Finite Group Databasebeta

← #29691280

Subgroups — #29691280

Order 15616.

1084 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839904C211yesmaximal, characteristic
2#21448335C211yesmaximal, characteristic, complemented
3#21448306C211yesmaximal, characteristic, complemented
4#21446699C211yesmaximal, characteristic, complemented
5#21446519C211yesmaximal, characteristic, complemented
6#21446509C211yesmaximal, characteristic, complemented
7#21446452C211yesmaximal, characteristic, complemented
8#21446442C211yesmaximal, characteristic, complemented
9#21446169C211yesmaximal, characteristic, complemented
10#21446151C211yesmaximal, characteristic, complemented
11#21446138C211yesmaximal, characteristic, complemented
12#21446017C211yesmaximal, characteristic, complemented
13#21445756C211yesmaximal, characteristic, complemented
14#21445582C211yesmaximal, characteristic, complemented
15C61×#1972C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C2×#14519748C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20C2×#14519737—21no—
21C2×#14519735C2211yescharacteristic
22C2×C42×D61C2211yescharacteristic
23#16839904C418yescomplemented
24C2×#14519710C2211yescharacteristic
25C2×#14519702C2211yescharacteristic
26C2×#14519702C2211yescharacteristic
27C2×#14519700C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519688C2211yescharacteristic
34#16839668C2211yescharacteristic
35#16839667C2211yescharacteristic
36#16839665C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839656—21no—
39#16839638—21no—
40#16839638—21no—
41#16839638—21no—
42#16839619C2211yescharacteristic
43C4⋊C4×Dic61C2211yescharacteristic
44C22⋊C4×Dic61—21no—
45C22⋊C4×Dic61—21no—
46C22⋊C4×Dic61—21no—
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53C22×D8×C61C2211yescharacteristic
54C2×#106×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#97×C61C2211yescharacteristic
58C61×#390C2211yescharacteristic
59C61×#390C2211yescharacteristic
60C2×#11758224—22no—
61C2×#11758224—41no—
62C2×#11758224—41no—
63C2×#11758224—41no—
64C2×#11758224—41no—
65C2×#11758224C2×C414yescomplemented
66C22×Dic122C2311yescharacteristic
67C22×C22⋊D61—21no—
68C22×C22⋊D61—21no—
69C23×Dic61—21no—
70C23×Dic61—21no—
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D411yescharacteristic
73C22×C4×D61C2311yescharacteristic
74C2×#11758200—41no—
75C2×#11758200—41no—
76C2×#11758200C2×C414yescomplemented
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79#14519748—22no—
80#14519748C2×C414yes—
81D4×Dic61—41no—
82D4×Dic61—41no—
83#14519737—44no—
84#14519735—41no—
85#14519735—41no—
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×#11758196—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61D411yescharacteristic
99C2×C4×Dic61D411yescharacteristic
100C2×C4×Dic61C2311yescharacteristic
101C42×D61—41no—
102C42×D61—41no—
103#14519710—41no—
104#14519702—41no—
105#14519702C2×C414yescomplemented
106#14519700—41no—
107#14519698—41no—
108#14519698—41no—
109#14519698C2×C414yescomplemented
110#14519689—22no—
111#14519689C2×C414yescomplemented
112#14519688—41no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120C22×D4×C61C2311yescharacteristic
121C22×D4×C61C2311yescharacteristic
122C2×D8×C61—41no—
123C2×D8×C61—41no—
124C2×D8×C61C2×C414yescomplemented
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C42×C61C2311yescharacteristic
134#106×C61—41no—
135#102×C61—41no—
136#102×C61—41no—
137#97×C61—41no—
138C24×C61—21no—
139C24×C61—21no—
140C23×D61C2×D411yescharacteristic
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61C22×C412yes—
152C2×D4×C61C22×C412yes—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2411yescharacteristic
158C2×C22⋊D61—24no—
159C2×C22⋊D61—24no—
160C2×C22⋊D61—42no—
161C2×C22⋊D61—42no—
162C2×C22⋊D61—42no—
163C2×C22⋊D61—42no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—24no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—42no—
170C22×Dic61—42no—
171C22×Dic61—42no—
172C22×Dic61—42no—
173C22×Dic61—42no—
174C22×Dic61C2×D411yescharacteristic
175C22×Dic61C2×D411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177#11758224—44no—
178#11758224—44no—
179#11758224—44no—
180#11758224—44no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—22no—
186C2×C4×D61—41no—
187C2×C4×D61—41no—
188C2×C4×D61—41no—
189C2×C4×D61—41no—
190C2×C4×D61—41no—
191C2×C4×D61C22×C412yes—
192C2×C4×D61#4112yes—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122C22×C412yes—
199D8×C61—44no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61C22×C412yes—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C22⋊C4×C61—42no—
211C22⋊C4×C61—42no—
212C22⋊C4×C61—42no—
213C22⋊C4×C61—42no—
214C42×C61—21no—
215C42×C61—21no—
216C22⋊Dic61—24no—
217C22⋊Dic61—42no—
218C22⋊Dic61—42no—
219C22⋊Dic61—42no—
220#11758200—44no—
221#11758198—42no—
222#11758198—42no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61C22×C412yes—
229#11758196—42no—
230C4×Dic61—21no—
231C4×Dic61—21no—
232C4×Dic61—41no—
233C4×Dic61—41no—
234C4×Dic61—42no—
235C4×Dic61—42no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418C22×C412yes—
242C23×C61—22no—
243C23×C61—22no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61C22×D411yescharacteristic
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61C4×D412yes—
264D4×C61—22no—
265D4×C61—22no—
266D4×C61—22no—
267D4×C61—22no—
268D4×C61—41no—
269D4×C61—41no—
270D4×C61—41no—
271D4×C61—41no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61C23×C411yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61H(5,𝔽2)11yescharacteristic
287C2×C4×C61H(5,𝔽2)11yescharacteristic
288C2×C4×C61H(5,𝔽2)11yescharacteristic
289C2×C4×C61H(5,𝔽2)11yescharacteristic
290C22⋊D61—48no—
291C22⋊D61—48no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—48no—
302C2×Dic61—41no—
303C2×Dic61—41no—
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×Dic61—84no—
313C2×Dic61C4×D412yes—
314C2×Dic61AGL(1,ℤ/8)12yes—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—22no—
319C4×D61—44no—
320C4×D61—44no—
321Dic122—22no—
322Dic122—22no—
323Dic122—41no—
324Dic122—41no—
325C8×C61—22no—
326C8×C61—41no—
327#92418—22no—
328#92418—41no—
329#22051—611nomaximal, Sylow
330C22×C61—42no—
331C22×C61—42no—
332C22×C61—42no—
333C22×C61—42no—
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61—81no—
340C22×C61—81no—
341C22×C61—81no—
342C22×C61—81no—
343C22×C61—81no—
344C22×C61C2×C4×D411yescharacteristic
345C22×C61#53411yescharacteristic
346C22×C61#53511yescharacteristic
347C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
348C22×C61#57511yescharacteristic
349C22×C61#57511yescharacteristic
350C22×C61#57511yescharacteristic
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—22no—
354C2×D61—41no—
355C2×D61—41no—
356C2×D61—41no—
357C2×D61—41no—
358C4×C61—41no—
359C4×C61—41no—
360C4×C61—81no—
361C4×C61—81no—
362C4×C61#51811yescharacteristic
363C4×C61#51811yescharacteristic
364C4×C61#53811yescharacteristic
365C4×C61#53811yescharacteristic
366Dic61—22no—
367Dic61—22no—
368Dic61—42no—
369Dic61—41no—
370Dic61—42no—
371Dic61—81no—
372Dic61—81no—
373C2×#449—611no—
374C4×#121—611no—
375#2297—611no—
376#1973—611no—
377#1972D6111yescharacteristic, complemented
378#1936—611no—
379#1935—611no—
380#1927—611no—
381#1925—611no—
382#1879—611no—
383#1877—611no—
384#1875—611no—
385#1854—611no—
386#1788—611no—
387#1749—611no—
388C2×C61—82no—
389C2×C61—82no—
390C2×C61#232111yescharacteristic
391C2×C61#294311yescharacteristic
392C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
393C2×C61#319411yescharacteristic
394C2×C61#319711yescharacteristic
395C2×C61#321411yescharacteristic
396C2×C61#321911yescharacteristic
397D61—42no—
398C22×#41—611no—
399C22×SD16—611no—
400C22×D8C2×D6111yescharacteristic
401C2×#121—611no—
402C2×C4×D4—611no—
403C2×C4×D4—1221no—
404C2×#117—611no—
405C22×C42—611no—
406#449—618no—
407C2×#107—611no—
408C2×#106C2×D6111yescharacteristic
409C2×#103—611no—
410C2×#103—611no—
411C2×#103—611no—
412C2×#102—611no—
413C2×#102—611no—
414C2×#102—611no—
415C2×#102C2×D6111yescharacteristic
416C2×#102C2×D6111yescharacteristic
417C2×C22⋊C8—611no—
418C2×C22⋊C8—611no—
419C2×#97—611no—
420C2×#97C2×D6111yescharacteristic
421#391—611no—
422#391—611no—
423#390—611no—
424#390C2×D6111yescharacteristic
425#390C2×D6111yescharacteristic
426#389—611no—
427#388—1221no—
428#386—1221no—
429#386—1221no—
430#386—1221no—
431#380—611no—
432C4×C4⋊C4—611no—
433C4×C22⋊C4—1221no—
434C4×C22⋊C4—1221no—
435C4×C22⋊C4—1221no—
436#340—611no—
437#340—611no—
438#340—611no—
439#340—611no—
440#336—611no—
441#336—611no—
442C61#2205111yescharacteristic, complemented, Sylow
443C2×#41—614no—
444C2×#41—1222no—
445C2×#41—2441no—
446C2×#41—2441no—
447C2×#41—2441no—
448C2×#41—2441no—
449C22×Q8—611no—
450C22×D4—1221no—
451C22×D4—1221no—
452C22×D4C22×D6111yescharacteristic
453C22×D4C22×D6111yescharacteristic
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—1221no—
458C23×C4—1221no—
459C2×SD16—614no—
460C2×SD16—2441no—
461C2×SD16—2441no—
462C2×D8—41no—
463C2×D8—41no—
464C2×D8C4×D6114yescomplemented
465C22×C8—611no—
466C22×C8—611no—
467C22×C8C22×D6111yescharacteristic
468C22×C8C22×D6111yescharacteristic
469#121—614no—
470#121—1222no—
471C4×D4—2441no—
472C4×D4—2441no—
473C4×D4—2444no—
474#117—2441no—
475#117—2441no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4C22×D6111yescharacteristic
481C2×C4⋊C4C22×D6111yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C42—611no—
493C2×C42—611no—
494C2×C42—611no—
495C2×C42—1221no—
496C2×C42—1221no—
497C2×C42—2441no—
498C2×C42—2441no—
499C2×C42C22×D6111yescharacteristic
500#107—2441no—
501#106—41no—
502#103—614no—
503#103—2441no—
504#103—2441no—
505#102—41no—
506#102—41no—
507#102—614no—
508#102—2441no—
509#102—2441no—
510C22⋊C8—614no—
511C22⋊C8—1222no—
512#97—41no—
513#97—2441no—
514#95—1221no—
515#95—1221no—
516#95—1221no—
517#95—1221no—
518#95—1221no—
519#95—1221no—
520#95—1221no—
521C24—21no—
522C24—21no—
523C24—611no—
524#41—2444no—
525#41—2444no—
526#41—2444no—
527#41—2444no—
528C2×Q8—612no—
529C2×Q8—1221no—
530C2×Q8—1221no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—1224no—
545C2×D4—1224no—
546C2×D4—2442no—
547C2×D4—2442no—
548C2×D4—2442no—
549C2×D4—2442no—
550C2×D4C2×C4×D6112yes—
551C2×D4C2×C4×D6112yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—611no—
559C22×C4—1222no—
560C22×C4—1224no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—2441no—
570C22×C4—2441no—
571C22×C4—2441no—
572C22×C4—2441no—
573C22×C4—2441no—
574C22×C4—2442no—
575C22×C4—2442no—
576C22×C4—2442no—
577C22×C4—2442no—
578C22×C4—2442no—
579C22×C4D4×D6111yescharacteristic
580C22×C4D4×D6111yescharacteristic
581C22×C4C23×D6111yescharacteristic
582SD16—2444no—
583D8—44no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—612no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8C2×C4×D6112yes—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—612no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—2442no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—1224no—
612C22⋊C4—2442no—
613C22⋊C4—2442no—
614C22⋊C4—2442no—
615C22⋊C4—2442no—
616C22⋊C4—2442no—
617C42—21no—
618C42—21no—
619C42—1221no—
620C42—1221no—
621C42—2441no—
622C42—2441no—
623C42—2442no—
624C42—2442no—
625C23—22no—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—612no—
640C23—1221no—
641C23—1221no—
642C23—1221no—
643C23—1221no—
644C23—1221no—
645C23—1221no—
646C23C2×D4×D6111yescharacteristic
647Q8—1222no—
648Q8—1222no—
649Q8—2441no—
650Q8—2441no—
651D4—22no—
652D4—22no—
653D4—22no—
654D4—22no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—2448no—
660D4—2448no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—612no—
674C2×C4—612no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—4884no—
689C2×C4—2444no—
690C2×C4—2444no—
691C2×C4—2448no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4C22×C4×D6111yescharacteristic
703C2×C4#41×D6111yescharacteristic
704C2×C4#1451982211yescharacteristic
705C2×C4#1451982211yescharacteristic
706C2×C4#1451982211yescharacteristic
707C2×C4#1451982311yescharacteristic
708C8—22no—
709C8—41no—
710C8—1222no—
711C8—2441no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—1222no—
727C22—1222no—
728C22—1222no—
729C22—2441no—
730C22—2441no—
731C22—2441no—
732C22—2441no—
733C22C4×D4×D6111yescharacteristic
734C22#1684032011yescharacteristic
735C22#1684032511yescharacteristic
736C22AGL(1,ℤ/8)×D6111yescharacteristic
737C22#1684055811yescharacteristic
738C22#1684055811yescharacteristic
739C22#1684055811yescharacteristic
740C4—41no—
741C4—41no—
742C4—81no—
743C4—81no—
744C4—1222no—
745C4—1222no—
746C4—4881no—
747C4—4881no—
748C4—2441no—
749C4—2442no—
750C4—2442no—
751C4#1684023411yescharacteristic
752C4#1684023511yescharacteristic
753C4#1684034411yescharacteristic
754C4#1684034611yescharacteristic
755C2—82no—
756C2—82no—
757C2—2442no—
758C2#2144847811yescharacteristic
759C2#2145461611yescharacteristic
760C2#2145463011yescharacteristic
761C2#2145662811yescharacteristic
762C2#2145665511yescharacteristic
763C2#2145680911yescharacteristic
764C2#2145685111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1972C2
socleC23×C61C22×D4
prime radicalC2×#16839904C2
cosocleC22×C4×C61C24
hypercenter#1972D61
hypocenterC61#22051
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1972

Complements

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

NH ≅ G/Ntype
2. #21448335C2semidirect
3. #21448306C2semidirect
4. #21446699C2semidirect
5. #21446519C2semidirect
6. #21446509C2semidirect
7. #21446452C2semidirect
8. #21446442C2semidirect
9. #21446169C2semidirect
10. #21446151C2semidirect
11. #21446138C2semidirect
12. #21446017C2semidirect
13. #21445756C2semidirect
14. #21445582C2semidirect
15. C61×#1972C2semidirect
23. #16839904C4semidirect
65. C2×#11758224C2×C4semidirect
76. C2×#11758200C2×C4semidirect
105. #14519702C2×C4semidirect
109. #14519698C2×C4semidirect
111. #14519689C2×C4semidirect
124. C2×D8×C61C2×C4semidirect
377. #1972D61semidirect
442. C61#22051semidirect
464. C2×D8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399042
#214483352
#214483062
#214466992
#214465192
#214465092
#214464522
#214464422
#214461692
#214461512
#214461382
#214460172
#214457562
#214455822
C61×#19722
#2205161