Finite Group Databasebeta

← C61×#22860 #29526293

Subgroups — C61×#22860 #29526293

Order 15616.

1174 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#449C211yesmaximal, characteristic
2C2×C61×#442C211yesmaximal, characteristic, complemented
3C2×C61×#416C211yesmaximal, characteristic, complemented
4C61×#2363C211yesmaximal, characteristic, complemented
5C61×#2339C211yesmaximal, characteristic, complemented
6C61×#1973C211yesmaximal, characteristic, complemented
7C61×#1935C211yesmaximal, characteristic, complemented
8C61×#1927C211yesmaximal, characteristic, complemented
9C61×#1893C211yesmaximal, characteristic, complemented
10C61×#1879C211yesmaximal, characteristic, complemented
11C61×#1877C211yesmaximal, characteristic, complemented
12C61×#1862C211yesmaximal, characteristic, complemented
13C61×#1854C211yesmaximal, characteristic, complemented
14C61×#1762C211yesmaximal, characteristic, complemented
15C61×#1752C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C22×D8×C61C2211yescharacteristic
19C23×C8×C61C2211yescharacteristic
20C2×#121×C61C2211yescharacteristic
21C2×C4×D4×C61C2211yescharacteristic
22C2×C4×D4×C61C2211yescharacteristic
23C2×C4×D4×C61C2211yescharacteristic
24C2×#117×C61C2211yescharacteristic
25C61×#449C418yescomplemented
26C61×#442—24no—
27C2×#107×C61C2211yescharacteristic
28C2×#106×C61C2211yescharacteristic
29C61×#416—24no—
30C2×#103×C61C2211yescharacteristic
31C2×#103×C61C2211yescharacteristic
32C2×#103×C61C2211yescharacteristic
33C2×#102×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic
35C2×#102×C61C2211yescharacteristic
36C2×#102×C61C2211yescharacteristic
37C2×#102×C61C2211yescharacteristic
38C2×C22⋊C8×C61C2211yescharacteristic
39C2×#97×C61C2211yescharacteristic
40C2×#97×C61C2211yescharacteristic
41C61×#391C2211yescharacteristic
42C61×#391C2211yescharacteristic
43C61×#390—21no—
44C61×#390C2211yescharacteristic
45C61×#389C2211yescharacteristic
46C61×#388—21no—
47C61×#386—21no—
48C61×#386—21no—
49C61×#386—21no—
50C61×#381—21no—
51C61×#380C2211yescharacteristic
52C4×C4⋊C4×C61C2211yescharacteristic
53C4×C22⋊C4×C61—21no—
54C4×C22⋊C4×C61C2211yescharacteristic
55C2×#95×C61—21no—
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C2×#41×C61—22no—
63C2×#41×C61—22no—
64C2×#41×C61—22no—
65C2×#41×C61—41no—
66C2×#41×C61—41no—
67C2×#41×C61C2×C414yescomplemented
68C22×Q8×C61C2311yescharacteristic
69C22×D4×C61—21no—
70C22×D4×C61—21no—
71C22×D4×C61C2311yescharacteristic
72C22×D4×C61C2311yescharacteristic
73C23×C4×C61—21no—
74C23×C4×C61—21no—
75C23×C4×C61—21no—
76C23×C4×C61—21no—
77C23×C4×C61C2311yescharacteristic
78C2×SD16×C61—41no—
79C2×SD16×C61—41no—
80C2×SD16×C61C2×C414yescomplemented
81C2×D8×C61—22no—
82C2×D8×C61—22no—
83C2×D8×C61C2×C414yes—
84C22×C8×C61—22no—
85C22×C8×C61—22no—
86C22×C8×C61—41no—
87C22×C8×C61C2311yescharacteristic
88C22×C8×C61C2311yescharacteristic
89C22×C8×C61C2311yescharacteristic
90C22×C8×C61C2311yescharacteristic
91#121×C61—22no—
92#121×C61C2×C414yescomplemented
93C4×D4×C61—22no—
94C4×D4×C61—22no—
95C4×D4×C61—22no—
96C4×D4×C61—41no—
97C4×D4×C61—41no—
98C4×D4×C61—41no—
99#117×C61—22no—
100#117×C61—41no—
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C4⋊C4×C61C2311yescharacteristic
104C2×C4⋊C4×C61C2311yescharacteristic
105C2×C4⋊C4×C61C2311yescharacteristic
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C22⋊C4×C61—21no—
108C2×C22⋊C4×C61—21no—
109C2×C22⋊C4×C61—21no—
110C2×C22⋊C4×C61—21no—
111C2×C22⋊C4×C61—21no—
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61D411yescharacteristic
116C2×C22⋊C4×C61D411yescharacteristic
117C2×C42×C61—21no—
118C2×C42×C61—21no—
119C2×C42×C61C2311yescharacteristic
120C2×C42×C61C2311yescharacteristic
121#107×C61—41no—
122#106×C61—22no—
123#103×C61—22no—
124#103×C61—22no—
125#103×C61C2×C414yescomplemented
126#102×C61—22no—
127#102×C61—22no—
128#102×C61—41no—
129#102×C61C2×C414yescomplemented
130#102×C61D414yescomplemented
131C22⋊C8×C61C2×C414yescomplemented
132#97×C61—22no—
133#97×C61—41no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61—21no—
137#95×C61—21no—
138#95×C61—21no—
139#95×C61—21no—
140#95×C61—21no—
141#95×C61D411yescharacteristic
142#95×C61D411yescharacteristic
143C24×C61—21no—
144C24×C61—21no—
145C24×C61C2×D411yescharacteristic
146#41×C61—28no—
147#41×C61—44no—
148#41×C61—44no—
149#41×C61—44no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61C22×C412yes—
156C2×D4×C61—24no—
157C2×D4×C61—24no—
158C2×D4×C61—21no—
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—21no—
166C2×D4×C61—42no—
167C2×D4×C61—42no—
168C2×D4×C61—81no—
169C2×D4×C61—81no—
170C2×D4×C61C22×C412yes—
171C2×D4×C61C22×C412yes—
172C2×D4×C61C2×D412yes—
173C2×D4×C61#4112yes—
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—21no—
181C22×C4×C61—24no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—42no—
186C22×C4×C61—42no—
187C22×C4×C61—42no—
188C22×C4×C61—42no—
189C22×C4×C61—42no—
190C22×C4×C61—42no—
191C22×C4×C61—42no—
192C22×C4×C61—42no—
193C22×C4×C61—81no—
194C22×C4×C61—81no—
195C22×C4×C61—81no—
196C22×C4×C61C22×C412yes—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61#4112yes—
203C22×C4×C61C2411yescharacteristic
204SD16×C61—44no—
205D8×C61—28no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—44no—
216C2×C8×C61C22×C412yes—
217C2×C8×C61C22×C412yes—
218C2×C8×C61C2×D412yes—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—81no—
228C4⋊C4×C61C22×C412yes—
229C4⋊C4×C61C2×D412yes—
230C22⋊C4×C61—24no—
231C22⋊C4×C61—41no—
232C22⋊C4×C61—41no—
233C22⋊C4×C61—42no—
234C22⋊C4×C61—42no—
235C22⋊C4×C61—42no—
236C22⋊C4×C61—42no—
237C22⋊C4×C61—42no—
238C22⋊C4×C61—81no—
239C22⋊C4×C61—81no—
240C42×C61—21no—
241C42×C61—21no—
242C42×C61—21no—
243C42×C61—21no—
244C42×C61—42no—
245C42×C61—81no—
246C23×C61—22no—
247C23×C61—21no—
248C23×C61—22no—
249C23×C61—22no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—22no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61C4×D412yes—
267C23×C61C22×D411yescharacteristic
268Q8×C61—22no—
269Q8×C61—22no—
270Q8×C61—41no—
271Q8×C61—41no—
272D4×C61—22no—
273D4×C61—22no—
274D4×C61—22no—
275D4×C61—22no—
276D4×C61—22no—
277D4×C61—48no—
278D4×C61—41no—
279D4×C61—41no—
280D4×C61—84no—
281D4×C61C4×D414yes—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—22no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—48no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—84no—
320C2×C4×C61—84no—
321C2×C4×C61—84no—
322C2×C4×C61C4×D412yes—
323C2×C4×C61C23×C411yescharacteristic
324C2×C4×C61C22×D411yescharacteristic
325C2×C4×C61C2×#4111yescharacteristic
326C2×C4×C61C2×#4111yescharacteristic
327C2×C4×C61H(5,𝔽2)11yescharacteristic
328C2×C4×C61H(5,𝔽2)11yescharacteristic
329C8×C61—22no—
330C8×C61—22no—
331C8×C61—22no—
332C8×C61—41no—
333#22860C6111yesmaximal, characteristic, direct product factor, Sylow
334C22×C61—22no—
335C22×C61—24no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—41no—
341C22×C61—42no—
342C22×C61—42no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—41no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—81no—
352C22×C61—81no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61C2×C4×D411yescharacteristic
356C22×C61D4211yescharacteristic
357C22×C61#54611yescharacteristic
358C22×C61#57511yescharacteristic
359C22×C61#57511yescharacteristic
360C22×C61#57611yescharacteristic
361C22×C61#57711yescharacteristic
362C4×C61—22no—
363C4×C61—42no—
364C4×C61—42no—
365C4×C61—41no—
366C4×C61—42no—
367C4×C61—41no—
368C4×C61—41no—
369C4×C61—41no—
370C4×C61—81no—
371C4×C61—81no—
372C4×C61—81no—
373C4×C61C2×C4×D411yescharacteristic
374C4×C61#51811yescharacteristic
375C4×C61#54611yescharacteristic
376C4×C61#55111yescharacteristic
377C2×#449C2×C6111yescharacteristic
378C2×#442C2×C6111yescharacteristic, complemented
379C2×#416C2×C6111yescharacteristic, complemented
380#2363C2×C6111yescharacteristic, complemented
381#2339C2×C6111yescharacteristic, complemented
382#1973C2×C6111yescharacteristic, complemented
383#1935C2×C6111yescharacteristic, complemented
384#1927C2×C6111yescharacteristic, complemented
385#1893C2×C6111yescharacteristic, complemented
386#1879C2×C6111yescharacteristic, complemented
387#1877C2×C6111yescharacteristic, complemented
388#1862C2×C6111yescharacteristic, complemented
389#1854C2×C6111yescharacteristic, complemented
390#1762C2×C6111yescharacteristic, complemented
391#1752C2×C6111yescharacteristic, complemented
392C2×C61—42no—
393C2×C61—44no—
394C2×C61—82no—
395C2×C61#235811yescharacteristic
396C2×C61#294311yescharacteristic
397C2×C61#294611yescharacteristic
398C2×C61#326711yescharacteristic
399C2×C61#326811yescharacteristic
400C2×C61#330711yescharacteristic
401C2×C61#331911yescharacteristic
402C22×#41C22×C6111yescharacteristic
403C22×SD16C22×C6111yescharacteristic
404C22×D8C22×C6111yescharacteristic
405C23×C8C22×C6111yescharacteristic
406C2×#121C22×C6111yescharacteristic
407C2×C4×D4C22×C6111yescharacteristic
408C2×C4×D4C22×C6111yescharacteristic
409C2×C4×D4C22×C6111yescharacteristic
410C2×#117C22×C6111yescharacteristic
411#449C4×C6118yescomplemented
412#442—24no—
413C2×#107C22×C6111yescharacteristic
414C2×#106C22×C6111yescharacteristic
415#416—24no—
416C2×#103C22×C6111yescharacteristic
417C2×#103C22×C6111yescharacteristic
418C2×#103C22×C6111yescharacteristic
419C2×#102C22×C6111yescharacteristic
420C2×#102C22×C6111yescharacteristic
421C2×#102C22×C6111yescharacteristic
422C2×#102C22×C6111yescharacteristic
423C2×#102C22×C6111yescharacteristic
424C2×C22⋊C8C22×C6111yescharacteristic
425C2×#97C22×C6111yescharacteristic
426C2×#97C22×C6111yescharacteristic
427#391C22×C6111yescharacteristic
428#391C22×C6111yescharacteristic
429#390—21no—
430#390C22×C6111yescharacteristic
431#389C22×C6111yescharacteristic
432#388—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#381—21no—
437#380C22×C6111yescharacteristic
438C4×C4⋊C4C22×C6111yescharacteristic
439C4×C22⋊C4—21no—
440C4×C22⋊C4C22×C6111yescharacteristic
441C2×#95—21no—
442#340C22×C6111yescharacteristic
443#340C22×C6111yescharacteristic
444#340C22×C6111yescharacteristic
445#340C22×C6111yescharacteristic
446#336C22×C6111yescharacteristic
447#336C22×C6111yescharacteristic
448C61#2286011yescharacteristic, direct product factor, Sylow
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—41no—
453C2×#41—41no—
454C2×#41C2×C4×C6114yescomplemented
455C22×Q8C23×C6111yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4C23×C6111yescharacteristic
459C22×D4C23×C6111yescharacteristic
460C23×C4—21no—
461C23×C4—21no—
462C23×C4—21no—
463C23×C4—21no—
464C23×C4C23×C6111yescharacteristic
465C2×SD16—41no—
466C2×SD16—41no—
467C2×SD16C2×C4×C6114yescomplemented
468C2×D8—22no—
469C2×D8—22no—
470C2×D8C2×C4×C6114yes—
471C22×C8—22no—
472C22×C8—22no—
473C22×C8—41no—
474C22×C8C23×C6111yescharacteristic
475C22×C8C23×C6111yescharacteristic
476C22×C8C23×C6111yescharacteristic
477C22×C8C23×C6111yescharacteristic
478#121—22no—
479#121C2×C4×C6114yescomplemented
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—41no—
484C4×D4—41no—
485C4×D4—41no—
486#117—22no—
487#117—41no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4C23×C6111yescharacteristic
490C2×C4⋊C4C23×C6111yescharacteristic
491C2×C4⋊C4C23×C6111yescharacteristic
492C2×C4⋊C4C23×C6111yescharacteristic
493C2×C4⋊C4C23×C6111yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4D4×C6111yescharacteristic
503C2×C22⋊C4D4×C6111yescharacteristic
504C2×C42—21no—
505C2×C42—21no—
506C2×C42C23×C6111yescharacteristic
507C2×C42C23×C6111yescharacteristic
508#107—41no—
509#106—22no—
510#103—22no—
511#103—22no—
512#103C2×C4×C6114yescomplemented
513#102—22no—
514#102—22no—
515#102—41no—
516#102C2×C4×C6114yescomplemented
517#102D4×C6114yescomplemented
518C22⋊C8C2×C4×C6114yescomplemented
519#97—22no—
520#97—41no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95D4×C6111yescharacteristic
529#95D4×C6111yescharacteristic
530C24—21no—
531C24—21no—
532C24C2×D4×C6111yescharacteristic
533#41—28no—
534#41—44no—
535#41—44no—
536#41—44no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8C22×C4×C6112yes—
543C2×D4—24no—
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—81no—
556C2×D4—81no—
557C2×D4C22×C4×C6112yes—
558C2×D4C22×C4×C6112yes—
559C2×D4C2×D4×C6112yes—
560C2×D4#41×C6112yes—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—24no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—81no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4C22×C4×C6112yes—
584C22×C4C2×D4×C6111yescharacteristic
585C22×C4C2×D4×C6111yescharacteristic
586C22×C4C2×D4×C6111yescharacteristic
587C22×C4C2×D4×C6111yescharacteristic
588C22×C4C2×D4×C6111yescharacteristic
589C22×C4#41×C6112yes—
590C22×C4C24×C6111yescharacteristic
591SD16—44no—
592D8—28no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—44no—
603C2×C8C22×C4×C6112yes—
604C2×C8C22×C4×C6112yes—
605C2×C8C2×D4×C6112yes—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—81no—
615C4⋊C4C22×C4×C6112yes—
616C4⋊C4C2×D4×C6112yes—
617C22⋊C4—24no—
618C22⋊C4—41no—
619C22⋊C4—41no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—42no—
632C42—81no—
633C23—21no—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23—22no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23C4×D4×C6112yes—
654C23C22×D4×C6111yescharacteristic
655Q8—22no—
656Q8—22no—
657Q8—41no—
658Q8—41no—
659D4—22no—
660D4—22no—
661D4—22no—
662D4—22no—
663D4—22no—
664D4—48no—
665D4—41no—
666D4—41no—
667D4—84no—
668D4C4×D4×C6114yes—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—48no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—84no—
707C2×C4—84no—
708C2×C4—84no—
709C2×C4C4×D4×C6112yes—
710C2×C4C23×C4×C6111yescharacteristic
711C2×C4C22×D4×C6111yescharacteristic
712C2×C4C2×#41×C6111yescharacteristic
713C2×C4C2×#41×C6111yescharacteristic
714C2×C4H(5,𝔽2)×C6111yescharacteristic
715C2×C4H(5,𝔽2)×C6111yescharacteristic
716C8—22no—
717C8—22no—
718C8—22no—
719C8—41no—
720C22—22no—
721C22—24no—
722C22—22no—
723C22—22no—
724C22—41no—
725C22—42no—
726C22—42no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—41no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22C2×C4×D4×C6111yescharacteristic
742C22D42×C6111yescharacteristic
743C22C61×#54611yescharacteristic
744C22C61×#57511yescharacteristic
745C22C61×#57511yescharacteristic
746C22C61×#57611yescharacteristic
747C22C61×#57711yescharacteristic
748C4—22no—
749C4—41no—
750C4—41no—
751C4—42no—
752C4—42no—
753C4—41no—
754C4—42no—
755C4—41no—
756C4—81no—
757C4—81no—
758C4—81no—
759C4C2×C4×D4×C6111yescharacteristic
760C4C61×#51811yescharacteristic
761C4C61×#54611yescharacteristic
762C4C61×#55111yescharacteristic
763C2—42no—
764C2—44no—
765C2—82no—
766C2C61×#235811yescharacteristic
767C2C61×#294311yescharacteristic
768C2C61×#294611yescharacteristic
769C2C61×#326711yescharacteristic
770C2C61×#326811yescharacteristic
771C2C61×#330711yescharacteristic
772C2C61×#331911yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutatorC2×C4C23×C4×C61
Frattini, cosocleC22×C4C24×C61
prime radicalC2×C61×#449C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C4×C22⋊C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#442C2semidirect
3. C2×C61×#416C2semidirect
4. C61×#2363C2semidirect
5. C61×#2339C2semidirect
6. C61×#1973C2semidirect
7. C61×#1935C2semidirect
8. C61×#1927C2semidirect
9. C61×#1893C2semidirect
10. C61×#1879C2semidirect
11. C61×#1877C2semidirect
12. C61×#1862C2semidirect
13. C61×#1854C2semidirect
14. C61×#1762C2semidirect
15. C61×#1752C2semidirect
25. C61×#449C4semidirect
67. C2×#41×C61C2×C4semidirect
80. C2×SD16×C61C2×C4semidirect
92. #121×C61C2×C4semidirect
125. #103×C61C2×C4semidirect
129. #102×C61C2×C4semidirect
130. #102×C61D4semidirect
131. C22⋊C8×C61C2×C4semidirect
333. #22860C61direct (N × H)
378. C2×#442C2×C61semidirect
379. C2×#416C2×C61semidirect
380. #2363C2×C61semidirect
381. #2339C2×C61semidirect
382. #1973C2×C61semidirect
383. #1935C2×C61semidirect
384. #1927C2×C61semidirect
385. #1893C2×C61semidirect
386. #1879C2×C61semidirect
387. #1877C2×C61semidirect
388. #1862C2×C61semidirect
389. #1854C2×C61semidirect
390. #1762C2×C61semidirect
391. #1752C2×C61semidirect
411. #449C4×C61semidirect
448. C61#22860direct (N × H)
454. C2×#41C2×C4×C61semidirect
467. C2×SD16C2×C4×C61semidirect
479. #121C2×C4×C61semidirect
512. #103C2×C4×C61semidirect
516. #102C2×C4×C61semidirect
517. #102D4×C61semidirect
518. C22⋊C8C2×C4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4492
C2×C61×#4422
C2×C61×#4162
C61×#23632
C61×#23392
C61×#19732
C61×#19352
C61×#19272
C61×#18932
C61×#18792
C61×#18772
C61×#18622
C61×#18542
C61×#17622
C61×#17522
#2286061