Finite Group Databasebeta

← #29713007

Subgroups — #29713007

Order 15616.

1462 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840083C211yesmaximal, characteristic, complemented
2C2×#16839758C211yesmaximal, characteristic, complemented
3#21450116C211yesmaximal, characteristic, complemented
4#21447055C211yesmaximal, characteristic, complemented
5#21447055C211yesmaximal, characteristic, complemented
6#21447019C211yesmaximal, characteristic, complemented
7#21447012C211yesmaximal, characteristic, complemented
8#21446248C211yesmaximal, characteristic, complemented
9#21446112C211yesmaximal, characteristic, complemented
10#21446080C211yesmaximal, characteristic, complemented
11#21446066C211yesmaximal, characteristic, complemented
12#21445759C211yesmaximal, characteristic, complemented
13#21445750C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic, complemented
15C2×C61×#546C211yesmaximal, characteristic
16C23×#92418C2211yescharacteristic, complemented
17C2×#14519736C2211yescharacteristic, complemented
18#16840083—24no—
19C2×#14519710C2211yescharacteristic, complemented
20C2×#14519708C2211yescharacteristic, complemented
21#16839758—24no—
22C2×#14519701C2211yescharacteristic, complemented
23C2×#14519701C2211yescharacteristic, complemented
24C2×#14519701C2211yescharacteristic, complemented
25C2×#14519701C2211yescharacteristic, complemented
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic, complemented
37#16839690—21no—
38#16839676—21no—
39#16839660C2211yescharacteristic, complemented
40#16839660C2211yescharacteristic, complemented
41#16839650—21no—
42#16839643—21no—
43#16839622C2211yescharacteristic
44#16839622C2211yescharacteristic
45#16839622C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839517C2211yescharacteristic, complemented
49#16839517C2211yescharacteristic, complemented
50C22×#41×C61C2211yescharacteristic
51C23×D4×C61C2211yescharacteristic
52C61×#546—24no—
53C61×#546—24no—
54C2×#124×C61C2211yescharacteristic
55C2×#123×C61—21no—
56C2×C22⋊Q8×C61C2211yescharacteristic
57C2×#121×C61—21no—
58C2×#121×C61C2211yescharacteristic
59C2×#120×C61—21no—
60C2×C4×D4×C61C2211yescharacteristic
61C2×C4×D4×C61C2211yescharacteristic
62C22×C22⋊C4×C61—21no—
63C22×#92418—22no—
64C22×#92418—41no—
65C22×#92418—41no—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70#14519736—22no—
71#14519736—22no—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C4×Dic61—21no—
83#14519710—22no—
84#14519708—22no—
85#14519701—22no—
86#14519701—22no—
87#14519701—41no—
88#14519701—41no—
89#14519698—22no—
90#14519698—22no—
91#14519698—22no—
92#14519698—22no—
93#14519698—22no—
94#14519698—22no—
95#14519698—41no—
96#14519698—41no—
97C22⋊#92418—22no—
98C22⋊#92418—41no—
99C22⋊#92418—41no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105C25×C61—21no—
106C2×#41×C61—22no—
107C2×#41×C61—22no—
108C2×#41×C61—22no—
109C2×#41×C61—41no—
110C2×#41×C61—41no—
111C2×#41×C61D414yes—
112C22×Q8×C61C2311yescharacteristic
113C22×D4×C61—21no—
114C22×D4×C61—21no—
115C22×D4×C61—22no—
116C22×D4×C61—22no—
117C22×D4×C61—22no—
118C22×D4×C61—22no—
119C22×D4×C61—21no—
120C22×D4×C61—41no—
121C22×D4×C61—41no—
122C22×D4×C61D411yescharacteristic
123C22×D4×C61C2311yescharacteristic
124C22×D4×C61C2311yescharacteristic
125C23×C4×C61—21no—
126C23×C4×C61—21no—
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129#124×C61—22no—
130#124×C61—22no—
131#123×C61—28no—
132C22⋊Q8×C61—22no—
133C22⋊Q8×C61—22no—
134#121×C61—28no—
135#121×C61—22no—
136#121×C61D414yes—
137#120×C61—28no—
138C4×D4×C61—22no—
139C4×D4×C61—22no—
140C4×D4×C61—22no—
141C4×D4×C61—22no—
142C2×C4⋊C4×C61—21no—
143C2×C4⋊C4×C61D411yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C22⋊C4×C61—28no—
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61—21no—
150C2×C22⋊C4×C61—21no—
151C2×C22⋊C4×C61D411yescharacteristic
152C2×C22⋊C4×C61D411yescharacteristic
153C2×C42×C61C2311yescharacteristic
154C24×C61—21no—
155C24×C61—24no—
156C24×C61—21no—
157C24×C61—42no—
158C24×C61—42no—
159C24×C61—42no—
160C24×C61—42no—
161C24×C61—81no—
162C24×C61—81no—
163C24×C61C2×D411yescharacteristic
164C24×C61C2×D411yescharacteristic
165#41×C61—28no—
166#41×C61—44no—
167#41×C61—44no—
168#41×C61—44no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61C2×D412yes—
175C2×D4×C61—24no—
176C2×D4×C61—22no—
177C2×D4×C61—24no—
178C2×D4×C61—22no—
179C2×D4×C61—24no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—41no—
189C2×D4×C61—42no—
190C2×D4×C61—42no—
191C2×D4×C61—44no—
192C2×D4×C61—44no—
193C2×D4×C61—44no—
194C2×D4×C61—42no—
195C2×D4×C61—42no—
196C2×D4×C61—44no—
197C2×D4×C61—81no—
198C2×D4×C61—81no—
199C2×D4×C61C2×D412yes—
200C2×D4×C61C2×D412yes—
201C2×D4×C61#4112yes—
202C2×D4×C61#4112yes—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—24no—
210C22×C4×C61—24no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—42no—
218C22×C4×C61—42no—
219C22×C4×C61—81no—
220C22×C4×C61—81no—
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D412yes—
226C22×C4×C61C2×D412yes—
227C22×C4×C61C2411yescharacteristic
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C4⋊C4×C61—24no—
233C4⋊C4×C61—22no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61C2×D412yes—
236C22⋊C4×C61—24no—
237C22⋊C4×C61—24no—
238C22⋊C4×C61—24no—
239C22⋊C4×C61—24no—
240C22⋊C4×C61—22no—
241C22⋊C4×C61—22no—
242C22⋊C4×C61—24no—
243C42×C61—21no—
244C42×C61—21no—
245C22⋊Dic61—42no—
246C22⋊Dic61—42no—
247C22⋊Dic61—81no—
248C22⋊Dic61—81no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257#11758196—42no—
258#11758196—81no—
259C4×Dic61—42no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—44no—
273C23×C61—21no—
274C23×C61—22no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—22no—
289C23×C61—48no—
290C23×C61—48no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—84no—
302C23×C61—84no—
303C23×C61—84no—
304C23×C61—84no—
305C23×C61—84no—
306C23×C61#12012yes—
307C23×C61#13512yes—
308C23×C61C22×D411yescharacteristic
309Q8×C61—22no—
310Q8×C61—22no—
311Q8×C61—41no—
312Q8×C61—41no—
313D4×C61—22no—
314D4×C61—22no—
315D4×C61—22no—
316D4×C61—22no—
317D4×C61—22no—
318D4×C61—44no—
319D4×C61—48no—
320D4×C61—48no—
321D4×C61—41no—
322D4×C61—41no—
323D4×C61—84no—
324D4×C61#12314yes—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—48no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—84no—
352C2×C4×C61#12012yes—
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C2×#4111yescharacteristic
356C2×C4×C61C2×#4111yescharacteristic
357C2×C4×C61H(5,𝔽2)11yescharacteristic
358C2×C4×C61H(5,𝔽2)11yescharacteristic
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371#92418—41no—
372#92418—41no—
373#92418—41no—
374#92418—41no—
375#24037—611nomaximal, Sylow
376C22×C61—22no—
377C22×C61—24no—
378C22×C61—22no—
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—41no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61—42no—
389C22×C61—41no—
390C22×C61—42no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—42no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—42no—
397C22×C61—42no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—816no—
401C22×C61—81no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61—81no—
405C22×C61C2×#12011yescharacteristic
406C22×C61#54611yescharacteristic
407C22×C61#54611yescharacteristic
408C22×C61C2×#13511yescharacteristic
409C22×C61#57511yescharacteristic
410C22×C61#57611yescharacteristic
411C22×C61#57711yescharacteristic
412C4×C61—22no—
413C4×C61—41no—
414C4×C61—42no—
415C4×C61—41no—
416C4×C61—41no—
417C4×C61—42no—
418C4×C61C2×#12311yescharacteristic
419C4×C61#53411yescharacteristic
420C4×C61#54611yescharacteristic
421C4×C61#54611yescharacteristic
422Dic61—81no—
423Dic61—81no—
424Dic61—81no—
425Dic61—81no—
426C2×#546D6111yescharacteristic
427C2×#482—611no—
428C2×#416—611no—
429#2485—611no—
430#2042—611no—
431#2042—611no—
432#2036—611no—
433#2035—611no—
434#1893—611no—
435#1869—611no—
436#1864—611no—
437#1862—611no—
438#1788—611no—
439#1786—611no—
440#1786—611no—
441C2×C61—42no—
442C2×C61—42no—
443C2×C61—44no—
444C2×C61—82no—
445C2×C61#240511yescharacteristic
446C2×C61#300211yescharacteristic
447C2×C61#301211yescharacteristic
448C2×C61#329611yescharacteristic
449C2×C61#329711yescharacteristic
450C2×C61#331111yescharacteristic
451C2×C61#331911yescharacteristic
452C22×#41C2×D6111yescharacteristic
453C23×D4C2×D6111yescharacteristic
454C23×C8—611no—
455#546—24no—
456#546—24no—
457C2×#124C2×D6111yescharacteristic
458C2×#123—21no—
459C2×C22⋊Q8C2×D6111yescharacteristic
460C2×#121—21no—
461C2×#121C2×D6111yescharacteristic
462C2×#120—21no—
463C2×C4×D4C2×D6111yescharacteristic
464C2×C4×D4C2×D6111yescharacteristic
465C2×#117—611no—
466C22×C22⋊C4—21no—
467#482—1224no—
468C2×#107—611no—
469C2×#106—611no—
470#416—1224no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#103—611no—
474C2×#103—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102—611no—
479C2×#102—611no—
480C2×#102—611no—
481C2×#102—611no—
482C2×#102—611no—
483C2×C22⋊C8—611no—
484C2×C22⋊C8—611no—
485C2×C22⋊C8—611no—
486#397—1221no—
487#394—1221no—
488#389—611no—
489#389—611no—
490#388—1221no—
491#387—1221no—
492#380—611no—
493#380—611no—
494#380—611no—
495#340—611no—
496#340—611no—
497#336—611no—
498#336—611no—
499C61#2403711yescharacteristic, complemented, Sylow
500C25—21no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C22⋊D6114yes—
507C22×Q8C22×D6111yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—22no—
514C22×D4—21no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4C22⋊D6111yescharacteristic
518C22×D4C22×D6111yescharacteristic
519C22×D4C22×D6111yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C22×D6111yescharacteristic
523C23×C4C22×D6111yescharacteristic
524C22×C8—611no—
525C22×C8—611no—
526C22×C8—611no—
527C22×C8—611no—
528C22×C8—1222no—
529C22×C8—2441no—
530C22×C8—2441no—
531#124—22no—
532#124—22no—
533#123—28no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536#121—28no—
537#121—22no—
538#121C22⋊D6114yes—
539#120—28no—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—22no—
544#117—1222no—
545#117—1222no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—611no—
548C2×C4⋊C4—611no—
549C2×C4⋊C4—611no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—1221no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4C22⋊D6111yescharacteristic
554C2×C4⋊C4C22×D6111yescharacteristic
555C2×C22⋊C4—28no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4C22⋊D6111yescharacteristic
566C2×C22⋊C4C22⋊D6111yescharacteristic
567C2×C42—1221no—
568C2×C42C22×D6111yescharacteristic
569#107—1222no—
570#106—1222no—
571#103—1222no—
572#103—1222no—
573#103—2441no—
574#103—2441no—
575#102—1222no—
576#102—1222no—
577#102—1222no—
578#102—1222no—
579#102—1222no—
580#102—1222no—
581#102—2441no—
582#102—2441no—
583C22⋊C8—1222no—
584C22⋊C8—2441no—
585C22⋊C8—2441no—
586#95—1221no—
587#95—1221no—
588#95—1221no—
589#95—1221no—
590#95—1221no—
591C24—21no—
592C24—24no—
593C24—21no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—42no—
598C24—81no—
599C24—81no—
600C24C2×C22⋊D6111yescharacteristic
601C24C2×C22⋊D6111yescharacteristic
602#41—28no—
603#41—44no—
604#41—44no—
605#41—44no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8C2×C22⋊D6112yes—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—22no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—41no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—44no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—44no—
634C2×D4—81no—
635C2×D4—81no—
636C2×D4#1175822412yes—
637C2×D4#1175822412yes—
638C2×D4C2×C22⋊D6112yes—
639C2×D4C2×C22⋊D6112yes—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—24no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—81no—
657C22×C4—81no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4C2×C22⋊D6111yescharacteristic
663C22×C4C2×C22⋊D6111yescharacteristic
664C22×C4C2×C22⋊D6111yescharacteristic
665C22×C4C2×C22⋊D6112yes—
666C22×C4C2×C22⋊D6112yes—
667C22×C4C2×C22⋊D6111yescharacteristic
668C22×C4C23×D6111yescharacteristic
669C2×C8—1221no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—2444no—
682C4⋊C4—24no—
683C4⋊C4—21no—
684C4⋊C4—22no—
685C4⋊C4—1221no—
686C4⋊C4—1221no—
687C4⋊C4—1221no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—4881no—
694C4⋊C4—2442no—
695C4⋊C4C2×C22⋊D6112yes—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—24no—
703C22⋊C4—4881no—
704C22⋊C4—4881no—
705C22⋊C4—2442no—
706C22⋊C4—2442no—
707C42—21no—
708C42—21no—
709C42—2442no—
710C23—21no—
711C23—22no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—48no—
727C23—48no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—84no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23—84no—
743C23#1451974612yes—
744C23#1451979712yes—
745C23C22×C22⋊D6111yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—41no—
749Q8—41no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—44no—
756D4—48no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—84no—
761D4#1451975814yes—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—48no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—84no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4#1451974612yes—
802C2×C4C22×C22⋊D6111yescharacteristic
803C2×C4C22×C22⋊D6111yescharacteristic
804C2×C4C2×#1175822411yescharacteristic
805C2×C4C2×#1175822411yescharacteristic
806C2×C4#1451982211yescharacteristic
807C2×C4#1451982211yescharacteristic
808C8—2441no—
809C8—2441no—
810C8—2441no—
811C8—2441no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—24no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—41no—
820C22—42no—
821C22—42no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—42no—
828C22—41no—
829C22—41no—
830C22—42no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—816no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22C2×#1451974611yescharacteristic
842C22#1684040611yescharacteristic
843C22#1684040611yescharacteristic
844C22C2×#1451979711yescharacteristic
845C22#1684056011yescharacteristic
846C22#1684056511yescharacteristic
847C22#1684057311yescharacteristic
848C4—22no—
849C4—41no—
850C4—42no—
851C4—41no—
852C4—42no—
853C4—41no—
854C4—4881no—
855C4—4881no—
856C4—4881no—
857C4—4881no—
858C4C2×#1451975811yescharacteristic
859C4#1684032111yescharacteristic
860C4#1684040611yescharacteristic
861C4#1684040611yescharacteristic
862C2—42no—
863C2—42no—
864C2—44no—
865C2—82no—
866C2#2144914211yescharacteristic
867C2#2145503711yescharacteristic
868C2#2145512311yescharacteristic
869C2#2145765411yescharacteristic
870C2#2145766911yescharacteristic
871C2#2145785511yescharacteristic
872C2#2145797511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#546C2
socleC23×C61C22×D4
hypercenterC2×#546D61
hypocenterC61#24037
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#16840083C2semidirect
2. C2×#16839758C2semidirect
3. #21450116C2semidirect
4. #21447055C2semidirect
5. #21447055C2semidirect
6. #21447019C2semidirect
7. #21447012C2semidirect
8. #21446248C2semidirect
9. #21446112C2semidirect
10. #21446080C2semidirect
11. #21446066C2semidirect
12. #21445759C2semidirect
13. #21445750C2semidirect
14. #21445750C2semidirect
16. C23×#92418C22semidirect
17. C2×#14519736C22semidirect
19. C2×#14519710C22semidirect
20. C2×#14519708C22semidirect
22. C2×#14519701C22semidirect
23. C2×#14519701C22semidirect
24. C2×#14519701C22semidirect
25. C2×#14519701C22semidirect
36. C2×C22⋊#92418C22semidirect
39. #16839660C22semidirect
40. #16839660C22semidirect
45. #16839622C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839517C22semidirect
49. #16839517C22semidirect
499. C61#24037semidirect

Maximal subgroups

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

subgroupindex
C2×#168400832
C2×#168397582
#214501162
#214470552
#214470192
#214470122
#214462482
#214461122
#214460802
#214460662
#214457592
#214457502
C2×C61×#5462
#2403761