Finite Group Databasebeta

← #29723867

Subgroups — #29723867

Order 15616.

1156 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839911C211yesmaximal, characteristic
2#21449338C211yesmaximal, characteristic, complemented
3D4×#11758198C211yesmaximal, characteristic
4#21447349C211yesmaximal, characteristic, complemented
5#21447253C211yesmaximal, characteristic, complemented
6#21447133C211yesmaximal, characteristic, complemented
7#21447013C211yesmaximal, characteristic, complemented
8#21446502C211yesmaximal, characteristic, complemented
9#21446425C211yesmaximal, characteristic, complemented
10#21446174C211yesmaximal, characteristic, complemented
11#21446155C211yesmaximal, characteristic, complemented
12#21446080C211yesmaximal, characteristic, complemented
13#21445817C211yesmaximal, 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×#14519708C2211yescharacteristic, complemented
23C2×#14519706C2211yescharacteristic, complemented
24C2×#14519701C2211yescharacteristic, complemented
25C2×#14519699C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32#16839697—21no—
33#16839693—21no—
34#16839669C2211yescharacteristic, complemented
35#16839664C2211yescharacteristic
36#16839663C2211yescharacteristic
37#16839660C2211yescharacteristic, complemented
38#16839653—21no—
39#16839646—21no—
40#16839641—21no—
41#16839639—21no—
42#16839631C2211yescharacteristic, 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×#11758196—21no—
87C2×#11758196—21no—
88C2×C22⋊Dic61—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—44no—
97C2×#11758198D411yescharacteristic
98C2×#11758198D411yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100#14519708—41no—
101#14519706—41no—
102#14519701—41no—
103#14519699—22no—
104#14519699—22no—
105#14519698—22no—
106#14519698—22no—
107#14519697—41no—
108#14519689—22no—
109#14519689—41no—
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—41no—
217#11758198—42no—
218#11758198—42no—
219#11758198—42no—
220#11758198—42no—
221#11758198—81no—
222#11758198—81no—
223#11758198—81no—
224#11758198SD1614yescomplemented
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231#11758196—42no—
232#11758196—42no—
233#11758196—81no—
234#11758196—81no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C23×C61—22no—
244C23×C61—22no—
245C23×C61—22no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61C22×D411yescharacteristic
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—22no—
258C22×D61—48no—
259C22×D61—48no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—84no—
267C22×D61—84no—
268C22×D61—84no—
269C22×D61—84no—
270C22×D61—84no—
271C22×D61C2×SD1612yes—
272Q8×C61—22no—
273Q8×C61—22no—
274Q8×C61—41no—
275Q8×C61—41no—
276D4×C61—22no—
277D4×C61—22no—
278D4×C61—22no—
279D4×C61#12314yes—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—22no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
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—41no—
293C2×C4×C61—41no—
294C2×C4×C61—84no—
295C2×C4×C61C2×SD1612yes—
296C2×C4×C61C22×D411yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C2×C4×C61C2×#4111yescharacteristic
299C2×C4×C61C2×#4111yescharacteristic
300C2×C4×C61H(5,𝔽2)11yescharacteristic
301C2×C4×C61H(5,𝔽2)11yescharacteristic
302C22⋊D61—48no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
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—41no—
320C2×Dic61—84no—
321C2×Dic61C2×SD1612yes—
322D244—22no—
323D244—22no—
324D244—41no—
325D244—41no—
326C4×D61—41no—
327C4×D61—41no—
328C4×D61—41no—
329C4×D61—41no—
330C8×C61—22no—
331C8×C61—41no—
332#92418—41no—
333#92418—41no—
334#24901—611nomaximal, Sylow
335C22×C61—24no—
336C22×C61—42no—
337C22×C61—42no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61#52511yescharacteristic
343C22×C61D4211yescharacteristic
344C22×C61#54611yescharacteristic
345C22×C61C22×SD1611yescharacteristic
346C22×C61#57511yescharacteristic
347C22×C61#57611yescharacteristic
348C22×C61#57711yescharacteristic
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—41no—
353C2×D61—41no—
354C2×D61—41no—
355C2×D61—41no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—816no—
360C2×D61—81no—
361C2×D61—81no—
362C2×D61—81no—
363C2×D61—81no—
364C4×C61—22no—
365C4×C61—42no—
366C4×C61—41no—
367C4×C61—81no—
368C4×C61—81no—
369C4×C61C2×#12311yescharacteristic
370C4×C61#53811yescharacteristic
371C4×C61#54611yescharacteristic
372C4×C61#55111yescharacteristic
373Dic61—22no—
374Dic61—41no—
375Dic61—41no—
376Dic61—81no—
377Dic61—81no—
378Dic61—81no—
379C2×#450—611no—
380C2×C4×SD16D6111yescharacteristic, complemented
381#2423—611no—
382D4×C22⋊C4—611no—
383#2094—611no—
384#2077—611no—
385#2055—611no—
386#2035—611no—
387#1934—611no—
388#1923—611no—
389#1880—611no—
390#1877—611no—
391#1864—611no—
392#1802—611no—
393#1786—611no—
394C2×C61—44no—
395C2×C61#241811yescharacteristic
396C2×C61#310111yescharacteristic
397C2×C61#311811yescharacteristic
398C2×C61#326811yescharacteristic
399C2×C61D4×SD1611yescharacteristic
400C2×C61#329511yescharacteristic
401C2×C61#332311yescharacteristic
402D61—42no—
403D61—82no—
404C23×D4—611no—
405C22×SD16—611no—
406C22×SD16C2×D6111yescharacteristic
407C2×C22⋊Q8—611no—
408C2×C4×Q8C2×D6111yescharacteristic, complemented
409C2×C4×D4—611no—
410C2×C4×D4C2×D6111yescharacteristic
411C22×C22⋊C4—1221no—
412#450—1224no—
413C4×SD16—24no—
414C2×#106—611no—
415C2×#106C2×D6111yescharacteristic, complemented
416C2×C4⋊C8—611no—
417C2×#103—611no—
418C2×#103C2×D6111yescharacteristic, complemented
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×#102C2×D6111yescharacteristic
425C2×C22⋊C8—611no—
426C2×C22⋊C8—611no—
427C2×C4×C8C2×D6111yescharacteristic, complemented
428#399—1221no—
429#398—1221no—
430#391—611no—
431#390—611no—
432#390—611no—
433#389—611no—
434#388—1221no—
435#387—1221no—
436#386—1221no—
437#386—1221no—
438#384—611no—
439#380—611no—
440#380—611no—
441#379—1221no—
442C4×C22⋊C4—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446#340—611no—
447#336—611no—
448#336—611no—
449C61#2490111yescharacteristic, complemented, Sylow
450C25—1221no—
451C22×Q8C22×D6111yescharacteristic
452C22×D4—611no—
453C22×D4—1221no—
454C22×D4—1222no—
455C22×D4—1222no—
456C22×D4—1222no—
457C22×D4—1222no—
458C22×D4—2441no—
459C22×D4—2441no—
460C22×D4C22×D6111yescharacteristic
461C23×C4—21no—
462C23×C4—611no—
463C23×C4—1221no—
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—1222no—
467C2×SD16—1222no—
468C2×SD16—2441no—
469C2×SD16C22⋊D6114yes—
470C22×C8—611no—
471C22×C8—611no—
472C22×C8C22×D6111yescharacteristic
473C22×C8C22×D6111yescharacteristic
474C22⋊Q8—1222no—
475C22⋊Q8—2441no—
476C4×Q8—22no—
477C4×Q8—41no—
478C4×D4—22no—
479C4×D4—41no—
480C4×D4—1222no—
481C4×D4—2441no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4C22×D6111yescharacteristic
491C2×C4⋊C4C22×D6111yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—611no—
494C2×C22⋊C4—611no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—2444no—
504C2×C42—21no—
505C2×C42—611no—
506C2×C42C22×D6111yescharacteristic
507#106—22no—
508#106—2441no—
509C4⋊C8—2441no—
510#103—22no—
511#103—2441no—
512#102—22no—
513#102—1222no—
514#102—1222no—
515#102—1222no—
516#102—1222no—
517#102—2441no—
518C22⋊C8—1222no—
519C22⋊C8—2441no—
520C4×C8—22no—
521#95—611no—
522#95—611no—
523#95—1221no—
524#95—1221no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528C24—21no—
529C24—611no—
530C24—1224no—
531C24—1221no—
532C24—4881no—
533C24—4881no—
534C24—2442no—
535C24—2442no—
536C24—2442no—
537C24—2442no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C2×C22⋊D6112yes—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—612no—
548C2×D4—1224no—
549C2×D4—1221no—
550C2×D4—1221no—
551C2×D4—1221no—
552C2×D4—1221no—
553C2×D4—1221no—
554C2×D4—2442no—
555C2×D4—2442no—
556C2×D4—2444no—
557C2×D4—2444no—
558C2×D4—2444no—
559C2×D4—2444no—
560C2×D4#1175822212yes—
561C2×D4#1175822212yes—
562C2×D4C2×C22⋊D6112yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—81no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—611no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—4881no—
582C22×C4—2442no—
583C22×C4—2442no—
584C22×C4D4×D6111yescharacteristic
585C22×C4D4×D6111yescharacteristic
586C22×C4C23×D6111yescharacteristic
587SD16—28no—
588SD16—2444no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8C2×C22⋊D6112yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—42no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—4881no—
613C4⋊C4—4881no—
614C4⋊C4—2442no—
615C4⋊C4—2442no—
616C22⋊C4—42no—
617C22⋊C4—614no—
618C22⋊C4—4881no—
619C22⋊C4—4881no—
620C22⋊C4—4881no—
621C22⋊C4—2441no—
622C22⋊C4—2442no—
623C22⋊C4—2442no—
624C22⋊C4—2442no—
625C22⋊C4—2442no—
626C22⋊C4—2442no—
627C42—21no—
628C42—21no—
629C42—42no—
630C42—1221no—
631C42—1221no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—612no—
640C23—1221no—
641C23—1221no—
642C23—1221no—
643C23—1221no—
644C23—1221no—
645C23—1221no—
646C23—1222no—
647C23—4884no—
648C23—4884no—
649C23—4884no—
650C23—4884no—
651C23—4884no—
652C23—2448no—
653C23—2448no—
654C23—2441no—
655C23—2441no—
656C23—2441no—
657C23—2441no—
658C23—2441no—
659C23—2441no—
660C23C2×D4×D6111yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—1222no—
669D4—1222no—
670D4—2448no—
671D4—2441no—
672D4—2441no—
673D4#1451976014yes—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—84no—
689C2×C4—612no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—4884no—
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—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4SD16×D6112yes—
713C2×C4C22×C22⋊D6111yescharacteristic
714C2×C4#41×D6111yescharacteristic
715C2×C4C2×#1175822211yescharacteristic
716C2×C4C2×#1175822211yescharacteristic
717C2×C4#1451982211yescharacteristic
718C2×C4#1451982311yescharacteristic
719C8—22no—
720C8—41no—
721C8—2441no—
722C8—2441no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—1222no—
731C22—1222no—
732C22—1222no—
733C22—48816no—
734C22—4881no—
735C22—4881no—
736C22—4881no—
737C22—4881no—
738C22—2442no—
739C22—2442no—
740C22—2442no—
741C22—2441no—
742C22—2441no—
743C22—2441no—
744C22—2441no—
745C22#1684027111yescharacteristic
746C22D4×C22⋊D6111yescharacteristic
747C22#1684040811yescharacteristic
748C22C2×SD16×D6111yescharacteristic
749C22#1684055911yescharacteristic
750C22#1684056411yescharacteristic
751C22#1684056811yescharacteristic
752C4—22no—
753C4—42no—
754C4—41no—
755C4—81no—
756C4—81no—
757C4—1222no—
758C4—4881no—
759C4—4881no—
760C4—4881no—
761C4—2441no—
762C4—2441no—
763C4C2×#1451976011yescharacteristic
764C4#1684034511yescharacteristic
765C4#1684040011yescharacteristic
766C4#1684044111yescharacteristic
767C2—44no—
768C2—4882no—
769C2—2442no—
770C2#2144927511yescharacteristic
771C2#2145582511yescharacteristic
772C2#2145600911yescharacteristic
773C2#2145735911yescharacteristic
774C2SD16×C22⋊D6111yescharacteristic
775C2#2145764511yescharacteristic
776C2#2145804011yescharacteristic
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#24901
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. #21449338C2semidirect
4. #21447349C2semidirect
5. #21447253C2semidirect
6. #21447133C2semidirect
7. #21447013C2semidirect
8. #21446502C2semidirect
9. #21446425C2semidirect
10. #21446174C2semidirect
11. #21446155C2semidirect
12. #21446080C2semidirect
13. #21445817C2semidirect
15. C2×C4×SD16×C61C2semidirect
22. C2×#14519708C22semidirect
23. C2×#14519706C22semidirect
24. C2×#14519701C22semidirect
34. #16839669C22semidirect
37. #16839660C22semidirect
42. #16839631C22semidirect
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
224. #11758198SD16semidirect
380. C2×C4×SD16D61semidirect
408. C2×C4×Q8C2×D61semidirect
415. C2×#106C2×D61semidirect
418. C2×#103C2×D61semidirect
427. C2×C4×C8C2×D61semidirect
449. C61#24901semidirect

Maximal subgroups

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

subgroupindex
C2×#168399112
#214493382
D4×#117581982
#214473492
#214472532
#214471332
#214470132
#214465022
#214464252
#214461742
#214461552
#214460802
#214458172
#214457482
C2×C4×SD16×C612
#2490161