Finite Group Databasebeta

← C61×#24518 #29527951

Subgroups — C61×#24518 #29527951

Order 15616.

938 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#448C211yesmaximal, characteristic
2C2×C61×#433C211yesmaximal, characteristic, complemented
3C61×#2624C211yesmaximal, characteristic
4C61×#2310C211yesmaximal, characteristic, complemented
5C61×#2068C211yesmaximal, characteristic, complemented
6C61×#2066C211yesmaximal, characteristic, complemented
7C61×#2055C211yesmaximal, characteristic, complemented
8C61×#2055C211yesmaximal, characteristic, complemented
9C61×#1973C211yesmaximal, characteristic, complemented
10C61×#1968C211yesmaximal, characteristic, complemented
11C61×#1935C211yesmaximal, characteristic, complemented
12C61×#1933C211yesmaximal, characteristic, complemented
13C61×#1875C211yesmaximal, characteristic
14C61×#1854C211yesmaximal, characteristic, complemented
15C61×#1787C211yesmaximal, characteristic, complemented
16C23×Q8×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C22×SD16×C61C2211yescharacteristic
19C2×#121×C61C2211yescharacteristic
20C2×#117×C61C2211yescharacteristic
21C2×#117×C61C2211yescharacteristic
22C61×#448—24no—
23C61×#433—24no—
24C2×#107×C61C2211yescharacteristic
25C2×#106×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C2×#103×C61C2211yescharacteristic
29C2×#103×C61C2211yescharacteristic
30C2×#103×C61C2211yescharacteristic
31C2×#103×C61C2211yescharacteristic
32C2×#103×C61C2211yescharacteristic
33C2×#103×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic
35C2×#102×C61C2211yescharacteristic
36C2×C22⋊C8×C61C2211yescharacteristic
37C2×C22⋊C8×C61C2211yescharacteristic
38C2×#97×C61C2211yescharacteristic
39C2×C4×C8×C61C2211yescharacteristic
40C61×#399—21no—
41C61×#397—21no—
42C61×#394—21no—
43C61×#394—21no—
44C61×#391—21no—
45C61×#391—21no—
46C61×#391C2211yescharacteristic
47C61×#391C2211yescharacteristic
48C61×#391C2211yescharacteristic
49C61×#391C2211yescharacteristic
50C61×#390C2211yescharacteristic
51C61×#390C2211yescharacteristic
52C61×#389C2211yescharacteristic
53C61×#389C2211yescharacteristic
54C61×#381—21no—
55C61×#381—21no—
56C61×#380C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×Q8×C61—22no—
62C22×Q8×C61—22no—
63C22×Q8×C61—21no—
64C22×Q8×C61—22no—
65C22×Q8×C61—22no—
66C22×Q8×C61—41no—
67C22×Q8×C61—41no—
68C22×Q8×C61C2311yescharacteristic
69C22×Q8×C61C2311yescharacteristic
70C22×D4×C61—21no—
71C22×D4×C61C2311yescharacteristic
72C23×C4×C61—21no—
73C23×C4×C61C2311yescharacteristic
74C2×SD16×C61—22no—
75C2×SD16×C61—22no—
76C2×SD16×C61—22no—
77C2×SD16×C61—22no—
78C2×SD16×C61—41no—
79C2×SD16×C61—41no—
80C22×C8×C61C2311yescharacteristic
81C22×C8×C61C2311yescharacteristic
82C22×C8×C61C2311yescharacteristic
83C22×C8×C61C2311yescharacteristic
84#121×C61—22no—
85#121×C61—22no—
86#117×C61—22no—
87#117×C61—22no—
88#117×C61—41no—
89#117×C61—41no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61D411yescharacteristic
93C2×C4⋊C4×C61D411yescharacteristic
94C2×C4⋊C4×C61C2311yescharacteristic
95C2×C4⋊C4×C61C2311yescharacteristic
96C2×C4⋊C4×C61C2311yescharacteristic
97C2×C4⋊C4×C61C2311yescharacteristic
98C2×C4⋊C4×C61C2311yescharacteristic
99C2×C22⋊C4×C61—21no—
100C2×C22⋊C4×C61—21no—
101C2×C22⋊C4×C61—21no—
102C2×C22⋊C4×C61—21no—
103C2×C22⋊C4×C61—21no—
104C2×C22⋊C4×C61—21no—
105C2×C22⋊C4×C61—21no—
106C2×C22⋊C4×C61D411yescharacteristic
107C2×C22⋊C4×C61D411yescharacteristic
108C2×C42×C61—21no—
109C2×C42×C61C2311yescharacteristic
110C2×C42×C61C2311yescharacteristic
111#107×C61—41no—
112#106×C61—41no—
113C4⋊C8×C61—22no—
114C4⋊C8×C61—22no—
115#103×C61—22no—
116#103×C61—22no—
117#103×C61—22no—
118#103×C61—22no—
119#103×C61—41no—
120#103×C61—41no—
121#102×C61—41no—
122#102×C61—41no—
123C22⋊C8×C61—22no—
124C22⋊C8×C61D414yes—
125#97×C61—22no—
126C4×C8×C61—22no—
127#95×C61—21no—
128#95×C61—21no—
129#95×C61—21no—
130#95×C61—21no—
131#95×C61—21no—
132#95×C61—21no—
133#95×C61—21no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61—21no—
137#95×C61—21no—
138C24×C61—21no—
139C24×C61C2×D411yescharacteristic
140C2×Q8×C61—24no—
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—44no—
152C2×Q8×C61—44no—
153C2×Q8×C61—44no—
154C2×Q8×C61—44no—
155C2×Q8×C61—42no—
156C2×Q8×C61—42no—
157C2×Q8×C61#4112yes—
158C2×Q8×C61#4112yes—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—42no—
166C2×D4×C61—81no—
167C2×D4×C61—81no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—24no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—42no—
181C22×C4×C61—42no—
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D412yes—
188C22×C4×C61#4112yes—
189C22×C4×C61C2411yescharacteristic
190SD16×C61—44no—
191SD16×C61—44no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61C2×D412yes—
203C2×C8×C61C2×D412yes—
204C4⋊C4×C61—22no—
205C4⋊C4×C61—22no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—81no—
217C4⋊C4×C61—81no—
218C22⋊C4×C61—22no—
219C22⋊C4×C61—22no—
220C22⋊C4×C61—42no—
221C22⋊C4×C61—42no—
222C22⋊C4×C61—81no—
223C22⋊C4×C61—81no—
224C22⋊C4×C61—81no—
225C22⋊C4×C61—81no—
226C22⋊C4×C61—81no—
227C42×C61—21no—
228C42×C61—21no—
229C42×C61—21no—
230C42×C61—21no—
231C42×C61—42no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61#12112yes—
246C23×C61C22×D411yescharacteristic
247Q8×C61—22no—
248Q8×C61—22no—
249Q8×C61—22no—
250Q8×C61—22no—
251Q8×C61—48no—
252Q8×C61—41no—
253Q8×C61—41no—
254Q8×C61—41no—
255Q8×C61—41no—
256D4×C61—41no—
257D4×C61—41no—
258D4×C61—41no—
259D4×C61—41no—
260D4×C61—84no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
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—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61#12112yes—
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C2×C4×C61H(5,𝔽2)11yescharacteristic
308C8×C61—22no—
309C8×C61—22no—
310C8×C61—41no—
311C8×C61—41no—
312#24518C6111yesmaximal, characteristic, direct product factor, Sylow
313C22×C61—22no—
314C22×C61—22no—
315C22×C61—22no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—81no—
321C22×C61—81no—
322C22×C61—81no—
323C22×C61—81no—
324C22×C61—81no—
325C22×C61—81no—
326C22×C61—81no—
327C22×C61C2×#12111yescharacteristic
328C22×C61#52511yescharacteristic
329C22×C61#53511yescharacteristic
330C22×C61#57711yescharacteristic
331C22×C61#57711yescharacteristic
332C22×C61#57711yescharacteristic
333C22×C61#57811yescharacteristic
334C4×C61—22no—
335C4×C61—42no—
336C4×C61—42no—
337C4×C61—41no—
338C4×C61—41no—
339C4×C61—41no—
340C4×C61—41no—
341C4×C61—81no—
342C4×C61—81no—
343C4×C61—81no—
344C4×C61—81no—
345C4×C61—81no—
346C4×C61#54611yescharacteristic
347C4×C61#54611yescharacteristic
348C4×C61#55111yescharacteristic
349C4×C61#55111yescharacteristic
350C2×#448C2×C6111yescharacteristic
351C2×#433C2×C6111yescharacteristic, complemented
352#2624C2×C6111yescharacteristic
353#2310C2×C6111yescharacteristic, complemented
354#2068C2×C6111yescharacteristic, complemented
355#2066C2×C6111yescharacteristic, complemented
356#2055C2×C6111yescharacteristic, complemented
357#2055C2×C6111yescharacteristic, complemented
358#1973C2×C6111yescharacteristic, complemented
359#1968C2×C6111yescharacteristic, complemented
360#1935C2×C6111yescharacteristic, complemented
361#1933C2×C6111yescharacteristic, complemented
362#1875C2×C6111yescharacteristic
363#1854C2×C6111yescharacteristic, complemented
364#1787C2×C6111yescharacteristic, complemented
365C2×C61—42no—
366C2×C61—161no—
367C2×C61#241111yescharacteristic
368C2×C61#305711yescharacteristic
369C2×C61#306311yescharacteristic
370C2×C61#312111yescharacteristic
371C2×C61#312611yescharacteristic
372C2×C61#322111yescharacteristic
373C2×C61#322511yescharacteristic
374C23×Q8C22×C6111yescharacteristic
375C22×SD16C22×C6111yescharacteristic
376C22×SD16C22×C6111yescharacteristic
377C2×#121C22×C6111yescharacteristic
378C2×#117C22×C6111yescharacteristic
379C2×#117C22×C6111yescharacteristic
380#448—24no—
381#433—24no—
382C2×#107C22×C6111yescharacteristic
383C2×#106C22×C6111yescharacteristic
384C2×C4⋊C8C22×C6111yescharacteristic
385C2×C4⋊C8C22×C6111yescharacteristic
386C2×#103C22×C6111yescharacteristic
387C2×#103C22×C6111yescharacteristic
388C2×#103C22×C6111yescharacteristic
389C2×#103C22×C6111yescharacteristic
390C2×#103C22×C6111yescharacteristic
391C2×#103C22×C6111yescharacteristic
392C2×#102C22×C6111yescharacteristic
393C2×#102C22×C6111yescharacteristic
394C2×C22⋊C8C22×C6111yescharacteristic
395C2×C22⋊C8C22×C6111yescharacteristic
396C2×#97C22×C6111yescharacteristic
397C2×C4×C8C22×C6111yescharacteristic
398#399—21no—
399#397—21no—
400#394—21no—
401#394—21no—
402#391—21no—
403#391—21no—
404#391C22×C6111yescharacteristic
405#391C22×C6111yescharacteristic
406#391C22×C6111yescharacteristic
407#391C22×C6111yescharacteristic
408#390C22×C6111yescharacteristic
409#390C22×C6111yescharacteristic
410#389C22×C6111yescharacteristic
411#389C22×C6111yescharacteristic
412#381—21no—
413#381—21no—
414#380C22×C6111yescharacteristic
415#340C22×C6111yescharacteristic
416#340C22×C6111yescharacteristic
417#340C22×C6111yescharacteristic
418#340C22×C6111yescharacteristic
419C61#2451811yescharacteristic, direct product factor, Sylow
420C22×Q8—22no—
421C22×Q8—22no—
422C22×Q8—21no—
423C22×Q8—22no—
424C22×Q8—22no—
425C22×Q8—41no—
426C22×Q8—41no—
427C22×Q8C23×C6111yescharacteristic
428C22×Q8C23×C6111yescharacteristic
429C22×D4—21no—
430C22×D4C23×C6111yescharacteristic
431C23×C4—21no—
432C23×C4C23×C6111yescharacteristic
433C2×SD16—22no—
434C2×SD16—22no—
435C2×SD16—22no—
436C2×SD16—22no—
437C2×SD16—41no—
438C2×SD16—41no—
439C22×C8C23×C6111yescharacteristic
440C22×C8C23×C6111yescharacteristic
441C22×C8C23×C6111yescharacteristic
442C22×C8C23×C6111yescharacteristic
443#121—22no—
444#121—22no—
445#117—22no—
446#117—22no—
447#117—41no—
448#117—41no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4D4×C6111yescharacteristic
452C2×C4⋊C4D4×C6111yescharacteristic
453C2×C4⋊C4C23×C6111yescharacteristic
454C2×C4⋊C4C23×C6111yescharacteristic
455C2×C4⋊C4C23×C6111yescharacteristic
456C2×C4⋊C4C23×C6111yescharacteristic
457C2×C4⋊C4C23×C6111yescharacteristic
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4D4×C6111yescharacteristic
466C2×C22⋊C4D4×C6111yescharacteristic
467C2×C42—21no—
468C2×C42C23×C6111yescharacteristic
469C2×C42C23×C6111yescharacteristic
470#107—41no—
471#106—41no—
472C4⋊C8—22no—
473C4⋊C8—22no—
474#103—22no—
475#103—22no—
476#103—22no—
477#103—22no—
478#103—41no—
479#103—41no—
480#102—41no—
481#102—41no—
482C22⋊C8—22no—
483C22⋊C8D4×C6114yes—
484#97—22no—
485C4×C8—22no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497C24—21no—
498C24C2×D4×C6111yescharacteristic
499C2×Q8—24no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—44no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×Q8—44no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8#41×C6112yes—
517C2×Q8#41×C6112yes—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—42no—
525C2×D4—81no—
526C2×D4—81no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4C2×D4×C6111yescharacteristic
542C22×C4C2×D4×C6111yescharacteristic
543C22×C4C2×D4×C6111yescharacteristic
544C22×C4C2×D4×C6111yescharacteristic
545C22×C4C2×D4×C6111yescharacteristic
546C22×C4C2×D4×C6112yes—
547C22×C4#41×C6112yes—
548C22×C4C24×C6111yescharacteristic
549SD16—44no—
550SD16—44no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8C2×D4×C6112yes—
562C2×C8C2×D4×C6112yes—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—81no—
576C4⋊C4—81no—
577C22⋊C4—22no—
578C22⋊C4—22no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—81no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C22⋊C4—81no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—42no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23#121×C6112yes—
605C23C22×D4×C6111yescharacteristic
606Q8—22no—
607Q8—22no—
608Q8—22no—
609Q8—22no—
610Q8—48no—
611Q8—41no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—84no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—48no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4#121×C6112yes—
661C2×C4C22×D4×C6111yescharacteristic
662C2×C4C2×#41×C6111yescharacteristic
663C2×C4C2×#41×C6111yescharacteristic
664C2×C4C2×#41×C6111yescharacteristic
665C2×C4H(5,𝔽2)×C6111yescharacteristic
666C2×C4H(5,𝔽2)×C6111yescharacteristic
667C8—22no—
668C8—22no—
669C8—41no—
670C8—41no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22C2×#121×C6111yescharacteristic
686C22C61×#52511yescharacteristic
687C22C61×#53511yescharacteristic
688C22C61×#57711yescharacteristic
689C22C61×#57711yescharacteristic
690C22C61×#57711yescharacteristic
691C22C61×#57811yescharacteristic
692C4—22no—
693C4—41no—
694C4—41no—
695C4—41no—
696C4—41no—
697C4—42no—
698C4—42no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4C61×#54611yescharacteristic
705C4C61×#54611yescharacteristic
706C4C61×#55111yescharacteristic
707C4C61×#55111yescharacteristic
708C2—42no—
709C2—161no—
710C2C61×#241111yescharacteristic
711C2C61×#305711yescharacteristic
712C2C61×#306311yescharacteristic
713C2C61×#312111yescharacteristic
714C2C61×#312611yescharacteristic
715C2C61×#322111yescharacteristic
716C2C61×#322511yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×#121×C61C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×#117×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#433C2semidirect
4. C61×#2310C2semidirect
5. C61×#2068C2semidirect
6. C61×#2066C2semidirect
7. C61×#2055C2semidirect
8. C61×#2055C2semidirect
9. C61×#1973C2semidirect
10. C61×#1968C2semidirect
11. C61×#1935C2semidirect
12. C61×#1933C2semidirect
14. C61×#1854C2semidirect
15. C61×#1787C2semidirect
312. #24518C61direct (N × H)
351. C2×#433C2×C61semidirect
353. #2310C2×C61semidirect
354. #2068C2×C61semidirect
355. #2066C2×C61semidirect
356. #2055C2×C61semidirect
357. #2055C2×C61semidirect
358. #1973C2×C61semidirect
359. #1968C2×C61semidirect
360. #1935C2×C61semidirect
361. #1933C2×C61semidirect
363. #1854C2×C61semidirect
364. #1787C2×C61semidirect
419. C61#24518direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#4482
C2×C61×#4332
C61×#26242
C61×#23102
C61×#20682
C61×#20662
C61×#20552
C61×#19732
C61×#19682
C61×#19352
C61×#19332
C61×#18752
C61×#18542
C61×#17872
#2451861