Finite Group Databasebeta

← #30571110

Subgroups — #30571110

Order 15616.

1706 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459624C211yesmaximal, characteristic, complemented
2C2×#16840484C211yesmaximal, characteristic
3#21458851C214yesmaximal, complemented
4#21458845C214yesmaximal, complemented
5#21458562C214yesmaximal, complemented
6#21458560C214yesmaximal, complemented
7#21456824C211yesmaximal, characteristic
8#21456821C212yesmaximal
9#21456818C211yesmaximal, characteristic
10#21456765C212yesmaximal, complemented
11#21455949C211yesmaximal, characteristic, complemented
12#21455946C212yesmaximal, complemented
13#21455824C212yesmaximal
14#21454903C211yesmaximal, characteristic, complemented
15C61×#3113C211yesmaximal, characteristic, complemented
16Q8×Dic122C2212yescomplemented
17#16840492C2212yescomplemented
18#16840490—22no—
19#16840490C2212yescomplemented
20#16840489—22no—
21#16840487C2212yescomplemented
22#16840484—22no—
23#16840484—22no—
24#16840484C2214yes—
25#16840484C2214yes—
26#16840391—21no—
27#16840391—21no—
28#16840390—21no—
29#16840319C2211yescharacteristic
30#16840314C2212yes—
31#16840314C2212yes—
32C2×#14519775C2211yescharacteristic
33C2×#14519772—21no—
34C2×#14519771—21no—
35C2×#14519766C2211yescharacteristic
36C2×#14519765C2211yescharacteristic
37C2×#14519755—21no—
38#16840239—21no—
39C2×C4×Dic122C2211yescharacteristic
40C2×#14519742C2211yescharacteristic
41C2×#14519739C2211yescharacteristic
42C2×#14519734—21no—
43#16840156C2212yes—
44#16840155C2214yes—
45#16840154C2212yes—
46#16840140C2214yescomplemented
47#16840124C2212yes—
48#16840123C2214yes—
49#16840122C2212yes—
50#16840111C2214yescomplemented
51#16840092C2212yes—
52#16840051C2214yes—
53#16840047C2212yescomplemented
54#16840046C2214yescomplemented
55#16839987C2214yes—
56#16839986C2214yes—
57#16839985C2214yes—
58#16839984C2214yes—
59#16839972C2212yescomplemented
60#16839971C2214yescomplemented
61#16839971C2214yescomplemented
62#16839970C2214yescomplemented
63#16839966C2214yes—
64#16839920C2212yes—
65#16839918C2212yes—
66#16839917C2212yes—
67#16839915C2212yes—
68#16839912C2212yes—
69#16839891C2214yescomplemented
70#16839890C2214yescomplemented
71#16839868C2214yescomplemented
72#16839867C2214yescomplemented
73#16839866C2214yescomplemented
74#16839849C2214yes—
75#16839847C2214yes—
76#16839819C2211yescharacteristic
77#16839816C2212yes—
78#16839812C2212yes—
79C61×#533C2211yescharacteristic
80C2×C4×Q8×C61C2211yescharacteristic
81C61×#483C2212yes—
82C61×#475C2212yescomplemented
83C61×#462C2212yescomplemented
84C61×#451C2212yes—
85C61×#441C2214yescomplemented
86C61×#432C2211yescharacteristic
87C22×Dic122D411yescharacteristic
88C22×Dic122C2311yescharacteristic
89C22×D244C2311yescharacteristic
90C22×C4×D61—21no—
91C2×Dic244C2314yes—
92C2×#11758202C2314yes—
93C2×#11758202C2314yes—
94C2×#11758190C2314yes—
95C2×#11758201C2314yes—
96#14519777—22no—
97#14519777C2311yescharacteristic
98#14519777C2311yescharacteristic
99#14519776—22no—
100#14519776—22no—
101#14519776—22no—
102#14519776C2312yes—
103#14519776C2312yes—
104#14519775—22no—
105#14519775—22no—
106#14519775—22no—
107#14519775C2312yes—
108#14519775C2314yes—
109#14519775C2312yes—
110#14519772—24no—
111#14519772—24no—
112#14519771—24no—
113#14519771—24no—
114#14519769—21no—
115#14519769—22no—
116#14519768—22no—
117#14519767—22no—
118#14519767—22no—
119#14519767—22no—
120#14519767—22no—
121#14519767—22no—
122#14519767—22no—
123#14519766—22no—
124#14519766C2314yes—
125#14519765—21no—
126#14519765—21no—
127#14519765C2312yes—
128#14519765C2312yes—
129#14519756—21no—
130#14519756C2312yes—
131#14519755—24no—
132#14519755—24no—
133#14519754—22no—
134#14519754—22no—
135Q8×Dic61C2312yes—
136Q8×Dic61C2312yes—
137C4×Dic122—22no—
138C4×Dic122—22no—
139C4×Dic122—21no—
140C4×Dic122D412yes—
141C4×Dic122D412yes—
142C4×Dic122C2312yes—
143C4×Dic122C2312yes—
144C4×Dic122C2312yes—
145#14519742—22no—
146#14519742—22no—
147#14519742—22no—
148#14519742—22no—
149#14519742—22no—
150#14519742C2314yes—
151#14519742C2312yes—
152#14519742C2312yes—
153#14519739—22no—
154#14519739C2314yes—
155#14519736—21no—
156#14519734—24no—
157#14519734—24no—
158#14519733—22no—
159#14519733—22no—
160C2×C4⋊Dic61D411yescharacteristic
161C2×#11758196—21no—
162C2×#11758196—21no—
163C2×#11758196—21no—
164C2×#11758196D411yescharacteristic
165C2×#11758196D411yescharacteristic
166C2×#11758198—21no—
167C2×#11758198—21no—
168C2×#11758198—21no—
169C2×#11758198—21no—
170C2×#11758198—21no—
171C2×C4×Dic61—21no—
172C2×C4×Dic61C2311yescharacteristic
173C2×C4×Dic61C2311yescharacteristic
174#14519708C2314yes—
175C4⋊#92418C2312yes—
176#14519706C2314yes—
177#14519706C2314yes—
178#14519702C2314yes—
179#14519701C2314yes—
180#14519700C2314yes—
181#14519700C2314yes—
182#14519699C2314yes—
183#14519697C2314yes—
184C22⋊#92418C2312yes—
185#14519688C2312yes—
186#14519687C2314yes—
187C8×Dic61C2314yes—
188C22×Q8×C61C2311yescharacteristic
189C2×Q16×C61C2314yes—
190C4⋊Q8×C61C2311yescharacteristic
191C4⋊Q8×C61C2311yescharacteristic
192#125×C61—21no—
193C22⋊Q8×C61—21no—
194C22⋊Q8×C61C2312yes—
195C4×Q8×C61—21no—
196C4×Q8×C61—21no—
197C4×Q8×C61—21no—
198C4×Q8×C61C2312yes—
199C4×Q8×C61C2312yes—
200C4×Q8×C61C2312yes—
201#117×C61—21no—
202C2×C4⋊C4×C61—21no—
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C42×C61—21no—
205C2×C42×C61C2311yescharacteristic
206#106×C61C2314yes—
207C4⋊C8×C61C2312yes—
208#103×C61C2314yes—
209#103×C61C2314yes—
210C22⋊C8×C61C2312yes—
211#97×C61C2312yes—
212C23×D61—21no—
213C2×Q8×C61—21no—
214C2×Q8×C61—21no—
215C2×Q8×C61—42no—
216C2×Q8×C61C2412yes—
217C2×Q8×C61C2412yes—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2411yescharacteristic
223C22×Dic61—21no—
224C22×Dic61C2×D411yescharacteristic
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C2×D244—21no—
229C2×D244—42no—
230C2×D244C2412yes—
231C2×C4×D61—24no—
232C2×C4×D61—44no—
233C2×Dic122—24no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—22no—
237C2×Dic122—22no—
238C2×Dic122—42no—
239C2×Dic122C2×D412yes—
240C2×Dic122C2×D412yes—
241C2×Dic122C2412yes—
242C2×Dic122C2412yes—
243Q16×C61—44no—
244C2×C8×C61C2414yes—
245C4⋊C4×C61—22no—
246C4⋊C4×C61—22no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—22no—
252C4⋊C4×C61—22no—
253C4⋊C4×C61C2412yes—
254C4⋊C4×C61C2412yes—
255C22⋊C4×C61—22no—
256C42×C61—22no—
257C42×C61—22no—
258C42×C61—22no—
259C42×C61C2×D411yescharacteristic
260C42×C61C2×D411yescharacteristic
261C42×C61C2411yescharacteristic
262C42×C61C2411yescharacteristic
263C22⋊Dic61—22no—
264#11758202—44no—
265#11758202—44no—
266#11758201—44no—
267#11758198—22no—
268#11758198—22no—
269#11758198—22no—
270#11758198—22no—
271#11758198—24no—
272#11758198—24no—
273#11758198—24no—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—22no—
278C4⋊Dic61—22no—
279C4⋊Dic61C2×D412yes—
280C4⋊Dic61C2×D412yes—
281C4⋊Dic61C2412yes—
282#11758196—22no—
283#11758196—22no—
284#11758196—24no—
285#11758196—24no—
286#11758196—24no—
287#11758196—22no—
288#11758196—22no—
289#11758196—22no—
290#11758196—22no—
291#11758196—22no—
292#11758196—22no—
293#11758196—22no—
294#11758196—22no—
295#11758196C2×D412yes—
296#11758196C2×D412yes—
297#11758196C2×D412yes—
298#11758196C2×D412yes—
299C4×Dic61—22no—
300C4×Dic61—24no—
301C4×Dic61—22no—
302C4×Dic61—22no—
303C4×Dic61—22no—
304C4×Dic61—22no—
305C4×Dic61C2×D412yes—
306C4×Dic61C2×D412yes—
307C4×Dic61C2412yes—
308C4×Dic61C2412yes—
309C2×#92418C2414yes—
310Dic244—44no—
311#11758190—44no—
312C23×C61C22×D411yescharacteristic
313C22×D61—22no—
314C22×D61—42no—
315C22×D61—42no—
316C22×D61—42no—
317Q8×C61—24no—
318Q8×C61—22no—
319Q8×C61—22no—
320Q8×C61—42no—
321Q8×C61—81no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—41no—
329C2×C4×C61—42no—
330C2×C4×C61—42no—
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C2511yescharacteristic
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—42no—
344C2×Dic61#13714yes—
345C2×Dic61C22×D412yes—
346C2×Dic61C22×D412yes—
347C2×Dic61C22×D412yes—
348C2×Dic61C22×D412yes—
349D244—24no—
350D244—42no—
351C4×D61—48no—
352Dic122—24no—
353Dic122—24no—
354Dic122—24no—
355Dic122—24no—
356Dic122—42no—
357Dic122—82no—
358Dic122—82no—
359Dic122—81no—
360C8×C61—24no—
361#92418—24no—
362#61889—611nomaximal, Sylow
363C22×C61—21no—
364C22×C61—21no—
365C22×C61C2×#13712yes—
366C22×C61C23×D411yescharacteristic
367C2×D61—42no—
368C2×D61—42no—
369C2×D61—42no—
370C2×D61—84no—
371C4×C61—21no—
372C4×C61—21no—
373C4×C61—21no—
374C4×C61—21no—
375C4×C61—21no—
376C4×C61—42no—
377C4×C61—42no—
378C4×C61—42no—
379C4×C61—42no—
380C4×C61#58512yes—
381Dic61—22no—
382Dic61—22no—
383Dic61—22no—
384Dic61—42no—
385Dic61—42no—
386Dic61—42no—
387Dic61C2×#13714yes—
388#3502—611no—
389C2×#556—611no—
390#3398—614no—
391#3398—614no—
392#3369—614no—
393#3369—614no—
394#3215—612no—
395#3215—611no—
396#3215—611no—
397#3209—612no—
398#3113—612no—
399#3113—611no—
400#3113D6111yescharacteristic, complemented
401#3101—612no—
402#2983—611no—
403C2×C61—22no—
404C2×C61#348711yescharacteristic
405C2×C61C22×#13711yescharacteristic
406C2×C61#358611yescharacteristic
407D61—82no—
408Q82—612no—
409Q82—612no—
410#557—612no—
411#557—612no—
412#557—1222no—
413#557—1222no—
414#556—614no—
415#556—614no—
416#556—1222no—
417#556—1222no—
418#544—1221no—
419#544—1221no—
420#544—1221no—
421#533—612no—
422#533—612no—
423#533—611no—
424#533C2×D6111yescharacteristic
425C2×C4⋊Q8—611no—
426C2×#126—1221no—
427C2×#126—1221no—
428C2×#124—611no—
429C2×#124—611no—
430C2×C22⋊Q8—1221no—
431#519—1221no—
432C2×C4×Q8—611no—
433C2×C4×Q8—611no—
434C2×C4×Q8C2×D6111yescharacteristic
435C2×C4×D4—611no—
436C2×#117—1221no—
437#497—614no—
438#497—612no—
439#497—612no—
440#494—614no—
441#489—612no—
442#489—614no—
443#489—612no—
444#487—614no—
445#483—612no—
446#483C2×D6112yes—
447#476—614no—
448#475—612no—
449#475—614no—
450#475C2×D6112yescomplemented
451#464—614no—
452#464—614no—
453#464—614no—
454#464—614no—
455#462—614no—
456#462—612no—
457#462—614no—
458#462—614no—
459#462C2×D6112yescomplemented
460#461—614no—
461#451—612no—
462#451—612no—
463#451—612no—
464#451C2×D6112yes—
465#450—612no—
466#450—612no—
467#446—614no—
468#446—614no—
469#441—614no—
470#441—614no—
471#441—614no—
472#441C2×D6114yescomplemented
473C4×SD16—614no—
474C4×SD16—614no—
475#432—611no—
476#432—612no—
477#432C2×D6111yescharacteristic
478#431—612no—
479C61#6188911yescharacteristic, complemented, Sylow
480C22×Q8—611no—
481C22×Q8—611no—
482C22×Q8C22×D6111yescharacteristic
483C22×D4—611no—
484C23×C4—1221no—
485C2×Q16—614no—
486C2×Q16—614no—
487C2×Q16—614no—
488C2×Q16C22×D6114yes—
489C2×SD16—614no—
490C2×SD16—614no—
491C4⋊Q8—612no—
492C4⋊Q8—612no—
493C4⋊Q8—614no—
494C4⋊Q8—612no—
495C4⋊Q8—612no—
496C4⋊Q8—611no—
497C4⋊Q8—611no—
498C4⋊Q8—1222no—
499C4⋊Q8—1222no—
500C4⋊Q8—1222no—
501C4⋊Q8—1222no—
502C4⋊Q8—1222no—
503C4⋊Q8—1222no—
504C4⋊Q8—1222no—
505C4⋊Q8C22×D6111yescharacteristic
506C4⋊Q8C22×D6111yescharacteristic
507#126—1224no—
508#126—1224no—
509#126—1224no—
510#126—1224no—
511#125—21no—
512#125—1222no—
513#125—1222no—
514#125—1222no—
515#125—1222no—
516#125—1222no—
517#125—1222no—
518#125—1222no—
519#125—1222no—
520#125—1221no—
521#124—614no—
522#124—612no—
523#124—612no—
524#124—1222no—
525#124—1221no—
526#124—1221no—
527C22⋊Q8—21no—
528C22⋊Q8—612no—
529C22⋊Q8—1222no—
530C22⋊Q8—1222no—
531C22⋊Q8—1224no—
532C22⋊Q8—1224no—
533C22⋊Q8—1221no—
534C22⋊Q8C22×D6112yes—
535C4×Q8—21no—
536C4×Q8—21no—
537C4×Q8—21no—
538C4×Q8—612no—
539C4×Q8—612no—
540C4×Q8—612no—
541C4×Q8—612no—
542C4×Q8—612no—
543C4×Q8—612no—
544C4×Q8—614no—
545C4×Q8—612no—
546C4×Q8—612no—
547C4×Q8—612no—
548C4×Q8—1222no—
549C4×Q8—1222no—
550C4×Q8—1222no—
551C4×Q8—1222no—
552C4×Q8—1222no—
553C4×Q8—1222no—
554C4×Q8—1222no—
555C4×Q8—1221no—
556C4×Q8C22×D6112yes—
557C4×Q8C22×D6112yes—
558C4×Q8C22×D6112yes—
559C4×D4—614no—
560C4×D4—1222no—
561#117—21no—
562#117—1224no—
563#117—1224no—
564#117—1222no—
565#117—1222no—
566#117—1221no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—611no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—611no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4—1221no—
574C2×C4⋊C4C22×D6111yescharacteristic
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C42—21no—
581C2×C42—611no—
582C2×C42—611no—
583C2×C42—1221no—
584C2×C42C22×D6111yescharacteristic
585#106—614no—
586#106C22×D6114yes—
587C4⋊C8—614no—
588C4⋊C8—614no—
589C4⋊C8—612no—
590C4⋊C8C22×D6112yes—
591#103—614no—
592#103—614no—
593#103—614no—
594#103—614no—
595#103C22×D6114yes—
596#103C22×D6114yes—
597#102—614no—
598#102—614no—
599C22⋊C8—612no—
600C22⋊C8C22×D6112yes—
601#97—614no—
602#97—612no—
603#97C22×D6112yes—
604C4×C8—614no—
605C24—1221no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—42no—
609C2×Q8—612no—
610C2×Q8—612no—
611C2×Q8—612no—
612C2×Q8—612no—
613C2×Q8—1224no—
614C2×Q8—1222no—
615C2×Q8—1222no—
616C2×Q8—1221no—
617C2×Q8—1221no—
618C2×Q8—2442no—
619C2×Q8C23×D6112yes—
620C2×Q8C23×D6112yes—
621C2×D4—612no—
622C2×D4—1221no—
623C2×D4—2442no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—1224no—
631C22×C4—1221no—
632C22×C4—2444no—
633C22×C4D4×D6111yescharacteristic
634C22×C4D4×D6111yescharacteristic
635C22×C4C23×D6111yescharacteristic
636Q16—44no—
637Q16—2444no—
638Q16—2444no—
639Q16—2444no—
640SD16—2444no—
641SD16—2444no—
642C2×C8—614no—
643C2×C8C23×D6114yes—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—22no—
652C4⋊C4—612no—
653C4⋊C4—612no—
654C4⋊C4—612no—
655C4⋊C4—612no—
656C4⋊C4—612no—
657C4⋊C4—612no—
658C4⋊C4—612no—
659C4⋊C4—1224no—
660C4⋊C4—1224no—
661C4⋊C4—1224no—
662C4⋊C4—1222no—
663C4⋊C4—1222no—
664C4⋊C4—1222no—
665C4⋊C4—1222no—
666C4⋊C4—1222no—
667C4⋊C4—1222no—
668C4⋊C4—1222no—
669C4⋊C4—1222no—
670C4⋊C4—1222no—
671C4⋊C4—1222no—
672C4⋊C4—1222no—
673C4⋊C4—1222no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4C23×D6112yes—
678C4⋊C4C23×D6112yes—
679C22⋊C4—22no—
680C22⋊C4—1224no—
681C22⋊C4—1224no—
682C22⋊C4—1224no—
683C22⋊C4—1222no—
684C22⋊C4—1222no—
685C22⋊C4—1222no—
686C22⋊C4—1222no—
687C22⋊C4—1222no—
688C42—22no—
689C42—22no—
690C42—22no—
691C42—612no—
692C42—612no—
693C42—612no—
694C42—612no—
695C42—1224no—
696C42—1222no—
697C42—1222no—
698C42—1222no—
699C42—1222no—
700C42—1222no—
701C42D4×D6111yescharacteristic
702C42D4×D6111yescharacteristic
703C42C23×D6111yescharacteristic
704C42C23×D6111yescharacteristic
705C23—1222no—
706C23—2442no—
707C23—2442no—
708C23—2442no—
709C23C2×D4×D6111yescharacteristic
710Q8—24no—
711Q8—22no—
712Q8—22no—
713Q8—42no—
714Q8—81no—
715Q8—1224no—
716Q8—1224no—
717Q8—1224no—
718Q8—1224no—
719Q8—4881no—
720Q8—4882no—
721Q8—4882no—
722Q8—2442no—
723D4—1224no—
724D4—2442no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—614no—
735C2×C4—612no—
736C2×C4—612no—
737C2×C4—612no—
738C2×C4—612no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—2448no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2442no—
747C2×C4C2×D4×D6111yescharacteristic
748C2×C4C2×D4×D6111yescharacteristic
749C2×C4C2×D4×D6111yescharacteristic
750C2×C4C2×D4×D6111yescharacteristic
751C2×C4C2×D4×D6111yescharacteristic
752C2×C4C24×D6111yescharacteristic
753C8—24no—
754C8—1224no—
755C22—21no—
756C22—21no—
757C22—4884no—
758C22—2442no—
759C22—2442no—
760C22—2442no—
761C22#137×D6112yes—
762C22C22×D4×D6111yescharacteristic
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—21no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—42no—
772C4—614no—
773C4—1222no—
774C4—1222no—
775C4—1222no—
776C4—2442no—
777C4—2442no—
778C4—2442no—
779C4#1684059812yes—
780C2—22no—
781C2—4882no—
782C2#2145947311yescharacteristic
783C2C2×#137×D6111yescharacteristic
784C2#2146060211yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3113C2
socleC22×C61C23×D4
prime radicalC22×D244C23
hypercenter#3113D61
hypocenterC61#61889
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3113

Complements

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

NH ≅ G/Ntype
1. #21459624C2semidirect
3. #21458851C2semidirect
4. #21458845C2semidirect
5. #21458562C2semidirect
6. #21458560C2semidirect
10. #21456765C2semidirect
11. #21455949C2semidirect
12. #21455946C2semidirect
14. #21454903C2semidirect
15. C61×#3113C2semidirect
16. Q8×Dic122C22semidirect
17. #16840492C22semidirect
19. #16840490C22semidirect
21. #16840487C22semidirect
46. #16840140C22semidirect
50. #16840111C22semidirect
53. #16840047C22semidirect
54. #16840046C22semidirect
59. #16839972C22semidirect
60. #16839971C22semidirect
61. #16839971C22semidirect
62. #16839970C22semidirect
69. #16839891C22semidirect
70. #16839890C22semidirect
71. #16839868C22semidirect
72. #16839867C22semidirect
73. #16839866C22semidirect
82. C61×#475C22semidirect
83. C61×#462C22semidirect
85. C61×#441C22semidirect
400. #3113D61semidirect
450. #475C2×D61semidirect
459. #462C2×D61semidirect
472. #441C2×D61semidirect
479. C61#61889semidirect

Maximal subgroups

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

subgroupindex
#214596242
C2×#168404842
#214588512
#214588452
#214585622
#214585602
#214568242
#214568212
#214568182
#214567652
#214559492
#214559462
#214558242
#214549032
C61×#31132
#6188961