Finite Group Databasebeta

← #29681995

Subgroups — #29681995

Order 15616.

1708 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840528C211yesmaximal, characteristic, complemented
2#21459148C211yesmaximal, characteristic
3#21454338C211yesmaximal, characteristic, complemented
4C2×#16839735C211yesmaximal, characteristic, complemented
5#21446343C214yesmaximal, complemented
6#21446338C214yesmaximal, complemented
7C2×#16839519C211yesmaximal, characteristic, complemented
8C2×#16839518C211yesmaximal, characteristic, complemented
9C61×#2896C211yesmaximal, characteristic, complemented
10C22×#11758222C2211yescharacteristic
11#16840528—22no—
12#16840528—22no—
13#16840528—22no—
14#16840528C2214yes—
15C2×#14519785—22no—
16C2×#14519783—22no—
17C22×#11758194C2211yescharacteristic
18C2×M16×D61—22no—
19#16840340—22no—
20#16840336C2212yes—
21#16840333C412yescomplemented
22#16840329C2212yes—
23#16840326C412yescomplemented
24#16840321—22no—
25#16840308C414yescomplemented
26#16840273—22no—
27#16840269—22no—
28C2×#14519736C2211yescharacteristic
29C2×#14519736C2211yescharacteristic
30#16839771C2212yescomplemented
31#16839767C2212yescomplemented
32#16839763—22no—
33#16839758—22no—
34#16839735—22no—
35#16839735C2214yes—
36C2×#14519691—22no—
37#16839519C2214yescomplemented
38#16839518C2214yescomplemented
39C22×#41×C61C2211yescharacteristic
40C22×M16×C61C2211yescharacteristic
41C2×#117×C61C2211yescharacteristic
42C61×#419C2212yescomplemented
43C61×#418C2212yescomplemented
44C61×#417—22no—
45C61×#416—22no—
46C2×#11758222—21no—
47C2×#11758222—21no—
48C2×#11758222—21no—
49C2×#11758222—21no—
50C2×#11758222—21no—
51C2×#11758222—21no—
52C2×#11758222—21no—
53C2×#11758222—21no—
54C2×#11758222C2×C412yes—
55C2×#11758222D412yes—
56C2×#11758222D412yes—
57C2×#11758222C2312yes—
58C22×Dic122C2×C411yescharacteristic
59C22×D244C2×C411yescharacteristic
60C22×C22⋊D61D412yes—
61C22×C4×D61D412yes—
62#14519785—28no—
63#14519785—28no—
64#14519783—28no—
65#14519783—28no—
66C2×#11758194—21no—
67C2×#11758194—21no—
68C2×#11758194—21no—
69C2×#11758194—21no—
70C2×#11758194D412yescomplemented
71C2×#11758194C2312yes—
72C2×#11758189—24no—
73M16×D61—28no—
74M16×D61—28no—
75C22×#92418D412yescomplemented
76C2×C8×D61—24no—
77#14519775C2×C414yescomplemented
78#14519773C2×C414yescomplemented
79#14519766C2×C414yescomplemented
80#14519764C2×C414yescomplemented
81#14519760—24no—
82#14519758—24no—
83#14519756—24no—
84#14519753—24no—
85#14519751—24no—
86#14519749—28no—
87#14519748—24no—
88#14519746—24no—
89#14519745—24no—
90C4×C22⋊D61—28no—
91#14519736—21no—
92#14519736—21no—
93#14519736—21no—
94#14519736—21no—
95#14519736—21no—
96#14519736C2×C412yes—
97#14519736C2312yes—
98#14519736C2312yes—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61—21no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61C2×C412yes—
105#14519701—24no—
106#14519698—24no—
107#14519691—28no—
108C2×#41×C61—21no—
109C2×#41×C61—21no—
110C2×#41×C61—21no—
111C2×#41×C61—21no—
112C2×#41×C61—21no—
113C2×#41×C61—21no—
114C2×#41×C61—21no—
115C2×#41×C61—21no—
116C2×#41×C61—21no—
117C2×#41×C61—21no—
118C2×#41×C61C2×C412yes—
119C2×#41×C61C2×C412yes—
120C22×Q8×C61C2311yescharacteristic
121C22×D4×C61—21no—
122C22×D4×C61C2311yescharacteristic
123C23×C4×C61—21no—
124C23×C4×C61C2311yescharacteristic
125C2×M16×C61—21no—
126C2×M16×C61—21no—
127C2×M16×C61—21no—
128C2×M16×C61—21no—
129C2×M16×C61D412yescomplemented
130C2×M16×C61C2312yes—
131C22×C8×C61D412yescomplemented
132#117×C61—21no—
133#117×C61—21no—
134#117×C61—21no—
135#117×C61C2312yes—
136C2×C4⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C42×C61—21no—
139#103×C61—24no—
140#102×C61—24no—
141C24×C61—21no—
142C24×C61C2×D411yescharacteristic
143C23×D61C22⋊C412yes—
144#41×C61—22no—
145#41×C61—22no—
146#41×C61—22no—
147#41×C61—22no—
148#41×C61—22no—
149#41×C61—22no—
150#41×C61—22no—
151#41×C61—22no—
152#41×C61—41no—
153#41×C61—41no—
154#41×C61—41no—
155#41×C61—41no—
156#41×C61—41no—
157#41×C61—41no—
158#41×C61—41no—
159#41×C61—41no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61C22×C412yes—
166C2×D4×C61—22no—
167C2×D4×C61—22no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—41no—
174C2×D4×C61—41no—
175C2×D4×C61—41no—
176C2×D4×C61—41no—
177C2×D4×C61C22×C412yes—
178C22×C4×C61—21no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—41no—
182C22×C4×C61—41no—
183C22×C4×C61—41no—
184C22×C4×C61—41no—
185C22×C4×C61—41no—
186C22×C4×C61C22×C411yescharacteristic
187C22×C4×C61C22×C411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61#4111yescharacteristic
196C22×C4×C61#4111yescharacteristic
197C22×C4×C61#4111yescharacteristic
198C22×C4×C61#4111yescharacteristic
199C22×C4×C61C2411yescharacteristic
200C2×C22⋊D61—22no—
201C2×C22⋊D61—22no—
202C2×C22⋊D61—22no—
203C2×C22⋊D61—22no—
204C2×C22⋊D61—28no—
205C2×C22⋊D61C22⋊C414yes—
206C2×C22⋊D61C2×D414yes—
207C22×Dic61—22no—
208C22×Dic61—41no—
209C22×Dic61C22⋊C412yes—
210#11758222—22no—
211#11758222—22no—
212#11758222—22no—
213#11758222—22no—
214#11758222—22no—
215#11758222—22no—
216#11758222—22no—
217#11758222—22no—
218#11758222—22no—
219#11758222—22no—
220#11758222—22no—
221#11758222—22no—
222#11758222—22no—
223#11758222—22no—
224#11758222—22no—
225#11758222—22no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244C22⋊C412yes—
231C2×D244C22×C412yes—
232C2×C4×D61—22no—
233C2×C4×D61—22no—
234C2×C4×D61—22no—
235C2×C4×D61—22no—
236C2×C4×D61C22⋊C414yes—
237C2×C4×D61C2×D414yes—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122C22⋊C412yes—
243C2×Dic122C22×C412yes—
244M16×C61—22no—
245M16×C61—22no—
246M16×C61—22no—
247M16×C61—22no—
248C2×C8×C61—22no—
249C2×C8×C61—22no—
250C2×C8×C61C2×D414yes—
251C4⋊C4×C61—22no—
252C4⋊C4×C61—41no—
253C22⋊C4×C61—22no—
254C22⋊C4×C61—41no—
255C42×C61—22no—
256C42×C61—41no—
257C22⋊Dic61—22no—
258C22⋊Dic61—22no—
259C22⋊Dic61—28no—
260C22⋊Dic61—22no—
261C22⋊Dic61—41no—
262#11758198—28no—
263C4⋊Dic61—22no—
264C4⋊Dic61—22no—
265C4⋊Dic61—22no—
266C4⋊Dic61—41no—
267#11758196—28no—
268C4×Dic61—22no—
269C4×Dic61—22no—
270C4×Dic61—41no—
271C4×Dic61C22×C414yes—
272#11758194—22no—
273#11758194—22no—
274#11758194—22no—
275#11758194—22no—
276C2×#92418—22no—
277C2×#92418—22no—
278C2×#92418C2×D414yes—
279#11758189—216no—
280C8×D61—216no—
281C23×C61—22no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—81no—
285C23×C61—82no—
286C23×C61C2×C22⋊C411yescharacteristic
287C23×C61C2×C22⋊C411yescharacteristic
288C23×C61#12111yescharacteristic
289C23×C61#12111yescharacteristic
290C23×C61#12111yescharacteristic
291C23×C61#12111yescharacteristic
292C23×C61C22×D411yescharacteristic
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—82no—
296C22×D61C2×C22⋊C414yes—
297Q8×C61—22no—
298Q8×C61—22no—
299Q8×C61—41no—
300Q8×C61—41no—
301D4×C61—22no—
302D4×C61—22no—
303D4×C61—42no—
304D4×C61—42no—
305D4×C61—42no—
306D4×C61—42no—
307D4×C61—41no—
308D4×C61—41no—
309C2×C4×C61—22no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—82no—
318C2×C4×C61C2×C22⋊C411yescharacteristic
319C2×C4×C61C2×C22⋊C411yescharacteristic
320C2×C4×C61C4×D411yescharacteristic
321C2×C4×C61C4×D411yescharacteristic
322C2×C4×C61C4×D411yescharacteristic
323C2×C4×C61C4×D411yescharacteristic
324C2×C4×C61C4×D411yescharacteristic
325C2×C4×C61C4×D411yescharacteristic
326C2×C4×C61C4×D411yescharacteristic
327C2×C4×C61C4×D411yescharacteristic
328C2×C4×C61#12011yescharacteristic
329C2×C4×C61#12011yescharacteristic
330C2×C4×C61#12011yescharacteristic
331C2×C4×C61#12011yescharacteristic
332C2×C4×C61#12111yescharacteristic
333C2×C4×C61#12111yescharacteristic
334C2×C4×C61#12111yescharacteristic
335C2×C4×C61#12111yescharacteristic
336C2×C4×C61#12311yescharacteristic
337C2×C4×C61#12311yescharacteristic
338C2×C4×C61#12311yescharacteristic
339C2×C4×C61#12311yescharacteristic
340C2×C4×C61C23×C411yescharacteristic
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C2×#4111yescharacteristic
345C2×C4×C61C2×#4111yescharacteristic
346C22⋊D61—24no—
347C22⋊D61—24no—
348C22⋊D61—24no—
349C22⋊D61—24no—
350C22⋊D61—88no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—24no—
354C2×Dic61—42no—
355C2×Dic61—82no—
356C2×Dic61—82no—
357C2×Dic61C2×C22⋊C414yes—
358D244—22no—
359D244—22no—
360D244—22no—
361D244—22no—
362C4×D61—24no—
363C4×D61—24no—
364C4×D61—24no—
365C4×D61—24no—
366Dic122—22no—
367Dic122—22no—
368Dic122—22no—
369Dic122—22no—
370C8×C61—24no—
371#92418—24no—
372#21009—611nomaximal, Sylow
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61—44no—
381C22×C61—42no—
382C22×C61—82no—
383C22×C61—82no—
384C22×C61#38611yescharacteristic
385C22×C61#38611yescharacteristic
386C22×C61#38611yescharacteristic
387C22×C61#38611yescharacteristic
388C22×C61C22×C22⋊C411yescharacteristic
389C22×C61C2×#12111yescharacteristic
390C22×C61C2×#12111yescharacteristic
391C2×D61—24no—
392C2×D61—44no—
393C2×D61—44no—
394C2×D61—82no—
395C4×C61—42no—
396C4×C61—82no—
397C4×C61#38611yescharacteristic
398C4×C61#38611yescharacteristic
399C4×C61#38611yescharacteristic
400C4×C61#38611yescharacteristic
401C4×C61C2×C4×D411yescharacteristic
402C4×C61C2×C4×D411yescharacteristic
403C4×C61C2×#12011yescharacteristic
404C4×C61C2×#12311yescharacteristic
405Dic61—24no—
406Dic61—44no—
407Dic61—82no—
408C2×#568—611no—
409#3449—611no—
410#2896—611no—
411#2896D6111yescharacteristic, complemented
412C2×#410—611no—
413#1910—614no—
414#1909—614no—
415C2×H(3,ℤ/4)—611no—
416C2×H(3,ℤ/4)—611no—
417C2×C61—21no—
418C2×C61—21no—
419C2×C61—21no—
420C2×C61—21no—
421C2×C61—21no—
422C2×C61—21no—
423C2×C61—21no—
424C2×C61—82no—
425C2×C61C2×#38611yescharacteristic
426D61—44no—
427C22×#41—611no—
428C22×#41C2×D6111yescharacteristic
429#568—614no—
430#568—1222no—
431#568—1222no—
432#568—1222no—
433C2×#131—1222no—
434C2×#131—1222no—
435C22×M16—611no—
436C22×M16—1222no—
437C22×M16C2×D6111yescharacteristic
438#537—1222no—
439#536—612no—
440#536—612no—
441#535—612no—
442#535—612no—
443#534—1222no—
444#532—614no—
445#525—1222no—
446#525—1222no—
447C2×#117—611no—
448C2×#117—611no—
449C2×#117C2×D6111yescharacteristic
450#419—612no—
451#419C2×D6112yescomplemented
452#418—612no—
453#418C2×D6112yescomplemented
454#417—22no—
455#417—1222no—
456#416—22no—
457#416—1222no—
458#410—614no—
459#410—1222no—
460C2×#99—1222no—
461H(3,ℤ/4)—614no—
462H(3,ℤ/4)—614no—
463C61#2100911yescharacteristic, complemented, Sylow
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—612no—
475C2×#41—612no—
476C2×#41—612no—
477C2×#41—612no—
478C2×#41—1221no—
479C2×#41—1221no—
480C2×#41—1221no—
481C2×#41—1221no—
482C2×#41—1221no—
483C2×#41—1221no—
484C2×#41—1221no—
485C2×#41—1221no—
486C2×#41C4×D6112yes—
487C2×#41C4×D6112yes—
488C22×Q8—611no—
489C22×Q8C22×D6111yescharacteristic
490C22×D4—21no—
491C22×D4—612no—
492C22×D4—611no—
493C22×D4C22×D6111yescharacteristic
494C23×C4—21no—
495C23×C4—612no—
496C23×C4C22×D6111yescharacteristic
497#131—1228no—
498#131—1228no—
499#131—1228no—
500#131—1228no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—612no—
506C2×M16—612no—
507C2×M16—1224no—
508C2×M16—1228no—
509C2×M16—1228no—
510C2×M16—1221no—
511C2×M16—1221no—
512C2×M16—1221no—
513C2×M16—1221no—
514C2×M16C22⋊D6112yescomplemented
515C2×M16C22×D6112yes—
516C22×C8—612no—
517C22×C8—1224no—
518C22×C8C22⋊D6112yescomplemented
519C4⋊Q8—614no—
520#127—614no—
521#124—614no—
522#124—614no—
523#123—1224no—
524#123—1224no—
525C22⋊Q8—1224no—
526C22⋊Q8—1224no—
527#121—1224no—
528#121—1224no—
529#121—1228no—
530#120—1224no—
531#120—1224no—
532C4×D4—1228no—
533#117—21no—
534#117—21no—
535#117—21no—
536#117—612no—
537#117—612no—
538#117—612no—
539#117—1221no—
540#117—1221no—
541#117—1221no—
542#117—1221no—
543#117—1221no—
544#117C22×D6112yes—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—1221no—
547C2×C4⋊C4—1221no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C42—21no—
552C2×C42—612no—
553C2×C42—1221no—
554#103—24no—
555#103—1224no—
556#102—24no—
557#102—1224no—
558#99—1228no—
559C24—21no—
560C24—612no—
561C24D4×D6111yescharacteristic
562#41—22no—
563#41—22no—
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—22no—
569#41—22no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—41no—
574#41—41no—
575#41—41no—
576#41—41no—
577#41—41no—
578#41—1222no—
579#41—1222no—
580#41—1222no—
581#41—1222no—
582#41—1222no—
583#41—1222no—
584#41—1222no—
585#41—1222no—
586#41—1222no—
587#41—1222no—
588#41—1222no—
589#41—1222no—
590#41—1222no—
591#41—1222no—
592#41—1222no—
593#41—1222no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—612no—
600C2×Q8—612no—
601C2×Q8—1221no—
602C2×Q8—1221no—
603C2×Q8—1221no—
604C2×Q8—1221no—
605C2×Q8C2×C4×D6112yes—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—41no—
616C2×D4—41no—
617C2×D4—614no—
618C2×D4—614no—
619C2×D4—612no—
620C2×D4—612no—
621C2×D4—1222no—
622C2×D4—1222no—
623C2×D4—1222no—
624C2×D4—1222no—
625C2×D4—1228no—
626C2×D4—1221no—
627C2×D4—1221no—
628C2×D4—1221no—
629C2×D4—1221no—
630C2×D4C2×C4×D6112yes—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—612no—
640C22×C4—614no—
641C22×C4—614no—
642C22×C4—1222no—
643C22×C4—1222no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—2441no—
648C22×C4C2×C4×D6111yescharacteristic
649C22×C4C2×C4×D6111yescharacteristic
650C22×C4#1175822211yescharacteristic
651C22×C4#1175822211yescharacteristic
652C22×C4D4×D6111yescharacteristic
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4D4×D6111yescharacteristic
656C22×C4D4×D6111yescharacteristic
657C22×C4#1175822411yescharacteristic
658C22×C4#1175822411yescharacteristic
659C22×C4C2×C22⋊D6111yescharacteristic
660C22×C4C2×C22⋊D6111yescharacteristic
661C22×C4C23×D6111yescharacteristic
662M16—22no—
663M16—22no—
664M16—22no—
665M16—22no—
666M16—12216no—
667M16—1222no—
668M16—1222no—
669M16—1222no—
670M16—1222no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—614no—
674C2×C8—12216no—
675C2×C8—1222no—
676C2×C8—1222no—
677C2×C8C2×C22⋊D6114yes—
678C4⋊C4—22no—
679C4⋊C4—41no—
680C4⋊C4—1228no—
681C4⋊C4—1222no—
682C4⋊C4—1222no—
683C4⋊C4—1222no—
684C4⋊C4—2441no—
685C22⋊C4—22no—
686C22⋊C4—41no—
687C22⋊C4—1228no—
688C22⋊C4—1228no—
689C22⋊C4—1222no—
690C22⋊C4—1222no—
691C22⋊C4—1222no—
692C22⋊C4—2441no—
693C42—22no—
694C42—41no—
695C42—614no—
696C42—1222no—
697C42—1222no—
698C42—2441no—
699C23—22no—
700C23—41no—
701C23—41no—
702C23—81no—
703C23—82no—
704C23—614no—
705C23—1222no—
706C23—1222no—
707C23—4882no—
708C23C22⋊C4×D6111yescharacteristic
709C23C22⋊C4×D6111yescharacteristic
710C23#1451974811yescharacteristic
711C23#1451974811yescharacteristic
712C23#1451975011yescharacteristic
713C23#1451975011yescharacteristic
714C23C2×D4×D6111yescharacteristic
715Q8—22no—
716Q8—22no—
717Q8—41no—
718Q8—41no—
719Q8—1222no—
720Q8—1222no—
721Q8—1222no—
722Q8—1222no—
723D4—22no—
724D4—22no—
725D4—42no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—41no—
730D4—41no—
731D4—1224no—
732D4—1224no—
733D4—1224no—
734D4—1224no—
735D4—1222no—
736D4—1222no—
737D4—1222no—
738D4—1222no—
739D4—4888no—
740C2×C4—22no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—82no—
749C2×C4—614no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1224no—
753C2×C4—1224no—
754C2×C4—1224no—
755C2×C4—1224no—
756C2×C4—1224no—
757C2×C4—4882no—
758C2×C4—4882no—
759C2×C4—2442no—
760C2×C4C22⋊C4×D6111yescharacteristic
761C2×C4C22⋊C4×D6111yescharacteristic
762C2×C4#1451973711yescharacteristic
763C2×C4#1451973711yescharacteristic
764C2×C4#1451973711yescharacteristic
765C2×C4#1451973711yescharacteristic
766C2×C4C4×C22⋊D6111yescharacteristic
767C2×C4C4×C22⋊D6111yescharacteristic
768C2×C4C4×C22⋊D6111yescharacteristic
769C2×C4C4×C22⋊D6111yescharacteristic
770C2×C4#1451974511yescharacteristic
771C2×C4#1451974511yescharacteristic
772C2×C4#1451974511yescharacteristic
773C2×C4#1451974511yescharacteristic
774C2×C4#1451974811yescharacteristic
775C2×C4#1451974811yescharacteristic
776C2×C4#1451975011yescharacteristic
777C2×C4#1451975011yescharacteristic
778C2×C4#1451975911yescharacteristic
779C2×C4#1451975911yescharacteristic
780C2×C4#1451975911yescharacteristic
781C2×C4#1451975911yescharacteristic
782C2×C4C22×C4×D6111yescharacteristic
783C2×C4C2×D4×D6111yescharacteristic
784C2×C4C2×D4×D6111yescharacteristic
785C2×C4C22×C22⋊D6111yescharacteristic
786C2×C4C2×#1175822411yescharacteristic
787C2×C4C2×#1175822211yescharacteristic
788C8—24no—
789C8—1224no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—44no—
798C22—42no—
799C22—82no—
800C22—82no—
801C22—1224no—
802C22—4882no—
803C22—2444no—
804C22—2444no—
805C22#1683963811yescharacteristic
806C22#1683963811yescharacteristic
807C22#1683963811yescharacteristic
808C22#1683963811yescharacteristic
809C22C2×C22⋊C4×D6111yescharacteristic
810C22C2×#1451974811yescharacteristic
811C22C2×#1451975011yescharacteristic
812C4—42no—
813C4—82no—
814C4—1224no—
815C4—4882no—
816C4—2444no—
817C4#1683963811yescharacteristic
818C4#1683963811yescharacteristic
819C4#1683963811yescharacteristic
820C4#1683963811yescharacteristic
821C4C2×#1451973711yescharacteristic
822C4C2×C4×C22⋊D6111yescharacteristic
823C4C2×#1451974511yescharacteristic
824C4C2×#1451975911yescharacteristic
825C2—21no—
826C2—21no—
827C2—21no—
828C2—21no—
829C2—21no—
830C2—21no—
831C2—21no—
832C2—82no—
833C2—2444no—
834C2C2×#1683963811yescharacteristic
subgroupG/H
centerC4#16839638
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2896C2
socleC2×C61C2×#386
prime radical#21459148C2
cosocleC22×C4×C61C24
hypercenter#2896D61
hypocenterC61#21009
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
1. C2×#16840528C2semidirect
3. #21454338C2semidirect
4. C2×#16839735C2semidirect
5. #21446343C2semidirect
6. #21446338C2semidirect
7. C2×#16839519C2semidirect
8. C2×#16839518C2semidirect
9. C61×#2896C2semidirect
21. #16840333C4semidirect
23. #16840326C4semidirect
25. #16840308C4semidirect
30. #16839771C22semidirect
31. #16839767C22semidirect
37. #16839519C22semidirect
38. #16839518C22semidirect
42. C61×#419C22semidirect
43. C61×#418C22semidirect
70. C2×#11758194D4semidirect
75. C22×#92418D4semidirect
77. #14519775C2×C4semidirect
78. #14519773C2×C4semidirect
79. #14519766C2×C4semidirect
80. #14519764C2×C4semidirect
129. C2×M16×C61D4semidirect
131. C22×C8×C61D4semidirect
411. #2896D61semidirect
451. #419C2×D61semidirect
453. #418C2×D61semidirect
463. C61#21009semidirect
514. C2×M16C22⋊D61semidirect
518. C22×C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405282
#214591482
#214543382
C2×#168397352
#214463432
#214463382
C2×#168395192
C2×#168395182
C61×#28962
#2100961