Finite Group Databasebeta

← C61×#26983 #29530416

Subgroups — C61×#26983 #29530416

Order 15616.

916 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#468C211yesmaximal, characteristic
2C2×C61×#440C211yesmaximal, characteristic, complemented
3C61×#2429C211yesmaximal, characteristic, complemented
4C61×#2422C211yesmaximal, characteristic
5C61×#2083C211yesmaximal, characteristic, complemented
6C61×#2036C211yesmaximal, characteristic, complemented
7C61×#2013C211yesmaximal, characteristic, complemented
8C61×#2000C211yesmaximal, characteristic
9C61×#1956C211yesmaximal, characteristic, complemented
10C61×#1935C211yesmaximal, characteristic, complemented
11C61×#1934C211yesmaximal, characteristic, complemented
12C61×#1894C211yesmaximal, characteristic, complemented
13C61×#1877C211yesmaximal, characteristic, complemented
14C61×#1863C211yesmaximal, characteristic, complemented
15C61×#1753C211yesmaximal, characteristic, complemented
16C22×SD16×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C22×M16×C61C2211yescharacteristic
19C2×C4⋊Q8×C61C2211yescharacteristic
20C2×#123×C61—21no—
21C2×C22⋊Q8×C61C2211yescharacteristic
22C2×C22⋊Q8×C61C2211yescharacteristic
23C2×#121×C61C2211yescharacteristic
24C2×C4×Q8×C61C2211yescharacteristic
25C2×C4×D4×C61C2211yescharacteristic
26C61×#468—24no—
27C61×#440—24no—
28C2×#107×C61C2211yescharacteristic
29C2×#107×C61C2211yescharacteristic
30C2×#103×C61C2211yescharacteristic
31C2×#103×C61C2211yescharacteristic
32C2×#103×C61C2211yescharacteristic
33C2×#103×C61C2211yescharacteristic
34C2×#103×C61C2211yescharacteristic
35C2×#103×C61C2211yescharacteristic
36C2×#102×C61C2211yescharacteristic
37C2×#102×C61C2211yescharacteristic
38C2×C22⋊C8×C61C2211yescharacteristic
39C2×#97×C61C2211yescharacteristic
40C2×C4×C8×C61C2211yescharacteristic
41C61×#398—21no—
42C61×#397—21no—
43C61×#396—21no—
44C61×#394—21no—
45C61×#391C2211yescharacteristic
46C61×#390C2211yescharacteristic
47C61×#389—21no—
48C61×#389C2211yescharacteristic
49C61×#389C2211yescharacteristic
50C61×#388—21no—
51C61×#385—21no—
52C61×#384C2211yescharacteristic
53C61×#380C2211yescharacteristic
54C4×C22⋊C4×C61C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×Q8×C61C2311yescharacteristic
62C22×Q8×C61C2311yescharacteristic
63C22×D4×C61—21no—
64C22×D4×C61C2311yescharacteristic
65C23×C4×C61—21no—
66C23×C4×C61C2311yescharacteristic
67C2×SD16×C61—22no—
68C2×SD16×C61—22no—
69C2×SD16×C61—22no—
70C2×SD16×C61—22no—
71C2×SD16×C61—22no—
72C2×SD16×C61—41no—
73C2×M16×C61—22no—
74C2×M16×C61—22no—
75C2×M16×C61—41no—
76C22×C8×C61C2311yescharacteristic
77C22×C8×C61C2311yescharacteristic
78C22×C8×C61C2311yescharacteristic
79C22×C8×C61C2311yescharacteristic
80C4⋊Q8×C61—22no—
81C4⋊Q8×C61—41no—
82#123×C61—44no—
83C22⋊Q8×C61—22no—
84C22⋊Q8×C61—22no—
85C22⋊Q8×C61—41no—
86C22⋊Q8×C61—41no—
87#121×C61—22no—
88#121×C61—41no—
89C4×Q8×C61—22no—
90C4×Q8×C61—41no—
91C4×D4×C61—22no—
92C4×D4×C61—41no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
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×C61D411yescharacteristic
115C2×C22⋊C4×C61D411yescharacteristic
116C2×C42×C61—21no—
117C2×C42×C61C2311yescharacteristic
118C2×C42×C61C2311yescharacteristic
119#107×C61—22no—
120#107×C61—22no—
121#103×C61—22no—
122#103×C61—22no—
123#103×C61—22no—
124#103×C61—22no—
125#103×C61—41no—
126#103×C61—41no—
127#102×C61—41no—
128#102×C61D414yes—
129C22⋊C8×C61—22no—
130#97×C61—22no—
131C4×C8×C61—41no—
132#95×C61—21no—
133#95×C61—21no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61—21no—
137#95×C61D411yescharacteristic
138#95×C61D411yescharacteristic
139C24×C61—21no—
140C24×C61C2×D411yescharacteristic
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—21no—
152C2×Q8×C61#4112yes—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—42no—
159C2×D4×C61—42no—
160C2×D4×C61—81no—
161C2×D4×C61C2×D412yes—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—42no—
176C22×C4×C61—42no—
177C22×C4×C61—81no—
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2411yescharacteristic
184SD16×C61—28no—
185SD16×C61—44no—
186M16×C61—44no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61C2×D412yes—
197C2×C8×C61#4112yes—
198C2×C8×C61#4112yes—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—42no—
209C4⋊C4×C61—42no—
210C4⋊C4×C61—42no—
211C4⋊C4×C61—42no—
212C4⋊C4×C61—42no—
213C4⋊C4×C61—42no—
214C4⋊C4×C61—42no—
215C4⋊C4×C61—42no—
216C4⋊C4×C61—81no—
217C4⋊C4×C61C2×D412yes—
218C22⋊C4×C61—22no—
219C22⋊C4×C61—22no—
220C22⋊C4×C61—42no—
221C22⋊C4×C61—42no—
222C22⋊C4×C61—42no—
223C22⋊C4×C61—42no—
224C22⋊C4×C61—42no—
225C22⋊C4×C61—42no—
226C22⋊C4×C61—42no—
227C42×C61—21no—
228C42×C61—21no—
229C42×C61—21no—
230C42×C61—21no—
231C42×C61—42no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—22no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61C22×D411yescharacteristic
247Q8×C61—22no—
248Q8×C61—22no—
249Q8×C61—41no—
250Q8×C61—41no—
251Q8×C61—41no—
252Q8×C61—41no—
253Q8×C61—41no—
254Q8×C61—41no—
255D4×C61—22no—
256D4×C61—22no—
257D4×C61—41no—
258D4×C61—41no—
259D4×C61—84no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—22no—
268C2×C4×C61—21no—
269C2×C4×C61—22no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
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—41no—
297C2×C4×C61—41no—
298C2×C4×C61—84no—
299C2×C4×C61AGL(1,ℤ/8)12yes—
300C2×C4×C61#13712yes—
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61H(5,𝔽2)11yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C8×C61—22no—
308C8×C61—22no—
309C8×C61—22no—
310C8×C61—41no—
311#26983C6111yesmaximal, characteristic, direct product factor, Sylow
312C22×C61—41no—
313C22×C61—41no—
314C22×C61—41no—
315C22×C61—42no—
316C22×C61—42no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—42no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61—81no—
323C22×C61—81no—
324C22×C61—81no—
325C22×C61—81no—
326C22×C61#53211yescharacteristic
327C22×C61D4211yescharacteristic
328C22×C61#54611yescharacteristic
329C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
330C22×C61C2×#13711yescharacteristic
331C22×C61#57711yescharacteristic
332C22×C61#57811yescharacteristic
333C4×C61—22no—
334C4×C61—22no—
335C4×C61—41no—
336C4×C61—42no—
337C4×C61—41no—
338C4×C61—42no—
339C4×C61—41no—
340C4×C61—81no—
341C4×C61—81no—
342C4×C61—81no—
343C4×C61—81no—
344C4×C61—81no—
345C4×C61#52511yescharacteristic
346C4×C61#54011yescharacteristic
347C4×C61#54611yescharacteristic
348C4×C61#55311yescharacteristic
349C2×#468C2×C6111yescharacteristic
350C2×#440C2×C6111yescharacteristic, complemented
351#2429C2×C6111yescharacteristic, complemented
352#2422C2×C6111yescharacteristic
353#2083C2×C6111yescharacteristic, complemented
354#2036C2×C6111yescharacteristic, complemented
355#2013C2×C6111yescharacteristic, complemented
356#2000C2×C6111yescharacteristic
357#1956C2×C6111yescharacteristic, complemented
358#1935C2×C6111yescharacteristic, complemented
359#1934C2×C6111yescharacteristic, complemented
360#1894C2×C6111yescharacteristic, complemented
361#1877C2×C6111yescharacteristic, complemented
362#1863C2×C6111yescharacteristic, complemented
363#1753C2×C6111yescharacteristic, complemented
364C2×C61—81no—
365C2×C61—82no—
366C2×C61#246411yescharacteristic
367C2×C61#317811yescharacteristic
368C2×C61#318211yescharacteristic
369C2×C61#327211yescharacteristic
370C2×C61#327611yescharacteristic
371C2×C61#330811yescharacteristic
372C2×C61#332011yescharacteristic
373C22×SD16C22×C6111yescharacteristic
374C22×SD16C22×C6111yescharacteristic
375C22×M16C22×C6111yescharacteristic
376C2×C4⋊Q8C22×C6111yescharacteristic
377C2×#123—21no—
378C2×C22⋊Q8C22×C6111yescharacteristic
379C2×C22⋊Q8C22×C6111yescharacteristic
380C2×#121C22×C6111yescharacteristic
381C2×C4×Q8C22×C6111yescharacteristic
382C2×C4×D4C22×C6111yescharacteristic
383#468—24no—
384#440—24no—
385C2×#107C22×C6111yescharacteristic
386C2×#107C22×C6111yescharacteristic
387C2×#103C22×C6111yescharacteristic
388C2×#103C22×C6111yescharacteristic
389C2×#103C22×C6111yescharacteristic
390C2×#103C22×C6111yescharacteristic
391C2×#103C22×C6111yescharacteristic
392C2×#103C22×C6111yescharacteristic
393C2×#102C22×C6111yescharacteristic
394C2×#102C22×C6111yescharacteristic
395C2×C22⋊C8C22×C6111yescharacteristic
396C2×#97C22×C6111yescharacteristic
397C2×C4×C8C22×C6111yescharacteristic
398#398—21no—
399#397—21no—
400#396—21no—
401#394—21no—
402#391C22×C6111yescharacteristic
403#390C22×C6111yescharacteristic
404#389—21no—
405#389C22×C6111yescharacteristic
406#389C22×C6111yescharacteristic
407#388—21no—
408#385—21no—
409#384C22×C6111yescharacteristic
410#380C22×C6111yescharacteristic
411C4×C22⋊C4C22×C6111yescharacteristic
412#340C22×C6111yescharacteristic
413#340C22×C6111yescharacteristic
414#340C22×C6111yescharacteristic
415#340C22×C6111yescharacteristic
416#336C22×C6111yescharacteristic
417#336C22×C6111yescharacteristic
418C61#2698311yescharacteristic, direct product factor, Sylow
419C22×Q8C23×C6111yescharacteristic
420C22×Q8C23×C6111yescharacteristic
421C22×D4—21no—
422C22×D4C23×C6111yescharacteristic
423C23×C4—21no—
424C23×C4C23×C6111yescharacteristic
425C2×SD16—22no—
426C2×SD16—22no—
427C2×SD16—22no—
428C2×SD16—22no—
429C2×SD16—22no—
430C2×SD16—41no—
431C2×M16—22no—
432C2×M16—22no—
433C2×M16—41no—
434C22×C8C23×C6111yescharacteristic
435C22×C8C23×C6111yescharacteristic
436C22×C8C23×C6111yescharacteristic
437C22×C8C23×C6111yescharacteristic
438C4⋊Q8—22no—
439C4⋊Q8—41no—
440#123—44no—
441C22⋊Q8—22no—
442C22⋊Q8—22no—
443C22⋊Q8—41no—
444C22⋊Q8—41no—
445#121—22no—
446#121—41no—
447C4×Q8—22no—
448C4×Q8—41no—
449C4×D4—22no—
450C4×D4—41no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4C23×C6111yescharacteristic
461C2×C4⋊C4C23×C6111yescharacteristic
462C2×C4⋊C4C23×C6111yescharacteristic
463C2×C4⋊C4C23×C6111yescharacteristic
464C2×C4⋊C4C23×C6111yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4D4×C6111yescharacteristic
473C2×C22⋊C4D4×C6111yescharacteristic
474C2×C42—21no—
475C2×C42C23×C6111yescharacteristic
476C2×C42C23×C6111yescharacteristic
477#107—22no—
478#107—22no—
479#103—22no—
480#103—22no—
481#103—22no—
482#103—22no—
483#103—41no—
484#103—41no—
485#102—41no—
486#102D4×C6114yes—
487C22⋊C8—22no—
488#97—22no—
489C4×C8—41no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95D4×C6111yescharacteristic
496#95D4×C6111yescharacteristic
497C24—21no—
498C24C2×D4×C6111yescharacteristic
499C2×Q8—21no—
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#41×C6112yes—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—81no—
519C2×D4C2×D4×C6112yes—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—81no—
536C22×C4C2×D4×C6111yescharacteristic
537C22×C4C2×D4×C6111yescharacteristic
538C22×C4C2×D4×C6111yescharacteristic
539C22×C4C2×D4×C6111yescharacteristic
540C22×C4C2×D4×C6111yescharacteristic
541C22×C4C24×C6111yescharacteristic
542SD16—28no—
543SD16—44no—
544M16—44no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8C2×D4×C6112yes—
555C2×C8#41×C6112yes—
556C2×C8#41×C6112yes—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—81no—
575C4⋊C4C2×D4×C6112yes—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—42no—
590C23—21no—
591C23—21no—
592C23—22no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23C22×D4×C6111yescharacteristic
605Q8—22no—
606Q8—22no—
607Q8—41no—
608Q8—41no—
609Q8—41no—
610Q8—41no—
611Q8—41no—
612Q8—41no—
613D4—22no—
614D4—22no—
615D4—41no—
616D4—41no—
617D4—84no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
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—41no—
656C2×C4—84no—
657C2×C4AGL(1,ℤ/8)×C6112yes—
658C2×C4#137×C6112yes—
659C2×C4C22×D4×C6111yescharacteristic
660C2×C4C2×#41×C6111yescharacteristic
661C2×C4C2×#41×C6111yescharacteristic
662C2×C4C2×#41×C6111yescharacteristic
663C2×C4H(5,𝔽2)×C6111yescharacteristic
664C2×C4H(5,𝔽2)×C6111yescharacteristic
665C8—22no—
666C8—22no—
667C8—22no—
668C8—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—42no—
675C22—42no—
676C22—41no—
677C22—41no—
678C22—42no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C61×#53211yescharacteristic
684C22D42×C6111yescharacteristic
685C22C61×#54611yescharacteristic
686C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
687C22C2×#137×C6111yescharacteristic
688C22C61×#57711yescharacteristic
689C22C61×#57811yescharacteristic
690C4—22no—
691C4—22no—
692C4—41no—
693C4—42no—
694C4—41no—
695C4—42no—
696C4—41no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4C61×#52511yescharacteristic
703C4C61×#54011yescharacteristic
704C4C61×#54611yescharacteristic
705C4C61×#55311yescharacteristic
706C2—81no—
707C2—82no—
708C2C61×#246411yescharacteristic
709C2C61×#317811yescharacteristic
710C2C61×#318211yescharacteristic
711C2C61×#327211yescharacteristic
712C2C61×#327611yescharacteristic
713C2C61×#330811yescharacteristic
714C2C61×#332011yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×#121×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
2. C2×C61×#440C2semidirect
3. C61×#2429C2semidirect
5. C61×#2083C2semidirect
6. C61×#2036C2semidirect
7. C61×#2013C2semidirect
9. C61×#1956C2semidirect
10. C61×#1935C2semidirect
11. C61×#1934C2semidirect
12. C61×#1894C2semidirect
13. C61×#1877C2semidirect
14. C61×#1863C2semidirect
15. C61×#1753C2semidirect
311. #26983C61direct (N × H)
350. C2×#440C2×C61semidirect
351. #2429C2×C61semidirect
353. #2083C2×C61semidirect
354. #2036C2×C61semidirect
355. #2013C2×C61semidirect
357. #1956C2×C61semidirect
358. #1935C2×C61semidirect
359. #1934C2×C61semidirect
360. #1894C2×C61semidirect
361. #1877C2×C61semidirect
362. #1863C2×C61semidirect
363. #1753C2×C61semidirect
418. C61#26983direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#4682
C2×C61×#4402
C61×#24292
C61×#24222
C61×#20832
C61×#20362
C61×#20132
C61×#20002
C61×#19562
C61×#19352
C61×#19342
C61×#18942
C61×#18772
C61×#18632
C61×#17532
#2698361