Finite Group Databasebeta

← #29681774

Subgroups — #29681774

Order 15616.

1954 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#525×D61C211yesmaximal, characteristic
2C22×#14519734C211yesmaximal, characteristic, complemented
3C2×#16839777C212yesmaximal, complemented
4#407×D61C211yesmaximal, characteristic, complemented
5#21446266C212yesmaximal, complemented
6#21446264C212yesmaximal, complemented
7#21446263C211yesmaximal, characteristic, complemented
8#21446262C211yesmaximal, characteristic, complemented
9#21446260C211yesmaximal, characteristic, complemented
10#21445527C212yesmaximal, complemented
11C61×#1896C211yesmaximal, characteristic, complemented
12C2×#41×D61C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C2×M16×D61C2212yes—
15#16840275C412yescomplemented
16#16840274C2211yescharacteristic
17#16840273C2211yescharacteristic
18#16840272C412yescomplemented
19#16840271—22no—
20#16840270—21no—
21#16840269C2211yescharacteristic
22#16840268—21no—
23#123×D61—21no—
24C22⋊Q8×D61C412yescomplemented
25#121×D61C412yescomplemented
26#120×D61—21no—
27C4×D4×D61—22no—
28C2×#14519734—28no—
29C2×#14519734—21no—
30C2×#14519734—21no—
31C2×#14519734C2212yes—
32C2×#14519734C2212yescomplemented
33#117×D61C2211yescharacteristic
34C22×#11758196—21no—
35C22×#11758198—21no—
36C22×C4×Dic61C2211yescharacteristic, complemented
37#16839777—28no—
38C2×#14519705C2212yescomplemented
39C2×#14519704C2212yescomplemented
40C2×#14519703C2212yescomplemented
41#16839726C2211yescharacteristic, complemented
42#16839725C2212yescomplemented
43#16839724—22no—
44C22⋊C8×D61—22no—
45#16839523C2212yescomplemented
46#16839522C2212yescomplemented
47#16839521C2212yescomplemented
48C61×#525C2211yescharacteristic
49C22×C42×C61C2211yescharacteristic, complemented
50C2×#104×C61C2212yescomplemented
51C61×#407C2211yescharacteristic, complemented
52C61×#339C2212yescomplemented
53C24×D61D411yescharacteristic
54C2×#11758226C2×C411yescharacteristic, complemented
55C2×#11758222—21no—
56C2×#11758222C2311yescharacteristic
57C2×#11758224—21no—
58C2×#11758224C2×C411yescharacteristic, complemented
59#41×D61—24no—
60#41×D61—24no—
61C2×Q8×D61C2×C411yescharacteristic, complemented
62C2×D4×D61—22no—
63C2×D4×D61—21no—
64C2×D4×D61C2×C411yescharacteristic, complemented
65C23×Dic61—21no—
66C23×Dic61D411yescharacteristic
67C22×C4×D61—24no—
68C22×C4×D61—24no—
69C22×C4×D61—21no—
70C22×C4×D61C2×C412yes—
71C22×C4×D61C2×C412yes—
72C22×C4×D61D411yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D412yes—
75C22×C4×D61D412yes—
76C22×C4×D61C2311yescharacteristic
77C22×C4×D61C2311yescharacteristic
78C2×#11758194C2312yes—
79C2×#11758189—22no—
80M16×D61—24no—
81M16×D61—24no—
82C2×C8×D61—22no—
83#14519762—22no—
84#14519761—21no—
85#14519760—21no—
86#14519759—22no—
87#14519758—21no—
88#14519757C2×C412yescomplemented
89#14519756C2×C412yes—
90#14519755—22no—
91#14519754—22no—
92#14519753C2×C412yescomplemented
93#14519752C2×C412yescomplemented
94#14519751C2×C412yes—
95#14519750—22no—
96#14519749—22no—
97#14519748C2×C412yescomplemented
98#14519747—22no—
99#14519747—21no—
100#14519746—21no—
101#14519745—22no—
102#14519745—21no—
103C4×D244—22no—
104D4×Dic61—22no—
105#14519739—22no—
106C4×C22⋊D61—22no—
107C4×C22⋊D61—22no—
108#14519737—22no—
109#14519737—22no—
110#14519736C2311yescharacteristic
111#14519735C2×C412yescomplemented
112#14519734—28no—
113#14519734—28no—
114#14519734—21no—
115#14519734—24no—
116#14519734—24no—
117#14519734—24no—
118#14519734D418yescomplemented
119#14519733—21no—
120C2×#11758196—28no—
121C2×#11758196—22no—
122C2×#11758196—22no—
123C4⋊C4×D61—22no—
124C4⋊C4×D61C2×C412yescomplemented
125C2×#11758198—28no—
126C2×#11758198—22no—
127C2×#11758198—22no—
128C22⋊C4×D61—22no—
129C22⋊C4×D61—21no—
130C22⋊C4×D61—22no—
131C2×C4×Dic61—21no—
132C2×C4×Dic61—24no—
133C2×C4×Dic61C2312yes—
134C42×D61—21no—
135#14519705—24no—
136#14519704—24no—
137#14519703—24no—
138C22⋊#92418—22no—
139#14519689—24no—
140C2×#41×C61C2311yescharacteristic
141C23×C4×C61—21no—
142C23×C4×C61C2311yescharacteristic
143C2×M16×C61C2312yes—
144#123×C61—21no—
145C22⋊Q8×C61C2×C412yes—
146#121×C61C2×C412yes—
147#120×C61—21no—
148C4×D4×C61—22no—
149#117×C61C2311yescharacteristic
150C2×C42×C61—21no—
151C2×C42×C61—24no—
152C2×C42×C61C2312yes—
153#104×C61—24no—
154C22⋊C8×C61—22no—
155C24×C61C2×D411yescharacteristic
156C23×D61—22no—
157C23×D61—22no—
158C23×D61—21no—
159C23×D61—44no—
160C23×D61C22⋊C412yes—
161C23×D61C22⋊C412yes—
162C23×D61C2×D411yescharacteristic
163C23×D61C2×D411yescharacteristic
164#41×C61—22no—
165#41×C61—22no—
166C2×Q8×C61C22×C411yescharacteristic
167C2×D4×C61—22no—
168C2×D4×C61—21no—
169C2×D4×C61C22×C411yescharacteristic
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—24no—
173C22×C4×C61—22no—
174C22×C4×C61—21no—
175C22×C4×C61—44no—
176C22×C4×C61C22×C412yes—
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D412yes—
179C22×C4×C61C2411yescharacteristic
180C2×C22⋊D61—22no—
181C2×C22⋊D61—21no—
182C2×C22⋊D61—21no—
183C2×C22⋊D61—22no—
184C2×C22⋊D61—21no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—24no—
188C22×Dic61—22no—
189C22×Dic61—21no—
190C22×Dic61—44no—
191C22×Dic61C22⋊C412yes—
192C22×Dic61C22⋊C412yes—
193C22×Dic61C2×D411yescharacteristic
194C22×Dic61C2×D411yescharacteristic
195#11758226—24no—
196Q8×D61—24no—
197#11758224—24no—
198#11758224—42no—
199#11758224—42no—
200D4×D61—24no—
201D4×D61—48no—
202D4×D61—42no—
203D4×D61—42no—
204#11758222—22no—
205#11758222—22no—
206#11758222—44no—
207C2×D244—21no—
208C2×D244—22no—
209C2×D244C22×C411yescharacteristic
210C2×C4×D61—22no—
211C2×C4×D61—22no—
212C2×C4×D61—22no—
213C2×C4×D61—22no—
214C2×C4×D61—22no—
215C2×C4×D61—22no—
216C2×C4×D61—28no—
217C2×C4×D61—28no—
218C2×C4×D61—28no—
219C2×C4×D61—28no—
220C2×C4×D61—21no—
221C2×C4×D61—22no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—44no—
225C2×C4×D61C22⋊C412yes—
226C2×C4×D61C22⋊C412yes—
227C2×C4×D61C22⋊C412yes—
228C2×C4×D61C22⋊C412yes—
229C2×C4×D61C22×C412yes—
230C2×C4×D61C22×C411yescharacteristic
231C2×C4×D61C22×C411yescharacteristic
232C2×C4×D61C2×D412yes—
233C2×C4×D61C2×D414yes—
234C2×C4×D61C2×D411yescharacteristic
235C2×C4×D61C2×D411yescharacteristic
236C2×C4×D61#4114yes—
237C2×Dic122—21no—
238C2×Dic122C22×C411yescharacteristic
239M16×C61—22no—
240M16×C61—22no—
241C2×C8×C61—22no—
242C4⋊C4×C61—22no—
243C4⋊C4×C61C22×C412yes—
244C22⋊C4×C61—22no—
245C22⋊C4×C61—21no—
246C22⋊C4×C61—22no—
247C42×C61—24no—
248C42×C61—22no—
249C42×C61—21no—
250C42×C61C2×D414yescomplemented
251C22⋊Dic61—22no—
252C22⋊Dic61—21no—
253C22⋊Dic61—22no—
254#11758198—28no—
255#11758198—22no—
256#11758198—22no—
257#11758198—22no—
258#11758198—28no—
259#11758198—22no—
260#11758198—22no—
261C4⋊Dic61—22no—
262C4⋊Dic61C22×C412yes—
263#11758196—28no—
264#11758196—22no—
265#11758196—22no—
266#11758196—22no—
267#11758196—28no—
268C4×Dic61—24no—
269C4×Dic61—21no—
270C4×Dic61—22no—
271C4×Dic61—22no—
272C4×Dic61C2×D414yescomplemented
273#11758194—22no—
274#11758194—22no—
275C2×#92418—22no—
276#11758189—44no—
277C8×D61—44no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—24no—
281C23×C61—21no—
282C23×C61C2×C22⋊C412yes—
283C23×C61C22×D411yescharacteristic
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—24no—
287C22×D61—24no—
288C22×D61—24no—
289C22×D61—24no—
290C22×D61—21no—
291C22×D61—42no—
292C22×D61—42no—
293C22×D61—42no—
294C22×D61—42no—
295C22×D61—44no—
296C22×D61—48no—
297C22×D61—48no—
298C22×D61—42no—
299C22×D61C2×C22⋊C412yes—
300C22×D61C2×C22⋊C411yescharacteristic
301C22×D61C2×C22⋊C411yescharacteristic
302C22×D61#12012yes—
303C22×D61#12312yes—
304Q8×C61—22no—
305D4×C61—22no—
306D4×C61—41no—
307D4×C61—41no—
308D4×C61—44no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—24no—
312C2×C4×C61—24no—
313C2×C4×C61—22no—
314C2×C4×C61—21no—
315C2×C4×C61—24no—
316C2×C4×C61—48no—
317C2×C4×C61—44no—
318C2×C4×C61—42no—
319C2×C4×C61C2×C22⋊C412yes—
320C2×C4×C61C23×C411yescharacteristic
321C2×C4×C61C22×D412yes—
322C2×C4×C61C22×D411yescharacteristic
323C2×C4×C61C2×#4112yes—
324C22⋊D61—44no—
325C22⋊D61—41no—
326C22⋊D61—41no—
327C22⋊D61—44no—
328C22⋊D61—42no—
329C22⋊D61—42no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—24no—
333C2×Dic61—24no—
334C2×Dic61—22no—
335C2×Dic61—21no—
336C2×Dic61—24no—
337C2×Dic61—48no—
338C2×Dic61—44no—
339C2×Dic61—42no—
340C2×Dic61C2×C22⋊C412yes—
341C2×Dic61C2×C22⋊C411yescharacteristic
342C2×Dic61C2×C22⋊C411yescharacteristic
343C2×Dic61#12012yes—
344C2×Dic61#12312yes—
345D244—22no—
346D244—44no—
347D244—42no—
348C4×D61—24no—
349C4×D61—24no—
350C4×D61—24no—
351C4×D61—24no—
352C4×D61—24no—
353C4×D61—24no—
354C4×D61—44no—
355C4×D61—42no—
356C4×D61—42no—
357C4×D61—42no—
358C4×D61C4×D414yes—
359C4×D61C4×D414yes—
360C4×D61#12114yes—
361C4×D61#12114yes—
362Dic122—22no—
363Dic122—42no—
364C8×C61—42no—
365#92418—42no—
366#20979—611nomaximal, Sylow
367C22×C61—24no—
368C22×C61—24no—
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—42no—
373C22×C61—41no—
374C22×C61#42114yescomplemented
375C22×C61C22×C22⋊C411yescharacteristic
376C22×C61C2×#12011yescharacteristic
377C22×C61C2×#12311yescharacteristic
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—48no—
386C2×D61—48no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—41no—
391C2×D61—84no—
392C2×D61#38612yes—
393C2×D61#38612yes—
394C4×C61—22no—
395C4×C61—44no—
396C4×C61—42no—
397C4×C61—41no—
398C4×C61C2×C4×D412yes—
399C4×C61C2×#12112yes—
400Dic61—22no—
401Dic61—44no—
402Dic61—42no—
403Dic61—41no—
404Dic61#38612yes—
405Dic61#38612yes—
406C2×#525—611no—
407C22×#117—611no—
408C2×#421—612no—
409C2×#407—611no—
410#1897—612no—
411#1897—612no—
412#1896—611no—
413#1896—611no—
414#1896—611no—
415#1896D6111yescharacteristic, complemented
416#1733—612no—
417C2×C61—21no—
418C2×C61—21no—
419C2×C61—24no—
420C2×C61—81no—
421C2×C61C2×#38611yescharacteristic
422C2×C61C2×#42112yes—
423D61—22no—
424D61—22no—
425D61—42no—
426D61—81no—
427C22×#41—611no—
428C24×C4—611no—
429C22×M16—612no—
430#525—611no—
431#525—611no—
432#525—612no—
433#525—612no—
434#525—611no—
435#525—1222no—
436#525—1221no—
437#525—1221no—
438#525C2×D6111yescharacteristic
439C2×#123—1221no—
440C2×C22⋊Q8—612no—
441C2×#121—612no—
442C2×#120—1221no—
443C2×C4×D4—1222no—
444C2×#117—612no—
445C2×#117—612no—
446C2×#117—611no—
447C2×#117—1228no—
448C2×#117—1221no—
449C2×#117—1221no—
450C22×C4⋊C4—1221no—
451C22×C22⋊C4—1221no—
452C22×C42—611no—
453C22×C42C2×D6111yescharacteristic, complemented
454#421—1228no—
455C2×#104—612no—
456C2×#104—612no—
457C2×#104—612no—
458C2×#104C2×D6112yescomplemented
459#407—611no—
460#407—612no—
461#407—1222no—
462#407C2×D6111yescharacteristic, complemented
463C2×C22⋊C8—1222no—
464#339—612no—
465#339—612no—
466#339—612no—
467#339C2×D6112yescomplemented
468C61#2097911yescharacteristic, complemented, Sylow
469C25—611no—
470C2×#41—611no—
471C2×#41—611no—
472C2×#41—611no—
473C2×#41—1221no—
474C2×#41—1221no—
475C2×#41—1224no—
476C2×#41—1224no—
477C2×#41C22×D6111yescharacteristic
478C22×Q8—611no—
479C22×D4—611no—
480C22×D4—1222no—
481C22×D4—1221no—
482C23×C4—21no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—612no—
486C23×C4—612no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—612no—
490C23×C4—612no—
491C23×C4—611no—
492C23×C4—1224no—
493C23×C4—1224no—
494C23×C4—1221no—
495C23×C4—1221no—
496C23×C4C22×D6111yescharacteristic
497C2×M16—612no—
498C2×M16—1222no—
499C2×M16—1224no—
500C2×M16—1224no—
501C2×M16C22×D6112yes—
502C22×C8—1222no—
503#123—21no—
504#123—1222no—
505#123—1221no—
506#123—1222no—
507#123—1221no—
508#123—1221no—
509C22⋊Q8—612no—
510C22⋊Q8—612no—
511C22⋊Q8—612no—
512C22⋊Q8—1222no—
513C22⋊Q8—1222no—
514C22⋊Q8C4×D6112yes—
515#121—612no—
516#121—612no—
517#121—612no—
518#121—1222no—
519#121—1222no—
520#121C4×D6112yes—
521#120—21no—
522#120—1221no—
523#120—1222no—
524#120—1222no—
525#120—1221no—
526#120—1221no—
527C4×D4—22no—
528C4×D4—1222no—
529C4×D4—1222no—
530C4×D4—1222no—
531C4×D4—1222no—
532C4×D4—1222no—
533C4×D4—1222no—
534C4×D4—1222no—
535#117—618no—
536#117—611no—
537#117—612no—
538#117—1224no—
539#117—1224no—
540#117—1221no—
541#117—1228no—
542#117—1228no—
543#117—1221no—
544#117—1224no—
545#117C22×D6111yescharacteristic
546C2×C4⋊C4—612no—
547C2×C4⋊C4—1222no—
548C2×C4⋊C4—1222no—
549C2×C4⋊C4—1222no—
550C2×C4⋊C4—1228no—
551C2×C22⋊C4—1222no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1222no—
554C2×C22⋊C4—1222no—
555C2×C22⋊C4—1222no—
556C2×C22⋊C4—1228no—
557C2×C42—21no—
558C2×C42—24no—
559C2×C42—612no—
560C2×C42—1221no—
561C2×C42—1224no—
562C2×C42—1221no—
563C2×C42C22×D6112yes—
564#104—24no—
565#104—1224no—
566#104—1224no—
567#104—1224no—
568C22⋊C8—22no—
569C22⋊C8—1224no—
570C22⋊C8—1222no—
571C24—611no—
572C24—612no—
573C24—612no—
574C24—611no—
575C24—1222no—
576C24—1222no—
577C24—1221no—
578C24—2444no—
579C24D4×D6111yescharacteristic
580#41—22no—
581#41—22no—
582#41—1224no—
583#41—1224no—
584#41—1222no—
585#41—1222no—
586#41—2444no—
587#41—2442no—
588#41—2442no—
589C2×Q8—611no—
590C2×Q8—1221no—
591C2×Q8—1224no—
592C2×Q8C2×C4×D6111yescharacteristic
593C2×D4—21no—
594C2×D4—22no—
595C2×D4—611no—
596C2×D4—1222no—
597C2×D4—1221no—
598C2×D4—1224no—
599C2×D4—1221no—
600C2×D4—1222no—
601C2×D4—1221no—
602C2×D4—1221no—
603C2×D4—1222no—
604C2×D4—2442no—
605C2×D4—2442no—
606C2×D4—2448no—
607C2×D4C2×C4×D6111yescharacteristic
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—24no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—44no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—614no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—614no—
621C22×C4—611no—
622C22×C4—612no—
623C22×C4—612no—
624C22×C4—612no—
625C22×C4—612no—
626C22×C4—612no—
627C22×C4—612no—
628C22×C4—612no—
629C22×C4—612no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4—1228no—
633C22×C4—1228no—
634C22×C4—1228no—
635C22×C4—1228no—
636C22×C4—1221no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4—1221no—
641C22×C4—1222no—
642C22×C4—1222no—
643C22×C4—1221no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1224no—
647C22×C4—1222no—
648C22×C4—1221no—
649C22×C4—2444no—
650C22×C4—2444no—
651C22×C4C2×C4×D6112yes—
652C22×C4D4×D6112yes—
653C22×C4D4×D6111yescharacteristic
654C22×C4C23×D6111yescharacteristic
655M16—22no—
656M16—22no—
657M16—1222no—
658M16—1222no—
659M16—2444no—
660C2×C8—22no—
661C2×C8—1222no—
662C2×C8—2444no—
663C4⋊C4—22no—
664C4⋊C4—612no—
665C4⋊C4—1222no—
666C4⋊C4—1228no—
667C4⋊C4—1222no—
668C4⋊C4—1222no—
669C4⋊C4—1228no—
670C4⋊C4—1222no—
671C4⋊C4C2×C4×D6112yes—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—1222no—
676C22⋊C4—1228no—
677C22⋊C4—1222no—
678C22⋊C4—1222no—
679C22⋊C4—1222no—
680C22⋊C4—1228no—
681C22⋊C4—1222no—
682C22⋊C4—1221no—
683C22⋊C4—1222no—
684C22⋊C4—1222no—
685C42—24no—
686C42—22no—
687C42—21no—
688C42—614no—
689C42—1222no—
690C42—1224no—
691C42—1222no—
692C42—1221no—
693C42D4×D6114yescomplemented
694C23—21no—
695C23—21no—
696C23—24no—
697C23—21no—
698C23—611no—
699C23—611no—
700C23—612no—
701C23—612no—
702C23—612no—
703C23—1224no—
704C23—1224no—
705C23—1221no—
706C23—1221no—
707C23—1224no—
708C23—1224no—
709C23—1221no—
710C23—2442no—
711C23—2442no—
712C23—2442no—
713C23—2442no—
714C23—2448no—
715C23—2448no—
716C23—2442no—
717C23—2444no—
718C23C22⋊C4×D6112yes—
719C23C2×D4×D6111yescharacteristic
720Q8—22no—
721Q8—1222no—
722Q8—2442no—
723D4—22no—
724D4—41no—
725D4—41no—
726D4—44no—
727D4—1222no—
728D4—2442no—
729D4—2444no—
730D4—2442no—
731D4—2442no—
732D4—2444no—
733D4—2441no—
734D4—2441no—
735D4—2444no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—24no—
743C2×C4—48no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—611no—
747C2×C4—611no—
748C2×C4—612no—
749C2×C4—612no—
750C2×C4—614no—
751C2×C4—614no—
752C2×C4—614no—
753C2×C4—614no—
754C2×C4—612no—
755C2×C4—1224no—
756C2×C4—1224no—
757C2×C4—1224no—
758C2×C4—1224no—
759C2×C4—1224no—
760C2×C4—1224no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—1224no—
764C2×C4—1224no—
765C2×C4—1222no—
766C2×C4—1221no—
767C2×C4—1224no—
768C2×C4—2442no—
769C2×C4—2442no—
770C2×C4—2444no—
771C2×C4—2442no—
772C2×C4—2448no—
773C2×C4—2444no—
774C2×C4—2442no—
775C2×C4C22⋊C4×D6112yes—
776C2×C4C22×C4×D6111yescharacteristic
777C2×C4C2×D4×D6112yes—
778C2×C4C2×D4×D6111yescharacteristic
779C2×C4#41×D6112yes—
780C8—42no—
781C8—2442no—
782C22—24no—
783C22—24no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—42no—
788C22—41no—
789C22—612no—
790C22—612no—
791C22—1222no—
792C22—1222no—
793C22—1222no—
794C22—1222no—
795C22—1222no—
796C22—4884no—
797C22—2442no—
798C22—2442no—
799C22—2448no—
800C22—2448no—
801C22—2442no—
802C22—2442no—
803C22—2442no—
804C22—2441no—
805C22#1683977714yescomplemented
806C22C2×C22⋊C4×D6111yescharacteristic
807C22#120×D6111yescharacteristic
808C22#123×D6111yescharacteristic
809C4—22no—
810C4—44no—
811C4—42no—
812C4—41no—
813C4—612no—
814C4—612no—
815C4—1222no—
816C4—2444no—
817C4—2442no—
818C4—2441no—
819C4C4×D4×D6112yes—
820C4#121×D6112yes—
821C2—21no—
822C2—21no—
823C2—24no—
824C2—81no—
825C2—1222no—
826C2—1222no—
827C2—4881no—
828C2—2442no—
829C2#386×D6111yescharacteristic
830C2C2×#1683977712yes—
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1896C2
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC22×C4×C61C24
hypercenter#1896D61
hypocenterC61#20979
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1896

Complements

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

NH ≅ G/Ntype
2. C22×#14519734C2semidirect
3. C2×#16839777C2semidirect
4. #407×D61C2semidirect
5. #21446266C2semidirect
6. #21446264C2semidirect
7. #21446263C2semidirect
8. #21446262C2semidirect
9. #21446260C2semidirect
10. #21445527C2semidirect
11. C61×#1896C2semidirect
15. #16840275C4semidirect
18. #16840272C4semidirect
24. C22⋊Q8×D61C4semidirect
25. #121×D61C4semidirect
32. C2×#14519734C22semidirect
36. C22×C4×Dic61C22semidirect
38. C2×#14519705C22semidirect
39. C2×#14519704C22semidirect
40. C2×#14519703C22semidirect
41. #16839726C22semidirect
42. #16839725C22semidirect
45. #16839523C22semidirect
46. #16839522C22semidirect
47. #16839521C22semidirect
49. C22×C42×C61C22semidirect
50. C2×#104×C61C22semidirect
51. C61×#407C22semidirect
52. C61×#339C22semidirect
54. C2×#11758226C2×C4semidirect
58. C2×#11758224C2×C4semidirect
61. C2×Q8×D61C2×C4semidirect
64. C2×D4×D61C2×C4semidirect
88. #14519757C2×C4semidirect
92. #14519753C2×C4semidirect
93. #14519752C2×C4semidirect
97. #14519748C2×C4semidirect
111. #14519735C2×C4semidirect
118. #14519734D4semidirect
124. C4⋊C4×D61C2×C4semidirect
250. C42×C61C2×D4semidirect
272. C4×Dic61C2×D4semidirect
374. C22×C61#421semidirect
415. #1896D61semidirect
453. C22×C42C2×D61semidirect
458. C2×#104C2×D61semidirect
462. #407C2×D61semidirect
467. #339C2×D61semidirect
468. C61#20979semidirect
693. C42D4×D61semidirect
805. C22#16839777semidirect

Maximal subgroups

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

subgroupindex
#525×D612
C22×#145197342
C2×#168397772
#407×D612
#214462662
#214462642
#214462632
#214462622
#214462602
#214455272
C61×#18962
#2097961