Finite Group Databasebeta

← #29691298

Subgroups — #29691298

Order 15616.

1080 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448503C211yesmaximal, characteristic, complemented
2#21448401C211yesmaximal, characteristic
3#21446702C211yesmaximal, characteristic, complemented
4#21446675C211yesmaximal, characteristic, complemented
5#21446518C211yesmaximal, characteristic, complemented
6#21446504C211yesmaximal, characteristic, complemented
7#21446448C211yesmaximal, characteristic, complemented
8#21446441C211yesmaximal, characteristic, complemented
9#21446176C211yesmaximal, characteristic, complemented
10#21446176C211yesmaximal, characteristic, complemented
11#21446132C211yesmaximal, characteristic, complemented
12#21446020C211yesmaximal, characteristic, complemented
13#21445750C211yesmaximal, characteristic
14#21445587C211yesmaximal, characteristic, complemented
15C2×C61×#450C211yesmaximal, characteristic
16C2×Q8×Dic61C2211yescharacteristic, complemented
17C2×#14519736C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C2×#14519711C2211yescharacteristic, complemented
20C2×#14519709C2211yescharacteristic, complemented
21C2×#14519701C2211yescharacteristic, complemented
22C2×#14519701C2211yescharacteristic, complemented
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×C22⋊#92418C2211yescharacteristic
28C2×#14519687C2211yescharacteristic, complemented
29C2×C8×Dic61C2211yescharacteristic, complemented
30#16839669C2211yescharacteristic, complemented
31#16839665—21no—
32#16839665—21no—
33#16839665C2211yescharacteristic
34#16839665C2211yescharacteristic
35#16839665C2211yescharacteristic
36#16839665C2211yescharacteristic
37#16839661—21no—
38#16839661C2211yescharacteristic, complemented
39#16839655—21no—
40#16839655—21no—
41#16839648—21no—
42#16839622C2211yescharacteristic
43#16839618—21no—
44#16839618—21no—
45C4⋊C4×Dic61C2211yescharacteristic, complemented
46#16839525C2211yescharacteristic, complemented
47#16839525C2211yescharacteristic, complemented
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839516C2211yescharacteristic, complemented
51#16839516C2211yescharacteristic, complemented
52C23×D4×C61C2211yescharacteristic
53C22×SD16×C61C2211yescharacteristic
54C22×SD16×C61C2211yescharacteristic
55C2×C22⋊Q8×C61C2211yescharacteristic
56C61×#450C418yescomplemented
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C22×#92418C2311yescharacteristic
61C22×#92418C2311yescharacteristic
62Q8×Dic61—41no—
63Q8×Dic61—41no—
64#14519736—41no—
65#14519736—41no—
66#14519736—41no—
67#14519736—41no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61D411yescharacteristic
71C2×C4⋊Dic61D411yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C22⋊Dic61—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—21no—
86C2×C22⋊Dic61D411yescharacteristic
87C2×C22⋊Dic61D411yescharacteristic
88C2×C4×Dic61—21no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61C2311yescharacteristic
92C2×C4×Dic61C2311yescharacteristic
93#14519711—41no—
94#14519709—41no—
95#14519701—41no—
96#14519701—41no—
97#14519698—41no—
98#14519698—41no—
99#14519698—41no—
100#14519698—41no—
101C22⋊#92418—22no—
102#14519687—41no—
103C8×Dic61—41no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109C25×C61—21no—
110C22×Q8×C61C2311yescharacteristic
111C22×D4×C61—21no—
112C22×D4×C61—22no—
113C22×D4×C61—41no—
114C22×D4×C61—41no—
115C22×D4×C61—41no—
116C22×D4×C61—41no—
117C22×D4×C61C2×C414yes—
118C22×D4×C61C2311yescharacteristic
119C22×D4×C61C2311yescharacteristic
120C23×C4×C61C2311yescharacteristic
121C2×SD16×C61—41no—
122C2×SD16×C61—41no—
123C2×SD16×C61—41no—
124C2×SD16×C61—41no—
125C2×SD16×C61C2×C414yes—
126C2×SD16×C61C2×C414yes—
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C22⋊Q8×C61—22no—
130C22⋊Q8×C61C2×C414yes—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C22⋊C4×C61—21no—
134#102×C61C2×C414yes—
135#102×C61C2×C414yes—
136C22⋊C8×C61C2×C414yes—
137C24×C61—21no—
138C24×C61—21no—
139C24×C61—24no—
140C24×C61—42no—
141C24×C61—42no—
142C24×C61—81no—
143C24×C61—81no—
144C24×C61—81no—
145C24×C61—81no—
146C24×C61C2×D411yescharacteristic
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61C22×C412yes—
153C2×D4×C61—24no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
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—44no—
165C2×D4×C61—44no—
166C2×D4×C61—42no—
167C2×D4×C61—42no—
168C2×D4×C61—44no—
169C2×D4×C61—44no—
170C2×D4×C61C22×C412yes—
171C2×D4×C61C22×C412yes—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61C22×C412yes—
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61#4112yes—
181C22×C4×C61C2411yescharacteristic
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61C2×D411yescharacteristic
187C22×Dic61C2×D411yescharacteristic
188C22×Dic61C2×D411yescharacteristic
189C22×Dic61C2×D411yescharacteristic
190SD16×C61—44no—
191SD16×C61—44no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61C22×C412yes—
197C2×C8×C61C22×C412yes—
198C4⋊C4×C61—24no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61C22×C412yes—
201C22⋊C4×C61—24no—
202C22⋊Dic61—41no—
203C22⋊Dic61—41no—
204C22⋊Dic61—42no—
205C22⋊Dic61—81no—
206C22⋊Dic61—81no—
207C22⋊Dic61—81no—
208C22⋊Dic61—81no—
209C22⋊Dic61—81no—
210C22⋊Dic61—81no—
211C22⋊Dic61—81no—
212C22⋊Dic61—81no—
213C22⋊Dic61—81no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—41no—
223C4⋊Dic61—41no—
224C4⋊Dic61—42no—
225C4⋊Dic61—81no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61—42no—
231C4×Dic61—42no—
232C4×Dic61—81no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—22no—
246C23×C61—22no—
247C23×C61—48no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—84no—
261C23×C61—84no—
262C23×C61—84no—
263C23×C61—84no—
264C23×C61—84no—
265C23×C61—84no—
266C23×C61C4×D412yes—
267C23×C61C22×D411yescharacteristic
268Q8×C61—22no—
269Q8×C61—22no—
270Q8×C61—41no—
271Q8×C61—41no—
272D4×C61—22no—
273D4×C61—22no—
274D4×C61—22no—
275D4×C61—22no—
276D4×C61—48no—
277D4×C61—41no—
278D4×C61—41no—
279D4×C61—41no—
280D4×C61—41no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61C4×D412yes—
294C2×C4×C61C23×C411yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61H(5,𝔽2)11yescharacteristic
297C2×C4×C61H(5,𝔽2)11yescharacteristic
298C2×C4×C61H(5,𝔽2)11yescharacteristic
299C2×C4×C61H(5,𝔽2)11yescharacteristic
300C2×Dic61—21no—
301C2×Dic61—21no—
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—41no—
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—
324C8×C61—22no—
325C8×C61—22no—
326#92418—41no—
327#92418—41no—
328#22052—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—42no—
337C22×C61—42no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—816no—
343C22×C61—81no—
344C22×C61—81no—
345C22×C61—81no—
346C22×C61—81no—
347C22×C61—81no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61C2×C4×D411yescharacteristic
352C22×C61#53411yescharacteristic
353C22×C61#53511yescharacteristic
354C22×C61#57611yescharacteristic
355C22×C61#57711yescharacteristic
356C22×C61#57711yescharacteristic
357C22×C61#57711yescharacteristic
358C4×C61—22no—
359C4×C61—42no—
360C4×C61—42no—
361C4×C61#51811yescharacteristic
362C4×C61#51811yescharacteristic
363C4×C61#53811yescharacteristic
364C4×C61#53811yescharacteristic
365Dic61—41no—
366Dic61—41no—
367Dic61—41no—
368Dic61—41no—
369Dic61—81no—
370Dic61—81no—
371Dic61—81no—
372Dic61—81no—
373C2×#450D6111yescharacteristic
374#2323—611no—
375#2309—611no—
376#1973—611no—
377#1968—611no—
378#1936—611no—
379#1934—611no—
380#1926—611no—
381#1925—611no—
382#1880—611no—
383#1880—611no—
384#1873—611no—
385#1854—611no—
386#1786—611no—
387#1750—611no—
388C2×C61—42no—
389C2×C61—82no—
390C2×C61—82no—
391C2×C61#232111yescharacteristic
392C2×C61#294611yescharacteristic
393C2×C61#294911yescharacteristic
394C2×C61#319811yescharacteristic
395C2×C61#320011yescharacteristic
396C2×C61#322211yescharacteristic
397C2×C61#322411yescharacteristic
398C23×D4C2×D6111yescharacteristic
399C22×SD16C2×D6111yescharacteristic
400C22×SD16C2×D6111yescharacteristic
401C2×C22⋊Q8C2×D6111yescharacteristic
402C2×C4×Q8—611no—
403C2×#117—611no—
404C2×#117—611no—
405#450Dic6118yescomplemented
406C2×#107—611no—
407C2×#106—611no—
408C2×#103—611no—
409C2×#103—611no—
410C2×#102—611no—
411C2×#102—611no—
412C2×#102—611no—
413C2×#102—611no—
414C2×#102C2×D6111yescharacteristic
415C2×#102C2×D6111yescharacteristic
416C2×C22⋊C8—611no—
417C2×C22⋊C8C2×D6111yescharacteristic
418C2×#97—611no—
419C2×C4×C8—611no—
420#391—611no—
421#390—611no—
422#390—611no—
423#390—611no—
424#390—611no—
425#390—1221no—
426#390—1221no—
427#389—611no—
428#389—1221no—
429#388—1221no—
430#388—1221no—
431#387—1221no—
432#380—611no—
433#379—1221no—
434#379—1221no—
435C4×C4⋊C4—611no—
436#340—611no—
437#340—611no—
438#340—611no—
439#340—611no—
440#336—611no—
441#336—611no—
442C61#2205211yescharacteristic, complemented, Sylow
443C25—21no—
444C22×Q8C22×D6111yescharacteristic
445C22×D4—21no—
446C22×D4—22no—
447C22×D4—41no—
448C22×D4—41no—
449C22×D4—41no—
450C22×D4—41no—
451C22×D4C2×Dic6114yes—
452C22×D4C22×D6111yescharacteristic
453C22×D4C22×D6111yescharacteristic
454C23×C4C22×D6111yescharacteristic
455C2×SD16—41no—
456C2×SD16—41no—
457C2×SD16—41no—
458C2×SD16—41no—
459C2×SD16C2×Dic6114yes—
460C2×SD16C2×Dic6114yes—
461C22×C8—611no—
462C22×C8—611no—
463C22×C8C22×D6111yescharacteristic
464C22×C8C22×D6111yescharacteristic
465C22⋊Q8—22no—
466C22⋊Q8C2×Dic6114yes—
467C4×Q8—2441no—
468C4×Q8—2441no—
469#117—2441no—
470#117—2441no—
471#117—2441no—
472#117—2441no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4C22×D6111yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—611no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C42—611no—
497C2×C42—611no—
498C2×C42—1221no—
499C2×C42—1221no—
500C2×C42—1221no—
501#107—2441no—
502#106—2441no—
503#103—2441no—
504#103—2441no—
505#102—2441no—
506#102—2441no—
507#102—2441no—
508#102—2441no—
509#102C2×Dic6114yes—
510#102C2×Dic6114yes—
511C22⋊C8—1222no—
512C22⋊C8C2×Dic6114yes—
513#97—2441no—
514C4×C8—2441no—
515#95—1221no—
516#95—1221no—
517#95—1221no—
518#95—1221no—
519#95—1221no—
520C24—21no—
521C24—21no—
522C24—24no—
523C24—42no—
524C24—42no—
525C24—81no—
526C24—81no—
527C24—81no—
528C24—81no—
529C24D4×D6111yescharacteristic
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8C22×Dic6112yes—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—24no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—44no—
552C2×D4—44no—
553C2×D4C22×Dic6112yes—
554C2×D4C22×Dic6112yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4D4×D6111yescharacteristic
570C22×C4#1175822412yes—
571C22×C4C22×Dic6112yes—
572C22×C4C23×D6111yescharacteristic
573SD16—44no—
574SD16—44no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8C22×Dic6112yes—
586C2×C8C22×Dic6112yes—
587C4⋊C4—21no—
588C4⋊C4—24no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—4881no—
598C4⋊C4—2441no—
599C4⋊C4—2441no—
600C4⋊C4—2442no—
601C4⋊C4C22×Dic6112yes—
602C22⋊C4—24no—
603C22⋊C4—4881no—
604C22⋊C4—4881no—
605C22⋊C4—4881no—
606C22⋊C4—4881no—
607C22⋊C4—4881no—
608C22⋊C4—4881no—
609C22⋊C4—4881no—
610C22⋊C4—4881no—
611C22⋊C4—4881no—
612C22⋊C4—2441no—
613C22⋊C4—2441no—
614C22⋊C4—2442no—
615C42—1221no—
616C42—1221no—
617C42—1221no—
618C42—1221no—
619C42—4881no—
620C42—2442no—
621C42—2442no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—22no—
629C23—22no—
630C23—48no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23D4×Dic6112yes—
650C23C2×D4×D6111yescharacteristic
651Q8—22no—
652Q8—22no—
653Q8—41no—
654Q8—41no—
655D4—22no—
656D4—22no—
657D4—22no—
658D4—22no—
659D4—48no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4D4×Dic6112yes—
701C2×C4C23×Dic6111yescharacteristic
702C2×C4C2×#1175822411yescharacteristic
703C2×C4#1451982211yescharacteristic
704C2×C4#1451982211yescharacteristic
705C2×C4#1451982211yescharacteristic
706C2×C4#1451982211yescharacteristic
707C8—22no—
708C8—22no—
709C8—2441no—
710C8—2441no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—816no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22C2×D4×Dic6111yescharacteristic
734C22#1684032211yescharacteristic
735C22#1684032711yescharacteristic
736C22#1684056611yescharacteristic
737C22#1684056811yescharacteristic
738C22#1684056811yescharacteristic
739C22#1684057211yescharacteristic
740C4—22no—
741C4—42no—
742C4—42no—
743C4—4881no—
744C4—4881no—
745C4—4881no—
746C4—4881no—
747C4—2441no—
748C4—2441no—
749C4—2441no—
750C4—2441no—
751C4#1684023711yescharacteristic
752C4#1684023711yescharacteristic
753C4#1684034711yescharacteristic
754C4#1684034711yescharacteristic
755C2—42no—
756C2—82no—
757C2—82no—
758C2#2144848011yescharacteristic
759C2#2145465211yescharacteristic
760C2#2145467911yescharacteristic
761C2#2145667511yescharacteristic
762C2#2145668811yescharacteristic
763C2#2145688711yescharacteristic
764C2#2145691711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#450C2
socleC23×C61C22×D4
prime radicalC23×D4×C61C22
cosocleC22×C4×C61C24
hypercenterC2×#450D61
hypocenterC61#22052
LCSG ▷ C2×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. #21448503C2semidirect
3. #21446702C2semidirect
4. #21446675C2semidirect
5. #21446518C2semidirect
6. #21446504C2semidirect
7. #21446448C2semidirect
8. #21446441C2semidirect
9. #21446176C2semidirect
10. #21446176C2semidirect
11. #21446132C2semidirect
12. #21446020C2semidirect
14. #21445587C2semidirect
16. C2×Q8×Dic61C22semidirect
19. C2×#14519711C22semidirect
20. C2×#14519709C22semidirect
21. C2×#14519701C22semidirect
22. C2×#14519701C22semidirect
28. C2×#14519687C22semidirect
29. C2×C8×Dic61C22semidirect
30. #16839669C22semidirect
38. #16839661C22semidirect
45. C4⋊C4×Dic61C22semidirect
46. #16839525C22semidirect
47. #16839525C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839516C22semidirect
51. #16839516C22semidirect
56. C61×#450C4semidirect
405. #450Dic61semidirect
442. C61#22052semidirect

Maximal subgroups

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

subgroupindex
#214485032
#214484012
#214467022
#214466752
#214465182
#214465042
#214464482
#214464412
#214461762
#214461322
#214460202
#214457502
#214455872
C2×C61×#4502
#2205261