Finite Group Databasebeta

← #29723927

Subgroups — #29723927

Order 15616.

1148 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×#16839911C211yesmaximal, characteristic
2#21449316C211yesmaximal, characteristic, complemented
3D4×#11758198C211yesmaximal, characteristic
4#21447341C211yesmaximal, characteristic, complemented
5#21447253C211yesmaximal, characteristic, complemented
6#21447133C211yesmaximal, characteristic, complemented
7#21447020C211yesmaximal, characteristic, complemented
8#21446502C211yesmaximal, characteristic, complemented
9#21446425C211yesmaximal, characteristic, complemented
10#21446174C211yesmaximal, characteristic, complemented
11#21446155C211yesmaximal, characteristic, complemented
12#21446066C211yesmaximal, characteristic, complemented
13#21445827C211yesmaximal, characteristic, complemented
14#21445748C211yesmaximal, characteristic
15C2×C4×SD16×C61C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C2×#14519753C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20C22×#11758198—21no—
21#16839911—24no—
22C2×#14519710C2211yescharacteristic, complemented
23C2×#14519706C2211yescharacteristic, complemented
24C2×#14519701C2211yescharacteristic, complemented
25C2×#14519699C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32#16839700—21no—
33#16839688—21no—
34#16839669C2211yescharacteristic, complemented
35#16839664C2211yescharacteristic
36#16839663C2211yescharacteristic
37#16839660C2211yescharacteristic, complemented
38#16839653—21no—
39#16839646—21no—
40#16839641—21no—
41#16839639—21no—
42#16839627C2211yescharacteristic, complemented
43#16839619C2211yescharacteristic
44#16839619C2211yescharacteristic
45#16839617—21no—
46C4×#11758198C2211yescharacteristic
47#16839525C2211yescharacteristic, complemented
48#16839525C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53C22×SD16×C61C2211yescharacteristic
54C2×C4×Q8×C61C2211yescharacteristic, complemented
55C2×C4×D4×C61C2211yescharacteristic
56C4×SD16×C61—24no—
57C2×#106×C61C2211yescharacteristic, complemented
58C2×#103×C61C2211yescharacteristic, complemented
59C2×#102×C61C2211yescharacteristic
60C2×C4×C8×C61C2211yescharacteristic, complemented
61C24×D61—21no—
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C2×D4×D61—22no—
65C2×D4×D61—22no—
66C2×D4×D61—22no—
67C2×D4×D61—22no—
68C2×D4×D61—41no—
69C2×D4×D61—41no—
70C23×Dic61—21no—
71C22×C4×D61C2311yescharacteristic
72C2×#11758201—22no—
73C2×#11758201—22no—
74C2×#11758201—41no—
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77#14519753—22no—
78#14519753—41no—
79D4×Dic61—22no—
80D4×Dic61—41no—
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×C22⋊Dic61—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—44no—
95C2×#11758198D411yescharacteristic
96C2×#11758198D411yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98#14519710—41no—
99#14519706—41no—
100#14519701—41no—
101#14519699—22no—
102#14519699—22no—
103#14519698—22no—
104#14519698—22no—
105#14519697—41no—
106#14519689—22no—
107#14519689—41no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684D411yescharacteristic
116#14519684D411yescharacteristic
117C22×Q8×C61C2311yescharacteristic
118C22×D4×C61C2311yescharacteristic
119C23×C4×C61—21no—
120C2×SD16×C61—22no—
121C2×SD16×C61—22no—
122C2×SD16×C61D414yes—
123C22×C8×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125C4×Q8×C61—22no—
126C4×Q8×C61—41no—
127C4×D4×C61—22no—
128C4×D4×C61—41no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C22⋊C4×C61—21no—
133C2×C42×C61—21no—
134C2×C42×C61C2311yescharacteristic
135#106×C61—22no—
136#103×C61—22no—
137#102×C61—22no—
138C4×C8×C61—22no—
139C24×C61—21no—
140C23×D61—21no—
141C23×D61—24no—
142C23×D61—42no—
143C23×D61—42no—
144C23×D61—42no—
145C23×D61—42no—
146C23×D61—81no—
147C23×D61—81no—
148C23×D61C2×D411yescharacteristic
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61C2×D412yes—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61C2×D412yes—
159C2×D4×C61#4112yes—
160C2×D4×C61#4112yes—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—42no—
165C22×C4×C61—42no—
166C22×C4×C61—81no—
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2411yescharacteristic
170C2×C22⋊D61—24no—
171C2×C22⋊D61—42no—
172C2×C22⋊D61—42no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—42no—
177C22×Dic61—42no—
178C22×Dic61—81no—
179C22×Dic61C2×D411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181C22×Dic61C2×D411yescharacteristic
182D4×D61—44no—
183D4×D61—44no—
184D4×D61—44no—
185D4×D61—44no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244#4112yes—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198SD16×C61—28no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61C2×D412yes—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—42no—
210C22⋊C4×C61—42no—
211C42×C61—21no—
212C42×C61—21no—
213C42×C61—42no—
214C22⋊Dic61—42no—
215#11758201—44no—
216#11758198—22no—
217#11758198—22no—
218#11758198—42no—
219#11758198—42no—
220#11758198—42no—
221#11758198—42no—
222#11758198—42no—
223#11758198—81no—
224#11758198—81no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231#11758196—42no—
232#11758196—42no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C23×C61—22no—
242C23×C61—22no—
243C23×C61—22no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61C22×D411yescharacteristic
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—22no—
256C22×D61—48no—
257C22×D61—48no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—84no—
265C22×D61—84no—
266C22×D61—84no—
267C22×D61—84no—
268C22×D61—84no—
269C22×D61#13512yes—
270Q8×C61—22no—
271Q8×C61—22no—
272Q8×C61—41no—
273Q8×C61—41no—
274D4×C61—22no—
275D4×C61—22no—
276D4×C61—22no—
277D4×C61#12314yes—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—22no—
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×C61—84no—
293C2×C4×C61AGL(1,ℤ/8)12yes—
294C2×C4×C61C22×D411yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C2×C4×C61H(5,𝔽2)11yescharacteristic
299C2×C4×C61H(5,𝔽2)11yescharacteristic
300C22⋊D61—48no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—84no—
320D244—22no—
321D244—22no—
322D244—41no—
323D244—41no—
324C4×D61—41no—
325C4×D61—41no—
326C4×D61—41no—
327C4×D61—41no—
328C8×C61—22no—
329C8×C61—41no—
330#92418—41no—
331#92418—41no—
332#24905—611nomaximal, Sylow
333C22×C61—24no—
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—42no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61#52511yescharacteristic
341C22×C61D4211yescharacteristic
342C22×C61#54611yescharacteristic
343C22×C61C2×#13511yescharacteristic
344C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
345C22×C61#57711yescharacteristic
346C22×C61#57711yescharacteristic
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—41no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—816no—
358C2×D61—81no—
359C2×D61—81no—
360C2×D61—81no—
361C2×D61—81no—
362C4×C61—22no—
363C4×C61—42no—
364C4×C61—41no—
365C4×C61—81no—
366C4×C61—81no—
367C4×C61C2×#12311yescharacteristic
368C4×C61#53811yescharacteristic
369C4×C61#54611yescharacteristic
370C4×C61#55111yescharacteristic
371Dic61—41no—
372Dic61—41no—
373Dic61—41no—
374Dic61—81no—
375Dic61—81no—
376Dic61—81no—
377C2×#450—611no—
378C2×C4×SD16D6111yescharacteristic, complemented
379#2421—611no—
380D4×C22⋊C4—611no—
381#2092—611no—
382#2077—611no—
383#2055—611no—
384#2036—611no—
385#1934—611no—
386#1923—611no—
387#1880—611no—
388#1877—611no—
389#1862—611no—
390#1804—611no—
391#1786—611no—
392C2×C61—44no—
393C2×C61#241811yescharacteristic
394C2×C61#310511yescharacteristic
395C2×C61#312311yescharacteristic
396C2×C61#326511yescharacteristic
397C2×C61#328211yescharacteristic
398C2×C61#329611yescharacteristic
399C2×C61#332411yescharacteristic
400D61—42no—
401D61—82no—
402C23×D4—611no—
403C22×SD16—611no—
404C22×SD16C2×D6111yescharacteristic
405C2×C22⋊Q8—611no—
406C2×C4×Q8C2×D6111yescharacteristic, complemented
407C2×C4×D4—611no—
408C2×C4×D4C2×D6111yescharacteristic
409C22×C22⋊C4—1221no—
410#450—1224no—
411C4×SD16—24no—
412C2×#107—611no—
413C2×#106C2×D6111yescharacteristic, complemented
414C2×C4⋊C8—611no—
415C2×#103—611no—
416C2×#103C2×D6111yescharacteristic, complemented
417C2×#102—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102C2×D6111yescharacteristic
423C2×C22⋊C8—611no—
424C2×C22⋊C8—611no—
425C2×C4×C8C2×D6111yescharacteristic, complemented
426#400—1221no—
427#397—1221no—
428#391—611no—
429#390—611no—
430#390—611no—
431#389—611no—
432#388—1221no—
433#387—1221no—
434#386—1221no—
435#386—1221no—
436#382—611no—
437#380—611no—
438#380—611no—
439#379—1221no—
440C4×C22⋊C4—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#340—611no—
445#336—611no—
446#336—611no—
447C61#2490511yescharacteristic, complemented, Sylow
448C25—1221no—
449C22×Q8C22×D6111yescharacteristic
450C22×D4—611no—
451C22×D4—1221no—
452C22×D4—1222no—
453C22×D4—1222no—
454C22×D4—1222no—
455C22×D4—1222no—
456C22×D4—2441no—
457C22×D4—2441no—
458C22×D4C22×D6111yescharacteristic
459C23×C4—21no—
460C23×C4—611no—
461C23×C4—1221no—
462C2×SD16—22no—
463C2×SD16—22no—
464C2×SD16—1222no—
465C2×SD16—1222no—
466C2×SD16—2441no—
467C2×SD16C22⋊D6114yes—
468C22×C8—611no—
469C22×C8—611no—
470C22×C8C22×D6111yescharacteristic
471C22×C8C22×D6111yescharacteristic
472C22⋊Q8—1222no—
473C22⋊Q8—2441no—
474C4×Q8—22no—
475C4×Q8—41no—
476C4×D4—22no—
477C4×D4—41no—
478C4×D4—1222no—
479C4×D4—2441no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4C22×D6111yescharacteristic
487C2×C4⋊C4C22×D6111yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—611no—
490C2×C22⋊C4—611no—
491C2×C22⋊C4—1221no—
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—2444no—
500C2×C42—21no—
501C2×C42—611no—
502C2×C42C22×D6111yescharacteristic
503#107—2441no—
504#106—22no—
505C4⋊C8—2441no—
506#103—22no—
507#103—2441no—
508#102—22no—
509#102—1222no—
510#102—1222no—
511#102—1222no—
512#102—1222no—
513#102—2441no—
514C22⋊C8—1222no—
515C22⋊C8—2441no—
516C4×C8—22no—
517#95—611no—
518#95—611no—
519#95—1221no—
520#95—1221no—
521#95—1221no—
522#95—1221no—
523#95—1221no—
524#95—1221no—
525#95—1221no—
526C24—21no—
527C24—611no—
528C24—1224no—
529C24—1221no—
530C24—4881no—
531C24—4881no—
532C24—2442no—
533C24—2442no—
534C24—2442no—
535C24—2442no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8C2×C22⋊D6112yes—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—612no—
546C2×D4—1224no—
547C2×D4—1221no—
548C2×D4—1221no—
549C2×D4—1221no—
550C2×D4—1221no—
551C2×D4—1221no—
552C2×D4—2442no—
553C2×D4—2442no—
554C2×D4—2444no—
555C2×D4—2444no—
556C2×D4—2444no—
557C2×D4—2444no—
558C2×D4#1175822212yes—
559C2×D4#1175822212yes—
560C2×D4C2×C22⋊D6112yes—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—4881no—
580C22×C4—2442no—
581C22×C4—2442no—
582C22×C4D4×D6111yescharacteristic
583C22×C4D4×D6111yescharacteristic
584C22×C4C23×D6111yescharacteristic
585SD16—28no—
586SD16—2444no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8C2×C22⋊D6112yes—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—42no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—2442no—
611C4⋊C4—2442no—
612C22⋊C4—42no—
613C22⋊C4—1222no—
614C22⋊C4—1222no—
615C22⋊C4—4881no—
616C22⋊C4—4881no—
617C22⋊C4—2442no—
618C22⋊C4—2442no—
619C22⋊C4—2442no—
620C22⋊C4—2442no—
621C22⋊C4—2442no—
622C22⋊C4—2442no—
623C42—21no—
624C42—21no—
625C42—42no—
626C42—1221no—
627C42—1221no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—612no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23—1221no—
641C23—1221no—
642C23—1222no—
643C23—4884no—
644C23—4884no—
645C23—4884no—
646C23—4884no—
647C23—4884no—
648C23—2448no—
649C23—2448no—
650C23—2441no—
651C23—2441no—
652C23—2441no—
653C23—2441no—
654C23—2441no—
655C23—2441no—
656C23C2×D4×D6111yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661D4—22no—
662D4—22no—
663D4—22no—
664D4—1222no—
665D4—1222no—
666D4—2448no—
667D4—2441no—
668D4—2441no—
669D4#1451976014yes—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—22no—
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—84no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—4884no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4#1451980412yes—
709C2×C4C22×C22⋊D6111yescharacteristic
710C2×C4#41×D6111yescharacteristic
711C2×C4C2×#1175822211yescharacteristic
712C2×C4C2×#1175822211yescharacteristic
713C2×C4#1451982211yescharacteristic
714C2×C4#1451982311yescharacteristic
715C8—22no—
716C8—41no—
717C8—2441no—
718C8—2441no—
719C22—24no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—1222no—
727C22—1222no—
728C22—1222no—
729C22—48816no—
730C22—4881no—
731C22—4881no—
732C22—4881no—
733C22—4881no—
734C22—2442no—
735C22—2442no—
736C22—2442no—
737C22—2441no—
738C22—2441no—
739C22—2441no—
740C22—2441no—
741C22#1684027111yescharacteristic
742C22D4×C22⋊D6111yescharacteristic
743C22#1684040811yescharacteristic
744C22#135×D6111yescharacteristic
745C22C2×#1451980411yescharacteristic
746C22#1684056811yescharacteristic
747C22#1684056911yescharacteristic
748C4—22no—
749C4—42no—
750C4—41no—
751C4—81no—
752C4—81no—
753C4—4881no—
754C4—4881no—
755C4—4881no—
756C4—2441no—
757C4—2441no—
758C4—2441no—
759C4C2×#1451976011yescharacteristic
760C4#1684034511yescharacteristic
761C4#1684040011yescharacteristic
762C4#1684044111yescharacteristic
763C2—44no—
764C2—4882no—
765C2—2442no—
766C2#2144927511yescharacteristic
767C2#2145587011yescharacteristic
768C2#2145606811yescharacteristic
769C2#2145731411yescharacteristic
770C2#2145752011yescharacteristic
771C2#2145765911yescharacteristic
772C2#2145805211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C4×SD16×C61C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
hypercenterC2×C4×SD16D61
hypocenterC61#24905
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. #21449316C2semidirect
4. #21447341C2semidirect
5. #21447253C2semidirect
6. #21447133C2semidirect
7. #21447020C2semidirect
8. #21446502C2semidirect
9. #21446425C2semidirect
10. #21446174C2semidirect
11. #21446155C2semidirect
12. #21446066C2semidirect
13. #21445827C2semidirect
15. C2×C4×SD16×C61C2semidirect
22. C2×#14519710C22semidirect
23. C2×#14519706C22semidirect
24. C2×#14519701C22semidirect
34. #16839669C22semidirect
37. #16839660C22semidirect
42. #16839627C22semidirect
47. #16839525C22semidirect
48. #16839525C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839517C22semidirect
52. #16839516C22semidirect
54. C2×C4×Q8×C61C22semidirect
57. C2×#106×C61C22semidirect
58. C2×#103×C61C22semidirect
60. C2×C4×C8×C61C22semidirect
378. C2×C4×SD16D61semidirect
406. C2×C4×Q8C2×D61semidirect
413. C2×#106C2×D61semidirect
416. C2×#103C2×D61semidirect
425. C2×C4×C8C2×D61semidirect
447. C61#24905semidirect

Maximal subgroups

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

subgroupindex
C2×#168399112
#214493162
D4×#117581982
#214473412
#214472532
#214471332
#214470202
#214465022
#214464252
#214461742
#214461552
#214460662
#214458272
#214457482
C2×C4×SD16×C612
#2490561