Finite Group Databasebeta

← C61×#25978 #29529411

Subgroups — C61×#25978 #29529411

Order 15616.

1032 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×#476C211yesmaximal, characteristic, complemented
2C2×C61×#417C211yesmaximal, characteristic
3C61×#2440C211yesmaximal, characteristic, complemented
4C61×#2339C211yesmaximal, characteristic
5C61×#2096C211yesmaximal, characteristic, complemented
6C61×#2068C211yesmaximal, characteristic, complemented
7C61×#2066C211yesmaximal, characteristic, complemented
8C61×#2024C211yesmaximal, characteristic, complemented
9C61×#1864C211yesmaximal, characteristic, complemented
10C61×#1862C211yesmaximal, characteristic, complemented
11C61×#1853C211yesmaximal, characteristic, complemented
12C61×#1851C211yesmaximal, characteristic, complemented
13C61×#1809C211yesmaximal, characteristic, complemented
14C61×#1802C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic
16C22×#41×C61C2211yescharacteristic
17C22×M16×C61C2211yescharacteristic
18C2×C4⋊Q8×C61C2211yescharacteristic
19C2×C22⋊Q8×C61—21no—
20C2×C4×D4×C61C2211yescharacteristic
21C2×C4×D4×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2211yescharacteristic
23C61×#476—24no—
24C2×#107×C61C2211yescharacteristic
25C2×#106×C61C2211yescharacteristic
26C2×#106×C61C2211yescharacteristic
27C2×#106×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×C4⋊C8×C61C2211yescharacteristic
30C61×#417—24no—
31C2×#103×C61C2211yescharacteristic
32C2×#103×C61C2211yescharacteristic
33C2×#103×C61C2211yescharacteristic
34C2×#103×C61C2211yescharacteristic
35C2×#102×C61C2211yescharacteristic
36C2×#102×C61C2211yescharacteristic
37C2×#102×C61C2211yescharacteristic
38C2×#102×C61C2211yescharacteristic
39C2×C22⋊C8×C61C2211yescharacteristic
40C61×#398—21no—
41C61×#395—21no—
42C61×#391C2211yescharacteristic
43C61×#391C2211yescharacteristic
44C61×#389C2211yescharacteristic
45C61×#389C2211yescharacteristic
46C61×#386—21no—
47C61×#386—21no—
48C61×#385—21no—
49C61×#384C2211yescharacteristic
50C61×#381—21no—
51C61×#380C2211yescharacteristic
52C61×#380C2211yescharacteristic
53C4×C22⋊C4×C61C2211yescharacteristic
54C2×#95×C61—21no—
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C2×#41×C61—22no—
62C2×#41×C61—22no—
63C2×#41×C61—22no—
64C2×#41×C61—41no—
65C2×#41×C61—41no—
66C2×#41×C61Q814yescomplemented
67C22×Q8×C61—21no—
68C22×Q8×C61C2311yescharacteristic
69C22×D4×C61—21no—
70C22×D4×C61C2311yescharacteristic
71C23×C4×C61—21no—
72C23×C4×C61—21no—
73C23×C4×C61—21no—
74C23×C4×C61—21no—
75C23×C4×C61C2311yescharacteristic
76C2×M16×C61—22no—
77C2×M16×C61—22no—
78C2×M16×C61—41no—
79C22×C8×C61C2311yescharacteristic
80C22×C8×C61C2311yescharacteristic
81C22×C8×C61C2311yescharacteristic
82C22×C8×C61C2311yescharacteristic
83C4⋊Q8×C61—22no—
84C4⋊Q8×C61—41no—
85C22⋊Q8×C61—44no—
86C4×D4×C61—22no—
87C4×D4×C61—22no—
88C4×D4×C61—41no—
89C4×D4×C61—41no—
90C2×C4⋊C4×C61—22no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—41no—
98C2×C4⋊C4×C61C2311yescharacteristic
99C2×C4⋊C4×C61C2311yescharacteristic
100C2×C4⋊C4×C61C2311yescharacteristic
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C4⋊C4×C61C2311yescharacteristic
104C2×C22⋊C4×C61—21no—
105C2×C22⋊C4×C61—21no—
106C2×C22⋊C4×C61—21no—
107C2×C22⋊C4×C61—21no—
108C2×C22⋊C4×C61D411yescharacteristic
109C2×C22⋊C4×C61D411yescharacteristic
110C2×C42×C61C2311yescharacteristic
111C2×C42×C61C2311yescharacteristic
112#107×C61—41no—
113#106×C61—22no—
114#106×C61—22no—
115#106×C61—41no—
116C4⋊C8×C61—22no—
117C4⋊C8×C61—41no—
118#103×C61—22no—
119#103×C61—22no—
120#103×C61—41no—
121#103×C61—41no—
122#102×C61—22no—
123#102×C61—22no—
124#102×C61—22no—
125#102×C61D414yes—
126C22⋊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×C61D411yescharacteristic
136#95×C61D411yescharacteristic
137C24×C61—21no—
138C24×C61C2×D411yescharacteristic
139#41×C61—28no—
140#41×C61—44no—
141#41×C61—44no—
142#41×C61—44no—
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—42no—
149C2×Q8×C61—42no—
150C2×Q8×C61—81no—
151C2×Q8×C61C2×Q812yes—
152C2×D4×C61—24no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—42no—
157C2×D4×C61—42no—
158C2×D4×C61C2×D412yes—
159C2×D4×C61C2×Q812yes—
160C2×D4×C61#4112yes—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—24no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—42no—
174C22×C4×C61—42no—
175C22×C4×C61—42no—
176C22×C4×C61—42no—
177C22×C4×C61—42no—
178C22×C4×C61—42no—
179C22×C4×C61—42no—
180C22×C4×C61—42no—
181C22×C4×C61—81no—
182C22×C4×C61—81no—
183C22×C4×C61—81no—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×Q812yes—
190C22×C4×C61#4112yes—
191C22×C4×C61C2411yescharacteristic
192M16×C61—44no—
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×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61C2×D412yes—
205C4⋊C4×C61—21no—
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—42no—
217C4⋊C4×C61—42no—
218C4⋊C4×C61—42no—
219C4⋊C4×C61—42no—
220C4⋊C4×C61—42no—
221C4⋊C4×C61—81no—
222C4⋊C4×C61C2×D412yes—
223C22⋊C4×C61—22no—
224C22⋊C4×C61—22no—
225C22⋊C4×C61—42no—
226C22⋊C4×C61—42no—
227C22⋊C4×C61—42no—
228C22⋊C4×C61—81no—
229C42×C61—21no—
230C42×C61—21no—
231C42×C61—21no—
232C42×C61—21no—
233C23×C61—22no—
234C23×C61—22no—
235C23×C61—21no—
236C23×C61—22no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61C22⋊Q812yes—
247C23×C61C22×D411yescharacteristic
248Q8×C61—22no—
249Q8×C61—22no—
250Q8×C61—41no—
251Q8×C61—41no—
252Q8×C61—84no—
253D4×C61—22no—
254D4×C61—22no—
255D4×C61—22no—
256D4×C61—48no—
257D4×C61C22⋊Q814yescomplemented
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—21no—
270C2×C4×C61—22no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—48no—
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×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—84no—
297C2×C4×C61—84no—
298C2×C4×C61—84no—
299C2×C4×C61C22⋊Q812yes—
300C2×C4×C61AGL(1,ℤ/8)12yes—
301C2×C4×C61#13712yes—
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×Q811yescharacteristic
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—41no—
310C8×C61—41no—
311C8×C61—41no—
312#25978C6111yesmaximal, characteristic, direct product factor, Sylow
313C22×C61—22no—
314C22×C61—22no—
315C22×C61—22no—
316C22×C61—24no—
317C22×C61—41no—
318C22×C61—42no—
319C22×C61—42no—
320C22×C61—42no—
321C22×C61—42no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61—42no—
325C22×C61—42no—
326C22×C61—41no—
327C22×C61C2×C22⋊Q811yescharacteristic
328C22×C61D4211yescharacteristic
329C22×C61#54611yescharacteristic
330C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
331C22×C61C2×#13711yescharacteristic
332C22×C61#57711yescharacteristic
333C22×C61#57711yescharacteristic
334C4×C61—22no—
335C4×C61—22no—
336C4×C61—22no—
337C4×C61—41no—
338C4×C61—42no—
339C4×C61—41no—
340C4×C61—42no—
341C4×C61—81no—
342C4×C61—81no—
343C4×C61—81no—
344C4×C61—81no—
345C4×C61—81no—
346C4×C61C2×C22⋊Q811yescharacteristic
347C4×C61#54311yescharacteristic
348C4×C61#54611yescharacteristic
349C4×C61#55111yescharacteristic
350C2×#476C2×C6111yescharacteristic, complemented
351C2×#417C2×C6111yescharacteristic
352#2440C2×C6111yescharacteristic, complemented
353#2339C2×C6111yescharacteristic
354#2096C2×C6111yescharacteristic, complemented
355#2068C2×C6111yescharacteristic, complemented
356#2066C2×C6111yescharacteristic, complemented
357#2024C2×C6111yescharacteristic, complemented
358#1864C2×C6111yescharacteristic, complemented
359#1862C2×C6111yescharacteristic, complemented
360#1853C2×C6111yescharacteristic, complemented
361#1851C2×C6111yescharacteristic, complemented
362#1809C2×C6111yescharacteristic, complemented
363#1802C2×C6111yescharacteristic, complemented
364#1788C2×C6111yescharacteristic
365C2×C61—42no—
366C2×C61—44no—
367C2×C61#243711yescharacteristic
368C2×C61#307911yescharacteristic
369C2×C61#308411yescharacteristic
370C2×C61#326611yescharacteristic
371C2×C61#327211yescharacteristic
372C2×C61#330611yescharacteristic
373C2×C61#333111yescharacteristic
374C22×#41C22×C6111yescharacteristic
375C22×M16C22×C6111yescharacteristic
376C2×C4⋊Q8C22×C6111yescharacteristic
377C2×C22⋊Q8—21no—
378C2×C4×D4C22×C6111yescharacteristic
379C2×C4×D4C22×C6111yescharacteristic
380C22×C4⋊C4C22×C6111yescharacteristic
381#476—24no—
382C2×#107C22×C6111yescharacteristic
383C2×#106C22×C6111yescharacteristic
384C2×#106C22×C6111yescharacteristic
385C2×#106C22×C6111yescharacteristic
386C2×C4⋊C8C22×C6111yescharacteristic
387C2×C4⋊C8C22×C6111yescharacteristic
388#417—24no—
389C2×#103C22×C6111yescharacteristic
390C2×#103C22×C6111yescharacteristic
391C2×#103C22×C6111yescharacteristic
392C2×#103C22×C6111yescharacteristic
393C2×#102C22×C6111yescharacteristic
394C2×#102C22×C6111yescharacteristic
395C2×#102C22×C6111yescharacteristic
396C2×#102C22×C6111yescharacteristic
397C2×C22⋊C8C22×C6111yescharacteristic
398#398—21no—
399#395—21no—
400#391C22×C6111yescharacteristic
401#391C22×C6111yescharacteristic
402#389C22×C6111yescharacteristic
403#389C22×C6111yescharacteristic
404#386—21no—
405#386—21no—
406#385—21no—
407#384C22×C6111yescharacteristic
408#381—21no—
409#380C22×C6111yescharacteristic
410#380C22×C6111yescharacteristic
411C4×C22⋊C4C22×C6111yescharacteristic
412C2×#95—21no—
413#340C22×C6111yescharacteristic
414#340C22×C6111yescharacteristic
415#340C22×C6111yescharacteristic
416#340C22×C6111yescharacteristic
417#336C22×C6111yescharacteristic
418#336C22×C6111yescharacteristic
419C61#2597811yescharacteristic, direct product factor, Sylow
420C2×#41—22no—
421C2×#41—22no—
422C2×#41—22no—
423C2×#41—41no—
424C2×#41—41no—
425C2×#41Q8×C6114yescomplemented
426C22×Q8—21no—
427C22×Q8C23×C6111yescharacteristic
428C22×D4—21no—
429C22×D4C23×C6111yescharacteristic
430C23×C4—21no—
431C23×C4—21no—
432C23×C4—21no—
433C23×C4—21no—
434C23×C4C23×C6111yescharacteristic
435C2×M16—22no—
436C2×M16—22no—
437C2×M16—41no—
438C22×C8C23×C6111yescharacteristic
439C22×C8C23×C6111yescharacteristic
440C22×C8C23×C6111yescharacteristic
441C22×C8C23×C6111yescharacteristic
442C4⋊Q8—22no—
443C4⋊Q8—41no—
444C22⋊Q8—44no—
445C4×D4—22no—
446C4×D4—22no—
447C4×D4—41no—
448C4×D4—41no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4C23×C6111yescharacteristic
458C2×C4⋊C4C23×C6111yescharacteristic
459C2×C4⋊C4C23×C6111yescharacteristic
460C2×C4⋊C4C23×C6111yescharacteristic
461C2×C4⋊C4C23×C6111yescharacteristic
462C2×C4⋊C4C23×C6111yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4D4×C6111yescharacteristic
468C2×C22⋊C4D4×C6111yescharacteristic
469C2×C42C23×C6111yescharacteristic
470C2×C42C23×C6111yescharacteristic
471#107—41no—
472#106—22no—
473#106—22no—
474#106—41no—
475C4⋊C8—22no—
476C4⋊C8—41no—
477#103—22no—
478#103—22no—
479#103—41no—
480#103—41no—
481#102—22no—
482#102—22no—
483#102—22no—
484#102D4×C6114yes—
485C22⋊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#95D4×C6111yescharacteristic
495#95D4×C6111yescharacteristic
496C24—21no—
497C24C2×D4×C6111yescharacteristic
498#41—28no—
499#41—44no—
500#41—44no—
501#41—44no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—81no—
510C2×Q8C2×Q8×C6112yes—
511C2×D4—24no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4C2×D4×C6112yes—
518C2×D4C2×Q8×C6112yes—
519C2×D4#41×C6112yes—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—81no—
541C22×C4—81no—
542C22×C4—81no—
543C22×C4C2×D4×C6111yescharacteristic
544C22×C4C2×D4×C6111yescharacteristic
545C22×C4C2×D4×C6111yescharacteristic
546C22×C4C2×D4×C6111yescharacteristic
547C22×C4C2×D4×C6111yescharacteristic
548C22×C4C2×Q8×C6112yes—
549C22×C4#41×C6112yes—
550C22×C4C24×C6111yescharacteristic
551M16—44no—
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×C8—21no—
562C2×C8—21no—
563C2×C8C2×D4×C6112yes—
564C4⋊C4—21no—
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—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—81no—
581C4⋊C4C2×D4×C6112yes—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—81no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C23—22no—
593C23—21no—
594C23—22no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—22no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C22⋊Q8×C6112yes—
606C23C22×D4×C6111yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—84no—
612D4—22no—
613D4—22no—
614D4—22no—
615D4—48no—
616D4C22⋊Q8×C6114yescomplemented
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—22no—
635C2×C4—48no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
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—84no—
656C2×C4—84no—
657C2×C4—84no—
658C2×C4C22⋊Q8×C6112yes—
659C2×C4AGL(1,ℤ/8)×C6112yes—
660C2×C4#137×C6112yes—
661C2×C4C22×D4×C6111yescharacteristic
662C2×C4C22×Q8×C6111yescharacteristic
663C2×C4C2×#41×C6111yescharacteristic
664C2×C4C2×#41×C6111yescharacteristic
665C2×C4H(5,𝔽2)×C6111yescharacteristic
666C2×C4H(5,𝔽2)×C6111yescharacteristic
667C8—22no—
668C8—41no—
669C8—41no—
670C8—41no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—24no—
675C22—42no—
676C22—41no—
677C22—41no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22—41no—
683C22—41no—
684C22—42no—
685C22C2×C22⋊Q8×C6111yescharacteristic
686C22D42×C6111yescharacteristic
687C22C61×#54611yescharacteristic
688C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
689C22C2×#137×C6111yescharacteristic
690C22C61×#57711yescharacteristic
691C22C61×#57711yescharacteristic
692C4—22no—
693C4—22no—
694C4—22no—
695C4—41no—
696C4—42no—
697C4—41no—
698C4—42no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4C2×C22⋊Q8×C6111yescharacteristic
705C4C61×#54311yescharacteristic
706C4C61×#54611yescharacteristic
707C4C61×#55111yescharacteristic
708C2—42no—
709C2—44no—
710C2C61×#243711yescharacteristic
711C2C61×#307911yescharacteristic
712C2C61×#308411yescharacteristic
713C2C61×#326611yescharacteristic
714C2C61×#327211yescharacteristic
715C2C61×#330611yescharacteristic
716C2C61×#333111yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC22×#41×C61C22
LCSG ▷ C22×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
1. C2×C61×#476C2semidirect
3. C61×#2440C2semidirect
5. C61×#2096C2semidirect
6. C61×#2068C2semidirect
7. C61×#2066C2semidirect
8. C61×#2024C2semidirect
9. C61×#1864C2semidirect
10. C61×#1862C2semidirect
11. C61×#1853C2semidirect
12. C61×#1851C2semidirect
13. C61×#1809C2semidirect
14. C61×#1802C2semidirect
66. C2×#41×C61Q8semidirect
257. D4×C61C22⋊Q8semidirect
312. #25978C61direct (N × H)
350. C2×#476C2×C61semidirect
352. #2440C2×C61semidirect
354. #2096C2×C61semidirect
355. #2068C2×C61semidirect
356. #2066C2×C61semidirect
357. #2024C2×C61semidirect
358. #1864C2×C61semidirect
359. #1862C2×C61semidirect
360. #1853C2×C61semidirect
361. #1851C2×C61semidirect
362. #1809C2×C61semidirect
363. #1802C2×C61semidirect
419. C61#25978direct (N × H)
425. C2×#41Q8×C61semidirect
616. D4C22⋊Q8×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4762
C2×C61×#4172
C61×#24402
C61×#23392
C61×#20962
C61×#20682
C61×#20662
C61×#20242
C61×#18642
C61×#18622
C61×#18532
C61×#18512
C61×#18092
C61×#18022
C61×#17882
#2597861