Finite Group Databasebeta

← C61×#25564 #29528997

Subgroups — C61×#25564 #29528997

Order 15616.

1250 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3491C211yesmaximal, characteristic, complemented
2C61×#2482C211yesmaximal, characteristic, complemented
3C61×#2411C212yesmaximal, complemented
4C61×#2062C211yesmaximal, characteristic, complemented
5C61×#2044C211yesmaximal, characteristic, complemented
6C61×#2029C211yesmaximal, characteristic, complemented
7C61×#2021C211yesmaximal, characteristic
8C61×#1899C212yesmaximal, complemented
9C61×#1889C212yesmaximal, complemented
10C61×#1867C212yesmaximal, complemented
11C61×#1740C211yesmaximal, characteristic, complemented
12C61×#552—22no—
13C61×#552—22no—
14C61×#551—22no—
15C61×#551—22no—
16C61×#543C2211yescharacteristic
17C61×#539—21no—
18C61×#539—21no—
19C61×#534C2211yescharacteristic
20C61×#529—21no—
21C61×#529—21no—
22C2×#123×C61C2212yes—
23C2×#120×C61C2212yes—
24C61×#518C2212yes—
25C2×#117×C61C2212yes—
26C2×#117×C61C2211yescharacteristic
27C22×C22⋊C4×C61C2211yescharacteristic
28C2×#99×C61C2212yes—
29C2×#99×C61C2212yes—
30C61×#399—21no—
31C61×#397—21no—
32C61×#396—22no—
33C61×#394—22no—
34C61×#390—22no—
35C61×#388—22no—
36C61×#388—21no—
37C61×#388—21no—
38C61×#386C2212yes—
39C61×#385C2211yescharacteristic
40C61×#385C2212yes—
41C61×#385C2211yescharacteristic
42C61×#381C2211yescharacteristic
43C61×#379C2211yescharacteristic
44C61×#379C2212yes—
45C61×#379C2211yescharacteristic
46C61×#342C2211yescharacteristic
47C61×#342C2211yescharacteristic
48C61×#342C2212yes—
49C61×#342C2212yes—
50C61×#342C2212yes—
51C25×C61C2311yescharacteristic
52C22×D4×C61—22no—
53C22×D4×C61C2312yes—
54C23×C4×C61C2311yescharacteristic
55C23×C4×C61C2311yescharacteristic
56#126×C61—22no—
57#126×C61—22no—
58#126×C61—22no—
59#126×C61—22no—
60#125×C61—22no—
61#125×C61—22no—
62#125×C61—21no—
63#125×C61—21no—
64#124×C61—21no—
65#124×C61—21no—
66#123×C61—22no—
67#123×C61—22no—
68#123×C61—22no—
69#123×C61—22no—
70#123×C61—22no—
71#123×C61—22no—
72#123×C61—22no—
73C22⋊Q8×C61—22no—
74C22⋊Q8×C61—22no—
75C22⋊Q8×C61—21no—
76C22⋊Q8×C61—21no—
77C22⋊Q8×C61—22no—
78C22⋊Q8×C61—22no—
79#121×C61—21no—
80#121×C61—21no—
81#120×C61—22no—
82#120×C61—24no—
83#120×C61—42no—
84C4×Q8×C61—21no—
85C4×Q8×C61—21no—
86C4×D4×C61—21no—
87C4×D4×C61—21no—
88C4×D4×C61—22no—
89C4×D4×C61—22no—
90C4×D4×C61—22no—
91C4×D4×C61—22no—
92#117×C61—22no—
93#117×C61—22no—
94#117×C61—22no—
95#117×C61—22no—
96#117×C61—22no—
97#117×C61—24no—
98#117×C61—42no—
99C2×C4⋊C4×C61—22no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61—22no—
103C2×C4⋊C4×C61D411yescharacteristic, complemented
104C2×C4⋊C4×C61D411yescharacteristic, complemented
105C2×C4⋊C4×C61D412yescomplemented
106C2×C4⋊C4×C61D412yescomplemented
107C2×C22⋊C4×C61—22no—
108C2×C22⋊C4×C61—22no—
109C2×C22⋊C4×C61—21no—
110C2×C22⋊C4×C61—21no—
111C2×C22⋊C4×C61—21no—
112C2×C22⋊C4×C61—22no—
113C2×C22⋊C4×C61—22no—
114C2×C22⋊C4×C61—22no—
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61—22no—
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—22no—
120C2×C22⋊C4×C61D412yescomplemented
121C2×C22⋊C4×C61D412yescomplemented
122C2×C22⋊C4×C61C2312yes—
123C2×C22⋊C4×C61C2311yescharacteristic
124C2×C22⋊C4×C61C2311yescharacteristic
125C2×C22⋊C4×C61C2311yescharacteristic
126C2×C22⋊C4×C61C2312yes—
127C2×C22⋊C4×C61C2311yescharacteristic
128C2×C22⋊C4×C61C2312yes—
129C2×C42×C61—22no—
130C2×C42×C61D411yescharacteristic, complemented
131C2×C42×C61D411yescharacteristic, complemented
132#99×C61—24no—
133#99×C61—42no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61—22no—
137#95×C61—21no—
138#95×C61—21no—
139#95×C61—22no—
140C24×C61—21no—
141C24×C61—22no—
142C24×C61—22no—
143C24×C61—21no—
144C24×C61—21no—
145C24×C61—42no—
146C24×C61—81no—
147C24×C61C2×D412yes—
148C24×C61C2411yescharacteristic
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×D4×C61—22no—
152C2×D4×C61—22no—
153C2×D4×C61—22no—
154C2×D4×C61—22no—
155C2×D4×C61—22no—
156C2×D4×C61—22no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—44no—
160C2×D4×C61—44no—
161C2×D4×C61—82no—
162C22×C4×C61—22no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—22no—
166C22×C4×C61—22no—
167C22×C4×C61—22no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—22no—
171C22×C4×C61—21no—
172C22×C4×C61—22no—
173C22×C4×C61—81no—
174C22×C4×C61C2×D412yes—
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D412yes—
178C22×C4×C61C2×D412yes—
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D412yes—
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D412yes—
185C4⋊C4×C61—22no—
186C4⋊C4×C61—22no—
187C4⋊C4×C61—22no—
188C4⋊C4×C61—22no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—22no—
194C4⋊C4×C61—22no—
195C4⋊C4×C61—22no—
196C4⋊C4×C61—22no—
197C4⋊C4×C61—22no—
198C4⋊C4×C61—22no—
199C4⋊C4×C61—44no—
200C4⋊C4×C61—82no—
201C4⋊C4×C61—81no—
202C4⋊C4×C61—81no—
203C22⋊C4×C61—22no—
204C22⋊C4×C61—22no—
205C22⋊C4×C61—22no—
206C22⋊C4×C61—22no—
207C22⋊C4×C61—22no—
208C22⋊C4×C61—22no—
209C22⋊C4×C61—22no—
210C22⋊C4×C61—22no—
211C22⋊C4×C61—22no—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—22no—
214C22⋊C4×C61—22no—
215C22⋊C4×C61—22no—
216C22⋊C4×C61—22no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—21no—
219C22⋊C4×C61—22no—
220C22⋊C4×C61—21no—
221C22⋊C4×C61—44no—
222C22⋊C4×C61—42no—
223C22⋊C4×C61—42no—
224C22⋊C4×C61—44no—
225C22⋊C4×C61—41no—
226C22⋊C4×C61—41no—
227C22⋊C4×C61—42no—
228C22⋊C4×C61—82no—
229C22⋊C4×C61—81no—
230C22⋊C4×C61—81no—
231C22⋊C4×C61—82no—
232C22⋊C4×C61#4114yes—
233C42×C61—22no—
234C42×C61—22no—
235C42×C61—21no—
236C42×C61—21no—
237C42×C61—21no—
238C42×C61—21no—
239C42×C61—44no—
240C23×C61—22no—
241C23×C61—24no—
242C23×C61—22no—
243C23×C61—22no—
244C23×C61—22no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—42no—
250C23×C61—42no—
251C23×C61—41no—
252C23×C61—42no—
253C23×C61—42no—
254C23×C61—42no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—42no—
259C23×C61—42no—
260C23×C61—84no—
261C23×C61—82no—
262C23×C61—82no—
263C23×C61C22×D411yescharacteristic
264C23×C61C22×D412yes—
265C23×C61C2×#4112yes—
266C23×C61H(5,𝔽2)11yescharacteristic
267C23×C612−1+411yescharacteristic
268Q8×C61—81no—
269Q8×C61—81no—
270D4×C61—42no—
271D4×C61—42no—
272D4×C61—42no—
273D4×C61—42no—
274D4×C61—81no—
275D4×C61—81no—
276D4×C61—88no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—24no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—41no—
298C2×C4×C61—42no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—42no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—42no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—42no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—42no—
317C2×C4×C61—82no—
318C2×C4×C61—82no—
319C2×C4×C61#12011yescharacteristic
320C2×C4×C61#12011yescharacteristic
321C2×C4×C61#12012yes—
322#25564C6111yesmaximal, characteristic, direct product factor, Sylow
323C22×C61—21no—
324C22×C61—22no—
325C22×C61—21no—
326C22×C61—22no—
327C22×C61—42no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—44no—
331C22×C61—42no—
332C22×C61—42no—
333C22×C61—44no—
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—42no—
338C22×C61—82no—
339C22×C61—82no—
340C22×C61—82no—
341C22×C61—81no—
342C22×C61—81no—
343C22×C61—82no—
344C22×C61—81no—
345C22×C61—81no—
346C22×C61C2×#12011yescharacteristic
347C22×C61#53211yescharacteristic
348C22×C61#53711yescharacteristic
349C22×C61#54612yes—
350C22×C61#54712yes—
351C4×C61—21no—
352C4×C61—22no—
353C4×C61—21no—
354C4×C61—44no—
355C4×C61—42no—
356C4×C61—41no—
357C4×C61—42no—
358C4×C61—41no—
359C4×C61—41no—
360C4×C61—42no—
361C4×C61—41no—
362C4×C61—82no—
363C4×C61—81no—
364C4×C61—81no—
365C4×C61—81no—
366#3491C2×C6111yescharacteristic, complemented
367#2482C2×C6111yescharacteristic, complemented
368#2411C2×C6112yescomplemented
369#2062C2×C6111yescharacteristic, complemented
370#2044C2×C6111yescharacteristic, complemented
371#2029C2×C6111yescharacteristic, complemented
372#2021C2×C6111yescharacteristic
373#1899C2×C6112yescomplemented
374#1889C2×C6112yescomplemented
375#1867C2×C6112yescomplemented
376#1740C2×C6111yescharacteristic, complemented
377C2×C61—22no—
378C2×C61—21no—
379C2×C61—21no—
380C2×C61—22no—
381C2×C61—82no—
382C2×C61—82no—
383C2×C61#243011yescharacteristic
384C2×C61#302511yescharacteristic
385C2×C61#302711yescharacteristic
386#552—22no—
387#552—22no—
388#551—22no—
389#551—22no—
390#543C22×C6111yescharacteristic
391#539—21no—
392#539—21no—
393#534C22×C6111yescharacteristic
394#529—21no—
395#529—21no—
396C2×#123C22×C6112yes—
397C2×#120C22×C6112yes—
398#518C22×C6112yes—
399C2×#117C22×C6112yes—
400C2×#117C22×C6111yescharacteristic
401C22×C22⋊C4C22×C6111yescharacteristic
402C2×#99C22×C6112yes—
403C2×#99C22×C6112yes—
404#399—21no—
405#397—21no—
406#396—22no—
407#394—22no—
408#390—22no—
409#388—22no—
410#388—21no—
411#388—21no—
412#386C22×C6112yes—
413#385C22×C6112yes—
414#385C22×C6111yescharacteristic
415#385C22×C6111yescharacteristic
416#381C22×C6111yescharacteristic
417#379C22×C6111yescharacteristic
418#379C22×C6112yes—
419#379C22×C6111yescharacteristic
420#342C22×C6112yes—
421#342C22×C6111yescharacteristic
422#342C22×C6112yes—
423#342C22×C6112yes—
424#342C22×C6111yescharacteristic
425C61#2556411yescharacteristic, direct product factor, Sylow
426C25C23×C6111yescharacteristic
427C22×D4—22no—
428C22×D4C23×C6112yes—
429C23×C4C23×C6111yescharacteristic
430C23×C4C23×C6111yescharacteristic
431#126—22no—
432#126—22no—
433#126—22no—
434#126—22no—
435#125—21no—
436#125—21no—
437#125—22no—
438#125—22no—
439#124—21no—
440#124—21no—
441#123—22no—
442#123—22no—
443#123—22no—
444#123—22no—
445#123—22no—
446#123—22no—
447#123—22no—
448C22⋊Q8—22no—
449C22⋊Q8—22no—
450C22⋊Q8—21no—
451C22⋊Q8—21no—
452C22⋊Q8—22no—
453C22⋊Q8—22no—
454#121—21no—
455#121—21no—
456#120—22no—
457#120—24no—
458#120—42no—
459C4×Q8—21no—
460C4×Q8—21no—
461C4×D4—21no—
462C4×D4—21no—
463C4×D4—22no—
464C4×D4—22no—
465C4×D4—22no—
466C4×D4—22no—
467#117—22no—
468#117—22no—
469#117—22no—
470#117—22no—
471#117—22no—
472#117—24no—
473#117—42no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4D4×C6111yescharacteristic, complemented
479C2×C4⋊C4D4×C6111yescharacteristic, complemented
480C2×C4⋊C4D4×C6112yescomplemented
481C2×C4⋊C4D4×C6112yescomplemented
482C2×C22⋊C4—22no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4D4×C6112yescomplemented
496C2×C22⋊C4D4×C6112yescomplemented
497C2×C22⋊C4C23×C6112yes—
498C2×C22⋊C4C23×C6111yescharacteristic
499C2×C22⋊C4C23×C6111yescharacteristic
500C2×C22⋊C4C23×C6111yescharacteristic
501C2×C22⋊C4C23×C6111yescharacteristic
502C2×C22⋊C4C23×C6112yes—
503C2×C22⋊C4C23×C6112yes—
504C2×C42—22no—
505C2×C42D4×C6111yescharacteristic, complemented
506C2×C42D4×C6111yescharacteristic, complemented
507#99—24no—
508#99—42no—
509#95—21no—
510#95—21no—
511#95—22no—
512#95—21no—
513#95—21no—
514#95—22no—
515C24—21no—
516C24—22no—
517C24—22no—
518C24—21no—
519C24—21no—
520C24—42no—
521C24—81no—
522C24C2×D4×C6112yes—
523C24C24×C6111yescharacteristic
524C2×Q8—21no—
525C2×Q8—21no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—82no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—81no—
549C22×C4C2×D4×C6112yes—
550C22×C4C2×D4×C6111yescharacteristic
551C22×C4C2×D4×C6111yescharacteristic
552C22×C4C2×D4×C6112yes—
553C22×C4C2×D4×C6112yes—
554C22×C4C2×D4×C6111yescharacteristic
555C22×C4C2×D4×C6111yescharacteristic
556C22×C4C2×D4×C6112yes—
557C22×C4C2×D4×C6111yescharacteristic
558C22×C4C2×D4×C6111yescharacteristic
559C22×C4C2×D4×C6112yes—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—44no—
575C4⋊C4—82no—
576C4⋊C4—81no—
577C4⋊C4—81no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—22no—
593C22⋊C4—21no—
594C22⋊C4—22no—
595C22⋊C4—21no—
596C22⋊C4—44no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—44no—
600C22⋊C4—41no—
601C22⋊C4—41no—
602C22⋊C4—42no—
603C22⋊C4—82no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—82no—
607C22⋊C4#41×C6114yes—
608C42—22no—
609C42—22no—
610C42—21no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—44no—
615C23—22no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—42no—
625C23—42no—
626C23—41no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—41no—
631C23—41no—
632C23—42no—
633C23—42no—
634C23—41no—
635C23—84no—
636C23—82no—
637C23—82no—
638C23C22×D4×C6111yescharacteristic
639C23C22×D4×C6112yes—
640C23C2×#41×C6112yes—
641C23H(5,𝔽2)×C6111yescharacteristic
642C232−1+4×C6111yescharacteristic
643Q8—81no—
644Q8—81no—
645D4—42no—
646D4—42no—
647D4—42no—
648D4—42no—
649D4—81no—
650D4—81no—
651D4—88no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—82no—
693C2×C4—82no—
694C2×C4#120×C6111yescharacteristic
695C2×C4#120×C6111yescharacteristic
696C2×C4#120×C6112yes—
697C22—21no—
698C22—22no—
699C22—21no—
700C22—22no—
701C22—42no—
702C22—41no—
703C22—41no—
704C22—44no—
705C22—42no—
706C22—42no—
707C22—44no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—82no—
713C22—82no—
714C22—82no—
715C22—81no—
716C22—81no—
717C22—82no—
718C22—81no—
719C22—81no—
720C22C2×#120×C6111yescharacteristic
721C22C61×#53211yescharacteristic
722C22C61×#53711yescharacteristic
723C22C61×#54612yes—
724C22C61×#54712yes—
725C4—21no—
726C4—22no—
727C4—21no—
728C4—44no—
729C4—42no—
730C4—41no—
731C4—42no—
732C4—41no—
733C4—41no—
734C4—42no—
735C4—41no—
736C4—82no—
737C4—81no—
738C4—81no—
739C4—81no—
740C2—22no—
741C2—21no—
742C2—21no—
743C2—22no—
744C2—82no—
745C2—82no—
746C2C61×#243011yescharacteristic
747C2C61×#302511yescharacteristic
748C2C61×#302711yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC24C24×C61
prime radicalC61×#2021C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3491C2semidirect
2. C61×#2482C2semidirect
3. C61×#2411C2semidirect
4. C61×#2062C2semidirect
5. C61×#2044C2semidirect
6. C61×#2029C2semidirect
8. C61×#1899C2semidirect
9. C61×#1889C2semidirect
10. C61×#1867C2semidirect
11. C61×#1740C2semidirect
103. C2×C4⋊C4×C61D4semidirect
104. C2×C4⋊C4×C61D4semidirect
105. C2×C4⋊C4×C61D4semidirect
106. C2×C4⋊C4×C61D4semidirect
120. C2×C22⋊C4×C61D4semidirect
121. C2×C22⋊C4×C61D4semidirect
130. C2×C42×C61D4semidirect
131. C2×C42×C61D4semidirect
322. #25564C61direct (N × H)
366. #3491C2×C61semidirect
367. #2482C2×C61semidirect
368. #2411C2×C61semidirect
369. #2062C2×C61semidirect
370. #2044C2×C61semidirect
371. #2029C2×C61semidirect
373. #1899C2×C61semidirect
374. #1889C2×C61semidirect
375. #1867C2×C61semidirect
376. #1740C2×C61semidirect
425. C61#25564direct (N × H)
478. C2×C4⋊C4D4×C61semidirect
479. C2×C4⋊C4D4×C61semidirect
480. C2×C4⋊C4D4×C61semidirect
481. C2×C4⋊C4D4×C61semidirect
495. C2×C22⋊C4D4×C61semidirect
496. C2×C22⋊C4D4×C61semidirect
505. C2×C42D4×C61semidirect
506. C2×C42D4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#34912
C61×#24822
C61×#24112
C61×#20622
C61×#20442
C61×#20292
C61×#20212
C61×#18992
C61×#18892
C61×#18672
C61×#17402
#2556461