Finite Group Databasebeta

← C61×#24390 #29527823

Subgroups — C61×#24390 #29527823

Order 15616.

1636 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#535C211yesmaximal, characteristic, complemented
2C2×C61×#469C211yesmaximal, characteristic, complemented
3C2×C61×#466C211yesmaximal, characteristic, complemented
4C2×C61×#447C211yesmaximal, characteristic, complemented
5C2×C61×#408C211yesmaximal, characteristic, complemented
6C61×#2615C211yesmaximal, characteristic, complemented
7C61×#2034C211yesmaximal, characteristic, complemented
8C61×#2033C211yesmaximal, characteristic, complemented
9C61×#1999C211yesmaximal, characteristic, complemented
10C61×#1999C211yesmaximal, characteristic, complemented
11C61×#1895C211yesmaximal, characteristic, complemented
12C61×#1893C211yesmaximal, characteristic, complemented
13C61×#1875C211yesmaximal, characteristic, complemented
14C61×#1854C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic
18C22×D8×C61C2211yescharacteristic
19C22×D8×C61C2211yescharacteristic
20C22×M16×C61C2211yescharacteristic, complemented
21C23×C8×C61C2211yescharacteristic, complemented
22C61×#535—24no—
23C61×#535—24no—
24C2×#127×C61—21no—
25C2×#124×C61—21no—
26C2×#121×C61C2211yescharacteristic
27C2×#121×C61C2211yescharacteristic
28C2×#121×C61C2211yescharacteristic
29C2×#121×C61C2211yescharacteristic
30C2×#121×C61C2211yescharacteristic
31C2×#121×C61C2211yescharacteristic, complemented
32C2×#121×C61C2211yescharacteristic, complemented
33C2×#120×C61—21no—
34C2×#120×C61—21no—
35C2×#117×C61C2211yescharacteristic
36C61×#469—24no—
37C61×#466—24no—
38C61×#447—24no—
39C2×#107×C61C2211yescharacteristic, complemented
40C2×#106×C61C2211yescharacteristic, complemented
41C2×#102×C61C2211yescharacteristic
42C2×#102×C61C2211yescharacteristic
43C2×#102×C61C2211yescharacteristic
44C2×#102×C61C2211yescharacteristic
45C2×#102×C61C2211yescharacteristic
46C2×#102×C61C2211yescharacteristic
47C2×#102×C61C2211yescharacteristic, complemented
48C2×#102×C61C2211yescharacteristic, complemented
49C61×#408—24no—
50C2×C22⋊C8×C61C2211yescharacteristic
51C2×C22⋊C8×C61C2211yescharacteristic
52C2×C22⋊C8×C61C2211yescharacteristic, complemented
53C2×C22⋊C8×C61C2211yescharacteristic, complemented
54C61×#393—21no—
55C61×#392—21no—
56C61×#392—21no—
57C61×#392—21no—
58C61×#380C2211yescharacteristic
59C61×#380C2211yescharacteristic, complemented
60C61×#380C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C61×#340C2211yescharacteristic, complemented
65C25×C61—21no—
66C2×#41×C61—22no—
67C2×#41×C61—22no—
68C2×#41×C61—22no—
69C2×#41×C61—22no—
70C2×#41×C61—41no—
71C2×#41×C61—41no—
72C22×Q8×C61D411yescharacteristic
73C22×D4×C61—21no—
74C22×D4×C61—21no—
75C22×D4×C61—21no—
76C22×D4×C61—21no—
77C22×D4×C61—22no—
78C22×D4×C61—22no—
79C22×D4×C61—21no—
80C22×D4×C61—21no—
81C22×D4×C61—21no—
82C22×D4×C61—21no—
83C22×D4×C61—22no—
84C22×D4×C61—22no—
85C22×D4×C61—41no—
86C22×D4×C61—41no—
87C22×D4×C61D411yescharacteristic
88C22×D4×C61D411yescharacteristic
89C22×D4×C61D411yescharacteristic
90C22×D4×C61C2311yescharacteristic
91C22×D4×C61C2311yescharacteristic
92C22×D4×C61C2311yescharacteristic
93C23×C4×C61C2311yescharacteristic
94C23×C4×C61C2311yescharacteristic
95C23×C4×C61C2311yescharacteristic
96C2×D8×C61—22no—
97C2×D8×C61—22no—
98C2×D8×C61—22no—
99C2×D8×C61—22no—
100C2×D8×C61—41no—
101C2×D8×C61—41no—
102C2×M16×C61—22no—
103C2×M16×C61—22no—
104C2×M16×C61—41no—
105C22×C8×C61—22no—
106C22×C8×C61—22no—
107C22×C8×C61—41no—
108C22×C8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C22×C8×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112#127×C61—28no—
113#124×C61—28no—
114#121×C61—22no—
115#121×C61—22no—
116#121×C61—22no—
117#121×C61—22no—
118#121×C61—22no—
119#121×C61—22no—
120#121×C61—22no—
121#121×C61—22no—
122#121×C61—22no—
123#121×C61—22no—
124#121×C61—41no—
125#121×C61—41no—
126#121×C61D414yescomplemented
127#121×C61D414yescomplemented
128#120×C61—28no—
129#120×C61—28no—
130#117×C61—22no—
131#117×C61—22no—
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61—21no—
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C42×C61—21no—
149#107×C61—22no—
150#106×C61—22no—
151#102×C61—22no—
152#102×C61—22no—
153#102×C61—22no—
154#102×C61—22no—
155#102×C61—22no—
156#102×C61—22no—
157#102×C61—41no—
158#102×C61—41no—
159C22⋊C8×C61—22no—
160C22⋊C8×C61—22no—
161C22⋊C8×C61—22no—
162C22⋊C8×C61D414yescomplemented
163#95×C61—21no—
164#95×C61—21no—
165#95×C61—21no—
166C24×C61—24no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—42no—
171C24×C61—42no—
172C24×C61—81no—
173C24×C61—81no—
174C24×C61—81no—
175C24×C61—81no—
176C24×C61C2×D411yescharacteristic
177C24×C61C2×D411yescharacteristic
178C24×C61C2×D411yescharacteristic
179#41×C61—44no—
180#41×C61—44no—
181#41×C61—44no—
182#41×C61—44no—
183C2×Q8×C61—22no—
184C2×Q8×C61—22no—
185C2×Q8×C61—41no—
186C2×D4×C61—24no—
187C2×D4×C61—22no—
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C2×D4×C61—24no—
192C2×D4×C61—24no—
193C2×D4×C61—24no—
194C2×D4×C61—24no—
195C2×D4×C61—22no—
196C2×D4×C61—22no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—21no—
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—44no—
214C2×D4×C61—44no—
215C2×D4×C61—44no—
216C2×D4×C61—44no—
217C2×D4×C61—41no—
218C2×D4×C61—41no—
219C2×D4×C61—41no—
220C2×D4×C61—42no—
221C2×D4×C61—42no—
222C2×D4×C61—42no—
223C2×D4×C61—42no—
224C2×D4×C61—42no—
225C2×D4×C61—81no—
226C2×D4×C61—81no—
227C2×D4×C61—81no—
228C2×D4×C61—81no—
229C2×D4×C61—81no—
230C2×D4×C61—81no—
231C2×D4×C61—81no—
232C2×D4×C61—81no—
233C2×D4×C61—81no—
234C2×D4×C61—81no—
235C2×D4×C61—81no—
236C2×D4×C61—81no—
237C2×D4×C61—81no—
238C2×D4×C61—81no—
239C2×D4×C61C2×D412yes—
240C2×D4×C61C2×D412yes—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61—21no—
260C22×C4×C61C2×D411yescharacteristic
261C22×C4×C61C2×D411yescharacteristic
262C22×C4×C61C2×D412yes—
263C22×C4×C61C2×D412yes—
264C22×C4×C61C2×D411yescharacteristic
265C22×C4×C61C2×D412yes—
266C22×C4×C61#4112yes—
267C22×C4×C61C2411yescharacteristic
268D8×C61—44no—
269D8×C61—44no—
270M16×C61—44no—
271C2×C8×C61—21no—
272C2×C8×C61—21no—
273C2×C8×C61—21no—
274C2×C8×C61—21no—
275C2×C8×C61—21no—
276C2×C8×C61—21no—
277C2×C8×C61—21no—
278C2×C8×C61—21no—
279C2×C8×C61—21no—
280C2×C8×C61—21no—
281C2×C8×C61—44no—
282C2×C8×C61C2×D412yes—
283C2×C8×C61C2×D412yes—
284C4⋊C4×C61—21no—
285C4⋊C4×C61—21no—
286C4⋊C4×C61—21no—
287C4⋊C4×C61—21no—
288C4⋊C4×C61—21no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61—21no—
291C4⋊C4×C61—21no—
292C4⋊C4×C61C2×D412yes—
293C4⋊C4×C61C2×D412yes—
294C22⋊C4×C61—24no—
295C22⋊C4×C61—24no—
296C22⋊C4×C61—24no—
297C22⋊C4×C61—24no—
298C22⋊C4×C61—24no—
299C22⋊C4×C61—42no—
300C22⋊C4×C61—42no—
301C22⋊C4×C61—42no—
302C22⋊C4×C61—81no—
303C22⋊C4×C61—81no—
304C22⋊C4×C61—81no—
305C42×C61—24no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—21no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—21no—
318C23×C61—22no—
319C23×C61—22no—
320C23×C61—21no—
321C23×C61—21no—
322C23×C61—21no—
323C23×C61—21no—
324C23×C61—21no—
325C23×C61—21no—
326C23×C61—21no—
327C23×C61—48no—
328C23×C61—41no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61—41no—
336C23×C61—41no—
337C23×C61—41no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—84no—
348C23×C61—84no—
349C23×C61—84no—
350C23×C61—84no—
351C23×C61—84no—
352C23×C61—84no—
353C23×C61#12012yes—
354C23×C61#12112yes—
355C23×C61C22×D411yescharacteristic
356Q8×C61—44no—
357D4×C61—22no—
358D4×C61—22no—
359D4×C61—22no—
360D4×C61—22no—
361D4×C61—44no—
362D4×C61—44no—
363D4×C61—48no—
364D4×C61—44no—
365D4×C61—41no—
366D4×C61—41no—
367D4×C61—41no—
368D4×C61—41no—
369D4×C61—41no—
370D4×C61—41no—
371D4×C61—41no—
372D4×C61—41no—
373D4×C61—84no—
374D4×C61—84no—
375D4×C61—84no—
376D4×C61—84no—
377D4×C61—84no—
378D4×C61—84no—
379D4×C61—84no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61—21no—
383C2×C4×C61—21no—
384C2×C4×C61—22no—
385C2×C4×C61—22no—
386C2×C4×C61—22no—
387C2×C4×C61—22no—
388C2×C4×C61—22no—
389C2×C4×C61—22no—
390C2×C4×C61—22no—
391C2×C4×C61—22no—
392C2×C4×C61—22no—
393C2×C4×C61—22no—
394C2×C4×C61—21no—
395C2×C4×C61—21no—
396C2×C4×C61—21no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61—41no—
401C2×C4×C61—41no—
402C2×C4×C61—41no—
403C2×C4×C61—41no—
404C2×C4×C61—41no—
405C2×C4×C61—41no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61—41no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61—41no—
414C2×C4×C61#12012yes—
415C2×C4×C61#12112yes—
416C2×C4×C61C22×D411yescharacteristic
417C2×C4×C61C22×D411yescharacteristic
418C2×C4×C61C22×D411yescharacteristic
419C2×C4×C61C2×#4111yescharacteristic
420C2×C4×C61H(5,𝔽2)11yescharacteristic
421C2×C4×C61H(5,𝔽2)11yescharacteristic
422C8×C61—22no—
423C8×C61—22no—
424C8×C61—41no—
425C8×C61—41no—
426#24390C6111yesmaximal, characteristic, direct product factor, Sylow
427C22×C61—22no—
428C22×C61—22no—
429C22×C61—22no—
430C22×C61—22no—
431C22×C61—22no—
432C22×C61—22no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61—41no—
441C22×C61—41no—
442C22×C61—42no—
443C22×C61—42no—
444C22×C61—41no—
445C22×C61—41no—
446C22×C61—41no—
447C22×C61—42no—
448C22×C61—42no—
449C22×C61—41no—
450C22×C61—42no—
451C22×C61—42no—
452C22×C61—41no—
453C22×C61—41no—
454C22×C61—816no—
455C22×C61—81no—
456C22×C61—81no—
457C22×C61—81no—
458C22×C61—81no—
459C22×C61—81no—
460C22×C61—81no—
461C22×C61—81no—
462C22×C61—81no—
463C22×C61—81no—
464C22×C61—81no—
465C22×C61—81no—
466C22×C61—81no—
467C22×C61—81no—
468C22×C61—81no—
469C22×C61—81no—
470C22×C61C2×#12011yescharacteristic
471C22×C61C2×#12111yescharacteristic
472C22×C61#53411yescharacteristic
473C22×C61#57611yescharacteristic
474C22×C61#57611yescharacteristic
475C22×C61#57611yescharacteristic
476C22×C61#57711yescharacteristic
477C4×C61—22no—
478C4×C61—22no—
479C4×C61—41no—
480C4×C61—42no—
481C4×C61—42no—
482C4×C61—81no—
483C4×C61—81no—
484C4×C61—81no—
485C4×C61D4211yescharacteristic
486C4×C61D4211yescharacteristic
487C4×C61#54611yescharacteristic
488C4×C61#54611yescharacteristic
489C2×#535C2×C6111yescharacteristic, complemented
490C2×#469C2×C6111yescharacteristic, complemented
491C2×#466C2×C6111yescharacteristic, complemented
492C2×#447C2×C6111yescharacteristic, complemented
493C2×#408C2×C6111yescharacteristic, complemented
494#2615C2×C6111yescharacteristic, complemented
495#2034C2×C6111yescharacteristic, complemented
496#2033C2×C6111yescharacteristic, complemented
497#1999C2×C6111yescharacteristic, complemented
498#1999C2×C6111yescharacteristic, complemented
499#1895C2×C6111yescharacteristic, complemented
500#1893C2×C6111yescharacteristic, complemented
501#1875C2×C6111yescharacteristic, complemented
502#1854C2×C6111yescharacteristic, complemented
503#1786C2×C6111yescharacteristic, complemented
504C2×C61—42no—
505C2×C61—42no—
506C2×C61—81no—
507C2×C61—82no—
508C2×C61—82no—
509C2×C61—161no—
510C2×C61#241011yescharacteristic
511C2×C61#300811yescharacteristic
512C2×C61#301211yescharacteristic
513C2×C61#305811yescharacteristic
514C2×C61#306211yescharacteristic
515C2×C61#319811yescharacteristic
516C2×C61#319911yescharacteristic
517C22×#41C22×C6111yescharacteristic
518C23×D4C22×C6111yescharacteristic
519C22×D8C22×C6111yescharacteristic
520C22×D8C22×C6111yescharacteristic
521C22×M16C22×C6111yescharacteristic, complemented
522C23×C8C22×C6111yescharacteristic, complemented
523#535—24no—
524#535—24no—
525C2×#127—21no—
526C2×#124—21no—
527C2×#121C22×C6111yescharacteristic
528C2×#121C22×C6111yescharacteristic
529C2×#121C22×C6111yescharacteristic
530C2×#121C22×C6111yescharacteristic
531C2×#121C22×C6111yescharacteristic
532C2×#121C22×C6111yescharacteristic, complemented
533C2×#121C22×C6111yescharacteristic, complemented
534C2×#120—21no—
535C2×#120—21no—
536C2×#117C22×C6111yescharacteristic
537#469—24no—
538#466—24no—
539#447—24no—
540C2×#107C22×C6111yescharacteristic, complemented
541C2×#106C22×C6111yescharacteristic, complemented
542C2×#102C22×C6111yescharacteristic
543C2×#102C22×C6111yescharacteristic
544C2×#102C22×C6111yescharacteristic
545C2×#102C22×C6111yescharacteristic
546C2×#102C22×C6111yescharacteristic
547C2×#102C22×C6111yescharacteristic
548C2×#102C22×C6111yescharacteristic, complemented
549C2×#102C22×C6111yescharacteristic, complemented
550#408—24no—
551C2×C22⋊C8C22×C6111yescharacteristic
552C2×C22⋊C8C22×C6111yescharacteristic
553C2×C22⋊C8C22×C6111yescharacteristic, complemented
554C2×C22⋊C8C22×C6111yescharacteristic, complemented
555#393—21no—
556#392—21no—
557#392—21no—
558#392—21no—
559#380C22×C6111yescharacteristic
560#380C22×C6111yescharacteristic, complemented
561#380C22×C6111yescharacteristic, complemented
562#340C22×C6111yescharacteristic, complemented
563#340C22×C6111yescharacteristic, complemented
564#340C22×C6111yescharacteristic, complemented
565#340C22×C6111yescharacteristic, complemented
566C61#2439011yescharacteristic, direct product factor, Sylow
567C25—21no—
568C2×#41—22no—
569C2×#41—22no—
570C2×#41—22no—
571C2×#41—22no—
572C2×#41—41no—
573C2×#41—41no—
574C22×Q8D4×C6111yescharacteristic
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—21no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—21no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—41no—
588C22×D4—41no—
589C22×D4D4×C6111yescharacteristic
590C22×D4D4×C6111yescharacteristic
591C22×D4D4×C6111yescharacteristic
592C22×D4C23×C6111yescharacteristic
593C22×D4C23×C6111yescharacteristic
594C22×D4C23×C6111yescharacteristic
595C23×C4C23×C6111yescharacteristic
596C23×C4C23×C6111yescharacteristic
597C23×C4C23×C6111yescharacteristic
598C2×D8—22no—
599C2×D8—22no—
600C2×D8—22no—
601C2×D8—22no—
602C2×D8—41no—
603C2×D8—41no—
604C2×M16—22no—
605C2×M16—22no—
606C2×M16—41no—
607C22×C8—22no—
608C22×C8—22no—
609C22×C8—41no—
610C22×C8C23×C6111yescharacteristic
611C22×C8C23×C6111yescharacteristic
612C22×C8C23×C6111yescharacteristic
613C22×C8C23×C6111yescharacteristic
614#127—28no—
615#124—28no—
616#121—22no—
617#121—22no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—41no—
627#121—41no—
628#121D4×C6114yescomplemented
629#121D4×C6114yescomplemented
630#120—28no—
631#120—28no—
632#117—22no—
633#117—22no—
634C2×C4⋊C4C23×C6111yescharacteristic
635C2×C4⋊C4C23×C6111yescharacteristic
636C2×C4⋊C4C23×C6111yescharacteristic
637C2×C4⋊C4C23×C6111yescharacteristic
638C2×C4⋊C4C23×C6111yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C42—21no—
651#107—22no—
652#106—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—22no—
658#102—22no—
659#102—41no—
660#102—41no—
661C22⋊C8—22no—
662C22⋊C8—22no—
663C22⋊C8—22no—
664C22⋊C8D4×C6114yescomplemented
665#95—21no—
666#95—21no—
667#95—21no—
668C24—24no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—42no—
673C24—42no—
674C24—81no—
675C24—81no—
676C24—81no—
677C24—81no—
678C24C2×D4×C6111yescharacteristic
679C24C2×D4×C6111yescharacteristic
680C24C2×D4×C6111yescharacteristic
681#41—44no—
682#41—44no—
683#41—44no—
684#41—44no—
685C2×Q8—22no—
686C2×Q8—22no—
687C2×Q8—41no—
688C2×D4—24no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—41no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—81no—
728C2×D4—81no—
729C2×D4—81no—
730C2×D4—81no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4—81no—
734C2×D4—81no—
735C2×D4—81no—
736C2×D4—81no—
737C2×D4—81no—
738C2×D4—81no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4C2×D4×C6112yes—
742C2×D4C2×D4×C6112yes—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4C2×D4×C6111yescharacteristic
763C22×C4C2×D4×C6111yescharacteristic
764C22×C4C2×D4×C6112yes—
765C22×C4C2×D4×C6112yes—
766C22×C4C2×D4×C6111yescharacteristic
767C22×C4C2×D4×C6112yes—
768C22×C4#41×C6112yes—
769C22×C4C24×C6111yescharacteristic
770D8—44no—
771D8—44no—
772M16—44no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—44no—
784C2×C8C2×D4×C6112yes—
785C2×C8C2×D4×C6112yes—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4C2×D4×C6112yes—
795C4⋊C4C2×D4×C6112yes—
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—24no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—42no—
804C22⋊C4—81no—
805C22⋊C4—81no—
806C22⋊C4—81no—
807C42—24no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—22no—
826C23—22no—
827C23—21no—
828C23—21no—
829C23—48no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—84no—
850C23—84no—
851C23—84no—
852C23—84no—
853C23—84no—
854C23—84no—
855C23#120×C6112yes—
856C23#121×C6112yes—
857C23C22×D4×C6111yescharacteristic
858Q8—44no—
859D4—22no—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—44no—
864D4—44no—
865D4—48no—
866D4—44no—
867D4—41no—
868D4—41no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—84no—
876D4—84no—
877D4—84no—
878D4—84no—
879D4—84no—
880D4—84no—
881D4—84no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—21no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4#120×C6112yes—
917C2×C4#121×C6112yes—
918C2×C4C22×D4×C6111yescharacteristic
919C2×C4C22×D4×C6111yescharacteristic
920C2×C4C22×D4×C6111yescharacteristic
921C2×C4C2×#41×C6111yescharacteristic
922C2×C4H(5,𝔽2)×C6111yescharacteristic
923C2×C4H(5,𝔽2)×C6111yescharacteristic
924C8—22no—
925C8—22no—
926C8—41no—
927C8—41no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—41no—
944C22—41no—
945C22—42no—
946C22—42no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—42no—
951C22—42no—
952C22—41no—
953C22—42no—
954C22—42no—
955C22—816no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22—81no—
963C22—81no—
964C22—81no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22C2×#120×C6111yescharacteristic
972C22C2×#121×C6111yescharacteristic
973C22C61×#53411yescharacteristic
974C22C61×#57611yescharacteristic
975C22C61×#57611yescharacteristic
976C22C61×#57611yescharacteristic
977C22C61×#57711yescharacteristic
978C4—22no—
979C4—22no—
980C4—41no—
981C4—42no—
982C4—42no—
983C4—81no—
984C4—81no—
985C4—81no—
986C4D42×C6111yescharacteristic
987C4D42×C6111yescharacteristic
988C4C61×#54611yescharacteristic
989C4C61×#54611yescharacteristic
990C2—42no—
991C2—42no—
992C2—81no—
993C2—82no—
994C2—82no—
995C2—161no—
996C2C61×#241011yescharacteristic
997C2C61×#300811yescharacteristic
998C2C61×#301211yescharacteristic
999C2C61×#305811yescharacteristic
1000C2C61×#306211yescharacteristic
1001C2C61×#319811yescharacteristic
1002C2C61×#319911yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C22×#41×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#535C2semidirect
2. C2×C61×#469C2semidirect
3. C2×C61×#466C2semidirect
4. C2×C61×#447C2semidirect
5. C2×C61×#408C2semidirect
6. C61×#2615C2semidirect
7. C61×#2034C2semidirect
8. C61×#2033C2semidirect
9. C61×#1999C2semidirect
10. C61×#1999C2semidirect
11. C61×#1895C2semidirect
12. C61×#1893C2semidirect
13. C61×#1875C2semidirect
14. C61×#1854C2semidirect
15. C61×#1786C2semidirect
20. C22×M16×C61C22semidirect
21. C23×C8×C61C22semidirect
31. C2×#121×C61C22semidirect
32. C2×#121×C61C22semidirect
39. C2×#107×C61C22semidirect
40. C2×#106×C61C22semidirect
47. C2×#102×C61C22semidirect
48. C2×#102×C61C22semidirect
52. C2×C22⋊C8×C61C22semidirect
53. C2×C22⋊C8×C61C22semidirect
59. C61×#380C22semidirect
60. C61×#380C22semidirect
61. C61×#340C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
64. C61×#340C22semidirect
126. #121×C61D4semidirect
127. #121×C61D4semidirect
162. C22⋊C8×C61D4semidirect
426. #24390C61direct (N × H)
489. C2×#535C2×C61semidirect
490. C2×#469C2×C61semidirect
491. C2×#466C2×C61semidirect
492. C2×#447C2×C61semidirect
493. C2×#408C2×C61semidirect
494. #2615C2×C61semidirect
495. #2034C2×C61semidirect
496. #2033C2×C61semidirect
497. #1999C2×C61semidirect
498. #1999C2×C61semidirect
499. #1895C2×C61semidirect
500. #1893C2×C61semidirect
501. #1875C2×C61semidirect
502. #1854C2×C61semidirect
503. #1786C2×C61semidirect
521. C22×M16C22×C61semidirect
522. C23×C8C22×C61semidirect
532. C2×#121C22×C61semidirect
533. C2×#121C22×C61semidirect
540. C2×#107C22×C61semidirect
541. C2×#106C22×C61semidirect
548. C2×#102C22×C61semidirect
549. C2×#102C22×C61semidirect
553. C2×C22⋊C8C22×C61semidirect
554. C2×C22⋊C8C22×C61semidirect
560. #380C22×C61semidirect
561. #380C22×C61semidirect
562. #340C22×C61semidirect
563. #340C22×C61semidirect
564. #340C22×C61semidirect
565. #340C22×C61semidirect
566. C61#24390direct (N × H)
628. #121D4×C61semidirect
629. #121D4×C61semidirect
664. C22⋊C8D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5352
C2×C61×#4692
C2×C61×#4662
C2×C61×#4472
C2×C61×#4082
C61×#26152
C61×#20342
C61×#20332
C61×#19992
C61×#18952
C61×#18932
C61×#18752
C61×#18542
C61×#17862
#2439061