Finite Group Databasebeta

← #30565059

Subgroups — #30565059

Order 15616.

2118 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459653C211yesmaximal, characteristic, complemented
2C2×#16840422C211yesmaximal, characteristic, complemented
3#21458090C214yesmaximal, complemented
4#21458067C214yesmaximal, complemented
5#21457473C214yesmaximal, complemented
6#21457454C214yesmaximal, complemented
7#21456783C212yesmaximal, complemented
8#21456640C211yesmaximal, characteristic, complemented
9#21456632C212yesmaximal, complemented
10#21455896C212yesmaximal, complemented
11#21455081C211yesmaximal, characteristic, complemented
12#21455069C211yesmaximal, characteristic, complemented
13#21455050C212yesmaximal, complemented
14#21454858C211yesmaximal, characteristic, complemented
15C61×#3193C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic, complemented
18C2×#14519810C2212yescomplemented
19C2×#14519806C2214yescomplemented
20C2×#14519803C2212yescomplemented
21#16840464C2212yescomplemented
22#16840455—22no—
23#16840447C2212yescomplemented
24#16840438—22no—
25#16840422—22no—
26#16840422—22no—
27#16840422C2214yes—
28#16840422C2214yescomplemented
29#16840418C2212yescomplemented
30#16840406C2212yescomplemented
31#16840357—21no—
32#16840349—21no—
33#16840321—21no—
34#16840293C2212yes—
35C2×#14519766C2211yescharacteristic, complemented
36C2×#14519763—21no—
37#16840272C2212yes—
38C2×#14519756C2211yescharacteristic
39C2×#14519755—21no—
40C2×#14519752C2211yescharacteristic, complemented
41C2×#14519750—21no—
42#16840237—21no—
43C2×#14519742C2211yescharacteristic, complemented
44C2×#14519739—21no—
45C2×C4×C22⋊D61C2211yescharacteristic
46#16840143C2214yescomplemented
47#16840118C2214yescomplemented
48#16840092C2212yescomplemented
49#16840090C2212yescomplemented
50#16840089C2214yescomplemented
51#16840068C2214yescomplemented
52#16840018C2214yescomplemented
53#16840014C2214yescomplemented
54#16840009C2214yescomplemented
55#16839987C2214yescomplemented
56#16839983C2214yescomplemented
57#16839979C2214yescomplemented
58#16839926C2214yescomplemented
59#16839920C2212yescomplemented
60#16839919C2214yescomplemented
61#16839918C2212yescomplemented
62#16839917C2212yescomplemented
63#16839915C2212yescomplemented
64#16839908C2214yescomplemented
65#16839905C2214yescomplemented
66#16839900C2212yes—
67#16839899C2214yescomplemented
68#16839895C2212yes—
69#16839856C2214yescomplemented
70#16839853C2214yescomplemented
71#16839838C2214yescomplemented
72#16839837C2214yescomplemented
73#16839812C2212yescomplemented
74#16839769C2214yescomplemented
75#16839764C2212yescomplemented
76#16839761C2212yescomplemented
77#16839726C2211yescharacteristic
78#16839724C2212yescomplemented
79C2×C22⋊Q8×C61C2211yescharacteristic
80C2×#121×C61C2211yescharacteristic
81C61×#484C2212yescomplemented
82C61×#480C2212yes—
83C61×#468C2214yescomplemented
84C61×#450C2212yescomplemented
85C61×#448C2212yes—
86C61×#407C2211yescharacteristic
87C2×#11758222—21no—
88C2×#11758222—21no—
89C2×#11758222—44no—
90C2×#11758222C2312yes—
91C2×#11758222C2312yes—
92C2×#11758224C2312yes—
93C22×Dic122—21no—
94C22×Dic122C2311yescharacteristic
95C22×Dic122C2311yescharacteristic
96C2×Q8×D61—22no—
97C2×Q8×D61—44no—
98C2×Q8×D61C2314yes—
99C22×D244—21no—
100C22×D244C2311yescharacteristic
101C22×C22⋊D61—21no—
102C22×C22⋊D61D411yescharacteristic
103C22×C4×D61—21no—
104C22×C4×D61—21no—
105C22×C4×D61C2311yescharacteristic
106#14519810—44no—
107#14519806—48no—
108#14519803—44no—
109C2×Dic244C2314yes—
110C2×#11758202C2314yes—
111C2×#11758190C2314yes—
112C2×#11758200C2314yes—
113C2×#11758199C2314yes—
114C2×#11758194C2312yes—
115C2×#11758189C2314yes—
116#14519772—22no—
117#14519770—22no—
118#14519770—22no—
119#14519768C2312yes—
120#14519767—22no—
121#14519766—22no—
122#14519766C2314yes—
123#14519764C2312yes—
124#14519763—24no—
125#14519763—24no—
126#14519763—22no—
127#14519761—22no—
128#14519760—22no—
129#14519759—22no—
130#14519758—22no—
131#14519758—22no—
132#14519757C2312yes—
133#14519756—21no—
134#14519756—21no—
135#14519756C2312yes—
136#14519756C2312yes—
137#14519755—24no—
138#14519755—24no—
139#14519754—22no—
140#14519752—22no—
141#14519752C2314yes—
142#14519750—24no—
143#14519750—24no—
144#14519749—22no—
145#14519749—22no—
146#14519749—22no—
147#14519748C2312yes—
148#14519746—22no—
149#14519745—22no—
150#14519742—22no—
151#14519742C2314yes—
152#14519742C2312yes—
153D4×Dic61—22no—
154D4×Dic61—22no—
155D4×Dic61—22no—
156D4×Dic61—22no—
157D4×Dic61C2312yes—
158#14519739—24no—
159#14519739—24no—
160C4×C22⋊D61D412yes—
161C4×C22⋊D61D412yes—
162C4×C22⋊D61C2312yes—
163C4×C22⋊D61C2312yes—
164#14519737—22no—
165#14519736—22no—
166#14519735C2312yes—
167#14519733—22no—
168C2×C4⋊Dic61C2311yescharacteristic
169C2×#11758196—21no—
170C2×#11758196—21no—
171C2×#11758196D411yescharacteristic
172C2×C22⋊Dic61—21no—
173C2×C22⋊Dic61—22no—
174C2×C22⋊Dic61D411yescharacteristic
175C2×#11758198—21no—
176C2×#11758198—21no—
177C2×#11758198—21no—
178C2×#11758198D411yescharacteristic
179C2×C4×Dic61—21no—
180C2×C4×Dic61C2311yescharacteristic
181#14519708C2314yes—
182#14519706C2314yes—
183#14519702C2314yes—
184#14519701C2314yes—
185#14519700C2314yes—
186#14519700C2314yes—
187#14519699C2314yes—
188#14519697C2314yes—
189C22⋊#92418C2312yes—
190C22⋊#92418C2312yes—
191#14519689C2314yes—
192C8×Dic61C2314yes—
193C22×Q8×C61C2311yescharacteristic
194C22×D4×C61—21no—
195C22×D4×C61C2311yescharacteristic
196C23×C4×C61C2311yescharacteristic
197C2×SD16×C61C2314yes—
198C2×M16×C61C2312yes—
199C22⋊Q8×C61—21no—
200C22⋊Q8×C61—21no—
201C22⋊Q8×C61C2312yes—
202C22⋊Q8×C61C2312yes—
203#121×C61—21no—
204#121×C61—21no—
205#121×C61C2312yes—
206#121×C61C2312yes—
207C2×C4⋊C4×C61—21no—
208C2×C4⋊C4×C61C2311yescharacteristic
209C2×C4⋊C4×C61C2311yescharacteristic
210C2×C22⋊C4×C61—21no—
211C2×C22⋊C4×C61—21no—
212#107×C61C2314yes—
213#103×C61C2314yes—
214#102×C61C2314yes—
215C22⋊C8×C61C2312yes—
216C22⋊C8×C61C2312yes—
217C24×C61—21no—
218C24×C61C2×D411yescharacteristic
219C23×D61—21no—
220C23×D61C2×D411yescharacteristic
221C2×Q8×C61—21no—
222C2×Q8×C61—42no—
223C2×Q8×C61C2412yes—
224C2×D4×C61—22no—
225C2×D4×C61—22no—
226C2×D4×C61—21no—
227C2×D4×C61—42no—
228C2×D4×C61—44no—
229C2×D4×C61C2412yes—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—42no—
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2411yescharacteristic
238C22×C4×C61C2411yescharacteristic
239C22×C4×C61C2411yescharacteristic
240C2×C22⋊D61—22no—
241C2×C22⋊D61—22no—
242C2×C22⋊D61—22no—
243C2×C22⋊D61—22no—
244C2×C22⋊D61—42no—
245C2×C22⋊D61—44no—
246C2×C22⋊D61C2×D412yes—
247C2×C22⋊D61C2×D412yes—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—22no—
252C22×Dic61—22no—
253C22×Dic61C2×D411yescharacteristic
254C22×Dic61C2×D411yescharacteristic
255C22×Dic61C2×D411yescharacteristic
256Q8×D61—28no—
257Q8×D61—44no—
258Q8×D61—48no—
259#11758224—44no—
260#11758222—24no—
261#11758222—24no—
262#11758222—42no—
263#11758222—42no—
264#11758222—44no—
265#11758222—44no—
266C2×D244—24no—
267C2×D244—21no—
268C2×D244—42no—
269C2×D244—44no—
270C2×D244C2412yes—
271C2×C4×D61—24no—
272C2×C4×D61—22no—
273C2×C4×D61—22no—
274C2×C4×D61—42no—
275C2×C4×D61—44no—
276C2×C4×D61—44no—
277C2×C4×D61C2×D412yes—
278C2×C4×D61C2412yes—
279C2×Dic122—21no—
280C2×Dic122—24no—
281C2×Dic122—24no—
282C2×Dic122—21no—
283C2×Dic122—42no—
284C2×Dic122—44no—
285C2×Dic122C2412yes—
286C2×Dic122C2412yes—
287SD16×C61—44no—
288M16×C61—42no—
289C2×C8×C61C2414yes—
290C4⋊C4×C61—22no—
291C4⋊C4×C61—22no—
292C4⋊C4×C61—21no—
293C4⋊C4×C61—21no—
294C4⋊C4×C61C2412yes—
295C4⋊C4×C61C2412yes—
296C22⋊C4×C61—22no—
297C22⋊C4×C61—22no—
298C22⋊C4×C61—22no—
299C22⋊C4×C61—22no—
300C22⋊Dic61—22no—
301C22⋊Dic61—22no—
302C22⋊Dic61—22no—
303C22⋊Dic61—22no—
304C22⋊Dic61—22no—
305C22⋊Dic61—22no—
306C22⋊Dic61C2×D412yes—
307C22⋊Dic61C2×D412yes—
308#11758202—44no—
309#11758200—28no—
310#11758199—44no—
311#11758198—22no—
312#11758198—22no—
313#11758198—24no—
314#11758198—24no—
315#11758198—24no—
316#11758198C2×D412yes—
317#11758198C2×D412yes—
318C4⋊Dic61—21no—
319C4⋊Dic61—22no—
320C4⋊Dic61—22no—
321C4⋊Dic61C2412yes—
322#11758196—22no—
323#11758196—22no—
324#11758196—24no—
325#11758196—22no—
326#11758196—22no—
327#11758196C2×D412yes—
328#11758196C2×D412yes—
329C4×Dic61—24no—
330C4×Dic61—22no—
331C4×Dic61—22no—
332C4×Dic61C2×D412yes—
333C4×Dic61C2412yes—
334#11758194—42no—
335C2×#92418C2414yes—
336Dic244—28no—
337#11758190—44no—
338#11758189—44no—
339C23×C61—22no—
340C23×C61—22no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—42no—
344C23×C61—81no—
345C23×C61—81no—
346C23×C61C22×D411yescharacteristic
347C23×C61C22×D411yescharacteristic
348C23×C61C22×D411yescharacteristic
349C22×D61—22no—
350C22×D61—22no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—42no—
354C22×D61—42no—
355C22×D61—42no—
356C22×D61C22×D412yes—
357Q8×C61—24no—
358Q8×C61—42no—
359D4×C61—24no—
360D4×C61—44no—
361D4×C61—44no—
362D4×C61—81no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—42no—
373C2×C4×C61—42no—
374C2×C4×C61—42no—
375C2×C4×C61C22×D411yescharacteristic
376C2×C4×C61C22×D411yescharacteristic
377C2×C4×C61C22×D411yescharacteristic
378C2×C4×C61C2511yescharacteristic
379C22⋊D61—42no—
380C22⋊D61—42no—
381C22⋊D61—44no—
382C22⋊D61—44no—
383C22⋊D61—82no—
384C22⋊D61—82no—
385C2×Dic61—24no—
386C2×Dic61—22no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—22no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—82no—
393C2×Dic61—82no—
394C2×Dic61—81no—
395C2×Dic61—81no—
396C2×Dic61C22×D412yes—
397C2×Dic61C22×D412yes—
398C2×Dic61C22×D412yes—
399D244—22no—
400D244—22no—
401D244—42no—
402D244—48no—
403C4×D61—24no—
404C4×D61—42no—
405C4×D61—44no—
406C4×D61—44no—
407C4×D61—48no—
408Dic122—24no—
409Dic122—22no—
410Dic122—24no—
411Dic122—48no—
412Dic122—81no—
413Dic122H(5,𝔽2)14yes—
414C8×C61—24no—
415#92418—24no—
416#61583—611nomaximal, Sylow
417C22×C61—21no—
418C22×C61—21no—
419C22×C61—21no—
420C22×C61—21no—
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—21no—
424C22×C61—21no—
425C22×C61—42no—
426C22×C61—42no—
427C22×C61—42no—
428C22×C61—82no—
429C22×C61—162no—
430C22×C61#57512yes—
431C22×C61C23×D411yescharacteristic
432C2×D61—22no—
433C2×D61—22no—
434C2×D61—22no—
435C2×D61—44no—
436C2×D61—42no—
437C2×D61—42no—
438C2×D61—42no—
439C2×D61—84no—
440C4×C61—21no—
441C4×C61—21no—
442C4×C61—21no—
443C4×C61—42no—
444C4×C61—42no—
445C4×C61—42no—
446C4×C61C2×H(5,𝔽2)12yes—
447Dic61—22no—
448Dic61—24no—
449Dic61—22no—
450Dic61—22no—
451Dic61—42no—
452Dic61—42no—
453#3505—611no—
454C2×#548—611no—
455#3327—614no—
456#3326—614no—
457#3277—614no—
458#3275—614no—
459#3211—612no—
460#3195—611no—
461#3194—612no—
462#3193D6111yescharacteristic, complemented
463#3108—612no—
464#3007—611no—
465#3006—611no—
466#3004—612no—
467#2975—611no—
468C2×C61—22no—
469C2×C61—41no—
470C2×C61—41no—
471C2×C61—82no—
472C2×C61#348411yescharacteristic
473C2×C61C2×#57511yescharacteristic
474C2×C61#358611yescharacteristic
475D61—42no—
476D61—82no—
477C22×#41—611no—
478C23×Q8—611no—
479C2×#137—614no—
480C2×#137—612no—
481C2×AGL(1,ℤ/8)—612no—
482#553—612no—
483#553—1222no—
484#552—612no—
485#551—1222no—
486#548—614no—
487#548—614no—
488#548—612no—
489#548—1222no—
490#548—1222no—
491#546—612no—
492#539—1221no—
493#538—1221no—
494#534—1221no—
495#529—612no—
496C2×#124—611no—
497C2×#124—1221no—
498#525—612no—
499C2×C22⋊Q8—611no—
500C2×C22⋊Q8—1221no—
501C2×C22⋊Q8C2×D6111yescharacteristic
502C2×#121—611no—
503C2×#121—1221no—
504C2×#121C2×D6111yescharacteristic
505#518—1221no—
506C2×C4×Q8—611no—
507C2×C4×D4—611no—
508C2×C4×D4—1221no—
509#495—614no—
510#488—614no—
511#484C2×D6112yescomplemented
512#483—612no—
513#483—612no—
514#482—614no—
515#480C2×D6112yes—
516#479—614no—
517#470—614no—
518#469—614no—
519#468—614no—
520#468C2×D6114yescomplemented
521#464—614no—
522#464—614no—
523#463—614no—
524#452—614no—
525#451—612no—
526#451—612no—
527#451—614no—
528#451—612no—
529#450—612no—
530#450C2×D6112yescomplemented
531#449—614no—
532#449—614no—
533#448—614no—
534#448—612no—
535#448C2×D6112yes—
536#447—612no—
537C4×Q16—614no—
538C4×SD16—614no—
539#436—614no—
540#436—614no—
541#431—612no—
542#419—614no—
543#417—612no—
544#417—612no—
545#407—611no—
546#407—612no—
547#407C2×D6111yescharacteristic
548C61#6158311yescharacteristic, complemented, Sylow
549C2×#41—612no—
550C2×#41—612no—
551C2×#41—612no—
552C2×#41—1221no—
553C2×#41—1221no—
554C2×#41—2444no—
555C22×Q8—614no—
556C22×Q8—611no—
557C22×Q8—611no—
558C22×Q8—1221no—
559C22×Q8—1222no—
560C22×Q8—2444no—
561C22×Q8C22×D6111yescharacteristic
562C22×D4—21no—
563C22×D4—611no—
564C22×D4—611no—
565C22×D4—1221no—
566C22×D4—1221no—
567C22×D4C22×D6111yescharacteristic
568C23×C4—611no—
569C23×C4—1221no—
570C23×C4—1221no—
571C23×C4C22×D6111yescharacteristic
572#137—2444no—
573#137—2448no—
574AGL(1,ℤ/8)—2444no—
575C2×Q16—614no—
576C2×Q16—614no—
577C2×SD16—614no—
578C2×SD16—614no—
579C2×SD16C22×D6114yes—
580C2×D8—614no—
581C2×M16—612no—
582C2×M16—614no—
583C2×M16C22×D6112yes—
584#126—1222no—
585#126—1222no—
586#126—1222no—
587#125—612no—
588#125—1222no—
589#124—614no—
590#124—612no—
591#124—1222no—
592#124—1224no—
593#124—1224no—
594#124—1222no—
595#123—1222no—
596#123—1222no—
597#123—1222no—
598#123—1222no—
599#123—1222no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—612no—
603C22⋊Q8—612no—
604C22⋊Q8—612no—
605C22⋊Q8—1222no—
606C22⋊Q8—1224no—
607C22⋊Q8—1224no—
608C22⋊Q8—1221no—
609C22⋊Q8—1221no—
610C22⋊Q8C22×D6112yes—
611C22⋊Q8C22×D6112yes—
612#121—21no—
613#121—21no—
614#121—612no—
615#121—614no—
616#121—1224no—
617#121—1224no—
618#121—1222no—
619#121—1222no—
620#121—1222no—
621#121—1222no—
622#121C22×D6112yes—
623#121C22×D6112yes—
624#120—1222no—
625#120—1222no—
626C4×Q8—614no—
627C4×Q8—612no—
628C4×Q8—1222no—
629C4×D4—612no—
630C4×D4—612no—
631C4×D4—612no—
632C4×D4—612no—
633C4×D4—612no—
634C4×D4—1222no—
635C4×D4—1224no—
636C4×D4—1224no—
637C4×D4—1222no—
638C4×D4—1222no—
639C4×D4—1222no—
640C4×D4—1222no—
641#117—612no—
642#117—1222no—
643#117—1222no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—611no—
646C2×C4⋊C4—611no—
647C2×C4⋊C4—1221no—
648C2×C4⋊C4—1221no—
649C2×C4⋊C4C22×D6111yescharacteristic
650C2×C4⋊C4C22×D6111yescharacteristic
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—611no—
654C2×C22⋊C4—611no—
655C2×C22⋊C4—1222no—
656C2×C22⋊C4—1221no—
657C2×C22⋊C4—1221no—
658C2×C22⋊C4—1221no—
659C2×C22⋊C4—1221no—
660C2×C42—611no—
661C2×C42—1221no—
662#107C22×D6114yes—
663#106—614no—
664C4⋊C8—614no—
665#103—614no—
666#103—614no—
667#103—614no—
668#103—614no—
669#103C22×D6114yes—
670#102—614no—
671#102—614no—
672#102C22×D6114yes—
673C22⋊C8—612no—
674C22⋊C8—612no—
675C22⋊C8—614no—
676C22⋊C8C22×D6112yes—
677C22⋊C8C22×D6112yes—
678C4×C8—614no—
679C24—21no—
680C24—611no—
681C24—1221no—
682C24D4×D6111yescharacteristic
683#41—1224no—
684#41—1224no—
685#41—2442no—
686#41—2442no—
687#41—2444no—
688#41—2444no—
689#41—2444no—
690C2×Q8—21no—
691C2×Q8—42no—
692C2×Q8—612no—
693C2×Q8—612no—
694C2×Q8—1224no—
695C2×Q8—1224no—
696C2×Q8—1221no—
697C2×Q8—1221no—
698C2×Q8—1228no—
699C2×Q8—2442no—
700C2×Q8—2444no—
701C2×Q8—2444no—
702C2×Q8—2448no—
703C2×Q8C23×D6112yes—
704C2×D4—22no—
705C2×D4—22no—
706C2×D4—21no—
707C2×D4—42no—
708C2×D4—44no—
709C2×D4—612no—
710C2×D4—612no—
711C2×D4—612no—
712C2×D4—1224no—
713C2×D4—1222no—
714C2×D4—1222no—
715C2×D4—1222no—
716C2×D4—1222no—
717C2×D4—1221no—
718C2×D4—2442no—
719C2×D4—2444no—
720C2×D4—2442no—
721C2×D4—2444no—
722C2×D4C23×D6112yes—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—42no—
727C22×C4—611no—
728C22×C4—611no—
729C22×C4—611no—
730C22×C4—612no—
731C22×C4—612no—
732C22×C4—1224no—
733C22×C4—1222no—
734C22×C4—1222no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1222no—
739C22×C4—1222no—
740C22×C4—2442no—
741C22×C4—2444no—
742C22×C4—2444no—
743C22×C4D4×D6111yescharacteristic
744C22×C4D4×D6111yescharacteristic
745C22×C4D4×D6111yescharacteristic
746C22×C4C23×D6111yescharacteristic
747C22×C4C23×D6111yescharacteristic
748C22×C4C23×D6111yescharacteristic
749Q16—1228no—
750Q16—2444no—
751SD16—44no—
752SD16—1228no—
753SD16—2444no—
754D8—2444no—
755M16—42no—
756M16—2444no—
757M16—2442no—
758C2×C8—614no—
759C2×C8C23×D6114yes—
760C4⋊C4—22no—
761C4⋊C4—22no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—612no—
765C4⋊C4—612no—
766C4⋊C4—612no—
767C4⋊C4—1224no—
768C4⋊C4—1222no—
769C4⋊C4—1222no—
770C4⋊C4—1222no—
771C4⋊C4—1222no—
772C4⋊C4—1221no—
773C4⋊C4—1222no—
774C4⋊C4—1222no—
775C4⋊C4C23×D6112yes—
776C4⋊C4C23×D6112yes—
777C22⋊C4—22no—
778C22⋊C4—22no—
779C22⋊C4—22no—
780C22⋊C4—22no—
781C22⋊C4—612no—
782C22⋊C4—612no—
783C22⋊C4—612no—
784C22⋊C4—612no—
785C22⋊C4—1224no—
786C22⋊C4—1224no—
787C22⋊C4—1224no—
788C22⋊C4—1222no—
789C22⋊C4—1222no—
790C22⋊C4—1222no—
791C22⋊C4—1222no—
792C22⋊C4—1222no—
793C22⋊C4—1222no—
794C22⋊C4—1222no—
795C22⋊C4—1222no—
796C42—612no—
797C42—612no—
798C42—1224no—
799C42—1222no—
800C42—1222no—
801C23—22no—
802C23—22no—
803C23—41no—
804C23—41no—
805C23—42no—
806C23—81no—
807C23—81no—
808C23—612no—
809C23—1222no—
810C23—1222no—
811C23—2441no—
812C23—2441no—
813C23—2442no—
814C23—2442no—
815C23—2442no—
816C23C2×D4×D6111yescharacteristic
817C23C2×D4×D6111yescharacteristic
818C23C2×D4×D6111yescharacteristic
819Q8—24no—
820Q8—42no—
821Q8—614no—
822Q8—1224no—
823Q8—1222no—
824Q8—1224no—
825Q8—4881no—
826Q8—2448no—
827D4—24no—
828D4—44no—
829D4—44no—
830D4—81no—
831D4—1222no—
832D4—1222no—
833D4—4882no—
834D4—4882no—
835D4—2442no—
836D4—2448no—
837D4—2442no—
838D4—2442no—
839D4—2444no—
840D4—2444no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—612no—
854C2×C4—612no—
855C2×C4—612no—
856C2×C4—1224no—
857C2×C4—1222no—
858C2×C4—1222no—
859C2×C4—1224no—
860C2×C4—1222no—
861C2×C4—1222no—
862C2×C4—4882no—
863C2×C4—4882no—
864C2×C4—4881no—
865C2×C4—4881no—
866C2×C4—2442no—
867C2×C4—2444no—
868C2×C4—2444no—
869C2×C4—2448no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4C2×D4×D6111yescharacteristic
873C2×C4C2×D4×D6111yescharacteristic
874C2×C4C2×D4×D6111yescharacteristic
875C2×C4C24×D6111yescharacteristic
876C8—24no—
877C8—1224no—
878C22—21no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—82no—
890C22—162no—
891C22—1222no—
892C22—1222no—
893C22—1222no—
894C22—4884no—
895C22—2444no—
896C22—2442no—
897C22—2442no—
898C22—2442no—
899C22#1684055812yes—
900C22C22×D4×D6111yescharacteristic
901C4—21no—
902C4—21no—
903C4—21no—
904C4—42no—
905C4—42no—
906C4—42no—
907C4—1222no—
908C4—1222no—
909C4—1222no—
910C4—1224no—
911C4—2442no—
912C4—2442no—
913C4H(5,𝔽2)×D6112yes—
914C2—22no—
915C2—41no—
916C2—41no—
917C2—82no—
918C2—4882no—
919C2—2442no—
920C2#2145945111yescharacteristic
921C2C2×#1684055811yescharacteristic
922C2#2146060211yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3193C2
socleC22×C61C23×D4
hypercenter#3193D61
hypocenterC61#61583
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3193

Complements

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

NH ≅ G/Ntype
1. #21459653C2semidirect
2. C2×#16840422C2semidirect
3. #21458090C2semidirect
4. #21458067C2semidirect
5. #21457473C2semidirect
6. #21457454C2semidirect
7. #21456783C2semidirect
8. #21456640C2semidirect
9. #21456632C2semidirect
10. #21455896C2semidirect
11. #21455081C2semidirect
12. #21455069C2semidirect
13. #21455050C2semidirect
14. #21454858C2semidirect
15. C61×#3193C2semidirect
17. C22×Q8×D61C22semidirect
18. C2×#14519810C22semidirect
19. C2×#14519806C22semidirect
20. C2×#14519803C22semidirect
21. #16840464C22semidirect
23. #16840447C22semidirect
28. #16840422C22semidirect
29. #16840418C22semidirect
30. #16840406C22semidirect
35. C2×#14519766C22semidirect
40. C2×#14519752C22semidirect
43. C2×#14519742C22semidirect
46. #16840143C22semidirect
47. #16840118C22semidirect
48. #16840092C22semidirect
49. #16840090C22semidirect
50. #16840089C22semidirect
51. #16840068C22semidirect
52. #16840018C22semidirect
53. #16840014C22semidirect
54. #16840009C22semidirect
55. #16839987C22semidirect
56. #16839983C22semidirect
57. #16839979C22semidirect
58. #16839926C22semidirect
59. #16839920C22semidirect
60. #16839919C22semidirect
61. #16839918C22semidirect
62. #16839917C22semidirect
63. #16839915C22semidirect
64. #16839908C22semidirect
65. #16839905C22semidirect
67. #16839899C22semidirect
69. #16839856C22semidirect
70. #16839853C22semidirect
71. #16839838C22semidirect
72. #16839837C22semidirect
73. #16839812C22semidirect
74. #16839769C22semidirect
75. #16839764C22semidirect
76. #16839761C22semidirect
78. #16839724C22semidirect
81. C61×#484C22semidirect
83. C61×#468C22semidirect
84. C61×#450C22semidirect
462. #3193D61semidirect
511. #484C2×D61semidirect
520. #468C2×D61semidirect
530. #450C2×D61semidirect
548. C61#61583semidirect

Maximal subgroups

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

subgroupindex
#214596532
C2×#168404222
#214580902
#214580672
#214574732
#214574542
#214567832
#214566402
#214566322
#214558962
#214550812
#214550692
#214550502
#214548582
C61×#31932
#6158361