Finite Group Databasebeta

← C2×#21446300 #29681879

Subgroups — C2×#21446300 #29681879

Order 15616.

1782 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519805C211yesmaximal, characteristic
2C2×#16840528C211yesmaximal, characteristic, complemented
3C2×#16839778C211yesmaximal, characteristic, complemented
4C2×#16839768C211yesmaximal, characteristic, complemented
5C22×#14519693C211yesmaximal, characteristic, complemented
6#21446300C218yesmaximal, direct product factor
7C2×#16839533C211yesmaximal, characteristic, complemented
8C2×C61×#338C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C23×D244C2211yescharacteristic
11C2×#14519805—22no—
12C2×#14519805—22no—
13C2×#14519805—22no—
14C2×#14519805—22no—
15C2×#14519805C414yescomplemented
16C2×#14519805C2214yes—
17C22×#11758190C412yescomplemented
18C22×D488C412yescomplemented
19#16840528—22no—
20#16840528—22no—
21#16840528—22no—
22#16840528C2214yescomplemented
23C2×#14519785—22no—
24C2×#14519783—22no—
25C22×#11758194C2211yescharacteristic
26C2×M16×D61—22no—
27C2×#14519736C2211yescharacteristic
28#16839778—22no—
29#16839778C2214yescomplemented
30C2×#14519703—22no—
31#16839768—22no—
32#16839768C2214yescomplemented
33C2×#14519699—22no—
34C2×#14519693—22no—
35C2×#14519693—22no—
36C2×#14519693C2214yescomplemented
37#16839533C2214yescomplemented
38C22×M16×C61C2211yescharacteristic
39C22×M16×C61C2211yescharacteristic
40C22×M16×C61C2211yescharacteristic
41C61×#338C2214yescomplemented
42C24×D61—21no—
43C2×#11758222—21no—
44C2×#11758222—21no—
45C2×#11758222—21no—
46C2×#11758222—21no—
47C2×#11758222—21no—
48C2×#11758222—21no—
49C2×#11758222C2×C412yes—
50C2×#11758222D412yes—
51C2×#11758222D412yes—
52C2×#11758222D412yes—
53C2×#11758222D412yes—
54C2×#11758222C2312yes—
55C22×Dic122C2×C411yescharacteristic
56C22×D244—21no—
57C22×D244—21no—
58C22×D244—21no—
59C22×D244—21no—
60C22×D244—21no—
61C22×D244—21no—
62C22×D244—21no—
63C22×D244—21no—
64C22×D244—21no—
65C22×D244—21no—
66C22×D244—21no—
67C22×D244C2×C412yes—
68C22×D244C2×C412yes—
69C22×D244C2×C411yescharacteristic
70C22×D244C2312yes—
71C22×C22⋊D61—21no—
72C22×C4×D61—21no—
73#14519805—28no—
74#14519805—28no—
75#14519805—28no—
76#14519805—28no—
77C2×#11758190—24no—
78C2×#11758190—24no—
79C2×#11758190C2×C418yescomplemented
80C2×D488—24no—
81C2×D488—24no—
82C2×D488C2×C418yescomplemented
83#14519785—28no—
84#14519785—28no—
85#14519783—28no—
86#14519783—28no—
87C2×#11758194—21no—
88C2×#11758194—21no—
89C2×#11758194—21no—
90C2×#11758194D412yes—
91C2×#11758194D412yes—
92C2×#11758194C2312yes—
93C2×#11758189—24no—
94M16×D61—28no—
95M16×D61—28no—
96C22×#92418—21no—
97C2×C8×D61—24no—
98#14519736—21no—
99#14519736—21no—
100#14519736—21no—
101#14519736C2312yes—
102C2×C4⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C4×Dic61—21no—
105#14519703—28no—
106#14519699—28no—
107#14519693—28no—
108C23×C4×C61C2311yescharacteristic
109C2×M16×C61—21no—
110C2×M16×C61—21no—
111C2×M16×C61—21no—
112C2×M16×C61—21no—
113C2×M16×C61—21no—
114C2×M16×C61—21no—
115C2×M16×C61—21no—
116C2×M16×C61—21no—
117C2×M16×C61—21no—
118C2×M16×C61—21no—
119C2×M16×C61—21no—
120C2×M16×C61—21no—
121C2×M16×C61—21no—
122C2×M16×C61C2×C412yes—
123C2×M16×C61D412yes—
124C2×M16×C61C2312yes—
125C2×M16×C61C2312yes—
126C2×M16×C61C2312yes—
127C22×C8×C61—21no—
128C22×C8×C61C2×C412yes—
129C22×C8×C61D412yes—
130C24×C61#4111yescharacteristic
131C23×D61—21no—
132C23×D61—22no—
133C23×D61—22no—
134C23×D61—22no—
135C23×D61—41no—
136C23×D61—41no—
137C23×D61—41no—
138C23×D61—41no—
139C23×D61—84no—
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61#4111yescharacteristic
151C22×C4×C61#4111yescharacteristic
152C22×C4×C61#4111yescharacteristic
153C22×C4×C61C2411yescharacteristic
154C2×C22⋊D61—22no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C22×Dic61—21no—
161C22×Dic61—41no—
162#11758222—22no—
163#11758222—22no—
164#11758222—22no—
165#11758222—22no—
166#11758222—22no—
167#11758222—22no—
168#11758222—22no—
169#11758222—22no—
170#11758222—22no—
171#11758222—22no—
172#11758222—22no—
173#11758222—22no—
174#11758222C22⋊C414yes—
175#11758222C22⋊C414yes—
176#11758222C2×D414yes—
177#11758222C2×D414yes—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—22no—
182C2×D244—22no—
183C2×D244—22no—
184C2×D244—22no—
185C2×D244—22no—
186C2×D244—22no—
187C2×D244—22no—
188C2×D244—22no—
189C2×D244—22no—
190C2×D244—22no—
191C2×D244—22no—
192C2×D244—22no—
193C2×D244—22no—
194C2×D244—22no—
195C2×D244—22no—
196C2×D244—41no—
197C2×D244—41no—
198C2×D244—41no—
199C2×D244—41no—
200C2×D244—41no—
201C2×D244—41no—
202C2×D244—41no—
203C2×D244—41no—
204C2×D244—41no—
205C2×D244—41no—
206C2×D244—41no—
207C2×D244—41no—
208C2×D244C22⋊C412yes—
209C2×D244C22⋊C412yes—
210C2×D244C22×C414yes—
211C2×D244C22×C412yes—
212C2×C4×D61—22no—
213C2×C4×D61—22no—
214C2×C4×D61—22no—
215C2×C4×D61—22no—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×Dic122—21no—
219C2×Dic122—21no—
220C2×Dic122—21no—
221C2×Dic122C22⋊C412yes—
222C2×Dic122C22⋊C412yes—
223C2×Dic122C22×C412yes—
224M16×C61—22no—
225M16×C61—22no—
226M16×C61—22no—
227M16×C61—22no—
228M16×C61—22no—
229M16×C61—22no—
230M16×C61—22no—
231M16×C61—22no—
232M16×C61—22no—
233M16×C61—22no—
234M16×C61—41no—
235M16×C61—41no—
236C2×C8×C61—22no—
237C2×C8×C61—22no—
238C2×C8×C61—22no—
239C2×C8×C61—22no—
240C2×C8×C61—22no—
241C2×C8×C61—41no—
242C2×C8×C61—41no—
243C2×C8×C61C22×C414yes—
244C2×C8×C61C2×D414yes—
245C22⋊Dic61—22no—
246C22⋊Dic61—41no—
247C4⋊Dic61—22no—
248C4⋊Dic61—41no—
249C4×Dic61—22no—
250C4×Dic61—41no—
251#11758194—22no—
252#11758194—22no—
253#11758194—22no—
254#11758194C2×D414yes—
255C2×#92418—22no—
256C2×#92418—22no—
257C2×#92418—22no—
258D488—216no—
259#11758190—216no—
260#11758189—216no—
261C8×D61—216no—
262C23×C61—42no—
263C23×C61C4×D411yescharacteristic
264C23×C61C4×D411yescharacteristic
265C23×C61#12111yescharacteristic
266C23×C61#12111yescharacteristic
267C23×C61#12311yescharacteristic
268C23×C61#12311yescharacteristic
269C23×C61C2×#4111yescharacteristic
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—24no—
274C22×D61—42no—
275C22×D61—42no—
276C22×D61—42no—
277C22×D61—42no—
278C22×D61—42no—
279C22×D61—42no—
280C22×D61—82no—
281C22×D61—84no—
282C22×D61—84no—
283C22×D61—84no—
284C22×D61—84no—
285C22×D61—84no—
286C22×D61—84no—
287C22×D61—84no—
288C2×C4×C61C2×C22⋊C411yescharacteristic
289C2×C4×C61C2×C22⋊C411yescharacteristic
290C2×C4×C61C2×C22⋊C411yescharacteristic
291C2×C4×C61C2×C22⋊C411yescharacteristic
292C2×C4×C61C4×D411yescharacteristic
293C2×C4×C61C4×D411yescharacteristic
294C2×C4×C61C4×D411yescharacteristic
295C2×C4×C61C4×D411yescharacteristic
296C2×C4×C61C4×D411yescharacteristic
297C2×C4×C61C4×D411yescharacteristic
298C2×C4×C61#12011yescharacteristic
299C2×C4×C61#12011yescharacteristic
300C2×C4×C61#12011yescharacteristic
301C2×C4×C61#12011yescharacteristic
302C2×C4×C61#12111yescharacteristic
303C2×C4×C61#12111yescharacteristic
304C2×C4×C61#12111yescharacteristic
305C2×C4×C61#12111yescharacteristic
306C2×C4×C61#12111yescharacteristic
307C2×C4×C61#12111yescharacteristic
308C2×C4×C61#12311yescharacteristic
309C2×C4×C61#12311yescharacteristic
310C2×C4×C61C23×C411yescharacteristic
311C2×C4×C61C22×D411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C22×D411yescharacteristic
314C2×C4×C61C22×D411yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C22⋊D61—24no—
317C22⋊D61—24no—
318C22⋊D61—24no—
319C22⋊D61—24no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—42no—
324C2×Dic61—82no—
325D244—24no—
326D244—22no—
327D244—24no—
328D244—22no—
329D244—22no—
330D244—42no—
331D244—42no—
332D244—42no—
333D244—42no—
334D244—42no—
335D244—42no—
336D244C2×C22⋊C414yes—
337C4×D61—24no—
338C4×D61—24no—
339C4×D61—24no—
340C4×D61—24no—
341Dic122—22no—
342Dic122—22no—
343Dic122—22no—
344Dic122C2×C22⋊C414yes—
345C8×C61—24no—
346C8×C61—24no—
347C8×C61—42no—
348#92418—24no—
349C2×#1903—611nomaximal, Sylow
350C22×C61—22no—
351C22×C61—22no—
352C22×C61—22no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61#38611yescharacteristic
358C22×C61#38611yescharacteristic
359C22×C61#38611yescharacteristic
360C22×C61#38611yescharacteristic
361C22×C61C2×C4×D411yescharacteristic
362C22×C61C2×#12111yescharacteristic
363C22×C61C2×#12311yescharacteristic
364C2×D61—24no—
365C2×D61—44no—
366C2×D61—44no—
367C2×D61—82no—
368C2×D61—82no—
369C2×D61—84no—
370C2×D61—84no—
371C2×D61—84no—
372C2×D61—84no—
373C2×D61—84no—
374C2×D61—84no—
375C2×D61—84no—
376C4×C61#38611yescharacteristic
377C4×C61#38611yescharacteristic
378C4×C61#38611yescharacteristic
379C4×C61#38611yescharacteristic
380C4×C61C22×C22⋊C411yescharacteristic
381C4×C61C2×C4×D411yescharacteristic
382C4×C61C2×#12011yescharacteristic
383C4×C61C2×#12111yescharacteristic
384Dic61—24no—
385Dic61—82no—
386C22×AGL(1,ℤ/8)—611no—
387C2×#568—611no—
388C2×#421—611no—
389C2×#418—611no—
390C22×#100—611no—
391#1903—618no—
392C2×#344—611no—
393C2×#338D6111yescharacteristic, complemented
394C2×C61—21no—
395C2×C61—21no—
396C2×C61—21no—
397C2×C61—21no—
398C2×C61—21no—
399C2×C61—21no—
400C2×C61#190312yescomplemented
401C2×C61C2×#38611yescharacteristic
402D61—44no—
403D61—84no—
404C22×#41—611no—
405C23×D4—611no—
406C2×AGL(1,ℤ/8)—614no—
407C2×AGL(1,ℤ/8)—614no—
408C2×AGL(1,ℤ/8)—1222no—
409C2×AGL(1,ℤ/8)—1222no—
410C2×AGL(1,ℤ/8)—1222no—
411C2×AGL(1,ℤ/8)—1222no—
412C22×SD16—612no—
413C22×D8—612no—
414#568—614no—
415#568—1222no—
416#568—1222no—
417#568—1222no—
418C2×#131—1222no—
419C2×#131—1222no—
420C22×M16—611no—
421C22×M16—1222no—
422C22×M16C2×D6111yescharacteristic
423C22×M16C2×D6111yescharacteristic
424C22×M16C2×D6111yescharacteristic
425C2×#117—611no—
426#421—614no—
427#421—1222no—
428C2×#104—1222no—
429#418—614no—
430#418—1222no—
431C2×#102—1222no—
432C2×#100—614no—
433C2×#100—1222no—
434C2×#100—1222no—
435#344—614no—
436#338C2×D6114yescomplemented
437C61C2×#190311yescharacteristic, complemented, Sylow
438C25—1221no—
439C2×#41—612no—
440C2×#41—612no—
441C2×#41—612no—
442C2×#41—612no—
443C2×#41—612no—
444C2×#41—612no—
445C2×#41—1221no—
446C2×#41—1221no—
447C2×#41—1221no—
448C2×#41—1221no—
449C2×#41—1221no—
450C2×#41—1221no—
451C22×Q8—611no—
452C22×D4—611no—
453C22×D4—612no—
454C22×D4—612no—
455C22×D4—612no—
456C22×D4—1221no—
457C22×D4—1221no—
458C22×D4—1221no—
459C22×D4—1221no—
460C22×D4—1221no—
461C22×D4—1221no—
462C22×D4—1221no—
463C22×D4—1221no—
464C22×D4—1221no—
465C22×D4—1221no—
466C22×D4—1221no—
467C22×D4—1221no—
468C23×C4—1221no—
469C23×C4C22×D6111yescharacteristic
470AGL(1,ℤ/8)—1228no—
471AGL(1,ℤ/8)—1228no—
472AGL(1,ℤ/8)—1228no—
473AGL(1,ℤ/8)—1228no—
474C2×SD16—618no—
475C2×SD16—1224no—
476C2×SD16—1224no—
477C2×D8—618no—
478C2×D8—1224no—
479C2×D8—1224no—
480#131—1228no—
481#131—1228no—
482#131—1228no—
483#131—1228no—
484C2×M16—21no—
485C2×M16—21no—
486C2×M16—21no—
487C2×M16—21no—
488C2×M16—21no—
489C2×M16—21no—
490C2×M16—21no—
491C2×M16—21no—
492C2×M16—21no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—21no—
497C2×M16—612no—
498C2×M16—612no—
499C2×M16—612no—
500C2×M16—1224no—
501C2×M16—1228no—
502C2×M16—1228no—
503C2×M16—1221no—
504C2×M16—1221no—
505C2×M16—1221no—
506C2×M16C4×D6112yes—
507C2×M16D24412yes—
508C2×M16C22×D6112yes—
509C2×M16C22×D6112yes—
510C2×M16C22×D6112yes—
511C22×C8—21no—
512C22×C8—1224no—
513C22×C8—1221no—
514C22×C8C4×D6112yes—
515C22×C8D24412yes—
516#117—612no—
517#117—1221no—
518#117—1221no—
519#117—1221no—
520C2×C4⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C42—1221no—
523#104—1228no—
524#102—1228no—
525#100—1228no—
526C24—1221no—
527C24—1222no—
528C24—1222no—
529C24—1222no—
530C24—4884no—
531C24—2441no—
532C24—2441no—
533C24—2441no—
534C24—2441no—
535C24#1175822611yescharacteristic
536#41—614no—
537#41—614no—
538#41—614no—
539#41—614no—
540#41—1222no—
541#41—1222no—
542#41—1222no—
543#41—1222no—
544#41—1222no—
545#41—1222no—
546#41—1222no—
547#41—1222no—
548#41—1222no—
549#41—1222no—
550#41—1222no—
551#41—1222no—
552C2×Q8—612no—
553C2×Q8—612no—
554C2×Q8—612no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×D4—612no—
559C2×D4—614no—
560C2×D4—612no—
561C2×D4—612no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—1222no—
565C2×D4—1222no—
566C2×D4—1222no—
567C2×D4—1222no—
568C2×D4—1222no—
569C2×D4—1222no—
570C2×D4—1222no—
571C2×D4—1222no—
572C2×D4—1222no—
573C2×D4—1222no—
574C2×D4—1222no—
575C2×D4—1222no—
576C2×D4—1222no—
577C2×D4—1221no—
578C2×D4—1222no—
579C2×D4—1222no—
580C2×D4—1221no—
581C2×D4—1221no—
582C2×D4—1222no—
583C2×D4—1222no—
584C2×D4—1222no—
585C2×D4—1222no—
586C2×D4—2441no—
587C2×D4—2441no—
588C2×D4—2441no—
589C2×D4—2441no—
590C2×D4—2441no—
591C2×D4—2441no—
592C2×D4—2441no—
593C2×D4—2441no—
594C2×D4—2441no—
595C2×D4—2441no—
596C2×D4—2441no—
597C2×D4—2441no—
598C22×C4—1221no—
599C22×C4—1222no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—2441no—
606C22×C4C2×C4×D6111yescharacteristic
607C22×C4C2×C4×D6111yescharacteristic
608C22×C4C2×D24411yescharacteristic
609C22×C4C2×D24411yescharacteristic
610C22×C4#1175822211yescharacteristic
611C22×C4#1175822211yescharacteristic
612C22×C4D4×D6111yescharacteristic
613C22×C4D4×D6111yescharacteristic
614C22×C4D4×D6111yescharacteristic
615C22×C4D4×D6111yescharacteristic
616C22×C4D4×D6111yescharacteristic
617C22×C4D4×D6111yescharacteristic
618C22×C4#1175822611yescharacteristic
619C22×C4C23×D6111yescharacteristic
620SD16—12216no—
621D8—12216no—
622M16—22no—
623M16—22no—
624M16—22no—
625M16—22no—
626M16—22no—
627M16—22no—
628M16—22no—
629M16—22no—
630M16—22no—
631M16—22no—
632M16—41no—
633M16—41no—
634M16—614no—
635M16—12216no—
636M16—1222no—
637M16—1222no—
638M16—1222no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—41no—
645C2×C8—41no—
646C2×C8—12216no—
647C2×C8—1222no—
648C2×C8—1222no—
649C2×C8—1222no—
650C2×C8C2×C4×D6114yes—
651C2×C8C2×D24414yes—
652C4⋊C4—1222no—
653C4⋊C4—2441no—
654C22⋊C4—1222no—
655C22⋊C4—2441no—
656C42—1222no—
657C42—2441no—
658C23—42no—
659C23—1222no—
660C23—1222no—
661C23—1222no—
662C23—1224no—
663C23—4884no—
664C23—4884no—
665C23—4884no—
666C23—4882no—
667C23—4884no—
668C23—4884no—
669C23—4884no—
670C23—4884no—
671C23—2442no—
672C23—2442no—
673C23—2442no—
674C23—2442no—
675C23—2442no—
676C23—2442no—
677C23#1451973911yescharacteristic
678C23#1451973911yescharacteristic
679C23#1451975211yescharacteristic
680C23#1451975211yescharacteristic
681C23#1451976211yescharacteristic
682C23#1451976211yescharacteristic
683C23C2×#1175822611yescharacteristic
684Q8—614no—
685Q8—1222no—
686Q8—1222no—
687Q8—1222no—
688D4—614no—
689D4—1224no—
690D4—1224no—
691D4—1224no—
692D4—1224no—
693D4—1224no—
694D4—1222no—
695D4—1224no—
696D4—1222no—
697D4—1222no—
698D4—2442no—
699D4—2442no—
700D4—2442no—
701D4—2442no—
702D4—2442no—
703D4—2442no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1224no—
708C2×C4—1224no—
709C2×C4—1224no—
710C2×C4—1224no—
711C2×C4—4882no—
712C2×C4—2442no—
713C2×C4C22⋊C4×D6111yescharacteristic
714C2×C4C22⋊C4×D6111yescharacteristic
715C2×C4C22⋊C4×D6111yescharacteristic
716C2×C4C22⋊C4×D6111yescharacteristic
717C2×C4#1451973911yescharacteristic
718C2×C4#1451973911yescharacteristic
719C2×C4C4×D24411yescharacteristic
720C2×C4C4×D24411yescharacteristic
721C2×C4C4×D24411yescharacteristic
722C2×C4C4×D24411yescharacteristic
723C2×C4#1451974711yescharacteristic
724C2×C4#1451974711yescharacteristic
725C2×C4#1451974711yescharacteristic
726C2×C4#1451974711yescharacteristic
727C2×C4#1451975011yescharacteristic
728C2×C4#1451975011yescharacteristic
729C2×C4#1451975011yescharacteristic
730C2×C4#1451975011yescharacteristic
731C2×C4#1451975211yescharacteristic
732C2×C4#1451975211yescharacteristic
733C2×C4#1451976211yescharacteristic
734C2×C4#1451976211yescharacteristic
735C2×C4C22×C4×D6111yescharacteristic
736C2×C4C2×D4×D6111yescharacteristic
737C2×C4C2×D4×D6111yescharacteristic
738C2×C4C2×D4×D6111yescharacteristic
739C2×C4C22×D24411yescharacteristic
740C2×C4C2×#1175822211yescharacteristic
741C8—24no—
742C8—24no—
743C8—42no—
744C8—1224no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—1224no—
753C22—4884no—
754C22—4884no—
755C22—4884no—
756C22—4884no—
757C22—4884no—
758C22—4884no—
759C22—4882no—
760C22—4882no—
761C22—4884no—
762C22—2444no—
763C22—2444no—
764C22#1683964011yescharacteristic
765C22#1683964011yescharacteristic
766C22#1683964011yescharacteristic
767C22#1683964011yescharacteristic
768C22C2×#1451973911yescharacteristic
769C22C2×#1451975211yescharacteristic
770C22C2×#1451976211yescharacteristic
771C4—1224no—
772C4—4882no—
773C4#1683964011yescharacteristic
774C4#1683964011yescharacteristic
775C4#1683964011yescharacteristic
776C4#1683964011yescharacteristic
777C4C2×C22⋊C4×D6111yescharacteristic
778C4C2×C4×D24411yescharacteristic
779C4C2×#1451974711yescharacteristic
780C4C2×#1451975011yescharacteristic
781C2—21no—
782C2—21no—
783C2—21no—
784C2—21no—
785C2—21no—
786C2—21no—
787C2—4884no—
788C2—2444no—
789C2#2144630012yesdirect product factor
790C2C2×#1683964011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#338C2
socleC22×C61#386
prime radicalC22×#14519805C2
cosocleC22×C4×C61C24
hypercenterC2×#338D61
hypocenterC61C2×#1903
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#338

Complements

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

NH ≅ G/Ntype
2. C2×#16840528C2semidirect
3. C2×#16839778C2semidirect
4. C2×#16839768C2semidirect
5. C22×#14519693C2semidirect
6. #21446300C2direct (N × H)
7. C2×#16839533C2semidirect
8. C2×C61×#338C2semidirect
15. C2×#14519805C4semidirect
17. C22×#11758190C4semidirect
18. C22×D488C4semidirect
22. #16840528C22semidirect
29. #16839778C22semidirect
32. #16839768C22semidirect
36. C2×#14519693C22semidirect
37. #16839533C22semidirect
41. C61×#338C22semidirect
79. C2×#11758190C2×C4semidirect
82. C2×D488C2×C4semidirect
393. C2×#338D61semidirect
400. C2×C61#1903semidirect
436. #338C2×D61semidirect
437. C61C2×#1903semidirect
789. C2#21446300direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198052
C2×#168405282
C2×#168397782
C2×#168397682
C22×#145196932
#214463002
C2×#168395332
C2×C61×#3382
C2×#190361