Finite Group Databasebeta

← #30564916

Subgroups — #30564916

Order 15616.

2126 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#21459660C211yesmaximal, characteristic, complemented
2C2×#16840411C211yesmaximal, characteristic, complemented
3#21457908C214yesmaximal, complemented
4#21457796C214yesmaximal, complemented
5#21457368C214yesmaximal, complemented
6#21457347C214yesmaximal, complemented
7#21456849C212yesmaximal, complemented
8#21456640C211yesmaximal, characteristic, complemented
9#21456626C211yesmaximal, characteristic, complemented
10#21456603C212yesmaximal, complemented
11#21455958C212yesmaximal, complemented
12#21455071C211yesmaximal, characteristic, complemented
13#21455038C212yesmaximal, complemented
14#21454846C211yesmaximal, characteristic, complemented
15C61×#3007C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic, complemented
17C2×#14519802C2212yescomplemented
18C2×#14519798C2214yescomplemented
19#16840460—22no—
20#16840460C2212yescomplemented
21#16840454C2212yescomplemented
22#16840439—22no—
23#16840423C2212yescomplemented
24#16840411—22no—
25#16840411—22no—
26#16840411C2214yes—
27#16840411C2214yescomplemented
28#16840403C2212yescomplemented
29#16840361—21no—
30#16840352—21no—
31#16840324—21no—
32C2×#14519775C2211yescharacteristic, complemented
33#16840298C2212yes—
34#16840275C2212yes—
35C2×#14519760—21no—
36C2×#14519758—21no—
37C2×#14519756C2211yescharacteristic
38C2×#14519753C2211yescharacteristic, complemented
39C2×#14519751C2211yescharacteristic
40C2×#14519749—21no—
41#16840235—21no—
42C2×D4×Dic61C2211yescharacteristic, complemented
43C2×C4×C22⋊D61C2211yescharacteristic
44C22×#11758196—21no—
45#16840155C2214yescomplemented
46#16840129C2214yescomplemented
47#16840102C2214yescomplemented
48#16840098C2212yescomplemented
49#16840092C2212yescomplemented
50#16840090C2212yescomplemented
51#16840076C2212yes—
52#16840060C2214yescomplemented
53#16840018C2214yescomplemented
54#16840008C2214yescomplemented
55#16840000C2214yescomplemented
56#16839994C2214yescomplemented
57#16839979C2214yescomplemented
58#16839970C2214yescomplemented
59#16839966C2214yescomplemented
60#16839923C2214yescomplemented
61#16839921C2214yescomplemented
62#16839918C2212yescomplemented
63#16839917C2212yescomplemented
64#16839915C2212yescomplemented
65#16839908C2214yescomplemented
66#16839907C2214yescomplemented
67#16839903C2212yes—
68#16839901C2212yes—
69#16839896C2212yes—
70#16839871C2214yescomplemented
71#16839863C2214yescomplemented
72#16839836C2214yescomplemented
73#16839831C2214yescomplemented
74#16839816C2212yescomplemented
75#16839763C2212yescomplemented
76#16839755C2214yescomplemented
77#16839726C2211yescharacteristic
78C22⋊C8×D61C2212yescomplemented
79C22×#41×C61C2211yescharacteristic
80C2×#137×C61C2212yescomplemented
81C2×C22⋊Q8×C61C2211yescharacteristic
82C61×#452C2214yescomplemented
83C61×#451C2212yescomplemented
84C61×#450C2212yescomplemented
85C61×#417C2212yescomplemented
86C61×#407C2211yescharacteristic
87C2×#11758226C2312yes—
88C2×#11758224—22no—
89C2×#11758224—44no—
90C2×#11758224C2314yes—
91C22×Dic122C2311yescharacteristic
92C22×D244C2311yescharacteristic
93C22×C22⋊D61—21no—
94C22×C22⋊D61—21no—
95C22×C22⋊D61D411yescharacteristic
96C23×Dic61—21no—
97C23×Dic61—21no—
98C22×C4×D61C2311yescharacteristic
99#14519802—44no—
100#14519798—48no—
101C2×#11758202C2314yes—
102C2×#11758190C2314yes—
103C2×#11758201C2314yes—
104C2×#11758199C2314yes—
105C2×#11758194C2312yes—
106C2×C8×D61C2314yes—
107#14519775—22no—
108#14519775C2314yes—
109#14519772—22no—
110#14519772—22no—
111#14519772—22no—
112#14519768—22no—
113#14519768C2312yes—
114#14519766—22no—
115#14519766C2312yes—
116#14519762—22no—
117#14519762—22no—
118#14519762—22no—
119#14519761—22no—
120#14519761—22no—
121#14519760—24no—
122#14519760—24no—
123#14519758—24no—
124#14519758—24no—
125#14519756—21no—
126#14519756—21no—
127#14519756C2312yes—
128#14519756C2312yes—
129#14519753—22no—
130#14519753—22no—
131#14519753C2312yes—
132#14519753C2314yes—
133#14519752—22no—
134#14519752C2312yes—
135#14519751—21no—
136#14519751—21no—
137#14519751—22no—
138#14519751—22no—
139#14519751C2312yes—
140#14519751C2312yes—
141#14519749—24no—
142#14519749—24no—
143#14519747—22no—
144#14519747—22no—
145Q8×Dic61C2312yes—
146D4×Dic61—22no—
147D4×Dic61C2314yes—
148#14519739—22no—
149#14519739C2312yes—
150C4×C22⋊D61—22no—
151C4×C22⋊D61—22no—
152C4×C22⋊D61D412yes—
153C4×C22⋊D61D412yes—
154C4×C22⋊D61C2312yes—
155C4×C22⋊D61C2312yes—
156#14519737—22no—
157#14519737—22no—
158#14519735—22no—
159#14519735C2312yes—
160#14519733—22no—
161C2×C4⋊Dic61C2311yescharacteristic
162C2×C4⋊Dic61C2311yescharacteristic
163C2×#11758196—21no—
164C2×#11758196—21no—
165C2×#11758196—21no—
166C2×#11758196—21no—
167C2×#11758196—24no—
168C2×#11758196—24no—
169C2×#11758196D411yescharacteristic
170C2×C22⋊Dic61—21no—
171C2×C22⋊Dic61—21no—
172C2×C22⋊Dic61D411yescharacteristic
173C2×#11758198—21no—
174C2×#11758198—21no—
175C2×#11758198D411yescharacteristic
176C22⋊C4×D61—22no—
177C2×C4×Dic61C2311yescharacteristic
178#14519711C2314yes—
179#14519708C2314yes—
180#14519706C2314yes—
181#14519702C2314yes—
182#14519701C2314yes—
183#14519701C2314yes—
184#14519700C2314yes—
185#14519699C2314yes—
186#14519698C2314yes—
187C22⋊#92418C2312yes—
188C22⋊#92418C2312yes—
189#14519689C2314yes—
190#14519687C2314yes—
191C2×#41×C61—21no—
192C2×#41×C61—21no—
193C2×#41×C61—44no—
194C2×#41×C61C2312yes—
195C2×#41×C61C2312yes—
196C22×Q8×C61C2311yescharacteristic
197C22×Q8×C61C2311yescharacteristic
198C22×D4×C61—21no—
199C22×D4×C61C2311yescharacteristic
200C23×C4×C61—21no—
201C23×C4×C61C2311yescharacteristic
202#137×C61—44no—
203C2×Q16×C61C2314yes—
204C2×SD16×C61C2314yes—
205C2×M16×C61C2312yes—
206C22⋊Q8×C61—21no—
207C22⋊Q8×C61—21no—
208C22⋊Q8×C61C2312yes—
209C22⋊Q8×C61C2312yes—
210C2×C4⋊C4×C61—21no—
211C2×C4⋊C4×C61C2311yescharacteristic
212C2×C22⋊C4×C61—21no—
213#103×C61C2314yes—
214#102×C61C2314yes—
215C22⋊C8×C61C2312yes—
216C22⋊C8×C61C2312yes—
217C24×C61—21no—
218C24×C61C2×D411yescharacteristic
219C23×D61—21no—
220C23×D61C2×D411yescharacteristic
221#41×C61—24no—
222#41×C61—24no—
223#41×C61—42no—
224#41×C61—42no—
225#41×C61—44no—
226#41×C61—44no—
227C2×Q8×C61—21no—
228C2×Q8×C61—21no—
229C2×Q8×C61—42no—
230C2×Q8×C61—42no—
231C2×Q8×C61C2412yes—
232C2×Q8×C61C2412yes—
233C2×D4×C61—24no—
234C2×D4×C61—22no—
235C2×D4×C61—22no—
236C2×D4×C61—21no—
237C2×D4×C61—44no—
238C2×D4×C61C2412yes—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—22no—
243C22×C4×C61—22no—
244C22×C4×C61—42no—
245C22×C4×C61—44no—
246C22×C4×C61C2×D411yescharacteristic
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2411yescharacteristic
250C22×C4×C61C2411yescharacteristic
251C22×C4×C61C2411yescharacteristic
252C2×C22⋊D61—22no—
253C2×C22⋊D61—22no—
254C2×C22⋊D61—24no—
255C2×C22⋊D61—42no—
256C2×C22⋊D61—44no—
257C2×C22⋊D61—44no—
258C2×C22⋊D61C2×D412yes—
259C2×C22⋊D61C2×D412yes—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—24no—
264C22×Dic61—24no—
265C22×Dic61—44no—
266C22×Dic61—44no—
267C22×Dic61C2×D411yescharacteristic
268C22×Dic61C2×D411yescharacteristic
269C22×Dic61C2×D411yescharacteristic
270#11758226—44no—
271#11758224—28no—
272#11758224—44no—
273#11758224—48no—
274C2×D244—22no—
275C2×D244—22no—
276C2×D244—21no—
277C2×D244—42no—
278C2×D244C2412yes—
279C2×C4×D61—22no—
280C2×C4×D61—22no—
281C2×C4×D61—42no—
282C2×C4×D61C2×D412yes—
283C2×C4×D61C2412yes—
284C2×Dic122—21no—
285C2×Dic122—42no—
286C2×Dic122C2412yes—
287Q16×C61—44no—
288SD16×C61—28no—
289M16×C61—42no—
290C2×C8×C61C2414yes—
291C4⋊C4×C61—22no—
292C4⋊C4×C61—22no—
293C4⋊C4×C61—21no—
294C4⋊C4×C61C2412yes—
295C22⋊C4×C61—22no—
296C22⋊C4×C61—22no—
297C22⋊Dic61—22no—
298C22⋊Dic61—22no—
299C22⋊Dic61—24no—
300C22⋊Dic61C2×D412yes—
301C22⋊Dic61C2×D412yes—
302#11758202—44no—
303#11758201—44no—
304#11758199—28no—
305#11758198—24no—
306#11758198—22no—
307#11758198—22no—
308#11758198—22no—
309#11758198—22no—
310#11758198—22no—
311#11758198—22no—
312#11758198—22no—
313#11758198—22no—
314#11758198C2×D412yes—
315#11758198C2×D412yes—
316C4⋊Dic61—21no—
317C4⋊Dic61—21no—
318C4⋊Dic61—22no—
319C4⋊Dic61—22no—
320C4⋊Dic61C2412yes—
321C4⋊Dic61C2412yes—
322#11758196—22no—
323#11758196—22no—
324#11758196—24no—
325#11758196—24no—
326#11758196—24no—
327#11758196—22no—
328#11758196—22no—
329#11758196C2×D412yes—
330#11758196C2×D412yes—
331C4×Dic61—22no—
332C4×Dic61—22no—
333C4×Dic61C2×D412yes—
334C4×Dic61C2412yes—
335#11758194—42no—
336C2×#92418C2414yes—
337#11758190—44no—
338C8×D61—44no—
339C23×C61—24no—
340C23×C61—22no—
341C23×C61—22no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—42no—
345C23×C61—42no—
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—81no—
355C22×D61—81no—
356C22×D61C22×D412yes—
357Q8×C61—22no—
358Q8×C61—24no—
359Q8×C61—22no—
360Q8×C61—42no—
361Q8×C61—81no—
362D4×C61—24no—
363D4×C61—22no—
364D4×C61—44no—
365D4×C61—44no—
366D4×C61H(5,𝔽2)14yes—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—22no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—44no—
377C2×C4×C61—44no—
378C2×C4×C61—42no—
379C2×C4×C61—81no—
380C2×C4×C61—81no—
381C2×C4×C61C22×D411yescharacteristic
382C2×C4×C61C22×D411yescharacteristic
383C2×C4×C61C22×D411yescharacteristic
384C2×C4×C61C2511yescharacteristic
385C22⋊D61—42no—
386C22⋊D61—42no—
387C22⋊D61—48no—
388C22⋊D61—44no—
389C22⋊D61—44no—
390C2×Dic61—22no—
391C2×Dic61—22no—
392C2×Dic61—22no—
393C2×Dic61—22no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—48no—
397C2×Dic61—48no—
398C2×Dic61—42no—
399C2×Dic61—42no—
400C2×Dic61—42no—
401C2×Dic61C22×D412yes—
402C2×Dic61C22×D412yes—
403C2×Dic61C22×D412yes—
404D244—24no—
405D244—81no—
406D244—82no—
407D244—82no—
408C4×D61—24no—
409C4×D61—42no—
410C4×D61—82no—
411C4×D61—82no—
412Dic122—24no—
413Dic122—42no—
414C8×C61—24no—
415#92418—24no—
416#61575—611nomaximal, Sylow
417C22×C61—21no—
418C22×C61—21no—
419C22×C61—21no—
420C22×C61—21no—
421C22×C61—24no—
422C22×C61—21no—
423C22×C61—21no—
424C22×C61—21no—
425C22×C61—21no—
426C22×C61—48no—
427C22×C61—42no—
428C22×C61—42no—
429C22×C61—82no—
430C22×C61#57512yes—
431C22×C61C23×D411yescharacteristic
432C2×D61—22no—
433C2×D61—22no—
434C2×D61—22no—
435C2×D61—42no—
436C2×D61—42no—
437C2×D61—42no—
438C2×D61—82no—
439C2×D61—162no—
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—22no—
449Dic61—22no—
450Dic61—42no—
451Dic61—42no—
452Dic61—42no—
453#3505—611no—
454C2×#547—611no—
455#3315—614no—
456#3307—614no—
457#3269—614no—
458#3267—614no—
459#3218—612no—
460#3195—611no—
461#3193—611no—
462#3190—612no—
463#3114—612no—
464#3007D6111yescharacteristic, complemented
465#3006—611no—
466#3002—612no—
467#2973—611no—
468C2×C61—22no—
469C2×C61—41no—
470C2×C61—41no—
471C2×C61—44no—
472C2×C61#348411yescharacteristic
473C2×C61C2×#57511yescharacteristic
474C2×C61#358611yescharacteristic
475D61—42no—
476D61—82no—
477C22×#41—611no—
478C22×#41C2×D6111yescharacteristic
479C2×#137C2×D6112yescomplemented
480C2×AGL(1,ℤ/8)—612no—
481C2×#135—614no—
482#553—612no—
483#553—1222no—
484#552—612no—
485#551—1222no—
486#548—612no—
487#547—614no—
488#547—614no—
489#547—1222no—
490#547—1222no—
491#546—612no—
492#539—1221no—
493#538—1221no—
494#534—1221no—
495C2×C4⋊Q8—611no—
496#529—612no—
497#525—612no—
498C2×#123—1221no—
499C2×#123—1221no—
500C2×C22⋊Q8—611no—
501C2×C22⋊Q8—611no—
502C2×C22⋊Q8C2×D6111yescharacteristic
503C2×#121—611no—
504C2×#121—1221no—
505#518—1221no—
506C2×C4×D4—611no—
507C2×C4×D4—611no—
508C22×C4⋊C4—1221no—
509#497—614no—
510#491—614no—
511#485—614no—
512#484—612no—
513#483—612no—
514#483—612no—
515#480—612no—
516#478—614no—
517#470—614no—
518#468—614no—
519#467—614no—
520#465—614no—
521#463—614no—
522#462—614no—
523#461—614no—
524#452—614no—
525#452—614no—
526#452C2×D6114yescomplemented
527#451—612no—
528#451—612no—
529#451C2×D6112yescomplemented
530#450—612no—
531#450C2×D6112yescomplemented
532#449—614no—
533#449—614no—
534#448—612no—
535#448—612no—
536#447—612no—
537#442—614no—
538#440—614no—
539#435—614no—
540#435—614no—
541#432—612no—
542#417—612no—
543#417C2×D6112yescomplemented
544#416—614no—
545#407—611no—
546#407C2×D6111yescharacteristic
547C2×C22⋊C8—612no—
548C61#6157511yescharacteristic, complemented, Sylow
549C2×#41—21no—
550C2×#41—21no—
551C2×#41—44no—
552C2×#41—612no—
553C2×#41—614no—
554C2×#41—1222no—
555C2×#41—2444no—
556C2×#41C22×D6112yes—
557C2×#41C22×D6112yes—
558C22×Q8—611no—
559C22×Q8C22×D6111yescharacteristic
560C22×Q8C22×D6111yescharacteristic
561C22×D4—21no—
562C22×D4—611no—
563C22×D4—611no—
564C22×D4—1221no—
565C22×D4—1221no—
566C22×D4C22×D6111yescharacteristic
567C23×C4—21no—
568C23×C4—611no—
569C23×C4—1221no—
570C23×C4—1221no—
571C23×C4C22×D6111yescharacteristic
572#137—44no—
573AGL(1,ℤ/8)—2444no—
574#135—2448no—
575C2×Q16—614no—
576C2×Q16C22×D6114yes—
577C2×SD16—614no—
578C2×SD16—614no—
579C2×SD16C22×D6114yes—
580C2×D8—614no—
581C2×M16—612no—
582C2×M16C22×D6112yes—
583C22×C8—614no—
584C4⋊Q8—614no—
585C4⋊Q8—1222no—
586#126—1222no—
587#126—1222no—
588#126—1222no—
589#125—612no—
590#125—1222no—
591#124—612no—
592#124—1222no—
593#123—1222no—
594#123—1222no—
595#123—1222no—
596#123—1224no—
597#123—1224no—
598#123—1224no—
599#123—1224no—
600#123—1222no—
601#123—1222no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—614no—
605C22⋊Q8—612no—
606C22⋊Q8—612no—
607C22⋊Q8—612no—
608C22⋊Q8—1222no—
609C22⋊Q8—1222no—
610C22⋊Q8—1221no—
611C22⋊Q8—1221no—
612C22⋊Q8C22×D6112yes—
613C22⋊Q8C22×D6112yes—
614#121—612no—
615#121—612no—
616#121—612no—
617#121—1222no—
618#121—1222no—
619#121—1222no—
620#121—1224no—
621#121—1224no—
622#121—1221no—
623#121—1221no—
624#120—1222no—
625#120—1222no—
626C4×Q8—612no—
627C4×D4—612no—
628C4×D4—612no—
629C4×D4—612no—
630C4×D4—612no—
631C4×D4—614no—
632C4×D4—612no—
633C4×D4—1222no—
634C4×D4—1222no—
635C4×D4—1222no—
636C4×D4—1222no—
637C4×D4—1222no—
638C4×D4—1222no—
639#117—612no—
640#117—1222no—
641#117—1222no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—611no—
644C2×C4⋊C4—611no—
645C2×C4⋊C4—611no—
646C2×C4⋊C4—1224no—
647C2×C4⋊C4—1224no—
648C2×C4⋊C4—1221no—
649C2×C4⋊C4—1221no—
650C2×C4⋊C4—1221no—
651C2×C4⋊C4—1221no—
652C2×C4⋊C4C22×D6111yescharacteristic
653C2×C22⋊C4—21no—
654C2×C22⋊C4—611no—
655C2×C22⋊C4—611no—
656C2×C22⋊C4—1222no—
657C2×C22⋊C4—1221no—
658C2×C22⋊C4—1221no—
659C2×C22⋊C4—1221no—
660C2×C22⋊C4—1221no—
661C2×C42—611no—
662#107—614no—
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—
678#97—614no—
679C24—21no—
680C24—611no—
681C24—1221no—
682C24D4×D6111yescharacteristic
683#41—24no—
684#41—24no—
685#41—42no—
686#41—42no—
687#41—44no—
688#41—44no—
689#41—1228no—
690#41—2444no—
691#41—2444no—
692#41—2448no—
693C2×Q8—21no—
694C2×Q8—21no—
695C2×Q8—42no—
696C2×Q8—42no—
697C2×Q8—612no—
698C2×Q8—1221no—
699C2×Q8—2442no—
700C2×Q8C23×D6112yes—
701C2×Q8C23×D6112yes—
702C2×D4—24no—
703C2×D4—22no—
704C2×D4—22no—
705C2×D4—21no—
706C2×D4—44no—
707C2×D4—612no—
708C2×D4—612no—
709C2×D4—612no—
710C2×D4—1222no—
711C2×D4—1222no—
712C2×D4—1224no—
713C2×D4—1222no—
714C2×D4—1222no—
715C2×D4—1221no—
716C2×D4—2442no—
717C2×D4—2442no—
718C2×D4—2444no—
719C2×D4—2444no—
720C2×D4C23×D6112yes—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—42no—
727C22×C4—44no—
728C22×C4—611no—
729C22×C4—611no—
730C22×C4—611no—
731C22×C4—612no—
732C22×C4—612no—
733C22×C4—1222no—
734C22×C4—1222no—
735C22×C4—1224no—
736C22×C4—1224no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
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—44no—
750Q16—2444no—
751SD16—28no—
752SD16—2444no—
753SD16—2444no—
754D8—1228no—
755M16—42no—
756M16—2442no—
757C2×C8—614no—
758C2×C8—2444no—
759C2×C8C23×D6114yes—
760C4⋊C4—22no—
761C4⋊C4—22no—
762C4⋊C4—21no—
763C4⋊C4—612no—
764C4⋊C4—612no—
765C4⋊C4—612no—
766C4⋊C4—612no—
767C4⋊C4—1224no—
768C4⋊C4—1224no—
769C4⋊C4—1224no—
770C4⋊C4—1222no—
771C4⋊C4—1222no—
772C4⋊C4—1222no—
773C4⋊C4—1222no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
776C4⋊C4—1222no—
777C4⋊C4—1222no—
778C4⋊C4C23×D6112yes—
779C22⋊C4—22no—
780C22⋊C4—22no—
781C22⋊C4—612no—
782C22⋊C4—612no—
783C22⋊C4—612no—
784C22⋊C4—612no—
785C22⋊C4—1222no—
786C22⋊C4—1222no—
787C22⋊C4—1222no—
788C22⋊C4—1222no—
789C22⋊C4—1224no—
790C22⋊C4—1222no—
791C22⋊C4—1222no—
792C22⋊C4—1224no—
793C22⋊C4—1222no—
794C22⋊C4—1222no—
795C22⋊C4—1222no—
796C22⋊C4—1222no—
797C42—612no—
798C42—612no—
799C42—1222no—
800C42—1222no—
801C23—24no—
802C23—22no—
803C23—22no—
804C23—41no—
805C23—41no—
806C23—42no—
807C23—42no—
808C23—612no—
809C23—1222no—
810C23—1222no—
811C23—4881no—
812C23—4881no—
813C23—2441no—
814C23—2441no—
815C23—2442no—
816C23C2×D4×D6111yescharacteristic
817C23C2×D4×D6111yescharacteristic
818C23C2×D4×D6111yescharacteristic
819Q8—24no—
820Q8—22no—
821Q8—22no—
822Q8—42no—
823Q8—81no—
824Q8—1224no—
825Q8—2442no—
826D4—24no—
827D4—22no—
828D4—44no—
829D4—44no—
830D4—1224no—
831D4—4881no—
832D4—4882no—
833D4—4882no—
834D4—2442no—
835D4—2442no—
836D4—2448no—
837D4—2444no—
838D4—2444no—
839D4#1451982214yes—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—42no—
852C2×C4—81no—
853C2×C4—81no—
854C2×C4—612no—
855C2×C4—612no—
856C2×C4—612no—
857C2×C4—1222no—
858C2×C4—1224no—
859C2×C4—1222no—
860C2×C4—1222no—
861C2×C4—1222no—
862C2×C4—4882no—
863C2×C4—4882no—
864C2×C4—2442no—
865C2×C4—2441no—
866C2×C4—2441no—
867C2×C4—2448no—
868C2×C4—2448no—
869C2×C4—2442no—
870C2×C4—2442no—
871C2×C4—2442no—
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—24no—
887C22—48no—
888C22—42no—
889C22—42no—
890C22—82no—
891C22—1222no—
892C22—1222no—
893C22—1222no—
894C22—9762no—
895C22—4882no—
896C22—2442no—
897C22—2442no—
898C22—2442no—
899C22#1684056112yes—
900C22C22×D4×D6111yescharacteristic
901C4—21no—
902C4—21no—
903C4—21no—
904C4—42no—
905C4—42no—
906C4—42no—
907C4—1222no—
908C4—1222no—
909C4—1222no—
910C4—2442no—
911C4—2442no—
912C4—2442no—
913C4C2×#1451982212yes—
914C2—22no—
915C2—41no—
916C2—41no—
917C2—44no—
918C2—4882no—
919C2—2442no—
920C2#2145944811yescharacteristic
921C2C2×#1684056111yescharacteristic
922C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3007C2
socleC22×C61C23×D4
hypercenter#3007D61
hypocenterC61#61575
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
1. #21459660C2semidirect
2. C2×#16840411C2semidirect
3. #21457908C2semidirect
4. #21457796C2semidirect
5. #21457368C2semidirect
6. #21457347C2semidirect
7. #21456849C2semidirect
8. #21456640C2semidirect
9. #21456626C2semidirect
10. #21456603C2semidirect
11. #21455958C2semidirect
12. #21455071C2semidirect
13. #21455038C2semidirect
14. #21454846C2semidirect
15. C61×#3007C2semidirect
16. C22×#11758224C22semidirect
17. C2×#14519802C22semidirect
18. C2×#14519798C22semidirect
20. #16840460C22semidirect
21. #16840454C22semidirect
23. #16840423C22semidirect
27. #16840411C22semidirect
28. #16840403C22semidirect
32. C2×#14519775C22semidirect
38. C2×#14519753C22semidirect
42. C2×D4×Dic61C22semidirect
45. #16840155C22semidirect
46. #16840129C22semidirect
47. #16840102C22semidirect
48. #16840098C22semidirect
49. #16840092C22semidirect
50. #16840090C22semidirect
52. #16840060C22semidirect
53. #16840018C22semidirect
54. #16840008C22semidirect
55. #16840000C22semidirect
56. #16839994C22semidirect
57. #16839979C22semidirect
58. #16839970C22semidirect
59. #16839966C22semidirect
60. #16839923C22semidirect
61. #16839921C22semidirect
62. #16839918C22semidirect
63. #16839917C22semidirect
64. #16839915C22semidirect
65. #16839908C22semidirect
66. #16839907C22semidirect
70. #16839871C22semidirect
71. #16839863C22semidirect
72. #16839836C22semidirect
73. #16839831C22semidirect
74. #16839816C22semidirect
75. #16839763C22semidirect
76. #16839755C22semidirect
78. C22⋊C8×D61C22semidirect
80. C2×#137×C61C22semidirect
82. C61×#452C22semidirect
83. C61×#451C22semidirect
84. C61×#450C22semidirect
85. C61×#417C22semidirect
464. #3007D61semidirect
479. C2×#137C2×D61semidirect
526. #452C2×D61semidirect
529. #451C2×D61semidirect
531. #450C2×D61semidirect
543. #417C2×D61semidirect
548. C61#61575semidirect

Maximal subgroups

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

subgroupindex
#214596602
C2×#168404112
#214579082
#214577962
#214573682
#214573472
#214568492
#214566402
#214566262
#214566032
#214559582
#214550712
#214550382
#214548462
C61×#30072
#6157561