Finite Group Databasebeta

← #30623920

Subgroups — #30623920

Order 15616.

1236 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840748C211yesmaximal, characteristic, complemented
2C2×#16840741C211yesmaximal, characteristic, complemented
3#21462081C212yesmaximal, complemented
4#21462078C212yesmaximal, complemented
5#21462074C214yesmaximal, complemented
6#21462070C214yesmaximal, complemented
7#21459148C211yesmaximal, characteristic
8C2×D61⋊M16—21no—
9C2×#14519856—21no—
10#16840748—21no—
11#16840748—21no—
12#16840748C2212yes—
13#16840748C2212yes—
14C2×#14519838—21no—
15C2×#14519837C2212yes—
16#16840741—21no—
17#16840741—21no—
18#16840741C2212yes—
19#16840741C2212yes—
20C2×#14519836—21no—
21C2×#14519835C2212yes—
22#16840664C2218yescomplemented
23#16840662C2218yescomplemented
24C22×#11758222C2211yescharacteristic
25#16840340—21no—
26#16840340—21no—
27#16840336C411yescharacteristic, complemented
28#16840336C2211yescharacteristic
29#16840333—21no—
30#16840329C411yescharacteristic, complemented
31#16840329C2211yescharacteristic
32#16840326—21no—
33#16840321C412yescomplemented
34#16840321C2212yes—
35#16840308—21no—
36#16840308—21no—
37#16840273C412yescomplemented
38#16840273C2212yes—
39#16840269—21no—
40#16840269—21no—
41C2×#14519736C411yescharacteristic, complemented
42C22×#41×C61C411yescharacteristic, complemented
43C2×#11758213—41no—
44D61⋊M16—22no—
45D61⋊M16—22no—
46D61⋊M16—41no—
47D61⋊M16—41no—
48C2×#11758217—22no—
49C2×D61⋊C8—41no—
50#14519856—22no—
51#14519856—22no—
52#14519856—41no—
53#14519856—41no—
54C2×C4⋊#6923—41no—
55C2×C22⋊#6923—22no—
56C2×C4×#6923—41no—
57#14519838—22no—
58#14519838—22no—
59#14519837—22no—
60#14519837C2314yes—
61#14519836—22no—
62#14519836—22no—
63#14519835—22no—
64#14519835C2314yes—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C2×#11758222—41no—
68C2×#11758222—41no—
69C2×#11758222C2×C411yescharacteristic
70C2×#11758222C2×C411yescharacteristic
71C2×#11758222D411yescharacteristic
72C2×#11758222D411yescharacteristic
73C2×#11758222D411yescharacteristic
74C2×#11758222D411yescharacteristic
75C2×#11758222C2311yescharacteristic
76C2×#11758222C2311yescharacteristic
77C22×Dic122D411yescharacteristic
78C22×D244D411yescharacteristic
79C22×C22⋊D61C2×C411yescharacteristic
80C22×C22⋊D61C2311yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83#14519775—21no—
84#14519775—21no—
85#14519773—21no—
86#14519773—21no—
87#14519766—21no—
88#14519766—21no—
89#14519764—21no—
90#14519764—21no—
91#14519760C2×C412yes—
92#14519760C2×C412yescomplemented
93#14519760C2×C412yescomplemented
94#14519760C2312yes—
95#14519758—22no—
96#14519758—22no—
97#14519756—22no—
98#14519756—22no—
99#14519753—21no—
100#14519753—21no—
101#14519753—21no—
102#14519753—21no—
103#14519751—22no—
104#14519751—22no—
105#14519749—22no—
106#14519749—22no—
107#14519749—22no—
108#14519749—22no—
109#14519748—21no—
110#14519748—21no—
111#14519748—21no—
112#14519748—21no—
113#14519746C2×C412yes—
114#14519746C2×C412yescomplemented
115#14519746C2×C412yescomplemented
116#14519746C2312yes—
117#14519745—22no—
118#14519745—22no—
119C4×C22⋊D61—22no—
120C4×C22⋊D61—22no—
121C4×C22⋊D61—22no—
122C4×C22⋊D61—22no—
123#14519736—21no—
124#14519736—21no—
125#14519736C2×C412yescomplemented
126#14519736C2×C411yescharacteristic, complemented
127#14519736C2×C411yescharacteristic, complemented
128C2×C4⋊Dic61—21no—
129C2×C22⋊Dic61C2×C412yes—
130C2×C4×Dic61—21no—
131C2×#41×C61—21no—
132C2×#41×C61—21no—
133C2×#41×C61—21no—
134C2×#41×C61—21no—
135C2×#41×C61—41no—
136C2×#41×C61—41no—
137C2×#41×C61—41no—
138C2×#41×C61—41no—
139C22×Q8×C61C2×C411yescharacteristic, complemented
140C22×D4×C61C2×C412yes—
141C22×D4×C61C2×C411yescharacteristic, complemented
142C23×C4×C61C2×C411yescharacteristic
143C23×C4×C61C2×C412yescomplemented
144C24×C61C22×C411yescharacteristic
145C24×C61C22×C412yes—
146C23×D61C22⋊C411yescharacteristic
147C23×D61C2×D411yescharacteristic
148C22×#6923—42no—
149#41×C61—42no—
150#41×C61—42no—
151#41×C61—42no—
152#41×C61—42no—
153#41×C61—42no—
154#41×C61—42no—
155#41×C61—41no—
156#41×C61—41no—
157#41×C61—41no—
158#41×C61—41no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—41no—
162C2×Q8×C61—41no—
163C2×D4×C61—22no—
164C2×D4×C61—22no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—41no—
168C2×D4×C61—41no—
169C2×D4×C61—42no—
170C2×D4×C61—42no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—42no—
178C22×C4×C61—42no—
179C22×C4×C61C22⋊C411yescharacteristic
180C22×C4×C61C22⋊C411yescharacteristic
181C22×C4×C61C22⋊C411yescharacteristic
182C22×C4×C61C22⋊C411yescharacteristic
183C22×C4×C61C22×C411yescharacteristic
184C22×C4×C61C22×C411yescharacteristic
185C22×C4×C61C22×C412yes—
186C2×C22⋊D61—22no—
187C2×C22⋊D61—22no—
188C2×C22⋊D61—22no—
189C2×C22⋊D61—22no—
190C2×C22⋊D61—41no—
191C2×C22⋊D61—41no—
192C2×C22⋊D61—41no—
193C2×C22⋊D61—41no—
194C2×C22⋊D61C22⋊C411yescharacteristic
195C2×C22⋊D61C22⋊C411yescharacteristic
196C2×C22⋊D61C22×C411yescharacteristic
197C2×C22⋊D61C22×C411yescharacteristic
198C2×C22⋊D61C22×C411yescharacteristic
199C2×C22⋊D61C2×D411yescharacteristic
200C2×C22⋊D61C2×D411yescharacteristic
201C2×C22⋊D61C2411yescharacteristic
202C22×Dic61—22no—
203C22×Dic61C22⋊C411yescharacteristic
204C22×Dic61C2×D411yescharacteristic
205#11758222—41no—
206#11758222—41no—
207#11758222—41no—
208#11758222—41no—
209#11758222—41no—
210#11758222—41no—
211#11758222—41no—
212#11758222—41no—
213#11758222—41no—
214#11758222—41no—
215#11758222—41no—
216#11758222—41no—
217#11758222—41no—
218#11758222—41no—
219#11758222—41no—
220#11758222—41no—
221C2×D244—41no—
222C2×D244—41no—
223C2×D244C22⋊C411yescharacteristic
224C2×D244C22⋊C411yescharacteristic
225C2×D244C2×D411yescharacteristic
226C2×D244C2×D411yescharacteristic
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61C22⋊C411yescharacteristic
236C2×C4×D61C22⋊C411yescharacteristic
237C2×C4×D61C22⋊C411yescharacteristic
238C2×C4×D61C22⋊C411yescharacteristic
239C2×C4×D61C2×D411yescharacteristic
240C2×C4×D61C2×D411yescharacteristic
241C2×C4×D61C2×D411yescharacteristic
242C2×C4×D61C2×D411yescharacteristic
243C2×Dic122—41no—
244C2×Dic122—41no—
245C2×Dic122C22⋊C411yescharacteristic
246C2×Dic122C22⋊C411yescharacteristic
247C2×Dic122C2×D411yescharacteristic
248C2×Dic122C2×D411yescharacteristic
249C22⋊#6923—24no—
250C22⋊#6923—42no—
251#11758217—24no—
252#11758217—42no—
253C2×#92420—42no—
254C4⋊#6923—42no—
255C4⋊#6923—42no—
256C4×#6923—42no—
257C4×#6923—42no—
258#11758213—42no—
259#11758213—42no—
260D61⋊C8—42no—
261D61⋊C8—42no—
262C22⋊Dic61—22no—
263C22⋊Dic61—22no—
264C22⋊Dic61—22no—
265C22⋊Dic61—22no—
266C22⋊Dic61—22no—
267C22⋊Dic61C22×C412yes—
268C22⋊Dic61C22×C412yes—
269#11758198—22no—
270#11758198—22no—
271#11758198—22no—
272#11758198—22no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—22no—
276#11758196—22no—
277#11758196—22no—
278#11758196—22no—
279#11758196—22no—
280C4×Dic61—22no—
281C4×Dic61—21no—
282C4×Dic61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—22no—
286C23×C61—42no—
287C23×C61—81no—
288C23×C61—82no—
289C23×C61C2×C22⋊C411yescharacteristic
290C23×C61C2×C22⋊C411yescharacteristic
291C23×C61C23×C411yescharacteristic
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—81no—
297C22×D61—81no—
298C22×D61C2×C22⋊C411yescharacteristic
299C22×D61C2×C22⋊C411yescharacteristic
300C22×D61C2×C22⋊C411yescharacteristic
301C22×D61C22×D411yescharacteristic
302C2×#6923—44no—
303C2×#6923—84no—
304Q8×C61—42no—
305Q8×C61—41no—
306Q8×C61—41no—
307D4×C61—42no—
308D4×C61—44no—
309D4×C61—42no—
310D4×C61—42no—
311D4×C61—41no—
312D4×C61—41no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—22no—
324C2×C4×C61—44no—
325C2×C4×C61—42no—
326C2×C4×C61—42no—
327C2×C4×C61—42no—
328C2×C4×C61#9911yescharacteristic
329C2×C4×C61#9911yescharacteristic
330C2×C4×C61#9911yescharacteristic
331C2×C4×C61#9911yescharacteristic
332C2×C4×C61C2×C22⋊C411yescharacteristic
333C2×C4×C61C2×C22⋊C411yescharacteristic
334C2×C4×C61C2×C22⋊C411yescharacteristic
335C2×C4×C61C2×C22⋊C411yescharacteristic
336C22⋊D61—41no—
337C22⋊D61—41no—
338C22⋊D61—41no—
339C22⋊D61—41no—
340C22⋊D61—41no—
341C22⋊D61—41no—
342C22⋊D61—41no—
343C22⋊D61—41no—
344C22⋊D61—82no—
345C22⋊D61—82no—
346C22⋊D61—82no—
347C22⋊D61—82no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—82no—
355C2×Dic61C2×C22⋊C411yescharacteristic
356C2×Dic61C2×C22⋊C411yescharacteristic
357C2×Dic61C2×C22⋊C411yescharacteristic
358C2×Dic61C22×D411yescharacteristic
359D244—41no—
360D244—41no—
361D244—41no—
362D244—41no—
363C4×D61—21no—
364C4×D61—21no—
365C4×D61—21no—
366C4×D61—21no—
367C4×D61—21no—
368C4×D61—21no—
369C4×D61—21no—
370C4×D61—21no—
371C4×D61—21no—
372C4×D61—21no—
373C4×D61—21no—
374C4×D61—21no—
375C4×D61—21no—
376C4×D61—21no—
377C4×D61—21no—
378C4×D61—21no—
379Dic122—41no—
380Dic122—41no—
381Dic122—41no—
382Dic122—41no—
383#92420—44no—
384#33347—611nomaximal, Sylow
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—42no—
391C22×C61—42no—
392C22×C61—42no—
393C22×C61—81no—
394C22×C61—81no—
395C22×C61—84no—
396C22×C61C2×#9911yescharacteristic
397C22×C61C2×#9911yescharacteristic
398C22×C61C22×C22⋊C411yescharacteristic
399C2×D61—21no—
400C2×D61—21no—
401C2×D61—21no—
402C2×D61—21no—
403C2×D61—42no—
404C2×D61—42no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—41no—
409C2×D61—81no—
410C2×D61—81no—
411#6923—84no—
412C4×C61—21no—
413C4×C61—21no—
414C4×C61—42no—
415C4×C61C2×#9911yescharacteristic
416C4×C61C2×#9911yescharacteristic
417C4×C61C2×#9911yescharacteristic
418C4×C61C2×#9911yescharacteristic
419Dic61—21no—
420Dic61—21no—
421Dic61—21no—
422Dic61—21no—
423Dic61—42no—
424Dic61—42no—
425#3449—611no—
426C2×#413—611no—
427C2×#410—611no—
428#2123—612no—
429#2122—612no—
430#2121—614no—
431#2120—614no—
432C2×C61—21no—
433C2×C61—21no—
434C2×C61—21no—
435C2×C61—41no—
436C2×C61—41no—
437C2×C61—82no—
438C2×C61C22×#9911yescharacteristic
439D61—41no—
440D61—41no—
441D61—41no—
442D61—41no—
443C22×#41—611no—
444C22×#41#692311yescharacteristic, complemented
445C22×M16—1221no—
446#537—1221no—
447#537—1221no—
448#536—611no—
449#536—611no—
450#536—1221no—
451#535—611no—
452#535—611no—
453#535—1221no—
454#534—612no—
455#534—612no—
456#532—1221no—
457#532—1221no—
458#525—612no—
459#525—612no—
460#525—1221no—
461#525—1221no—
462C2×#117—611no—
463C2×#117—1221no—
464#413—612no—
465#413—612no—
466#413—1221no—
467#413—1221no—
468C2×#101—1221no—
469C2×#100—612no—
470#410—612no—
471#410—612no—
472#410—1221no—
473#410—1221no—
474C2×#99—612no—
475C2×#99—1221no—
476#352—618no—
477AΣL(1,𝔽16)—618no—
478C61#3334711yescharacteristic, complemented, Sylow
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C2×#41—611no—
488C2×#41—611no—
489C2×#41—611no—
490C2×#41—611no—
491C2×#41—611no—
492C2×#41—611no—
493C2×#41—611no—
494C2×#41—611no—
495C2×#41—2441no—
496C2×#41—2441no—
497C2×#41—2441no—
498C2×#41—2441no—
499C22×Q8—611no—
500C22×Q8C2×#692311yescharacteristic, complemented
501C22×D4—611no—
502C22×D4—611no—
503C22×D4—611no—
504C22×D4C2×#692312yes—
505C22×D4C2×#692311yescharacteristic, complemented
506C23×C4—611no—
507C23×C4—611no—
508C23×C4C2×#692311yescharacteristic
509C23×C4C2×#692312yescomplemented
510C2×M16—1222no—
511C2×M16—1222no—
512C2×M16—1222no—
513C2×M16—2441no—
514C2×M16—2441no—
515C2×M16—2441no—
516C22×C8—2441no—
517C4⋊Q8—1221no—
518C4⋊Q8—1221no—
519#127—1221no—
520#127—1221no—
521#124—1221no—
522#124—1221no—
523#124—1221no—
524#124—1221no—
525#123—612no—
526#123—612no—
527#123—612no—
528#123—612no—
529#123—1222no—
530#123—1222no—
531C22⋊Q8—1222no—
532C22⋊Q8—1222no—
533C22⋊Q8—1221no—
534C22⋊Q8—1221no—
535C22⋊Q8—1221no—
536C22⋊Q8—1221no—
537#121—1222no—
538#121—1222no—
539#121—1221no—
540#121—1221no—
541#121—1221no—
542#121—1221no—
543#121—1222no—
544#121—1222no—
545#121—1222no—
546#121—1222no—
547#120—612no—
548#120—612no—
549#120—612no—
550#120—612no—
551#120—1222no—
552#120—1222no—
553C4×D4—1222no—
554C4×D4—1222no—
555C4×D4—1222no—
556C4×D4—1222no—
557#117—612no—
558#117—611no—
559#117—611no—
560#117—1221no—
561#117—1221no—
562#117—1222no—
563#117—1222no—
564#117—2441no—
565#117—2441no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4—2441no—
568C2×C22⋊C4—612no—
569C2×C22⋊C4—1222no—
570C2×C42—1221no—
571C2×C42—2441no—
572#101—1222no—
573#101—1222no—
574#100—614no—
575#100—1222no—
576#99—614no—
577#99—1222no—
578#99—1222no—
579#99—1222no—
580C24—611no—
581C24—611no—
582C24C22×#692311yescharacteristic
583C24C22×#692312yes—
584#41—42no—
585#41—42no—
586#41—42no—
587#41—42no—
588#41—42no—
589#41—42no—
590#41—41no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—2441no—
595#41—2441no—
596#41—2441no—
597#41—2441no—
598#41—2441no—
599#41—2441no—
600#41—2441no—
601#41—2441no—
602#41—2441no—
603#41—2441no—
604#41—2441no—
605#41—2441no—
606#41—2441no—
607#41—2441no—
608#41—2441no—
609#41—2441no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—41no—
613C2×Q8—41no—
614C2×Q8—611no—
615C2×Q8—611no—
616C2×Q8—611no—
617C2×Q8—611no—
618C2×Q8—2441no—
619C2×Q8—2441no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—611no—
629C2×D4—611no—
630C2×D4—611no—
631C2×D4—611no—
632C2×D4—611no—
633C2×D4—611no—
634C2×D4—611no—
635C2×D4—611no—
636C2×D4—611no—
637C2×D4—611no—
638C2×D4—611no—
639C2×D4—611no—
640C2×D4—1222no—
641C2×D4—1222no—
642C2×D4—1222no—
643C2×D4—1222no—
644C2×D4—2441no—
645C2×D4—2441no—
646C2×D4—2441no—
647C2×D4—2441no—
648C2×D4—2441no—
649C2×D4—2441no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1222no—
677C22×C4—2442no—
678C22×C4C22⋊#692311yescharacteristic
679C22×C4C22⋊#692311yescharacteristic
680C22×C4C22⋊#692311yescharacteristic
681C22×C4C22⋊#692311yescharacteristic
682C22×C4C22×#692311yescharacteristic
683C22×C4C22×#692311yescharacteristic
684C22×C4C22×#692312yes—
685M16—1224no—
686M16—2442no—
687M16—2442no—
688M16—2442no—
689C2×C8—2442no—
690C2×C8—2442no—
691C2×C8—2442no—
692C4⋊C4—1222no—
693C4⋊C4—1222no—
694C4⋊C4—1222no—
695C4⋊C4—1222no—
696C4⋊C4—1222no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—2442no—
700C4⋊C4—2442no—
701C22⋊C4—612no—
702C22⋊C4—612no—
703C22⋊C4—1222no—
704C22⋊C4—1222no—
705C22⋊C4—1222no—
706C22⋊C4—1222no—
707C22⋊C4—1222no—
708C22⋊C4—1222no—
709C22⋊C4—1222no—
710C22⋊C4—1222no—
711C22⋊C4—1222no—
712C22⋊C4—1224no—
713C22⋊C4—2442no—
714C42—1222no—
715C42—1221no—
716C42—1221no—
717C42—2442no—
718C42—2442no—
719C23—21no—
720C23—21no—
721C23—22no—
722C23—42no—
723C23—81no—
724C23—82no—
725C23—611no—
726C23—611no—
727C23—611no—
728C23—611no—
729C23—1221no—
730C23—1221no—
731C23—1221no—
732C23—1221no—
733C23—4881no—
734C23—4881no—
735C23C2×C22⋊#692311yescharacteristic
736C23C2×C22⋊#692311yescharacteristic
737C23C23×#692311yescharacteristic
738Q8—42no—
739Q8—41no—
740Q8—41no—
741Q8—2441no—
742Q8—2441no—
743Q8—2441no—
744Q8—2441no—
745D4—42no—
746D4—44no—
747D4—42no—
748D4—42no—
749D4—41no—
750D4—41no—
751D4—4882no—
752D4—4882no—
753D4—4882no—
754D4—4882no—
755D4—2441no—
756D4—2441no—
757D4—2441no—
758D4—2441no—
759D4—2441no—
760D4—2441no—
761D4—2441no—
762D4—2441no—
763D4—2441no—
764D4—2441no—
765D4—2441no—
766D4—2441no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—44no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—611no—
783C2×C4—611no—
784C2×C4—611no—
785C2×C4—611no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—1221no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—4884no—
809C2×C4—4882no—
810C2×C4—2444no—
811C2×C4#1451983511yescharacteristic
812C2×C4#1451983511yescharacteristic
813C2×C4#1451983511yescharacteristic
814C2×C4#1451983511yescharacteristic
815C2×C4C2×C22⋊#692311yescharacteristic
816C2×C4C2×C22⋊#692311yescharacteristic
817C2×C4C2×C22⋊#692311yescharacteristic
818C2×C4C2×C22⋊#692311yescharacteristic
819C8—2444no—
820C22—21no—
821C22—21no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—81no—
829C22—81no—
830C22—84no—
831C22—1221no—
832C22—1221no—
833C22—1221no—
834C22—1221no—
835C22—4881no—
836C22—4881no—
837C22—2441no—
838C22—2441no—
839C22—2441no—
840C22—2441no—
841C22—2442no—
842C22—2442no—
843C22C2×#1451983511yescharacteristic
844C22C2×#1451983511yescharacteristic
845C22C22×C22⋊#692311yescharacteristic
846C4—21no—
847C4—21no—
848C4—42no—
849C4—1221no—
850C4—1221no—
851C4—1221no—
852C4—1221no—
853C4—4884no—
854C4—2442no—
855C4—2442no—
856C4C2×#1451983511yescharacteristic
857C4C2×#1451983511yescharacteristic
858C4C2×#1451983511yescharacteristic
859C4C2×#1451983511yescharacteristic
860C2—21no—
861C2—21no—
862C2—21no—
863C2—41no—
864C2—41no—
865C2—82no—
866C2—2441no—
867C2—2441no—
868C2—2441no—
869C2—2441no—
870C2C22×#1451983511yescharacteristic
subgroupG/H
centerC4C2×#14519835
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×#41×C61C4
socleC2×C61C22×#99
prime radical#21459148C2
cosocleC2×C22⋊D61C24
hypercenterC22×#41#6923
hypocenterC61#33347
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#16840748C2semidirect
2. C2×#16840741C2semidirect
3. #21462081C2semidirect
4. #21462078C2semidirect
5. #21462074C2semidirect
6. #21462070C2semidirect
22. #16840664C22semidirect
23. #16840662C22semidirect
27. #16840336C4semidirect
30. #16840329C4semidirect
33. #16840321C4semidirect
37. #16840273C4semidirect
41. C2×#14519736C4semidirect
42. C22×#41×C61C4semidirect
92. #14519760C2×C4semidirect
93. #14519760C2×C4semidirect
114. #14519746C2×C4semidirect
115. #14519746C2×C4semidirect
125. #14519736C2×C4semidirect
126. #14519736C2×C4semidirect
127. #14519736C2×C4semidirect
139. C22×Q8×C61C2×C4semidirect
141. C22×D4×C61C2×C4semidirect
143. C23×C4×C61C2×C4semidirect
444. C22×#41#6923semidirect
478. C61#33347semidirect
500. C22×Q8C2×#6923semidirect
505. C22×D4C2×#6923semidirect
509. C23×C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407482
C2×#168407412
#214620812
#214620782
#214620742
#214620702
#214591482
#3334761