Finite Group Databasebeta

← #29682045

Subgroups — #29682045

Order 15616.

1692 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840528C211yesmaximal, characteristic, complemented
2#21459148C211yesmaximal, characteristic
3C2×#16839746C211yesmaximal, characteristic, complemented
4C2×#16839744C211yesmaximal, characteristic, complemented
5#21446368C214yesmaximal, complemented
6#21446363C214yesmaximal, complemented
7C2×#16839534C211yesmaximal, characteristic, complemented
8C2×#16839533C211yesmaximal, characteristic, complemented
9C2×C61×#413C211yesmaximal, characteristic, complemented
10C22×#11758222C2211yescharacteristic
11#16840528—22no—
12#16840528—22no—
13#16840528—22no—
14#16840528C2214yes—
15C2×#14519785—22no—
16C2×#14519783—22no—
17C22×#11758194C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C2×M16×D61—22no—
20#16840340—22no—
21#16840336C2212yes—
22#16840333—21no—
23#16840329C2212yes—
24#16840326—21no—
25#16840321C414yes—
26#16840308—22no—
27#16840273C414yes—
28#16840269—22no—
29C2×#14519736C2211yescharacteristic
30#16839746—22no—
31#16839746—22no—
32#16839744—22no—
33#16839744C2214yes—
34C2×#14519696C2212yescomplemented
35C2×#14519695—21no—
36C2×#14519694C2212yescomplemented
37C2×#14519693—21no—
38#16839534C2214yescomplemented
39#16839533C2214yescomplemented
40C22×#41×C61C2211yescharacteristic
41C22×M16×C61C2211yescharacteristic
42C22×M16×C61C2211yescharacteristic
43C61×#413—22no—
44C61×#413—22no—
45C2×#101×C61C2212yescomplemented
46C2×#100×C61C2212yescomplemented
47C2×#11758222—21no—
48C2×#11758222—21no—
49C2×#11758222—21no—
50C2×#11758222—21no—
51C2×#11758222—21no—
52C2×#11758222—21no—
53C2×#11758222—21no—
54C2×#11758222—21no—
55C2×#11758222C2×C412yes—
56C2×#11758222D412yes—
57C2×#11758222D412yes—
58C2×#11758222C2312yes—
59C22×Dic122D411yescharacteristic
60C22×D244D411yescharacteristic
61C22×C22⋊D61C2×C412yes—
62C22×C4×D61D412yes—
63#14519785—28no—
64#14519785—28no—
65#14519783—28no—
66#14519783—28no—
67C2×#11758194—21no—
68C2×#11758194—21no—
69C2×#11758194—21no—
70C2×#11758194—21no—
71C2×#11758194—21no—
72C2×#11758194—21no—
73C2×#11758194—21no—
74C2×#11758194—21no—
75C2×#11758194D412yescomplemented
76C2×#11758194D412yescomplemented
77C2×#11758194C2312yes—
78C2×#11758194C2312yes—
79C2×#11758189—24no—
80M16×D61—28no—
81M16×D61—28no—
82C22×#92418—21no—
83C22×#92418—21no—
84C2×C8×D61—24no—
85#14519775—22no—
86#14519773—22no—
87#14519766—22no—
88#14519764—22no—
89#14519760C2×C418yes—
90#14519758—24no—
91#14519756—24no—
92#14519753—24no—
93#14519751—24no—
94#14519749—28no—
95#14519748—24no—
96#14519746C2×C418yes—
97#14519745—24no—
98C4×C22⋊D61—28no—
99#14519736—21no—
100#14519736—21no—
101#14519736C2×C412yes—
102#14519736C2312yes—
103C2×C4⋊Dic61—21no—
104C2×C22⋊Dic61C2×C412yes—
105C2×C4×Dic61—21no—
106#14519696—24no—
107#14519695—24no—
108#14519694—24no—
109#14519693—24no—
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×C61—21no—
119C2×#41×C61—21no—
120C2×#41×C61—21no—
121C2×#41×C61—21no—
122C22×Q8×C61C2311yescharacteristic
123C22×D4×C61C2×C412yes—
124C22×D4×C61C2311yescharacteristic
125C23×C4×C61C2×C412yes—
126C23×C4×C61C2311yescharacteristic
127C2×M16×C61—21no—
128C2×M16×C61—21no—
129C2×M16×C61—21no—
130C2×M16×C61—21no—
131C2×M16×C61—21no—
132C2×M16×C61—21no—
133C2×M16×C61—21no—
134C2×M16×C61—21no—
135C2×M16×C61D412yescomplemented
136C2×M16×C61D412yescomplemented
137C2×M16×C61C2312yes—
138C2×M16×C61C2312yes—
139C22×C8×C61—21no—
140C22×C8×C61—21no—
141#101×C61—24no—
142#100×C61—24no—
143C24×C61C22×C412yes—
144C24×C61C22×C411yescharacteristic
145C23×D61C22⋊C412yes—
146#41×C61—41no—
147#41×C61—41no—
148#41×C61—41no—
149#41×C61—41no—
150#41×C61—41no—
151#41×C61—41no—
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—
160#41×C61—41no—
161#41×C61—41no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×D4×C61—22no—
169C2×D4×C61—22no—
170C2×D4×C61—22no—
171C2×D4×C61—22no—
172C2×D4×C61—22no—
173C2×D4×C61—22no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61C22×C412yes—
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×C61C2×D411yescharacteristic
196C22×C4×C61#4111yescharacteristic
197C22×C4×C61#4111yescharacteristic
198C22×C4×C61#4111yescharacteristic
199C22×C4×C61#4111yescharacteristic
200C22×C4×C61C2411yescharacteristic
201C2×C22⋊D61—22no—
202C2×C22⋊D61—22no—
203C2×C22⋊D61—22no—
204C2×C22⋊D61—22no—
205C2×C22⋊D61—28no—
206C2×C22⋊D61C22⋊C414yes—
207C2×C22⋊D61C22×C414yes—
208C22×Dic61—22no—
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×D244C2×D412yes—
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×Dic122C2×D412yes—
244M16×C61—22no—
245M16×C61—22no—
246M16×C61—22no—
247M16×C61—22no—
248M16×C61—22no—
249M16×C61—41no—
250M16×C61—41no—
251M16×C61C2×D414yes—
252C2×C8×C61—22no—
253C2×C8×C61—22no—
254C2×C8×C61—22no—
255C2×C8×C61—22no—
256C2×C8×C61—41no—
257C2×C8×C61—41no—
258C22⋊Dic61—22no—
259C22⋊Dic61—28no—
260C22⋊Dic61C22×C414yes—
261#11758198—28no—
262C4⋊Dic61—22no—
263C4⋊Dic61—22no—
264#11758196—28no—
265C4×Dic61—22no—
266C4×Dic61—22no—
267#11758194—22no—
268#11758194—22no—
269#11758194—22no—
270#11758194—22no—
271#11758194—22no—
272#11758194—41no—
273#11758194—41no—
274#11758194C2×D414yes—
275C2×#92418—22no—
276C2×#92418—22no—
277C2×#92418—22no—
278C2×#92418—22no—
279C2×#92418—41no—
280C2×#92418—41no—
281#11758189—216no—
282C8×D61—216no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—81no—
287C23×C61—82no—
288C23×C61C2×C22⋊C411yescharacteristic
289C23×C61C2×C22⋊C411yescharacteristic
290C23×C61C4×D411yescharacteristic
291C23×C61C4×D411yescharacteristic
292C23×C61C4×D411yescharacteristic
293C23×C61C4×D411yescharacteristic
294C23×C61C23×C411yescharacteristic
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—82no—
298C22×D61C2×C22⋊C414yes—
299Q8×C61—41no—
300Q8×C61—41no—
301Q8×C61—41no—
302Q8×C61—41no—
303D4×C61—42no—
304D4×C61—42no—
305D4×C61—42no—
306D4×C61—42no—
307D4×C61—41no—
308D4×C61—41no—
309D4×C61—41no—
310D4×C61—41no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
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×C61#12011yescharacteristic
325C2×C4×C61#12011yescharacteristic
326C2×C4×C61#12011yescharacteristic
327C2×C4×C61#12011yescharacteristic
328C2×C4×C61#12111yescharacteristic
329C2×C4×C61#12111yescharacteristic
330C2×C4×C61#12111yescharacteristic
331C2×C4×C61#12111yescharacteristic
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×C61C22×D411yescharacteristic
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—82no—
355C2×Dic61C2×C22⋊C414yes—
356D244—22no—
357D244—22no—
358D244—22no—
359D244—22no—
360C4×D61—24no—
361C4×D61—24no—
362C4×D61—24no—
363C4×D61—24no—
364Dic122—22no—
365Dic122—22no—
366Dic122—22no—
367Dic122—22no—
368C8×C61—24no—
369C8×C61—42no—
370#92418—24no—
371#92418—42no—
372#21017—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×C4×D411yescharacteristic
390C22×C61C2×C4×D411yescharacteristic
391C2×D61—24no—
392C2×D61—44no—
393C2×D61—44no—
394C2×D61—82no—
395C4×C61—42no—
396C4×C61#38611yescharacteristic
397C4×C61#38611yescharacteristic
398C4×C61#38611yescharacteristic
399C4×C61#38611yescharacteristic
400C4×C61C2×#12011yescharacteristic
401C4×C61C2×#12111yescharacteristic
402C4×C61C2×#12111yescharacteristic
403C4×C61C2×#12311yescharacteristic
404Dic61—24no—
405Dic61—44no—
406C2×#568—611no—
407#3449—611no—
408C2×#413—611no—
409C2×#413—611no—
410C2×#413D6111yescharacteristic, complemented
411#1915—614no—
412#1914—614no—
413C2×#344—611no—
414C2×#344—611no—
415C2×C61—21no—
416C2×C61—21no—
417C2×C61—21no—
418C2×C61—21no—
419C2×C61—21no—
420C2×C61—21no—
421C2×C61—21no—
422C2×C61—82no—
423C2×C61C2×#38611yescharacteristic
424D61—44no—
425C22×#41—611no—
426C22×#41C2×D6111yescharacteristic
427#568—614no—
428#568—1222no—
429#568—1222no—
430#568—1222no—
431C2×#131—1222no—
432C2×#131—1222no—
433C22×M16—611no—
434C22×M16—611no—
435C22×M16—1222no—
436C22×M16C2×D6111yescharacteristic
437C22×M16C2×D6111yescharacteristic
438#537—1222no—
439#536—612no—
440#536—1221no—
441#535—612no—
442#535—1221no—
443#534—614no—
444#532—1222no—
445#525—614no—
446#525—1222no—
447C2×#117—611no—
448#413—22no—
449#413—22no—
450#413—614no—
451#413—1222no—
452#413—1222no—
453#413—1222no—
454C2×#101—612no—
455C2×#101—1221no—
456C2×#101C2×D6112yescomplemented
457C2×#100—612no—
458C2×#100—1221no—
459C2×#100C2×D6112yescomplemented
460#344—614no—
461#344—614no—
462C61#2101711yescharacteristic, complemented, Sylow
463C2×#41—21no—
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—21no—
475C2×#41—612no—
476C2×#41—612no—
477C2×#41—612no—
478C2×#41—612no—
479C2×#41—1221no—
480C2×#41—1221no—
481C2×#41—1221no—
482C2×#41—1221no—
483C2×#41—1221no—
484C2×#41—1221no—
485C2×#41—1221no—
486C2×#41—1221no—
487C22×Q8—611no—
488C22×Q8C22×D6111yescharacteristic
489C22×D4—612no—
490C22×D4—611no—
491C22×D4C4×D6112yes—
492C22×D4C22×D6111yescharacteristic
493C23×C4—612no—
494C23×C4C4×D6112yes—
495C23×C4C22×D6111yescharacteristic
496#131—1228no—
497#131—1228no—
498#131—1228no—
499#131—1228no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—21no—
506C2×M16—21no—
507C2×M16—21no—
508C2×M16—612no—
509C2×M16—612no—
510C2×M16—612no—
511C2×M16—612no—
512C2×M16—1224no—
513C2×M16—1228no—
514C2×M16—1228no—
515C2×M16—1221no—
516C2×M16—1221no—
517C2×M16—1221no—
518C2×M16—1221no—
519C2×M16—1221no—
520C2×M16—1221no—
521C2×M16—1221no—
522C2×M16—1221no—
523C2×M16C22⋊D6112yescomplemented
524C2×M16C22⋊D6112yescomplemented
525C2×M16C22×D6112yes—
526C2×M16C22×D6112yes—
527C22×C8—21no—
528C22×C8—21no—
529C22×C8—1224no—
530C22×C8—1221no—
531C22×C8—1221no—
532C4⋊Q8—1222no—
533#127—1222no—
534#124—1222no—
535#124—1222no—
536#123—618no—
537#123—1224no—
538C22⋊Q8—1224no—
539C22⋊Q8—1224no—
540#121—1224no—
541#121—1224no—
542#121—1228no—
543#120—618no—
544#120—1224no—
545C4×D4—1228no—
546#117—612no—
547#117—612no—
548#117—1221no—
549#117—1221no—
550C2×C4⋊C4—1221no—
551C2×C22⋊C4—612no—
552C2×C42—1221no—
553#101—24no—
554#101—1224no—
555#101—1224no—
556#100—24no—
557#100—1224no—
558#100—1224no—
559C24—612no—
560C24C2×C4×D6112yes—
561C24C2×C4×D6111yescharacteristic
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—41no—
568#41—41no—
569#41—41no—
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—21no—
600C2×Q8—612no—
601C2×Q8—612no—
602C2×Q8—1221no—
603C2×Q8—1221no—
604C2×Q8—1221no—
605C2×Q8—1221no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—614no—
619C2×D4—614no—
620C2×D4—612no—
621C2×D4—612no—
622C2×D4—1222no—
623C2×D4—1222no—
624C2×D4—1222no—
625C2×D4—1222no—
626C2×D4—1228no—
627C2×D4—1221no—
628C2×D4—1221no—
629C2×D4—1221no—
630C2×D4—1221no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—612no—
638C22×C4—614no—
639C22×C4—614no—
640C22×C4—1222no—
641C22×C4—1222no—
642C22×C4—1222no—
643C22×C4—1222no—
644C22×C4—1222no—
645C22×C4C2×C4×D6112yes—
646C22×C4C2×C4×D6111yescharacteristic
647C22×C4#1175822211yescharacteristic
648C22×C4#1175822211yescharacteristic
649C22×C4D4×D6111yescharacteristic
650C22×C4D4×D6111yescharacteristic
651C22×C4D4×D6111yescharacteristic
652C22×C4D4×D6111yescharacteristic
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4#1175822411yescharacteristic
656C22×C4#1175822411yescharacteristic
657C22×C4C2×C22⋊D6111yescharacteristic
658C22×C4C2×C22⋊D6111yescharacteristic
659C22×C4C23×D6111yescharacteristic
660M16—22no—
661M16—22no—
662M16—22no—
663M16—22no—
664M16—22no—
665M16—41no—
666M16—41no—
667M16—614no—
668M16—12216no—
669M16—1222no—
670M16—1222no—
671M16—1222no—
672M16—1222no—
673M16—1222no—
674M16—2441no—
675M16—2441no—
676M16C2×C22⋊D6114yes—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—41no—
682C2×C8—41no—
683C2×C8—12216no—
684C2×C8—1222no—
685C2×C8—1222no—
686C2×C8—1222no—
687C2×C8—1222no—
688C2×C8—2441no—
689C2×C8—2441no—
690C4⋊C4—1228no—
691C4⋊C4—1222no—
692C4⋊C4—1222no—
693C22⋊C4—614no—
694C22⋊C4—1228no—
695C22⋊C4—1228no—
696C22⋊C4—1222no—
697C42—1222no—
698C42—1222no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—81no—
703C23—82no—
704C23—614no—
705C23—1222no—
706C23—1222no—
707C23—4882no—
708C23C22⋊C4×D6111yescharacteristic
709C23C22⋊C4×D6111yescharacteristic
710C23#1451973711yescharacteristic
711C23#1451973711yescharacteristic
712C23C4×C22⋊D6111yescharacteristic
713C23C4×C22⋊D6111yescharacteristic
714C23C22×C4×D6111yescharacteristic
715Q8—41no—
716Q8—41no—
717Q8—41no—
718Q8—41no—
719Q8—1222no—
720Q8—1222no—
721Q8—1222no—
722Q8—1222no—
723D4—42no—
724D4—42no—
725D4—42no—
726D4—42no—
727D4—41no—
728D4—41no—
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—22no—
742C2×C4—22no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—614no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1224no—
751C2×C4—1224no—
752C2×C4—1224no—
753C2×C4—1224no—
754C2×C4—1224no—
755C2×C4—4882no—
756C2×C4C22⋊C4×D6111yescharacteristic
757C2×C4C22⋊C4×D6111yescharacteristic
758C2×C4#1451973711yescharacteristic
759C2×C4#1451973711yescharacteristic
760C2×C4C4×C22⋊D6111yescharacteristic
761C2×C4C4×C22⋊D6111yescharacteristic
762C2×C4#1451974511yescharacteristic
763C2×C4#1451974511yescharacteristic
764C2×C4#1451974511yescharacteristic
765C2×C4#1451974511yescharacteristic
766C2×C4#1451974811yescharacteristic
767C2×C4#1451974811yescharacteristic
768C2×C4#1451974811yescharacteristic
769C2×C4#1451974811yescharacteristic
770C2×C4#1451975011yescharacteristic
771C2×C4#1451975011yescharacteristic
772C2×C4#1451975011yescharacteristic
773C2×C4#1451975011yescharacteristic
774C2×C4#1451975911yescharacteristic
775C2×C4#1451975911yescharacteristic
776C2×C4#1451975911yescharacteristic
777C2×C4#1451975911yescharacteristic
778C2×C4C2×D4×D6111yescharacteristic
779C2×C4C2×D4×D6111yescharacteristic
780C2×C4C2×D4×D6111yescharacteristic
781C2×C4C22×C22⋊D6111yescharacteristic
782C2×C4C2×#1175822411yescharacteristic
783C2×C4C2×#1175822211yescharacteristic
784C8—24no—
785C8—42no—
786C8—1224no—
787C8—2442no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—44no—
796C22—42no—
797C22—82no—
798C22—82no—
799C22—1224no—
800C22—4882no—
801C22—2444no—
802C22—2444no—
803C22#1683963811yescharacteristic
804C22#1683963811yescharacteristic
805C22#1683963811yescharacteristic
806C22#1683963811yescharacteristic
807C22C2×C22⋊C4×D6111yescharacteristic
808C22C2×#1451973711yescharacteristic
809C22C2×C4×C22⋊D6111yescharacteristic
810C4—42no—
811C4—1224no—
812C4—2444no—
813C4#1683963811yescharacteristic
814C4#1683963811yescharacteristic
815C4#1683963811yescharacteristic
816C4#1683963811yescharacteristic
817C4C2×#1451974511yescharacteristic
818C4C2×#1451974811yescharacteristic
819C4C2×#1451975011yescharacteristic
820C4C2×#1451975911yescharacteristic
821C2—21no—
822C2—21no—
823C2—21no—
824C2—21no—
825C2—21no—
826C2—21no—
827C2—21no—
828C2—82no—
829C2—2444no—
830C2C2×#1683963811yescharacteristic
subgroupG/H
centerC4#16839638
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#413C2
socleC2×C61C2×#386
prime radical#21459148C2
cosocleC22×C4×C61C24
hypercenterC2×#413D61
hypocenterC61#21017
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
1. C2×#16840528C2semidirect
3. C2×#16839746C2semidirect
4. C2×#16839744C2semidirect
5. #21446368C2semidirect
6. #21446363C2semidirect
7. C2×#16839534C2semidirect
8. C2×#16839533C2semidirect
9. C2×C61×#413C2semidirect
34. C2×#14519696C22semidirect
36. C2×#14519694C22semidirect
38. #16839534C22semidirect
39. #16839533C22semidirect
45. C2×#101×C61C22semidirect
46. C2×#100×C61C22semidirect
75. C2×#11758194D4semidirect
76. C2×#11758194D4semidirect
135. C2×M16×C61D4semidirect
136. C2×M16×C61D4semidirect
410. C2×#413D61semidirect
456. C2×#101C2×D61semidirect
459. C2×#100C2×D61semidirect
462. C61#21017semidirect
523. C2×M16C22⋊D61semidirect
524. C2×M16C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405282
#214591482
C2×#168397462
C2×#168397442
#214463682
#214463632
C2×#168395342
C2×#168395332
C2×C61×#4132
#2101761