Finite Group Databasebeta

← #29723929

Subgroups — #29723929

Order 15616.

1148 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic61C211yesmaximal, characteristic, complemented
2#21449318C211yesmaximal, characteristic, complemented
3D4×C22⋊Dic61C211yesmaximal, characteristic
4#21447342C211yesmaximal, characteristic, complemented
5#21447252C211yesmaximal, characteristic, complemented
6#21447132C211yesmaximal, characteristic, complemented
7#21447019C211yesmaximal, characteristic, complemented
8#21446499C211yesmaximal, characteristic, complemented
9#21446422C211yesmaximal, characteristic, complemented
10#21446176C211yesmaximal, characteristic, complemented
11#21446155C211yesmaximal, characteristic, complemented
12#21446064C211yesmaximal, characteristic, complemented
13#21445827C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic
15C2×C61×#450C211yesmaximal, characteristic
16C2×Q8×Dic61C2211yescharacteristic, complemented
17C2×D4×Dic61C2211yescharacteristic
18C2×D4×Dic61C2211yescharacteristic
19C22×C22⋊Dic61—21no—
20SD16×Dic61—24no—
21C2×#14519710C2211yescharacteristic, complemented
22C2×#14519709C2211yescharacteristic, complemented
23C2×#14519706C2211yescharacteristic, complemented
24C2×#14519701C2211yescharacteristic, complemented
25C2×#14519701C2211yescharacteristic, complemented
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×C8×Dic61C2211yescharacteristic, complemented
32#16839701—21no—
33#16839687—21no—
34#16839669C2211yescharacteristic, complemented
35#16839665C2211yescharacteristic
36#16839665C2211yescharacteristic
37#16839658C2211yescharacteristic, complemented
38#16839650—21no—
39#16839643—21no—
40#16839642—21no—
41#16839642—21no—
42#16839627C2211yescharacteristic, complemented
43#16839622C2211yescharacteristic
44#16839622C2211yescharacteristic
45#16839618—21no—
46C4×C22⋊Dic61C2211yescharacteristic
47#16839525C2211yescharacteristic, complemented
48#16839525C2211yescharacteristic, complemented
49#16839525C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839516C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53C23×D4×C61C2211yescharacteristic
54C22×SD16×C61C2211yescharacteristic
55C22×SD16×C61C2211yescharacteristic
56C2×C22⋊Q8×C61C2211yescharacteristic
57C61×#450—24no—
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C23×Dic61—21no—
62C23×Dic61—21no—
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65Q8×Dic61—22no—
66Q8×Dic61—41no—
67D4×Dic61—22no—
68D4×Dic61—22no—
69D4×Dic61—41no—
70D4×Dic61—41no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×#11758196—21no—
77C2×C22⋊Dic61—21no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—44no—
86C2×C22⋊Dic61D411yescharacteristic
87C2×C22⋊Dic61D411yescharacteristic
88C2×C4×Dic61—21no—
89C2×C4×Dic61C2311yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91#14519710—41no—
92#14519709—22no—
93#14519706—41no—
94#14519701—22no—
95#14519701—41no—
96#14519698—22no—
97#14519698—22no—
98#14519698—22no—
99#14519698—41no—
100C22⋊#92418—41no—
101C8×Dic61—22no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684D411yescharacteristic
110#14519684D411yescharacteristic
111C25×C61—21no—
112C22×Q8×C61C2311yescharacteristic
113C22×D4×C61—22no—
114C22×D4×C61—22no—
115C22×D4×C61—22no—
116C22×D4×C61—22no—
117C22×D4×C61—21no—
118C22×D4×C61—41no—
119C22×D4×C61—41no—
120C22×D4×C61C2311yescharacteristic
121C22×D4×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C2×SD16×C61—22no—
124C2×SD16×C61—22no—
125C2×SD16×C61—22no—
126C2×SD16×C61—22no—
127C2×SD16×C61—41no—
128C2×SD16×C61D414yes—
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C22⋊Q8×C61—22no—
132C22⋊Q8×C61—41no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C22⋊C4×C61—21no—
136#102×C61—22no—
137#102×C61—22no—
138C22⋊C8×C61—22no—
139C24×C61—21no—
140C24×C61—24no—
141C24×C61—21no—
142C24×C61—42no—
143C24×C61—42no—
144C24×C61—42no—
145C24×C61—42no—
146C24×C61—81no—
147C24×C61—81no—
148C24×C61C2×D411yescharacteristic
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61C2×D412yes—
155C2×D4×C61—24no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—42no—
165C2×D4×C61—42no—
166C2×D4×C61—44no—
167C2×D4×C61—44no—
168C2×D4×C61—44no—
169C2×D4×C61—44no—
170C2×D4×C61C2×D412yes—
171C2×D4×C61#4112yes—
172C2×D4×C61#4112yes—
173C2×D4×C61#4112yes—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2411yescharacteristic
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—42no—
189C22×Dic61—42no—
190C22×Dic61—42no—
191C22×Dic61—42no—
192C22×Dic61—81no—
193C22×Dic61—81no—
194C22×Dic61C2×D411yescharacteristic
195C22×Dic61C2×D411yescharacteristic
196C22×Dic61C2×D411yescharacteristic
197C22×Dic61C2×D411yescharacteristic
198SD16×C61—28no—
199SD16×C61—44no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61C2×D412yes—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—42no—
209C22⋊C4×C61—42no—
210C22⋊Dic61—22no—
211C22⋊Dic61—22no—
212C22⋊Dic61—42no—
213C22⋊Dic61—42no—
214C22⋊Dic61—42no—
215C22⋊Dic61—42no—
216C22⋊Dic61—42no—
217C22⋊Dic61—42no—
218C22⋊Dic61—81no—
219C22⋊Dic61—81no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—42no—
229#11758196—42no—
230C4×Dic61—21no—
231C4×Dic61—21no—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C4×Dic61—42no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C23×C61—21no—
242C23×C61—22no—
243C23×C61—22no—
244C23×C61—21no—
245C23×C61—22no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—22no—
251C23×C61—48no—
252C23×C61—48no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—84no—
264C23×C61—84no—
265C23×C61—84no—
266C23×C61—84no—
267C23×C61—84no—
268C23×C61#13512yes—
269C23×C61C22×D411yescharacteristic
270Q8×C61—22no—
271Q8×C61—22no—
272Q8×C61—41no—
273Q8×C61—41no—
274D4×C61—22no—
275D4×C61—22no—
276D4×C61—22no—
277D4×C61—22no—
278D4×C61—22no—
279D4×C61—48no—
280D4×C61—41no—
281D4×C61—41no—
282D4×C61#12314yes—
283C2×C4×C61—21no—
284C2×C4×C61—22no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61C22×D411yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C2×C4×C61C2×#4111yescharacteristic
299C2×C4×C61C2×#4111yescharacteristic
300C2×C4×C61H(5,𝔽2)11yescharacteristic
301C2×C4×C61H(5,𝔽2)11yescharacteristic
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—84no—
326C2×Dic61—84no—
327C2×Dic61AGL(1,ℤ/8)12yes—
328C8×C61—22no—
329C8×C61—41no—
330#92418—41no—
331#92418—41no—
332#24905—611nomaximal, Sylow
333C22×C61—22no—
334C22×C61—24no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—42no—
338C22×C61—41no—
339C22×C61—42no—
340C22×C61—41no—
341C22×C61—42no—
342C22×C61—41no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—41no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—816no—
351C22×C61—81no—
352C22×C61—81no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61#52511yescharacteristic
356C22×C61D4211yescharacteristic
357C22×C61#54611yescharacteristic
358C22×C61C2×#13511yescharacteristic
359C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
360C22×C61#57711yescharacteristic
361C22×C61#57711yescharacteristic
362C4×C61—41no—
363C4×C61—42no—
364C4×C61—81no—
365C4×C61C2×#12311yescharacteristic
366C4×C61#53811yescharacteristic
367C4×C61#54611yescharacteristic
368C4×C61#55111yescharacteristic
369Dic61—22no—
370Dic61—41no—
371Dic61—41no—
372Dic61—41no—
373Dic61—81no—
374Dic61—81no—
375Dic61—81no—
376Dic61—81no—
377C2×#450D6111yescharacteristic
378C2×C4×SD16—611no—
379#2421—611no—
380D4×C22⋊C4—611no—
381#2092—611no—
382#2077—611no—
383#2055—611no—
384#2036—611no—
385#1934—611no—
386#1923—611no—
387#1880—611no—
388#1877—611no—
389#1862—611no—
390#1804—611no—
391#1786—611no—
392C2×C61—42no—
393C2×C61—44no—
394C2×C61—82no—
395C2×C61#241811yescharacteristic
396C2×C61#310511yescharacteristic
397C2×C61#312311yescharacteristic
398C2×C61#326511yescharacteristic
399C2×C61#328211yescharacteristic
400C2×C61#329611yescharacteristic
401C2×C61#332411yescharacteristic
402C23×D4C2×D6111yescharacteristic
403C22×SD16C2×D6111yescharacteristic
404C22×SD16C2×D6111yescharacteristic
405C2×C22⋊Q8C2×D6111yescharacteristic
406C2×C4×Q8—611no—
407C2×C4×D4—611no—
408C2×C4×D4—611no—
409C22×C22⋊C4—1221no—
410#450—24no—
411C4×SD16—1224no—
412C2×#107—611no—
413C2×#106—611no—
414C2×C4⋊C8—611no—
415C2×#103—611no—
416C2×#103—611no—
417C2×#102—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102C2×D6111yescharacteristic
422C2×#102C2×D6111yescharacteristic
423C2×C22⋊C8—611no—
424C2×C22⋊C8C2×D6111yescharacteristic
425C2×C4×C8—611no—
426#400—1221no—
427#397—1221no—
428#391—611no—
429#390—611no—
430#390—611no—
431#389—611no—
432#388—1221no—
433#387—1221no—
434#386—1221no—
435#386—1221no—
436#382—611no—
437#380—611no—
438#380—611no—
439#379—1221no—
440C4×C22⋊C4—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#340—611no—
445#336—611no—
446#336—611no—
447C61#2490511yescharacteristic, complemented, Sylow
448C25—21no—
449C22×Q8C22×D6111yescharacteristic
450C22×D4—22no—
451C22×D4—22no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—21no—
455C22×D4—41no—
456C22×D4—41no—
457C22×D4C22×D6111yescharacteristic
458C22×D4C22×D6111yescharacteristic
459C23×C4—1221no—
460C23×C4—1221no—
461C23×C4C22×D6111yescharacteristic
462C2×SD16—22no—
463C2×SD16—22no—
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—41no—
467C2×SD16C22⋊D6114yes—
468C22×C8—611no—
469C22×C8—611no—
470C22×C8C22×D6111yescharacteristic
471C22×C8C22×D6111yescharacteristic
472C22⋊Q8—22no—
473C22⋊Q8—41no—
474C4×Q8—1222no—
475C4×Q8—2441no—
476C4×D4—1222no—
477C4×D4—1222no—
478C4×D4—2441no—
479C4×D4—2441no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4C22×D6111yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—611no—
490C2×C22⋊C4—611no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—2444no—
500C2×C42—611no—
501C2×C42—611no—
502C2×C42—1221no—
503#107—2441no—
504#106—1222no—
505C4⋊C8—2441no—
506#103—1222no—
507#103—2441no—
508#102—22no—
509#102—22no—
510#102—1222no—
511#102—1222no—
512#102—1222no—
513#102—2441no—
514C22⋊C8—22no—
515C22⋊C8—2441no—
516C4×C8—1222no—
517#95—611no—
518#95—611no—
519#95—1221no—
520#95—1221no—
521#95—1221no—
522#95—1221no—
523#95—1221no—
524#95—1221no—
525#95—1221no—
526C24—21no—
527C24—24no—
528C24—21no—
529C24—42no—
530C24—42no—
531C24—42no—
532C24—42no—
533C24—81no—
534C24—81no—
535C24D4×D6111yescharacteristic
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8C2×C22⋊D6112yes—
542C2×D4—24no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4#1175822412yes—
558C2×D4#1175822412yes—
559C2×D4#1175822412yes—
560C2×D4C2×C22⋊D6112yes—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—611no—
572C22×C4—611no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—4881no—
578C22×C4—4881no—
579C22×C4—2442no—
580C22×C4—2442no—
581C22×C4—2442no—
582C22×C4—2442no—
583C22×C4D4×D6111yescharacteristic
584C22×C4C23×D6111yescharacteristic
585SD16—28no—
586SD16—44no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8C2×C22⋊D6112yes—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—42no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—2442no—
611C4⋊C4—2442no—
612C22⋊C4—42no—
613C22⋊C4—1222no—
614C22⋊C4—1222no—
615C22⋊C4—4881no—
616C22⋊C4—4881no—
617C22⋊C4—2442no—
618C22⋊C4—2442no—
619C22⋊C4—2442no—
620C22⋊C4—2442no—
621C22⋊C4—2442no—
622C22⋊C4—2442no—
623C42—1221no—
624C42—1221no—
625C42—1221no—
626C42—1221no—
627C42—2442no—
628C23—21no—
629C23—22no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—22no—
638C23—48no—
639C23—48no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23#1451979812yes—
656C23C2×D4×D6111yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661D4—22no—
662D4—22no—
663D4—22no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—41no—
668D4—41no—
669D4#1451975814yes—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—612no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—4884no—
696C2×C4—4884no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4C22×C22⋊D6111yescharacteristic
710C2×C4C2×#1175822411yescharacteristic
711C2×C4C2×#1175822411yescharacteristic
712C2×C4C2×#1175822411yescharacteristic
713C2×C4#1451982211yescharacteristic
714C2×C4#1451982211yescharacteristic
715C8—22no—
716C8—41no—
717C8—2441no—
718C8—2441no—
719C22—24no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—42no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—816no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22#1684026811yescharacteristic
742C22D4×C22⋊D6111yescharacteristic
743C22#1684039911yescharacteristic
744C22C2×#1451979811yescharacteristic
745C22AGL(1,ℤ/8)×D6111yescharacteristic
746C22#1684056811yescharacteristic
747C22#1684057211yescharacteristic
748C4—41no—
749C4—42no—
750C4—81no—
751C4—1222no—
752C4—4881no—
753C4—4881no—
754C4—4881no—
755C4—4881no—
756C4—2441no—
757C4—2441no—
758C4—2441no—
759C4C2×#1451975811yescharacteristic
760C4#1684034711yescharacteristic
761C4#1684040611yescharacteristic
762C4#1684044311yescharacteristic
763C2—42no—
764C2—44no—
765C2—82no—
766C2#2144927711yescharacteristic
767C2#2145586711yescharacteristic
768C2#2145606511yescharacteristic
769C2#2145730811yescharacteristic
770C2#2145752611yescharacteristic
771C2#2145765811yescharacteristic
772C2#2145804311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#450C2
socleC23×C61C22×D4
prime radicalC23×D4×C61C22
hypercenterC2×#450D61
hypocenterC61#24905
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×SD16×Dic61C2semidirect
2. #21449318C2semidirect
4. #21447342C2semidirect
5. #21447252C2semidirect
6. #21447132C2semidirect
7. #21447019C2semidirect
8. #21446499C2semidirect
9. #21446422C2semidirect
10. #21446176C2semidirect
11. #21446155C2semidirect
12. #21446064C2semidirect
13. #21445827C2semidirect
16. C2×Q8×Dic61C22semidirect
21. C2×#14519710C22semidirect
22. C2×#14519709C22semidirect
23. C2×#14519706C22semidirect
24. C2×#14519701C22semidirect
25. C2×#14519701C22semidirect
31. C2×C8×Dic61C22semidirect
34. #16839669C22semidirect
37. #16839658C22semidirect
42. #16839627C22semidirect
47. #16839525C22semidirect
48. #16839525C22semidirect
49. #16839525C22semidirect
50. #16839524C22semidirect
51. #16839516C22semidirect
52. #16839516C22semidirect
447. C61#24905semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic612
#214493182
D4×C22⋊Dic612
#214473422
#214472522
#214471322
#214470192
#214464992
#214464222
#214461762
#214461552
#214460642
#214458272
#214457502
C2×C61×#4502
#2490561