Finite Group Databasebeta

← #29737564

Subgroups — #29737564

Order 15616.

876 conjugacy classes of subgroups.

The subgroup lattice has 716 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#21447341C211yesmaximal, characteristic, complemented
5#21447178C211yesmaximal, characteristic, complemented
6#21447176C211yesmaximal, characteristic, complemented
7#21446972C211yesmaximal, characteristic, complemented
8#21446096C211yesmaximal, characteristic, complemented
9#21446093C211yesmaximal, characteristic, complemented
10#21446052C211yesmaximal, characteristic, complemented
11#21446049C211yesmaximal, characteristic, complemented
12#21445881C211yesmaximal, characteristic, complemented
13#21445879C211yesmaximal, characteristic, complemented
14#21445771C211yesmaximal, characteristic
15C61×#3084C211yesmaximal, 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#16839627C2211yescharacteristic, 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×#476—21no—
61C61×#475—21no—
62C61×#428C2211yescharacteristic, complemented
63C2×#106×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
95C4⋊C4×D61—21no—
96C2×#11758198—41no—
97C2×C4×Dic61C2311yescharacteristic
98#14519713—41no—
99#14519712—41no—
100#14519710—21no—
101#14519710—21no—
102#14519710—21no—
103#14519708—21no—
104C4⋊#92418—21no—
105C4⋊#92418—21no—
106#14519704—22no—
107#14519703—22no—
108#14519701—21no—
109#14519700—21no—
110#14519700—21no—
111#14519700D411yescharacteristic
112#14519700D411yescharacteristic
113#14519699—21no—
114#14519699—21no—
115#14519698—21no—
116#14519697—21no—
117#14519697—21no—
118#14519697—21no—
119#14519697—21no—
120#14519697—21no—
121#14519697—21no—
122#14519697—21no—
123#14519697—21no—
124#14519697D411yescharacteristic
125#14519697D411yescharacteristic
126#14519693—41no—
127#14519684—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#106×C61—21no—
147#106×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—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C4×Dic61—41no—
235#11758194—21no—
236#11758194—21no—
237#11758194—21no—
238#11758194—21no—
239#11758194—21no—
240#11758194—21no—
241#11758194—42no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—42no—
248C2×#92418C2×D411yescharacteristic
249C2×#92418C2×D411yescharacteristic
250#11758189—42no—
251C8×D61—42no—
252C23×C61—21no—
253C23×C61H(5,𝔽2)11yescharacteristic
254C22×D61—21no—
255C22×D61—22no—
256C22×D61—44no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—81no—
260C22×D61—81no—
261C22×D61—161no—
262C22×D61—161no—
263Q8×C61—21no—
264Q8×C61—161no—
265Q8×C61C22⋊Q812yes—
266D4×C61—22no—
267D4×C61—22no—
268D4×C61—21no—
269D4×C61C22⋊Q812yes—
270C2×C4×C61—21no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—81no—
280C2×C4×C61—81no—
281C2×C4×C61—161no—
282C2×C4×C61C22×D411yescharacteristic
283C2×C4×C61C22×D411yescharacteristic
284C2×C4×C61C22×Q811yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61H(5,𝔽2)11yescharacteristic
288C22⋊D61—22no—
289C22⋊D61—22no—
290C22⋊D61—44no—
291C2×Dic61—21no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—81no—
297D244—22no—
298D244—22no—
299D244—21no—
300D244—44no—
301D244—41no—
302D244—41no—
303D244C22⋊Q812yes—
304C4×D61—22no—
305C4×D61—22no—
306C4×D61—44no—
307C4×D61—161no—
308Dic122—21no—
309Dic122C22⋊Q812yes—
310C8×C61—21no—
311C8×C61—21no—
312C8×C61—41no—
313#92418—21no—
314#92418—21no—
315#92418—41no—
316#92418—41no—
317#92418—41no—
318#25984—611nomaximal, Sylow
319C22×C61—21no—
320C22×C61—21no—
321C22×C61—22no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61#54311yescharacteristic
325C22×C61D4211yescharacteristic
326C22×C61#55111yescharacteristic
327C2×D61—22no—
328C2×D61—41no—
329C2×D61—41no—
330C2×D61—42no—
331C2×D61—81no—
332C2×D61—81no—
333C2×D61—82no—
334C2×D61—164no—
335C2×D61—161no—
336C4×C61—22no—
337C4×C61—41no—
338C4×C61—41no—
339C4×C61—41no—
340C4×C61—41no—
341C4×C61—81no—
342C4×C61—81no—
343C4×C61C2×C22⋊Q811yescharacteristic
344C4×C61C2×C22⋊Q811yescharacteristic
345C4×C61#54611yescharacteristic
346C4×C61#54611yescharacteristic
347Dic61—22no—
348Dic61—81no—
349Dic61—81no—
350#3084D6111yescharacteristic, complemented
351#3083—611no—
352#2897—611no—
353#2897—611no—
354#2092—611no—
355#2063—611no—
356#2063—611no—
357#2027—611no—
358#1866—611no—
359#1866—611no—
360#1860—611no—
361#1860—611no—
362#1816—611no—
363#1815—611no—
364#1792—611no—
365C2×C61—21no—
366C2×C61—21no—
367C2×C61—42no—
368C2×C61#243711yescharacteristic
369C2×C61#328811yescharacteristic
370C2×C61#329011yescharacteristic
371D61—42no—
372D61—82no—
373C2×H(5,𝔽2)—611no—
374C2×#131—611no—
375C2×#131—611no—
376#544C2×D6111yescharacteristic, complemented
377#520—611no—
378#520C2×D6111yescharacteristic
379#479—21no—
380#479—1221no—
381#478—21no—
382#478—1221no—
383#477—1221no—
384#476—21no—
385#475—21no—
386#474—1221no—
387C2×#108—611no—
388C2×#108—611no—
389#428—611no—
390#428C2×D6111yescharacteristic, complemented
391C2×#107—611no—
392C2×#106C2×D6111yescharacteristic, complemented
393#424—611no—
394#424C2×D6111yescharacteristic, complemented
395C2×#104—611no—
396C2×#104—611no—
397#418—611no—
398#418—611no—
399#418—1221no—
400#418—1221no—
401#417—611no—
402#417—611no—
403#417—611no—
404#417—1221no—
405#417—1221no—
406#417C2×D6111yescharacteristic
407#416—611no—
408#416—1221no—
409#416—1221no—
410#416C2×D6111yescharacteristic
411C2×#102—611no—
412C2×#102—611no—
413C2×#102—1221no—
414C2×#102—1221no—
415C2×#100—611no—
416#390—611no—
417#382—611no—
418#343—611no—
419#343—611no—
420#343—611no—
421#339—611no—
422#339—611no—
423#336—611no—
424C61#2598411yescharacteristic, complemented, Sylow
425H(5,𝔽2)—614no—
426H(5,𝔽2)—1222no—
427H(5,𝔽2)—1222no—
428H(5,𝔽2)—2441no—
429C2×#41—611no—
430C2×#41—1221no—
431C2×#41—1221no—
432C2×#41C22×D6111yescharacteristic
433C22×D4—611no—
434C22×D4—1221no—
435C22×D4—1221no—
436C22×D4—2441no—
437#131—1222no—
438#131—1222no—
439#131—2441no—
440#131—2441no—
441C2×M16—611no—
442C2×M16—611no—
443C2×M16—611no—
444C2×M16—1221no—
445C2×M16—1221no—
446C2×M16C22×D6111yescharacteristic
447C22×C8—611no—
448C22×C8—1221no—
449C22×C8—1221no—
450C22×C8C22×D6111yescharacteristic
451C4⋊Q8—21no—
452C4⋊Q8—21no—
453#125—21no—
454#125—21no—
455C22⋊Q8—41no—
456C4×Q8—21no—
457C4×Q8—1221no—
458C4×D4—21no—
459C4×D4—41no—
460C4×D4—1221no—
461C4×D4—2441no—
462#117—21no—
463#117—1221no—
464#117C22×D6111yescharacteristic
465#117C22×D6111yescharacteristic
466C2×C4⋊C4—21no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—1221no—
469C2×C4⋊C4C22×D6111yescharacteristic
470C2×C4⋊C4C22×D6111yescharacteristic
471C2×C22⋊C4—2441no—
472C2×C42—611no—
473#108—2441no—
474#108—2441no—
475#107—21no—
476#107—1221no—
477#107—1221no—
478#107—1221no—
479#106—21no—
480#106—21no—
481#106—21no—
482#106—1221no—
483C4⋊C8—21no—
484C4⋊C8—21no—
485C4⋊C8—1221no—
486C4⋊C8—1221no—
487#104—1222no—
488#104—1222no—
489#103—21no—
490#103—611no—
491#103—611no—
492#103—1221no—
493#103—1221no—
494#103—1221no—
495#103C22⋊D6111yescharacteristic
496#103C22⋊D6111yescharacteristic
497#102—21no—
498#102—611no—
499#102—611no—
500#102—1221no—
501#102—1221no—
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#102C22⋊D6111yescharacteristic
512#102C22⋊D6111yescharacteristic
513#100—2441no—
514#95—2441no—
515C24—1221no—
516C24—2441no—
517#41—21no—
518#41—21no—
519#41—612no—
520#41—612no—
521#41—1224no—
522#41—1221no—
523#41—1221no—
524#41—1224no—
525#41—2442no—
526#41—2442no—
527#41Q8×D6112yes—
528#41#1175822612yes—
529C2×Q8—41no—
530C2×Q8—611no—
531C2×Q8C2×C22⋊D6111yescharacteristic
532C2×D4—21no—
533C2×D4—611no—
534C2×D4—612no—
535C2×D4—1224no—
536C2×D4—1221no—
537C2×D4—1224no—
538C2×D4—1221no—
539C2×D4—1221no—
540C2×D4—1221no—
541C2×D4—1221no—
542C2×D4—1221no—
543C2×D4—2442no—
544C2×D4—2441no—
545C2×D4—2442no—
546C2×D4—2441no—
547C2×D4—2444no—
548C2×D4—2444no—
549C2×D4C2×C22⋊D6111yescharacteristic
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—41no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—2441no—
558C22×C4—2441no—
559C22×C4C23×D6111yescharacteristic
560M16—21no—
561M16—21no—
562M16—1221no—
563M16—1221no—
564M16—1221no—
565M16—1221no—
566M16—1221no—
567M16—1221no—
568M16—2442no—
569M16—2442no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—611no—
574C2×C8—611no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—2442no—
581C2×C8—2442no—
582C2×C8C2×C22⋊D6111yescharacteristic
583C2×C8C2×C22⋊D6111yescharacteristic
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—41no—
589C4⋊C4—41no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—2441no—
595C4⋊C4D4×D6111yescharacteristic
596C4⋊C4D4×D6111yescharacteristic
597C4⋊C4C2×C22⋊D6111yescharacteristic
598C4⋊C4C2×C22⋊D6111yescharacteristic
599C22⋊C4—21no—
600C22⋊C4—21no—
601C22⋊C4—41no—
602C22⋊C4—4882no—
603C22⋊C4—2441no—
604C42—21no—
605C42—21no—
606C42—41no—
607C42—1221no—
608C42—1221no—
609C42—2441no—
610C23—21no—
611C23—1221no—
612C23—1222no—
613C23—9761no—
614C23—9761no—
615C23—4881no—
616C23—4881no—
617C23—2444no—
618C23—2441no—
619C23—2441no—
620C23#1451982211yescharacteristic
621Q8—21no—
622Q8—161no—
623Q8—612no—
624Q8—1221no—
625Q8#1451975312yes—
626D4—22no—
627D4—22no—
628D4—21no—
629D4—612no—
630D4—1222no—
631D4—1222no—
632D4—1222no—
633D4—1222no—
634D4—1221no—
635D4—2444no—
636D4—2444no—
637D4—2441no—
638D4—2441no—
639D4#1451975312yes—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—81no—
650C2×C4—81no—
651C2×C4—161no—
652C2×C4—1221no—
653C2×C4—1222no—
654C2×C4—1222no—
655C2×C4—9761no—
656C2×C4—4881no—
657C2×C4—2444no—
658C2×C4—2441no—
659C2×C4—2441no—
660C2×C4—2441no—
661C2×C4—2441no—
662C2×C4C2×D4×D6111yescharacteristic
663C2×C4C22×C22⋊D6111yescharacteristic
664C2×C4C2×Q8×D6111yescharacteristic
665C2×C4#41×D6111yescharacteristic
666C2×C4C2×#1175822611yescharacteristic
667C2×C4#1451982311yescharacteristic
668C8—21no—
669C8—21no—
670C8—41no—
671C8—1221no—
672C8—1221no—
673C8—2441no—
674C8—2441no—
675C8—2441no—
676C22—21no—
677C22—21no—
678C22—22no—
679C22—41no—
680C22—41no—
681C22—1222no—
682C22—9761no—
683C22—9764no—
684C22—4882no—
685C22—4881no—
686C22—4881no—
687C22—2442no—
688C22—2441no—
689C22—2441no—
690C22#1684038711yescharacteristic
691C22D4×C22⋊D6111yescharacteristic
692C22#1684043911yescharacteristic
693C4—22no—
694C4—41no—
695C4—41no—
696C4—41no—
697C4—41no—
698C4—81no—
699C4—81no—
700C4—1222no—
701C4—4881no—
702C4—4881no—
703C4C22⋊Q8×D6111yescharacteristic
704C4C2×#1451975311yescharacteristic
705C4#1684040011yescharacteristic
706C4#1684040311yescharacteristic
707C2—21no—
708C2—21no—
709C2—42no—
710C2—4882no—
711C2—2442no—
712C2#2144948211yescharacteristic
713C2#2145758111yescharacteristic
714C2#2145759911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#3084C2
socleC22×C61D42
prime radicalC2×#14519823C22
hypercenter#3084D61
hypocenterC61#25984
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #3084

Complements

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

NH ≅ G/Ntype
1. #21455666C2semidirect
4. #21447341C2semidirect
5. #21447178C2semidirect
6. #21447176C2semidirect
7. #21446972C2semidirect
8. #21446096C2semidirect
9. #21446093C2semidirect
10. #21446052C2semidirect
11. #21446049C2semidirect
12. #21445881C2semidirect
13. #21445879C2semidirect
15. C61×#3084C2semidirect
24. C2×#14519713C22semidirect
25. C2×#14519712C22semidirect
26. #16839805C22semidirect
27. C2×#14519710C22semidirect
28. #16839789C22semidirect
49. #16839627C22semidirect
50. #16839531C22semidirect
51. #16839531C22semidirect
52. #16839530C22semidirect
53. #16839521C22semidirect
54. #16839521C22semidirect
55. #16839516C22semidirect
56. C61×#544C22semidirect
62. C61×#428C22semidirect
63. C2×#106×C61C22semidirect
64. C61×#424C22semidirect
70. #14519823Q8semidirect
350. #3084D61semidirect
376. #544C2×D61semidirect
390. #428C2×D61semidirect
392. C2×#106C2×D61semidirect
394. #424C2×D61semidirect
424. C61#25984semidirect

Maximal subgroups

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

subgroupindex
#214556662
#214543422
#214543412
#214473412
#214471782
#214471762
#214469722
#214460962
#214460932
#214460522
#214460492
#214458812
#214458792
#214457712
C61×#30842
#2598461