Finite Group Databasebeta

← #29723862

Subgroups — #29723862

Order 15616.

1014 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×#16839907C211yesmaximal, characteristic
2C2×#16839847C211yesmaximal, characteristic, complemented
3#21449313C211yesmaximal, characteristic, complemented
4#21448660C211yesmaximal, characteristic, complemented
5#21447338C211yesmaximal, characteristic, complemented
6#21447255C211yesmaximal, characteristic, complemented
7#21447128C211yesmaximal, characteristic, complemented
8#21447002C211yesmaximal, characteristic, complemented
9#21446504C211yesmaximal, characteristic, complemented
10#21446428C211yesmaximal, characteristic, complemented
11#21446172C211yesmaximal, characteristic, complemented
12#21446164C211yesmaximal, characteristic, complemented
13#21446075C211yesmaximal, characteristic, complemented
14#21445832C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C2×Q8×Dic61C2211yescharacteristic
21C2×#14519739C2211yescharacteristic
22#16839907—24no—
23#16839847—24no—
24C2×#14519711C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29C2×#14519699C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×C8×Dic61C2211yescharacteristic
33#16839689—21no—
34#16839678—21no—
35#16839665—21no—
36#16839665—21no—
37#16839665C2211yescharacteristic
38#16839665C2211yescharacteristic
39#16839663C2211yescharacteristic
40#16839661C2211yescharacteristic
41#16839638—21no—
42#16839627C2211yescharacteristic
43#16839624—21no—
44#16839622—21no—
45#16839622C2211yescharacteristic
46C4×C22⋊Dic61—21no—
47C4×C22⋊Dic61C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×#41×C61C2211yescharacteristic
55C2×#103×C61C2211yescharacteristic
56C2×#103×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C61×#380C2211yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C22×C4×D61—21no—
64C2×#11758201—22no—
65C2×#11758201—22no—
66C2×#11758201D414yes—
67C2×#11758199—22no—
68C2×#11758199—22no—
69C2×#11758199—41no—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519751—22no—
73#14519751—41no—
74Q8×Dic61—22no—
75Q8×Dic61—22no—
76Q8×Dic61—41no—
77Q8×Dic61—41no—
78#14519739—22no—
79#14519739—41no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61—21no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61D411yescharacteristic
92C2×C22⋊Dic61D411yescharacteristic
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61C2311yescharacteristic
100C2×C4×Dic61C2311yescharacteristic
101#14519711—41no—
102#14519708—22no—
103#14519706—41no—
104#14519701—22no—
105#14519699—22no—
106#14519699—41no—
107#14519698—22no—
108C22⋊#92418—22no—
109C8×Dic61—22no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684D411yescharacteristic
115#14519684D411yescharacteristic
116C2×#41×C61—22no—
117C2×#41×C61—22no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—41no—
121C2×#41×C61—41no—
122C22×Q8×C61C2311yescharacteristic
123C22×D4×C61—21no—
124C22×D4×C61C2311yescharacteristic
125C23×C4×C61—21no—
126C23×C4×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C22⋊C4×C61—21no—
132#103×C61—22no—
133#103×C61—22no—
134#102×C61—22no—
135#102×C61—41no—
136C22⋊C8×C61—41no—
137#95×C61—21no—
138C24×C61—21no—
139C24×C61C2×D411yescharacteristic
140C23×D61—21no—
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×C61C2×D412yes—
149C2×Q8×C61#4112yes—
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—42no—
158C2×D4×C61—42no—
159C2×D4×C61#4112yes—
160C22×C4×C61—21no—
161C22×C4×C61—24no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—42no—
171C22×C4×C61—42no—
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2411yescharacteristic
174C2×C22⋊D61—42no—
175C2×C22⋊D61—42no—
176C2×C22⋊D61—81no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61C2×D411yescharacteristic
181C22×Dic61C2×D411yescharacteristic
182C22×Dic61C2×D411yescharacteristic
183C22×Dic61C2×D411yescharacteristic
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244C2×D412yes—
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×C4×D61—81no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C22⋊C4×C61—81no—
204C22⋊Dic61—22no—
205C22⋊Dic61—41no—
206C22⋊Dic61—42no—
207C22⋊Dic61—42no—
208C22⋊Dic61—81no—
209C22⋊Dic61—81no—
210C22⋊Dic61—81no—
211#11758201—28no—
212#11758199—44no—
213#11758198—42no—
214#11758198—42no—
215#11758198—81no—
216#11758198—81no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—42no—
224C4⋊Dic61—42no—
225C4⋊Dic61—81no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61—42no—
231C4×Dic61—42no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418C2×D412yes—
238C23×C61—21no—
239C23×C61—22no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61C22×D411yescharacteristic
253C22×D61—22no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260Q8×C61—22no—
261Q8×C61—22no—
262Q8×C61—22no—
263Q8×C61#12314yes—
264D4×C61—22no—
265D4×C61—22no—
266D4×C61—48no—
267D4×C61—41no—
268D4×C61—41no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—48no—
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×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61C22×D411yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61H(5,𝔽2)11yescharacteristic
291C2×C4×C61H(5,𝔽2)11yescharacteristic
292C22⋊D61—84no—
293C2×Dic61—21no—
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—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61#13512yes—
314D244—22no—
315D244—22no—
316D244—41no—
317D244—41no—
318C4×D61—84no—
319C8×C61—41no—
320C8×C61—41no—
321#92418—22no—
322#92418—41no—
323#24900—611nomaximal, Sylow
324C22×C61—41no—
325C22×C61—42no—
326C22×C61—41no—
327C22×C61—42no—
328C22×C61—42no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—81no—
335C22×C61—81no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61#52511yescharacteristic
339C22×C61D4211yescharacteristic
340C22×C61#54611yescharacteristic
341C22×C61C2×#13511yescharacteristic
342C22×C61#57511yescharacteristic
343C22×C61#57611yescharacteristic
344C22×C61#57711yescharacteristic
345C2×D61—42no—
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—81no—
349C2×D61—81no—
350C2×D61—81no—
351C2×D61—81no—
352C4×C61—24no—
353C4×C61—41no—
354C4×C61—81no—
355C4×C61—81no—
356C4×C61C2×#12311yescharacteristic
357C4×C61#53811yescharacteristic
358C4×C61#54611yescharacteristic
359C4×C61#55111yescharacteristic
360Dic61—22no—
361Dic61—41no—
362Dic61—41no—
363Dic61—41no—
364Dic61—81no—
365Dic61—81no—
366Dic61—81no—
367C2×#449—611no—
368C2×C4×SD16—611no—
369#2420—611no—
370#2341—611no—
371#2092—611no—
372#2077—611no—
373#2054—611no—
374#2033—611no—
375#1934—611no—
376#1923—611no—
377#1880—611no—
378#1879—611no—
379#1863—611no—
380#1805—611no—
381#1788D6111yescharacteristic, complemented
382C2×C61—81no—
383C2×C61—82no—
384C2×C61#241811yescharacteristic
385C2×C61#310211yescharacteristic
386C2×C61#311911yescharacteristic
387C2×C61#326811yescharacteristic
388C2×C61#328211yescharacteristic
389C2×C61#330511yescharacteristic
390C2×C61#332611yescharacteristic
391D61—82no—
392C22×#41C2×D6111yescharacteristic
393C22×SD16—611no—
394C22×D8—611no—
395C2×#121—611no—
396C2×C4×Q8—611no—
397C2×C4×Q8—611no—
398C2×C4×D4—611no—
399#449—1224no—
400C4×SD16—1224no—
401C2×#107—611no—
402C2×#106—611no—
403C2×C4⋊C8—611no—
404C2×#103—611no—
405C2×#103C2×D6111yescharacteristic
406C2×#103C2×D6111yescharacteristic
407C2×#102—611no—
408C2×#102—611no—
409C2×#102—611no—
410C2×#102C2×D6111yescharacteristic
411C2×#102C2×D6111yescharacteristic
412C2×C22⋊C8—611no—
413C2×C22⋊C8C2×D6111yescharacteristic
414C2×C4×C8—611no—
415#397—1221no—
416#394—1221no—
417#390—611no—
418#390—611no—
419#390—611no—
420#390—1221no—
421#390—1221no—
422#389—611no—
423#386—1221no—
424#382—611no—
425#381—1221no—
426#380—611no—
427#380—1221no—
428#380C2×D6111yescharacteristic
429C4×C22⋊C4—611no—
430C4×C22⋊C4—1221no—
431#340—611no—
432#340—611no—
433#340—611no—
434#340—611no—
435#336—611no—
436#336—611no—
437C61#2490011yescharacteristic, 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—611no—
447C22×D4—1221no—
448C22×D4C22×D6111yescharacteristic
449C23×C4—21no—
450C23×C4—1221no—
451C23×C4C22×D6111yescharacteristic
452C2×SD16—614no—
453C2×SD16—1222no—
454C2×SD16—1222no—
455C2×D8—1222no—
456C2×D8—1222no—
457C2×D8—2441no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8C22×D6111yescharacteristic
461C22×C8C22×D6111yescharacteristic
462#121—1222no—
463#121—2441no—
464C4×Q8—1222no—
465C4×Q8—1222no—
466C4×Q8—2441no—
467C4×Q8—2441no—
468C4×D4—1222no—
469C4×D4—2441no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4C22×D6111yescharacteristic
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—
492C2×C42—1221no—
493C2×C42—1221no—
494#107—2441no—
495#106—1222no—
496C4⋊C8—2441no—
497#103—22no—
498#103—22no—
499#103—1222no—
500#102—22no—
501#102—41no—
502#102—1222no—
503#102—1222no—
504#102—2441no—
505C22⋊C8—41no—
506C22⋊C8—1222no—
507C4×C8—1222no—
508#95—21no—
509#95—611no—
510#95—611no—
511#95—1221no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515C24—21no—
516C24—1221no—
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#1175822212yes—
526C2×Q8D4×D6112yes—
527C2×Q8#1175822412yes—
528C2×D4—24no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—612no—
537C2×D4—1221no—
538C2×D4—1221no—
539C2×D4—1221no—
540C2×D4—1221no—
541C2×D4—1221no—
542C2×D4—4881no—
543C2×D4—2442no—
544C2×D4—2442no—
545C2×D4#1175822412yes—
546C22×C4—21no—
547C22×C4—24no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—4881no—
566C22×C4—2442no—
567C22×C4—2442no—
568C22×C4D4×D6111yescharacteristic
569C22×C4C23×D6111yescharacteristic
570SD16—1228no—
571D8—2444no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—612no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—4881no—
595C4⋊C4—2442no—
596C4⋊C4—2442no—
597C22⋊C4—81no—
598C22⋊C4—1222no—
599C22⋊C4—4881no—
600C22⋊C4—4881no—
601C22⋊C4—4881no—
602C22⋊C4—4881no—
603C22⋊C4—4881no—
604C22⋊C4—2442no—
605C22⋊C4—2442no—
606C22⋊C4—2442no—
607C22⋊C4—2441no—
608C22⋊C4—2442no—
609C42—1221no—
610C42—1221no—
611C42—1221no—
612C42—1221no—
613C42—2442no—
614C42—2442no—
615C23—21no—
616C23—22no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—1222no—
630C23—2441no—
631C23—2441no—
632C23—2441no—
633C23—2441no—
634C23—2441no—
635C23—2441no—
636C23C2×D4×D6111yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—22no—
640Q8#1451975914yes—
641D4—22no—
642D4—22no—
643D4—48no—
644D4—41no—
645D4—41no—
646D4—1222no—
647D4—1222no—
648D4—4884no—
649D4—2441no—
650D4—2441no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—48no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—612no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—4884no—
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—2441no—
690C2×C4C2×D4×D6111yescharacteristic
691C2×C4C2×#1175822411yescharacteristic
692C2×C4C2×#1175822411yescharacteristic
693C2×C4C2×#1175822211yescharacteristic
694C2×C4#1451982211yescharacteristic
695C2×C4#1451982211yescharacteristic
696C8—41no—
697C8—41no—
698C8—1222no—
699C8—2441no—
700C22—42no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—42no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—4881no—
715C22—4881no—
716C22—4881no—
717C22—4881no—
718C22—2442no—
719C22—2442no—
720C22—2442no—
721C22#1684026811yescharacteristic
722C22#1684039411yescharacteristic
723C22#1684040211yescharacteristic
724C22#135×D6111yescharacteristic
725C22#1684056111yescharacteristic
726C22#1684056411yescharacteristic
727C22#1684057211yescharacteristic
728C4—24no—
729C4—41no—
730C4—81no—
731C4—81no—
732C4—1222no—
733C4—4881no—
734C4—4881no—
735C4—4881no—
736C4—2441no—
737C4—2441no—
738C4—2441no—
739C4C2×#1451975911yescharacteristic
740C4#1684034711yescharacteristic
741C4#1684039911yescharacteristic
742C4#1684043811yescharacteristic
743C2—81no—
744C2—82no—
745C2—4882no—
746C2#2144928511yescharacteristic
747C2#2145583811yescharacteristic
748C2#2145601111yescharacteristic
749C2#2145736211yescharacteristic
750C2#2145752911yescharacteristic
751C2#2145776511yescharacteristic
752C2#2145807311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1788C2
socleC23×C61C22×D4
prime radicalC2×#16839907C2
hypercenter#1788D61
hypocenterC61#24900
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#16839847C2semidirect
3. #21449313C2semidirect
4. #21448660C2semidirect
5. #21447338C2semidirect
6. #21447255C2semidirect
7. #21447128C2semidirect
8. #21447002C2semidirect
9. #21446504C2semidirect
10. #21446428C2semidirect
11. #21446172C2semidirect
12. #21446164C2semidirect
13. #21446075C2semidirect
14. #21445832C2semidirect
15. C61×#1788C2semidirect
381. #1788D61semidirect
437. C61#24900semidirect

Maximal subgroups

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

subgroupindex
C2×#168399072
C2×#168398472
#214493132
#214486602
#214473382
#214472552
#214471282
#214470022
#214465042
#214464282
#214461722
#214461642
#214460752
#214458322
C61×#17882
#2490061