Finite Group Databasebeta

← C61×#15280 #29518713

Subgroups — C61×#15280 #29518713

Order 15616.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C61C211yesmaximal, characteristic, complemented
2C2×C61×#396C211yesmaximal, characteristic, complemented
3C2×C61×#393C211yesmaximal, characteristic, complemented
4C2×C61×#391C211yesmaximal, characteristic, complemented
5C2×C61×#390C211yesmaximal, characteristic
6C2×C61×#386C211yesmaximal, characteristic
7C61×#1444C211yesmaximal, characteristic, complemented
8C61×#1441C211yesmaximal, characteristic, complemented
9C61×#1439C211yesmaximal, characteristic, complemented
10C61×#1439C211yesmaximal, characteristic, complemented
11C61×#1439C211yesmaximal, characteristic, complemented
12C61×#1439C211yesmaximal, characteristic, complemented
13C61×#1438C211yesmaximal, characteristic
14C61×#1436C211yesmaximal, characteristic, complemented
15C61×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×Q8×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic
18C24×C4×C61C2211yescharacteristic
19C2×C22⋊Q8×C61—24no—
20C2×C22⋊Q8×C61—24no—
21C2×C22⋊Q8×C61—24no—
22C22×C4⋊C4×C61C2211yescharacteristic
23C22×C4⋊C4×C61C2211yescharacteristic
24C22×C4⋊C4×C61C2211yescharacteristic
25C22×C4⋊C4×C61C2211yescharacteristic
26C22×C4⋊C4×C61C2211yescharacteristic
27C22×C4⋊C4×C61C2211yescharacteristic
28C22×C22⋊C4×C61C2211yescharacteristic
29C22×C22⋊C4×C61C2211yescharacteristic
30C22×C22⋊C4×C61C2211yescharacteristic
31C22×C22⋊C4×C61C2211yescharacteristic
32C22×C22⋊C4×C61C2211yescharacteristic
33C22×C22⋊C4×C61C2211yescharacteristic
34C22×C22⋊C4×C61C2211yescharacteristic
35C22×C22⋊C4×C61C2211yescharacteristic
36C22×C22⋊C4×C61C2211yescharacteristic
37C22×C22⋊C4×C61C2211yescharacteristic
38C22×C22⋊C4×C61C2211yescharacteristic
39C22×C42×C61C2211yescharacteristic
40C61×#396—24no—
41C61×#393—24no—
42C61×#391—24no—
43C61×#390—24no—
44C61×#386—24no—
45C2×#95×C61C2211yescharacteristic
46C2×#95×C61C2211yescharacteristic
47C2×#95×C61C2211yescharacteristic
48C2×#95×C61C2211yescharacteristic
49C2×#95×C61C2211yescharacteristic
50C2×#95×C61C2211yescharacteristic
51C2×#95×C61C2211yescharacteristic
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C2×#95×C61C2211yescharacteristic
59C25×C61C2311yescharacteristic
60C25×C61C2311yescharacteristic
61C22×Q8×C61—22no—
62C22×Q8×C61—22no—
63C22×Q8×C61—22no—
64C22×Q8×C61—22no—
65C22×Q8×C61—41no—
66C22×Q8×C61—41no—
67C22×Q8×C61D414yescomplemented
68C22×D4×C61—22no—
69C22×D4×C61—22no—
70C22×D4×C61—22no—
71C22×D4×C61—22no—
72C22×D4×C61—41no—
73C22×D4×C61—41no—
74C22×D4×C61Q814yescomplemented
75C23×C4×C61—22no—
76C23×C4×C61—22no—
77C23×C4×C61—22no—
78C23×C4×C61—22no—
79C23×C4×C61—22no—
80C23×C4×C61—41no—
81C23×C4×C61—41no—
82C23×C4×C61C2311yescharacteristic
83C23×C4×C61C2311yescharacteristic
84C23×C4×C61C2311yescharacteristic
85C23×C4×C61C2311yescharacteristic
86C23×C4×C61C2311yescharacteristic
87C23×C4×C61C2311yescharacteristic
88C23×C4×C61C2311yescharacteristic
89C23×C4×C61C2311yescharacteristic
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C23×C4×C61C2311yescharacteristic
93C23×C4×C61C2311yescharacteristic
94C23×C4×C61C2311yescharacteristic
95C22⋊Q8×C61—232no—
96C2×C4⋊C4×C61—22no—
97C2×C4⋊C4×C61—22no—
98C2×C4⋊C4×C61—22no—
99C2×C4⋊C4×C61—22no—
100C2×C4⋊C4×C61—22no—
101C2×C4⋊C4×C61—22no—
102C2×C4⋊C4×C61—22no—
103C2×C4⋊C4×C61—22no—
104C2×C4⋊C4×C61—22no—
105C2×C4⋊C4×C61—22no—
106C2×C4⋊C4×C61—22no—
107C2×C4⋊C4×C61—22no—
108C2×C4⋊C4×C61—22no—
109C2×C4⋊C4×C61—41no—
110C2×C4⋊C4×C61—41no—
111C2×C4⋊C4×C61—41no—
112C2×C4⋊C4×C61—41no—
113C2×C4⋊C4×C61D414yescomplemented
114C2×C22⋊C4×C61—22no—
115C2×C22⋊C4×C61—22no—
116C2×C22⋊C4×C61—22no—
117C2×C22⋊C4×C61—22no—
118C2×C22⋊C4×C61—22no—
119C2×C22⋊C4×C61—22no—
120C2×C22⋊C4×C61—22no—
121C2×C22⋊C4×C61—22no—
122C2×C22⋊C4×C61—22no—
123C2×C22⋊C4×C61—22no—
124C2×C22⋊C4×C61—22no—
125C2×C22⋊C4×C61—22no—
126C2×C22⋊C4×C61—22no—
127C2×C22⋊C4×C61—22no—
128C2×C22⋊C4×C61—22no—
129C2×C22⋊C4×C61—22no—
130C2×C22⋊C4×C61—22no—
131C2×C22⋊C4×C61—22no—
132C2×C22⋊C4×C61—22no—
133C2×C22⋊C4×C61—22no—
134C2×C22⋊C4×C61—22no—
135C2×C22⋊C4×C61—22no—
136C2×C22⋊C4×C61—41no—
137C2×C22⋊C4×C61—41no—
138C2×C22⋊C4×C61—41no—
139C2×C22⋊C4×C61—41no—
140C2×C22⋊C4×C61—41no—
141C2×C22⋊C4×C61—41no—
142C2×C22⋊C4×C61—41no—
143C2×C22⋊C4×C61—41no—
144C2×C22⋊C4×C61—41no—
145C2×C22⋊C4×C61—41no—
146C2×C22⋊C4×C61D414yes—
147C2×C42×C61—22no—
148C2×C42×C61—22no—
149C2×C42×C61—41no—
150#95×C61—22no—
151#95×C61—22no—
152#95×C61—22no—
153#95×C61—22no—
154#95×C61—22no—
155#95×C61—22no—
156#95×C61—22no—
157#95×C61—22no—
158#95×C61—22no—
159#95×C61—22no—
160#95×C61—41no—
161#95×C61—41no—
162#95×C61—41no—
163#95×C61D414yes—
164C24×C61—21no—
165C24×C61—21no—
166C24×C61—21no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—21no—
171C24×C61—21no—
172C24×C61—21no—
173C24×C61—21no—
174C24×C61—21no—
175C24×C61—21no—
176C24×C61—21no—
177C24×C61—21no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61—21no—
181C24×C61—21no—
182C24×C61—21no—
183C24×C61—21no—
184C24×C61—21no—
185C24×C61—21no—
186C24×C61—21no—
187C24×C61—21no—
188C24×C61—21no—
189C24×C61—21no—
190C24×C61C2×D412yes—
191C24×C61C2×Q812yes—
192C24×C61C2×Q812yes—
193C24×C61#4112yes—
194C24×C61C2411yescharacteristic
195C2×Q8×C61—28no—
196C2×Q8×C61—28no—
197C2×Q8×C61—44no—
198C2×Q8×C61—44no—
199C2×Q8×C61—44no—
200C2×Q8×C61—44no—
201C2×Q8×C61—44no—
202C2×D4×C61—28no—
203C2×D4×C61—28no—
204C2×D4×C61—44no—
205C2×D4×C61—44no—
206C2×D4×C61—44no—
207C2×D4×C61—44no—
208C2×D4×C61—44no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—28no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
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×C61—21no—
261C22×C4×C61—21no—
262C22×C4×C61—21no—
263C22×C4×C61—21no—
264C22×C4×C61—21no—
265C22×C4×C61—21no—
266C22×C4×C61—21no—
267C22×C4×C61—21no—
268C22×C4×C61—21no—
269C22×C4×C61—21no—
270C22×C4×C61—21no—
271C22×C4×C61—21no—
272C22×C4×C61—21no—
273C22×C4×C61—21no—
274C22×C4×C61—21no—
275C22×C4×C61—21no—
276C22×C4×C61—21no—
277C22×C4×C61—21no—
278C22×C4×C61—21no—
279C22×C4×C61—21no—
280C22×C4×C61—21no—
281C22×C4×C61—21no—
282C22×C4×C61—21no—
283C22×C4×C61—21no—
284C22×C4×C61—21no—
285C22×C4×C61—21no—
286C22×C4×C61—44no—
287C22×C4×C61—44no—
288C22×C4×C61—44no—
289C22×C4×C61—44no—
290C22×C4×C61—44no—
291C22×C4×C61—44no—
292C22×C4×C61C2×D412yes—
293C22×C4×C61C2×D412yes—
294C22×C4×C61C2×D412yes—
295C22×C4×C61C2×D412yes—
296C22×C4×C61C2×D412yes—
297C22×C4×C61C2×D412yes—
298C22×C4×C61C2×D412yes—
299C22×C4×C61C2×D412yes—
300C22×C4×C61C2×D412yes—
301C22×C4×C61C2×D412yes—
302C22×C4×C61C2×D412yes—
303C22×C4×C61C2×Q812yes—
304C22×C4×C61#4112yes—
305C22×C4×C61#4112yes—
306C22×C4×C61#4112yes—
307C4⋊C4×C61—28no—
308C4⋊C4×C61—28no—
309C4⋊C4×C61—28no—
310C4⋊C4×C61—44no—
311C4⋊C4×C61—44no—
312C4⋊C4×C61—44no—
313C22⋊C4×C61—28no—
314C22⋊C4×C61—28no—
315C22⋊C4×C61—44no—
316C22⋊C4×C61—44no—
317C22⋊C4×C61—44no—
318C22⋊C4×C61—44no—
319C22⋊C4×C61—44no—
320C22⋊C4×C61—44no—
321C22⋊C4×C61—44no—
322C22⋊C4×C61—44no—
323C22⋊C4×C61—44no—
324C42×C61—44no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—22no—
331C23×C61—22no—
332C23×C61—22no—
333C23×C61—22no—
334C23×C61—22no—
335C23×C61—22no—
336C23×C61—22no—
337C23×C61—22no—
338C23×C61—22no—
339C23×C61—22no—
340C23×C61—22no—
341C23×C61—22no—
342C23×C61—22no—
343C23×C61—22no—
344C23×C61—22no—
345C23×C61—22no—
346C23×C61—22no—
347C23×C61—22no—
348C23×C61—22no—
349C23×C61—22no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61—41no—
353C23×C61—41no—
354C23×C61—41no—
355C23×C61—41no—
356C23×C61—41no—
357C23×C61—41no—
358C23×C61—41no—
359C23×C61—41no—
360C23×C61—41no—
361C23×C61—41no—
362C23×C61—41no—
363C23×C61—41no—
364C23×C61—41no—
365C23×C61—41no—
366C23×C61—41no—
367C23×C61—41no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—41no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61—41no—
375C23×C61—41no—
376C23×C61—41no—
377C23×C61—41no—
378C23×C61—41no—
379C23×C61—41no—
380C23×C61—41no—
381C23×C61—41no—
382C23×C61—41no—
383C23×C61—41no—
384C23×C61—41no—
385C23×C61—41no—
386C23×C61—41no—
387C23×C61—41no—
388C23×C61—41no—
389C23×C61—41no—
390C23×C61—41no—
391C23×C61—41no—
392C23×C61—41no—
393C23×C61—41no—
394C23×C61C22⋊Q814yes—
395C23×C61C22×D411yescharacteristic
396C23×C61C22×D411yescharacteristic
397C23×C61C22×D411yescharacteristic
398C23×C61C22×D411yescharacteristic
399C23×C61C22×Q811yescharacteristic
400C23×C61C2×#4111yescharacteristic
401C23×C61C2×#4111yescharacteristic
402C23×C61C2×#4111yescharacteristic
403C23×C61C2×#4111yescharacteristic
404C23×C61H(5,𝔽2)11yescharacteristic
405C23×C61H(5,𝔽2)11yescharacteristic
406C23×C61H(5,𝔽2)11yescharacteristic
407C23×C61H(5,𝔽2)11yescharacteristic
408C23×C612−1+411yescharacteristic
409C23×C612−1+411yescharacteristic
410Q8×C61—416no—
411D4×C61—416no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—22no—
415C2×C4×C61—22no—
416C2×C4×C61—22no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
422C2×C4×C61—22no—
423C2×C4×C61—22no—
424C2×C4×C61—22no—
425C2×C4×C61—22no—
426C2×C4×C61—22no—
427C2×C4×C61—22no—
428C2×C4×C61—22no—
429C2×C4×C61—22no—
430C2×C4×C61—22no—
431C2×C4×C61—22no—
432C2×C4×C61—22no—
433C2×C4×C61—22no—
434C2×C4×C61—22no—
435C2×C4×C61—22no—
436C2×C4×C61—22no—
437C2×C4×C61—22no—
438C2×C4×C61—22no—
439C2×C4×C61—22no—
440C2×C4×C61—22no—
441C2×C4×C61—22no—
442C2×C4×C61—22no—
443C2×C4×C61—22no—
444C2×C4×C61—22no—
445C2×C4×C61—22no—
446C2×C4×C61—22no—
447C2×C4×C61—22no—
448C2×C4×C61—416no—
449C2×C4×C61—41no—
450C2×C4×C61—41no—
451C2×C4×C61—41no—
452C2×C4×C61—41no—
453C2×C4×C61—41no—
454C2×C4×C61—41no—
455C2×C4×C61—41no—
456C2×C4×C61—41no—
457C2×C4×C61—41no—
458C2×C4×C61—41no—
459C2×C4×C61—41no—
460C2×C4×C61—41no—
461C2×C4×C61—41no—
462C2×C4×C61—41no—
463C2×C4×C61—41no—
464C2×C4×C61—41no—
465C2×C4×C61—41no—
466C2×C4×C61—41no—
467C2×C4×C61—41no—
468C2×C4×C61—41no—
469C2×C4×C61—41no—
470C2×C4×C61—41no—
471C2×C4×C61—41no—
472C2×C4×C61—41no—
473C2×C4×C61—41no—
474C2×C4×C61—41no—
475C2×C4×C61—41no—
476C2×C4×C61—41no—
477C2×C4×C61—41no—
478C2×C4×C61—41no—
479C2×C4×C61—41no—
480C2×C4×C61—41no—
481C2×C4×C61—41no—
482C2×C4×C61—41no—
483C2×C4×C61—41no—
484C2×C4×C61—41no—
485C2×C4×C61—41no—
486C2×C4×C61—41no—
487C2×C4×C61—41no—
488C2×C4×C61—41no—
489C2×C4×C61—41no—
490C2×C4×C61—41no—
491C2×C4×C61—41no—
492C2×C4×C61—41no—
493C2×C4×C61—41no—
494C2×C4×C61—41no—
495C2×C4×C61—41no—
496C2×C4×C61—41no—
497C2×C4×C61—41no—
498C2×C4×C61—41no—
499C2×C4×C61—41no—
500C2×C4×C61—41no—
501C2×C4×C61#12014yes—
502C2×C4×C61#12114yes—
503C2×C4×C61C22⋊Q814yescomplemented
504#15280C6111yesmaximal, characteristic, direct product factor, Sylow
505C22×C61—24no—
506C22×C61—24no—
507C22×C61—24no—
508C22×C61—42no—
509C22×C61—42no—
510C22×C61—42no—
511C22×C61—42no—
512C22×C61—42no—
513C22×C61—42no—
514C22×C61—42no—
515C22×C61—42no—
516C22×C61—42no—
517C22×C61—42no—
518C22×C61—42no—
519C22×C61—42no—
520C22×C61—42no—
521C22×C61—42no—
522C22×C61—42no—
523C22×C61—42no—
524C22×C61—42no—
525C22×C61—42no—
526C22×C61—42no—
527C22×C61—81no—
528C22×C61—81no—
529C22×C61—81no—
530C22×C61—81no—
531C22×C61—81no—
532C22×C61—81no—
533C22×C61—81no—
534C22×C61—81no—
535C22×C61C2×#12011yescharacteristic
536C22×C61C2×#12111yescharacteristic
537C22×C61C2×C22⋊Q811yescharacteristic
538C22×C61C2×C22⋊Q811yescharacteristic
539C22×C61#52911yescharacteristic
540C22×C61#53211yescharacteristic
541C22×C61#53411yescharacteristic
542C22×C61#53511yescharacteristic
543C22×C61#53611yescharacteristic
544C22×C61#53711yescharacteristic
545C22×C61#53811yescharacteristic
546C22×C61#53911yescharacteristic
547C22×C61#54211yescharacteristic
548C22×C61#54211yescharacteristic
549C22×C61#54311yescharacteristic
550C22×C61D4211yescharacteristic
551C22×C61D4211yescharacteristic
552C22×C61#54611yescharacteristic
553C22×C61#54611yescharacteristic
554C22×C61#54611yescharacteristic
555C22×C61#54611yescharacteristic
556C22×C61#54611yescharacteristic
557C22×C61#54811yescharacteristic
558C22×C61#54811yescharacteristic
559C22×C61#54811yescharacteristic
560C22×C61D4×Q811yescharacteristic
561C22×C61D4×Q811yescharacteristic
562C22×C61#55011yescharacteristic
563C22×C61#55011yescharacteristic
564C22×C61#55111yescharacteristic
565C22×C61#55411yescharacteristic
566C22×C61#55411yescharacteristic
567C22×C61#55611yescharacteristic
568C22×C61#56211yescharacteristic
569C22×C61#56211yescharacteristic
570C4×C61—24no—
571C4×C61—24no—
572C4×C61—24no—
573C4×C61—42no—
574C4×C61—42no—
575C4×C61—42no—
576C4×C61—42no—
577C4×C61—42no—
578C4×C61—42no—
579C4×C61—81no—
580C4×C61—81no—
581C4×C61—81no—
582C4×C61—81no—
583C22×C22⋊Q8C2×C6111yescharacteristic, complemented
584C2×#396C2×C6111yescharacteristic, complemented
585C2×#393C2×C6111yescharacteristic, complemented
586C2×#391C2×C6111yescharacteristic, complemented
587C2×#390C2×C6111yescharacteristic
588C2×#386C2×C6111yescharacteristic
589#1444C2×C6111yescharacteristic, complemented
590#1441C2×C6111yescharacteristic, complemented
591#1439C2×C6111yescharacteristic, complemented
592#1439C2×C6111yescharacteristic, complemented
593#1439C2×C6111yescharacteristic, complemented
594#1439C2×C6111yescharacteristic, complemented
595#1438C2×C6111yescharacteristic
596#1436C2×C6111yescharacteristic, complemented
597C22⋊#95C2×C6111yescharacteristic, complemented
598C2×C61—44no—
599C2×C61—82no—
600C2×C61#240911yescharacteristic
601C2×C61#241011yescharacteristic
602C2×C61#242611yescharacteristic
603C2×C61#243111yescharacteristic
604C2×C61#243711yescharacteristic
605C2×C61#245011yescharacteristic
606C2×C61#245211yescharacteristic
607C2×C61#253811yescharacteristic
608C2×C61#256011yescharacteristic
609C2×C61#267611yescharacteristic
610C2×C61#268111yescharacteristic
611C2×C61#269211yescharacteristic
612C2×C61#270011yescharacteristic
613C2×C61#273011yescharacteristic
614C2×C61#273211yescharacteristic
615C23×Q8C22×C6111yescharacteristic
616C23×D4C22×C6111yescharacteristic
617C24×C4C22×C6111yescharacteristic
618C2×C22⋊Q8—24no—
619C2×C22⋊Q8—24no—
620C2×C22⋊Q8—24no—
621C22×C4⋊C4C22×C6111yescharacteristic
622C22×C4⋊C4C22×C6111yescharacteristic
623C22×C4⋊C4C22×C6111yescharacteristic
624C22×C4⋊C4C22×C6111yescharacteristic
625C22×C4⋊C4C22×C6111yescharacteristic
626C22×C4⋊C4C22×C6111yescharacteristic
627C22×C22⋊C4C22×C6111yescharacteristic
628C22×C22⋊C4C22×C6111yescharacteristic
629C22×C22⋊C4C22×C6111yescharacteristic
630C22×C22⋊C4C22×C6111yescharacteristic
631C22×C22⋊C4C22×C6111yescharacteristic
632C22×C22⋊C4C22×C6111yescharacteristic
633C22×C22⋊C4C22×C6111yescharacteristic
634C22×C22⋊C4C22×C6111yescharacteristic
635C22×C22⋊C4C22×C6111yescharacteristic
636C22×C22⋊C4C22×C6111yescharacteristic
637C22×C22⋊C4C22×C6111yescharacteristic
638C22×C42C22×C6111yescharacteristic
639#396—24no—
640#393—24no—
641#391—24no—
642#390—24no—
643#386—24no—
644C2×#95C22×C6111yescharacteristic
645C2×#95C22×C6111yescharacteristic
646C2×#95C22×C6111yescharacteristic
647C2×#95C22×C6111yescharacteristic
648C2×#95C22×C6111yescharacteristic
649C2×#95C22×C6111yescharacteristic
650C2×#95C22×C6111yescharacteristic
651C2×#95C22×C6111yescharacteristic
652C2×#95C22×C6111yescharacteristic
653C2×#95C22×C6111yescharacteristic
654C2×#95C22×C6111yescharacteristic
655C2×#95C22×C6111yescharacteristic
656C2×#95C22×C6111yescharacteristic
657C2×#95C22×C6111yescharacteristic
658C61#1528011yescharacteristic, direct product factor, Sylow
659C25C23×C6111yescharacteristic
660C25C23×C6111yescharacteristic
661C22×Q8—22no—
662C22×Q8—22no—
663C22×Q8—22no—
664C22×Q8—22no—
665C22×Q8—41no—
666C22×Q8—41no—
667C22×Q8D4×C6114yescomplemented
668C22×D4—22no—
669C22×D4—22no—
670C22×D4—22no—
671C22×D4—22no—
672C22×D4—41no—
673C22×D4—41no—
674C22×D4Q8×C6114yescomplemented
675C23×C4—22no—
676C23×C4—22no—
677C23×C4—22no—
678C23×C4—22no—
679C23×C4—22no—
680C23×C4—41no—
681C23×C4—41no—
682C23×C4C23×C6111yescharacteristic
683C23×C4C23×C6111yescharacteristic
684C23×C4C23×C6111yescharacteristic
685C23×C4C23×C6111yescharacteristic
686C23×C4C23×C6111yescharacteristic
687C23×C4C23×C6111yescharacteristic
688C23×C4C23×C6111yescharacteristic
689C23×C4C23×C6111yescharacteristic
690C23×C4C23×C6111yescharacteristic
691C23×C4C23×C6111yescharacteristic
692C23×C4C23×C6111yescharacteristic
693C23×C4C23×C6111yescharacteristic
694C23×C4C23×C6111yescharacteristic
695C22⋊Q8—232no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4—22no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4—22no—
708C2×C4⋊C4—22no—
709C2×C4⋊C4—41no—
710C2×C4⋊C4—41no—
711C2×C4⋊C4—41no—
712C2×C4⋊C4—41no—
713C2×C4⋊C4D4×C6114yescomplemented
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—41no—
737C2×C22⋊C4—41no—
738C2×C22⋊C4—41no—
739C2×C22⋊C4—41no—
740C2×C22⋊C4—41no—
741C2×C22⋊C4—41no—
742C2×C22⋊C4—41no—
743C2×C22⋊C4—41no—
744C2×C22⋊C4—41no—
745C2×C22⋊C4—41no—
746C2×C22⋊C4D4×C6114yes—
747C2×C42—22no—
748C2×C42—22no—
749C2×C42—41no—
750#95—22no—
751#95—22no—
752#95—22no—
753#95—22no—
754#95—22no—
755#95—22no—
756#95—22no—
757#95—22no—
758#95—22no—
759#95—22no—
760#95—41no—
761#95—41no—
762#95—41no—
763#95D4×C6114yes—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24C2×D4×C6112yes—
791C24C2×Q8×C6112yes—
792C24C2×Q8×C6112yes—
793C24#41×C6112yes—
794C24C24×C6111yescharacteristic
795C2×Q8—28no—
796C2×Q8—28no—
797C2×Q8—44no—
798C2×Q8—44no—
799C2×Q8—44no—
800C2×Q8—44no—
801C2×Q8—44no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—44no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—28no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4C2×D4×C6112yes—
893C22×C4C2×D4×C6112yes—
894C22×C4C2×D4×C6112yes—
895C22×C4C2×D4×C6112yes—
896C22×C4C2×D4×C6112yes—
897C22×C4C2×D4×C6112yes—
898C22×C4C2×D4×C6112yes—
899C22×C4C2×D4×C6112yes—
900C22×C4C2×D4×C6112yes—
901C22×C4C2×D4×C6112yes—
902C22×C4C2×D4×C6112yes—
903C22×C4C2×Q8×C6112yes—
904C22×C4#41×C6112yes—
905C22×C4#41×C6112yes—
906C22×C4#41×C6112yes—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—28no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C42—44no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23C22⋊Q8×C6114yes—
995C23C22×D4×C6111yescharacteristic
996C23C22×D4×C6111yescharacteristic
997C23C22×D4×C6111yescharacteristic
998C23C22×D4×C6111yescharacteristic
999C23C22×Q8×C6111yescharacteristic
1000C23C2×#41×C6111yescharacteristic
1001C23C2×#41×C6111yescharacteristic
1002C23C2×#41×C6111yescharacteristic
1003C23C2×#41×C6111yescharacteristic
1004C23H(5,𝔽2)×C6111yescharacteristic
1005C23H(5,𝔽2)×C6111yescharacteristic
1006C23H(5,𝔽2)×C6111yescharacteristic
1007C23H(5,𝔽2)×C6111yescharacteristic
1008C232−1+4×C6111yescharacteristic
1009C232−1+4×C6111yescharacteristic
1010Q8—416no—
1011D4—416no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—416no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4#120×C6114yes—
1102C2×C4#121×C6114yes—
1103C2×C4C22⋊Q8×C6114yescomplemented
1104C22—24no—
1105C22—24no—
1106C22—24no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—81no—
1127C22—81no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22C2×#120×C6111yescharacteristic
1135C22C2×#121×C6111yescharacteristic
1136C22C2×C22⋊Q8×C6111yescharacteristic
1137C22C2×C22⋊Q8×C6111yescharacteristic
1138C22C61×#52911yescharacteristic
1139C22C61×#53211yescharacteristic
1140C22C61×#53411yescharacteristic
1141C22C61×#53511yescharacteristic
1142C22C61×#53611yescharacteristic
1143C22C61×#53711yescharacteristic
1144C22C61×#53811yescharacteristic
1145C22C61×#53911yescharacteristic
1146C22C61×#54211yescharacteristic
1147C22C61×#54211yescharacteristic
1148C22C61×#54311yescharacteristic
1149C22D42×C6111yescharacteristic
1150C22D42×C6111yescharacteristic
1151C22C61×#54611yescharacteristic
1152C22C61×#54611yescharacteristic
1153C22C61×#54611yescharacteristic
1154C22C61×#54611yescharacteristic
1155C22C61×#54611yescharacteristic
1156C22C61×#54811yescharacteristic
1157C22C61×#54811yescharacteristic
1158C22C61×#54811yescharacteristic
1159C22D4×Q8×C6111yescharacteristic
1160C22D4×Q8×C6111yescharacteristic
1161C22C61×#55011yescharacteristic
1162C22C61×#55011yescharacteristic
1163C22C61×#55111yescharacteristic
1164C22C61×#55411yescharacteristic
1165C22C61×#55411yescharacteristic
1166C22C61×#55611yescharacteristic
1167C22C61×#56211yescharacteristic
1168C22C61×#56211yescharacteristic
1169C4—24no—
1170C4—24no—
1171C4—24no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—42no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C2—44no—
1183C2—82no—
1184C2C61×#240911yescharacteristic
1185C2C61×#241011yescharacteristic
1186C2C61×#242611yescharacteristic
1187C2C61×#243111yescharacteristic
1188C2C61×#243711yescharacteristic
1189C2C61×#245011yescharacteristic
1190C2C61×#245211yescharacteristic
1191C2C61×#253811yescharacteristic
1192C2C61×#256011yescharacteristic
1193C2C61×#267611yescharacteristic
1194C2C61×#268111yescharacteristic
1195C2C61×#269211yescharacteristic
1196C2C61×#270011yescharacteristic
1197C2C61×#273011yescharacteristic
1198C2C61×#273211yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutator, Frattini, cosocleC24C24×C61
prime radicalC23×D4×C61C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊Q8×C61C2semidirect
2. C2×C61×#396C2semidirect
3. C2×C61×#393C2semidirect
4. C2×C61×#391C2semidirect
7. C61×#1444C2semidirect
8. C61×#1441C2semidirect
9. C61×#1439C2semidirect
10. C61×#1439C2semidirect
11. C61×#1439C2semidirect
12. C61×#1439C2semidirect
14. C61×#1436C2semidirect
15. C61×C22⋊#95C2semidirect
67. C22×Q8×C61D4semidirect
74. C22×D4×C61Q8semidirect
113. C2×C4⋊C4×C61D4semidirect
503. C2×C4×C61C22⋊Q8semidirect
504. #15280C61direct (N × H)
583. C22×C22⋊Q8C2×C61semidirect
584. C2×#396C2×C61semidirect
585. C2×#393C2×C61semidirect
586. C2×#391C2×C61semidirect
589. #1444C2×C61semidirect
590. #1441C2×C61semidirect
591. #1439C2×C61semidirect
592. #1439C2×C61semidirect
593. #1439C2×C61semidirect
594. #1439C2×C61semidirect
596. #1436C2×C61semidirect
597. C22⋊#95C2×C61semidirect
658. C61#15280direct (N × H)
667. C22×Q8D4×C61semidirect
674. C22×D4Q8×C61semidirect
713. C2×C4⋊C4D4×C61semidirect
1103. C2×C4C22⋊Q8×C61semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C612
C2×C61×#3962
C2×C61×#3932
C2×C61×#3912
C2×C61×#3902
C2×C61×#3862
C61×#14442
C61×#14412
C61×#14392
C61×#14382
C61×#14362
C61×C22⋊#952
#1528061