Finite Group Databasebeta

← C61×#25106 #29528539

Subgroups — C61×#25106 #29528539

Order 15616.

1230 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#469C211yesmaximal, characteristic, complemented
2C2×C61×#463C211yesmaximal, characteristic, complemented
3C2×C61×#449C211yesmaximal, characteristic, complemented
4C2×C61×#417C211yesmaximal, characteristic, complemented
5C61×#2431C211yesmaximal, characteristic, complemented
6C61×#2361C211yesmaximal, characteristic, complemented
7C61×#2065C211yesmaximal, characteristic, complemented
8C61×#2055C211yesmaximal, characteristic, complemented
9C61×#2042C211yesmaximal, characteristic, complemented
10C61×#2011C211yesmaximal, characteristic, complemented
11C61×#1982C211yesmaximal, characteristic, complemented
12C61×#1927C211yesmaximal, characteristic, complemented
13C61×#1879C211yesmaximal, characteristic, complemented
14C61×#1874C211yesmaximal, characteristic, complemented
15C61×#1851C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C22×D8×C61C2211yescharacteristic
19C22×D8×C61C2211yescharacteristic
20C22×M16×C61C2211yescharacteristic
21C2×#127×C61C2211yescharacteristic
22C2×#124×C61C2211yescharacteristic
23C2×#121×C61C2211yescharacteristic
24C2×#121×C61C2211yescharacteristic
25C2×C4×D4×C61—21no—
26C2×C4×D4×C61C2211yescharacteristic
27C22×C4⋊C4×C61C2211yescharacteristic
28C61×#469—24no—
29C61×#463—24no—
30C61×#449—24no—
31C2×#106×C61C2211yescharacteristic
32C2×C4⋊C8×C61C2211yescharacteristic
33C2×C4⋊C8×C61C2211yescharacteristic
34C61×#417—24no—
35C2×#103×C61C2211yescharacteristic
36C2×#103×C61C2211yescharacteristic
37C2×#103×C61C2211yescharacteristic
38C2×#102×C61C2211yescharacteristic
39C2×#102×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic
42C2×#102×C61C2211yescharacteristic
43C2×#102×C61C2211yescharacteristic
44C2×#102×C61C2211yescharacteristic
45C2×C22⋊C8×C61C2211yescharacteristic
46C61×#392—21no—
47C61×#392—21no—
48C61×#391C2211yescharacteristic
49C61×#390C2211yescharacteristic
50C61×#390C2211yescharacteristic
51C61×#389C2211yescharacteristic
52C61×#388—21no—
53C61×#386—21no—
54C61×#386—21no—
55C61×#386—21no—
56C61×#385—21no—
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C22⋊C4×C61C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C2×#41×C61—22no—
64C2×#41×C61—22no—
65C2×#41×C61—22no—
66C2×#41×C61—22no—
67C2×#41×C61—41no—
68C2×#41×C61—41no—
69C22×Q8×C61C2311yescharacteristic
70C22×D4×C61—21no—
71C22×D4×C61—21no—
72C22×D4×C61—21no—
73C22×D4×C61—21no—
74C22×D4×C61—21no—
75C22×D4×C61C2311yescharacteristic
76C22×D4×C61C2311yescharacteristic
77C22×D4×C61C2311yescharacteristic
78C23×C4×C61—21no—
79C23×C4×C61—21no—
80C23×C4×C61—21no—
81C23×C4×C61C2311yescharacteristic
82C2×SD16×C61—22no—
83C2×SD16×C61—22no—
84C2×SD16×C61—41no—
85C2×D8×C61—22no—
86C2×D8×C61—22no—
87C2×D8×C61—22no—
88C2×D8×C61—22no—
89C2×D8×C61—41no—
90C2×D8×C61—41no—
91C2×M16×C61—22no—
92C2×M16×C61—22no—
93C2×M16×C61—41no—
94C22×C8×C61C2311yescharacteristic
95C22×C8×C61C2311yescharacteristic
96C22×C8×C61C2311yescharacteristic
97C22×C8×C61C2311yescharacteristic
98#127×C61—22no—
99#127×C61—41no—
100#124×C61—22no—
101#124×C61—41no—
102#121×C61—22no—
103#121×C61—22no—
104#121×C61—22no—
105#121×C61D414yescomplemented
106C4×D4×C61—22no—
107C4×D4×C61—41no—
108C4×D4×C61—44no—
109C2×C4⋊C4×C61—22no—
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61—41no—
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—21no—
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61D411yescharacteristic
127C2×C22⋊C4×C61D411yescharacteristic
128C2×C42×C61—21no—
129C2×C42×C61C2311yescharacteristic
130C2×C42×C61C2311yescharacteristic
131#106×C61—22no—
132C4⋊C8×C61—22no—
133C4⋊C8×C61—41no—
134#103×C61—22no—
135#103×C61—22no—
136#103×C61D414yescomplemented
137#102×C61—22no—
138#102×C61—22no—
139#102×C61—22no—
140#102×C61—22no—
141#102×C61—22no—
142#102×C61—22no—
143#102×C61—41no—
144C22⋊C8×C61—22no—
145#95×C61—21no—
146#95×C61—21no—
147#95×C61—21no—
148#95×C61—21no—
149#95×C61D411yescharacteristic
150#95×C61D411yescharacteristic
151C24×C61—21no—
152C24×C61—21no—
153C24×C61—21no—
154C24×C61C2×D411yescharacteristic
155#41×C61—28no—
156#41×C61—44no—
157#41×C61—44no—
158#41×C61—44no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61C2×D412yes—
165C2×D4×C61—24no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—42no—
183C2×D4×C61—42no—
184C2×D4×C61—42no—
185C2×D4×C61—42no—
186C2×D4×C61—42no—
187C2×D4×C61—42no—
188C2×D4×C61—42no—
189C2×D4×C61—42no—
190C2×D4×C61—42no—
191C2×D4×C61—42no—
192C2×D4×C61—81no—
193C2×D4×C61—81no—
194C2×D4×C61—81no—
195C2×D4×C61—81no—
196C2×D4×C61C2×D412yes—
197C2×D4×C61#4112yes—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—42no—
208C22×C4×C61—42no—
209C22×C4×C61—42no—
210C22×C4×C61—42no—
211C22×C4×C61—42no—
212C22×C4×C61—42no—
213C22×C4×C61—42no—
214C22×C4×C61—81no—
215C22×C4×C61—81no—
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D412yes—
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61#4112yes—
223C22×C4×C61C2411yescharacteristic
224SD16×C61—44no—
225D8×C61—44no—
226D8×C61—44no—
227M16×C61—44no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61C2×D412yes—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—42no—
247C4⋊C4×C61—42no—
248C4⋊C4×C61C2×D412yes—
249C4⋊C4×C61C2×D412yes—
250C22⋊C4×C61—24no—
251C22⋊C4×C61—22no—
252C22⋊C4×C61—41no—
253C22⋊C4×C61—42no—
254C22⋊C4×C61—42no—
255C22⋊C4×C61—42no—
256C22⋊C4×C61—42no—
257C22⋊C4×C61—42no—
258C22⋊C4×C61—81no—
259C22⋊C4×C61—81no—
260C22⋊C4×C61—81no—
261C42×C61—21no—
262C42×C61—21no—
263C42×C61—21no—
264C42×C61—21no—
265C42×C61—42no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61#12112yes—
294C23×C61C22×D411yescharacteristic
295Q8×C61—22no—
296Q8×C61—22no—
297Q8×C61—41no—
298Q8×C61—41no—
299D4×C61—22no—
300D4×C61—22no—
301D4×C61—22no—
302D4×C61—22no—
303D4×C61—48no—
304D4×C61—48no—
305D4×C61—41no—
306D4×C61—41no—
307D4×C61—41no—
308D4×C61—41no—
309D4×C61—41no—
310D4×C61—41no—
311D4×C61—41no—
312D4×C61—41no—
313D4×C61—84no—
314D4×C61—84no—
315D4×C61—84no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—48no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—84no—
350C2×C4×C61—84no—
351C2×C4×C61#12112yes—
352C2×C4×C61AGL(1,ℤ/8)12yes—
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C2×#4111yescharacteristic
356C2×C4×C61C2×#4111yescharacteristic
357C2×C4×C61H(5,𝔽2)11yescharacteristic
358C2×C4×C61H(5,𝔽2)11yescharacteristic
359C8×C61—22no—
360C8×C61—41no—
361C8×C61—41no—
362C8×C61—41no—
363#25106C6111yesmaximal, characteristic, direct product factor, Sylow
364C22×C61—22no—
365C22×C61—22no—
366C22×C61—22no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61—81no—
378C22×C61—81no—
379C22×C61—81no—
380C22×C61—81no—
381C22×C61—81no—
382C22×C61—81no—
383C22×C61—81no—
384C22×C61—81no—
385C22×C61—81no—
386C22×C61—81no—
387C22×C61—81no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61—81no—
391C22×C61—81no—
392C22×C61C2×#12111yescharacteristic
393C22×C61D4211yescharacteristic
394C22×C61#54611yescharacteristic
395C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
396C22×C61#57511yescharacteristic
397C22×C61#57611yescharacteristic
398C22×C61#57711yescharacteristic
399C4×C61—22no—
400C4×C61—22no—
401C4×C61—42no—
402C4×C61—41no—
403C4×C61—41no—
404C4×C61—42no—
405C4×C61—42no—
406C4×C61—41no—
407C4×C61—81no—
408C4×C61—81no—
409C4×C61#52511yescharacteristic
410C4×C61#53811yescharacteristic
411C4×C61D4211yescharacteristic
412C4×C61#54611yescharacteristic
413C2×#469C2×C6111yescharacteristic, complemented
414C2×#463C2×C6111yescharacteristic, complemented
415C2×#449C2×C6111yescharacteristic, complemented
416C2×#417C2×C6111yescharacteristic, complemented
417#2431C2×C6111yescharacteristic, complemented
418#2361C2×C6111yescharacteristic, complemented
419#2065C2×C6111yescharacteristic, complemented
420#2055C2×C6111yescharacteristic, complemented
421#2042C2×C6111yescharacteristic, complemented
422#2011C2×C6111yescharacteristic, complemented
423#1982C2×C6111yescharacteristic, complemented
424#1927C2×C6111yescharacteristic, complemented
425#1879C2×C6111yescharacteristic, complemented
426#1874C2×C6111yescharacteristic, complemented
427#1851C2×C6111yescharacteristic, complemented
428C2×C61—42no—
429C2×C61—82no—
430C2×C61—82no—
431C2×C61—161no—
432C2×C61#242411yescharacteristic
433C2×C61#303611yescharacteristic
434C2×C61#304511yescharacteristic
435C2×C61#327111yescharacteristic
436C2×C61#327411yescharacteristic
437C2×C61#330611yescharacteristic
438C2×C61#332211yescharacteristic
439C22×#41C22×C6111yescharacteristic
440C22×SD16C22×C6111yescharacteristic
441C22×D8C22×C6111yescharacteristic
442C22×D8C22×C6111yescharacteristic
443C22×M16C22×C6111yescharacteristic
444C2×#127C22×C6111yescharacteristic
445C2×#124C22×C6111yescharacteristic
446C2×#121C22×C6111yescharacteristic
447C2×#121C22×C6111yescharacteristic
448C2×C4×D4—21no—
449C2×C4×D4C22×C6111yescharacteristic
450C22×C4⋊C4C22×C6111yescharacteristic
451#469—24no—
452#463—24no—
453#449—24no—
454C2×#106C22×C6111yescharacteristic
455C2×C4⋊C8C22×C6111yescharacteristic
456C2×C4⋊C8C22×C6111yescharacteristic
457#417—24no—
458C2×#103C22×C6111yescharacteristic
459C2×#103C22×C6111yescharacteristic
460C2×#103C22×C6111yescharacteristic
461C2×#102C22×C6111yescharacteristic
462C2×#102C22×C6111yescharacteristic
463C2×#102C22×C6111yescharacteristic
464C2×#102C22×C6111yescharacteristic
465C2×#102C22×C6111yescharacteristic
466C2×#102C22×C6111yescharacteristic
467C2×#102C22×C6111yescharacteristic
468C2×C22⋊C8C22×C6111yescharacteristic
469#392—21no—
470#392—21no—
471#391C22×C6111yescharacteristic
472#390C22×C6111yescharacteristic
473#390C22×C6111yescharacteristic
474#389C22×C6111yescharacteristic
475#388—21no—
476#386—21no—
477#386—21no—
478#386—21no—
479#385—21no—
480C4×C4⋊C4C22×C6111yescharacteristic
481C4×C22⋊C4C22×C6111yescharacteristic
482#340C22×C6111yescharacteristic
483#340C22×C6111yescharacteristic
484#336C22×C6111yescharacteristic
485#336C22×C6111yescharacteristic
486C61#2510611yescharacteristic, direct product factor, Sylow
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—41no—
492C2×#41—41no—
493C22×Q8C23×C6111yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4C23×C6111yescharacteristic
500C22×D4C23×C6111yescharacteristic
501C22×D4C23×C6111yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C23×C6111yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—41no—
509C2×D8—22no—
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—41no—
514C2×D8—41no—
515C2×M16—22no—
516C2×M16—22no—
517C2×M16—41no—
518C22×C8C23×C6111yescharacteristic
519C22×C8C23×C6111yescharacteristic
520C22×C8C23×C6111yescharacteristic
521C22×C8C23×C6111yescharacteristic
522#127—22no—
523#127—41no—
524#124—22no—
525#124—41no—
526#121—22no—
527#121—22no—
528#121—22no—
529#121D4×C6114yescomplemented
530C4×D4—22no—
531C4×D4—41no—
532C4×D4—44no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4C23×C6111yescharacteristic
538C2×C4⋊C4C23×C6111yescharacteristic
539C2×C4⋊C4C23×C6111yescharacteristic
540C2×C4⋊C4C23×C6111yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C6111yescharacteristic
551C2×C22⋊C4D4×C6111yescharacteristic
552C2×C42—21no—
553C2×C42C23×C6111yescharacteristic
554C2×C42C23×C6111yescharacteristic
555#106—22no—
556C4⋊C8—22no—
557C4⋊C8—41no—
558#103—22no—
559#103—22no—
560#103D4×C6114yescomplemented
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—41no—
568C22⋊C8—22no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95D4×C6111yescharacteristic
574#95D4×C6111yescharacteristic
575C24—21no—
576C24—21no—
577C24—21no—
578C24C2×D4×C6111yescharacteristic
579#41—28no—
580#41—44no—
581#41—44no—
582#41—44no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8C2×D4×C6112yes—
589C2×D4—24no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4—81no—
620C2×D4C2×D4×C6112yes—
621C2×D4#41×C6112yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—81no—
639C22×C4—81no—
640C22×C4C2×D4×C6111yescharacteristic
641C22×C4C2×D4×C6111yescharacteristic
642C22×C4C2×D4×C6111yescharacteristic
643C22×C4C2×D4×C6111yescharacteristic
644C22×C4C2×D4×C6112yes—
645C22×C4C2×D4×C6111yescharacteristic
646C22×C4#41×C6112yes—
647C22×C4C24×C6111yescharacteristic
648SD16—44no—
649D8—44no—
650D8—44no—
651M16—44no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8C2×D4×C6112yes—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4C2×D4×C6112yes—
673C4⋊C4C2×D4×C6112yes—
674C22⋊C4—24no—
675C22⋊C4—22no—
676C22⋊C4—41no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—81no—
683C22⋊C4—81no—
684C22⋊C4—81no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42—42no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—22no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23#121×C6112yes—
718C23C22×D4×C6111yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—41no—
722Q8—41no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—48no—
728D4—48no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—84no—
738D4—84no—
739D4—84no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—48no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4#121×C6112yes—
776C2×C4AGL(1,ℤ/8)×C6112yes—
777C2×C4C22×D4×C6111yescharacteristic
778C2×C4C22×D4×C6111yescharacteristic
779C2×C4C2×#41×C6111yescharacteristic
780C2×C4C2×#41×C6111yescharacteristic
781C2×C4H(5,𝔽2)×C6111yescharacteristic
782C2×C4H(5,𝔽2)×C6111yescharacteristic
783C8—22no—
784C8—41no—
785C8—41no—
786C8—41no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22C2×#121×C6111yescharacteristic
816C22D42×C6111yescharacteristic
817C22C61×#54611yescharacteristic
818C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
819C22C61×#57511yescharacteristic
820C22C61×#57611yescharacteristic
821C22C61×#57711yescharacteristic
822C4—22no—
823C4—22no—
824C4—42no—
825C4—41no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—42no—
830C4—81no—
831C4—81no—
832C4C61×#52511yescharacteristic
833C4C61×#53811yescharacteristic
834C4D42×C6111yescharacteristic
835C4C61×#54611yescharacteristic
836C2—42no—
837C2—82no—
838C2—82no—
839C2—161no—
840C2C61×#242411yescharacteristic
841C2C61×#303611yescharacteristic
842C2C61×#304511yescharacteristic
843C2C61×#327111yescharacteristic
844C2C61×#327411yescharacteristic
845C2C61×#330611yescharacteristic
846C2C61×#332211yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
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×#469C2semidirect
2. C2×C61×#463C2semidirect
3. C2×C61×#449C2semidirect
4. C2×C61×#417C2semidirect
5. C61×#2431C2semidirect
6. C61×#2361C2semidirect
7. C61×#2065C2semidirect
8. C61×#2055C2semidirect
9. C61×#2042C2semidirect
10. C61×#2011C2semidirect
11. C61×#1982C2semidirect
12. C61×#1927C2semidirect
13. C61×#1879C2semidirect
14. C61×#1874C2semidirect
15. C61×#1851C2semidirect
105. #121×C61D4semidirect
136. #103×C61D4semidirect
363. #25106C61direct (N × H)
413. C2×#469C2×C61semidirect
414. C2×#463C2×C61semidirect
415. C2×#449C2×C61semidirect
416. C2×#417C2×C61semidirect
417. #2431C2×C61semidirect
418. #2361C2×C61semidirect
419. #2065C2×C61semidirect
420. #2055C2×C61semidirect
421. #2042C2×C61semidirect
422. #2011C2×C61semidirect
423. #1982C2×C61semidirect
424. #1927C2×C61semidirect
425. #1879C2×C61semidirect
426. #1874C2×C61semidirect
427. #1851C2×C61semidirect
486. C61#25106direct (N × H)
529. #121D4×C61semidirect
560. #103D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4692
C2×C61×#4632
C2×C61×#4492
C2×C61×#4172
C61×#24312
C61×#23612
C61×#20652
C61×#20552
C61×#20422
C61×#20112
C61×#19822
C61×#19272
C61×#18792
C61×#18742
C61×#18512
#2510661