Finite Group Databasebeta

← #29682736

Subgroups — #29682736

Order 15616.

1338 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839765C211yesmaximal, characteristic
2C2×#16839765C211yesmaximal, characteristic
3C2×#16839714C211yesmaximal, characteristic, complemented
4#21448300C211yesmaximal, characteristic, complemented
5#390×D61C211yesmaximal, characteristic
6#21446519C211yesmaximal, characteristic, complemented
7#21446516C211yesmaximal, characteristic, complemented
8#21446515C211yesmaximal, characteristic, complemented
9#21446504C211yesmaximal, characteristic, complemented
10#21446503C211yesmaximal, characteristic, complemented
11#21446500C211yesmaximal, characteristic, complemented
12#21446499C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14#21445537C211yesmaximal, characteristic, complemented
15C61×#1936C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C2×#14519735C2211yescharacteristic
20C2×#14519735C2211yescharacteristic
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C22⋊C4×D61—21no—
23C2×C22⋊C4×D61—21no—
24C2×C42×D61C2211yescharacteristic
25#16839765—24no—
26#16839765C418yescomplemented
27C2×#14519699C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33#16839714—24no—
34C2×#14519688C2211yescharacteristic, complemented
35C2×C8×Dic61C2211yescharacteristic, complemented
36C2×C8×Dic61C2211yescharacteristic, complemented
37#16839665C2211yescharacteristic
38#16839664C2211yescharacteristic
39#16839663C2211yescharacteristic
40#16839662—21no—
41#16839662—21no—
42#16839661C2211yescharacteristic, complemented
43#16839660C2211yescharacteristic, complemented
44#16839658C2211yescharacteristic, complemented
45#16839636—21no—
46#16839633—21no—
47C4⋊C4×Dic61—21no—
48#16839613—21no—
49#16839525C2211yescharacteristic, complemented
50#16839525C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55C2×#102×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#97×C61C2211yescharacteristic, complemented
58C61×#390C2211yescharacteristic
59C61×#389C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C24×D61—21no—
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C2×D4×D61—22no—
66C2×D4×D61—22no—
67C2×D4×D61—22no—
68C2×D4×D61—22no—
69C2×D4×D61—22no—
70C2×D4×D61C2×C414yes—
71C22×C4×D61—21no—
72C22×C4×D61D411yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61C2311yescharacteristic
75C2×#11758189—22no—
76C2×#11758189—22no—
77C2×#11758189—22no—
78C2×#11758189—22no—
79C2×#11758189C2×C414yes—
80C2×#11758189D414yes—
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83#14519735—22no—
84#14519735—22no—
85#14519735—22no—
86#14519735C2×C414yes—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×#11758196—21no—
94C4⋊C4×D61—22no—
95C4⋊C4×D61—22no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C22⋊C4×D61—44no—
105C22⋊C4×D61—44no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C42×D61—22no—
112C42×D61—22no—
113#14519699—22no—
114#14519699C2×C414yescomplemented
115#14519698—22no—
116#14519698C2×C414yescomplemented
117#14519697—22no—
118#14519697C2×C414yescomplemented
119#14519688—22no—
120C8×Dic61—22no—
121C8×Dic61—22no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125C22×D4×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C42×C61C2311yescharacteristic
135#102×C61—22no—
136#102×C61C2×C414yescomplemented
137#97×C61—22no—
138#95×C61—21no—
139C24×C61—21no—
140C23×D61—21no—
141C23×D61—24no—
142C23×D61—42no—
143C23×D61—42no—
144C23×D61—42no—
145C23×D61—42no—
146C23×D61—42no—
147C23×D61—42no—
148C23×D61C2×D411yescharacteristic
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61C22×C412yes—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2411yescharacteristic
161C2×C22⋊D61—24no—
162C2×C22⋊D61—42no—
163C2×C22⋊D61—42no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169C22×Dic61C2×D411yescharacteristic
170D4×D61—28no—
171D4×D61—28no—
172D4×D61—44no—
173D4×D61—44no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244C22×C412yes—
180C2×C4×D61—22no—
181C2×C4×D61—22no—
182C2×C4×D61—22no—
183C2×C4×D61—22no—
184C2×C4×D61—41no—
185C2×C4×D61—41no—
186C2×C4×D61—42no—
187C2×C4×D61—42no—
188C2×C4×D61—42no—
189C2×C4×D61C22×C412yes—
190C2×C4×D61C2×D412yes—
191C2×C4×D61#4112yes—
192C2×C4×D61#4112yes—
193C2×C4×D61#4112yes—
194C2×C4×D61#4112yes—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61C22×C412yes—
200C2×C8×C61C2×D412yes—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—42no—
207C4⋊C4×C61C22×C412yes—
208C22⋊C4×C61—42no—
209C22⋊C4×C61—42no—
210C42×C61—21no—
211C42×C61—21no—
212C22⋊Dic61—42no—
213C22⋊Dic61—42no—
214#11758198—24no—
215#11758198—42no—
216#11758198—42no—
217#11758198—42no—
218#11758198—42no—
219#11758198—42no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—42no—
226C4⋊Dic61C22×C412yes—
227#11758196—42no—
228#11758196—42no—
229#11758196—42no—
230C4×Dic61—21no—
231C4×Dic61—21no—
232C4×Dic61—24no—
233C4×Dic61—22no—
234C4×Dic61—22no—
235C4×Dic61—42no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418C22×C412yes—
241C2×#92418C2×D412yes—
242#11758189—28no—
243#11758189—28no—
244C23×C61—22no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61C22×D411yescharacteristic
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—22no—
257C22×D61—48no—
258C22×D61—48no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—48no—
266C22×D61—84no—
267C22×D61—84no—
268C22×D61—84no—
269C22×D61—84no—
270C22×D61C4×D412yes—
271C22×D61#12112yes—
272C22×D61#12412yes—
273D4×C61—22no—
274D4×C61—22no—
275D4×C61—41no—
276D4×C61—41no—
277C2×C4×C61—22no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61C23×C411yescharacteristic
293C2×C4×C61C22×D411yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C22⋊D61—48no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—22no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61C4×D412yes—
313C2×Dic61#12112yes—
314C2×Dic61#12412yes—
315C2×Dic61AGL(1,ℤ/8)12yes—
316C2×Dic61AGL(1,ℤ/8)12yes—
317D244—22no—
318D244—22no—
319D244—41no—
320D244—41no—
321C4×D61—44no—
322C4×D61—44no—
323C4×D61—84no—
324C4×D61#11714yes—
325C4×D61C4×D414yes—
326C4×D61#12314yes—
327C4×D61#12614yes—
328C8×C61—22no—
329C8×C61—22no—
330#92418—22no—
331#92418—22no—
332#21095—611nomaximal, Sylow
333C22×C61—42no—
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61—81no—
340C22×C61C2×C4×D411yescharacteristic
341C22×C61C2×#12111yescharacteristic
342C22×C61C2×#12411yescharacteristic
343C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
344C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
345C22×C61#57511yescharacteristic
346C22×C61#57511yescharacteristic
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—816no—
357C2×D61—81no—
358C2×D61—81no—
359C2×D61—81no—
360C2×D61—81no—
361C2×D61#38814yes—
362C4×C61—42no—
363C4×C61—41no—
364C4×C61—41no—
365C4×C61—81no—
366C4×C61—81no—
367C4×C61C2×#11711yescharacteristic
368C4×C61C2×C4×D411yescharacteristic
369C4×C61C2×#12311yescharacteristic
370C4×C61C2×#12611yescharacteristic
371Dic61—22no—
372Dic61—22no—
373Dic61—42no—
374Dic61—81no—
375Dic61—81no—
376Dic61#38814yes—
377C2×#418—611no—
378C2×#418—611no—
379C2×C4×M16—611no—
380#2296—611no—
381C2×#390—611no—
382#1936—611no—
383#1936—611no—
384#1936—611no—
385#1936D6111yescharacteristic, complemented
386#1934—611no—
387#1934—611no—
388#1934—611no—
389#1934—611no—
390#1736—611no—
391#1736—611no—
392C2×C61—82no—
393C2×C61C2×#38811yescharacteristic
394C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
395C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
396C2×C61#305511yescharacteristic
397C2×C61#305511yescharacteristic
398C2×C61#313811yescharacteristic
399C2×C61#314011yescharacteristic
400D61—24no—
401D61—82no—
402C23×D4—611no—
403C22×M16—611no—
404C22×M16—611no—
405C2×#117—611no—
406C2×#117—611no—
407C22×C4⋊C4—611no—
408C22×C22⋊C4—1221no—
409C22×C22⋊C4—1221no—
410C22×C42—611no—
411#418—618no—
412#418—1224no—
413C2×#102—611no—
414C2×#102—611no—
415C2×#102—611no—
416C2×#102—611no—
417C2×#102—611no—
418C2×#102—611no—
419C2×#102C2×D6111yescharacteristic
420C2×#102C2×D6111yescharacteristic
421C4×M16—1224no—
422C2×#97—611no—
423C2×#97C2×D6111yescharacteristic, complemented
424C2×C4×C8—611no—
425C2×C4×C8—611no—
426#390—611no—
427#390—611no—
428#390—611no—
429#390—1221no—
430#390—1221no—
431#390C2×D6111yescharacteristic
432#389—611no—
433#389—611no—
434#389—611no—
435#389C2×D6111yescharacteristic, complemented
436#385—1221no—
437#385—1221no—
438C4×C4⋊C4—1221no—
439C4×C4⋊C4—1221no—
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446#340C2×D6111yescharacteristic, complemented
447#340C2×D6111yescharacteristic, complemented
448C61#2109511yescharacteristic, complemented, Sylow
449C25—1221no—
450C22×D4—614no—
451C22×D4—611no—
452C22×D4—1222no—
453C22×D4—1222no—
454C22×D4—1222no—
455C22×D4—1222no—
456C22×D4—1222no—
457C22×D4—1221no—
458C22×D4C22×D6111yescharacteristic
459C23×C4—611no—
460C23×C4—611no—
461C23×C4—611no—
462C23×C4—1221no—
463C2×M16—614no—
464C2×M16—614no—
465C2×M16—1222no—
466C2×M16—1222no—
467C2×M16—1222no—
468C2×M16—1222no—
469C22×C8—611no—
470C22×C8—611no—
471C22×C8C22×D6111yescharacteristic
472C22×C8C22×D6111yescharacteristic
473#117—614no—
474#117—1222no—
475#117—1222no—
476#117—1222no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—1222no—
482C2×C4⋊C4—1222no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4C22×D6111yescharacteristic
488C2×C4⋊C4C22×D6111yescharacteristic
489C2×C4⋊C4C22×D6111yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—2444no—
501C2×C22⋊C4—2444no—
502C2×C42—611no—
503C2×C42—611no—
504C2×C42—611no—
505C2×C42—1222no—
506C2×C42—1222no—
507C2×C42—1221no—
508C2×C42—1221no—
509C2×C42C22×D6111yescharacteristic
510#102—22no—
511#102—614no—
512#102—614no—
513#102—614no—
514#102—1222no—
515#102—1222no—
516#102—1222no—
517#102C4×D6114yescomplemented
518#97—22no—
519#97—1222no—
520C4×C8—1222no—
521C4×C8—1222no—
522#95—21no—
523#95—1221no—
524#95—1221no—
525#95—1221no—
526C24—21no—
527C24—611no—
528C24—1224no—
529C24—1221no—
530C24—2442no—
531C24—2442no—
532C24—2442no—
533C24—2442no—
534C24—2442no—
535C24—2442no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—612no—
542C2×D4—1228no—
543C2×D4—1228no—
544C2×D4—1224no—
545C2×D4—1221no—
546C2×D4—1221no—
547C2×D4—1221no—
548C2×D4—1221no—
549C2×D4—1221no—
550C2×D4—2444no—
551C2×D4—2444no—
552C2×D4—2442no—
553C2×D4—2442no—
554C2×D4C2×C4×D6112yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—611no—
559C22×C4—612no—
560C22×C4—612no—
561C22×C4—612no—
562C22×C4—612no—
563C22×C4—612no—
564C22×C4—612no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—2441no—
575C22×C4—2441no—
576C22×C4—2442no—
577C22×C4—2442no—
578C22×C4—2442no—
579C22×C4D4×D6111yescharacteristic
580C22×C4D4×D6111yescharacteristic
581C22×C4C23×D6111yescharacteristic
582M16—1228no—
583M16—1228no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—612no—
589C2×C8—612no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8C2×C4×D6112yes—
595C2×C8D4×D6112yes—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—42no—
602C4⋊C4—612no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—2442no—
609C4⋊C4—2442no—
610C4⋊C4—2442no—
611C4⋊C4—2442no—
612C4⋊C4C2×C4×D6112yes—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—1224no—
616C22⋊C4—2442no—
617C22⋊C4—2442no—
618C22⋊C4—2442no—
619C22⋊C4—2442no—
620C22⋊C4—2442no—
621C22⋊C4—2442no—
622C22⋊C4—2442no—
623C42—21no—
624C42—21no—
625C42—1222no—
626C42—1222no—
627C42—1224no—
628C42—1221no—
629C42—1221no—
630C42—2442no—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—612no—
639C23—612no—
640C23—612no—
641C23—1221no—
642C23—1221no—
643C23—1221no—
644C23—1221no—
645C23—1222no—
646C23—4884no—
647C23—4884no—
648C23—4884no—
649C23—4884no—
650C23—2448no—
651C23—2448no—
652C23—2448no—
653C23—2441no—
654C23—2441no—
655C23—2441no—
656C23—2441no—
657C23—2441no—
658C23—2441no—
659C23C2×D4×D6111yescharacteristic
660D4—22no—
661D4—22no—
662D4—41no—
663D4—41no—
664D4—1222no—
665D4—1222no—
666D4—2448no—
667D4—2441no—
668D4—2441no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—612no—
685C2×C4—612no—
686C2×C4—612no—
687C2×C4—614no—
688C2×C4—614no—
689C2×C4—614no—
690C2×C4—614no—
691C2×C4—612no—
692C2×C4—612no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1222no—
698C2×C4—4884no—
699C2×C4—2444no—
700C2×C4—2444no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4C22×C4×D6111yescharacteristic
710C2×C4C2×D4×D6111yescharacteristic
711C2×C4#41×D6111yescharacteristic
712C2×C4#41×D6111yescharacteristic
713C2×C4#41×D6111yescharacteristic
714C2×C4#41×D6111yescharacteristic
715C8—22no—
716C8—22no—
717C8—1222no—
718C8—1222no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—614no—
727C22—1222no—
728C22—1222no—
729C22—1222no—
730C22—1222no—
731C22—1222no—
732C22—1222no—
733C22—48816no—
734C22—4881no—
735C22—4881no—
736C22—4881no—
737C22—4881no—
738C22—2442no—
739C22—2442no—
740C22—2442no—
741C22C4×D4×D6111yescharacteristic
742C22#121×D6111yescharacteristic
743C22#124×D6111yescharacteristic
744C22AGL(1,ℤ/8)×D6111yescharacteristic
745C22AGL(1,ℤ/8)×D6111yescharacteristic
746C22#1684055811yescharacteristic
747C22#1684056111yescharacteristic
748C4—42no—
749C4—41no—
750C4—41no—
751C4—81no—
752C4—81no—
753C4—614no—
754C4—1222no—
755C4—1222no—
756C4—4881no—
757C4—4881no—
758C4—2442no—
759C4#117×D6111yescharacteristic
760C4C4×D4×D6111yescharacteristic
761C4#123×D6111yescharacteristic
762C4#126×D6111yescharacteristic
763C2—82no—
764C2—1224no—
765C2—4882no—
766C2#388×D6111yescharacteristic
767C2#2145462411yescharacteristic
768C2#2145463011yescharacteristic
769C2#2145543311yescharacteristic
770C2#2145543711yescharacteristic
771C2#2145619211yescharacteristic
772C2#2145620411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1936C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenter#1936D61
hypocenterC61#21095
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
3. C2×#16839714C2semidirect
4. #21448300C2semidirect
6. #21446519C2semidirect
7. #21446516C2semidirect
8. #21446515C2semidirect
9. #21446504C2semidirect
10. #21446503C2semidirect
11. #21446500C2semidirect
12. #21446499C2semidirect
13. #21445537C2semidirect
14. #21445537C2semidirect
15. C61×#1936C2semidirect
26. #16839765C4semidirect
34. C2×#14519688C22semidirect
35. C2×C8×Dic61C22semidirect
36. C2×C8×Dic61C22semidirect
42. #16839661C22semidirect
43. #16839660C22semidirect
44. #16839658C22semidirect
49. #16839525C22semidirect
50. #16839525C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
53. #16839524C22semidirect
54. #16839524C22semidirect
57. C2×#97×C61C22semidirect
59. C61×#389C22semidirect
60. C61×#340C22semidirect
61. C61×#340C22semidirect
114. #14519699C2×C4semidirect
116. #14519698C2×C4semidirect
118. #14519697C2×C4semidirect
136. #102×C61C2×C4semidirect
385. #1936D61semidirect
423. C2×#97C2×D61semidirect
435. #389C2×D61semidirect
446. #340C2×D61semidirect
447. #340C2×D61semidirect
448. C61#21095semidirect
517. #102C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168397652
C2×#168397142
#214483002
#390×D612
#214465192
#214465162
#214465152
#214465042
#214465032
#214465002
#214464992
#214455372
C61×#19362
#2109561