Finite Group Databasebeta

← #29715142

Subgroups — #29715142

Order 15616.

1612 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839974C211yesmaximal, characteristic, complemented
2C2×#16839954C211yesmaximal, characteristic, complemented
3C2×#16839907C211yesmaximal, characteristic, complemented
4C2×#16839896C211yesmaximal, characteristic, complemented
5#21448512C211yesmaximal, characteristic, complemented
6#21447055C211yesmaximal, characteristic, complemented
7#21447050C211yesmaximal, characteristic, complemented
8#21446896C211yesmaximal, characteristic, complemented
9#21446890C211yesmaximal, characteristic, complemented
10#21446752C211yesmaximal, characteristic, complemented
11#21446747C211yesmaximal, characteristic, complemented
12#21445803C211yesmaximal, characteristic, complemented
13#21445759C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic, complemented
15C2×C61×#535C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic, complemented
17C22×#11758199C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C22×#11758199C2211yescharacteristic, complemented
20C2×#14519751C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic, complemented
22#16839974—24no—
23#16839954—24no—
24#16839907—24no—
25#16839896—24no—
26C2×C4⋊#92418C2211yescharacteristic, complemented
27C2×C4⋊#92418C2211yescharacteristic, complemented
28C2×#14519701C2211yescharacteristic, complemented
29C2×#14519701C2211yescharacteristic, complemented
30C2×#14519701C2211yescharacteristic, complemented
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic, complemented
38C2×#14519698C2211yescharacteristic, complemented
39C2×#14519698C2211yescharacteristic, complemented
40C2×C22⋊#92418C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42#16839664C2211yescharacteristic, complemented
43#16839662—21no—
44#16839660C2211yescharacteristic, complemented
45#16839652—21no—
46#16839638—21no—
47#16839633—21no—
48#16839622C2211yescharacteristic
49C4×C4⋊Dic61C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52C22×#41×C61C2211yescharacteristic
53C23×D4×C61C2211yescharacteristic
54C61×#535—24no—
55C61×#535—24no—
56C2×#127×C61C2211yescharacteristic
57C2×#127×C61C2211yescharacteristic
58C2×#124×C61C2211yescharacteristic
59C2×#124×C61C2211yescharacteristic
60C2×#121×C61—21no—
61C2×#121×C61—21no—
62C2×#120×C61—21no—
63C2×#120×C61—21no—
64C2×#117×C61C2211yescharacteristic
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C4×D61—21no—
68C2×#11758201—22no—
69C2×#11758201—22no—
70C2×#11758201—41no—
71C2×#11758199—22no—
72C2×#11758199—22no—
73C2×#11758199—22no—
74C2×#11758199—22no—
75C2×#11758199—22no—
76C2×#11758199—22no—
77C2×#11758199—41no—
78C2×#11758199—41no—
79C2×#11758199—41no—
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84#14519751—22no—
85#14519751D414yescomplemented
86C4×D244—22no—
87C4×D244—22no—
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×#11758196—21no—
92C2×C22⋊Dic61—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×C4×Dic61—21no—
98C4⋊#92418—22no—
99C4⋊#92418—22no—
100#14519701—22no—
101#14519701—22no—
102#14519701—41no—
103#14519698—22no—
104#14519698—22no—
105#14519698—22no—
106#14519698—22no—
107#14519698—22no—
108#14519698—22no—
109#14519698—41no—
110#14519698—41no—
111#14519698—41no—
112C22⋊#92418—22no—
113C22⋊#92418—22no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117C25×C61—21no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—22no—
121C2×#41×C61—22no—
122C2×#41×C61—41no—
123C2×#41×C61—41no—
124C22×Q8×C61C2311yescharacteristic
125C22×D4×C61—21no—
126C22×D4×C61—22no—
127C22×D4×C61—22no—
128C22×D4×C61—21no—
129C22×D4×C61—21no—
130C22×D4×C61—21no—
131C22×D4×C61—21no—
132C22×D4×C61—21no—
133C22×D4×C61—22no—
134C22×D4×C61—22no—
135C22×D4×C61—41no—
136C22×D4×C61—41no—
137C22×D4×C61C2311yescharacteristic
138C22×D4×C61C2311yescharacteristic
139C22×D4×C61C2311yescharacteristic
140C23×C4×C61—21no—
141C23×C4×C61C2311yescharacteristic
142#127×C61—22no—
143#127×C61—22no—
144#127×C61—22no—
145#127×C61D414yescomplemented
146#124×C61—22no—
147#124×C61—22no—
148#124×C61—22no—
149#124×C61D414yescomplemented
150#121×C61—28no—
151#121×C61—28no—
152#120×C61—28no—
153#120×C61—28no—
154#117×C61—22no—
155#117×C61—22no—
156C2×C4⋊C4×C61D411yescharacteristic
157C2×C4⋊C4×C61D411yescharacteristic
158C2×C22⋊C4×C61—21no—
159C2×C22⋊C4×C61—21no—
160C2×C22⋊C4×C61—21no—
161C2×C22⋊C4×C61—21no—
162C2×C22⋊C4×C61D411yescharacteristic
163C2×C22⋊C4×C61D411yescharacteristic
164C2×C42×C61C2311yescharacteristic
165C2×C42×C61C2311yescharacteristic
166C24×C61—24no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—42no—
171C24×C61—42no—
172C24×C61—81no—
173C24×C61—81no—
174C24×C61—81no—
175C24×C61—81no—
176C24×C61C2×D411yescharacteristic
177C23×D61—21no—
178#41×C61—44no—
179#41×C61—44no—
180#41×C61—44no—
181#41×C61—44no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61C2×D412yes—
188C2×D4×C61—24no—
189C2×D4×C61—24no—
190C2×D4×C61—24no—
191C2×D4×C61—24no—
192C2×D4×C61—24no—
193C2×D4×C61—24no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—44no—
210C2×D4×C61—44no—
211C2×D4×C61—44no—
212C2×D4×C61—44no—
213C2×D4×C61—42no—
214C2×D4×C61—42no—
215C2×D4×C61—42no—
216C2×D4×C61—42no—
217C2×D4×C61—81no—
218C2×D4×C61—81no—
219C2×D4×C61—81no—
220C2×D4×C61—81no—
221C2×D4×C61—81no—
222C2×D4×C61—81no—
223C2×D4×C61—81no—
224C2×D4×C61—81no—
225C2×D4×C61C2×D412yes—
226C2×D4×C61C2×D412yes—
227C2×D4×C61C2×D412yes—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—24no—
233C22×C4×C61—21no—
234C22×C4×C61—42no—
235C22×C4×C61—42no—
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2×D411yescharacteristic
240C22×C4×C61C2×D411yescharacteristic
241C22×C4×C61C2×D412yes—
242C22×C4×C61#4112yes—
243C22×C4×C61C2411yescharacteristic
244C2×C22⋊D61—24no—
245C2×C22⋊D61—81no—
246C2×C22⋊D61—81no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C2×D244—21no—
251C2×D244—21no—
252C2×D244—21no—
253C2×D244—21no—
254C2×D244—21no—
255C2×D244C2×D412yes—
256C2×C4×D61—42no—
257C2×C4×D61—81no—
258C2×C4×D61—81no—
259C4⋊C4×C61—22no—
260C4⋊C4×C61—22no—
261C22⋊C4×C61—24no—
262C22⋊C4×C61—24no—
263C22⋊C4×C61—24no—
264C22⋊C4×C61—24no—
265C22⋊C4×C61—22no—
266C22⋊C4×C61—22no—
267C42×C61—21no—
268C42×C61—21no—
269C42×C61C2×D412yes—
270C42×C61C2×D412yes—
271C22⋊Dic61—81no—
272#11758201—44no—
273#11758199—44no—
274#11758199—44no—
275#11758199—44no—
276#11758198—24no—
277#11758198—42no—
278#11758198—81no—
279#11758198—81no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61C2×D412yes—
286#11758196—81no—
287C4×Dic61—81no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—21no—
295C2×#92418—21no—
296C2×#92418—21no—
297C2×#92418—21no—
298C2×#92418—21no—
299C2×#92418—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—48no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—41no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61—41no—
327C23×C61—41no—
328C23×C61—84no—
329C23×C61—84no—
330C23×C61—84no—
331C23×C61—84no—
332C23×C61—84no—
333C23×C61—84no—
334C23×C61#12112yes—
335C23×C61C22×D411yescharacteristic
336C22×D61—22no—
337C22×D61—41no—
338C22×D61—41no—
339C22×D61—41no—
340C22×D61—41no—
341C22×D61—41no—
342C22×D61—41no—
343Q8×C61—22no—
344Q8×C61—22no—
345Q8×C61—41no—
346Q8×C61—41no—
347D4×C61—22no—
348D4×C61—22no—
349D4×C61—22no—
350D4×C61—22no—
351D4×C61—22no—
352D4×C61—22no—
353D4×C61—48no—
354D4×C61—48no—
355D4×C61—41no—
356D4×C61—41no—
357D4×C61—41no—
358D4×C61—41no—
359D4×C61—41no—
360D4×C61—41no—
361D4×C61—84no—
362D4×C61—84no—
363D4×C61—84no—
364D4×C61—84no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—22no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61—48no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61#12012yes—
386C2×C4×C61#12012yes—
387C2×C4×C61#12112yes—
388C2×C4×C61C22×D411yescharacteristic
389C2×C4×C61C22×D411yescharacteristic
390C2×C4×C61C22×D411yescharacteristic
391C2×C4×C61C2×#4111yescharacteristic
392C2×C4×C61H(5,𝔽2)11yescharacteristic
393C2×C4×C61H(5,𝔽2)11yescharacteristic
394C22⋊D61—84no—
395C2×Dic61—22no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403C2×Dic61—41no—
404D244—22no—
405D244—22no—
406D244—41no—
407D244—41no—
408C4×D61—84no—
409#92418—41no—
410#92418—41no—
411#92418—41no—
412#92418—41no—
413#24218—611nomaximal, Sylow
414C22×C61—22no—
415C22×C61—22no—
416C22×C61—22no—
417C22×C61—41no—
418C22×C61—41no—
419C22×C61—41no—
420C22×C61—41no—
421C22×C61—42no—
422C22×C61—42no—
423C22×C61—42no—
424C22×C61—42no—
425C22×C61—42no—
426C22×C61—42no—
427C22×C61—42no—
428C22×C61—42no—
429C22×C61—42no—
430C22×C61—816no—
431C22×C61—81no—
432C22×C61—81no—
433C22×C61—81no—
434C22×C61—81no—
435C22×C61—81no—
436C22×C61—81no—
437C22×C61—81no—
438C22×C61—81no—
439C22×C61—81no—
440C22×C61—81no—
441C22×C61—81no—
442C22×C61—81no—
443C22×C61C2×#12011yescharacteristic
444C22×C61C2×#12111yescharacteristic
445C22×C61#53511yescharacteristic
446C22×C61#57611yescharacteristic
447C22×C61#57611yescharacteristic
448C22×C61#57611yescharacteristic
449C22×C61#57711yescharacteristic
450C2×D61—42no—
451C2×D61—42no—
452C2×D61—42no—
453C2×D61—81no—
454C2×D61—81no—
455C2×D61—81no—
456C2×D61—81no—
457C4×C61—22no—
458C4×C61—22no—
459C4×C61—22no—
460C4×C61—42no—
461C4×C61—41no—
462C4×C61—41no—
463C4×C61D4211yescharacteristic
464C4×C61D4211yescharacteristic
465C4×C61#54611yescharacteristic
466C4×C61#54611yescharacteristic
467Dic61—42no—
468Dic61—81no—
469Dic61—81no—
470C2×#535D6111yescharacteristic, complemented
471C2×#463—611no—
472C2×#459—611no—
473C2×#449—611no—
474C2×#447—611no—
475#2324—611no—
476#2042—611no—
477#2041—611no—
478#2012—611no—
479#2011—611no—
480#1983—611no—
481#1982—611no—
482#1798—611no—
483#1788—611no—
484#1786—611no—
485C2×C61—42no—
486C2×C61—82no—
487C2×C61—82no—
488C2×C61—82no—
489C2×C61#240811yescharacteristic
490C2×C61#300811yescharacteristic
491C2×C61#301211yescharacteristic
492C2×C61#304111yescharacteristic
493C2×C61#304511yescharacteristic
494C2×C61#322011yescharacteristic
495C2×C61#322411yescharacteristic
496D61—82no—
497C22×#41C2×D6111yescharacteristic
498C23×D4C2×D6111yescharacteristic
499C22×SD16—611no—
500C22×D8—611no—
501C22×D8—611no—
502C22×D8—611no—
503#535—24no—
504#535—24no—
505C2×#127C2×D6111yescharacteristic
506C2×#127C2×D6111yescharacteristic
507C2×#124C2×D6111yescharacteristic
508C2×#124C2×D6111yescharacteristic
509C2×#121—21no—
510C2×#121—21no—
511C2×#121—611no—
512C2×#120—21no—
513C2×#120—21no—
514C2×C4×D4—611no—
515C2×#117C2×D6111yescharacteristic
516#463—1224no—
517#459—1224no—
518#449—1224no—
519#447—1224no—
520C2×C4⋊C8—611no—
521C2×C4⋊C8—611no—
522C2×#103—611no—
523C2×#103—611no—
524C2×#103—611no—
525C2×#102—611no—
526C2×#102—611no—
527C2×#102—611no—
528C2×#102—611no—
529C2×#102—611no—
530C2×#102—611no—
531C2×#102—611no—
532C2×#102—611no—
533C2×#102—611no—
534C2×C22⋊C8—611no—
535C2×C22⋊C8—611no—
536#390—611no—
537#390—1221no—
538#389—611no—
539#388—1221no—
540#386—1221no—
541#385—1221no—
542#380—611no—
543C4×C4⋊C4—611no—
544#336—611no—
545#336—611no—
546C61#2421811yescharacteristic, complemented, Sylow
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8C22×D6111yescharacteristic
555C22×D4—21no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—22no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4—611no—
568C22×D4—1221no—
569C22×D4C22×D6111yescharacteristic
570C22×D4C22×D6111yescharacteristic
571C22×D4C22×D6111yescharacteristic
572C23×C4—21no—
573C23×C4—1221no—
574C23×C4C22×D6111yescharacteristic
575C2×SD16—1222no—
576C2×SD16—1222no—
577C2×SD16—2441no—
578C2×D8—1222no—
579C2×D8—1222no—
580C2×D8—1222no—
581C2×D8—1222no—
582C2×D8—1222no—
583C2×D8—1222no—
584C2×D8—2441no—
585C2×D8—2441no—
586C2×D8—2441no—
587C22×C8—611no—
588C22×C8—611no—
589C22×C8—611no—
590C22×C8—611no—
591#127—22no—
592#127—22no—
593#127—22no—
594#127C22⋊D6114yescomplemented
595#124—22no—
596#124—22no—
597#124—22no—
598#124C22⋊D6114yescomplemented
599#121—28no—
600#121—28no—
601#121—614no—
602#121—1222no—
603#120—28no—
604#120—28no—
605C4×D4—1222no—
606C4×D4—1222no—
607#117—22no—
608#117—22no—
609C2×C4⋊C4—611no—
610C2×C4⋊C4—611no—
611C2×C4⋊C4—611no—
612C2×C4⋊C4—1221no—
613C2×C4⋊C4C22⋊D6111yescharacteristic
614C2×C4⋊C4C22⋊D6111yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—1221no—
620C2×C22⋊C4—1221no—
621C2×C22⋊C4—1221no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C22⋊C4C22⋊D6111yescharacteristic
625C2×C22⋊C4C22⋊D6111yescharacteristic
626C2×C42—1221no—
627C2×C42C22×D6111yescharacteristic
628C2×C42C22×D6111yescharacteristic
629C4⋊C8—1222no—
630C4⋊C8—1222no—
631#103—1222no—
632#103—1222no—
633#103—2441no—
634#102—1222no—
635#102—1222no—
636#102—1222no—
637#102—1222no—
638#102—1222no—
639#102—1222no—
640#102—2441no—
641#102—2441no—
642#102—2441no—
643C22⋊C8—1222no—
644C22⋊C8—1222no—
645#95—1221no—
646#95—1221no—
647#95—1221no—
648C24—24no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24—1221no—
659C24C2×C22⋊D6111yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8C2×C22⋊D6112yes—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—612no—
708C2×D4—1224no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—4881no—
715C2×D4—4881no—
716C2×D4C2×C22⋊D6112yes—
717C2×D4C2×C22⋊D6112yes—
718C2×D4C2×C22⋊D6112yes—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—24no—
724C22×C4—21no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—4881no—
731C22×C4—4881no—
732C22×C4—2442no—
733C22×C4D4×D6112yes—
734C22×C4#1175822412yes—
735C22×C4C2×C22⋊D6111yescharacteristic
736C22×C4C2×C22⋊D6111yescharacteristic
737C22×C4C2×C22⋊D6111yescharacteristic
738C22×C4C2×C22⋊D6111yescharacteristic
739C22×C4C2×C22⋊D6111yescharacteristic
740C22×C4C23×D6111yescharacteristic
741SD16—2444no—
742D8—2444no—
743D8—2444no—
744D8—2444no—
745C2×C8—1221no—
746C2×C8—1221no—
747C2×C8—1221no—
748C2×C8—1221no—
749C2×C8—1221no—
750C2×C8—1221no—
751C2×C8—1221no—
752C2×C8—1221no—
753C2×C8—1221no—
754C2×C8—1221no—
755C2×C8—1221no—
756C2×C8—1221no—
757C4⋊C4—22no—
758C4⋊C4—22no—
759C4⋊C4—612no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—4881no—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—1224no—
773C22⋊C4—4881no—
774C22⋊C4—4881no—
775C22⋊C4—4881no—
776C22⋊C4—2442no—
777C42—21no—
778C42—21no—
779C42—4881no—
780C42C2×C22⋊D6112yes—
781C42C2×C22⋊D6112yes—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—48no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—84no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23—1222no—
817C23—2441no—
818C23—2441no—
819C23—2441no—
820C23—2441no—
821C23—2441no—
822C23—2441no—
823C23#1451974812yes—
824C23C22×C22⋊D6111yescharacteristic
825Q8—22no—
826Q8—22no—
827Q8—41no—
828Q8—41no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—48no—
836D4—48no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—84no—
844D4—84no—
845D4—84no—
846D4—84no—
847D4—1222no—
848D4—1222no—
849D4—4884no—
850D4—2441no—
851D4—2441no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—22no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—48no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—1222no—
873C2×C4—4884no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4#1451974612yes—
883C2×C4#1451974612yes—
884C2×C4#1451974812yes—
885C2×C4C2×D4×D6111yescharacteristic
886C2×C4C22×C22⋊D6111yescharacteristic
887C2×C4C22×C22⋊D6111yescharacteristic
888C2×C4C2×#1175822411yescharacteristic
889C2×C4#1451982211yescharacteristic
890C2×C4#1451982211yescharacteristic
891C8—2441no—
892C8—2441no—
893C8—2441no—
894C8—2441no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—816no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—4881no—
925C22—4881no—
926C22—4881no—
927C22—4881no—
928C22—2442no—
929C22—2442no—
930C22—2442no—
931C22C2×#1451974611yescharacteristic
932C22C2×#1451974811yescharacteristic
933C22#1684032911yescharacteristic
934C22#1684056511yescharacteristic
935C22#1684056511yescharacteristic
936C22#1684056511yescharacteristic
937C22#1684057311yescharacteristic
938C4—22no—
939C4—22no—
940C4—22no—
941C4—41no—
942C4—42no—
943C4—41no—
944C4—4881no—
945C4—4881no—
946C4—2442no—
947C4D4×C22⋊D6111yescharacteristic
948C4D4×C22⋊D6111yescharacteristic
949C4#1684040611yescharacteristic
950C4#1684040611yescharacteristic
951C2—42no—
952C2—82no—
953C2—82no—
954C2—82no—
955C2—4882no—
956C2#2144916911yescharacteristic
957C2#2145508711yescharacteristic
958C2#2145512311yescharacteristic
959C2#2145531811yescharacteristic
960C2#2145535411yescharacteristic
961C2#2145686911yescharacteristic
962C2#2145691311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#535C2
socleC23×C61C22×D4
hypercenterC2×#535D61
hypocenterC61#24218
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#16839974C2semidirect
2. C2×#16839954C2semidirect
3. C2×#16839907C2semidirect
4. C2×#16839896C2semidirect
5. #21448512C2semidirect
6. #21447055C2semidirect
7. #21447050C2semidirect
8. #21446896C2semidirect
9. #21446890C2semidirect
10. #21446752C2semidirect
11. #21446747C2semidirect
12. #21445803C2semidirect
13. #21445759C2semidirect
14. #21445750C2semidirect
15. C2×C61×#535C2semidirect
16. C22×#11758201C22semidirect
19. C22×#11758199C22semidirect
21. C2×C4×D244C22semidirect
26. C2×C4⋊#92418C22semidirect
27. C2×C4⋊#92418C22semidirect
28. C2×#14519701C22semidirect
29. C2×#14519701C22semidirect
30. C2×#14519701C22semidirect
37. C2×#14519698C22semidirect
38. C2×#14519698C22semidirect
39. C2×#14519698C22semidirect
42. #16839664C22semidirect
44. #16839660C22semidirect
49. C4×C4⋊Dic61C22semidirect
50. #16839517C22semidirect
51. #16839517C22semidirect
85. #14519751D4semidirect
145. #127×C61D4semidirect
149. #124×C61D4semidirect
470. C2×#535D61semidirect
546. C61#24218semidirect
594. #127C22⋊D61semidirect
598. #124C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399742
C2×#168399542
C2×#168399072
C2×#168398962
#214485122
#214470552
#214470502
#214468962
#214468902
#214467522
#214467472
#214458032
#214457592
#214457502
C2×C61×#5352
#2421861