Finite Group Databasebeta

← C61×#15317 #29518750

Subgroups — C61×#15317 #29518750

Order 15616.

2306 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C61C211yesmaximal, characteristic, complemented
2C2×C61×#394C211yesmaximal, characteristic, complemented
3C2×C61×#393C211yesmaximal, characteristic, complemented
4C2×C61×#392C211yesmaximal, characteristic
5C2×C61×#391C211yesmaximal, characteristic, complemented
6C2×C61×#390C211yesmaximal, characteristic, complemented
7C61×#1440C211yesmaximal, characteristic, complemented
8C61×#1439C211yesmaximal, characteristic, complemented
9C61×#1439C211yesmaximal, characteristic, complemented
10C61×#1438C211yesmaximal, characteristic, complemented
11C61×#1438C211yesmaximal, characteristic, complemented
12C61×#1438C211yesmaximal, characteristic, complemented
13C61×#1437C211yesmaximal, characteristic, complemented
14C61×#1437C211yesmaximal, characteristic, complemented
15C61×#1436C211yesmaximal, characteristic, complemented
16C23×Q8×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic
18C23×D4×C61C2211yescharacteristic
19C23×D4×C61C2211yescharacteristic
20C2×#124×C61—24no—
21C2×#124×C61—24no—
22C2×#124×C61—24no—
23C22×C4⋊C4×C61C2211yescharacteristic
24C22×C4⋊C4×C61C2211yescharacteristic
25C22×C22⋊C4×C61C2211yescharacteristic
26C22×C22⋊C4×C61C2211yescharacteristic
27C22×C22⋊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×C22⋊C4×C61C2211yescharacteristic
40C22×C42×C61C2211yescharacteristic
41C22×C42×C61C2211yescharacteristic
42C61×#394—24no—
43C61×#393—24no—
44C61×#392—24no—
45C61×#391—24no—
46C61×#390—24no—
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
61C25×C61C2311yescharacteristic
62C22×Q8×C61—22no—
63C22×Q8×C61—22no—
64C22×Q8×C61—22no—
65C22×Q8×C61—22no—
66C22×Q8×C61—41no—
67C22×Q8×C61—41no—
68C22×Q8×C61D414yescomplemented
69C22×D4×C61—22no—
70C22×D4×C61—22no—
71C22×D4×C61—22no—
72C22×D4×C61—22no—
73C22×D4×C61—22no—
74C22×D4×C61—22no—
75C22×D4×C61—22no—
76C22×D4×C61—22no—
77C22×D4×C61—22no—
78C22×D4×C61—22no—
79C22×D4×C61—22no—
80C22×D4×C61—22no—
81C22×D4×C61—22no—
82C22×D4×C61—41no—
83C22×D4×C61—41no—
84C22×D4×C61—41no—
85C22×D4×C61—41no—
86C22×D4×C61—41no—
87C22×D4×C61—41no—
88C22×D4×C61—41no—
89C22×D4×C61—41no—
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C23×C4×C61C2311yescharacteristic
93C23×C4×C61C2311yescharacteristic
94C23×C4×C61C2311yescharacteristic
95C23×C4×C61C2311yescharacteristic
96C23×C4×C61C2311yescharacteristic
97C23×C4×C61C2311yescharacteristic
98C23×C4×C61C2311yescharacteristic
99C23×C4×C61C2311yescharacteristic
100C23×C4×C61C2311yescharacteristic
101C23×C4×C61C2311yescharacteristic
102#124×C61—232no—
103C2×C4⋊C4×C61—22no—
104C2×C4⋊C4×C61—22no—
105C2×C4⋊C4×C61—22no—
106C2×C4⋊C4×C61—22no—
107C2×C4⋊C4×C61—41no—
108C2×C4⋊C4×C61—41no—
109C2×C22⋊C4×C61—22no—
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—22no—
113C2×C22⋊C4×C61—22no—
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—22no—
137C2×C22⋊C4×C61—22no—
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×C61—41no—
147C2×C22⋊C4×C61—41no—
148C2×C22⋊C4×C61—41no—
149C2×C22⋊C4×C61—41no—
150C2×C22⋊C4×C61—41no—
151C2×C22⋊C4×C61—41no—
152C2×C22⋊C4×C61D414yescomplemented
153C2×C22⋊C4×C61D414yescomplemented
154C2×C42×C61—22no—
155C2×C42×C61—22no—
156C2×C42×C61—22no—
157C2×C42×C61—22no—
158C2×C42×C61—22no—
159C2×C42×C61—41no—
160#95×C61—22no—
161#95×C61—22no—
162#95×C61—22no—
163#95×C61—22no—
164#95×C61—22no—
165#95×C61—22no—
166#95×C61—22no—
167#95×C61—22no—
168#95×C61—41no—
169#95×C61—41no—
170#95×C61—41no—
171#95×C61D414yes—
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×C61—21no—
191C24×C61—21no—
192C24×C61—21no—
193C24×C61—21no—
194C24×C61—21no—
195C24×C61—21no—
196C24×C61—21no—
197C24×C61—21no—
198C24×C61—21no—
199C24×C61—21no—
200C24×C61—21no—
201C24×C61—21no—
202C24×C61—21no—
203C24×C61—21no—
204C24×C61—21no—
205C24×C61—21no—
206C24×C61—21no—
207C24×C61—21no—
208C24×C61—21no—
209C24×C61—21no—
210C24×C61—21no—
211C24×C61—21no—
212C24×C61—21no—
213C24×C61—21no—
214C24×C61C2×D412yes—
215C24×C61C2×D412yes—
216C24×C61#4112yes—
217C24×C61C2411yescharacteristic
218C2×Q8×C61—28no—
219C2×Q8×C61—28no—
220C2×Q8×C61—44no—
221C2×Q8×C61—44no—
222C2×Q8×C61—44no—
223C2×Q8×C61—44no—
224C2×Q8×C61—44no—
225C2×D4×C61—28no—
226C2×D4×C61—28no—
227C2×D4×C61—44no—
228C2×D4×C61—44no—
229C2×D4×C61—44no—
230C2×D4×C61—44no—
231C2×D4×C61—44no—
232C2×D4×C61—44no—
233C2×D4×C61—44no—
234C2×D4×C61—44no—
235C2×D4×C61—44no—
236C2×D4×C61—44no—
237C2×D4×C61—44no—
238C2×D4×C61—44no—
239C2×D4×C61—44no—
240C2×D4×C61—44no—
241C2×D4×C61—44no—
242C2×D4×C61—44no—
243C2×D4×C61—44no—
244C2×D4×C61—44no—
245C2×D4×C61—44no—
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—21no—
287C22×C4×C61—21no—
288C22×C4×C61—21no—
289C22×C4×C61—21no—
290C22×C4×C61—21no—
291C22×C4×C61—21no—
292C22×C4×C61—21no—
293C22×C4×C61—21no—
294C22×C4×C61—21no—
295C22×C4×C61—21no—
296C22×C4×C61—21no—
297C22×C4×C61—21no—
298C22×C4×C61—21no—
299C22×C4×C61—21no—
300C22×C4×C61—21no—
301C22×C4×C61—21no—
302C22×C4×C61—21no—
303C22×C4×C61—21no—
304C22×C4×C61—21no—
305C22×C4×C61—21no—
306C22×C4×C61—21no—
307C22×C4×C61—21no—
308C22×C4×C61—21no—
309C22×C4×C61—21no—
310C22×C4×C61—21no—
311C22×C4×C61—21no—
312C22×C4×C61—21no—
313C22×C4×C61—21no—
314C22×C4×C61—21no—
315C22×C4×C61—21no—
316C22×C4×C61C2×D412yes—
317C22×C4×C61C2×D412yes—
318C22×C4×C61C2×D412yes—
319C22×C4×C61C2×D412yes—
320C22×C4×C61C2×D412yes—
321C22×C4×C61C2×D412yes—
322C22×C4×C61C2×D412yes—
323C22×C4×C61C2×D412yes—
324C22×C4×C61C2×D412yes—
325C22×C4×C61C2×D412yes—
326C22×C4×C61#4112yes—
327C22×C4×C61#4112yes—
328C22×C4×C61#4112yes—
329C22×C4×C61#4112yes—
330C4⋊C4×C61—44no—
331C4⋊C4×C61—44no—
332C22⋊C4×C61—28no—
333C22⋊C4×C61—28no—
334C22⋊C4×C61—28no—
335C22⋊C4×C61—28no—
336C22⋊C4×C61—44no—
337C22⋊C4×C61—44no—
338C22⋊C4×C61—44no—
339C22⋊C4×C61—44no—
340C22⋊C4×C61—44no—
341C22⋊C4×C61—44no—
342C22⋊C4×C61—44no—
343C22⋊C4×C61—44no—
344C22⋊C4×C61—44no—
345C22⋊C4×C61—44no—
346C22⋊C4×C61—44no—
347C42×C61—28no—
348C42×C61—44no—
349C23×C61—22no—
350C23×C61—22no—
351C23×C61—22no—
352C23×C61—22no—
353C23×C61—22no—
354C23×C61—22no—
355C23×C61—22no—
356C23×C61—22no—
357C23×C61—22no—
358C23×C61—22no—
359C23×C61—22no—
360C23×C61—22no—
361C23×C61—22no—
362C23×C61—22no—
363C23×C61—22no—
364C23×C61—22no—
365C23×C61—22no—
366C23×C61—22no—
367C23×C61—22no—
368C23×C61—22no—
369C23×C61—22no—
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×C61—41no—
395C23×C61—41no—
396C23×C61—41no—
397C23×C61—41no—
398C23×C61—41no—
399C23×C61—41no—
400C23×C61—41no—
401C23×C61—41no—
402C23×C61—41no—
403C23×C61—41no—
404C23×C61—41no—
405C23×C61—41no—
406C23×C61—41no—
407C23×C61—41no—
408C23×C61—41no—
409C23×C61—41no—
410C23×C61—41no—
411C23×C61—41no—
412C23×C61—41no—
413C23×C61—41no—
414C23×C61—41no—
415C23×C61—41no—
416C23×C61—41no—
417C23×C61—41no—
418C23×C61—41no—
419C23×C61—41no—
420C23×C61—41no—
421C23×C61—41no—
422C23×C61—41no—
423C23×C61—41no—
424C23×C61—41no—
425C23×C61—41no—
426C23×C61—41no—
427C23×C61—41no—
428C23×C61—41no—
429C23×C61—41no—
430C23×C61—41no—
431C23×C61—41no—
432C23×C61—41no—
433C23×C61—41no—
434C23×C61—41no—
435C23×C61—41no—
436C23×C61—41no—
437C23×C61—41no—
438C23×C61—41no—
439C23×C61—41no—
440C23×C61—41no—
441C23×C61—41no—
442C23×C61—41no—
443C23×C61—41no—
444C23×C61—41no—
445C23×C61—41no—
446C23×C61—41no—
447C23×C61—41no—
448C23×C61—41no—
449C23×C61—41no—
450C23×C61—41no—
451C23×C61—41no—
452C23×C61—41no—
453C23×C61—41no—
454C23×C61C22×D411yescharacteristic
455C23×C61C22×D411yescharacteristic
456C23×C61C22×D411yescharacteristic
457C23×C61C22×D411yescharacteristic
458C23×C61C2×#4111yescharacteristic
459C23×C61C2×#4111yescharacteristic
460C23×C61C2×#4111yescharacteristic
461C23×C61C2×#4111yescharacteristic
462C23×C61C2×#4111yescharacteristic
463C23×C61H(5,𝔽2)11yescharacteristic
464C23×C61H(5,𝔽2)11yescharacteristic
465C23×C61H(5,𝔽2)11yescharacteristic
466C23×C61H(5,𝔽2)11yescharacteristic
467C23×C61H(5,𝔽2)11yescharacteristic
468C23×C612−1+411yescharacteristic
469Q8×C61—416no—
470D4×C61—416no—
471D4×C61—416no—
472D4×C61—416no—
473C2×C4×C61—22no—
474C2×C4×C61—22no—
475C2×C4×C61—22no—
476C2×C4×C61—22no—
477C2×C4×C61—22no—
478C2×C4×C61—22no—
479C2×C4×C61—22no—
480C2×C4×C61—22no—
481C2×C4×C61—22no—
482C2×C4×C61—22no—
483C2×C4×C61—22no—
484C2×C4×C61—22no—
485C2×C4×C61—22no—
486C2×C4×C61—22no—
487C2×C4×C61—22no—
488C2×C4×C61—22no—
489C2×C4×C61—22no—
490C2×C4×C61—22no—
491C2×C4×C61—22no—
492C2×C4×C61—22no—
493C2×C4×C61—22no—
494C2×C4×C61—22no—
495C2×C4×C61—22no—
496C2×C4×C61—22no—
497C2×C4×C61—22no—
498C2×C4×C61—22no—
499C2×C4×C61—22no—
500C2×C4×C61—22no—
501C2×C4×C61—22no—
502C2×C4×C61—22no—
503C2×C4×C61—22no—
504C2×C4×C61—22no—
505C2×C4×C61—22no—
506C2×C4×C61—41no—
507C2×C4×C61—41no—
508C2×C4×C61—41no—
509C2×C4×C61—41no—
510C2×C4×C61—41no—
511C2×C4×C61—41no—
512C2×C4×C61—41no—
513C2×C4×C61—41no—
514C2×C4×C61—41no—
515C2×C4×C61—41no—
516C2×C4×C61—41no—
517C2×C4×C61—41no—
518C2×C4×C61—41no—
519C2×C4×C61—41no—
520C2×C4×C61—41no—
521C2×C4×C61—41no—
522C2×C4×C61—41no—
523C2×C4×C61—41no—
524C2×C4×C61—41no—
525C2×C4×C61—41no—
526C2×C4×C61—41no—
527C2×C4×C61—41no—
528C2×C4×C61—41no—
529C2×C4×C61—41no—
530C2×C4×C61—41no—
531C2×C4×C61—41no—
532C2×C4×C61—41no—
533C2×C4×C61—41no—
534C2×C4×C61—41no—
535C2×C4×C61—41no—
536C2×C4×C61—41no—
537C2×C4×C61—41no—
538C2×C4×C61—41no—
539C2×C4×C61—41no—
540C2×C4×C61—41no—
541C2×C4×C61—41no—
542C2×C4×C61—41no—
543C2×C4×C61—41no—
544C2×C4×C61—41no—
545C2×C4×C61—41no—
546C2×C4×C61—41no—
547C2×C4×C61—41no—
548C2×C4×C61—41no—
549C2×C4×C61—41no—
550C2×C4×C61—41no—
551C2×C4×C61—41no—
552C2×C4×C61—41no—
553C2×C4×C61—41no—
554C2×C4×C61#12014yes—
555C2×C4×C61#12114yes—
556C2×C4×C61#12414yescomplemented
557#15317C6111yesmaximal, characteristic, direct product factor, Sylow
558C22×C61—42no—
559C22×C61—42no—
560C22×C61—42no—
561C22×C61—42no—
562C22×C61—42no—
563C22×C61—42no—
564C22×C61—42no—
565C22×C61—42no—
566C22×C61—42no—
567C22×C61—42no—
568C22×C61—42no—
569C22×C61—42no—
570C22×C61—42no—
571C22×C61—42no—
572C22×C61—42no—
573C22×C61—42no—
574C22×C61—42no—
575C22×C61—42no—
576C22×C61—42no—
577C22×C61—42no—
578C22×C61—42no—
579C22×C61—81no—
580C22×C61—81no—
581C22×C61—81no—
582C22×C61—81no—
583C22×C61—81no—
584C22×C61—81no—
585C22×C61—81no—
586C22×C61—81no—
587C22×C61—81no—
588C22×C61—81no—
589C22×C61—81no—
590C22×C61—81no—
591C22×C61—81no—
592C22×C61—81no—
593C22×C61—81no—
594C22×C61—81no—
595C22×C61—81no—
596C22×C61—81no—
597C22×C61—81no—
598C22×C61—81no—
599C22×C61—81no—
600C22×C61—81no—
601C22×C61—81no—
602C22×C61—81no—
603C22×C61C2×#12011yescharacteristic
604C22×C61C2×#12111yescharacteristic
605C22×C61#52511yescharacteristic
606C22×C61C2×#12411yescharacteristic
607C22×C61#52911yescharacteristic
608C22×C61#53211yescharacteristic
609C22×C61#53411yescharacteristic
610C22×C61#53511yescharacteristic
611C22×C61#53511yescharacteristic
612C22×C61#53711yescharacteristic
613C22×C61#53811yescharacteristic
614C22×C61#53811yescharacteristic
615C22×C61#53811yescharacteristic
616C22×C61#54211yescharacteristic
617C22×C61#54211yescharacteristic
618C22×C61D4211yescharacteristic
619C22×C61D4211yescharacteristic
620C22×C61#54611yescharacteristic
621C22×C61#54611yescharacteristic
622C22×C61#54611yescharacteristic
623C22×C61#54611yescharacteristic
624C22×C61#54611yescharacteristic
625C22×C61#54611yescharacteristic
626C22×C61#54711yescharacteristic
627C22×C61#54811yescharacteristic
628C22×C61#54811yescharacteristic
629C22×C61#55011yescharacteristic
630C22×C61#55011yescharacteristic
631C22×C61#55011yescharacteristic
632C22×C61#55111yescharacteristic
633C22×C61#55511yescharacteristic
634C22×C61#55911yescharacteristic
635C22×C61#55911yescharacteristic
636C22×C61H(3,𝔽4)11yescharacteristic
637C22×C61#56211yescharacteristic
638C4×C61—24no—
639C4×C61—24no—
640C4×C61—24no—
641C4×C61—42no—
642C4×C61—42no—
643C4×C61—42no—
644C4×C61—42no—
645C4×C61—42no—
646C4×C61—81no—
647C4×C61—81no—
648C4×C61—81no—
649C4×C61—81no—
650C22×#124C2×C6111yescharacteristic, complemented
651C2×#394C2×C6111yescharacteristic, complemented
652C2×#393C2×C6111yescharacteristic, complemented
653C2×#392C2×C6111yescharacteristic
654C2×#391C2×C6111yescharacteristic, complemented
655C2×#390C2×C6111yescharacteristic, complemented
656#1440C2×C6111yescharacteristic, complemented
657#1439C2×C6111yescharacteristic, complemented
658#1439C2×C6111yescharacteristic, complemented
659#1438C2×C6111yescharacteristic, complemented
660#1438C2×C6111yescharacteristic, complemented
661#1438C2×C6111yescharacteristic, complemented
662#1437C2×C6111yescharacteristic, complemented
663#1437C2×C6111yescharacteristic, complemented
664#1436C2×C6111yescharacteristic, complemented
665C2×C61—82no—
666C2×C61—82no—
667C2×C61—82no—
668C2×C61#240711yescharacteristic
669C2×C61#241011yescharacteristic
670C2×C61#242611yescharacteristic
671C2×C61#243111yescharacteristic
672C2×C61#245911yescharacteristic
673C2×C61#247211yescharacteristic
674C2×C61#249111yescharacteristic
675C2×C61#254811yescharacteristic
676C2×C61#255711yescharacteristic
677C2×C61#267011yescharacteristic
678C2×C61#267611yescharacteristic
679C2×C61#271011yescharacteristic
680C2×C61#271211yescharacteristic
681C2×C61#273011yescharacteristic
682C2×C61#273311yescharacteristic
683C23×Q8C22×C6111yescharacteristic
684C23×D4C22×C6111yescharacteristic
685C23×D4C22×C6111yescharacteristic
686C23×D4C22×C6111yescharacteristic
687C2×#124—24no—
688C2×#124—24no—
689C2×#124—24no—
690C22×C4⋊C4C22×C6111yescharacteristic
691C22×C4⋊C4C22×C6111yescharacteristic
692C22×C22⋊C4C22×C6111yescharacteristic
693C22×C22⋊C4C22×C6111yescharacteristic
694C22×C22⋊C4C22×C6111yescharacteristic
695C22×C22⋊C4C22×C6111yescharacteristic
696C22×C22⋊C4C22×C6111yescharacteristic
697C22×C22⋊C4C22×C6111yescharacteristic
698C22×C22⋊C4C22×C6111yescharacteristic
699C22×C22⋊C4C22×C6111yescharacteristic
700C22×C22⋊C4C22×C6111yescharacteristic
701C22×C22⋊C4C22×C6111yescharacteristic
702C22×C22⋊C4C22×C6111yescharacteristic
703C22×C22⋊C4C22×C6111yescharacteristic
704C22×C22⋊C4C22×C6111yescharacteristic
705C22×C22⋊C4C22×C6111yescharacteristic
706C22×C22⋊C4C22×C6111yescharacteristic
707C22×C42C22×C6111yescharacteristic
708C22×C42C22×C6111yescharacteristic
709#394—24no—
710#393—24no—
711#392—24no—
712#391—24no—
713#390—24no—
714C2×#95C22×C6111yescharacteristic
715C2×#95C22×C6111yescharacteristic
716C2×#95C22×C6111yescharacteristic
717C2×#95C22×C6111yescharacteristic
718C2×#95C22×C6111yescharacteristic
719C2×#95C22×C6111yescharacteristic
720C2×#95C22×C6111yescharacteristic
721C2×#95C22×C6111yescharacteristic
722C2×#95C22×C6111yescharacteristic
723C2×#95C22×C6111yescharacteristic
724C2×#95C22×C6111yescharacteristic
725C2×#95C22×C6111yescharacteristic
726C61#1531711yescharacteristic, direct product factor, Sylow
727C25C23×C6111yescharacteristic
728C25C23×C6111yescharacteristic
729C25C23×C6111yescharacteristic
730C22×Q8—22no—
731C22×Q8—22no—
732C22×Q8—22no—
733C22×Q8—22no—
734C22×Q8—41no—
735C22×Q8—41no—
736C22×Q8D4×C6114yescomplemented
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—22no—
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—41no—
751C22×D4—41no—
752C22×D4—41no—
753C22×D4—41no—
754C22×D4—41no—
755C22×D4—41no—
756C22×D4—41no—
757C22×D4—41no—
758C23×C4C23×C6111yescharacteristic
759C23×C4C23×C6111yescharacteristic
760C23×C4C23×C6111yescharacteristic
761C23×C4C23×C6111yescharacteristic
762C23×C4C23×C6111yescharacteristic
763C23×C4C23×C6111yescharacteristic
764C23×C4C23×C6111yescharacteristic
765C23×C4C23×C6111yescharacteristic
766C23×C4C23×C6111yescharacteristic
767C23×C4C23×C6111yescharacteristic
768C23×C4C23×C6111yescharacteristic
769C23×C4C23×C6111yescharacteristic
770#124—232no—
771C2×C4⋊C4—22no—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—22no—
774C2×C4⋊C4—22no—
775C2×C4⋊C4—41no—
776C2×C4⋊C4—41no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4D4×C6114yescomplemented
821C2×C22⋊C4D4×C6114yescomplemented
822C2×C42—22no—
823C2×C42—22no—
824C2×C42—22no—
825C2×C42—22no—
826C2×C42—22no—
827C2×C42—41no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—41no—
837#95—41no—
838#95—41no—
839#95D4×C6114yes—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24C2×D4×C6112yes—
883C24C2×D4×C6112yes—
884C24#41×C6112yes—
885C24C24×C6111yescharacteristic
886C2×Q8—28no—
887C2×Q8—28no—
888C2×Q8—44no—
889C2×Q8—44no—
890C2×Q8—44no—
891C2×Q8—44no—
892C2×Q8—44no—
893C2×D4—28no—
894C2×D4—28no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4C2×D4×C6112yes—
985C22×C4C2×D4×C6112yes—
986C22×C4C2×D4×C6112yes—
987C22×C4C2×D4×C6112yes—
988C22×C4C2×D4×C6112yes—
989C22×C4C2×D4×C6112yes—
990C22×C4C2×D4×C6112yes—
991C22×C4C2×D4×C6112yes—
992C22×C4C2×D4×C6112yes—
993C22×C4C2×D4×C6112yes—
994C22×C4#41×C6112yes—
995C22×C4#41×C6112yes—
996C22×C4#41×C6112yes—
997C22×C4#41×C6112yes—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C22⋊C4—28no—
1001C22⋊C4—28no—
1002C22⋊C4—28no—
1003C22⋊C4—28no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C42—28no—
1016C42—44no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23C22×D4×C6111yescharacteristic
1123C23C22×D4×C6111yescharacteristic
1124C23C22×D4×C6111yescharacteristic
1125C23C22×D4×C6111yescharacteristic
1126C23C2×#41×C6111yescharacteristic
1127C23C2×#41×C6111yescharacteristic
1128C23C2×#41×C6111yescharacteristic
1129C23C2×#41×C6111yescharacteristic
1130C23C2×#41×C6111yescharacteristic
1131C23H(5,𝔽2)×C6111yescharacteristic
1132C23H(5,𝔽2)×C6111yescharacteristic
1133C23H(5,𝔽2)×C6111yescharacteristic
1134C23H(5,𝔽2)×C6111yescharacteristic
1135C23H(5,𝔽2)×C6111yescharacteristic
1136C232−1+4×C6111yescharacteristic
1137Q8—416no—
1138D4—416no—
1139D4—416no—
1140D4—416no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4#120×C6114yes—
1223C2×C4#121×C6114yes—
1224C2×C4#124×C6114yescomplemented
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22C2×#120×C6111yescharacteristic
1271C22C2×#121×C6111yescharacteristic
1272C22C61×#52511yescharacteristic
1273C22C2×#124×C6111yescharacteristic
1274C22C61×#52911yescharacteristic
1275C22C61×#53211yescharacteristic
1276C22C61×#53411yescharacteristic
1277C22C61×#53511yescharacteristic
1278C22C61×#53511yescharacteristic
1279C22C61×#53711yescharacteristic
1280C22C61×#53811yescharacteristic
1281C22C61×#53811yescharacteristic
1282C22C61×#53811yescharacteristic
1283C22C61×#54211yescharacteristic
1284C22C61×#54211yescharacteristic
1285C22D42×C6111yescharacteristic
1286C22D42×C6111yescharacteristic
1287C22C61×#54611yescharacteristic
1288C22C61×#54611yescharacteristic
1289C22C61×#54611yescharacteristic
1290C22C61×#54611yescharacteristic
1291C22C61×#54611yescharacteristic
1292C22C61×#54611yescharacteristic
1293C22C61×#54711yescharacteristic
1294C22C61×#54811yescharacteristic
1295C22C61×#54811yescharacteristic
1296C22C61×#55011yescharacteristic
1297C22C61×#55011yescharacteristic
1298C22C61×#55011yescharacteristic
1299C22C61×#55111yescharacteristic
1300C22C61×#55511yescharacteristic
1301C22C61×#55911yescharacteristic
1302C22C61×#55911yescharacteristic
1303C22C61×H(3,𝔽4)11yescharacteristic
1304C22C61×#56211yescharacteristic
1305C4—24no—
1306C4—24no—
1307C4—24no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C2—82no—
1318C2—82no—
1319C2—82no—
1320C2C61×#240711yescharacteristic
1321C2C61×#241011yescharacteristic
1322C2C61×#242611yescharacteristic
1323C2C61×#243111yescharacteristic
1324C2C61×#245911yescharacteristic
1325C2C61×#247211yescharacteristic
1326C2C61×#249111yescharacteristic
1327C2C61×#254811yescharacteristic
1328C2C61×#255711yescharacteristic
1329C2C61×#267011yescharacteristic
1330C2C61×#267611yescharacteristic
1331C2C61×#271011yescharacteristic
1332C2C61×#271211yescharacteristic
1333C2C61×#273011yescharacteristic
1334C2C61×#273311yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutator, Frattini, cosocleC24C24×C61
prime radicalC2×C61×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#124×C61C2semidirect
2. C2×C61×#394C2semidirect
3. C2×C61×#393C2semidirect
5. C2×C61×#391C2semidirect
6. C2×C61×#390C2semidirect
7. C61×#1440C2semidirect
8. C61×#1439C2semidirect
9. C61×#1439C2semidirect
10. C61×#1438C2semidirect
11. C61×#1438C2semidirect
12. C61×#1438C2semidirect
13. C61×#1437C2semidirect
14. C61×#1437C2semidirect
15. C61×#1436C2semidirect
68. C22×Q8×C61D4semidirect
152. C2×C22⋊C4×C61D4semidirect
153. C2×C22⋊C4×C61D4semidirect
556. C2×C4×C61#124semidirect
557. #15317C61direct (N × H)
650. C22×#124C2×C61semidirect
651. C2×#394C2×C61semidirect
652. C2×#393C2×C61semidirect
654. C2×#391C2×C61semidirect
655. C2×#390C2×C61semidirect
656. #1440C2×C61semidirect
657. #1439C2×C61semidirect
658. #1439C2×C61semidirect
659. #1438C2×C61semidirect
660. #1438C2×C61semidirect
661. #1438C2×C61semidirect
662. #1437C2×C61semidirect
663. #1437C2×C61semidirect
664. #1436C2×C61semidirect
726. C61#15317direct (N × H)
736. C22×Q8D4×C61semidirect
820. C2×C22⋊C4D4×C61semidirect
821. C2×C22⋊C4D4×C61semidirect
1224. C2×C4#124×C61semidirect

Maximal subgroups

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

subgroupindex
C22×#124×C612
C2×C61×#3942
C2×C61×#3932
C2×C61×#3922
C2×C61×#3912
C2×C61×#3902
C61×#14402
C61×#14392
C61×#14382
C61×#14372
C61×#14362
#1531761