Finite Group Databasebeta

← #30570284

Subgroups — #30570284

Order 15616.

1984 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459902C211yesmaximal, characteristic, complemented
2C2×#16840427C211yesmaximal, characteristic, complemented
3#21458722C212yesmaximal, complemented
4#21458715C214yesmaximal, complemented
5#21458678C212yesmaximal, complemented
6#21458610C212yesmaximal, complemented
7#21458608C214yesmaximal, complemented
8#21458453C212yesmaximal, complemented
9#21457052C212yesmaximal, complemented
10#21456947C211yesmaximal, characteristic, complemented
11#21456945C212yesmaximal, complemented
12#21455911C211yesmaximal, characteristic, complemented
13#21455907C212yesmaximal, complemented
14#21455869C212yesmaximal, complemented
15#21455862C211yesmaximal, characteristic, complemented
16#21454909C211yesmaximal, characteristic, complemented
17C61×#3239C211yesmaximal, characteristic, complemented
18C22×Q8×D61—21no—
19#16840497C2211yescharacteristic, complemented
20#16840494C2212yescomplemented
21Q8×Dic122C2211yescharacteristic, complemented
22#16840469C2211yescharacteristic, complemented
23#16840468C2212yescomplemented
24#16840433C2211yescharacteristic, complemented
25#16840427—21no—
26#16840427—22no—
27#16840427—21no—
28#16840427C2212yes—
29#16840427C2214yes—
30#16840427C2212yes—
31#16840421—21no—
32#16840416—21no—
33#16840410—22no—
34#16840383—21no—
35#16840378—22no—
36#16840312C2211yescharacteristic
37#16840307C2212yes—
38C2×#14519776C2212yes—
39#16840298C2212yes—
40C2×#14519755—22no—
41C2×#14519753—21no—
42#16840242—21no—
43C2×C4×Dic122C2211yescharacteristic
44C2×C4×D244C2211yescharacteristic
45C2×#14519739C2212yes—
46#16840170C2214yescomplemented
47#16840159C2214yescomplemented
48#16840158C2212yescomplemented
49#16840123C2214yescomplemented
50#16840110C2212yescomplemented
51#16840107C2214yescomplemented
52#16840095C2211yescharacteristic
53#16840081C2212yes—
54#16840080C2212yes—
55#16840080C2212yes—
56#16840078C2211yescharacteristic
57#16840065C2214yes—
58#16840059C2212yes—
59#16840053C2212yes—
60#16840051C2214yes—
61#16840051C2214yescomplemented
62#16840050C2214yescomplemented
63#16840049C2214yescomplemented
64#16840045C2214yescomplemented
65#16840041C2214yescomplemented
66#16839980C2214yes—
67#16839974C2212yes—
68#16839958C2212yes—
69#16839956C2214yes—
70#16839912C2211yescharacteristic
71#16839898C2212yes—
72#16839895C2211yescharacteristic
73#16839890C2214yescomplemented
74#16839889C2212yescomplemented
75#16839886C2212yescomplemented
76#16839875C2214yes—
77#16839873C2214yes—
78#16839871C2214yes—
79C4×#11758201C2212yes—
80#16839847C2214yes—
81#16839844C2214yes—
82C4×#11758199C2212yes—
83#16839816C2212yes—
84#16839815C2211yescharacteristic
85#16839812C2212yes—
86C2×C4⋊Q8×C61C2211yescharacteristic
87C61×#529C2211yescharacteristic
88C61×#501C2212yescomplemented
89C61×#489C2212yescomplemented
90C61×#484C2212yes—
91C61×#481C2212yes—
92C61×#475C2212yescomplemented
93C61×#474C2212yescomplemented
94C61×#432C2211yescharacteristic
95C2×#11758222—21no—
96C2×#11758222—21no—
97C2×#11758224—22no—
98C22×Dic122—22no—
99C22×Dic122D411yescharacteristic
100C2×Q8×D61—24no—
101C2×Q8×D61—22no—
102C2×Q8×D61—22no—
103C2×Q8×D61—48no—
104C22×D244C2311yescharacteristic
105C22×C4×D61—21no—
106C22×C4×D61—22no—
107C2×#11758201C2312yes—
108C2×D488C2314yes—
109C2×#11758199C2312yes—
110#14519777—21no—
111#14519777C2311yescharacteristic
112#14519776—22no—
113#14519776—22no—
114#14519776—22no—
115#14519776C2312yes—
116#14519776C2314yes—
117#14519776C2314yes—
118#14519774C2311yescharacteristic
119#14519773C2312yes—
120#14519772—22no—
121#14519768C2312yes—
122#14519766C2312yes—
123#14519765—21no—
124#14519765—21no—
125#14519763—22no—
126#14519763—22no—
127#14519762—22no—
128#14519761—22no—
129#14519761—22no—
130#14519759—22no—
131#14519757—22no—
132#14519756—21no—
133#14519755—22no—
134#14519755—22no—
135#14519755—24no—
136#14519755—24no—
137#14519755—24no—
138#14519755—24no—
139#14519754—22no—
140#14519753—22no—
141#14519753—22no—
142#14519753—24no—
143#14519751—21no—
144#14519751—21no—
145#14519751C2312yes—
146#14519750—22no—
147#14519749—22no—
148Q8×Dic61C2312yes—
149C4×Dic122—21no—
150C4×Dic122D411yescharacteristic
151C4×Dic122D412yes—
152C4×Dic122D411yescharacteristic
153C4×Dic122C2312yes—
154C4×Dic122C2311yescharacteristic
155C4×Dic122C2311yescharacteristic
156C4×D244—21no—
157C4×D244—21no—
158C4×D244—21no—
159C4×D244—21no—
160C4×D244C2312yes—
161C4×D244C2312yes—
162C4×D244C2312yes—
163D4×Dic61C2312yes—
164#14519739—22no—
165#14519739—22no—
166#14519739C2314yes—
167#14519739C2312yes—
168#14519739C2312yes—
169#14519739C2314yes—
170#14519737—22no—
171#14519737—22no—
172#14519737—22no—
173#14519735—22no—
174C2×C4⋊Dic61—21no—
175C2×C4⋊Dic61D411yescharacteristic
176C2×C4⋊Dic61C2311yescharacteristic
177C2×#11758196—22no—
178C2×#11758196D412yes—
179C4⋊C4×D61—22no—
180C2×#11758198—21no—
181C2×#11758198—22no—
182C2×C4×Dic61C2312yes—
183#14519710C2312yes—
184#14519709C2314yes—
185#14519708C2314yes—
186#14519708C2314yes—
187#14519708C2312yes—
188C4⋊#92418C2312yes—
189#14519706C2314yes—
190#14519706C2314yes—
191#14519701C2312yes—
192#14519699C2314yes—
193#14519699C2314yes—
194#14519698C2312yes—
195#14519697C2314yes—
196#14519697C2314yes—
197#14519697C2312yes—
198#14519697C2312yes—
199C22⋊#92418C2311yescharacteristic
200C22⋊#92418C2311yescharacteristic
201#14519687C2314yes—
202C4×#92418C2312yes—
203C8×Dic61C2314yes—
204C22×Q8×C61—21no—
205C4⋊Q8×C61—21no—
206C4⋊Q8×C61—21no—
207C4⋊Q8×C61C2312yes—
208C4⋊Q8×C61C2312yes—
209#126×C61—21no—
210#125×C61C2311yescharacteristic
211#124×C61C2311yescharacteristic
212#123×C61—21no—
213C22⋊Q8×C61C2311yescharacteristic
214#121×C61C2311yescharacteristic
215C4×Q8×C61C2311yescharacteristic
216C4×D4×C61—21no—
217C4×D4×C61C2311yescharacteristic
218#117×C61—21no—
219C2×C4⋊C4×C61—21no—
220C2×C4⋊C4×C61C2312yes—
221C2×C42×C61C2311yescharacteristic
222#107×C61C2314yes—
223#106×C61C2314yes—
224C4⋊C8×C61C2312yes—
225#103×C61C2314yes—
226#102×C61C2314yes—
227C22⋊C8×C61C2312yes—
228#97×C61C2312yes—
229C23×D61—21no—
230C2×Q8×C61—22no—
231C2×Q8×C61—22no—
232C2×Q8×C61—44no—
233C2×Q8×C61C2411yescharacteristic
234C2×D4×C61—21no—
235C2×D4×C61C2411yescharacteristic
236C22×C4×C61—22no—
237C22×C4×C61—21no—
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2×D411yescharacteristic
240C22×C4×C61C2411yescharacteristic
241C2×C22⋊D61—22no—
242C2×C22⋊D61—22no—
243C2×C22⋊D61—22no—
244C22×Dic61—21no—
245C22×Dic61—22no—
246C22×Dic61C2×D412yes—
247C22×Dic61C2×D412yes—
248Q8×D61—48no—
249Q8×D61—416no—
250Q8×D61—48no—
251#11758224—84no—
252#11758222—44no—
253#11758222—82no—
254C2×D244—21no—
255C2×D244—24no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244C2412yes—
259C2×D244C2412yes—
260C2×C4×D61—22no—
261C2×C4×D61—22no—
262C2×C4×D61—24no—
263C2×C4×D61—24no—
264C2×C4×D61—22no—
265C2×C4×D61—22no—
266C2×C4×D61—22no—
267C2×C4×D61—48no—
268C2×C4×D61—44no—
269C2×Dic122—24no—
270C2×Dic122—24no—
271C2×Dic122—24no—
272C2×Dic122—21no—
273C2×Dic122—22no—
274C2×Dic122—48no—
275C2×Dic122C2×D412yes—
276C2×Dic122C2×D411yescharacteristic
277C2×Dic122C2×D411yescharacteristic
278C2×C8×C61C2414yes—
279C4⋊C4×C61—22no—
280C4⋊C4×C61—22no—
281C4⋊C4×C61—22no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61—21no—
285C4⋊C4×C61—21no—
286C4⋊C4×C61C2414yes—
287C4⋊C4×C61C2411yescharacteristic
288C4⋊C4×C61C2411yescharacteristic
289C22⋊C4×C61—21no—
290C22⋊C4×C61—21no—
291C22⋊C4×C61—21no—
292C22⋊C4×C61—21no—
293C22⋊C4×C61—21no—
294C42×C61—21no—
295C42×C61C2×D411yescharacteristic
296C42×C61C2×D411yescharacteristic
297C42×C61C2411yescharacteristic
298C42×C61C2411yescharacteristic
299C22⋊Dic61—22no—
300#11758201—24no—
301#11758199—24no—
302#11758198—22no—
303#11758198—22no—
304#11758198—22no—
305#11758198—22no—
306#11758198—24no—
307#11758198—24no—
308#11758198—22no—
309#11758198—22no—
310#11758198—22no—
311#11758198—22no—
312C4⋊Dic61—21no—
313C4⋊Dic61—21no—
314C4⋊Dic61—22no—
315C4⋊Dic61—22no—
316C4⋊Dic61C2×D411yescharacteristic
317C4⋊Dic61C2×D411yescharacteristic
318C4⋊Dic61C2×D412yes—
319C4⋊Dic61C2412yes—
320C4⋊Dic61C2412yes—
321#11758196—22no—
322#11758196—24no—
323#11758196—24no—
324#11758196—22no—
325#11758196C2×D412yes—
326#11758196C2×D412yes—
327#11758196C2×D412yes—
328#11758196C2×D412yes—
329C4×Dic61—22no—
330C4×Dic61C2×D412yes—
331C4×Dic61C2×D412yes—
332C4×Dic61C2412yes—
333C4×Dic61C2412yes—
334C2×#92418C2412yes—
335C2×#92418C2412yes—
336D488—28no—
337C23×C61—21no—
338C23×C61C22×D411yescharacteristic
339C22×D61—24no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—42no—
343C22×D61—42no—
344Q8×C61—22no—
345Q8×C61—44no—
346Q8×C61—44no—
347D4×C61—22no—
348D4×C61—42no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—24no—
356C2×C4×C61—44no—
357C2×C4×C61—42no—
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C22×D411yescharacteristic
361C2×C4×C61C22×D411yescharacteristic
362C2×C4×C61C22×D411yescharacteristic
363C2×C4×C61C2511yescharacteristic
364C22⋊D61—44no—
365C22⋊D61—44no—
366C22⋊D61—82no—
367C2×Dic61—24no—
368C2×Dic61—24no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—42no—
372C2×Dic61—82no—
373C2×Dic61C22×D412yes—
374C2×Dic61C22×D412yes—
375C2×Dic61C22×D412yes—
376C2×Dic61C22×D412yes—
377D244—24no—
378D244—22no—
379D244—24no—
380D244—42no—
381D244—81no—
382D2442−1+414yes—
383C4×D61—48no—
384C4×D61—44no—
385C4×D61—44no—
386C4×D61—48no—
387C4×D61—44no—
388C4×D61—82no—
389C4×D61—82no—
390Dic122—22no—
391Dic122—24no—
392Dic122—48no—
393Dic122—48no—
394Dic122—82no—
395Dic122—81no—
396Dic122AGL(1,ℤ/8)14yes—
397C8×C61—24no—
398#92418—22no—
399#92418—22no—
400#61843—611nomaximal, Sylow
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—41no—
404C22×C61—41no—
405C22×C61—41no—
406C22×C61#57712yes—
407C22×C61C23×D411yescharacteristic
408C2×D61—24no—
409C2×D61—48no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C4×C61—21no—
416C4×C61—21no—
417C4×C61—21no—
418C4×C61—21no—
419C4×C61—41no—
420C4×C61—44no—
421C4×C61—41no—
422C4×C61—41no—
423C4×C61C2×AGL(1,ℤ/8)12yes—
424C4×C61C2×2−1+412yes—
425Dic61—22no—
426Dic61—22no—
427Dic61—22no—
428Dic61—42no—
429Dic61—42no—
430Dic61C2×AGL(1,ℤ/8)14yes—
431#3522—611no—
432C2×D4×Q8—611no—
433#3384—614no—
434#3384—612no—
435Q8×SD16—612no—
436#3373—614no—
437#3373—612no—
438#3358—612no—
439#3239—612no—
440#3239D6111yescharacteristic, complemented
441#3227—612no—
442#3227—611no—
443#3109—612no—
444#3109—611no—
445#3105—612no—
446#3105—611no—
447#2984—611no—
448C2×C61—22no—
449C2×C61—81no—
450C2×C61#348611yescharacteristic
451C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
452C2×C61C2×#57711yescharacteristic
453D61—44no—
454D61—82no—
455C23×Q8—1221no—
456#559—612no—
457#559—611no—
458Q82—611no—
459#554—612no—
460#554—611no—
461#550—611no—
462D4×Q8—612no—
463D4×Q8—614no—
464D4×Q8—612no—
465D4×Q8—1221no—
466D4×Q8—1222no—
467D4×Q8—1221no—
468#548—1221no—
469#547—1221no—
470#547—1222no—
471#542—1221no—
472#542—1222no—
473#532—612no—
474#532—611no—
475C2×C4⋊Q8—612no—
476C2×C4⋊Q8C2×D6111yescharacteristic
477#529—612no—
478#529C2×D6111yescharacteristic
479C2×C22⋊Q8—1222no—
480C2×C22⋊Q8—1221no—
481#520—1221no—
482C2×C4×Q8—611no—
483C2×C4×D4—612no—
484C2×C4×D4—611no—
485#501—614no—
486#501C2×D6112yescomplemented
487#498—612no—
488#498—614no—
489#489—614no—
490#489C2×D6112yescomplemented
491#486—612no—
492#486—614no—
493#484—611no—
494#484C2×D6112yes—
495#481—611no—
496#481—612no—
497#481—612no—
498#481—612no—
499#481C2×D6112yes—
500#478—612no—
501#478—614no—
502#476—614no—
503#476—614no—
504#476—614no—
505#476—612no—
506#476—614no—
507#475—614no—
508#475C2×D6112yescomplemented
509#474—614no—
510#474C2×D6112yescomplemented
511#463—612no—
512#463—614no—
513#459—612no—
514#459—614no—
515#450—611no—
516#447—611no—
517#447—612no—
518#446—612no—
519#446—614no—
520C8×Q8—612no—
521#442—614no—
522#442—614no—
523#442—614no—
524C4×SD16—612no—
525C4×SD16—614no—
526C4×D8—612no—
527C4×D8—614no—
528#432—612no—
529#432C2×D6111yescharacteristic
530#431—611no—
531#431—612no—
532C61#6184311yescharacteristic, complemented, Sylow
533C2×#41—1221no—
534C2×#41—1222no—
535C2×#41—1221no—
536C22×Q8—21no—
537C22×Q8—611no—
538C22×Q8—1222no—
539C22×Q8—1222no—
540C22×Q8—1224no—
541C22×Q8—1222no—
542C22×Q8—2448no—
543C22×D4—611no—
544C23×C4—1222no—
545C23×C4—1221no—
546C2×SD16—612no—
547C2×D8—612no—
548C2×D8—614no—
549C4⋊Q8—21no—
550C4⋊Q8—21no—
551C4⋊Q8—614no—
552C4⋊Q8—614no—
553C4⋊Q8—612no—
554C4⋊Q8—611no—
555C4⋊Q8—1221no—
556C4⋊Q8—1222no—
557C4⋊Q8—1222no—
558C4⋊Q8—1222no—
559C4⋊Q8C22×D6112yes—
560C4⋊Q8C22×D6112yes—
561#127—612no—
562#127—611no—
563#126—21no—
564#126—1222no—
565#125—612no—
566#125C22×D6111yescharacteristic
567#124—612no—
568#124—1221no—
569#124—1222no—
570#124—1222no—
571#124—1221no—
572#124C22×D6111yescharacteristic
573#123—21no—
574#123—1222no—
575#123—1222no—
576#123—1222no—
577#123—1222no—
578C22⋊Q8—1222no—
579C22⋊Q8—1224no—
580C22⋊Q8—1224no—
581C22⋊Q8—1224no—
582C22⋊Q8—1224no—
583C22⋊Q8—1222no—
584C22⋊Q8—1222no—
585C22⋊Q8—1222no—
586C22⋊Q8—1222no—
587C22⋊Q8—1222no—
588C22⋊Q8—1224no—
589C22⋊Q8—1221no—
590C22⋊Q8C22×D6111yescharacteristic
591#121—612no—
592#121—1222no—
593#121—1221no—
594#121—1222no—
595#121—1221no—
596#121C22×D6111yescharacteristic
597C4×Q8—611no—
598C4×Q8—612no—
599C4×Q8—611no—
600C4×Q8—611no—
601C4×Q8—612no—
602C4×Q8—611no—
603C4×Q8—612no—
604C4×Q8—1221no—
605C4×Q8C22×D6111yescharacteristic
606C4×D4—21no—
607C4×D4—612no—
608C4×D4—614no—
609C4×D4—614no—
610C4×D4—612no—
611C4×D4—612no—
612C4×D4—612no—
613C4×D4—612no—
614C4×D4—612no—
615C4×D4—1221no—
616C4×D4—1222no—
617C4×D4—1222no—
618C4×D4—1222no—
619C4×D4—1222no—
620C4×D4—1222no—
621C4×D4—1221no—
622C4×D4—1221no—
623C4×D4—1221no—
624C4×D4C22×D6111yescharacteristic
625#117—21no—
626#117—1222no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—612no—
629C2×C4⋊C4—611no—
630C2×C4⋊C4—611no—
631C2×C4⋊C4—1222no—
632C2×C4⋊C4—1221no—
633C2×C4⋊C4—1222no—
634C2×C4⋊C4C22×D6112yes—
635C2×C22⋊C4—1222no—
636C2×C22⋊C4—1221no—
637C2×C42—612no—
638C2×C42C22×D6111yescharacteristic
639#107—612no—
640#107C22×D6114yes—
641#106—614no—
642#106—612no—
643#106—614no—
644#106—614no—
645#106C22×D6114yes—
646C4⋊C8—614no—
647C4⋊C8—614no—
648C4⋊C8—612no—
649C4⋊C8C22×D6112yes—
650#103—612no—
651#103C22×D6114yes—
652#102—612no—
653#102—614no—
654#102—614no—
655#102—612no—
656#102—614no—
657#102—612no—
658#102—614no—
659#102C22×D6114yes—
660C22⋊C8—611no—
661C22⋊C8—611no—
662C22⋊C8C22×D6112yes—
663#97—614no—
664#97C22×D6112yes—
665C4×C8—614no—
666C4×C8—612no—
667C24—1221no—
668#41—4882no—
669#41—4884no—
670#41—2444no—
671C2×Q8—22no—
672C2×Q8—22no—
673C2×Q8—44no—
674C2×Q8—611no—
675C2×Q8—612no—
676C2×Q8—611no—
677C2×Q8—1222no—
678C2×Q8—1224no—
679C2×Q8—1224no—
680C2×Q8—1224no—
681C2×Q8—1221no—
682C2×Q8—2448no—
683C2×Q8—2448no—
684C2×Q8—24416no—
685C2×Q8—2448no—
686C2×Q8C23×D6111yescharacteristic
687C2×D4—21no—
688C2×D4—612no—
689C2×D4—612no—
690C2×D4—1224no—
691C2×D4—1222no—
692C2×D4—1222no—
693C2×D4—1222no—
694C2×D4—1221no—
695C2×D4—1221no—
696C2×D4—1221no—
697C2×D4C23×D6111yescharacteristic
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—612no—
701C22×C4—612no—
702C22×C4—1222no—
703C22×C4—1222no—
704C22×C4—1224no—
705C22×C4—1224no—
706C22×C4—1222no—
707C22×C4—1221no—
708C22×C4—1222no—
709C22×C4—1222no—
710C22×C4—1222no—
711C22×C4—2444no—
712C22×C4—2448no—
713C22×C4D4×D6111yescharacteristic
714C22×C4D4×D6111yescharacteristic
715C22×C4C23×D6111yescharacteristic
716SD16—1224no—
717D8—1228no—
718D8—1224no—
719C2×C8—612no—
720C2×C8—612no—
721C2×C8C23×D6114yes—
722C4⋊C4—22no—
723C4⋊C4—22no—
724C4⋊C4—21no—
725C4⋊C4—22no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—612no—
730C4⋊C4—611no—
731C4⋊C4—612no—
732C4⋊C4—612no—
733C4⋊C4—612no—
734C4⋊C4—611no—
735C4⋊C4—612no—
736C4⋊C4—612no—
737C4⋊C4—612no—
738C4⋊C4—1222no—
739C4⋊C4—1222no—
740C4⋊C4—1224no—
741C4⋊C4—1224no—
742C4⋊C4—1222no—
743C4⋊C4—1222no—
744C4⋊C4—1221no—
745C4⋊C4—1221no—
746C4⋊C4C23×D6114yes—
747C4⋊C4C23×D6111yescharacteristic
748C4⋊C4C23×D6111yescharacteristic
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—1224no—
755C22⋊C4—1224no—
756C22⋊C4—1222no—
757C22⋊C4—1222no—
758C22⋊C4—1222no—
759C22⋊C4—1222no—
760C22⋊C4—1222no—
761C22⋊C4—1222no—
762C22⋊C4—1222no—
763C22⋊C4—1222no—
764C22⋊C4—1222no—
765C42—21no—
766C42—612no—
767C42—612no—
768C42—612no—
769C42—612no—
770C42—1222no—
771C42D4×D6111yescharacteristic
772C42D4×D6111yescharacteristic
773C42C23×D6111yescharacteristic
774C42C23×D6111yescharacteristic
775C23—21no—
776C23—1224no—
777C23—1222no—
778C23—1222no—
779C23—2442no—
780C23—2442no—
781C23C2×D4×D6111yescharacteristic
782Q8—22no—
783Q8—44no—
784Q8—44no—
785Q8—614no—
786Q8—1224no—
787Q8—1222no—
788Q8—4881no—
789Q8—4882no—
790Q8—2448no—
791Q8—2448no—
792D4—22no—
793D4—42no—
794D4—614no—
795D4—1224no—
796D4—1222no—
797D4—1224no—
798D4—4881no—
799D4—4882no—
800D4—2444no—
801D4—2444no—
802D4—2442no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—24no—
810C2×C4—44no—
811C2×C4—42no—
812C2×C4—612no—
813C2×C4—612no—
814C2×C4—612no—
815C2×C4—612no—
816C2×C4—1224no—
817C2×C4—1224no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—4882no—
821C2×C4—4882no—
822C2×C4—4882no—
823C2×C4—2444no—
824C2×C4—2448no—
825C2×C4—2444no—
826C2×C4—2448no—
827C2×C4—2442no—
828C2×C4—2444no—
829C2×C4C2×D4×D6111yescharacteristic
830C2×C4C2×D4×D6111yescharacteristic
831C2×C4C2×D4×D6111yescharacteristic
832C2×C4C2×D4×D6111yescharacteristic
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4C24×D6111yescharacteristic
835C8—24no—
836C8—1222no—
837C8—1222no—
838C22—21no—
839C22—21no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—1224no—
844C22—2448no—
845C22—2442no—
846C22—2442no—
847C22—2442no—
848C22—2442no—
849C22—2442no—
850C22#1684057112yes—
851C22C22×D4×D6111yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—41no—
857C4—41no—
858C4—44no—
859C4—41no—
860C4—614no—
861C4—1222no—
862C4—1222no—
863C4—1222no—
864C4—2442no—
865C4—2442no—
866C4AGL(1,ℤ/8)×D6112yes—
867C42−1+4×D6112yes—
868C2—22no—
869C2—81no—
870C2—4882no—
871C2—2444no—
872C2#2145946811yescharacteristic
873C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
874C2C2×#1684057111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3239C2
socleC22×C61C23×D4
hypercenter#3239D61
hypocenterC61#61843
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3239

Complements

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

NH ≅ G/Ntype
1. #21459902C2semidirect
2. C2×#16840427C2semidirect
3. #21458722C2semidirect
4. #21458715C2semidirect
5. #21458678C2semidirect
6. #21458610C2semidirect
7. #21458608C2semidirect
8. #21458453C2semidirect
9. #21457052C2semidirect
10. #21456947C2semidirect
11. #21456945C2semidirect
12. #21455911C2semidirect
13. #21455907C2semidirect
14. #21455869C2semidirect
15. #21455862C2semidirect
16. #21454909C2semidirect
17. C61×#3239C2semidirect
19. #16840497C22semidirect
20. #16840494C22semidirect
21. Q8×Dic122C22semidirect
22. #16840469C22semidirect
23. #16840468C22semidirect
24. #16840433C22semidirect
46. #16840170C22semidirect
47. #16840159C22semidirect
48. #16840158C22semidirect
49. #16840123C22semidirect
50. #16840110C22semidirect
51. #16840107C22semidirect
61. #16840051C22semidirect
62. #16840050C22semidirect
63. #16840049C22semidirect
64. #16840045C22semidirect
65. #16840041C22semidirect
73. #16839890C22semidirect
74. #16839889C22semidirect
75. #16839886C22semidirect
88. C61×#501C22semidirect
89. C61×#489C22semidirect
92. C61×#475C22semidirect
93. C61×#474C22semidirect
440. #3239D61semidirect
486. #501C2×D61semidirect
490. #489C2×D61semidirect
508. #475C2×D61semidirect
510. #474C2×D61semidirect
532. C61#61843semidirect

Maximal subgroups

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

subgroupindex
#214599022
C2×#168404272
#214587222
#214587152
#214586782
#214586102
#214586082
#214584532
#214570522
#214569472
#214569452
#214559112
#214559072
#214558692
#214558622
#214549092
C61×#32392
#6184361