Finite Group Databasebeta

← #29681083

Subgroups — #29681083

Order 15616.

1326 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840527C211yesmaximal, characteristic
2C2×#108×D61C211yesmaximal, characteristic, complemented
3#21454380C211yesmaximal, characteristic, complemented
4C2×#16839777C211yesmaximal, characteristic
5#416×D61C211yesmaximal, characteristic
6#21446097C211yesmaximal, characteristic, complemented
7#21446096C211yesmaximal, characteristic, complemented
8#21446095C211yesmaximal, characteristic, complemented
9#21446094C211yesmaximal, characteristic, complemented
10#21446093C211yesmaximal, characteristic, complemented
11#21446092C211yesmaximal, characteristic, complemented
12#21446091C211yesmaximal, characteristic, complemented
13#21445527C211yesmaximal, characteristic, complemented
14#21445514C211yesmaximal, characteristic, complemented
15C61×#1866C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17#16840527—24no—
18#16840527—24no—
19C2×#14519785—21no—
20C2×#14519785C2211yescharacteristic
21C2×#14519784C2211yescharacteristic
22C2×#14519783—21no—
23C2×#14519783C2211yescharacteristic
24C22×#11758189—21no—
25C22×#11758189C2211yescharacteristic
26C2×M16×D61—21no—
27C2×M16×D61C2211yescharacteristic
28C2×M16×D61C2211yescharacteristic
29C22×C8×D61C2211yescharacteristic
30C2×#14519734C2211yescharacteristic
31#117×D61C2211yescharacteristic
32C2×#14519713C2211yescharacteristic, complemented
33C2×#14519712C2211yescharacteristic, complemented
34C2×#14519712C2211yescharacteristic, complemented
35#108×D61—24no—
36#16839790C2211yescharacteristic, complemented
37#16839789C2211yescharacteristic, complemented
38#16839788C2211yescharacteristic, complemented
39#16839787—21no—
40#16839787—21no—
41#16839784—21no—
42#16839784—21no—
43#16839777—24no—
44C2×#14519705C2211yescharacteristic
45C2×#14519704C2211yescharacteristic
46C2×#14519703C2211yescharacteristic
47#16839759C2211yescharacteristic
48#16839758C2211yescharacteristic
49#16839757C411yescharacteristic, complemented
50#16839757C411yescharacteristic, complemented
51#16839756C2211yescharacteristic
52#16839755C411yescharacteristic, complemented
53#16839755C411yescharacteristic, complemented
54#103×D61C411yescharacteristic, complemented
55#103×D61C411yescharacteristic, complemented
56#102×D61C411yescharacteristic, complemented
57#102×D61C411yescharacteristic, complemented
58#16839523C2211yescharacteristic, complemented
59#16839522C2211yescharacteristic, complemented
60#16839521C2211yescharacteristic, complemented
61#16839517C2211yescharacteristic, complemented
62#16839516C2211yescharacteristic, complemented
63#16839516C2211yescharacteristic, complemented
64C2×#131×C61C2211yescharacteristic
65C2×#108×C61C2211yescharacteristic, complemented
66C61×#424C2211yescharacteristic, complemented
67C2×#104×C61C2211yescharacteristic
68C61×#416C2211yescharacteristic
69C61×#339C2211yescharacteristic, complemented
70C61×#336C2211yescharacteristic, complemented
71C2×#11758226C2×C411yescharacteristic
72C2×#11758222—21no—
73C2×#11758222C2311yescharacteristic
74C2×#11758224—21no—
75C2×#11758224C2×C411yescharacteristic
76#41×D61—22no—
77#41×D61—22no—
78#41×D61D414yes—
79#41×D61Q814yes—
80C2×Q8×D61C2×C411yescharacteristic
81C2×D4×D61—21no—
82C2×D4×D61C2×C411yescharacteristic
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85#14519785—28no—
86#14519785—22no—
87#14519785—22no—
88#14519784—22no—
89#14519784—22no—
90#14519783—28no—
91#14519783—22no—
92#14519783—22no—
93C2×#11758194—21no—
94C2×#11758194C2311yescharacteristic
95C2×#11758194C2311yescharacteristic
96C2×#11758189—28no—
97C2×#11758189—21no—
98C2×#11758189—22no—
99C2×#11758189—22no—
100C2×#11758189—21no—
101C2×#11758189—21no—
102C2×#11758189—21no—
103C2×#11758189D411yescharacteristic
104C2×#11758189D411yescharacteristic
105C2×#11758189D411yescharacteristic
106C2×#11758189D411yescharacteristic
107M16×D61—28no—
108M16×D61—22no—
109M16×D61—22no—
110M16×D61—22no—
111M16×D61D414yes—
112C22×#92418—21no—
113C22×#92418C2311yescharacteristic
114C22×#92418C2311yescharacteristic
115C2×C8×D61—22no—
116C2×C8×D61—21no—
117C2×C8×D61—22no—
118C2×C8×D61—21no—
119C2×C8×D61—21no—
120C2×C8×D61—21no—
121C2×C8×D61C2×C411yescharacteristic
122C2×C8×D61C2×C411yescharacteristic
123C2×C8×D61C2×C411yescharacteristic
124C2×C8×D61C2×C411yescharacteristic
125#14519736C2311yescharacteristic
126#14519735C2×C411yescharacteristic
127#14519735C2×C411yescharacteristic
128#14519734—21no—
129#14519734—22no—
130#14519734—22no—
131#14519733—21no—
132C2×#11758196—21no—
133C4⋊C4×D61C2×C411yescharacteristic
134C4⋊C4×D61C2×C411yescharacteristic
135C2×#11758198—21no—
136C22⋊C4×D61—21no—
137C2×C4×Dic61C2311yescharacteristic
138C42×D61—21no—
139#14519713—22no—
140#14519712—22no—
141#14519712—22no—
142C4⋊#92418—21no—
143C4⋊#92418—21no—
144#14519706—21no—
145#14519706—21no—
146#14519706—21no—
147#14519706—21no—
148#14519705—22no—
149#14519704—22no—
150#14519703—22no—
151#14519702C2×C411yescharacteristic
152#14519702C2×C411yescharacteristic
153#14519701C2×C411yescharacteristic
154#14519701C2×C411yescharacteristic
155#14519700C2×C411yescharacteristic
156#14519700C2×C411yescharacteristic
157#14519699C2×C411yescharacteristic
158#14519699C2×C411yescharacteristic
159#14519698C2×C411yescharacteristic
160#14519698C2×C411yescharacteristic
161#14519697C2×C411yescharacteristic
162#14519697C2×C411yescharacteristic
163C2×#41×C61C2311yescharacteristic
164#131×C61—22no—
165#131×C61—22no—
166C2×M16×C61—21no—
167C2×M16×C61C2311yescharacteristic
168C2×M16×C61C2311yescharacteristic
169C22×C8×C61—21no—
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172#117×C61C2311yescharacteristic
173C2×C42×C61C2311yescharacteristic
174#108×C61—22no—
175C4⋊C8×C61—21no—
176C4⋊C8×C61—21no—
177#104×C61—22no—
178#103×C61C2×C411yescharacteristic
179#103×C61C2×C411yescharacteristic
180#102×C61C2×C411yescharacteristic
181#102×C61C2×C411yescharacteristic
182C23×D61—21no—
183C23×D61#4111yescharacteristic
184#41×C61—21no—
185#41×C61—21no—
186#41×C61C2×D412yes—
187#41×C61C2×Q812yes—
188C2×Q8×C61C22×C411yescharacteristic
189C2×D4×C61—21no—
190C2×D4×C61C22×C411yescharacteristic
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61C2411yescharacteristic
194C2×C22⋊D61—21no—
195C2×C22⋊D61—21no—
196C2×C22⋊D61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61#4111yescharacteristic
200#11758226—22no—
201#11758226C4⋊C414yes—
202Q8×D61—22no—
203Q8×D61C4⋊C414yes—
204#11758224—24no—
205#11758224—24no—
206#11758224—22no—
207#11758224C4⋊C414yes—
208D4×D61—24no—
209D4×D61—24no—
210D4×D61—22no—
211D4×D61C4⋊C414yes—
212#11758222—21no—
213#11758222—21no—
214#11758222—24no—
215#11758222—24no—
216#11758222C2×D412yes—
217#11758222C2×Q812yes—
218C2×D244—21no—
219C2×D244C22×C411yescharacteristic
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—24no—
224C2×C4×D61—24no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61C22×C411yescharacteristic
228C2×C4×D61C22×C411yescharacteristic
229C2×C4×D61C2×D412yes—
230C2×C4×D61C2×D412yes—
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×C4×D61C2×Q812yes—
234C2×C4×D61#4112yes—
235C2×Dic122—21no—
236C2×Dic122C22×C411yescharacteristic
237M16×C61—24no—
238M16×C61—21no—
239M16×C61—21no—
240M16×C61—21no—
241M16×C61C2×D412yes—
242C2×C8×C61—24no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61C22×C411yescharacteristic
250C2×C8×C61C22×C411yescharacteristic
251C2×C8×C61C2×D411yescharacteristic
252C2×C8×C61C2×D411yescharacteristic
253C4⋊C4×C61C22×C411yescharacteristic
254C4⋊C4×C61C22×C411yescharacteristic
255C22⋊C4×C61—21no—
256C42×C61—21no—
257C42×C61—21no—
258C42×C61—21no—
259C22⋊Dic61—21no—
260#11758198—21no—
261#11758198—21no—
262#11758198—42no—
263C4⋊Dic61C22×C411yescharacteristic
264C4⋊Dic61C22×C411yescharacteristic
265#11758196—21no—
266#11758196—21no—
267#11758196—42no—
268C4×Dic61—21no—
269C4×Dic61—21no—
270C4×Dic61—21no—
271C4×Dic61—21no—
272C4×Dic61—21no—
273#11758194—24no—
274#11758194—21no—
275#11758194—21no—
276#11758194—21no—
277#11758194C2×D412yes—
278C2×#92418—24no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418C22×C411yescharacteristic
286C2×#92418C22×C411yescharacteristic
287C2×#92418C2×D411yescharacteristic
288C2×#92418C2×D411yescharacteristic
289#11758189—24no—
290#11758189—24no—
291#11758189—22no—
292#11758189—24no—
293#11758189—22no—
294#11758189—22no—
295#11758189—22no—
296#11758189—42no—
297C8×D61—24no—
298C8×D61—24no—
299C8×D61—22no—
300C8×D61—22no—
301C8×D61—22no—
302C8×D61—22no—
303C8×D61—24no—
304C8×D61—42no—
305C23×C61—21no—
306C23×C61C2×#4111yescharacteristic
307C22×D61—21no—
308C22×D61—24no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—81no—
312C22×D61—81no—
313C22×D61C4×D411yescharacteristic
314C22×D61C4×D411yescharacteristic
315C22×D61C22⋊Q812yes—
316C22×D61#12312yes—
317Q8×C61—21no—
318Q8×C61C2×C4⋊C412yes—
319D4×C61—22no—
320D4×C61—22no—
321D4×C61—21no—
322D4×C61C2×C4⋊C412yes—
323C2×C4×C61—21no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61C23×C411yescharacteristic
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C22×Q811yescharacteristic
336C2×C4×C61C2×#4111yescharacteristic
337C22⋊D61—22no—
338C22⋊D61—22no—
339C22⋊D61—24no—
340C22⋊D61—24no—
341C2×Dic61—21no—
342C2×Dic61—24no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61C4×D411yescharacteristic
349C2×Dic61C4×D411yescharacteristic
350C2×Dic61C22⋊Q812yes—
351C2×Dic61#12312yes—
352D244—24no—
353D244—21no—
354D244C2×C4⋊C412yes—
355C4×D61—24no—
356C4×D61—22no—
357C4×D61—22no—
358C4×D61—24no—
359C4×D61—81no—
360C4×D61—81no—
361C4×D61C2×C4⋊C412yes—
362C4×D61C2×C4⋊C412yes—
363C4×D61C4×D412yes—
364C4×D61C4×D412yes—
365C4×D61#12012yes—
366C4×D61#12012yes—
367C4×D61C22⋊Q812yes—
368C4×D61C22⋊Q812yes—
369Dic122—21no—
370Dic122—24no—
371Dic122C2×C4⋊C412yes—
372C8×C61—21no—
373C8×C61—21no—
374C8×C61—22no—
375C8×C61—21no—
376C8×C61—21no—
377C8×C61—41no—
378#92418—21no—
379#92418—21no—
380#92418—22no—
381#92418—21no—
382#92418—21no—
383#92418—41no—
384#20886—611nomaximal, Sylow
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—22no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61C2×C4×D411yescharacteristic
391C22×C61C2×C22⋊Q811yescharacteristic
392C22×C61C2×#12311yescharacteristic
393C2×D61—21no—
394C2×D61—21no—
395C2×D61—21no—
396C2×D61—21no—
397C2×D61—22no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—84no—
403C2×D61#38512yes—
404C2×D61#38512yes—
405C4×C61—22no—
406C4×C61—41no—
407C4×C61—41no—
408C4×C61—81no—
409C4×C61C22×C4⋊C411yescharacteristic
410C4×C61C2×C4×D411yescharacteristic
411C4×C61C2×#12011yescharacteristic
412C4×C61C2×C22⋊Q811yescharacteristic
413Dic61—22no—
414Dic61—41no—
415Dic61—41no—
416Dic61—81no—
417Dic61#38512yes—
418Dic61#38512yes—
419C2×#568—611no—
420C22×#108—611no—
421#2905—611no—
422C2×#421—611no—
423C2×#416—611no—
424#1866—611no—
425#1866—611no—
426#1866—611no—
427#1866—611no—
428#1866—611no—
429#1866—611no—
430#1866—611no—
431#1866D6111yescharacteristic, complemented
432#1733—611no—
433#1729—611no—
434C2×C61—21no—
435C2×C61—21no—
436C2×C61—42no—
437C2×C61C2×#38511yescharacteristic
438C2×C61#295711yescharacteristic
439C2×C61#295711yescharacteristic
440D61—22no—
441D61—22no—
442D61—42no—
443C22×#41—611no—
444#568—1224no—
445#568—1224no—
446C2×#131—611no—
447C2×#131—611no—
448C2×#131—611no—
449C2×#131—1221no—
450C2×#131—1221no—
451C2×#131C2×D6111yescharacteristic
452C22×M16—611no—
453C22×M16—611no—
454C22×M16—611no—
455C22×M16—1221no—
456C22×M16—1221no—
457C23×C8—611no—
458C2×#117—611no—
459C2×#117—611no—
460C2×#108—611no—
461C2×#108—611no—
462C2×#108—611no—
463C2×#108—1224no—
464C2×#108C2×D6111yescharacteristic, complemented
465#424—611no—
466#424—611no—
467#424—611no—
468#424—1221no—
469#424—1221no—
470#424C2×D6111yescharacteristic, complemented
471#423—1221no—
472#423—1221no—
473#421—1224no—
474C2×#104—611no—
475C2×#104—611no—
476C2×#104—611no—
477C2×#104C2×D6111yescharacteristic
478#416—611no—
479#416—611no—
480#416—611no—
481#416—611no—
482#416—611no—
483#416—611no—
484#416—611no—
485#416C2×D6111yescharacteristic
486C2×#103—611no—
487C2×#103—611no—
488C2×#102—611no—
489C2×#102—611no—
490#339—611no—
491#339—611no—
492#339—611no—
493#339C2×D6111yescharacteristic, complemented
494#336—611no—
495#336—611no—
496#336—611no—
497#336C2×D6111yescharacteristic, complemented
498C61#2088611yescharacteristic, complemented, Sylow
499C2×#41—614no—
500C2×#41—614no—
501C2×#41—611no—
502C2×#41—611no—
503C2×#41—611no—
504C2×#41—1221no—
505C2×#41—1221no—
506C2×#41—1222no—
507C2×#41—1222no—
508C2×#41C22×D6111yescharacteristic
509C22×Q8—611no—
510C22×D4—611no—
511C22×D4—1221no—
512C23×C4—611no—
513C23×C4—1221no—
514#131—22no—
515#131—22no—
516#131—1222no—
517#131—1222no—
518#131—1228no—
519#131—1222no—
520#131—1228no—
521#131—1222no—
522#131—1222no—
523#131—1222no—
524C2×M16—21no—
525C2×M16—611no—
526C2×M16—611no—
527C2×M16—611no—
528C2×M16—611no—
529C2×M16—611no—
530C2×M16—614no—
531C2×M16—611no—
532C2×M16—1221no—
533C2×M16—1221no—
534C2×M16—1222no—
535C2×M16—1222no—
536C2×M16—1228no—
537C2×M16—1221no—
538C2×M16—1221no—
539C2×M16—1222no—
540C2×M16—1228no—
541C2×M16—1221no—
542C2×M16—1222no—
543C2×M16—1222no—
544C2×M16C22×D6111yescharacteristic
545C2×M16C22×D6111yescharacteristic
546C22×C8—21no—
547C22×C8—611no—
548C22×C8—611no—
549C22×C8—611no—
550C22×C8—611no—
551C22×C8—611no—
552C22×C8—611no—
553C22×C8—1221no—
554C22×C8—1222no—
555C22×C8—1222no—
556C22×C8—1221no—
557C22×C8—1221no—
558C22×C8—1221no—
559C22×C8—1221no—
560C22×C8C22×D6111yescharacteristic
561C22×C8C22×D6111yescharacteristic
562#117—611no—
563#117—611no—
564#117—611no—
565#117—1221no—
566#117—1222no—
567#117—1222no—
568#117—1221no—
569#117C22×D6111yescharacteristic
570C2×C4⋊C4—611no—
571C2×C4⋊C4—611no—
572C2×C4⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C42—611no—
576C2×C42—1221no—
577C2×C42C22×D6111yescharacteristic
578#108—22no—
579#108—1222no—
580#108—1222no—
581#108—1222no—
582C4⋊C8—21no—
583C4⋊C8—21no—
584C4⋊C8—1221no—
585C4⋊C8—1221no—
586C4⋊C8—1221no—
587C4⋊C8—1221no—
588C4⋊C8—1221no—
589C4⋊C8—1221no—
590#104—22no—
591#104—1222no—
592#104—1222no—
593#104—1222no—
594#103—611no—
595#103—611no—
596#103—611no—
597#103—611no—
598#103—611no—
599#103—611no—
600#103C4×D6111yescharacteristic
601#103C4×D6111yescharacteristic
602#102—611no—
603#102—611no—
604#102—611no—
605#102—611no—
606#102—611no—
607#102—611no—
608#102C4×D6111yescharacteristic
609#102C4×D6111yescharacteristic
610C24—611no—
611C24—1221no—
612#41—21no—
613#41—21no—
614#41—614no—
615#41—614no—
616#41—612no—
617#41—612no—
618#41—1224no—
619#41—1224no—
620#41—1224no—
621#41—1224no—
622#41—1222no—
623#41—1222no—
624#41—1221no—
625#41—1221no—
626#41D4×D6112yes—
627#41Q8×D6112yes—
628C2×Q8—614no—
629C2×Q8—611no—
630C2×Q8—1221no—
631C2×Q8—1222no—
632C2×Q8C2×C4×D6111yescharacteristic
633C2×D4—21no—
634C2×D4—614no—
635C2×D4—611no—
636C2×D4—1221no—
637C2×D4—1222no—
638C2×D4—1221no—
639C2×D4—1224no—
640C2×D4—1224no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4C2×C4×D6111yescharacteristic
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—611no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—612no—
650C22×C4—612no—
651C22×C4—611no—
652C22×C4—611no—
653C22×C4—612no—
654C22×C4—612no—
655C22×C4—1224no—
656C22×C4—1221no—
657C22×C4—1224no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4C23×D6111yescharacteristic
665M16—24no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—612no—
670M16—1222no—
671M16—1224no—
672M16—1222no—
673M16—1222no—
674M16—1222no—
675M16—1224no—
676M16—1224no—
677M16—1224no—
678M16—1221no—
679M16—1221no—
680M16—1221no—
681M16—2442no—
682M16D4×D6112yes—
683C2×C8—24no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—611no—
691C2×C8—611no—
692C2×C8—611no—
693C2×C8—611no—
694C2×C8—1222no—
695C2×C8—1222no—
696C2×C8—1222no—
697C2×C8—1222no—
698C2×C8—1224no—
699C2×C8—1224no—
700C2×C8—1224no—
701C2×C8—1224no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—2442no—
709C2×C8C2×C4×D6111yescharacteristic
710C2×C8C2×C4×D6111yescharacteristic
711C2×C8D4×D6111yescharacteristic
712C2×C8D4×D6111yescharacteristic
713C4⋊C4—611no—
714C4⋊C4—611no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—2442no—
718C4⋊C4C2×C4×D6111yescharacteristic
719C4⋊C4C2×C4×D6111yescharacteristic
720C22⋊C4—21no—
721C22⋊C4—1221no—
722C22⋊C4—1221no—
723C22⋊C4—1221no—
724C22⋊C4—2442no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—1221no—
729C42—1221no—
730C42—1221no—
731C42—1221no—
732C42—1221no—
733C23—21no—
734C23—611no—
735C23—611no—
736C23—612no—
737C23—612no—
738C23—1224no—
739C23—1221no—
740C23—4881no—
741C23—4881no—
742C23—2441no—
743C23—2441no—
744C23#41×D6111yescharacteristic
745Q8—21no—
746Q8—612no—
747Q8—1224no—
748Q8—1221no—
749Q8C4⋊C4×D6112yes—
750D4—22no—
751D4—22no—
752D4—21no—
753D4—612no—
754D4—1224no—
755D4—1224no—
756D4—1224no—
757D4—1222no—
758D4—1222no—
759D4—1221no—
760D4C4⋊C4×D6112yes—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—611no—
770C2×C4—611no—
771C2×C4—612no—
772C2×C4—612no—
773C2×C4—612no—
774C2×C4—612no—
775C2×C4—612no—
776C2×C4—612no—
777C2×C4—612no—
778C2×C4—612no—
779C2×C4—612no—
780C2×C4—612no—
781C2×C4—1224no—
782C2×C4—1224no—
783C2×C4—1224no—
784C2×C4—1221no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—4881no—
790C2×C4—4881no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4C22×C4×D6111yescharacteristic
795C2×C4C2×D4×D6111yescharacteristic
796C2×C4C2×D4×D6111yescharacteristic
797C2×C4C2×D4×D6111yescharacteristic
798C2×C4C2×Q8×D6111yescharacteristic
799C2×C4#41×D6111yescharacteristic
800C8—21no—
801C8—21no—
802C8—21no—
803C8—22no—
804C8—21no—
805C8—41no—
806C8—1221no—
807C8—1221no—
808C8—1221no—
809C8—1221no—
810C8—1222no—
811C8—2441no—
812C22—21no—
813C22—21no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—612no—
818C22—612no—
819C22—1221no—
820C22—1221no—
821C22—1221no—
822C22—1221no—
823C22—1222no—
824C22—4884no—
825C22—2442no—
826C22—2442no—
827C22—2441no—
828C22—2441no—
829C22C4×D4×D6111yescharacteristic
830C22C22⋊Q8×D6111yescharacteristic
831C22#123×D6111yescharacteristic
832C4—22no—
833C4—41no—
834C4—41no—
835C4—81no—
836C4—612no—
837C4—612no—
838C4—1222no—
839C4—4881no—
840C4—2441no—
841C4—2441no—
842C4C2×C4⋊C4×D6111yescharacteristic
843C4C4×D4×D6111yescharacteristic
844C4#120×D6111yescharacteristic
845C4C22⋊Q8×D6111yescharacteristic
846C2—21no—
847C2—21no—
848C2—42no—
849C2—1222no—
850C2—1222no—
851C2—2442no—
852C2#385×D6111yescharacteristic
853C2#2145473111yescharacteristic
854C2#2145473311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1866C2
socleC22×C61C2×C4×D4
prime radicalC2×#41×D61C22
cosocleC22×C4×C61C24
hypercenter#1866D61
hypocenterC61#20886
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
2. C2×#108×D61C2semidirect
3. #21454380C2semidirect
6. #21446097C2semidirect
7. #21446096C2semidirect
8. #21446095C2semidirect
9. #21446094C2semidirect
10. #21446093C2semidirect
11. #21446092C2semidirect
12. #21446091C2semidirect
13. #21445527C2semidirect
14. #21445514C2semidirect
15. C61×#1866C2semidirect
32. C2×#14519713C22semidirect
33. C2×#14519712C22semidirect
34. C2×#14519712C22semidirect
36. #16839790C22semidirect
37. #16839789C22semidirect
38. #16839788C22semidirect
49. #16839757C4semidirect
50. #16839757C4semidirect
52. #16839755C4semidirect
53. #16839755C4semidirect
54. #103×D61C4semidirect
55. #103×D61C4semidirect
56. #102×D61C4semidirect
57. #102×D61C4semidirect
58. #16839523C22semidirect
59. #16839522C22semidirect
60. #16839521C22semidirect
61. #16839517C22semidirect
62. #16839516C22semidirect
63. #16839516C22semidirect
65. C2×#108×C61C22semidirect
66. C61×#424C22semidirect
69. C61×#339C22semidirect
70. C61×#336C22semidirect
431. #1866D61semidirect
464. C2×#108C2×D61semidirect
470. #424C2×D61semidirect
493. #339C2×D61semidirect
497. #336C2×D61semidirect
498. C61#20886semidirect

Maximal subgroups

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

subgroupindex
C2×#168405272
C2×#108×D612
#214543802
C2×#168397772
#416×D612
#214460972
#214460962
#214460952
#214460942
#214460932
#214460922
#214460912
#214455272
#214455142
C61×#18662
#2088661