Finite Group Databasebeta

← C61×#22584 #29526017

Subgroups — C61×#22584 #29526017

Order 15616.

1150 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#418C211yesmaximal, characteristic
2C61×#2346C211yesmaximal, characteristic, complemented
3D4×C22⋊C4×C61C211yesmaximal, characteristic
4C61×#1936C211yesmaximal, characteristic, complemented
5C61×#1934C211yesmaximal, characteristic, complemented
6C61×#1926C211yesmaximal, characteristic, complemented
7C61×#1925C211yesmaximal, characteristic, complemented
8C61×#1864C211yesmaximal, characteristic, complemented
9C61×#1862C211yesmaximal, characteristic, complemented
10C61×#1825C211yesmaximal, characteristic, complemented
11C61×#1809C211yesmaximal, characteristic, complemented
12C61×#1786C211yesmaximal, characteristic
13C61×#1762C211yesmaximal, characteristic, complemented
14C4×#102×C61C211yesmaximal, characteristic, complemented
15C61×#1753C211yesmaximal, characteristic, complemented
16C23×D4×C61C2211yescharacteristic
17C22×M16×C61C2211yescharacteristic
18C2×C4×D4×C61C2211yescharacteristic
19C2×C4×D4×C61C2211yescharacteristic
20C2×#117×C61C2211yescharacteristic
21C22×C22⋊C4×C61—21no—
22C2×#107×C61C2211yescharacteristic, complemented
23C2×#106×C61C2211yescharacteristic, complemented
24C61×#418C418yescomplemented
25C2×#102×C61C2211yescharacteristic
26C2×#102×C61C2211yescharacteristic
27C2×#102×C61C2211yescharacteristic
28C2×#102×C61C2211yescharacteristic
29C2×#102×C61C2211yescharacteristic
30C2×#102×C61C2211yescharacteristic
31C2×#102×C61C2211yescharacteristic
32C2×#102×C61C2211yescharacteristic
33C2×C22⋊C8×C61C2211yescharacteristic
34C2×#97×C61C2211yescharacteristic, complemented
35C2×C4×C8×C61C2211yescharacteristic, complemented
36C61×#390C2211yescharacteristic
37C61×#390C2211yescharacteristic
38C61×#389C2211yescharacteristic, complemented
39C61×#389C2211yescharacteristic, complemented
40C61×#388—21no—
41C61×#388—21no—
42C61×#386—21no—
43C61×#386—21no—
44C61×#382—21no—
45C61×#380C2211yescharacteristic
46C61×#380C2211yescharacteristic
47C61×#379—21no—
48C4×C4⋊C4×C61C2211yescharacteristic, complemented
49C4×C4⋊C4×C61C2211yescharacteristic, complemented
50C4×C22⋊C4×C61C2211yescharacteristic
51C61×#376—21no—
52C61×#340C2211yescharacteristic, complemented
53C61×#340C2211yescharacteristic, complemented
54C61×#340C2211yescharacteristic, complemented
55C61×#340C2211yescharacteristic, complemented
56C61×#340C2211yescharacteristic, complemented
57C61×#340C2211yescharacteristic, complemented
58C61×#336C2211yescharacteristic, complemented
59C61×#336C2211yescharacteristic, complemented
60C25×C61—21no—
61C22×D4×C61—22no—
62C22×D4×C61—22no—
63C22×D4×C61—21no—
64C22×D4×C61—22no—
65C22×D4×C61—41no—
66C22×D4×C61—41no—
67C22×D4×C61C2×C414yes—
68C22×D4×C61C2311yescharacteristic
69C22×D4×C61C2311yescharacteristic
70C23×C4×C61—21no—
71C23×C4×C61—21no—
72C23×C4×C61C2311yescharacteristic
73C2×M16×C61—41no—
74C2×M16×C61—41no—
75C2×M16×C61C2×C414yescomplemented
76C22×C8×C61C2311yescharacteristic
77C22×C8×C61C2311yescharacteristic
78C22×C8×C61C2311yescharacteristic
79C22×C8×C61C2311yescharacteristic
80C4×D4×C61—22no—
81C4×D4×C61—22no—
82C4×D4×C61—41no—
83C4×D4×C61—41no—
84#117×C61—22no—
85#117×C61C2×C414yescomplemented
86C2×C4⋊C4×C61—21no—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61C2311yescharacteristic
89C2×C4⋊C4×C61C2311yescharacteristic
90C2×C4⋊C4×C61C2311yescharacteristic
91C2×C4⋊C4×C61C2311yescharacteristic
92C2×C4⋊C4×C61C2311yescharacteristic
93C2×C4⋊C4×C61C2311yescharacteristic
94C2×C22⋊C4×C61—21no—
95C2×C22⋊C4×C61—21no—
96C2×C22⋊C4×C61—21no—
97C2×C22⋊C4×C61—21no—
98C2×C22⋊C4×C61—21no—
99C2×C22⋊C4×C61—21no—
100C2×C22⋊C4×C61—21no—
101C2×C22⋊C4×C61—21no—
102C2×C22⋊C4×C61—21no—
103C2×C22⋊C4×C61—44no—
104C2×C22⋊C4×C61D411yescharacteristic
105C2×C22⋊C4×C61D411yescharacteristic
106C2×C42×C61—21no—
107C2×C42×C61—21no—
108C2×C42×C61—21no—
109C2×C42×C61C2311yescharacteristic
110C2×C42×C61C2311yescharacteristic
111#107×C61—41no—
112#106×C61—41no—
113#102×C61—22no—
114#102×C61—22no—
115#102×C61—41no—
116#102×C61—41no—
117#102×C61C2×C414yes—
118#102×C61C2×C414yes—
119#102×C61C2×C414yescomplemented
120#102×C61C2×C414yescomplemented
121C22⋊C8×C61—22no—
122#97×C61—41no—
123C4×C8×C61—41no—
124#95×C61—21no—
125#95×C61—21no—
126#95×C61—21no—
127#95×C61—21no—
128#95×C61—21no—
129#95×C61—21no—
130#95×C61D411yescharacteristic
131#95×C61D411yescharacteristic
132C24×C61—21no—
133C24×C61—21no—
134C24×C61—24no—
135C24×C61—42no—
136C24×C61—42no—
137C24×C61—42no—
138C24×C61—42no—
139C24×C61—81no—
140C24×C61—81no—
141C24×C61C2×D411yescharacteristic
142C2×D4×C61—28no—
143C2×D4×C61—24no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—44no—
153C2×D4×C61—44no—
154C2×D4×C61—44no—
155C2×D4×C61—42no—
156C2×D4×C61—42no—
157C2×D4×C61C22×C412yes—
158C2×D4×C61C22×C412yes—
159C2×D4×C61#4112yes—
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—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—42no—
172C22×C4×C61—42no—
173C22×C4×C61—42no—
174C22×C4×C61—42no—
175C22×C4×C61—81no—
176C22×C4×C61—81no—
177C22×C4×C61C22×C412yes—
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61#4112yes—
184C22×C4×C61C2411yescharacteristic
185M16×C61—44no—
186C2×C8×C61—21no—
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×C61C22×C412yes—
197C2×C8×C61C22×C412yes—
198C4⋊C4×C61—21no—
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—81no—
209C4⋊C4×C61—81no—
210C4⋊C4×C61C22×C412yes—
211C4⋊C4×C61C22×C412yes—
212C22⋊C4×C61—24no—
213C22⋊C4×C61—22no—
214C22⋊C4×C61—41no—
215C22⋊C4×C61—42no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—42no—
218C22⋊C4×C61—42no—
219C22⋊C4×C61—42no—
220C22⋊C4×C61—81no—
221C22⋊C4×C61—81no—
222C22⋊C4×C61—81no—
223C42×C61—24no—
224C42×C61—21no—
225C42×C61—21no—
226C42×C61—21no—
227C42×C61—21no—
228C42×C61—42no—
229C42×C61—42no—
230C23×C61—22no—
231C23×C61—22no—
232C23×C61—22no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—22no—
240C23×C61—48no—
241C23×C61—48no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—84no—
253C23×C61—84no—
254C23×C61—84no—
255C23×C61—84no—
256C23×C61—84no—
257C23×C61C4×D412yes—
258C23×C61C22×D411yescharacteristic
259D4×C61—22no—
260D4×C61—22no—
261D4×C61—22no—
262D4×C61—22no—
263D4×C61—22no—
264D4×C61—48no—
265D4×C61—41no—
266D4×C61—41no—
267D4×C61#11714yes—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
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—41no—
302C2×C4×C61—41no—
303C2×C4×C61—84no—
304C2×C4×C61—84no—
305C2×C4×C61C4×D412yes—
306C2×C4×C61AGL(1,ℤ/8)12yes—
307C2×C4×C61C23×C411yescharacteristic
308C2×C4×C61C2×#4111yescharacteristic
309C2×C4×C61C2×#4111yescharacteristic
310C2×C4×C61C2×#4111yescharacteristic
311C2×C4×C61H(5,𝔽2)11yescharacteristic
312C2×C4×C61H(5,𝔽2)11yescharacteristic
313C8×C61—22no—
314C8×C61—22no—
315C8×C61—41no—
316C8×C61—41no—
317#22584C6111yesmaximal, characteristic, direct product factor, Sylow
318C22×C61—22no—
319C22×C61—24no—
320C22×C61—22no—
321C22×C61—22no—
322C22×C61—42no—
323C22×C61—42no—
324C22×C61—42no—
325C22×C61—41no—
326C22×C61—41no—
327C22×C61—42no—
328C22×C61—41no—
329C22×C61—42no—
330C22×C61—42no—
331C22×C61—41no—
332C22×C61—42no—
333C22×C61—42no—
334C22×C61—42no—
335C22×C61—816no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61—81no—
340C22×C61C2×C4×D411yescharacteristic
341C22×C61#54611yescharacteristic
342C22×C61#54611yescharacteristic
343C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
344C22×C61#57511yescharacteristic
345C22×C61#57611yescharacteristic
346C22×C61#57711yescharacteristic
347C4×C61—22no—
348C4×C61—22no—
349C4×C61—42no—
350C4×C61—42no—
351C4×C61—41no—
352C4×C61—41no—
353C4×C61—41no—
354C4×C61—81no—
355C4×C61—81no—
356C4×C61—81no—
357C4×C61—81no—
358C4×C61C2×#11711yescharacteristic
359C4×C61#51811yescharacteristic
360C4×C61#55111yescharacteristic
361C4×C61#55111yescharacteristic
362C2×#418C2×C6111yescharacteristic
363#2346C2×C6111yescharacteristic, complemented
364D4×C22⋊C4C2×C6111yescharacteristic
365#1936C2×C6111yescharacteristic, complemented
366#1934C2×C6111yescharacteristic, complemented
367#1926C2×C6111yescharacteristic, complemented
368#1925C2×C6111yescharacteristic, complemented
369#1864C2×C6111yescharacteristic, complemented
370#1862C2×C6111yescharacteristic, complemented
371#1825C2×C6111yescharacteristic, complemented
372#1809C2×C6111yescharacteristic, complemented
373#1786C2×C6111yescharacteristic
374#1762C2×C6111yescharacteristic, complemented
375C4×#102C2×C6111yescharacteristic, complemented
376#1753C2×C6111yescharacteristic, complemented
377C2×C61—42no—
378C2×C61—44no—
379C2×C61—82no—
380C2×C61#234211yescharacteristic
381C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
382C2×C61#294611yescharacteristic
383C2×C61#331011yescharacteristic
384C2×C61#331911yescharacteristic
385C2×C61#332311yescharacteristic
386C2×C61#332511yescharacteristic
387C23×D4C22×C6111yescharacteristic
388C22×M16C22×C6111yescharacteristic
389C2×C4×D4C22×C6111yescharacteristic
390C2×C4×D4C22×C6111yescharacteristic
391C2×#117C22×C6111yescharacteristic
392C22×C22⋊C4—21no—
393C2×#107C22×C6111yescharacteristic, complemented
394C2×#106C22×C6111yescharacteristic, complemented
395#418C4×C6118yescomplemented
396C2×#102C22×C6111yescharacteristic
397C2×#102C22×C6111yescharacteristic
398C2×#102C22×C6111yescharacteristic
399C2×#102C22×C6111yescharacteristic
400C2×#102C22×C6111yescharacteristic
401C2×#102C22×C6111yescharacteristic
402C2×#102C22×C6111yescharacteristic
403C2×#102C22×C6111yescharacteristic
404C2×C22⋊C8C22×C6111yescharacteristic
405C2×#97C22×C6111yescharacteristic, complemented
406C2×C4×C8C22×C6111yescharacteristic, complemented
407#390C22×C6111yescharacteristic
408#390C22×C6111yescharacteristic
409#389C22×C6111yescharacteristic, complemented
410#389C22×C6111yescharacteristic, complemented
411#388—21no—
412#388—21no—
413#386—21no—
414#386—21no—
415#382—21no—
416#380C22×C6111yescharacteristic
417#380C22×C6111yescharacteristic
418#379—21no—
419C4×C4⋊C4C22×C6111yescharacteristic, complemented
420C4×C4⋊C4C22×C6111yescharacteristic, complemented
421C4×C22⋊C4C22×C6111yescharacteristic
422#376—21no—
423#340C22×C6111yescharacteristic, complemented
424#340C22×C6111yescharacteristic, complemented
425#340C22×C6111yescharacteristic, complemented
426#340C22×C6111yescharacteristic, complemented
427#340C22×C6111yescharacteristic, complemented
428#340C22×C6111yescharacteristic, complemented
429#336C22×C6111yescharacteristic, complemented
430#336C22×C6111yescharacteristic, complemented
431C61#2258411yescharacteristic, direct product factor, Sylow
432C25—21no—
433C22×D4—22no—
434C22×D4—22no—
435C22×D4—21no—
436C22×D4—22no—
437C22×D4—41no—
438C22×D4—41no—
439C22×D4C2×C4×C6114yes—
440C22×D4C23×C6111yescharacteristic
441C22×D4C23×C6111yescharacteristic
442C23×C4—21no—
443C23×C4—21no—
444C23×C4C23×C6111yescharacteristic
445C2×M16—41no—
446C2×M16—41no—
447C2×M16C2×C4×C6114yescomplemented
448C22×C8C23×C6111yescharacteristic
449C22×C8C23×C6111yescharacteristic
450C22×C8C23×C6111yescharacteristic
451C22×C8C23×C6111yescharacteristic
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—41no—
455C4×D4—41no—
456#117—22no—
457#117C2×C4×C6114yescomplemented
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×C4⋊C4C23×C6111yescharacteristic
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⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—44no—
476C2×C22⋊C4D4×C6111yescharacteristic
477C2×C22⋊C4D4×C6111yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42C23×C6111yescharacteristic
482C2×C42C23×C6111yescharacteristic
483#107—41no—
484#106—41no—
485#102—22no—
486#102—22no—
487#102—41no—
488#102—41no—
489#102C2×C4×C6114yes—
490#102C2×C4×C6114yes—
491#102C2×C4×C6114yescomplemented
492#102C2×C4×C6114yescomplemented
493C22⋊C8—22no—
494#97—41no—
495C4×C8—41no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95D4×C6111yescharacteristic
503#95D4×C6111yescharacteristic
504C24—21no—
505C24—21no—
506C24—24no—
507C24—42no—
508C24—42no—
509C24—42no—
510C24—42no—
511C24—81no—
512C24—81no—
513C24C2×D4×C6111yescharacteristic
514C2×D4—28no—
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4C22×C4×C6112yes—
530C2×D4C22×C4×C6112yes—
531C2×D4#41×C6112yes—
532C2×D4#41×C6112yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—81no—
548C22×C4—81no—
549C22×C4C22×C4×C6112yes—
550C22×C4C2×D4×C6111yescharacteristic
551C22×C4C2×D4×C6111yescharacteristic
552C22×C4C2×D4×C6111yescharacteristic
553C22×C4C2×D4×C6111yescharacteristic
554C22×C4C2×D4×C6111yescharacteristic
555C22×C4#41×C6112yes—
556C22×C4C24×C6111yescharacteristic
557M16—44no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8C22×C4×C6112yes—
569C2×C8C22×C4×C6112yes—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—81no—
581C4⋊C4—81no—
582C4⋊C4C22×C4×C6112yes—
583C4⋊C4C22×C4×C6112yes—
584C22⋊C4—24no—
585C22⋊C4—22no—
586C22⋊C4—41no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—81no—
593C22⋊C4—81no—
594C22⋊C4—81no—
595C42—24no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—42no—
601C42—42no—
602C23—22no—
603C23—22no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—22no—
611C23—22no—
612C23—48no—
613C23—48no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—84no—
625C23—84no—
626C23—84no—
627C23—84no—
628C23—84no—
629C23C4×D4×C6112yes—
630C23C22×D4×C6111yescharacteristic
631D4—22no—
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—48no—
637D4—41no—
638D4—41no—
639D4#117×C6114yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—84no—
676C2×C4—84no—
677C2×C4C4×D4×C6112yes—
678C2×C4AGL(1,ℤ/8)×C6112yes—
679C2×C4C23×C4×C6111yescharacteristic
680C2×C4C2×#41×C6111yescharacteristic
681C2×C4C2×#41×C6111yescharacteristic
682C2×C4C2×#41×C6111yescharacteristic
683C2×C4H(5,𝔽2)×C6111yescharacteristic
684C2×C4H(5,𝔽2)×C6111yescharacteristic
685C8—22no—
686C8—22no—
687C8—41no—
688C8—41no—
689C22—22no—
690C22—24no—
691C22—22no—
692C22—22no—
693C22—42no—
694C22—41no—
695C22—41no—
696C22—42no—
697C22—41no—
698C22—42no—
699C22—42no—
700C22—41no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—816no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22C2×C4×D4×C6111yescharacteristic
712C22C61×#54611yescharacteristic
713C22C61×#54611yescharacteristic
714C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
715C22C61×#57511yescharacteristic
716C22C61×#57611yescharacteristic
717C22C61×#57711yescharacteristic
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—42no—
724C4—42no—
725C4—81no—
726C4—81no—
727C4—81no—
728C4—81no—
729C4C2×#117×C6111yescharacteristic
730C4C61×#51811yescharacteristic
731C4C61×#55111yescharacteristic
732C4C61×#55111yescharacteristic
733C2—42no—
734C2—44no—
735C2—82no—
736C2C61×#234211yescharacteristic
737C2C4×AGL(1,ℤ/8)×C6111yescharacteristic
738C2C61×#294611yescharacteristic
739C2C61×#331011yescharacteristic
740C2C61×#331911yescharacteristic
741C2C61×#332311yescharacteristic
742C2C61×#332511yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutatorC2×C4C23×C4×C61
Frattini, cosocleC22×C4C24×C61
prime radicalC23×D4×C61C22
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. C61×#2346C2semidirect
4. C61×#1936C2semidirect
5. C61×#1934C2semidirect
6. C61×#1926C2semidirect
7. C61×#1925C2semidirect
8. C61×#1864C2semidirect
9. C61×#1862C2semidirect
10. C61×#1825C2semidirect
11. C61×#1809C2semidirect
13. C61×#1762C2semidirect
14. C4×#102×C61C2semidirect
15. C61×#1753C2semidirect
22. C2×#107×C61C22semidirect
23. C2×#106×C61C22semidirect
24. C61×#418C4semidirect
34. C2×#97×C61C22semidirect
35. C2×C4×C8×C61C22semidirect
38. C61×#389C22semidirect
39. C61×#389C22semidirect
48. C4×C4⋊C4×C61C22semidirect
49. C4×C4⋊C4×C61C22semidirect
52. C61×#340C22semidirect
53. C61×#340C22semidirect
54. C61×#340C22semidirect
55. C61×#340C22semidirect
56. C61×#340C22semidirect
57. C61×#340C22semidirect
58. C61×#336C22semidirect
59. C61×#336C22semidirect
75. C2×M16×C61C2×C4semidirect
85. #117×C61C2×C4semidirect
119. #102×C61C2×C4semidirect
120. #102×C61C2×C4semidirect
317. #22584C61direct (N × H)
363. #2346C2×C61semidirect
365. #1936C2×C61semidirect
366. #1934C2×C61semidirect
367. #1926C2×C61semidirect
368. #1925C2×C61semidirect
369. #1864C2×C61semidirect
370. #1862C2×C61semidirect
371. #1825C2×C61semidirect
372. #1809C2×C61semidirect
374. #1762C2×C61semidirect
375. C4×#102C2×C61semidirect
376. #1753C2×C61semidirect
393. C2×#107C22×C61semidirect
394. C2×#106C22×C61semidirect
395. #418C4×C61semidirect
405. C2×#97C22×C61semidirect
406. C2×C4×C8C22×C61semidirect
409. #389C22×C61semidirect
410. #389C22×C61semidirect
419. C4×C4⋊C4C22×C61semidirect
420. C4×C4⋊C4C22×C61semidirect
423. #340C22×C61semidirect
424. #340C22×C61semidirect
425. #340C22×C61semidirect
426. #340C22×C61semidirect
427. #340C22×C61semidirect
428. #340C22×C61semidirect
429. #336C22×C61semidirect
430. #336C22×C61semidirect
431. C61#22584direct (N × H)
447. C2×M16C2×C4×C61semidirect
457. #117C2×C4×C61semidirect
491. #102C2×C4×C61semidirect
492. #102C2×C4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4182
C61×#23462
D4×C22⋊C4×C612
C61×#19362
C61×#19342
C61×#19262
C61×#19252
C61×#18642
C61×#18622
C61×#18252
C61×#18092
C61×#17862
C61×#17622
C4×#102×C612
C61×#17532
#2258461