Finite Group Databasebeta

← #29723824

Subgroups — #29723824

Order 15616.

1016 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic61C211yesmaximal, characteristic, complemented
2#21449329C211yesmaximal, characteristic
3Q8×C22⋊Dic61C211yesmaximal, characteristic, complemented
4#21447360C211yesmaximal, characteristic, complemented
5#21447252C211yesmaximal, characteristic, complemented
6#21447132C211yesmaximal, characteristic, complemented
7#21447005C211yesmaximal, characteristic
8#21446492C211yesmaximal, characteristic, complemented
9#21446422C211yesmaximal, characteristic, complemented
10#21446176C211yesmaximal, characteristic, complemented
11#21446155C211yesmaximal, characteristic, complemented
12#21446085C211yesmaximal, characteristic, complemented
13#21445822C211yesmaximal, characteristic, complemented
14#21445754C211yesmaximal, characteristic, complemented
15C2×C61×#448C211yesmaximal, characteristic
16C2×#14519758—21no—
17C2×Q8×Dic61C2211yescharacteristic
18C2×Q8×Dic61C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20SD16×Dic61—24no—
21C2×#14519709C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×#14519706C2211yescharacteristic
24C2×#14519701C2211yescharacteristic
25C2×#14519701C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×C8×Dic61C2211yescharacteristic
32#16839690—21no—
33#16839676—21no—
34#16839669—21no—
35#16839669—21no—
36#16839669C2211yescharacteristic
37#16839669C2211yescharacteristic
38#16839665C2211yescharacteristic
39#16839658C2211yescharacteristic
40#16839634—21no—
41#16839631C2211yescharacteristic
42#16839622—21no—
43#16839622C2211yescharacteristic
44#16839622C2211yescharacteristic
45C4×C22⋊Dic61—21no—
46C4×C22⋊Dic61C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53C23×Q8×C61C2211yescharacteristic
54C22×SD16×C61C2211yescharacteristic
55C22×SD16×C61C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C61×#448—24no—
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C23×Dic61—21no—
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64#14519758—44no—
65Q8×Dic61—22no—
66Q8×Dic61—22no—
67Q8×Dic61—41no—
68Q8×Dic61—41no—
69D4×Dic61—22no—
70D4×Dic61—41no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61D411yescharacteristic
86C2×C22⋊Dic61D411yescharacteristic
87C2×C4×Dic61—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61C2311yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91#14519709—22no—
92#14519708—41no—
93#14519706—41no—
94#14519701—22no—
95#14519701—22no—
96#14519701—22no—
97#14519701—41no—
98#14519698—22no—
99#14519698—41no—
100C22⋊#92418—41no—
101C8×Dic61—22no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684D411yescharacteristic
110#14519684D411yescharacteristic
111C22×Q8×C61—22no—
112C22×Q8×C61—22no—
113C22×Q8×C61—21no—
114C22×Q8×C61—22no—
115C22×Q8×C61—22no—
116C22×Q8×C61—41no—
117C22×Q8×C61—41no—
118C22×Q8×C61C2311yescharacteristic
119C22×Q8×C61C2311yescharacteristic
120C22×D4×C61—21no—
121C22×D4×C61C2311yescharacteristic
122C23×C4×C61—21no—
123C23×C4×C61C2311yescharacteristic
124C2×SD16×C61—22no—
125C2×SD16×C61—22no—
126C2×SD16×C61—22no—
127C2×SD16×C61—22no—
128C2×SD16×C61—41no—
129C2×SD16×C61D414yes—
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132#121×C61—22no—
133#121×C61—41no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C22⋊C4×C61—21no—
136#103×C61—22no—
137#103×C61—22no—
138C22⋊C8×C61—22no—
139C24×C61—21no—
140C24×C61C2×D411yescharacteristic
141C2×Q8×C61—24no—
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—42no—
151C2×Q8×C61—42no—
152C2×Q8×C61—44no—
153C2×Q8×C61—44no—
154C2×Q8×C61—44no—
155C2×Q8×C61—44no—
156C2×Q8×C61C2×D412yes—
157C2×Q8×C61#4112yes—
158C2×Q8×C61#4112yes—
159C2×Q8×C61#4112yes—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—42no—
166C2×D4×C61—42no—
167C2×D4×C61—81no—
168C2×D4×C61C2×D412yes—
169C22×C4×C61—21no—
170C22×C4×C61—24no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—42no—
180C22×C4×C61—42no—
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2411yescharacteristic
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—42no—
188C22×Dic61—42no—
189C22×Dic61—81no—
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192C22×Dic61C2×D411yescharacteristic
193C22×Dic61C2×D411yescharacteristic
194SD16×C61—28no—
195SD16×C61—44no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61C2×D412yes—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C22⋊C4×C61—42no—
205C22⋊Dic61—41no—
206C22⋊Dic61—42no—
207C22⋊Dic61—42no—
208C22⋊Dic61—42no—
209C22⋊Dic61—42no—
210C22⋊Dic61—42no—
211C22⋊Dic61SD1614yescomplemented
212C4⋊Dic61—21no—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—42no—
221C4⋊Dic61—42no—
222#11758196—42no—
223#11758196—42no—
224#11758196—81no—
225C4×Dic61—21no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C4×Dic61—42no—
230C4×Dic61—42no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—22no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61C2×SD1612yes—
251C23×C61C22×D411yescharacteristic
252Q8×C61—22no—
253Q8×C61—22no—
254Q8×C61—22no—
255Q8×C61—22no—
256Q8×C61—22no—
257Q8×C61—48no—
258Q8×C61—41no—
259Q8×C61—41no—
260Q8×C61#12314yescomplemented
261D4×C61—22no—
262D4×C61—22no—
263D4×C61—41no—
264D4×C61—41no—
265D4×C61—84no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—48no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61C22×D411yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61H(5,𝔽2)11yescharacteristic
288C2×C4×C61H(5,𝔽2)11yescharacteristic
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
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—84no—
312C2×Dic61C2×SD1612yes—
313C2×Dic61C2×SD1612yes—
314C8×C61—22no—
315C8×C61—41no—
316#92418—41no—
317#92418—41no—
318#24898—611nomaximal, Sylow
319C22×C61—22no—
320C22×C61—22no—
321C22×C61—22no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61—41no—
326C22×C61—42no—
327C22×C61—42no—
328C22×C61—42no—
329C22×C61—81no—
330C22×C61—81no—
331C22×C61—81no—
332C22×C61—81no—
333C22×C61#52511yescharacteristic
334C22×C61D4211yescharacteristic
335C22×C61#54611yescharacteristic
336C22×C61C22×SD1611yescharacteristic
337C22×C61#57511yescharacteristic
338C22×C61#57711yescharacteristic
339C22×C61#57811yescharacteristic
340C4×C61—24no—
341C4×C61—41no—
342C4×C61—42no—
343C4×C61—81no—
344C4×C61C2×#12311yescharacteristic
345C4×C61#53811yescharacteristic
346C4×C61#54611yescharacteristic
347C4×C61#55111yescharacteristic
348Dic61—22no—
349Dic61—22no—
350Dic61—41no—
351Dic61—41no—
352Dic61—81no—
353Dic61—81no—
354Dic61—81no—
355Dic61—81no—
356C2×#448D6111yescharacteristic
357C2×C4×SD16—611no—
358#2422—611no—
359Q8×C22⋊C4—611no—
360#2096—611no—
361#2077—611no—
362#2055—611no—
363#2034—611no—
364#1933—611no—
365#1923—611no—
366#1880—611no—
367#1877—611no—
368#1865—611no—
369#1803—611no—
370#1787—611no—
371C2×C61—42no—
372C2×C61—82no—
373C2×C61#241811yescharacteristic
374C2×C61#310311yescharacteristic
375C2×C61#312111yescharacteristic
376C2×C61#326911yescharacteristic
377C2×C61D4×SD1611yescharacteristic
378C2×C61#329811yescharacteristic
379C2×C61#332611yescharacteristic
380C23×Q8C2×D6111yescharacteristic
381C22×SD16C2×D6111yescharacteristic
382C22×SD16C2×D6111yescharacteristic
383C2×#123—1221no—
384C2×#121C2×D6111yescharacteristic
385C2×C4×Q8—611no—
386C2×C4×Q8—611no—
387C2×C4×D4—611no—
388#448—24no—
389C4×SD16—1224no—
390C2×#106—611no—
391C2×#106—611no—
392C2×C4⋊C8—611no—
393C2×#103—611no—
394C2×#103—611no—
395C2×#103—611no—
396C2×#103—611no—
397C2×#103C2×D6111yescharacteristic
398C2×#103C2×D6111yescharacteristic
399C2×#102—611no—
400C2×#102—611no—
401C2×C22⋊C8—611no—
402C2×C22⋊C8C2×D6111yescharacteristic
403C2×C4×C8—611no—
404#397—1221no—
405#394—1221no—
406#391—611no—
407#391—611no—
408#391—1221no—
409#391—1221no—
410#390—611no—
411#389—611no—
412#385—1221no—
413#384—611no—
414#380—611no—
415#380—611no—
416#380—1221no—
417C4×C22⋊C4—611no—
418C4×C22⋊C4—1221no—
419#340—611no—
420#340—611no—
421#340—611no—
422#340—611no—
423#336—611no—
424#336—611no—
425C61#2489811yescharacteristic, complemented, Sylow
426C22×Q8—22no—
427C22×Q8—22no—
428C22×Q8—21no—
429C22×Q8—22no—
430C22×Q8—22no—
431C22×Q8—41no—
432C22×Q8—41no—
433C22×Q8C22×D6111yescharacteristic
434C22×Q8C22×D6111yescharacteristic
435C22×D4—21no—
436C22×D4C22×D6111yescharacteristic
437C23×C4—21no—
438C23×C4—1221no—
439C23×C4C22×D6111yescharacteristic
440C2×SD16—22no—
441C2×SD16—22no—
442C2×SD16—22no—
443C2×SD16—22no—
444C2×SD16—41no—
445C2×SD16C22⋊D6114yes—
446C22×C8—611no—
447C22×C8—611no—
448C22×C8C22×D6111yescharacteristic
449C22×C8C22×D6111yescharacteristic
450#123—2444no—
451#121—22no—
452#121—41no—
453C4×Q8—1222no—
454C4×Q8—1222no—
455C4×Q8—2441no—
456C4×Q8—2441no—
457C4×D4—1222no—
458C4×D4—2441no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4—1221no—
464C2×C4⋊C4—1221no—
465C2×C4⋊C4—1221no—
466C2×C4⋊C4—1221no—
467C2×C4⋊C4—1221no—
468C2×C4⋊C4C22×D6111yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—611no—
471C2×C22⋊C4—611no—
472C2×C22⋊C4—1221no—
473C2×C22⋊C4—1221no—
474C2×C22⋊C4—1221no—
475C2×C22⋊C4—1221no—
476C2×C22⋊C4—1221no—
477C2×C42—611no—
478C2×C42—611no—
479C2×C42—1221no—
480C2×C42—1221no—
481#106—1222no—
482#106—2441no—
483C4⋊C8—2441no—
484#103—22no—
485#103—22no—
486#103—1222no—
487#103—1222no—
488#103—1222no—
489#103—2441no—
490#102—1222no—
491#102—2441no—
492C22⋊C8—22no—
493C22⋊C8—2441no—
494C4×C8—1222no—
495#95—611no—
496#95—611no—
497#95—1221no—
498#95—1221no—
499#95—1221no—
500#95—1221no—
501#95—1221no—
502#95—1221no—
503#95—1221no—
504C24—21no—
505C24D4×D6111yescharacteristic
506C2×Q8—24no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—44no—
520C2×Q8—44no—
521C2×Q8#1175822412yes—
522C2×Q8#1175822412yes—
523C2×Q8#1175822412yes—
524C2×Q8C2×C22⋊D6112yes—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—81no—
533C2×D4C2×C22⋊D6112yes—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—4881no—
555C22×C4—2442no—
556C22×C4—2442no—
557C22×C4D4×D6111yescharacteristic
558C22×C4C23×D6111yescharacteristic
559SD16—28no—
560SD16—44no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—1221no—
567C2×C8—1221no—
568C2×C8—1221no—
569C2×C8—1221no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8C2×C22⋊D6112yes—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—1221no—
576C4⋊C4—1221no—
577C4⋊C4—1221no—
578C4⋊C4—1221no—
579C4⋊C4—1221no—
580C4⋊C4—1221no—
581C4⋊C4—1221no—
582C4⋊C4—1221no—
583C4⋊C4—4881no—
584C4⋊C4—2442no—
585C4⋊C4—2442no—
586C4⋊C4—2442no—
587C4⋊C4—2442no—
588C22⋊C4—42no—
589C22⋊C4—614no—
590C22⋊C4—2442no—
591C22⋊C4—2441no—
592C22⋊C4—2442no—
593C22⋊C4—2442no—
594C22⋊C4—2442no—
595C22⋊C4—2442no—
596C42—1221no—
597C42—1221no—
598C42—1221no—
599C42—1221no—
600C42—2442no—
601C42—2442no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—22no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23SD16×D6112yes—
616C23C2×D4×D6111yescharacteristic
617Q8—22no—
618Q8—22no—
619Q8—22no—
620Q8—22no—
621Q8—22no—
622Q8—48no—
623Q8—41no—
624Q8—41no—
625Q8#1451975814yescomplemented
626D4—22no—
627D4—22no—
628D4—41no—
629D4—41no—
630D4—84no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—48no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—612no—
649C2×C4—612no—
650C2×C4—1221no—
651C2×C4—1221no—
652C2×C4—1221no—
653C2×C4—1221no—
654C2×C4—1221no—
655C2×C4—1221no—
656C2×C4—1221no—
657C2×C4—1221no—
658C2×C4—1221no—
659C2×C4—1221no—
660C2×C4—4884no—
661C2×C4—2441no—
662C2×C4—2441no—
663C2×C4—2441no—
664C2×C4—2441no—
665C2×C4—2441no—
666C2×C4—2441no—
667C2×C4—2441no—
668C2×C4—2441no—
669C2×C4—2441no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4C22×C22⋊D6111yescharacteristic
674C2×C4C2×#1175822411yescharacteristic
675C2×C4C2×#1175822411yescharacteristic
676C2×C4C2×#1175822411yescharacteristic
677C2×C4#1451982211yescharacteristic
678C2×C4#1451982211yescharacteristic
679C8—22no—
680C8—41no—
681C8—2441no—
682C8—2441no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22#1684026811yescharacteristic
698C22D4×C22⋊D6111yescharacteristic
699C22#1684039911yescharacteristic
700C22C2×SD16×D6111yescharacteristic
701C22#1684056111yescharacteristic
702C22#1684056811yescharacteristic
703C22#1684057811yescharacteristic
704C4—24no—
705C4—41no—
706C4—42no—
707C4—81no—
708C4—1222no—
709C4—1222no—
710C4—4881no—
711C4—4881no—
712C4—4881no—
713C4—4881no—
714C4—2441no—
715C4—2441no—
716C4C2×#1451975811yescharacteristic
717C4#1684034711yescharacteristic
718C4#1684040611yescharacteristic
719C4#1684044311yescharacteristic
720C2—42no—
721C2—82no—
722C2#2144927711yescharacteristic
723C2#2145584511yescharacteristic
724C2#2145604111yescharacteristic
725C2#2145736811yescharacteristic
726C2SD16×C22⋊D6111yescharacteristic
727C2#2145767711yescharacteristic
728C2#2145807611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#448C2
socleC23×C61C22×D4
prime radicalC2×#121×C61C22
hypercenterC2×#448D61
hypocenterC61#24898
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×SD16×Dic61C2semidirect
3. Q8×C22⋊Dic61C2semidirect
4. #21447360C2semidirect
5. #21447252C2semidirect
6. #21447132C2semidirect
8. #21446492C2semidirect
9. #21446422C2semidirect
10. #21446176C2semidirect
11. #21446155C2semidirect
12. #21446085C2semidirect
13. #21445822C2semidirect
14. #21445754C2semidirect
211. C22⋊Dic61SD16semidirect
260. Q8×C61#123semidirect
425. C61#24898semidirect
625. Q8#14519758semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic612
#214493292
Q8×C22⋊Dic612
#214473602
#214472522
#214471322
#214470052
#214464922
#214464222
#214461762
#214461552
#214460852
#214458222
#214457542
C2×C61×#4482
#2489861