Finite Group Databasebeta

← #29718899

Subgroups — #29718899

Order 15616.

986 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839820C211yesmaximal, characteristic, complemented
2#21451609C211yesmaximal, characteristic, complemented
3#21448411C211yesmaximal, characteristic, complemented
4#21447198C211yesmaximal, characteristic, complemented
5#21447191C211yesmaximal, characteristic, complemented
6#21447132C211yesmaximal, characteristic, complemented
7#21447127C211yesmaximal, characteristic, complemented
8#21446696C211yesmaximal, characteristic, complemented
9#21446675C211yesmaximal, characteristic, complemented
10#21446506C211yesmaximal, characteristic, complemented
11#21446499C211yesmaximal, characteristic, complemented
12#21446137C211yesmaximal, characteristic, complemented
13#21446014C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C2×C61×#449C211yesmaximal, characteristic
16C2×#14519736C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18#16839820—24no—
19C2×#14519709C2211yescharacteristic
20C2×#14519709C2211yescharacteristic
21C2×#14519706C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23C2×#14519701C2211yescharacteristic
24C2×#14519701C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×#14519687C2211yescharacteristic
31C2×C8×Dic61C2211yescharacteristic
32#16839698—21no—
33#16839687—21no—
34#16839676—21no—
35#16839676—21no—
36#16839669C2211yescharacteristic
37#16839669C2211yescharacteristic
38#16839665C2211yescharacteristic
39#16839665C2211yescharacteristic
40#16839665C2211yescharacteristic
41#16839665C2211yescharacteristic
42#16839658C2211yescharacteristic
43#16839658C2211yescharacteristic
44#16839642—21no—
45#16839642—21no—
46#16839622—21no—
47#16839622—21no—
48#16839622C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C22×#41×C61C2211yescharacteristic
54C22×SD16×C61C2211yescharacteristic
55C22×D8×C61C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C61×#449—24no—
58C2×#103×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C23×Dic61—21no—
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64#14519736—22no—
65#14519736—22no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61—41no—
68C2×C4⋊Dic61—41no—
69C2×C4⋊Dic61D411yescharacteristic
70C2×C4⋊Dic61D411yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×C22⋊Dic61—21no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61D411yescharacteristic
87C2×C22⋊Dic61D411yescharacteristic
88C2×C4×Dic61C2311yescharacteristic
89C2×C4×Dic61C2311yescharacteristic
90#14519709—41no—
91#14519709—41no—
92#14519706—22no—
93#14519706—22no—
94#14519701—22no—
95#14519701—41no—
96#14519698—22no—
97#14519698—41no—
98#14519698—41no—
99#14519698—41no—
100C22⋊#92418—22no—
101#14519687—22no—
102C8×Dic61—22no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110C2×#41×C61—22no—
111C2×#41×C61—22no—
112C2×#41×C61—22no—
113C2×#41×C61—22no—
114C2×#41×C61—41no—
115C2×#41×C61—41no—
116C22×Q8×C61C2311yescharacteristic
117C22×D4×C61—21no—
118C22×D4×C61—21no—
119C22×D4×C61C2311yescharacteristic
120C22×D4×C61C2311yescharacteristic
121C23×C4×C61—21no—
122C23×C4×C61C2311yescharacteristic
123C2×SD16×C61—22no—
124C2×SD16×C61—22no—
125C2×SD16×C61—41no—
126C2×D8×C61—22no—
127C2×D8×C61—22no—
128C2×D8×C61—41no—
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131#121×C61—22no—
132#121×C61—22no—
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C22⋊C4×C61—21no—
135#103×C61—22no—
136#102×C61—22no—
137C22⋊C8×C61D414yes—
138C24×C61—21no—
139C24×C61—21no—
140C24×C61C2×D411yescharacteristic
141#41×C61—44no—
142#41×C61—44no—
143#41×C61—44no—
144#41×C61—44no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61#4112yes—
151C2×D4×C61—24no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—42no—
164C2×D4×C61—42no—
165C2×D4×C61—42no—
166C2×D4×C61—81no—
167C2×D4×C61—81no—
168C2×D4×C61#4112yes—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—24no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—42no—
177C22×C4×C61—42no—
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D412yes—
180C22×C4×C61#4112yes—
181C22×C4×C61C2411yescharacteristic
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—42no—
187C22×Dic61—81no—
188C22×Dic61—81no—
189C22×Dic61C2×D411yescharacteristic
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192C22×Dic61C2×D411yescharacteristic
193SD16×C61—44no—
194D8×C61—44no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61C2×D412yes—
200C2×C8×C61C2×D412yes—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C22⋊C4×C61—42no—
204C22⋊Dic61—22no—
205C22⋊Dic61—22no—
206C22⋊Dic61—81no—
207C22⋊Dic61—81no—
208C22⋊Dic61—81no—
209C22⋊Dic61—81no—
210C22⋊Dic61—81no—
211C22⋊Dic61—81no—
212C22⋊Dic61—81no—
213C22⋊Dic61—81no—
214C22⋊Dic61—81no—
215C4⋊Dic61—22no—
216C4⋊Dic61—22no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—42no—
226#11758196—81no—
227#11758196—81no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61—21no—
231C4×Dic61—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—22no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61#12112yes—
259C23×C61C22×D411yescharacteristic
260Q8×C61—22no—
261Q8×C61—22no—
262Q8×C61—41no—
263Q8×C61—41no—
264D4×C61—22no—
265D4×C61—22no—
266D4×C61—48no—
267D4×C61—41no—
268D4×C61—41no—
269D4×C61—41no—
270D4×C61—41no—
271D4×C61—41no—
272D4×C61—41no—
273D4×C61—84no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—48no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61#12112yes—
288C2×C4×C61C22×D411yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61H(5,𝔽2)11yescharacteristic
293C2×C4×C61H(5,𝔽2)11yescharacteristic
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
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—84no—
319C8×C61—22no—
320C8×C61—22no—
321#92418—41no—
322#92418—41no—
323#24519—611nomaximal, Sylow
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—42no—
332C22×C61—42no—
333C22×C61—42no—
334C22×C61—81no—
335C22×C61—81no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61—81no—
340C22×C61—81no—
341C22×C61—81no—
342C22×C61—81no—
343C22×C61—81no—
344C22×C61—81no—
345C22×C61C2×#12111yescharacteristic
346C22×C61#52511yescharacteristic
347C22×C61#53511yescharacteristic
348C22×C61#57611yescharacteristic
349C22×C61#57711yescharacteristic
350C22×C61#57711yescharacteristic
351C22×C61#57711yescharacteristic
352C4×C61—22no—
353C4×C61—42no—
354C4×C61—81no—
355C4×C61#54611yescharacteristic
356C4×C61#54611yescharacteristic
357C4×C61#55111yescharacteristic
358C4×C61#55111yescharacteristic
359Dic61—41no—
360Dic61—41no—
361Dic61—41no—
362Dic61—41no—
363Dic61—81no—
364Dic61—81no—
365Dic61—81no—
366Dic61—81no—
367C2×#449D6111yescharacteristic
368C2×#433—611no—
369#2624—611no—
370#2311—611no—
371#2066—611no—
372#2065—611no—
373#2055—611no—
374#2054—611no—
375#1972—611no—
376#1968—611no—
377#1935—611no—
378#1934—611no—
379#1874—611no—
380#1853—611no—
381#1788—611no—
382C2×C61—42no—
383C2×C61—82no—
384C2×C61—161no—
385C2×C61#241111yescharacteristic
386C2×C61#306011yescharacteristic
387C2×C61#306211yescharacteristic
388C2×C61#311911yescharacteristic
389C2×C61#312511yescharacteristic
390C2×C61#322111yescharacteristic
391C2×C61#322411yescharacteristic
392C22×#41C2×D6111yescharacteristic
393C22×SD16C2×D6111yescharacteristic
394C22×D8C2×D6111yescharacteristic
395C2×#121C2×D6111yescharacteristic
396C2×#117—611no—
397C22×C4⋊C4—611no—
398#449—24no—
399#433—1224no—
400C2×#106—611no—
401C2×#106—611no—
402C2×C4⋊C8—611no—
403C2×C4⋊C8—611no—
404C2×#103—611no—
405C2×#103—611no—
406C2×#103C2×D6111yescharacteristic
407C2×#102—611no—
408C2×#102—611no—
409C2×#102—611no—
410C2×#102—611no—
411C2×#102C2×D6111yescharacteristic
412C2×C22⋊C8—611no—
413C2×C22⋊C8C2×D6111yescharacteristic
414C2×#97—611no—
415C2×C4×C8—611no—
416#399—1221no—
417#397—1221no—
418#394—1221no—
419#394—1221no—
420#391—611no—
421#391—611no—
422#390—611no—
423#390—611no—
424#390—611no—
425#390—611no—
426#389—611no—
427#389—611no—
428#386—1221no—
429#386—1221no—
430#380—611no—
431#380—1221no—
432#380—1221no—
433#340—611no—
434#340—611no—
435#340—611no—
436#340—611no—
437C61#2451911yescharacteristic, complemented, Sylow
438C2×#41—22no—
439C2×#41—22no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—41no—
443C2×#41—41no—
444C22×Q8C22×D6111yescharacteristic
445C22×D4—21no—
446C22×D4—21no—
447C22×D4C22×D6111yescharacteristic
448C22×D4C22×D6111yescharacteristic
449C23×C4—21no—
450C23×C4—1221no—
451C23×C4C22×D6111yescharacteristic
452C2×SD16—22no—
453C2×SD16—22no—
454C2×SD16—41no—
455C2×D8—22no—
456C2×D8—22no—
457C2×D8—41no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8C22×D6111yescharacteristic
461C22×C8C22×D6111yescharacteristic
462#121—22no—
463#121—22no—
464#117—1222no—
465#117—1222no—
466C2×C4⋊C4—611no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—2441no—
476C2×C4⋊C4—2441no—
477C2×C4⋊C4C22×D6111yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—611no—
480C2×C22⋊C4—611no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4—1221no—
485C2×C22⋊C4—1221no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C42—611no—
491C2×C42—611no—
492#106—2441no—
493#106—2441no—
494C4⋊C8—1222no—
495C4⋊C8—1222no—
496#103—22no—
497#103—1222no—
498#103—2441no—
499#102—22no—
500#102—1222no—
501#102—2441no—
502#102—2441no—
503#102—2441no—
504C22⋊C8—1222no—
505C22⋊C8C22⋊D6114yes—
506#97—1222no—
507C4×C8—1222no—
508#95—1221no—
509#95—1221no—
510#95—1221no—
511#95—1221no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515C24—21no—
516C24—21no—
517C24D4×D6111yescharacteristic
518#41—44no—
519#41—44no—
520#41—44no—
521#41—44no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8#1175822412yes—
528C2×D4—24no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—81no—
544C2×D4—81no—
545C2×D4#1175822412yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—4881no—
564C22×C4—4881no—
565C22×C4—2442no—
566C22×C4D4×D6111yescharacteristic
567C22×C4#1175822412yes—
568C22×C4C2×C22⋊D6112yes—
569C22×C4C23×D6111yescharacteristic
570SD16—44no—
571D8—44no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8C2×C22⋊D6112yes—
583C2×C8C2×C22⋊D6112yes—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—1222no—
587C4⋊C4—1222no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—4881no—
597C4⋊C4—4881no—
598C4⋊C4—2442no—
599C22⋊C4—42no—
600C22⋊C4—1222no—
601C22⋊C4—1222no—
602C22⋊C4—4881no—
603C22⋊C4—4881no—
604C22⋊C4—4881no—
605C22⋊C4—4881no—
606C22⋊C4—4881no—
607C22⋊C4—4881no—
608C22⋊C4—4881no—
609C22⋊C4—4881no—
610C22⋊C4—4881no—
611C42—1221no—
612C42—1221no—
613C42—1221no—
614C42—1221no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—22no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23#1451974812yes—
636C23C2×D4×D6111yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—41no—
640Q8—41no—
641D4—22no—
642D4—22no—
643D4—48no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—84no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—48no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—4884no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4#1451974812yes—
690C2×C4C22×C22⋊D6111yescharacteristic
691C2×C4C2×#1175822411yescharacteristic
692C2×C4C2×#1175822411yescharacteristic
693C2×C4C2×#1175822411yescharacteristic
694C2×C4#1451982211yescharacteristic
695C2×C4#1451982211yescharacteristic
696C8—22no—
697C8—22no—
698C8—2441no—
699C8—2441no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22C2×#1451974811yescharacteristic
722C22#1684026811yescharacteristic
723C22#1684032711yescharacteristic
724C22#1684056611yescharacteristic
725C22#1684056911yescharacteristic
726C22#1684056911yescharacteristic
727C22#1684057211yescharacteristic
728C4—22no—
729C4—42no—
730C4—81no—
731C4—4881no—
732C4—4881no—
733C4—4881no—
734C4—4881no—
735C4—2441no—
736C4—2441no—
737C4—2441no—
738C4—2441no—
739C4#1684040611yescharacteristic
740C4#1684040611yescharacteristic
741C4#1684044311yescharacteristic
742C4#1684044311yescharacteristic
743C2—42no—
744C2—82no—
745C2—161no—
746C2#2144920011yescharacteristic
747C2#2145547711yescharacteristic
748C2#2145549311yescharacteristic
749C2#2145601911yescharacteristic
750C2#2145609711yescharacteristic
751C2#2145687811yescharacteristic
752C2#2145691111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#449C2
socleC23×C61C22×D4
hypercenterC2×#449D61
hypocenterC61#24519
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#16839820C2semidirect
2. #21451609C2semidirect
3. #21448411C2semidirect
4. #21447198C2semidirect
5. #21447191C2semidirect
6. #21447132C2semidirect
7. #21447127C2semidirect
8. #21446696C2semidirect
9. #21446675C2semidirect
10. #21446506C2semidirect
11. #21446499C2semidirect
12. #21446137C2semidirect
13. #21446014C2semidirect
14. #21445759C2semidirect
437. C61#24519semidirect

Maximal subgroups

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

subgroupindex
C2×#168398202
#214516092
#214484112
#214471982
#214471912
#214471322
#214471272
#214466962
#214466752
#214465062
#214464992
#214461372
#214460142
#214457592
C2×C61×#4492
#2451961