Finite Group Databasebeta

← C61×#24325 #29527758

Subgroups — C61×#24325 #29527758

Order 15616.

960 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3504C211yesmaximal, characteristic
2C61×#3078C211yesmaximal, characteristic, complemented
3C4×#137×C61C211yesmaximal, characteristic
4C61×#2565C211yesmaximal, characteristic, complemented
5C61×#2061C211yesmaximal, characteristic, complemented
6C61×#2060C211yesmaximal, characteristic, complemented
7C61×#2028C211yesmaximal, characteristic, complemented
8C61×#2028C211yesmaximal, characteristic, complemented
9C61×#1998C211yesmaximal, characteristic, complemented
10C61×#1986C211yesmaximal, characteristic, complemented
11C61×#1882C211yesmaximal, characteristic
12C61×#1882C211yesmaximal, characteristic
13C61×#1860C211yesmaximal, characteristic
14C61×#1859C211yesmaximal, characteristic
15C61×#1806C211yesmaximal, characteristic
16C2×#137×C61C2211yescharacteristic
17C61×#557—21no—
18C61×#557—21no—
19C61×#554—21no—
20C61×#554—21no—
21C61×#554—22no—
22C61×#554—22no—
23C61×#544—21no—
24C61×#544—21no—
25C61×#544C2211yescharacteristic
26C61×#544C2211yescharacteristic
27C61×#533—21no—
28C61×#533C2211yescharacteristic
29C2×#125×C61—21no—
30C2×#125×C61C2211yescharacteristic
31C61×#520C2211yescharacteristic
32C61×#520C2211yescharacteristic
33C4×#41×C61C2211yescharacteristic
34C2×C4×Q8×C61C2211yescharacteristic
35C61×#479—21no—
36C61×#479—21no—
37C61×#477—21no—
38C61×#475—21no—
39C61×#441—21no—
40C61×#440—21no—
41C4×Q16×C61—21no—
42C4×SD16×C61—21no—
43C61×#428C2211yescharacteristic
44C61×#428C2211yescharacteristic
45C61×#428C2211yescharacteristic
46C61×#423C2211yescharacteristic
47C2×#104×C61C2211yescharacteristic
48C2×#104×C61C2211yescharacteristic
49C61×#419C2211yescharacteristic
50C61×#419C2211yescharacteristic
51C61×#419C2211yescharacteristic
52C61×#417C2211yescharacteristic
53C4×M16×C61C2211yescharacteristic
54C61×#398—22no—
55C61×#391C2211yescharacteristic
56C61×#391C2211yescharacteristic
57C61×#387—22no—
58C61×#384C2211yescharacteristic
59C61×#382C2211yescharacteristic
60C4×C4⋊C4×C61C2211yescharacteristic
61C61×#343C2211yescharacteristic
62C61×#343C2211yescharacteristic
63C61×#343C2211yescharacteristic
64C61×#343C2211yescharacteristic
65C61×#339C2211yescharacteristic
66C61×#339C2211yescharacteristic
67C61×#339C2211yescharacteristic
68C61×#339C2211yescharacteristic
69C61×#339C2211yescharacteristic
70C61×#339C2211yescharacteristic
71C2×#41×C61C2311yescharacteristic
72C22×Q8×C61C2311yescharacteristic
73#137×C61—22no—
74#137×C61Q814yescomplemented
75C2×Q16×C61—21no—
76C2×SD16×C61—21no—
77C2×M16×C61C2311yescharacteristic
78C2×M16×C61C2311yescharacteristic
79C2×M16×C61C2311yescharacteristic
80C2×M16×C61C2311yescharacteristic
81C4⋊Q8×C61—22no—
82C4⋊Q8×C61—22no—
83C4⋊Q8×C61—21no—
84C4⋊Q8×C61—21no—
85C4⋊Q8×C61—21no—
86C4⋊Q8×C61—21no—
87C4⋊Q8×C61D411yescharacteristic
88C4⋊Q8×C61D411yescharacteristic
89#125×C61—22no—
90#125×C61—22no—
91#125×C61—22no—
92#125×C61—22no—
93#125×C61—21no—
94#125×C61—21no—
95#125×C61—21no—
96#125×C61—21no—
97#125×C61—21no—
98#125×C61—21no—
99#125×C61—21no—
100#125×C61—21no—
101#125×C61D411yescharacteristic
102#125×C61D411yescharacteristic
103C22⋊Q8×C61—22no—
104C22⋊Q8×C61—22no—
105C22⋊Q8×C61—22no—
106C22⋊Q8×C61—22no—
107C22⋊Q8×C61—22no—
108C22⋊Q8×C61—22no—
109C22⋊Q8×C61—21no—
110C22⋊Q8×C61—21no—
111C22⋊Q8×C61—22no—
112C22⋊Q8×C61—22no—
113C4×Q8×C61—22no—
114C4×Q8×C61—22no—
115C4×Q8×C61—21no—
116C4×Q8×C61—21no—
117C4×Q8×C61—21no—
118C4×Q8×C61—21no—
119C4×Q8×C61—21no—
120C4×Q8×C61—21no—
121C4×Q8×C61—21no—
122C4×Q8×C61—21no—
123C4×Q8×C61D411yescharacteristic
124C4×Q8×C61D411yescharacteristic
125C4×D4×C61—21no—
126C4×D4×C61—21no—
127C4×D4×C61—21no—
128C4×D4×C61—21no—
129C4×D4×C61—22no—
130C4×D4×C61—22no—
131C4×D4×C61D411yescharacteristic
132C4×D4×C61D411yescharacteristic
133#117×C61—21no—
134#117×C61—21no—
135#117×C61—21no—
136#117×C61C2311yescharacteristic
137#117×C61C2311yescharacteristic
138#117×C61C2311yescharacteristic
139C2×C4⋊C4×C61—22no—
140C2×C4⋊C4×C61—22no—
141C2×C4⋊C4×C61—21no—
142C2×C4⋊C4×C61—21no—
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61—22no—
145C2×C4⋊C4×C61—21no—
146C2×C4⋊C4×C61D412yes—
147C2×C4⋊C4×C61D412yes—
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C42×C61—21no—
152C2×C42×C61—21no—
153C2×C42×C61C2311yescharacteristic
154C2×C42×C61C2311yescharacteristic
155C2×C42×C61C2311yescharacteristic
156#107×C61—21no—
157#107×C61—21no—
158#107×C61—21no—
159#106×C61—21no—
160#106×C61—21no—
161#106×C61—21no—
162C4⋊C8×C61—21no—
163C4⋊C8×C61—21no—
164#104×C61—22no—
165#104×C61—22no—
166#103×C61—21no—
167#103×C61—21no—
168#103×C61—21no—
169#103×C61—21no—
170#103×C61—21no—
171#103×C61—21no—
172#103×C61—21no—
173#102×C61—21no—
174#97×C61—21no—
175C4×C8×C61—21no—
176#95×C61—21no—
177#95×C61—22no—
178#95×C61—22no—
179#95×C61—22no—
180#41×C61—21no—
181#41×C61—21no—
182#41×C61C2×Q812yes—
183#41×C61#4112yes—
184C2×Q8×C61—22no—
185C2×Q8×C61—22no—
186C2×Q8×C61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61—21no—
191C2×Q8×C61—21no—
192C2×Q8×C61—21no—
193C2×Q8×C61C2×D411yescharacteristic
194C2×Q8×C61C2×Q812yes—
195C2×D4×C61—21no—
196C2×D4×C61C2×D411yescharacteristic
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—22no—
201C22×C4×C61—22no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61C2×D412yes—
207C22×C4×C61C2×D412yes—
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2411yescharacteristic
211Q16×C61—24no—
212SD16×C61—24no—
213M16×C61—21no—
214M16×C61—21no—
215M16×C61—21no—
216M16×C61—21no—
217M16×C61—21no—
218M16×C61—21no—
219M16×C61—21no—
220M16×C61C2×Q812yes—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C4⋊C4×C61—22no—
226C4⋊C4×C61—22no—
227C4⋊C4×C61—22no—
228C4⋊C4×C61—22no—
229C4⋊C4×C61—22no—
230C4⋊C4×C61—22no—
231C4⋊C4×C61—22no—
232C4⋊C4×C61—22no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—22no—
236C4⋊C4×C61—22no—
237C4⋊C4×C61—22no—
238C4⋊C4×C61—22no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—42no—
252C4⋊C4×C61—44no—
253C4⋊C4×C61—41no—
254C4⋊C4×C61—41no—
255C4⋊C4×C61C2×D411yescharacteristic
256C4⋊C4×C61C2×D411yescharacteristic
257C4⋊C4×C61C2×D411yescharacteristic
258C4⋊C4×C61C2×D411yescharacteristic
259C4⋊C4×C61C2×D411yescharacteristic
260C4⋊C4×C61C2×D411yescharacteristic
261C22⋊C4×C61—22no—
262C22⋊C4×C61—22no—
263C22⋊C4×C61—21no—
264C22⋊C4×C61—21no—
265C22⋊C4×C61—21no—
266C22⋊C4×C61—21no—
267C22⋊C4×C61—21no—
268C42×C61—22no—
269C42×C61—22no—
270C42×C61—21no—
271C42×C61—21no—
272C42×C61—21no—
273C42×C61—21no—
274C42×C61—21no—
275C42×C61—21no—
276C42×C61—21no—
277C42×C61—21no—
278C42×C61—21no—
279C42×C61—41no—
280C42×C61—41no—
281C42×C61C2×D411yescharacteristic
282C42×C61C2×D411yescharacteristic
283C42×C61C2×D411yescharacteristic
284C42×C61C2×D411yescharacteristic
285C23×C61—21no—
286C23×C61C22×D411yescharacteristic
287Q8×C61—21no—
288Q8×C61—22no—
289Q8×C61—22no—
290Q8×C61—41no—
291Q8×C61—41no—
292Q8×C61—81no—
293Q8×C61—81no—
294Q8×C61—82no—
295Q8×C61—82no—
296Q8×C61C22⋊Q812yes—
297D4×C61—22no—
298D4×C61—22no—
299D4×C61—21no—
300D4×C61C22⋊Q812yes—
301C2×C4×C61—21no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—22no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61—41no—
323C2×C4×C61—42no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—81no—
328C2×C4×C61—81no—
329C2×C4×C61—82no—
330C2×C4×C61—82no—
331C2×C4×C61#12011yescharacteristic
332C2×C4×C61#12011yescharacteristic
333C2×C4×C61#12011yescharacteristic
334C2×C4×C61#12011yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C22×Q811yescharacteristic
338C2×C4×C61C2×#4111yescharacteristic
339C2×C4×C612−1+411yescharacteristic
340C2×C4×C612−1+411yescharacteristic
341C8×C61—22no—
342C8×C61—41no—
343C8×C61—41no—
344C8×C61—41no—
345#24325C6111yesmaximal, characteristic, direct product factor, Sylow
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—22no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61C2×#12011yescharacteristic
352C22×C61#54811yescharacteristic
353C22×C61D4×Q811yescharacteristic
354C4×C61—22no—
355C4×C61—21no—
356C4×C61—21no—
357C4×C61—21no—
358C4×C61—21no—
359C4×C61—42no—
360C4×C61—42no—
361C4×C61—42no—
362C4×C61—41no—
363C4×C61—41no—
364C4×C61—41no—
365C4×C61—42no—
366C4×C61—41no—
367C4×C61—41no—
368C4×C61—41no—
369C4×C61—81no—
370C4×C61—81no—
371C4×C61C2×C22⋊Q811yescharacteristic
372C4×C61#53611yescharacteristic
373C4×C61#54811yescharacteristic
374C4×C61D4×Q811yescharacteristic
375#3504C2×C6111yescharacteristic
376#3078C2×C6111yescharacteristic, complemented
377C4×#137C2×C6111yescharacteristic
378#2565C2×C6111yescharacteristic, complemented
379#2061C2×C6111yescharacteristic, complemented
380#2060C2×C6111yescharacteristic, complemented
381#2028C2×C6111yescharacteristic, complemented
382#2028C2×C6111yescharacteristic, complemented
383#1998C2×C6111yescharacteristic, complemented
384#1986C2×C6111yescharacteristic, complemented
385#1882C2×C6111yescharacteristic
386#1882C2×C6111yescharacteristic
387#1860C2×C6111yescharacteristic
388#1859C2×C6111yescharacteristic
389#1806C2×C6111yescharacteristic
390C2×C61—21no—
391C2×C61—21no—
392C2×C61—42no—
393C2×C61#240911yescharacteristic
394C2×C61#301811yescharacteristic
395C2×C61#302211yescharacteristic
396C2×#137C22×C6111yescharacteristic
397#557—21no—
398#557—21no—
399#554—21no—
400#554—21no—
401#554—22no—
402#554—22no—
403#544—21no—
404#544—21no—
405#544C22×C6111yescharacteristic
406#544C22×C6111yescharacteristic
407#533—21no—
408#533C22×C6111yescharacteristic
409C2×#125—21no—
410C2×#125C22×C6111yescharacteristic
411#520C22×C6111yescharacteristic
412#520C22×C6111yescharacteristic
413C4×#41C22×C6111yescharacteristic
414C2×C4×Q8C22×C6111yescharacteristic
415#479—21no—
416#479—21no—
417#477—21no—
418#475—21no—
419#441—21no—
420#440—21no—
421C4×Q16—21no—
422C4×SD16—21no—
423#428C22×C6111yescharacteristic
424#428C22×C6111yescharacteristic
425#428C22×C6111yescharacteristic
426#423C22×C6111yescharacteristic
427C2×#104C22×C6111yescharacteristic
428C2×#104C22×C6111yescharacteristic
429#419C22×C6111yescharacteristic
430#419C22×C6111yescharacteristic
431#419C22×C6111yescharacteristic
432#417C22×C6111yescharacteristic
433C4×M16C22×C6111yescharacteristic
434#398—22no—
435#391C22×C6111yescharacteristic
436#391C22×C6111yescharacteristic
437#387—22no—
438#384C22×C6111yescharacteristic
439#382C22×C6111yescharacteristic
440C4×C4⋊C4C22×C6111yescharacteristic
441#343C22×C6111yescharacteristic
442#343C22×C6111yescharacteristic
443#343C22×C6111yescharacteristic
444#343C22×C6111yescharacteristic
445#339C22×C6111yescharacteristic
446#339C22×C6111yescharacteristic
447#339C22×C6111yescharacteristic
448#339C22×C6111yescharacteristic
449#339C22×C6111yescharacteristic
450#339C22×C6111yescharacteristic
451C61#2432511yescharacteristic, direct product factor, Sylow
452C2×#41C23×C6111yescharacteristic
453C22×Q8C23×C6111yescharacteristic
454#137—22no—
455#137Q8×C6114yescomplemented
456C2×Q16—21no—
457C2×SD16—21no—
458C2×M16C23×C6111yescharacteristic
459C2×M16C23×C6111yescharacteristic
460C2×M16C23×C6111yescharacteristic
461C2×M16C23×C6111yescharacteristic
462C4⋊Q8—22no—
463C4⋊Q8—22no—
464C4⋊Q8—21no—
465C4⋊Q8—21no—
466C4⋊Q8—21no—
467C4⋊Q8—21no—
468C4⋊Q8D4×C6111yescharacteristic
469C4⋊Q8D4×C6111yescharacteristic
470#125—22no—
471#125—22no—
472#125—22no—
473#125—22no—
474#125—21no—
475#125—21no—
476#125—21no—
477#125—21no—
478#125—21no—
479#125—21no—
480#125—21no—
481#125—21no—
482#125D4×C6111yescharacteristic
483#125D4×C6111yescharacteristic
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—22no—
489C22⋊Q8—22no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×Q8—21no—
497C4×Q8—21no—
498C4×Q8—21no—
499C4×Q8—21no—
500C4×Q8—21no—
501C4×Q8—21no—
502C4×Q8—21no—
503C4×Q8—21no—
504C4×Q8D4×C6111yescharacteristic
505C4×Q8D4×C6111yescharacteristic
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4D4×C6111yescharacteristic
513C4×D4D4×C6111yescharacteristic
514#117—21no—
515#117—21no—
516#117—21no—
517#117C23×C6111yescharacteristic
518#117C23×C6111yescharacteristic
519#117C23×C6111yescharacteristic
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4D4×C6112yes—
528C2×C4⋊C4D4×C6112yes—
529C2×C4⋊C4C23×C6111yescharacteristic
530C2×C4⋊C4C23×C6111yescharacteristic
531C2×C4⋊C4C23×C6111yescharacteristic
532C2×C42—21no—
533C2×C42—21no—
534C2×C42C23×C6111yescharacteristic
535C2×C42C23×C6111yescharacteristic
536C2×C42C23×C6111yescharacteristic
537#107—21no—
538#107—21no—
539#107—21no—
540#106—21no—
541#106—21no—
542#106—21no—
543C4⋊C8—21no—
544C4⋊C8—21no—
545#104—22no—
546#104—22no—
547#103—21no—
548#103—21no—
549#103—21no—
550#103—21no—
551#103—21no—
552#103—21no—
553#103—21no—
554#102—21no—
555#97—21no—
556C4×C8—21no—
557#95—21no—
558#95—22no—
559#95—22no—
560#95—22no—
561#41—21no—
562#41—21no—
563#41C2×Q8×C6112yes—
564#41#41×C6112yes—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8C2×D4×C6111yescharacteristic
575C2×Q8C2×Q8×C6112yes—
576C2×D4—21no—
577C2×D4C2×D4×C6111yescharacteristic
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4C2×D4×C6112yes—
588C22×C4C2×D4×C6112yes—
589C22×C4C2×D4×C6111yescharacteristic
590C22×C4C2×D4×C6111yescharacteristic
591C22×C4C24×C6111yescharacteristic
592Q16—24no—
593SD16—24no—
594M16—21no—
595M16—21no—
596M16—21no—
597M16—21no—
598M16—21no—
599M16—21no—
600M16—21no—
601M16C2×Q8×C6112yes—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—42no—
633C4⋊C4—44no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4C2×D4×C6111yescharacteristic
637C4⋊C4C2×D4×C6111yescharacteristic
638C4⋊C4C2×D4×C6111yescharacteristic
639C4⋊C4C2×D4×C6111yescharacteristic
640C4⋊C4C2×D4×C6111yescharacteristic
641C4⋊C4C2×D4×C6111yescharacteristic
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C42—22no—
650C42—22no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—41no—
661C42—41no—
662C42C2×D4×C6111yescharacteristic
663C42C2×D4×C6111yescharacteristic
664C42C2×D4×C6111yescharacteristic
665C42C2×D4×C6111yescharacteristic
666C23—21no—
667C23C22×D4×C6111yescharacteristic
668Q8—21no—
669Q8—22no—
670Q8—22no—
671Q8—41no—
672Q8—41no—
673Q8—81no—
674Q8—81no—
675Q8—82no—
676Q8—82no—
677Q8C22⋊Q8×C6112yes—
678D4—22no—
679D4—22no—
680D4—21no—
681D4C22⋊Q8×C6112yes—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—82no—
711C2×C4—82no—
712C2×C4#120×C6111yescharacteristic
713C2×C4#120×C6111yescharacteristic
714C2×C4#120×C6111yescharacteristic
715C2×C4#120×C6111yescharacteristic
716C2×C4C22×D4×C6111yescharacteristic
717C2×C4C22×D4×C6111yescharacteristic
718C2×C4C22×Q8×C6111yescharacteristic
719C2×C4C2×#41×C6111yescharacteristic
720C2×C42−1+4×C6111yescharacteristic
721C2×C42−1+4×C6111yescharacteristic
722C8—22no—
723C8—41no—
724C8—41no—
725C8—41no—
726C22—21no—
727C22—21no—
728C22—22no—
729C22—41no—
730C22—41no—
731C22C2×#120×C6111yescharacteristic
732C22C61×#54811yescharacteristic
733C22D4×Q8×C6111yescharacteristic
734C4—22no—
735C4—21no—
736C4—21no—
737C4—21no—
738C4—21no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—42no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—81no—
750C4—81no—
751C4C2×C22⋊Q8×C6111yescharacteristic
752C4C61×#53611yescharacteristic
753C4C61×#54811yescharacteristic
754C4D4×Q8×C6111yescharacteristic
755C2—21no—
756C2—21no—
757C2—42no—
758C2C61×#240911yescharacteristic
759C2C61×#301811yescharacteristic
760C2C61×#302211yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×#41×C61C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#3078C2semidirect
4. C61×#2565C2semidirect
5. C61×#2061C2semidirect
6. C61×#2060C2semidirect
7. C61×#2028C2semidirect
8. C61×#2028C2semidirect
9. C61×#1998C2semidirect
10. C61×#1986C2semidirect
74. #137×C61Q8semidirect
345. #24325C61direct (N × H)
376. #3078C2×C61semidirect
378. #2565C2×C61semidirect
379. #2061C2×C61semidirect
380. #2060C2×C61semidirect
381. #2028C2×C61semidirect
382. #2028C2×C61semidirect
383. #1998C2×C61semidirect
384. #1986C2×C61semidirect
451. C61#24325direct (N × H)
455. #137Q8×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#35042
C61×#30782
C4×#137×C612
C61×#25652
C61×#20612
C61×#20602
C61×#20282
C61×#19982
C61×#19862
C61×#18822
C61×#18602
C61×#18592
C61×#18062
#2432561