Finite Group Databasebeta

← #30571179

Subgroups — #30571179

Order 15616.

1794 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840497C211yesmaximal, characteristic, complemented
2#21458903C214yesmaximal, complemented
3#21458885C214yesmaximal, complemented
4#21458587C214yesmaximal, complemented
5#21458572C214yesmaximal, complemented
6#21456834C212yesmaximal, complemented
7#21456818C211yesmaximal, characteristic, complemented
8#21456802C211yesmaximal, characteristic, complemented
9#21456780C212yesmaximal, complemented
10#21455986C212yesmaximal, complemented
11#21455914C211yesmaximal, characteristic, complemented
12#21455906C211yesmaximal, characteristic, complemented
13#21455862C212yesmaximal, complemented
14#21454904C211yesmaximal, characteristic, complemented
15C61×#3507C211yesmaximal, characteristic, complemented
16#16840497—22no—
17#16840497—22no—
18#16840497C2214yes—
19#16840497C2214yes—
20C2×#14519774C2211yescharacteristic
21C2×#14519766—21no—
22C2×#14519765C2211yescharacteristic
23C2×#14519765C2211yescharacteristic
24C2×#14519762—21no—
25C2×#14519762—21no—
26C2×C4×Dic122C2211yescharacteristic
27C2×C4×D244C2211yescharacteristic
28C2×C4×D244C2211yescharacteristic
29C2×#14519739—21no—
30#16840154C2212yescomplemented
31#16840152C2214yes—
32#16840149C2212yescomplemented
33#16840144C2214yescomplemented
34#16840128C2214yes—
35#16840124C2212yescomplemented
36#16840124C2212yescomplemented
37#16840119C2214yescomplemented
38#16840095C2212yes—
39#16840078C2212yes—
40#16840066C2214yescomplemented
41#16840059C2214yescomplemented
42#16840049C2212yescomplemented
43#16840039C2212yescomplemented
44#16839984C2214yescomplemented
45#16839984C2214yescomplemented
46#16839981C2214yescomplemented
47#16839977C2214yescomplemented
48#16839977C2214yescomplemented
49#16839974C2214yescomplemented
50#16839964C2212yescomplemented
51#16839962C2214yes—
52#16839957C2214yes—
53#16839954C2212yescomplemented
54#16839917C2212yes—
55#16839912C2212yes—
56#16839912C2212yes—
57#16839900C2212yes—
58#16839895C2212yes—
59#16839895C2212yes—
60#16839893C2214yescomplemented
61#16839893C2214yescomplemented
62#16839872C2214yescomplemented
63#16839867C2214yescomplemented
64#16839862C2214yescomplemented
65#16839860C2214yescomplemented
66C4×#11758201C2214yescomplemented
67C4×#11758199C2214yescomplemented
68#16839819C2211yescharacteristic
69#16839819C2211yescharacteristic
70#16839819C2212yes—
71#16839815C2212yes—
72C61×#559C2212yescomplemented
73C61×#557C2212yescomplemented
74C61×#556—22no—
75C61×#556C2212yescomplemented
76C61×#554C2212yescomplemented
77C61×#552—22no—
78C61×#539—21no—
79C61×#539—21no—
80C61×#536—21no—
81C61×#533C2211yescharacteristic
82C61×#532C2211yescharacteristic
83C61×#529C2212yes—
84C61×#529C2212yes—
85C61×#520—21no—
86C2×C4×Q8×C61C2211yescharacteristic
87C22×Dic122C2311yescharacteristic
88C22×D244—21no—
89C22×D244—21no—
90C22×D244C2311yescharacteristic
91C22×D244C2311yescharacteristic
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C2×#11758202C2314yes—
95C2×#11758200C2314yes—
96C2×#11758201C2314yes—
97C2×#11758201C2314yes—
98C2×#11758199C2314yes—
99C2×#11758199C2314yes—
100#14519774—22no—
101#14519774C2314yes—
102#14519766—24no—
103#14519766—24no—
104#14519765—22no—
105#14519765—21no—
106#14519765—21no—
107#14519765C2312yes—
108#14519765C2314yes—
109#14519765C2312yes—
110#14519762—24no—
111#14519762—24no—
112#14519762—24no—
113#14519762—24no—
114C4×Dic122—22no—
115C4×Dic122C2314yes—
116C4×D244—22no—
117C4×D244—21no—
118C4×D244—21no—
119C4×D244C2312yes—
120C4×D244C2312yes—
121C4×D244C2314yes—
122#14519739—24no—
123#14519739—24no—
124C2×C4⋊Dic61C2311yescharacteristic
125C2×#11758196—21no—
126C2×#11758198—21no—
127C2×#11758198—21no—
128C2×#11758198—21no—
129C2×#11758198—21no—
130C2×#11758198—21no—
131C2×#11758198—21no—
132C2×C4×Dic61—21no—
133#14519710C2314yes—
134#14519708C2314yes—
135C4⋊#92418C2312yes—
136C4⋊#92418C2314yes—
137C4⋊#92418C2312yes—
138C4⋊#92418C2314yes—
139#14519701C2314yes—
140#14519700C2314yes—
141#14519700C2314yes—
142#14519698C2314yes—
143#14519697C2314yes—
144#14519697C2314yes—
145#14519697C2314yes—
146#14519697C2314yes—
147C22⋊#92418C2312yes—
148C22⋊#92418C2312yes—
149#14519688C2312yes—
150#14519688C2314yes—
151#14519688C2312yes—
152C4×#92418C2314yes—
153C2×#41×C61—21no—
154C22×Q8×C61D411yescharacteristic
155C4⋊Q8×C61—22no—
156C4⋊Q8×C61C2311yescharacteristic
157C4⋊Q8×C61C2311yescharacteristic
158C4⋊Q8×C61C2311yescharacteristic
159#127×C61C2311yescharacteristic
160#126×C61—22no—
161#126×C61—22no—
162#126×C61—22no—
163#126×C61—22no—
164#125×C61—22no—
165#125×C61—22no—
166#125×C61—21no—
167#125×C61C2312yes—
168#125×C61C2312yes—
169#124×C61—22no—
170#124×C61—21no—
171#124×C61C2312yes—
172#124×C61C2312yes—
173#123×C61—22no—
174#123×C61—22no—
175#123×C61—22no—
176#123×C61—22no—
177C22⋊Q8×C61—22no—
178C22⋊Q8×C61—22no—
179C22⋊Q8×C61—21no—
180C22⋊Q8×C61—22no—
181C22⋊Q8×C61—22no—
182C22⋊Q8×C61C2312yes—
183#121×C61—21no—
184#121×C61C2312yes—
185C4×Q8×C61—22no—
186C4×Q8×C61—21no—
187C4×Q8×C61D412yes—
188C4×Q8×C61D412yes—
189C4×Q8×C61C2312yes—
190C4×Q8×C61C2312yes—
191C4×Q8×C61C2312yes—
192C4×Q8×C61C2312yes—
193C4×Q8×C61C2312yes—
194C4×D4×C61—22no—
195C4×D4×C61—22no—
196C4×D4×C61—22no—
197C4×D4×C61—21no—
198C4×D4×C61C2312yes—
199C4×D4×C61C2312yes—
200C4×D4×C61C2312yes—
201#117×C61—21no—
202#117×C61—22no—
203#117×C61—22no—
204#117×C61—22no—
205C2×C4⋊C4×C61—22no—
206C2×C4⋊C4×C61D411yescharacteristic
207C2×C4⋊C4×C61D411yescharacteristic
208C2×C4⋊C4×C61D411yescharacteristic
209C2×C42×C61C2311yescharacteristic
210C2×C42×C61C2311yescharacteristic
211C2×C42×C61C2311yescharacteristic
212C23×D61—21no—
213C23×D61—21no—
214#41×C61—44no—
215C2×Q8×C61—21no—
216C2×Q8×C61—21no—
217C2×Q8×C61—42no—
218C2×Q8×C61C2×D412yes—
219C2×Q8×C61C2×D412yes—
220C2×Q8×C61C2412yes—
221C2×D4×C61—22no—
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61C2412yes—
225C22×C4×C61—22no—
226C22×C4×C61—22no—
227C22×C4×C61—22no—
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2411yescharacteristic
235C22×Dic61—21no—
236C22×Dic61—21no—
237C2×D244—24no—
238C2×D244—21no—
239C2×D244—21no—
240C2×D244—24no—
241C2×D244—42no—
242C2×D244—42no—
243C2×D244—44no—
244C2×D244—82no—
245C2×D244C2412yes—
246C2×D244C2412yes—
247C2×C4×D61—24no—
248C2×C4×D61—22no—
249C2×C4×D61—22no—
250C2×C4×D61—82no—
251C2×C4×D61—82no—
252C2×Dic122—21no—
253C2×Dic122—42no—
254C2×Dic122C2412yes—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—22no—
257C4⋊C4×C61—22no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—22no—
260C4⋊C4×C61—22no—
261C4⋊C4×C61—22no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—22no—
265C4⋊C4×C61—22no—
266C4⋊C4×C61—22no—
267C4⋊C4×C61C2×D412yes—
268C4⋊C4×C61C2×D412yes—
269C4⋊C4×C61C2×D412yes—
270C4⋊C4×C61C2×D412yes—
271C4⋊C4×C61C2×D412yes—
272C4⋊C4×C61C2×D412yes—
273C4⋊C4×C61C2412yes—
274C4⋊C4×C61C2412yes—
275C22⋊C4×C61—22no—
276C22⋊C4×C61—22no—
277C22⋊C4×C61—22no—
278C22⋊C4×C61—22no—
279C22⋊C4×C61—22no—
280C22⋊C4×C61—22no—
281C22⋊C4×C61—22no—
282C22⋊C4×C61—22no—
283C22⋊C4×C61—22no—
284C42×C61—22no—
285C42×C61—22no—
286C42×C61—22no—
287C42×C61C2×D412yes—
288C42×C61C2×D412yes—
289C42×C61C2×D411yescharacteristic
290C42×C61C2×D411yescharacteristic
291C42×C61C2411yescharacteristic
292C42×C61C2412yes—
293C42×C61C2412yes—
294C42×C61C2411yescharacteristic
295#11758202—44no—
296#11758201—44no—
297#11758201—44no—
298#11758200—44no—
299#11758199—44no—
300#11758199—44no—
301#11758198—24no—
302#11758198—22no—
303#11758198—22no—
304#11758198—22no—
305#11758198—24no—
306#11758198—22no—
307#11758198—22no—
308#11758198—24no—
309#11758198—22no—
310C4⋊Dic61—21no—
311C4⋊Dic61C2412yes—
312#11758196—24no—
313C4×Dic61—24no—
314C2×#92418C2414yes—
315C2×#92418C2414yes—
316C23×C61—22no—
317C23×C61C22×D411yescharacteristic
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—42no—
321C22×D61—42no—
322C22×D61—42no—
323C22×D61—42no—
324C22×D61—42no—
325C22×D61—42no—
326Q8×C61—24no—
327Q8×C61—42no—
328Q8×C61—42no—
329Q8×C61—42no—
330Q8×C61—81no—
331D4×C61—24no—
332D4×C61—42no—
333D4×C61—44no—
334D4×C61—81no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—44no—
346C2×C4×C61—82no—
347C2×C4×C61—82no—
348C2×C4×C61C22×D412yes—
349C2×C4×C61C22×D412yes—
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C22×D412yes—
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D412yes—
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C2511yescharacteristic
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—42no—
361C2×Dic61—42no—
362D244—22no—
363D244—24no—
364D244—22no—
365D244—42no—
366D244—42no—
367D244—48no—
368D244—84no—
369C4×D61—84no—
370C4×D61—82no—
371C4×D61—82no—
372Dic122—24no—
373Dic122—42no—
374#92418—24no—
375#92418—24no—
376#61895—611nomaximal, Sylow
377C22×C61—21no—
378C22×C61—21no—
379C22×C61—42no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61#57512yes—
383C22×C61C23×D411yescharacteristic
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—84no—
391C2×D61—84no—
392C4×C61—22no—
393C4×C61—21no—
394C4×C61—21no—
395C4×C61—22no—
396C4×C61—21no—
397C4×C61—22no—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—22no—
401C4×C61—42no—
402C4×C61—42no—
403C4×C61—42no—
404C4×C61#58512yes—
405Dic61—42no—
406Dic61—42no—
407#3507D6111yescharacteristic, complemented
408C2×#559—611no—
409#3403—614no—
410#3401—614no—
411#3371—614no—
412#3370—614no—
413#3217—612no—
414#3215—611no—
415#3213—611no—
416#3211—612no—
417#3117—612no—
418#3110—611no—
419#3109—611no—
420#3105—612no—
421#2983—611no—
422C2×C61—22no—
423C2×C61—82no—
424C2×C61#348711yescharacteristic
425C2×C61C2×#57511yescharacteristic
426C2×C61#358511yescharacteristic
427D61—82no—
428D61—82no—
429#559—614no—
430#559—614no—
431#559—1222no—
432#559—1222no—
433#559C2×D6112yescomplemented
434#557C2×D6112yescomplemented
435#556—22no—
436#556C2×D6112yescomplemented
437#554C2×D6112yescomplemented
438#552—22no—
439#539—21no—
440#539—21no—
441#536—21no—
442#533C2×D6111yescharacteristic
443#532C2×D6111yescharacteristic
444C2×#127—611no—
445#529C2×D6112yes—
446#529C2×D6112yes—
447C2×#124—611no—
448C2×#124—611no—
449C2×#124—1221no—
450C2×#123—1221no—
451C2×#123—1221no—
452#520—21no—
453C2×C4×Q8—611no—
454C2×C4×Q8C2×D6111yescharacteristic
455C2×C4×D4—611no—
456C2×C4×D4—611no—
457C2×C4×D4—1221no—
458#497—612no—
459#496—612no—
460#496—614no—
461#495—614no—
462#490—614no—
463#489—612no—
464#489—612no—
465#488—614no—
466#484—612no—
467#481—612no—
468#479—614no—
469#478—614no—
470#476—612no—
471#474—612no—
472#464—614no—
473#464—614no—
474#464—614no—
475#463—614no—
476#463—614no—
477#463—614no—
478#461—612no—
479#460—614no—
480#459—612no—
481#459—614no—
482#451—612no—
483#450—612no—
484#450—612no—
485#448—612no—
486#447—612no—
487#447—612no—
488#446—614no—
489#446—614no—
490#442—614no—
491#441—614no—
492#440—614no—
493#440—614no—
494C4×SD16—614no—
495C4×D8—614no—
496#432—611no—
497#432—611no—
498#432—612no—
499#431—612no—
500C61#6189511yescharacteristic, complemented, Sylow
501C2×#41—21no—
502C22×Q8—611no—
503C22×Q8C22⋊D6111yescharacteristic
504C22×D4—611no—
505C22×D4—611no—
506C22×D4—1221no—
507C22×D4—1221no—
508C23×C4—1221no—
509C23×C4—1221no—
510C2×Q16—614no—
511C2×SD16—614no—
512C2×SD16—614no—
513C2×SD16—614no—
514C2×D8—614no—
515C2×D8—614no—
516C4⋊Q8—22no—
517C4⋊Q8C22×D6111yescharacteristic
518C4⋊Q8C22×D6111yescharacteristic
519C4⋊Q8C22×D6111yescharacteristic
520#127—614no—
521#127—1222no—
522#127C22×D6111yescharacteristic
523#126—22no—
524#126—22no—
525#126—22no—
526#126—22no—
527#125—22no—
528#125—22no—
529#125—21no—
530#125C22×D6112yes—
531#125C22×D6112yes—
532#124—22no—
533#124—21no—
534#124—612no—
535#124—614no—
536#124—612no—
537#124—1224no—
538#124—1224no—
539#124—1222no—
540#124—1221no—
541#124—1221no—
542#124C22×D6112yes—
543#124C22×D6112yes—
544#123—22no—
545#123—22no—
546#123—22no—
547#123—22no—
548#123—1224no—
549#123—1224no—
550#123—1224no—
551#123—1224no—
552C22⋊Q8—22no—
553C22⋊Q8—22no—
554C22⋊Q8—21no—
555C22⋊Q8—22no—
556C22⋊Q8—22no—
557C22⋊Q8C22×D6112yes—
558#121—21no—
559#121C22×D6112yes—
560C4×Q8—22no—
561C4×Q8—21no—
562C4×Q8—614no—
563C4×Q8—1222no—
564C4×Q8C22⋊D6112yes—
565C4×Q8C22⋊D6112yes—
566C4×Q8C22×D6112yes—
567C4×Q8C22×D6112yes—
568C4×Q8C22×D6112yes—
569C4×Q8C22×D6112yes—
570C4×Q8C22×D6112yes—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—21no—
575C4×D4—614no—
576C4×D4—612no—
577C4×D4—612no—
578C4×D4—1224no—
579C4×D4—1224no—
580C4×D4—1222no—
581C4×D4—1221no—
582C4×D4—1221no—
583C4×D4C22×D6112yes—
584C4×D4C22×D6112yes—
585C4×D4C22×D6112yes—
586#117—21no—
587#117—22no—
588#117—22no—
589#117—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—1221no—
593C2×C4⋊C4C22⋊D6111yescharacteristic
594C2×C4⋊C4C22⋊D6111yescharacteristic
595C2×C4⋊C4C22⋊D6111yescharacteristic
596C2×C22⋊C4—1221no—
597C2×C22⋊C4—1221no—
598C2×C22⋊C4—1221no—
599C2×C22⋊C4—1221no—
600C2×C22⋊C4—1221no—
601C2×C22⋊C4—1221no—
602C2×C42—1221no—
603C2×C42C22×D6111yescharacteristic
604C2×C42C22×D6111yescharacteristic
605C2×C42C22×D6111yescharacteristic
606#107—614no—
607#106—614no—
608C4⋊C8—614no—
609C4⋊C8—614no—
610C4⋊C8—612no—
611C4⋊C8—612no—
612#103—614no—
613#103—614no—
614#103—614no—
615#102—614no—
616#102—614no—
617#102—614no—
618#102—614no—
619#102—614no—
620C22⋊C8—612no—
621C22⋊C8—612no—
622#97—612no—
623#97—614no—
624#97—612no—
625C4×C8—614no—
626C24—1221no—
627C24—1221no—
628#41—44no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—42no—
632C2×Q8—612no—
633C2×Q8—1221no—
634C2×Q8—2442no—
635C2×Q8C2×C22⋊D6112yes—
636C2×Q8C2×C22⋊D6112yes—
637C2×Q8C23×D6112yes—
638C2×D4—22no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—612no—
642C2×D4—612no—
643C2×D4—1224no—
644C2×D4—1224no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—4882no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4—2444no—
651C2×D4C23×D6112yes—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1224no—
658C22×C4—1222no—
659C22×C4—1222no—
660C22×C4—4882no—
661C22×C4—4882no—
662C22×C4C2×C22⋊D6111yescharacteristic
663C22×C4C2×C22⋊D6111yescharacteristic
664C22×C4C2×C22⋊D6111yescharacteristic
665C22×C4C2×C22⋊D6111yescharacteristic
666C22×C4C2×C22⋊D6111yescharacteristic
667C22×C4C2×C22⋊D6111yescharacteristic
668C22×C4C23×D6111yescharacteristic
669Q16—2444no—
670SD16—2444no—
671SD16—2444no—
672SD16—2444no—
673D8—2444no—
674D8—2444no—
675C2×C8—614no—
676C2×C8—614no—
677C4⋊C4—21no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—21no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—612no—
690C4⋊C4—1221no—
691C4⋊C4—1224no—
692C4⋊C4C2×C22⋊D6112yes—
693C4⋊C4C2×C22⋊D6112yes—
694C4⋊C4C2×C22⋊D6112yes—
695C4⋊C4C2×C22⋊D6112yes—
696C4⋊C4C2×C22⋊D6112yes—
697C4⋊C4C2×C22⋊D6112yes—
698C4⋊C4C23×D6112yes—
699C4⋊C4C23×D6112yes—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—1222no—
710C22⋊C4—1224no—
711C22⋊C4—1222no—
712C22⋊C4—1224no—
713C22⋊C4—1222no—
714C22⋊C4—1222no—
715C22⋊C4—1222no—
716C22⋊C4—1224no—
717C22⋊C4—1222no—
718C42—22no—
719C42—22no—
720C42—22no—
721C42—1224no—
722C42C2×C22⋊D6112yes—
723C42C2×C22⋊D6112yes—
724C42C2×C22⋊D6111yescharacteristic
725C42C2×C22⋊D6111yescharacteristic
726C42C23×D6112yes—
727C42C23×D6111yescharacteristic
728C42C23×D6111yescharacteristic
729C42C23×D6112yes—
730C23—22no—
731C23—1222no—
732C23—1222no—
733C23—2442no—
734C23—2442no—
735C23—2442no—
736C23—2442no—
737C23—2442no—
738C23—2442no—
739C23C22×C22⋊D6111yescharacteristic
740Q8—24no—
741Q8—42no—
742Q8—42no—
743Q8—42no—
744Q8—81no—
745Q8—1224no—
746Q8—2442no—
747D4—24no—
748D4—42no—
749D4—44no—
750D4—81no—
751D4—1222no—
752D4—1224no—
753D4—1222no—
754D4—4884no—
755D4—2442no—
756D4—2442no—
757D4—2448no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—44no—
769C2×C4—82no—
770C2×C4—82no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—4884no—
774C2×C4—4882no—
775C2×C4—4882no—
776C2×C4—2442no—
777C2×C4—2442no—
778C2×C4C22×C22⋊D6111yescharacteristic
779C2×C4C22×C22⋊D6112yes—
780C2×C4C22×C22⋊D6112yes—
781C2×C4C22×C22⋊D6112yes—
782C2×C4C22×C22⋊D6111yescharacteristic
783C2×C4C22×C22⋊D6112yes—
784C2×C4C22×C22⋊D6111yescharacteristic
785C2×C4C22×C22⋊D6111yescharacteristic
786C2×C4C22×C22⋊D6111yescharacteristic
787C2×C4C24×D6111yescharacteristic
788C8—1224no—
789C8—1224no—
790C22—21no—
791C22—21no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—4884no—
796C22—4884no—
797C22—2442no—
798C22—2442no—
799C22—2442no—
800C22—2442no—
801C22—2442no—
802C22—2442no—
803C22#1684056012yes—
804C22C23×C22⋊D6111yescharacteristic
805C4—21no—
806C4—21no—
807C4—21no—
808C4—22no—
809C4—22no—
810C4—22no—
811C4—22no—
812C4—21no—
813C4—21no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—2442no—
818C4—2442no—
819C4#1684059912yes—
820C2—22no—
821C2—82no—
822C2—4882no—
823C2—4882no—
824C2#2145947411yescharacteristic
825C2C2×#1684056011yescharacteristic
826C2#2146059811yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3507C2
socleC22×C61C23×D4
hypercenter#3507D61
hypocenterC61#61895
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #3507

Complements

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

NH ≅ G/Ntype
1. C2×#16840497C2semidirect
2. #21458903C2semidirect
3. #21458885C2semidirect
4. #21458587C2semidirect
5. #21458572C2semidirect
6. #21456834C2semidirect
7. #21456818C2semidirect
8. #21456802C2semidirect
9. #21456780C2semidirect
10. #21455986C2semidirect
11. #21455914C2semidirect
12. #21455906C2semidirect
13. #21455862C2semidirect
14. #21454904C2semidirect
15. C61×#3507C2semidirect
30. #16840154C22semidirect
32. #16840149C22semidirect
33. #16840144C22semidirect
35. #16840124C22semidirect
36. #16840124C22semidirect
37. #16840119C22semidirect
40. #16840066C22semidirect
41. #16840059C22semidirect
42. #16840049C22semidirect
43. #16840039C22semidirect
44. #16839984C22semidirect
45. #16839984C22semidirect
46. #16839981C22semidirect
47. #16839977C22semidirect
48. #16839977C22semidirect
49. #16839974C22semidirect
50. #16839964C22semidirect
53. #16839954C22semidirect
60. #16839893C22semidirect
61. #16839893C22semidirect
62. #16839872C22semidirect
63. #16839867C22semidirect
64. #16839862C22semidirect
65. #16839860C22semidirect
66. C4×#11758201C22semidirect
67. C4×#11758199C22semidirect
72. C61×#559C22semidirect
73. C61×#557C22semidirect
75. C61×#556C22semidirect
76. C61×#554C22semidirect
407. #3507D61semidirect
433. #559C2×D61semidirect
434. #557C2×D61semidirect
436. #556C2×D61semidirect
437. #554C2×D61semidirect
500. C61#61895semidirect

Maximal subgroups

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

subgroupindex
C2×#168404972
#214589032
#214588852
#214585872
#214585722
#214568342
#214568182
#214568022
#214567802
#214559862
#214559142
#214559062
#214558622
#214549042
C61×#35072
#6189561