Finite Group Databasebeta

← #29712874

Subgroups — #29712874

Order 15616.

1404 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455739C211yesmaximal, characteristic, complemented
2C2×#16839763C211yesmaximal, characteristic, complemented
3#21450291C211yesmaximal, characteristic, complemented
4#21447040C212yesmaximal, complemented
5#21447026C212yesmaximal, complemented
6#21446283C211yesmaximal, characteristic, complemented
7#21446122C211yesmaximal, characteristic, complemented
8#21446045C212yesmaximal, complemented
9#21445773C212yesmaximal, complemented
10#21445763C211yesmaximal, characteristic, complemented
11C61×#3488C211yesmaximal, characteristic
12C22×#11758194C2211yescharacteristic, complemented
13C2×#14519758—22no—
14C22×C4⋊Dic61C2211yescharacteristic, complemented
15#16840095—21no—
16#16840090—21no—
17#16840078—21no—
18#16840073—21no—
19#16839805C2212yescomplemented
20C2×#14519704C2212yes—
21C2×#14519704C2212yescomplemented
22C2×#14519704C2212yescomplemented
23#16839763—21no—
24#16839763—21no—
25#16839763C2212yes—
26#16839763C2212yescomplemented
27#16839763C2212yescomplemented
28C2×#14519701—21no—
29C2×#14519698—21no—
30C2×#14519694C2212yescomplemented
31#16839726C2211yescharacteristic, complemented
32#16839698—22no—
33#16839665C2212yescomplemented
34#16839631C2212yescomplemented
35C4×C22⋊Dic61C2211yescharacteristic, complemented
36#16839531C2212yescomplemented
37#16839521C2212yescomplemented
38C2×H(5,𝔽2)×C61C2211yescharacteristic
39C22×#41×C61C2211yescharacteristic
40C61×#550—21no—
41C61×#548—21no—
42C61×#546—21no—
43C61×#546—22no—
44D42×C61—22no—
45D42×C61—21no—
46C61×#537—21no—
47C61×#537C2211yescharacteristic
48C61×#535—21no—
49C61×#535C2211yescharacteristic
50C61×#525—21no—
51C61×#525C2211yescharacteristic
52C2×#121×C61—21no—
53C2×#121×C61C2211yescharacteristic
54C61×#520C2211yescharacteristic
55C23×Dic61—21no—
56C2×#11758194—21no—
57C2×#11758194—42no—
58C2×#11758194C2312yes—
59C2×#11758194C2312yes—
60C22×#92418—21no—
61#14519758—48no—
62C2×C4⋊Dic61—21no—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61C2312yes—
68C2×#11758196—24no—
69C2×C22⋊Dic61—21no—
70C2×C22⋊Dic61—24no—
71C2×C4×Dic61C2312yes—
72#14519710—22no—
73#14519708—22no—
74#14519704—24no—
75#14519704—42no—
76#14519704—42no—
77#14519701—22no—
78#14519701—22no—
79#14519701—22no—
80#14519698—22no—
81#14519698—22no—
82#14519698—22no—
83#14519694—42no—
84C22⋊#92418—21no—
85C22⋊#92418—21no—
86#14519684—21no—
87H(5,𝔽2)×C61—24no—
88H(5,𝔽2)×C61—42no—
89C2×#41×C61—21no—
90C2×#41×C61—21no—
91C2×#41×C61—21no—
92C2×#41×C61—21no—
93C2×#41×C61—24no—
94C2×#41×C61—42no—
95C2×#41×C61D411yescharacteristic
96C2×#41×C61D411yescharacteristic
97C2×#41×C61C2311yescharacteristic
98C2×#41×C61C2311yescharacteristic
99C2×#41×C61C2311yescharacteristic
100C22×Q8×C61D411yescharacteristic
101C22×D4×C61—21no—
102C22×D4×C61—22no—
103C22×D4×C61—22no—
104C22×D4×C61—21no—
105C22×D4×C61—21no—
106C22×D4×C61D411yescharacteristic
107C22×D4×C61D412yes—
108C22×D4×C61C2311yescharacteristic
109C23×C4×C61—21no—
110C23×C4×C61C2311yescharacteristic
111#127×C61—22no—
112#127×C61—21no—
113#124×C61—22no—
114#124×C61—21no—
115#123×C61—22no—
116#123×C61—21no—
117C22⋊Q8×C61—22no—
118C22⋊Q8×C61—21no—
119C22⋊Q8×C61—21no—
120C22⋊Q8×C61D411yescharacteristic
121C22⋊Q8×C61D411yescharacteristic
122#121×C61—22no—
123#121×C61—22no—
124#121×C61—22no—
125#121×C61—22no—
126#121×C61—22no—
127#121×C61—21no—
128#121×C61—21no—
129#121×C61—21no—
130#121×C61—22no—
131#121×C61—21no—
132#121×C61—21no—
133#121×C61—21no—
134#121×C61—21no—
135#121×C61—21no—
136#121×C61D411yescharacteristic
137#121×C61D411yescharacteristic
138#120×C61—22no—
139#120×C61—22no—
140#120×C61—22no—
141#120×C61—22no—
142#120×C61—21no—
143C4×Q8×C61—21no—
144C4×D4×C61—22no—
145C4×D4×C61—22no—
146C4×D4×C61—21no—
147C4×D4×C61—22no—
148C4×D4×C61—21no—
149C4×D4×C61—21no—
150#117×C61—21no—
151#117×C61C2311yescharacteristic
152C2×C4⋊C4×C61—21no—
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C22⋊C4×C61—22no—
155C2×C22⋊C4×C61D412yes—
156C24×C61—22no—
157C24×C61—21no—
158C24×C61C2×D411yescharacteristic
159C24×C61C2×D412yes—
160#41×C61—22no—
161#41×C61—22no—
162#41×C61—22no—
163#41×C61—22no—
164#41×C61—22no—
165#41×C61—22no—
166#41×C61—22no—
167#41×C61—44no—
168#41×C61—41no—
169#41×C61—41no—
170#41×C61—44no—
171#41×C61—44no—
172#41×C61—42no—
173#41×C61—42no—
174#41×C61#4114yes—
175C2×Q8×C61—21no—
176C2×Q8×C61—22no—
177C2×Q8×C61—41no—
178C2×Q8×C61C2×D411yescharacteristic
179C2×Q8×C61C2×D411yescharacteristic
180C2×Q8×C61C2×D411yescharacteristic
181C2×D4×C61—21no—
182C2×D4×C61—22no—
183C2×D4×C61—22no—
184C2×D4×C61—22no—
185C2×D4×C61—22no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—22no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61—21no—
195C2×D4×C61—22no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—22no—
200C2×D4×C61—22no—
201C2×D4×C61—41no—
202C2×D4×C61—44no—
203C2×D4×C61—44no—
204C2×D4×C61—48no—
205C2×D4×C61—42no—
206C2×D4×C61—42no—
207C2×D4×C61—44no—
208C2×D4×C61—84no—
209C2×D4×C61C2×D411yescharacteristic
210C2×D4×C61C2×D411yescharacteristic
211C2×D4×C61C2×D411yescharacteristic
212C22×C4×C61—21no—
213C22×C4×C61—22no—
214C22×C4×C61—22no—
215C22×C4×C61—22no—
216C22×C4×C61—21no—
217C22×C4×C61—22no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—44no—
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D412yes—
229C22×C4×C61C2411yescharacteristic
230C22×Dic61—22no—
231C22×Dic61—22no—
232C22×Dic61—44no—
233C22×Dic61—41no—
234C22×Dic61—41no—
235C4⋊C4×C61—22no—
236C4⋊C4×C61—22no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61C2×D411yescharacteristic
242C4⋊C4×C61C2×D411yescharacteristic
243C22⋊C4×C61—22no—
244C22⋊C4×C61—22no—
245C22⋊C4×C61—22no—
246C22⋊C4×C61—22no—
247C22⋊C4×C61—22no—
248C22⋊C4×C61—21no—
249C22⋊C4×C61—21no—
250C22⋊C4×C61—21no—
251C22⋊C4×C61—21no—
252C22⋊C4×C61—22no—
253C22⋊C4×C61—22no—
254C22⋊C4×C61—21no—
255C42×C61—22no—
256C42×C61—21no—
257C22⋊Dic61—24no—
258C22⋊Dic61—48no—
259C4⋊Dic61—22no—
260C4⋊Dic61—22no—
261C4⋊Dic61—41no—
262C4⋊Dic61—41no—
263#11758196—48no—
264C4×Dic61—22no—
265C4×Dic61—22no—
266#11758194—22no—
267#11758194—22no—
268#11758194—22no—
269#11758194—22no—
270#11758194—42no—
271C2×#92418—22no—
272C2×#92418—22no—
273C2×#92418—42no—
274C23×C61—21no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—24no—
281C23×C61—41no—
282C23×C61—42no—
283C23×C61—44no—
284C23×C61—42no—
285C23×C61—42no—
286C23×C61—42no—
287C23×C61—81no—
288C23×C61—82no—
289C23×C61—82no—
290C23×C61#12011yescharacteristic
291C23×C61#12011yescharacteristic
292C23×C61C22×D411yescharacteristic
293Q8×C61—21no—
294Q8×C61—21no—
295Q8×C61—21no—
296Q8×C61—22no—
297Q8×C61—42no—
298Q8×C61#12312yescomplemented
299D4×C61—24no—
300D4×C61—21no—
301D4×C61—21no—
302D4×C61—21no—
303D4×C61—22no—
304D4×C61—42no—
305D4×C61—42no—
306D4×C61—44no—
307D4×C61—42no—
308D4×C61—44no—
309D4×C61—42no—
310D4×C61—42no—
311D4×C61—44no—
312D4×C61—42no—
313D4×C61—41no—
314D4×C61—41no—
315D4×C61—42no—
316D4×C61—81no—
317D4×C61—82no—
318D4×C61—82no—
319D4×C61—82no—
320D4×C61—82no—
321D4×C61#12312yescomplemented
322C2×C4×C61—21no—
323C2×C4×C61—22no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—24no—
331C2×C4×C61—21no—
332C2×C4×C61—22no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—42no—
337C2×C4×C61—42no—
338C2×C4×C61—42no—
339C2×C4×C61—44no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—42no—
343C2×C4×C61—42no—
344C2×C4×C61—82no—
345C2×C4×C61#12011yescharacteristic
346C2×C4×C61#12011yescharacteristic
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C61C2×#4112yes—
350C2×C4×C61H(5,𝔽2)12yes—
351C2×Dic61—24no—
352C2×Dic61—42no—
353C2×Dic61—42no—
354C2×Dic61—44no—
355C2×Dic61—42no—
356C2×Dic61—82no—
357C2×Dic61—82no—
358#92418—42no—
359#92418—42no—
360#24026—611nomaximal, Sylow
361C22×C61—21no—
362C22×C61—21no—
363C22×C61—21no—
364C22×C61—21no—
365C22×C61—21no—
366C22×C61—22no—
367C22×C61—21no—
368C22×C61—21no—
369C22×C61—44no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—42no—
380C22×C61—41no—
381C22×C61—84no—
382C22×C61—84no—
383C22×C61—164no—
384C22×C61#45312yes—
385C22×C61C2×#12011yescharacteristic
386C22×C61#54612yes—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—22no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61—42no—
393C4×C61—41no—
394C4×C61—41no—
395C4×C61C2×#12311yescharacteristic
396C4×C61#53411yescharacteristic
397C4×C61#54612yes—
398Dic61—44no—
399Dic61—82no—
400#3488D6111yescharacteristic
401#3092—611no—
402C2×#417—611no—
403#2501—611no—
404#2039—612no—
405#2037—612no—
406#1900—611no—
407#1871—611no—
408#1859—612no—
409#1792—612no—
410#1789—611no—
411C2×C61—22no—
412C2×C61—22no—
413C2×C61—41no—
414C2×C61—42no—
415C2×C61—81no—
416C2×C61—82no—
417C2×C61—81no—
418C2×C61#240511yescharacteristic
419C2×C61C2×#45311yescharacteristic
420C2×C61#302211yescharacteristic
421C2×H(5,𝔽2)C2×D6111yescharacteristic
422C22×#41C2×D6111yescharacteristic
423C22×M16—611no—
424#550—21no—
425#548—21no—
426#546—21no—
427#546—22no—
428D42—22no—
429D42—21no—
430#537—21no—
431#537C2×D6111yescharacteristic
432#535—21no—
433#535C2×D6111yescharacteristic
434#525—21no—
435#525C2×D6111yescharacteristic
436C2×#123—1222no—
437C2×#121—21no—
438C2×#121C2×D6111yescharacteristic
439#520C2×D6111yescharacteristic
440C22×C4⋊C4—611no—
441#484—1221no—
442#483—1221no—
443#481—1221no—
444#480—1221no—
445#428—612no—
446C2×#104—612no—
447C2×#104—612no—
448C2×#104—612no—
449#417—612no—
450#417—612no—
451#417—612no—
452#417—1221no—
453#417—1221no—
454C2×#103—1221no—
455C2×#102—1221no—
456C2×#100—612no—
457#407—611no—
458#399—1222no—
459#390—612no—
460#384—612no—
461C4×C22⋊C4—611no—
462#343—612no—
463#339—612no—
464C61#2402611yescharacteristic, complemented, Sylow
465H(5,𝔽2)—24no—
466H(5,𝔽2)—42no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—24no—
472C2×#41—42no—
473C2×#41C22⋊D6111yescharacteristic
474C2×#41C22⋊D6111yescharacteristic
475C2×#41C22×D6111yescharacteristic
476C2×#41C22×D6111yescharacteristic
477C2×#41C22×D6111yescharacteristic
478C22×Q8C22⋊D6111yescharacteristic
479C22×D4—21no—
480C22×D4—22no—
481C22×D4—22no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4C22⋊D6111yescharacteristic
485C22×D4C22⋊D6112yes—
486C22×D4C22×D6111yescharacteristic
487C23×C4—21no—
488C23×C4—1221no—
489C23×C4C22×D6111yescharacteristic
490C2×M16—612no—
491C2×M16—612no—
492C2×M16—1221no—
493C2×M16—2442no—
494C22×C8—1221no—
495#127—22no—
496#127—21no—
497#124—22no—
498#124—21no—
499#123—22no—
500#123—21no—
501#123—2448no—
502C22⋊Q8—22no—
503C22⋊Q8—21no—
504C22⋊Q8—21no—
505C22⋊Q8C22⋊D6111yescharacteristic
506C22⋊Q8C22⋊D6111yescharacteristic
507#121—22no—
508#121—22no—
509#121—22no—
510#121—22no—
511#121—22no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—22no—
519#121—21no—
520#121—21no—
521#121C22⋊D6111yescharacteristic
522#121C22⋊D6111yescharacteristic
523#120—22no—
524#120—22no—
525#120—22no—
526#120—21no—
527#120—22no—
528C4×Q8—21no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—21no—
532C4×D4—22no—
533C4×D4—21no—
534C4×D4—21no—
535#117—21no—
536#117C22×D6111yescharacteristic
537C2×C4⋊C4—21no—
538C2×C4⋊C4—612no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—1224no—
545C2×C4⋊C4C22×D6111yescharacteristic
546C2×C22⋊C4—22no—
547C2×C22⋊C4—1221no—
548C2×C22⋊C4—1224no—
549C2×C22⋊C4C22⋊D6112yes—
550C2×C42—612no—
551#107—1222no—
552#106—1222no—
553#104—1224no—
554#104—2442no—
555#104—2442no—
556#103—1222no—
557#103—1222no—
558#103—1222no—
559#102—1222no—
560#102—1222no—
561#102—1222no—
562#100—2442no—
563C22⋊C8—1221no—
564C22⋊C8—1221no—
565#95—1221no—
566C24—22no—
567C24—21no—
568C24C2×C22⋊D6111yescharacteristic
569C24C2×C22⋊D6112yes—
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—22no—
577#41—44no—
578#41—41no—
579#41—41no—
580#41—44no—
581#41—44no—
582#41—42no—
583#41—42no—
584#41#1175822414yes—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—41no—
588C2×Q8C2×C22⋊D6111yescharacteristic
589C2×Q8C2×C22⋊D6111yescharacteristic
590C2×Q8C2×C22⋊D6111yescharacteristic
591C2×D4—21no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—21no—
611C2×D4—41no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—48no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—44no—
618C2×D4—84no—
619C2×D4C2×C22⋊D6111yescharacteristic
620C2×D4C2×C22⋊D6111yescharacteristic
621C2×D4C2×C22⋊D6111yescharacteristic
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—44no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—2444no—
636C22×C4—2441no—
637C22×C4—2441no—
638C22×C4C2×C22⋊D6111yescharacteristic
639C22×C4C2×C22⋊D6111yescharacteristic
640C22×C4C2×C22⋊D6111yescharacteristic
641C22×C4C2×C22⋊D6111yescharacteristic
642C22×C4C2×C22⋊D6111yescharacteristic
643C22×C4C2×C22⋊D6112yes—
644C22×C4C23×D6111yescharacteristic
645M16—1222no—
646M16—1222no—
647M16—1222no—
648M16—1222no—
649M16—2442no—
650C2×C8—1222no—
651C2×C8—1222no—
652C2×C8—2442no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—1222no—
660C4⋊C4—1222no—
661C4⋊C4—2448no—
662C4⋊C4—2441no—
663C4⋊C4—2441no—
664C4⋊C4C2×C22⋊D6111yescharacteristic
665C4⋊C4C2×C22⋊D6111yescharacteristic
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—21no—
678C22⋊C4—1224no—
679C22⋊C4—2448no—
680C42—22no—
681C42—21no—
682C42—1222no—
683C42—1222no—
684C23—21no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—21no—
689C23—21no—
690C23—24no—
691C23—41no—
692C23—42no—
693C23—44no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—81no—
698C23—82no—
699C23—82no—
700C23#1451974611yescharacteristic
701C23#1451974611yescharacteristic
702C23C22×C22⋊D6111yescharacteristic
703Q8—21no—
704Q8—21no—
705Q8—21no—
706Q8—22no—
707Q8—42no—
708Q8#1451975812yescomplemented
709D4—24no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—22no—
714D4—42no—
715D4—42no—
716D4—44no—
717D4—42no—
718D4—44no—
719D4—42no—
720D4—42no—
721D4—44no—
722D4—42no—
723D4—41no—
724D4—41no—
725D4—42no—
726D4—81no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4—82no—
731D4#1451975812yescomplemented
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—21no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—82no—
755C2×C4—1224no—
756C2×C4—4882no—
757C2×C4—4882no—
758C2×C4—2444no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4#1451974611yescharacteristic
763C2×C4#1451974611yescharacteristic
764C2×C4C22×C22⋊D6111yescharacteristic
765C2×C4C22×C22⋊D6111yescharacteristic
766C2×C4C2×#1175822412yes—
767C2×C4#1451982212yes—
768C8—2442no—
769C8—2442no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—22no—
778C22—44no—
779C22—41no—
780C22—41no—
781C22—42no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—42no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—42no—
790C22—84no—
791C22—84no—
792C22—164no—
793C22#1683993012yes—
794C22C2×#1451974611yescharacteristic
795C22#1684040612yes—
796C4—21no—
797C4—21no—
798C4—22no—
799C4—42no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—4882no—
805C4—2444no—
806C4C2×#1451975811yescharacteristic
807C4#1684032111yescharacteristic
808C4#1684040612yes—
809C2—22no—
810C2—22no—
811C2—41no—
812C2—42no—
813C2—81no—
814C2—82no—
815C2—81no—
816C2#2144914211yescharacteristic
817C2C2×#1683993011yescharacteristic
818C2#2145519811yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#3488C2
socleC22×C61C2×#120
hypercenter#3488D61
hypocenterC61#24026
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3488

Complements

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

NH ≅ G/Ntype
1. #21455739C2semidirect
2. C2×#16839763C2semidirect
3. #21450291C2semidirect
4. #21447040C2semidirect
5. #21447026C2semidirect
6. #21446283C2semidirect
7. #21446122C2semidirect
8. #21446045C2semidirect
9. #21445773C2semidirect
10. #21445763C2semidirect
12. C22×#11758194C22semidirect
14. C22×C4⋊Dic61C22semidirect
19. #16839805C22semidirect
21. C2×#14519704C22semidirect
22. C2×#14519704C22semidirect
26. #16839763C22semidirect
27. #16839763C22semidirect
30. C2×#14519694C22semidirect
31. #16839726C22semidirect
33. #16839665C22semidirect
34. #16839631C22semidirect
35. C4×C22⋊Dic61C22semidirect
36. #16839531C22semidirect
37. #16839521C22semidirect
298. Q8×C61#123semidirect
321. D4×C61#123semidirect
464. C61#24026semidirect
708. Q8#14519758semidirect
731. D4#14519758semidirect

Maximal subgroups

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

subgroupindex
#214557392
C2×#168397632
#214502912
#214470402
#214470262
#214462832
#214461222
#214460452
#214457732
#214457632
C61×#34882
#2402661