Finite Group Databasebeta

← #29602345

Subgroups — #29602345

Order 15616.

2314 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D61C211yesmaximal, characteristic
2C2×#16839662C212yesmaximal
3C2×#16839624C211yesmaximal, characteristic, complemented
4#21444067C212yesmaximal, complemented
5#21444066C212yesmaximal, complemented
6#21444047C212yesmaximal, complemented
7#21444047C211yesmaximal, characteristic, complemented
8#21444042C211yesmaximal, characteristic, complemented
9#21444040C211yesmaximal, characteristic, complemented
10#95×Dic61C211yesmaximal, characteristic, complemented
11C2×C61×#381C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C2×C4×C22⋊D61—28no—
15C2×C4×C22⋊D61C418yescomplemented
16C22×#11758196C2212yes—
17C22×#11758196C2211yescharacteristic
18C22×C22⋊Dic61C2212yes—
19C22×C22⋊Dic61C2211yescharacteristic
20C22×#11758198C2212yes—
21C22×#11758198C2212yes—
22C22×#11758198C2211yescharacteristic
23C22×C4×Dic61C2212yes—
24C22×C4×Dic61C2211yescharacteristic
25#16839662—28no—
26#16839624—24no—
27C2×#14519684C2211yescharacteristic
28C2×#14519684C2212yes—
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C24×C4×C61C2211yescharacteristic
35C22×C22⋊C4×C61C2212yes—
36C61×#381—24no—
37C2×#95×C61C2211yescharacteristic
38C2×#95×C61C2212yes—
39C2×#95×C61C2211yescharacteristic
40C24×D61C2311yescharacteristic
41C22×C22⋊D61—22no—
42C22×C22⋊D61—24no—
43C22×C22⋊D61—22no—
44C22×C22⋊D61C2×C414yes—
45C22×C22⋊D61D418yes—
46C23×Dic61C2312yes—
47C23×Dic61C2311yescharacteristic
48C23×Dic61C2311yescharacteristic
49C23×Dic61C2312yes—
50C23×Dic61C2311yescharacteristic
51C22×C4×D61—24no—
52C22×C4×D61—22no—
53C22×C4×D61—22no—
54C22×C4×D61—42no—
55C22×C4×D61C2×C414yes—
56C4×C22⋊D61—232no—
57C2×#11758196—24no—
58C2×#11758196—24no—
59C2×#11758196—24no—
60C2×#11758196—24no—
61C2×#11758196C2×C414yes—
62C2×C22⋊Dic61—24no—
63C2×C22⋊Dic61—24no—
64C2×C22⋊Dic61—24no—
65C2×C22⋊Dic61—42no—
66C2×C22⋊Dic61C2×C414yes—
67C2×#11758198—24no—
68C2×#11758198—24no—
69C2×#11758198—24no—
70C2×#11758198—24no—
71C2×#11758198—24no—
72C2×#11758198—42no—
73C2×#11758198—42no—
74C2×#11758198C2×C414yes—
75C2×C4×Dic61—24no—
76C2×C4×Dic61—24no—
77C2×C4×Dic61—24no—
78C2×C4×Dic61—24no—
79C2×C4×Dic61C2×C414yes—
80#14519684—24no—
81#14519684—22no—
82#14519684—22no—
83#14519684—24no—
84#14519684—42no—
85#14519684—42no—
86#14519684—42no—
87C25×C61C2311yescharacteristic
88C23×C4×C61—24no—
89C23×C4×C61—22no—
90C23×C4×C61—22no—
91C23×C4×C61—42no—
92C23×C4×C61C2×C414yes—
93C23×C4×C61C2312yes—
94C23×C4×C61C2311yescharacteristic
95C23×C4×C61C2312yes—
96C23×C4×C61C2311yescharacteristic
97C2×C22⋊C4×C61—24no—
98C2×C22⋊C4×C61—24no—
99C2×C22⋊C4×C61—42no—
100#95×C61—24no—
101#95×C61—22no—
102#95×C61D414yescomplemented
103C24×C61—21no—
104C24×C61—22no—
105C24×C61—21no—
106C24×C61—21no—
107C24×C61—21no—
108C24×C61—22no—
109C24×C61—22no—
110C24×C61—21no—
111C24×C61—21no—
112C24×C61C22×C412yes—
113C24×C61C2×D414yes—
114C24×C61C2411yescharacteristic
115C23×D61—21no—
116C23×D61—21no—
117C23×D61—22no—
118C23×D61—21no—
119C23×D61—21no—
120C23×D61—22no—
121C23×D61—22no—
122C23×D61—21no—
123C23×D61—21no—
124C23×D61C22×C412yes—
125C23×D61C2×D414yes—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—28no—
129C22×C4×C61—21no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—21no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—28no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—44no—
148C22×C4×C61—48no—
149C22×C4×C61—48no—
150C22×C4×C61C22×C412yes—
151C22×C4×C61C22×C412yes—
152C22×C4×C61C2×D414yes—
153C22×C4×C61C2×D412yes—
154C22×C4×C61#4112yes—
155C2×C22⋊D61—28no—
156C2×C22⋊D61—28no—
157C2×C22⋊D61—216no—
158C2×C22⋊D61—216no—
159C2×C22⋊D61C22⋊C4116yes—
160C22×Dic61—21no—
161C22×Dic61—22no—
162C22×Dic61—22no—
163C22×Dic61—22no—
164C22×Dic61—21no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—21no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—21no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61C22×C412yes—
182C22×Dic61C22×C412yes—
183C22×Dic61C22×C412yes—
184C22×Dic61C2×D414yes—
185C22×Dic61#4114yes—
186C22×Dic61#4112yes—
187C22×Dic61#4114yes—
188C22×Dic61#4112yes—
189C2×C4×D61—28no—
190C2×C4×D61—28no—
191C2×C4×D61—44no—
192C2×C4×D61—48no—
193C2×C4×D61—48no—
194C22⋊C4×C61—48no—
195C22⋊Dic61—28no—
196C22⋊Dic61—48no—
197#11758198—28no—
198#11758198—48no—
199#11758198—48no—
200#11758196—28no—
201#11758196—48no—
202C4×Dic61—28no—
203C4×Dic61—48no—
204C23×C61—22no—
205C23×C61—22no—
206C23×C61—22no—
207C23×C61—22no—
208C23×C61—22no—
209C23×C61—22no—
210C23×C61—24no—
211C23×C61—24no—
212C23×C61—24no—
213C23×C61—24no—
214C23×C61—24no—
215C23×C61—24no—
216C23×C61—42no—
217C23×C61—42no—
218C23×C61—42no—
219C23×C61—42no—
220C23×C61—41no—
221C23×C61—41no—
222C23×C61—42no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61—42no—
226C23×C61C2×C22⋊C414yes—
227C23×C61C23×C411yescharacteristic
228C23×C61C22×D412yes—
229C23×C61C22×D411yescharacteristic
230C23×C61C2×#4112yes—
231C23×C61C2×#4111yescharacteristic
232C23×C61C2×#4111yescharacteristic
233C23×C61C2×#4111yescharacteristic
234C23×C61C2×#4112yes—
235C23×C61H(5,𝔽2)12yes—
236C23×C61H(5,𝔽2)11yescharacteristic
237C23×C612−1+411yescharacteristic
238C22×D61—22no—
239C22×D61—22no—
240C22×D61—22no—
241C22×D61—22no—
242C22×D61—22no—
243C22×D61—22no—
244C22×D61—24no—
245C22×D61—24no—
246C22×D61—24no—
247C22×D61—24no—
248C22×D61—24no—
249C22×D61—24no—
250C22×D61—42no—
251C22×D61—42no—
252C22×D61—42no—
253C22×D61—42no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—42no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—42no—
260C22×D61C2×C22⋊C414yes—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—24no—
264C2×C4×C61—24no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—24no—
269C2×C4×C61—24no—
270C2×C4×C61—24no—
271C2×C4×C61—416no—
272C2×C4×C61—42no—
273C2×C4×C61—42no—
274C2×C4×C61—42no—
275C2×C4×C61—42no—
276C2×C4×C61—42no—
277C2×C4×C61—42no—
278C2×C4×C61—42no—
279C2×C4×C61—42no—
280C2×C4×C61—42no—
281C2×C4×C61—42no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—42no—
285C2×C4×C61C4×D414yes—
286C22⋊D61—232no—
287C2×Dic61—22no—
288C2×Dic61—22no—
289C2×Dic61—22no—
290C2×Dic61—22no—
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—24no—
294C2×Dic61—24no—
295C2×Dic61—24no—
296C2×Dic61—42no—
297C2×Dic61—42no—
298C2×Dic61—42no—
299C2×Dic61—42no—
300C2×Dic61—42no—
301C2×Dic61—42no—
302C2×Dic61—42no—
303C2×Dic61—42no—
304C2×Dic61—42no—
305C2×Dic61—42no—
306C2×Dic61—42no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61C2×C22⋊C414yes—
312C2×Dic61#11714yes—
313C2×Dic61#11714yes—
314C2×Dic61#12318yes—
315C2×Dic61#12318yes—
316C4×D61—416no—
317#13916—611nomaximal, Sylow
318C22×C61—24no—
319C22×C61—24no—
320C22×C61—24no—
321C22×C61—42no—
322C22×C61—42no—
323C22×C61—42no—
324C22×C61—44no—
325C22×C61—44no—
326C22×C61—44no—
327C22×C61—44no—
328C22×C61—42no—
329C22×C61C22×C22⋊C411yescharacteristic
330C22×C61C2×#11711yescharacteristic
331C22×C61C2×#11711yescharacteristic
332C22×C61C2×C4×D411yescharacteristic
333C22×C61C4×#4111yescharacteristic
334C22×C61#51811yescharacteristic
335C22×C61#52011yescharacteristic
336C22×C61C2×#12312yes—
337C22×C61C2×#12312yes—
338C22×C61#52912yes—
339C22×C61#53212yes—
340C22×C61#54012yes—
341C22×C61#54212yes—
342C22×C61D4212yes—
343C22×C61#54612yes—
344C22×C61#54612yes—
345C22×C61#54712yes—
346C22×C61#54711yescharacteristic
347C22×C61#55011yescharacteristic
348C22×C61#55312yes—
349C22×C61#55511yescharacteristic
350C22×C61#55611yescharacteristic
351C22×C61#55912yes—
352C2×D61—24no—
353C2×D61—24no—
354C2×D61—24no—
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—44no—
359C2×D61—44no—
360C2×D61—44no—
361C2×D61—44no—
362C2×D61—42no—
363C4×C61—24no—
364C4×C61—42no—
365C4×C61—44no—
366C4×C61—82no—
367Dic61—42no—
368Dic61—42no—
369Dic61—44no—
370Dic61—82no—
371Dic61#38118yescomplemented
372C22×C4×D4—611no—
373C2×#390—612no—
374C2×#381—611no—
375C2×#381D6111yescharacteristic, complemented
376#1440—612no—
377#1440—612no—
378C4⋊#95—612no—
379C4⋊#95—611no—
380C22⋊#95—611no—
381C22⋊#95—611no—
382C4×#95—611no—
383C2×C61—44no—
384C2×C61C2×#38111yescharacteristic
385C2×C61#229311yescharacteristic
386C2×C61#231911yescharacteristic
387C2×C61D4×C22⋊C411yescharacteristic
388C2×C61#233911yescharacteristic
389C2×C61#235411yescharacteristic
390C2×C61#235711yescharacteristic
391C2×C61#242012yes—
392C2×C61#242212yes—
393C2×C61#244512yes—
394C2×C61#244712yes—
395D61—44no—
396C23×D4—611no—
397C24×C4—611no—
398C24×C4C2×D6111yescharacteristic
399C2×C4×D4—618no—
400C2×C4×D4—1228no—
401C22×C4⋊C4—611no—
402C22×C4⋊C4—612no—
403C22×C22⋊C4—611no—
404C22×C22⋊C4—611no—
405C22×C22⋊C4—612no—
406C22×C22⋊C4—612no—
407C22×C22⋊C4—612no—
408C22×C22⋊C4C2×D6112yes—
409C22×C42—611no—
410C22×C42—612no—
411#390—1228no—
412#381—24no—
413#381—1224no—
414C2×#95—611no—
415C2×#95—612no—
416C2×#95—611no—
417C2×#95—612no—
418C2×#95—612no—
419C2×#95—612no—
420C2×#95—612no—
421C2×#95C2×D6111yescharacteristic
422C2×#95C2×D6112yes—
423C2×#95C2×D6111yescharacteristic
424C61#1391611yescharacteristic, complemented, Sylow
425C25—611no—
426C25C22×D6111yescharacteristic
427C22×D4—614no—
428C22×D4—618no—
429C22×D4—1222no—
430C22×D4—1224no—
431C22×D4—1222no—
432C23×C4—24no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—42no—
436C23×C4—611no—
437C23×C4—611no—
438C23×C4—612no—
439C23×C4—611no—
440C23×C4—614no—
441C23×C4—612no—
442C23×C4—1224no—
443C23×C4—1222no—
444C23×C4—1222no—
445C23×C4—2442no—
446C23×C4C4×D6114yes—
447C23×C4C22×D6112yes—
448C23×C4C22×D6111yescharacteristic
449C23×C4C22×D6112yes—
450C23×C4C22×D6111yescharacteristic
451C4×D4—12232no—
452C2×C4⋊C4—614no—
453C2×C4⋊C4—1224no—
454C2×C4⋊C4—1224no—
455C2×C4⋊C4—1224no—
456C2×C4⋊C4—1224no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—614no—
461C2×C22⋊C4—614no—
462C2×C22⋊C4—1224no—
463C2×C22⋊C4—1224no—
464C2×C22⋊C4—1224no—
465C2×C22⋊C4—1224no—
466C2×C22⋊C4—1224no—
467C2×C22⋊C4—1224no—
468C2×C22⋊C4—1224no—
469C2×C22⋊C4—1224no—
470C2×C22⋊C4—2442no—
471C2×C22⋊C4—2442no—
472C2×C22⋊C4—2442no—
473C2×C42—614no—
474C2×C42—1224no—
475C2×C42—1224no—
476C2×C42—1224no—
477C2×C42—1224no—
478#95—24no—
479#95—22no—
480#95—1224no—
481#95—1222no—
482#95—1224no—
483#95—1222no—
484#95—2442no—
485#95—2442no—
486#95—2442no—
487#95C22⋊D6114yescomplemented
488C24—21no—
489C24—22no—
490C24—21no—
491C24—21no—
492C24—22no—
493C24—21no—
494C24—22no—
495C24—21no—
496C24—21no—
497C24—612no—
498C24—614no—
499C24—1221no—
500C24—1222no—
501C24—1221no—
502C24—1221no—
503C24—1222no—
504C24—1221no—
505C24—1222no—
506C24—1221no—
507C24—1221no—
508C24C2×C4×D6112yes—
509C24D4×D6114yes—
510C24C23×D6111yescharacteristic
511C2×D4—6116no—
512C2×D4—1228no—
513C2×D4—1228no—
514C2×D4—12216no—
515C2×D4—12216no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—44no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—612no—
541C22×C4—614no—
542C22×C4—612no—
543C22×C4—614no—
544C22×C4—612no—
545C22×C4—612no—
546C22×C4—612no—
547C22×C4—614no—
548C22×C4—1228no—
549C22×C4—1222no—
550C22×C4—1222no—
551C22×C4—1222no—
552C22×C4—1221no—
553C22×C4—1222no—
554C22×C4—1222no—
555C22×C4—1222no—
556C22×C4—1222no—
557C22×C4—1221no—
558C22×C4—1222no—
559C22×C4—1222no—
560C22×C4—1221no—
561C22×C4—1222no—
562C22×C4—1221no—
563C22×C4—1228no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—2444no—
572C22×C4—2448no—
573C22×C4—2448no—
574C22×C4C2×C4×D6112yes—
575C22×C4C2×C4×D6112yes—
576C22×C4#1175822212yes—
577C22×C4C2×C22⋊D6114yes—
578C22×C4C2×C22⋊D6112yes—
579C4⋊C4—1228no—
580C4⋊C4—2448no—
581C22⋊C4—48no—
582C22⋊C4—1228no—
583C22⋊C4—1228no—
584C22⋊C4—2448no—
585C22⋊C4—2448no—
586C22⋊C4—2448no—
587C42—1228no—
588C42—2448no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—42no—
602C23—41no—
603C23—41no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—41no—
610C23—41no—
611C23—614no—
612C23—1222no—
613C23—1222no—
614C23—1222no—
615C23—1222no—
616C23—1222no—
617C23—1222no—
618C23—1224no—
619C23—1224no—
620C23—1224no—
621C23—1224no—
622C23—1224no—
623C23—1224no—
624C23—2442no—
625C23—2441no—
626C23—2441no—
627C23—2442no—
628C23—2442no—
629C23—2442no—
630C23—2442no—
631C23—2442no—
632C23—2441no—
633C23—2441no—
634C23C22⋊C4×D6114yes—
635C23C22×C4×D6111yescharacteristic
636C23C2×D4×D6112yes—
637C23C22×C22⋊D6111yescharacteristic
638C23#41×D6111yescharacteristic
639C23#41×D6112yes—
640C23#41×D6111yescharacteristic
641C23#41×D6112yes—
642C23C2×#1175822211yescharacteristic
643C23#1451982212yes—
644C23#1451982311yescharacteristic
645C23#1451982411yescharacteristic
646D4—12232no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—416no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—614no—
672C2×C4—614no—
673C2×C4—614no—
674C2×C4—618no—
675C2×C4—618no—
676C2×C4—1224no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1224no—
684C2×C4—1224no—
685C2×C4—24416no—
686C2×C4—2442no—
687C2×C4—2442no—
688C2×C4—2442no—
689C2×C4—2442no—
690C2×C4—2442no—
691C2×C4—2442no—
692C2×C4—2442no—
693C2×C4—2442no—
694C2×C4—2442no—
695C2×C4—2442no—
696C2×C4—2442no—
697C2×C4—2442no—
698C2×C4—2442no—
699C2×C4—2442no—
700C2×C4—2442no—
701C2×C4C4×C22⋊D6114yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—44no—
710C22—44no—
711C22—44no—
712C22—44no—
713C22—1224no—
714C22—1224no—
715C22—1224no—
716C22—2442no—
717C22—2442no—
718C22—2442no—
719C22—2442no—
720C22—2444no—
721C22—2444no—
722C22—2444no—
723C22—2444no—
724C22C2×C22⋊C4×D6111yescharacteristic
725C22#117×D6111yescharacteristic
726C22#117×D6111yescharacteristic
727C22C2×C4×C22⋊D6111yescharacteristic
728C22#1684023011yescharacteristic
729C22#1684023511yescharacteristic
730C22#1684024211yescharacteristic
731C22#123×D6112yes—
732C22#123×D6112yes—
733C22#1684029012yes—
734C22#1684030812yes—
735C22#1684036412yes—
736C22#1684038012yes—
737C22D4×C22⋊D6112yes—
738C22#1684040212yes—
739C22#1684040412yes—
740C22#1684041012yes—
741C22#1684041111yescharacteristic
742C22#1684043111yescharacteristic
743C22#1684045712yes—
744C22#1684047511yescharacteristic
745C22#1684048011yescharacteristic
746C22#1684049612yes—
747C4—24no—
748C4—44no—
749C4—42no—
750C4—82no—
751C4—618no—
752C4—4882no—
753C4—2444no—
754C4—2442no—
755C4—2442no—
756C2—44no—
757C2—2444no—
758C2#381×D6111yescharacteristic
759C2#2144827811yescharacteristic
760C2#2144845911yescharacteristic
761C2C22⋊C4×C22⋊D6111yescharacteristic
762C2#2144864311yescharacteristic
763C2#2144876911yescharacteristic
764C2#2144878711yescharacteristic
765C2#2144931012yes—
766C2#2144933012yes—
767C2#2144958312yes—
768C2#2144960512yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#381C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#381D61
hypocenterC61#13916
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
3. C2×#16839624C2semidirect
4. #21444067C2semidirect
5. #21444066C2semidirect
6. #21444047C2semidirect
7. #21444047C2semidirect
8. #21444042C2semidirect
9. #21444040C2semidirect
10. #95×Dic61C2semidirect
11. C2×C61×#381C2semidirect
15. C2×C4×C22⋊D61C4semidirect
102. #95×C61D4semidirect
371. Dic61#381semidirect
375. C2×#381D61semidirect
424. C61#13916semidirect
487. #95C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D612
C2×#168396622
C2×#168396242
#214440672
#214440662
#214440472
#214440422
#214440402
#95×Dic612
C2×C61×#3812
#1391661