—21no—
120#14519697—21no—
121#14519697—21no—
122#14519697—21no—
123#14519697—21no—
124#14519697—21no—
125#14519697D411yescharacteristic
126#14519697D411yescharacteristic
127#14519693—41no—
128C2×#41×C61C2311yescharacteristic
129C2×M16×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C4⋊Q8×C61—21no—
132C4⋊Q8×C61—21no—
133#125×C61—21no—
134#125×C61—21no—
135C22⋊Q8×C61—41no—
136C4×Q8×C61—21no—
137C4×D4×C61—21no—
138C4×D4×C61—41no—
139#117×C61—21no—
140#117×C61C2311yescharacteristic
141#117×C61C2311yescharacteristic
142C2×C4⋊C4×C61—21no—
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145#107×C61—21no—
146#107×C61—21no—
147#107×C61—21no—
148#106×C61—21no—
149C4⋊C8×C61—21no—
150C4⋊C8×C61—21no—
151#103×C61—21no—
152#103×C61D411yescharacteristic
153#103×C61D411yescharacteristic
154#102×C61—21no—
155#102×C61D411yescharacteristic
156#102×C61D411yescharacteristic
157C23×D61—21no—
158C23×D61—41no—
159#41×C61—21no—
160#41×C61—21no—
161#41×C61C2×Q812yes—
162#41×C61#4112yes—
163C2×Q8×C61—41no—
164C2×Q8×C61C2×D411yescharacteristic
165C2×D4×C61—21no—
166C2×D4×C61C2×D411yescharacteristic
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—41no—
171C22×C4×C61C2411yescharacteristic
172C2×C22⋊D61—21no—
173C2×C22⋊D61—41no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176#11758226—24no—
177#11758226—42no—
178D4×D61—24no—
179D4×D61—42no—
180D4×D61—44no—
181D4×D61—44no—
182#11758222—21no—
183#11758222—21no—
184#11758222—24no—
185#11758222—42no—
186#11758222C2×Q812yes—
187#11758222#4112yes—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244—24no—
193C2×D244—21no—
194C2×D244—42no—
195C2×D244—41no—
196C2×D244C2×D411yescharacteristic
197C2×D244C2×Q812yes—
198C2×C4×D61—21no—
199C2×C4×D61—41no—
200C2×C4×D61—41no—
201C2×Dic122C2×D411yescharacteristic
202M16×C61—21no—
203M16×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61C2×D411yescharacteristic
208C2×C8×C61C2×D411yescharacteristic
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—41no—
214C4⋊C4×C61—41no—
215C4⋊C4×C61—41no—
216C4⋊C4×C61—41no—
217C4⋊C4×C61C2×D411yescharacteristic
218C4⋊C4×C61C2×D411yescharacteristic
219C4⋊C4×C61C2×D411yescharacteristic
220C4⋊C4×C61C2×D411yescharacteristic
221C22⋊C4×C61—21no—
222C22⋊C4×C61—21no—
223C22⋊C4×C61—41no—
224C42×C61—21no—
225C42×C61—21no—
226C42×C61—41no—
227#11758198—41no—
228#11758198—82no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231#11758196—41no—
232#11758196—82no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61—41no—
236#11758194—21no—
237#11758194—21no—
238#11758194—21no—
239#11758194—21no—
240#11758194—21no—
241#11758194—21no—
242#11758194—42no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—42no—
249C2×#92418C2×D411yescharacteristic
250C2×#92418C2×D411yescharacteristic
251#11758189—42no—
252C8×D61—42no—
253C23×C61—21no—
254C23×C61H(5,𝔽2)11yescharacteristic
255C22×D61—21no—
256C22×D61—22no—
257C22×D61—44no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—81no—
261C22×D61—81no—
262C22×D61—161no—
263C22×D61—161no—
264Q8×C61—21no—
265Q8×C61—161no—
266Q8×C61C22⋊Q812yes—
267D4×C61—22no—
268D4×C61—22no—
269D4×C61—21no—
270D4×C61C22⋊Q812yes—
271C2×C4×C61—21no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—81no—
281C2×C4×C61—81no—
282C2×C4×C61—161no—
283C2×C4×C61C22×D411yescharacteristic
284C2×C4×C61C22×D411yescharacteristic
285C2×C4×C61C22×Q811yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×C4×C61H(5,𝔽2)11yescharacteristic
289C22⋊D61—22no—
290C22⋊D61—22no—
291C22⋊D61—44no—
292C2×Dic61—21no—
293C2×Dic61—22no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—81no—
298D244—22no—
299D244—22no—
300D244—21no—
301D244—44no—
302D244—41no—
303D244—41no—
304D244C22⋊Q812yes—
305C4×D61—22no—
306C4×D61—22no—
307C4×D61—44no—
308C4×D61—161no—
309Dic122—21no—
310Dic122C22⋊Q812yes—
311C8×C61—21no—
312C8×C61—21no—
313C8×C61—41no—
314#92418—21no—
315#92418—21no—
316#92418—41no—
317#92418—41no—
318#92418—41no—
319#25982—611nomaximal, Sylow
320C22×C61—21no—
321C22×C61—21no—
322C22×C61—22no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61#54311yescharacteristic
326C22×C61D4211yescharacteristic
327C22×C61#55111yescharacteristic
328C2×D61—22no—
329C2×D61—41no—
330C2×D61—41no—
331C2×D61—42no—
332C2×D61—81no—
333C2×D61—81no—
334C2×D61—82no—
335C2×D61—164no—
336C2×D61—161no—
337C4×C61—22no—
338C4×C61—41no—
339C4×C61—41no—
340C4×C61—41no—
341C4×C61—41no—
342C4×C61—81no—
343C4×C61—81no—
344C4×C61C2×C22⋊Q811yescharacteristic
345C4×C61C2×C22⋊Q811yescharacteristic
346C4×C61#54611yescharacteristic
347C4×C61#54611yescharacteristic
348Dic61—22no—
349Dic61—42no—
350Dic61—81no—
351#3083—611no—
352#3083D6111yescharacteristic, complemented
353#2897—611no—
354#2897—611no—
355#2093—611no—
356#2063—611no—
357#2063—611no—
358#2027—611no—
359#1866—611no—
360#1866—611no—
361#1859—611no—
362#1859—611no—
363#1816—611no—
364#1816—611no—
365#1792—611no—
366C2×C61—21no—
367C2×C61—21no—
368C2×C61—42no—
369C2×C61#243711yescharacteristic
370C2×C61#328911yescharacteristic
371C2×C61#329211yescharacteristic
372D61—42no—
373D61—82no—
374C2×H(5,𝔽2)—611no—
375C2×#131—611no—
376C2×#131—611no—
377#544C2×D6111yescharacteristic, complemented
378#520—611no—
379#520C2×D6111yescharacteristic
380#479—21no—
381#479—1221no—
382#478—21no—
383#478—1221no—
384#477—21no—
385#477—1221no—
386#474—21no—
387#474—1221no—
388C2×#108—611no—
389C2×#108—611no—
390#428—611no—
391#428C2×D6111yescharacteristic, complemented
392C2×#107—611no—
393C2×#107C2×D6111yescharacteristic, complemented
394#424—611no—
395#424C2×D6111yescharacteristic, complemented
396C2×#104—611no—
397C2×#104—611no—
398#418—611no—
399#418—611no—
400#418—1221no—
401#418—1221no—
402#417—611no—
403#417—611no—
404#417—611no—
405#417—1221no—
406#417—1221no—
407#417C2×D6111yescharacteristic
408#416—611no—
409#416—1221no—
410#416—1221no—
411#416C2×D6111yescharacteristic
412C2×#102—611no—
413C2×#102—611no—
414C2×#102—1221no—
415C2×#102—1221no—
416C2×#100—611no—
417#390—611no—
418#384—611no—
419#343—611no—
420#343—611no—
421#343—611no—
422#339—611no—
423#339—611no—
424#336—611no—
425C61#2598211yescharacteristic, complemented, Sylow
426H(5,𝔽2)—614no—
427H(5,𝔽2)—1222no—
428H(5,𝔽2)—1222no—
429H(5,𝔽2)—2441no—
430C2×#41—611no—
431C2×#41—1221no—
432C2×#41—1221no—
433C2×#41C22×D6111yescharacteristic
434C22×D4—611no—
435C22×D4—1221no—
436C22×D4—1221no—
437C22×D4—2441no—
438#131—1222no—
439#131—1222no—
440#131—2441no—
441#131—2441no—
442C2×M16—611no—
443C2×M16—611no—
444C2×M16—611no—
445C2×M16—1221no—
446C2×M16—1221no—
447C2×M16C22×D6111yescharacteristic
448C22×C8—611no—
449C22×C8—1221no—
450C22×C8—1221no—
451C22×C8C22×D6111yescharacteristic
452C4⋊Q8—21no—
453C4⋊Q8—21no—
454#125—21no—
455#125—21no—
456C22⋊Q8—41no—
457C4×Q8—21no—
458C4×Q8—1221no—
459C4×D4—21no—
460C4×D4—41no—
461C4×D4—1221no—
462C4×D4—2441no—
463#117—21no—
464#117—1221no—
465#117C22×D6111yescharacteristic
466#117C22×D6111yescharacteristic
467C2×C4⋊C4—21no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—1221no—
470C2×C4⋊C4—2441no—
471C2×C4⋊C4C22×D6111yescharacteristic
472C2×C4⋊C4C22×D6111yescharacteristic
473C2×C22⋊C4—2441no—
474C2×C42—611no—
475#108—2441no—
476#108—2441no—
477#107—21no—
478#107—21no—
479#107—21no—
480#107—1221no—
481#107—1221no—
482#107—1221no—
483#106—21no—
484#106—1221no—
485C4⋊C8—21no—
486C4⋊C8—21no—
487C4⋊C8—1221no—
488C4⋊C8—1221no—
489#104—1222no—
490#104—1222no—
491#103—21no—
492#103—611no—
493#103—611no—
494#103—1221no—
495#103—1221no—
496#103—1221no—
497#103C22⋊D6111yescharacteristic
498#103C22⋊D6111yescharacteristic
499#102—21no—
500#102—611no—
501#102—611no—
502#102—1221no—
503#102—1221no—
504#102—1221no—
505#102—1221no—
506#102—1221no—
507#102—1221no—
508#102—1221no—
509#102—1221no—
510#102—1221no—
511#102—1221no—
512#102—1221no—
513#102C22⋊D6111yescharacteristic
514#102C22⋊D6111yescharacteristic
515#100—2441no—
516C24—1221no—
517C24—2441no—
518#41—21no—
519#41—21no—
520#41—612no—
521#41—612no—
522#41—1224no—
523#41—1221no—
524#41—1221no—
525#41—1224no—
526#41—2442no—
527#41—2442no—
528#41Q8×D6112yes—
529#41#1175822612yes—
530C2×Q8—41no—
531C2×Q8—611no—
532C2×Q8C2×C22⋊D6111yescharacteristic
533C2×D4—21no—
534C2×D4—611no—
535C2×D4—612no—
536C2×D4—1224no—
537C2×D4—1221no—
538C2×D4—1224no—
539C2×D4—1221no—
540C2×D4—1221no—
541C2×D4—1221no—
542C2×D4—1221no—
543C2×D4—1221no—
544C2×D4—2442no—
545C2×D4—2441no—
546C2×D4—2442no—
547C2×D4—2441no—
548C2×D4—2444no—
549C2×D4—2444no—
550C2×D4C2×C22⋊D6111yescharacteristic
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—41no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—2441no—
559C22×C4—2441no—
560C22×C4C23×D6111yescharacteristic
561M16—21no—
562M16—21no—
563M16—1221no—
564M16—1221no—
565M16—1221no—
566M16—1221no—
567M16—1221no—
568M16—1221no—
569M16—2442no—
570M16—2442no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—611no—
575C2×C8—611no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—2442no—
582C2×C8—2442no—
583C2×C8C2×C22⋊D6111yescharacteristic
584C2×C8C2×C22⋊D6111yescharacteristic
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—41no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—4882no—
596C4⋊C4—2441no—
597C4⋊C4D4×D6111yescharacteristic
598C4⋊C4D4×D6111yescharacteristic
599C4⋊C4C2×C22⋊D6111yescharacteristic
600C4⋊C4C2×C22⋊D6111yescharacteristic
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—41no—
604C22⋊C4—4882no—
605C22⋊C4—2441no—
606C42—21no—
607C42—21no—
608C42—41no—
609C42—1221no—
610C42—1221no—
611C42—2441no—
612C23—21no—
613C23—1221no—
614C23—1222no—
615C23—9761no—
616C23—9761no—
617C23—4881no—
618C23—4881no—
619C23—2444no—
620C23—2441no—
621C23—2441no—
622C23#1451982211yescharacteristic
623Q8—21no—
624Q8—161no—
625Q8—612no—
626Q8—1221no—
627Q8#1451975312yes—
628D4—22no—
629D4—22no—
630D4—21no—
631D4—612no—
632D4—1222no—
633D4—1222no—
634D4—1222no—
635D4—1222no—
636D4—1221no—
637D4—2444no—
638D4—2444no—
639D4—2441no—
640D4—2441no—
641D4#1451975312yes—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—81no—
652C2×C4—81no—
653C2×C4—161no—
654C2×C4—1221no—
655C2×C4—1222no—
656C2×C4—1222no—
657C2×C4—1222no—
658C2×C4—9761no—
659C2×C4—4881no—
660C2×C4—2444no—
661C2×C4—2441no—
662C2×C4—2441no—
663C2×C4—2441no—
664C2×C4C2×D4×D6111yescharacteristic
665C2×C4C22×C22⋊D6111yescharacteristic
666C2×C4C2×Q8×D6111yescharacteristic
667C2×C4#41×D6111yescharacteristic
668C2×C4C2×#1175822611yescharacteristic
669C2×C4#1451982311yescharacteristic
670C8—21no—
671C8—21no—
672C8—41no—
673C8—1221no—
674C8—1221no—
675C8—2441no—
676C8—2441no—
677C8—2441no—
678C22—21no—
679C22—21no—
680C22—22no—
681C22—41no—
682C22—41no—
683C22—1222no—
684C22—9761no—
685C22—9764no—
686C22—4882no—
687C22—4881no—
688C22—4881no—
689C22—2442no—
690C22—2441no—
691C22—2441no—
692C22#1684038711yescharacteristic
693C22D4×C22⋊D6111yescharacteristic
694C22#1684043911yescharacteristic
695C4—22no—
696C4—41no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—81no—
701C4—81no—
702C4—1222no—
703C4—4881no—
704C4—2442no—
705C4C22⋊Q8×D6111yescharacteristic
706C4C2×#1451975311yescharacteristic
707C4#1684040011yescharacteristic
708C4#1684040311yescharacteristic
709C2—21no—
710C2—21no—
711C2—42no—
712C2—4882no—
713C2—2442no—
714C2#2144948211yescharacteristic
715C2#2145759011yescharacteristic
716C2#2145761611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#3083C2
socleC22×C61D42
prime radicalC2×#14519823C22
hypercenter#3083D61
hypocenterC61#25982
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #3083

Complements

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

NH ≅ G/Ntype
1. #21455666C2semidirect
4. #21447344C2semidirect
5. #21447178C2semidirect
6. #21447176C2semidirect
7. #21446972C2semidirect
8. #21446096C2semidirect
9. #21446093C2semidirect
10. #21446045C2semidirect
11. #21446042C2semidirect
12. #21445884C2semidirect
13. #21445881C2semidirect
15. C61×#3083C2semidirect
24. C2×#14519713C22semidirect
25. C2×#14519712C22semidirect
26. #16839805C22semidirect
27. C2×#14519710C22semidirect
28. #16839789C22semidirect
49. #16839631C22semidirect
50. #16839531C22semidirect
51. #16839531C22semidirect
52. #16839530C22semidirect
53. #16839521C22semidirect
54. #16839521C22semidirect
55. #16839516C22semidirect
56. C61×#544C22semidirect
62. C61×#428C22semidirect
63. C2×#107×C61C22semidirect
64. C61×#424C22semidirect
70. #14519823Q8semidirect
352. #3083D61semidirect
377. #544C2×D61semidirect
391. #428C2×D61semidirect
393. C2×#107C2×D61semidirect
395. #424C2×D61semidirect
425. C61#25982semidirect

Maximal subgroups

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

subgroupindex
#214556662
#214543422
#214543412
#214473442
#214471782
#214471762
#214469722
#214460962
#214460932
#214460452
#214460422
#214458842
#214458812
#214457712
C61×#30832
#2598261