Finite Group Databasebeta

← #29681232

Subgroups — #29681232

Order 15616.

1986 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840274C211yesmaximal, characteristic
2C2×#117×D61C211yesmaximal, characteristic, complemented
3C2×#16839759C211yesmaximal, characteristic, complemented
4C2×#16839756C211yesmaximal, characteristic, complemented
5C22×#14519689C211yesmaximal, characteristic, complemented
6#21446140C212yesmaximal, complemented
7#21446135C212yesmaximal, complemented
8#21446130C212yesmaximal, complemented
9#21446125C212yesmaximal, complemented
10#21445535C211yesmaximal, characteristic, complemented
11C61×#1735C211yesmaximal, characteristic, complemented
12C22×#11758222C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C23×#92418C2211yescharacteristic
15#16840274—24no—
16#16840274C418yescomplemented
17C2×#14519761—21no—
18C2×#14519757C2211yescharacteristic
19C2×#14519757C2211yescharacteristic
20C2×#14519752C2211yescharacteristic
21C2×#14519752C2211yescharacteristic
22C2×#14519747—21no—
23C2×C4×D244—21no—
24C2×C4×D244—21no—
25C2×#14519736C2211yescharacteristic
26C2×#14519735C2212yes—
27C2×#14519734—21no—
28C2×#14519733—21no—
29#117×D61—24no—
30#117×D61—24no—
31C2×C4⋊C4×D61C2212yes—
32C2×C22⋊C4×D61—21no—
33C2×C42×D61—21no—
34#16839759—24no—
35#16839756—24no—
36C2×#14519702C2212yescomplemented
37C2×#14519700C2212yescomplemented
38C2×#14519699C2212yescomplemented
39C2×#14519697C2212yescomplemented
40C2×#14519689—24no—
41C2×#14519689C2212yes—
42C2×#14519689C2212yes—
43#16839524C2212yescomplemented
44#16839524C2212yescomplemented
45C23×C8×C61C2211yescharacteristic
46C2×#117×C61C2211yescharacteristic
47C2×#117×C61C2211yescharacteristic
48C61×#340C2212yescomplemented
49C61×#340C2212yescomplemented
50C24×D61D411yescharacteristic
51C2×#11758222—22no—
52C2×#11758222—22no—
53C2×#11758222—22no—
54C2×#11758222—22no—
55C2×#11758222—22no—
56C2×#11758222C2×C414yescomplemented
57C22×Dic122C2311yescharacteristic
58C22×D244—21no—
59C22×D244—21no—
60C22×D244C2311yescharacteristic
61C22×C22⋊D61—21no—
62C23×Dic61D411yescharacteristic
63C22×C4×D61—22no—
64C22×C4×D61—22no—
65C22×C4×D61—22no—
66C22×C4×D61—22no—
67C22×C4×D61—22no—
68C22×C4×D61—21no—
69C22×C4×D61C2×C414yes—
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D414yes—
73C22×C4×D61C2311yescharacteristic
74C22×C4×D61C2311yescharacteristic
75C22×#92418—22no—
76C22×#92418—22no—
77C22×#92418—22no—
78C22×#92418C2312yes—
79#14519761—28no—
80#14519757—22no—
81#14519757—22no—
82#14519757C2×C414yes—
83#14519757C2×C414yescomplemented
84#14519752—22no—
85#14519752—22no—
86#14519752C2×C414yes—
87#14519752C2×C414yescomplemented
88#14519747—28no—
89C4×D244—28no—
90C4×D244—28no—
91#14519736—22no—
92#14519736D414yescomplemented
93#14519735—24no—
94#14519735—24no—
95#14519734—28no—
96#14519733—28no—
97C2×C4⋊Dic61—21no—
98C2×C4⋊Dic61—21no—
99C2×C4⋊Dic61C2312yes—
100C2×#11758196—22no—
101C4⋊C4×D61—24no—
102C4⋊C4×D61—24no—
103C2×C22⋊Dic61—21no—
104C2×#11758198—22no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C22⋊C4×D61—28no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61—22no—
112C42×D61—28no—
113#14519702—24no—
114#14519700—24no—
115#14519699—24no—
116#14519697—24no—
117#14519689—24no—
118#14519689—24no—
119C23×C4×C61C2311yescharacteristic
120C22×C8×C61—22no—
121C22×C8×C61—22no—
122C22×C8×C61—22no—
123C22×C8×C61C2312yes—
124#117×C61—22no—
125#117×C61—22no—
126#117×C61C2×C414yescomplemented
127#117×C61D414yescomplemented
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2312yes—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C42×C61—21no—
134C2×C42×C61—21no—
135C24×C61C2×D411yescharacteristic
136C23×D61—22no—
137C23×D61—22no—
138C23×D61—24no—
139C23×D61—21no—
140C23×D61—42no—
141C23×D61C22⋊C414yes—
142C23×D61C2×D411yescharacteristic
143C23×D61C2×D411yescharacteristic
144C22×C4×C61—22no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61C22×C412yes—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D412yes—
150C22×C4×C61C2×D412yes—
151C22×C4×C61C2×D412yes—
152C22×C4×C61#4112yes—
153C22×C4×C61#4112yes—
154C22×C4×C61C2411yescharacteristic
155C2×C22⋊D61—24no—
156C2×C22⋊D61—42no—
157C2×C22⋊D61—42no—
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—21no—
161C22×Dic61—22no—
162C22×Dic61C22⋊C414yes—
163C22×Dic61C2×D411yescharacteristic
164C22×Dic61C2×D411yescharacteristic
165#11758222—28no—
166#11758222—28no—
167#11758222—44no—
168#11758222—44no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—24no—
174C2×D244—24no—
175C2×D244—21no—
176C2×D244—44no—
177C2×D244—44no—
178C2×D244C22×C412yes—
179C2×C4×D61—28no—
180C2×C4×D61—28no—
181C2×C4×D61—22no—
182C2×C4×D61—22no—
183C2×C4×D61—28no—
184C2×C4×D61—28no—
185C2×C4×D61—22no—
186C2×C4×D61—22no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—28no—
196C2×C4×D61—24no—
197C2×C4×D61—44no—
198C2×C4×D61—44no—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61C22⋊C414yes—
202C2×C4×D61C22⋊C414yes—
203C2×C4×D61C22×C412yes—
204C2×C4×D61C22×C412yes—
205C2×C4×D61C2×D412yes—
206C2×C4×D61C2×D412yes—
207C2×Dic122—21no—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122—21no—
211C2×Dic122—21no—
212C2×Dic122C22×C412yes—
213C2×C8×C61—22no—
214C2×C8×C61—22no—
215C2×C8×C61—22no—
216C2×C8×C61—44no—
217C4⋊C4×C61—22no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61C22×C412yes—
221C4⋊C4×C61C22×C412yes—
222C4⋊C4×C61C2×D414yes—
223C22⋊C4×C61—24no—
224C22⋊C4×C61—24no—
225C42×C61—24no—
226C42×C61—24no—
227C22⋊Dic61—24no—
228#11758198—28no—
229#11758198—24no—
230#11758198—24no—
231#11758198—24no—
232#11758198—24no—
233C4⋊Dic61—22no—
234C4⋊Dic61—24no—
235C4⋊Dic61—24no—
236C4⋊Dic61C2×D414yes—
237#11758196—28no—
238C4×Dic61—28no—
239C4×Dic61—24no—
240C2×#92418—22no—
241C2×#92418—22no—
242C2×#92418—22no—
243C2×#92418—44no—
244C23×C61—22no—
245C23×C61—22no—
246C23×C61C2×C22⋊C412yes—
247C23×C61#12012yes—
248C23×C61#12312yes—
249C23×C61C22×D411yescharacteristic
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—22no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—28no—
258C22×D61—28no—
259C22×D61—22no—
260C22×D61—44no—
261C22×D61—48no—
262C22×D61—48no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—42no—
266C22×D61—42no—
267C22×D61C2×C22⋊C412yes—
268C22×D61C2×C22⋊C412yes—
269C22×D61#13514yes—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—24no—
273C2×C4×C61—42no—
274C2×C4×C61—42no—
275C2×C4×C61—42no—
276C2×C4×C61—42no—
277C2×C4×C61C2×C22⋊C412yes—
278C2×C4×C61C4×D414yes—
279C2×C4×C61C4×D414yes—
280C2×C4×C61#12012yes—
281C2×C4×C61#12114yes—
282C2×C4×C61#12114yes—
283C2×C4×C61#12312yes—
284C2×C4×C61C23×C411yescharacteristic
285C2×C4×C61C22×D411yescharacteristic
286C2×C4×C61C22×D411yescharacteristic
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C22⋊D61—48no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—28no—
296C2×Dic61—22no—
297C2×Dic61—24no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—42no—
301C2×Dic61—42no—
302C2×Dic61C2×C22⋊C412yes—
303C2×Dic61C2×C22⋊C412yes—
304D244—22no—
305D244—22no—
306D244—48no—
307D244—48no—
308D244—41no—
309D244—41no—
310C4×D61—22no—
311C4×D61—22no—
312C4×D61—22no—
313C4×D61—22no—
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—28no—
319C4×D61—28no—
320C4×D61—416no—
321C4×D61—48no—
322Dic122—22no—
323Dic122—22no—
324Dic122—41no—
325Dic122—41no—
326C8×C61—42no—
327#92418—42no—
328#20908—611nomaximal, Sylow
329C22×C61—24no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—24no—
333C22×C61#38614yes—
334C22×C61C22×C22⋊C411yescharacteristic
335C22×C61C2×#12011yescharacteristic
336C22×C61C2×#12311yescharacteristic
337C22×C61C2×#13512yes—
338C22×C61#57512yes—
339C2×D61—24no—
340C2×D61—22no—
341C2×D61—24no—
342C2×D61—22no—
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—416no—
347C2×D61—42no—
348C2×D61—42no—
349C2×D61—42no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—82no—
353C2×D61—82no—
354C2×D61#41614yescomplemented
355C4×C61—42no—
356C4×C61—42no—
357C4×C61—44no—
358C4×C61#38614yes—
359C4×C61C2×C4×D411yescharacteristic
360C4×C61C2×C4×D411yescharacteristic
361C4×C61C2×#12111yescharacteristic
362C4×C61C2×#12111yescharacteristic
363Dic61—22no—
364Dic61—22no—
365Dic61—44no—
366Dic61—42no—
367C2×#525—611no—
368C22×#117—611no—
369C2×#416—611no—
370C2×#416—611no—
371C22×C22⋊C8—611no—
372#1875—612no—
373#1874—612no—
374#1873—612no—
375#1872—612no—
376#1735—611no—
377#1735D6111yescharacteristic, complemented
378C2×C61—24no—
379C2×C61C2×#38611yescharacteristic
380C2×C61C2×#41611yescharacteristic
381C2×C61#289611yescharacteristic
382C2×C61#300212yes—
383C2×C61#309112yes—
384D61—24no—
385D61—42no—
386D61—82no—
387C22×#41—611no—
388C24×C4—611no—
389C23×C8—611no—
390C23×C8C2×D6111yescharacteristic
391#525—618no—
392#525—1224no—
393C2×#123—1221no—
394C2×C22⋊Q8—611no—
395C2×C22⋊Q8—611no—
396C2×#121—611no—
397C2×#121—611no—
398C2×#120—1221no—
399C2×C4×D4—1221no—
400C2×C4×D4—1221no—
401C2×#117—611no—
402C2×#117—612no—
403C2×#117—1221no—
404C2×#117—1221no—
405C2×#117—1224no—
406C2×#117—1224no—
407C2×#117C2×D6111yescharacteristic
408C2×#117C2×D6111yescharacteristic
409C22×C4⋊C4—612no—
410C22×C22⋊C4—1221no—
411C22×C42—1221no—
412#416—1224no—
413#416—1224no—
414C2×#103—612no—
415C2×#103—612no—
416C2×#102—612no—
417C2×#102—612no—
418C2×C22⋊C8—612no—
419C2×C22⋊C8—612no—
420C2×C22⋊C8—1224no—
421#340—612no—
422#340—612no—
423#340C2×D6112yescomplemented
424#340C2×D6112yescomplemented
425C61#2090811yescharacteristic, complemented, Sylow
426C25—611no—
427C2×#41—614no—
428C2×#41—1222no—
429C2×#41—1222no—
430C2×#41—1222no—
431C2×#41—1222no—
432C2×#41—1222no—
433C22×Q8—611no—
434C22×D4—611no—
435C22×D4—1221no—
436C22×D4—1221no—
437C22×D4—1221no—
438C23×C4—611no—
439C23×C4—614no—
440C23×C4—614no—
441C23×C4—611no—
442C23×C4—611no—
443C23×C4—611no—
444C23×C4—611no—
445C23×C4—1222no—
446C23×C4—1222no—
447C23×C4—1222no—
448C23×C4—1222no—
449C23×C4—1222no—
450C23×C4—1221no—
451C23×C4C22×D6111yescharacteristic
452C22×C8—22no—
453C22×C8—22no—
454C22×C8—22no—
455C22×C8—612no—
456C22×C8—1222no—
457C22×C8—1222no—
458C22×C8—1222no—
459C22×C8C22×D6112yes—
460#123—1228no—
461C22⋊Q8—614no—
462C22⋊Q8—614no—
463C22⋊Q8—1222no—
464C22⋊Q8—1222no—
465#121—614no—
466#121—614no—
467#121—1222no—
468#121—1222no—
469#120—1228no—
470C4×D4—1228no—
471C4×D4—1228no—
472#117—22no—
473#117—22no—
474#117—614no—
475#117—1228no—
476#117—1228no—
477#117—1224no—
478#117—1222no—
479#117—1224no—
480#117C4×D6114yescomplemented
481#117D24414yescomplemented
482C2×C4⋊C4—612no—
483C2×C4⋊C4—1224no—
484C2×C4⋊C4—1222no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1224no—
488C2×C4⋊C4C22×D6111yescharacteristic
489C2×C4⋊C4C22×D6111yescharacteristic
490C2×C4⋊C4C22×D6112yes—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—1228no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1222no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C42—21no—
501C2×C42—21no—
502C2×C42—1228no—
503C2×C42—1222no—
504C2×C42—1221no—
505#103—1224no—
506#103—1224no—
507#102—1224no—
508#102—1224no—
509C22⋊C8—1224no—
510C22⋊C8—1224no—
511C24—611no—
512C24—611no—
513C24—614no—
514C24—1224no—
515C24—1222no—
516C24—1222no—
517C24—1221no—
518C24—2442no—
519C24D4×D6111yescharacteristic
520#41—1228no—
521#41—1228no—
522#41—2444no—
523#41—2444no—
524C2×Q8—612no—
525C2×Q8—1221no—
526C2×Q8—1221no—
527C2×Q8—1221no—
528C2×Q8—1221no—
529C2×Q8—1221no—
530C2×D4—612no—
531C2×D4—1224no—
532C2×D4—1224no—
533C2×D4—1224no—
534C2×D4—1221no—
535C2×D4—1221no—
536C2×D4—1221no—
537C2×D4—1221no—
538C2×D4—1221no—
539C2×D4—2444no—
540C2×D4—2444no—
541C2×D4—2442no—
542C2×D4—2442no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—614no—
549C22×C4—612no—
550C22×C4—612no—
551C22×C4—612no—
552C22×C4—612no—
553C22×C4—614no—
554C22×C4—614no—
555C22×C4—1228no—
556C22×C4—1222no—
557C22×C4—1222no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1228no—
567C22×C4—1228no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1228no—
571C22×C4—1228no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1221no—
576C22×C4—1224no—
577C22×C4—2444no—
578C22×C4—2444no—
579C22×C4—2442no—
580C22×C4—2442no—
581C22×C4C2×C4×D6112yes—
582C22×C4C2×D24412yes—
583C22×C4#1175822212yes—
584C22×C4D4×D6112yes—
585C22×C4D4×D6112yes—
586C22×C4D4×D6111yescharacteristic
587C22×C4#1175822612yes—
588C22×C4C23×D6111yescharacteristic
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—44no—
593C2×C8—1222no—
594C2×C8—1222no—
595C2×C8—1222no—
596C2×C8—2444no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—614no—
601C4⋊C4—1224no—
602C4⋊C4—1224no—
603C4⋊C4—1228no—
604C4⋊C4—1222no—
605C4⋊C4C2×C4×D6112yes—
606C4⋊C4C2×C4×D6112yes—
607C4⋊C4C2×D24414yes—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—1224no—
611C22⋊C4—1224no—
612C22⋊C4—1224no—
613C22⋊C4—1224no—
614C22⋊C4—1228no—
615C22⋊C4—1224no—
616C42—24no—
617C42—24no—
618C42—1228no—
619C42—1224no—
620C23—22no—
621C23—22no—
622C23—612no—
623C23—614no—
624C23—612no—
625C23—1228no—
626C23—1221no—
627C23—1221no—
628C23—1222no—
629C23—1221no—
630C23—1221no—
631C23—1222no—
632C23—1222no—
633C23—1228no—
634C23—1222no—
635C23—2444no—
636C23—2448no—
637C23—2448no—
638C23—2441no—
639C23—2441no—
640C23—2442no—
641C23—2442no—
642C23C22⋊C4×D6112yes—
643C23#1451974712yes—
644C23#1451976212yes—
645C23C2×D4×D6111yescharacteristic
646Q8—1222no—
647Q8—1222no—
648Q8—2441no—
649Q8—2441no—
650D4—1222no—
651D4—1222no—
652D4—2448no—
653D4—2448no—
654D4—2448no—
655D4—2441no—
656D4—2441no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—612no—
665C2×C4—612no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1228no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1228no—
680C2×C4—1228no—
681C2×C4—1222no—
682C2×C4—1224no—
683C2×C4—24416no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2442no—
687C2×C4—2442no—
688C2×C4—2448no—
689C2×C4C22⋊C4×D6112yes—
690C2×C4#1451973914yes—
691C2×C4C4×D24414yes—
692C2×C4#1451974712yes—
693C2×C4#1451975014yes—
694C2×C4#1451975214yes—
695C2×C4#1451976212yes—
696C2×C4C22×C4×D6111yescharacteristic
697C2×C4C2×D4×D6111yescharacteristic
698C2×C4C2×D4×D6111yescharacteristic
699C2×C4C22×D24411yescharacteristic
700C2×C4C2×#1175822211yescharacteristic
701C2×C4C2×#1175822611yescharacteristic
702C8—42no—
703C8—2442no—
704C22—24no—
705C22—24no—
706C22—22no—
707C22—22no—
708C22—614no—
709C22—1222no—
710C22—1224no—
711C22—1224no—
712C22—1222no—
713C22—1222no—
714C22—1222no—
715C22—1222no—
716C22—4882no—
717C22—4882no—
718C22—24416no—
719C22—2442no—
720C22—2442no—
721C22—2442no—
722C22—2442no—
723C22—2442no—
724C22#1683964014yes—
725C22C2×C22⋊C4×D6111yescharacteristic
726C22C2×#1451974711yescharacteristic
727C22C2×#1451976211yescharacteristic
728C22#135×D6112yes—
729C22#1684055912yes—
730C4—44no—
731C4—42no—
732C4—42no—
733C4—1222no—
734C4—1222no—
735C4—2442no—
736C4—2444no—
737C4#1683964014yes—
738C4C2×#1451973911yescharacteristic
739C4C2×C4×D24411yescharacteristic
740C4C2×#1451975011yescharacteristic
741C4C2×#1451975211yescharacteristic
742C2—24no—
743C2—1224no—
744C2—4882no—
745C2—2442no—
746C2C2×#1683964011yescharacteristic
747C2#416×D6111yescharacteristic
748C2#2145433411yescharacteristic
749C2#2145503912yes—
750C2#2145573612yes—
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1735C2
socleC23×C61C22×D4
prime radicalC2×#16840274C2
cosocleC22×C4×C61C24
hypercenter#1735D61
hypocenterC61#20908
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ #1735

Complements

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

NH ≅ G/Ntype
2. C2×#117×D61C2semidirect
3. C2×#16839759C2semidirect
4. C2×#16839756C2semidirect
5. C22×#14519689C2semidirect
6. #21446140C2semidirect
7. #21446135C2semidirect
8. #21446130C2semidirect
9. #21446125C2semidirect
10. #21445535C2semidirect
11. C61×#1735C2semidirect
16. #16840274C4semidirect
36. C2×#14519702C22semidirect
37. C2×#14519700C22semidirect
38. C2×#14519699C22semidirect
39. C2×#14519697C22semidirect
43. #16839524C22semidirect
44. #16839524C22semidirect
48. C61×#340C22semidirect
49. C61×#340C22semidirect
56. C2×#11758222C2×C4semidirect
83. #14519757C2×C4semidirect
87. #14519752C2×C4semidirect
92. #14519736D4semidirect
126. #117×C61C2×C4semidirect
127. #117×C61D4semidirect
354. C2×D61#416semidirect
377. #1735D61semidirect
423. #340C2×D61semidirect
424. #340C2×D61semidirect
425. C61#20908semidirect
480. #117C4×D61semidirect
481. #117D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168402742
C2×#117×D612
C2×#168397592
C2×#168397562
C22×#145196892
#214461402
#214461352
#214461302
#214461252
#214455352
C61×#17352
#2090861