Finite Group Databasebeta

← C61×#15370 #29518803

Subgroups — C61×#15370 #29518803

Order 15616.

2442 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C61C211yesmaximal, characteristic, complemented
2C2×C61×#399C211yesmaximal, characteristic, complemented
3C2×C61×#394C211yesmaximal, characteristic, complemented
4C2×C61×#394C211yesmaximal, characteristic, complemented
5C2×C61×#392C211yesmaximal, characteristic
6C2×C61×#390C211yesmaximal, characteristic, complemented
7C2×C61×#386C211yesmaximal, characteristic, complemented
8C2×C61×#385C211yesmaximal, characteristic, complemented
9C61×#1444C211yesmaximal, characteristic, complemented
10C61×#1439C211yesmaximal, characteristic, complemented
11C61×#1439C211yesmaximal, characteristic, complemented
12C61×#1439C211yesmaximal, characteristic, complemented
13C61×#1438C211yesmaximal, characteristic, complemented
14C61×#1437C211yesmaximal, characteristic, complemented
15C61×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic
18C23×D4×C61C2211yescharacteristic
19C24×C4×C61C2211yescharacteristic
20C2×#123×C61—24no—
21C2×#123×C61—24no—
22C2×#123×C61—24no—
23C22×C4⋊C4×C61C2211yescharacteristic
24C22×C4⋊C4×C61C2211yescharacteristic
25C22×C4⋊C4×C61C2211yescharacteristic
26C22×C4⋊C4×C61C2211yescharacteristic
27C22×C4⋊C4×C61C2211yescharacteristic
28C22×C4⋊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×C22⋊C4×C61C2211yescharacteristic
41C22×C22⋊C4×C61C2211yescharacteristic
42C22×C22⋊C4×C61C2211yescharacteristic
43C22×C42×C61C2211yescharacteristic
44C61×#399—24no—
45C61×#394—24no—
46C61×#394—24no—
47C61×#392—24no—
48C61×#390—24no—
49C61×#386—24no—
50C61×#385—24no—
51C2×#95×C61C2211yescharacteristic
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C2×#95×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C2×#95×C61C2211yescharacteristic
61C25×C61C2311yescharacteristic
62C25×C61C2311yescharacteristic
63C25×C61C2311yescharacteristic
64C22×D4×C61—22no—
65C22×D4×C61—22no—
66C22×D4×C61—22no—
67C22×D4×C61—22no—
68C22×D4×C61—22no—
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—41no—
80C22×D4×C61—41no—
81C22×D4×C61—41no—
82C22×D4×C61—41no—
83C22×D4×C61—41no—
84C22×D4×C61—41no—
85C23×C4×C61—22no—
86C23×C4×C61—22no—
87C23×C4×C61—22no—
88C23×C4×C61—22no—
89C23×C4×C61—22no—
90C23×C4×C61—41no—
91C23×C4×C61—41no—
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
102C23×C4×C61C2311yescharacteristic
103C23×C4×C61C2311yescharacteristic
104#123×C61—232no—
105C2×C4⋊C4×C61—22no—
106C2×C4⋊C4×C61—22no—
107C2×C4⋊C4×C61—22no—
108C2×C4⋊C4×C61—22no—
109C2×C4⋊C4×C61—22no—
110C2×C4⋊C4×C61—22no—
111C2×C4⋊C4×C61—22no—
112C2×C4⋊C4×C61—22no—
113C2×C4⋊C4×C61—22no—
114C2×C4⋊C4×C61—22no—
115C2×C4⋊C4×C61—22no—
116C2×C4⋊C4×C61—22no—
117C2×C4⋊C4×C61—22no—
118C2×C4⋊C4×C61—41no—
119C2×C4⋊C4×C61—41no—
120C2×C4⋊C4×C61—41no—
121C2×C4⋊C4×C61—41no—
122C2×C4⋊C4×C61D414yescomplemented
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—22no—
139C2×C22⋊C4×C61—22no—
140C2×C22⋊C4×C61—22no—
141C2×C22⋊C4×C61—22no—
142C2×C22⋊C4×C61—22no—
143C2×C22⋊C4×C61—22no—
144C2×C22⋊C4×C61—22no—
145C2×C22⋊C4×C61—22no—
146C2×C22⋊C4×C61—22no—
147C2×C22⋊C4×C61—22no—
148C2×C22⋊C4×C61—22no—
149C2×C22⋊C4×C61—22no—
150C2×C22⋊C4×C61—22no—
151C2×C22⋊C4×C61—41no—
152C2×C22⋊C4×C61—41no—
153C2×C22⋊C4×C61—41no—
154C2×C22⋊C4×C61—41no—
155C2×C22⋊C4×C61—41no—
156C2×C22⋊C4×C61—41no—
157C2×C22⋊C4×C61—41no—
158C2×C22⋊C4×C61—41no—
159C2×C22⋊C4×C61—41no—
160C2×C22⋊C4×C61—41no—
161C2×C22⋊C4×C61D414yes—
162C2×C22⋊C4×C61D414yescomplemented
163C2×C22⋊C4×C61D414yescomplemented
164C2×C22⋊C4×C61D414yescomplemented
165C2×C42×C61—22no—
166C2×C42×C61—22no—
167C2×C42×C61—41no—
168#95×C61—22no—
169#95×C61—22no—
170#95×C61—22no—
171#95×C61—22no—
172#95×C61—22no—
173#95×C61—22no—
174#95×C61—22no—
175#95×C61—22no—
176#95×C61—22no—
177#95×C61—41no—
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×C61—21no—
215C24×C61—21no—
216C24×C61—21no—
217C24×C61—21no—
218C24×C61C2×D412yes—
219C24×C61C2×D412yes—
220C24×C61C2×D412yes—
221C24×C61C2×D412yes—
222C24×C61#4112yes—
223C24×C61C2411yescharacteristic
224C2×D4×C61—28no—
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—
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—28no—
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×C61—44no—
317C22×C4×C61—44no—
318C22×C4×C61—44no—
319C22×C4×C61—44no—
320C22×C4×C61—44no—
321C22×C4×C61—44no—
322C22×C4×C61C2×D412yes—
323C22×C4×C61C2×D412yes—
324C22×C4×C61C2×D412yes—
325C22×C4×C61C2×D412yes—
326C22×C4×C61C2×D412yes—
327C22×C4×C61C2×D412yes—
328C22×C4×C61C2×D412yes—
329C22×C4×C61C2×D412yes—
330C22×C4×C61C2×D412yes—
331C22×C4×C61C2×D412yes—
332C22×C4×C61C2×D412yes—
333C22×C4×C61#4112yes—
334C22×C4×C61#4112yes—
335C22×C4×C61#4112yes—
336C4⋊C4×C61—28no—
337C4⋊C4×C61—28no—
338C4⋊C4×C61—44no—
339C4⋊C4×C61—44no—
340C4⋊C4×C61—44no—
341C4⋊C4×C61—44no—
342C22⋊C4×C61—28no—
343C22⋊C4×C61—28no—
344C22⋊C4×C61—28no—
345C22⋊C4×C61—28no—
346C22⋊C4×C61—44no—
347C22⋊C4×C61—44no—
348C22⋊C4×C61—44no—
349C22⋊C4×C61—44no—
350C22⋊C4×C61—44no—
351C22⋊C4×C61—44no—
352C22⋊C4×C61—44no—
353C22⋊C4×C61—44no—
354C22⋊C4×C61—44no—
355C22⋊C4×C61—44no—
356C42×C61—44no—
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—22no—
371C23×C61—22no—
372C23×C61—22no—
373C23×C61—22no—
374C23×C61—22no—
375C23×C61—22no—
376C23×C61—22no—
377C23×C61—22no—
378C23×C61—22no—
379C23×C61—22no—
380C23×C61—22no—
381C23×C61—22no—
382C23×C61—22no—
383C23×C61—22no—
384C23×C61—22no—
385C23×C61—22no—
386C23×C61—22no—
387C23×C61—22no—
388C23×C61—22no—
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×C61—41no—
455C23×C61—41no—
456C23×C61—41no—
457C23×C61—41no—
458C23×C61—41no—
459C23×C61—41no—
460C23×C61—41no—
461C23×C61#12714yes—
462C23×C61C22×D411yescharacteristic
463C23×C61C22×D411yescharacteristic
464C23×C61C22×D411yescharacteristic
465C23×C61C22×D411yescharacteristic
466C23×C61C22×D411yescharacteristic
467C23×C61C2×#4111yescharacteristic
468C23×C61C2×#4111yescharacteristic
469C23×C61C2×#4111yescharacteristic
470C23×C61C2×#4111yescharacteristic
471C23×C61H(5,𝔽2)11yescharacteristic
472C23×C61H(5,𝔽2)11yescharacteristic
473C23×C61H(5,𝔽2)11yescharacteristic
474C23×C61H(5,𝔽2)11yescharacteristic
475C23×C612−1+411yescharacteristic
476C23×C612−1+411yescharacteristic
477D4×C61—416no—
478D4×C61—416no—
479D4×C61—416no—
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—22no—
507C2×C4×C61—22no—
508C2×C4×C61—22no—
509C2×C4×C61—22no—
510C2×C4×C61—22no—
511C2×C4×C61—22no—
512C2×C4×C61—22no—
513C2×C4×C61—22no—
514C2×C4×C61—22no—
515C2×C4×C61—22no—
516C2×C4×C61—416no—
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—41no—
555C2×C4×C61—41no—
556C2×C4×C61—41no—
557C2×C4×C61—41no—
558C2×C4×C61—41no—
559C2×C4×C61—41no—
560C2×C4×C61—41no—
561C2×C4×C61—41no—
562C2×C4×C61—41no—
563C2×C4×C61#12014yes—
564C2×C4×C61#12314yescomplemented
565#15370C6111yesmaximal, characteristic, direct product factor, Sylow
566C22×C61—24no—
567C22×C61—24no—
568C22×C61—24no—
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—42no—
580C22×C61—42no—
581C22×C61—42no—
582C22×C61—42no—
583C22×C61—42no—
584C22×C61—42no—
585C22×C61—42no—
586C22×C61—42no—
587C22×C61—42no—
588C22×C61—42no—
589C22×C61—42no—
590C22×C61—42no—
591C22×C61—42no—
592C22×C61—42no—
593C22×C61—42no—
594C22×C61—42no—
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×C61—81no—
604C22×C61—81no—
605C22×C61—81no—
606C22×C61—81no—
607C22×C61—81no—
608C22×C61—81no—
609C22×C61—81no—
610C22×C61—81no—
611C22×C61C2×#12011yescharacteristic
612C22×C61C2×#12311yescharacteristic
613C22×C61#52511yescharacteristic
614C22×C61#52511yescharacteristic
615C22×C61C2×#12711yescharacteristic
616C22×C61#53211yescharacteristic
617C22×C61#53411yescharacteristic
618C22×C61#53511yescharacteristic
619C22×C61#53611yescharacteristic
620C22×C61#53711yescharacteristic
621C22×C61#53711yescharacteristic
622C22×C61#53811yescharacteristic
623C22×C61#53911yescharacteristic
624C22×C61#54011yescharacteristic
625C22×C61#54211yescharacteristic
626C22×C61D4211yescharacteristic
627C22×C61D4211yescharacteristic
628C22×C61D4211yescharacteristic
629C22×C61D4211yescharacteristic
630C22×C61#54611yescharacteristic
631C22×C61#54611yescharacteristic
632C22×C61#54611yescharacteristic
633C22×C61#54611yescharacteristic
634C22×C61#54611yescharacteristic
635C22×C61#54711yescharacteristic
636C22×C61#54711yescharacteristic
637C22×C61#54711yescharacteristic
638C22×C61#54711yescharacteristic
639C22×C61#54711yescharacteristic
640C22×C61#54811yescharacteristic
641C22×C61#55011yescharacteristic
642C22×C61#55111yescharacteristic
643C22×C61#55911yescharacteristic
644C22×C61#56211yescharacteristic
645C22×C61#56211yescharacteristic
646C4×C61—24no—
647C4×C61—24no—
648C4×C61—42no—
649C4×C61—42no—
650C4×C61—42no—
651C4×C61—42no—
652C4×C61—42no—
653C4×C61—42no—
654C4×C61—42no—
655C4×C61—42no—
656C4×C61—81no—
657C4×C61—81no—
658C22×#123C2×C6111yescharacteristic, complemented
659C2×#399C2×C6111yescharacteristic, complemented
660C2×#394C2×C6111yescharacteristic, complemented
661C2×#394C2×C6111yescharacteristic, complemented
662C2×#392C2×C6111yescharacteristic
663C2×#390C2×C6111yescharacteristic, complemented
664C2×#386C2×C6111yescharacteristic, complemented
665C2×#385C2×C6111yescharacteristic, complemented
666#1444C2×C6111yescharacteristic, complemented
667#1439C2×C6111yescharacteristic, complemented
668#1439C2×C6111yescharacteristic, complemented
669#1439C2×C6111yescharacteristic, complemented
670#1438C2×C6111yescharacteristic, complemented
671#1437C2×C6111yescharacteristic, complemented
672C4⋊#95C2×C6111yescharacteristic, complemented
673C2×C61—44no—
674C2×C61—82no—
675C2×C61—82no—
676C2×C61#240711yescharacteristic
677C2×C61#241811yescharacteristic
678C2×C61#243011yescharacteristic
679C2×C61#243311yescharacteristic
680C2×C61#244511yescharacteristic
681C2×C61#245511yescharacteristic
682C2×C61#246111yescharacteristic
683C2×C61#250111yescharacteristic
684C2×C61#253911yescharacteristic
685C2×C61#267111yescharacteristic
686C2×C61#267211yescharacteristic
687C2×C61#268111yescharacteristic
688C2×C61#268211yescharacteristic
689C2×C61#270611yescharacteristic
690C2×C61#271011yescharacteristic
691C23×D4C22×C6111yescharacteristic
692C23×D4C22×C6111yescharacteristic
693C23×D4C22×C6111yescharacteristic
694C24×C4C22×C6111yescharacteristic
695C2×#123—24no—
696C2×#123—24no—
697C2×#123—24no—
698C22×C4⋊C4C22×C6111yescharacteristic
699C22×C4⋊C4C22×C6111yescharacteristic
700C22×C4⋊C4C22×C6111yescharacteristic
701C22×C4⋊C4C22×C6111yescharacteristic
702C22×C4⋊C4C22×C6111yescharacteristic
703C22×C4⋊C4C22×C6111yescharacteristic
704C22×C22⋊C4C22×C6111yescharacteristic
705C22×C22⋊C4C22×C6111yescharacteristic
706C22×C22⋊C4C22×C6111yescharacteristic
707C22×C22⋊C4C22×C6111yescharacteristic
708C22×C22⋊C4C22×C6111yescharacteristic
709C22×C22⋊C4C22×C6111yescharacteristic
710C22×C22⋊C4C22×C6111yescharacteristic
711C22×C22⋊C4C22×C6111yescharacteristic
712C22×C22⋊C4C22×C6111yescharacteristic
713C22×C22⋊C4C22×C6111yescharacteristic
714C22×C22⋊C4C22×C6111yescharacteristic
715C22×C22⋊C4C22×C6111yescharacteristic
716C22×C22⋊C4C22×C6111yescharacteristic
717C22×C22⋊C4C22×C6111yescharacteristic
718C22×C42C22×C6111yescharacteristic
719#399—24no—
720#394—24no—
721#394—24no—
722#392—24no—
723#390—24no—
724#386—24no—
725#385—24no—
726C2×#95C22×C6111yescharacteristic
727C2×#95C22×C6111yescharacteristic
728C2×#95C22×C6111yescharacteristic
729C2×#95C22×C6111yescharacteristic
730C2×#95C22×C6111yescharacteristic
731C2×#95C22×C6111yescharacteristic
732C2×#95C22×C6111yescharacteristic
733C2×#95C22×C6111yescharacteristic
734C2×#95C22×C6111yescharacteristic
735C2×#95C22×C6111yescharacteristic
736C61#1537011yescharacteristic, direct product factor, Sylow
737C25C23×C6111yescharacteristic
738C25C23×C6111yescharacteristic
739C25C23×C6111yescharacteristic
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—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—22no—
755C22×D4—41no—
756C22×D4—41no—
757C22×D4—41no—
758C22×D4—41no—
759C22×D4—41no—
760C22×D4—41no—
761C23×C4—22no—
762C23×C4—22no—
763C23×C4—22no—
764C23×C4—22no—
765C23×C4—22no—
766C23×C4—41no—
767C23×C4—41no—
768C23×C4C23×C6111yescharacteristic
769C23×C4C23×C6111yescharacteristic
770C23×C4C23×C6111yescharacteristic
771C23×C4C23×C6111yescharacteristic
772C23×C4C23×C6111yescharacteristic
773C23×C4C23×C6111yescharacteristic
774C23×C4C23×C6111yescharacteristic
775C23×C4C23×C6111yescharacteristic
776C23×C4C23×C6111yescharacteristic
777C23×C4C23×C6111yescharacteristic
778C23×C4C23×C6111yescharacteristic
779C23×C4C23×C6111yescharacteristic
780#123—232no—
781C2×C4⋊C4—22no—
782C2×C4⋊C4—22no—
783C2×C4⋊C4—22no—
784C2×C4⋊C4—22no—
785C2×C4⋊C4—22no—
786C2×C4⋊C4—22no—
787C2×C4⋊C4—22no—
788C2×C4⋊C4—22no—
789C2×C4⋊C4—22no—
790C2×C4⋊C4—22no—
791C2×C4⋊C4—22no—
792C2×C4⋊C4—22no—
793C2×C4⋊C4—22no—
794C2×C4⋊C4—41no—
795C2×C4⋊C4—41no—
796C2×C4⋊C4—41no—
797C2×C4⋊C4—41no—
798C2×C4⋊C4D4×C6114yescomplemented
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—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—22no—
819C2×C22⋊C4—22no—
820C2×C22⋊C4—22no—
821C2×C22⋊C4—22no—
822C2×C22⋊C4—22no—
823C2×C22⋊C4—22no—
824C2×C22⋊C4—22no—
825C2×C22⋊C4—22no—
826C2×C22⋊C4—22no—
827C2×C22⋊C4—41no—
828C2×C22⋊C4—41no—
829C2×C22⋊C4—41no—
830C2×C22⋊C4—41no—
831C2×C22⋊C4—41no—
832C2×C22⋊C4—41no—
833C2×C22⋊C4—41no—
834C2×C22⋊C4—41no—
835C2×C22⋊C4—41no—
836C2×C22⋊C4—41no—
837C2×C22⋊C4D4×C6114yes—
838C2×C22⋊C4D4×C6114yescomplemented
839C2×C22⋊C4D4×C6114yescomplemented
840C2×C22⋊C4D4×C6114yescomplemented
841C2×C42—22no—
842C2×C42—22no—
843C2×C42—41no—
844#95—22no—
845#95—22no—
846#95—22no—
847#95—22no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—22no—
853#95—41no—
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—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24C2×D4×C6112yes—
895C24C2×D4×C6112yes—
896C24C2×D4×C6112yes—
897C24C2×D4×C6112yes—
898C24#41×C6112yes—
899C24C24×C6111yescharacteristic
900C2×D4—28no—
901C2×D4—28no—
902C2×D4—28no—
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—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
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—28no—
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×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4C2×D4×C6112yes—
999C22×C4C2×D4×C6112yes—
1000C22×C4C2×D4×C6112yes—
1001C22×C4C2×D4×C6112yes—
1002C22×C4C2×D4×C6112yes—
1003C22×C4C2×D4×C6112yes—
1004C22×C4C2×D4×C6112yes—
1005C22×C4C2×D4×C6112yes—
1006C22×C4C2×D4×C6112yes—
1007C22×C4C2×D4×C6112yes—
1008C22×C4C2×D4×C6112yes—
1009C22×C4#41×C6112yes—
1010C22×C4#41×C6112yes—
1011C22×C4#41×C6112yes—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C22⋊C4—28no—
1019C22⋊C4—28no—
1020C22⋊C4—28no—
1021C22⋊C4—28no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C42—44no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
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—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23#127×C6114yes—
1138C23C22×D4×C6111yescharacteristic
1139C23C22×D4×C6111yescharacteristic
1140C23C22×D4×C6111yescharacteristic
1141C23C22×D4×C6111yescharacteristic
1142C23C22×D4×C6111yescharacteristic
1143C23C2×#41×C6111yescharacteristic
1144C23C2×#41×C6111yescharacteristic
1145C23C2×#41×C6111yescharacteristic
1146C23C2×#41×C6111yescharacteristic
1147C23H(5,𝔽2)×C6111yescharacteristic
1148C23H(5,𝔽2)×C6111yescharacteristic
1149C23H(5,𝔽2)×C6111yescharacteristic
1150C23H(5,𝔽2)×C6111yescharacteristic
1151C232−1+4×C6111yescharacteristic
1152C232−1+4×C6111yescharacteristic
1153D4—416no—
1154D4—416no—
1155D4—416no—
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—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—416no—
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—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4#120×C6114yes—
1240C2×C4#123×C6114yescomplemented
1241C22—24no—
1242C22—24no—
1243C22—24no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22C2×#120×C6111yescharacteristic
1287C22C2×#123×C6111yescharacteristic
1288C22C61×#52511yescharacteristic
1289C22C61×#52511yescharacteristic
1290C22C2×#127×C6111yescharacteristic
1291C22C61×#53211yescharacteristic
1292C22C61×#53411yescharacteristic
1293C22C61×#53511yescharacteristic
1294C22C61×#53611yescharacteristic
1295C22C61×#53711yescharacteristic
1296C22C61×#53711yescharacteristic
1297C22C61×#53811yescharacteristic
1298C22C61×#53911yescharacteristic
1299C22C61×#54011yescharacteristic
1300C22C61×#54211yescharacteristic
1301C22D42×C6111yescharacteristic
1302C22D42×C6111yescharacteristic
1303C22D42×C6111yescharacteristic
1304C22D42×C6111yescharacteristic
1305C22C61×#54611yescharacteristic
1306C22C61×#54611yescharacteristic
1307C22C61×#54611yescharacteristic
1308C22C61×#54611yescharacteristic
1309C22C61×#54611yescharacteristic
1310C22C61×#54711yescharacteristic
1311C22C61×#54711yescharacteristic
1312C22C61×#54711yescharacteristic
1313C22C61×#54711yescharacteristic
1314C22C61×#54711yescharacteristic
1315C22C61×#54811yescharacteristic
1316C22C61×#55011yescharacteristic
1317C22C61×#55111yescharacteristic
1318C22C61×#55911yescharacteristic
1319C22C61×#56211yescharacteristic
1320C22C61×#56211yescharacteristic
1321C4—24no—
1322C4—24no—
1323C4—42no—
1324C4—42no—
1325C4—42no—
1326C4—42no—
1327C4—42no—
1328C4—42no—
1329C4—42no—
1330C4—42no—
1331C4—81no—
1332C4—81no—
1333C2—44no—
1334C2—82no—
1335C2—82no—
1336C2C61×#240711yescharacteristic
1337C2C61×#241811yescharacteristic
1338C2C61×#243011yescharacteristic
1339C2C61×#243311yescharacteristic
1340C2C61×#244511yescharacteristic
1341C2C61×#245511yescharacteristic
1342C2C61×#246111yescharacteristic
1343C2C61×#250111yescharacteristic
1344C2C61×#253911yescharacteristic
1345C2C61×#267111yescharacteristic
1346C2C61×#267211yescharacteristic
1347C2C61×#268111yescharacteristic
1348C2C61×#268211yescharacteristic
1349C2C61×#270611yescharacteristic
1350C2C61×#271011yescharacteristic
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×#123×C61C2semidirect
2. C2×C61×#399C2semidirect
3. C2×C61×#394C2semidirect
4. C2×C61×#394C2semidirect
6. C2×C61×#390C2semidirect
7. C2×C61×#386C2semidirect
8. C2×C61×#385C2semidirect
9. C61×#1444C2semidirect
10. C61×#1439C2semidirect
11. C61×#1439C2semidirect
12. C61×#1439C2semidirect
13. C61×#1438C2semidirect
14. C61×#1437C2semidirect
15. C61×C4⋊#95C2semidirect
122. C2×C4⋊C4×C61D4semidirect
162. C2×C22⋊C4×C61D4semidirect
163. C2×C22⋊C4×C61D4semidirect
164. C2×C22⋊C4×C61D4semidirect
564. C2×C4×C61#123semidirect
565. #15370C61direct (N × H)
658. C22×#123C2×C61semidirect
659. C2×#399C2×C61semidirect
660. C2×#394C2×C61semidirect
661. C2×#394C2×C61semidirect
663. C2×#390C2×C61semidirect
664. C2×#386C2×C61semidirect
665. C2×#385C2×C61semidirect
666. #1444C2×C61semidirect
667. #1439C2×C61semidirect
668. #1439C2×C61semidirect
669. #1439C2×C61semidirect
670. #1438C2×C61semidirect
671. #1437C2×C61semidirect
672. C4⋊#95C2×C61semidirect
736. C61#15370direct (N × H)
798. C2×C4⋊C4D4×C61semidirect
838. C2×C22⋊C4D4×C61semidirect
839. C2×C22⋊C4D4×C61semidirect
840. C2×C22⋊C4D4×C61semidirect
1240. C2×C4#123×C61semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C612
C2×C61×#3992
C2×C61×#3942
C2×C61×#3922
C2×C61×#3902
C2×C61×#3862
C2×C61×#3852
C61×#14442
C61×#14392
C61×#14382
C61×#14372
C61×C4⋊#952
#1537061