Finite Group Databasebeta

← C61×#15376 #29518809

Subgroups — C61×#15376 #29518809

Order 15616.

2370 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#394C211yesmaximal, characteristic, complemented
2C2×C61×#392C211yesmaximal, characteristic
3C2×C61×#386C211yesmaximal, characteristic, complemented
4C2×C61×#386C211yesmaximal, characteristic, complemented
5C2×C61×#386C211yesmaximal, characteristic, complemented
6C2×C61×#386C211yesmaximal, characteristic, complemented
7C2×C61×#385C211yesmaximal, characteristic, complemented
8C2×C61×#380C211yesmaximal, characteristic, complemented
9C61×#1443C211yesmaximal, characteristic, complemented
10C61×#1442C211yesmaximal, characteristic, complemented
11C61×#1440C211yesmaximal, characteristic, complemented
12C61×#1439C211yesmaximal, characteristic, complemented
13C61×#1439C211yesmaximal, characteristic, complemented
14C61×#1439C211yesmaximal, characteristic, complemented
15C61×#1438C211yesmaximal, characteristic, complemented
16C23×D4×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic
18C23×D4×C61C2211yescharacteristic
19C24×C4×C61C2211yescharacteristic
20C24×C4×C61C2211yescharacteristic
21C22×C4⋊C4×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2211yescharacteristic
23C22×C4⋊C4×C61C2211yescharacteristic
24C22×C22⋊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
37C61×#394—24no—
38C61×#392—24no—
39C61×#386—24no—
40C61×#386—24no—
41C61×#386—24no—
42C61×#386—24no—
43C61×#385—24no—
44C61×#380—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
61C25×C61C2311yescharacteristic
62C22×D4×C61—22no—
63C22×D4×C61—22no—
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—41no—
77C22×D4×C61—41no—
78C22×D4×C61—41no—
79C22×D4×C61—41no—
80C22×D4×C61—41no—
81C22×D4×C61—41no—
82C22×D4×C61D414yes—
83C23×C4×C61—22no—
84C23×C4×C61—22no—
85C23×C4×C61—22no—
86C23×C4×C61—22no—
87C23×C4×C61—22no—
88C23×C4×C61—22no—
89C23×C4×C61—22no—
90C23×C4×C61—22no—
91C23×C4×C61—41no—
92C23×C4×C61—41no—
93C23×C4×C61—41no—
94C23×C4×C61—41no—
95C23×C4×C61—41no—
96C23×C4×C61—41no—
97C23×C4×C61C2311yescharacteristic
98C23×C4×C61C2311yescharacteristic
99C23×C4×C61C2311yescharacteristic
100C23×C4×C61C2311yescharacteristic
101C23×C4×C61C2311yescharacteristic
102C23×C4×C61C2311yescharacteristic
103C23×C4×C61C2311yescharacteristic
104C23×C4×C61C2311yescharacteristic
105C23×C4×C61C2311yescharacteristic
106C23×C4×C61C2311yescharacteristic
107C23×C4×C61C2311yescharacteristic
108C23×C4×C61C2311yescharacteristic
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—41no—
115C2×C4⋊C4×C61—41no—
116C2×C4⋊C4×C61—41no—
117C2×C4⋊C4×C61—41no—
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—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—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×C61—41no—
153C2×C22⋊C4×C61—41no—
154C2×C22⋊C4×C61—41no—
155C2×C22⋊C4×C61—41no—
156C2×C22⋊C4×C61D414yescomplemented
157#95×C61—22no—
158#95×C61—22no—
159#95×C61—22no—
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—41no—
168#95×C61—41no—
169#95×C61D414yescomplemented
170#95×C61D414yescomplemented
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×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×C61C2×D412yes—
210C24×C61C2×D412yes—
211C24×C61C2×D412yes—
212C24×C61#4112yes—
213C24×C61#4112yes—
214C24×C61#4112yes—
215C24×C61#4112yes—
216C24×C61C2411yescharacteristic
217C2×D4×C61—28no—
218C2×D4×C61—28no—
219C2×D4×C61—28no—
220C2×D4×C61—28no—
221C2×D4×C61—44no—
222C2×D4×C61—44no—
223C2×D4×C61—44no—
224C2×D4×C61—44no—
225C2×D4×C61—44no—
226C2×D4×C61—44no—
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—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—28no—
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—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—44no—
314C22×C4×C61—44no—
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—
324C22×C4×C61—44no—
325C22×C4×C61—44no—
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×C61C2×D412yes—
334C22×C4×C61C2×D412yes—
335C22×C4×C61#4112yes—
336C4⋊C4×C61—44no—
337C4⋊C4×C61—44no—
338C4⋊C4×C61—44no—
339C22⋊C4×C61—28no—
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—
347C22⋊C4×C61—44no—
348C22⋊C4×C61—44no—
349C22⋊C4×C61—44no—
350C22⋊C4×C61—44no—
351C22⋊C4×C61—44no—
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—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—22no—
390C23×C61—22no—
391C23×C61—22no—
392C23×C61—22no—
393C23×C61—22no—
394C23×C61—22no—
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#12114yes—
456C23×C61#12314yes—
457C23×C61C22×D411yescharacteristic
458C23×C61C22×D411yescharacteristic
459C23×C61C22×D411yescharacteristic
460C23×C61C22×D411yescharacteristic
461C23×C61C2×#4111yescharacteristic
462C23×C61C2×#4111yescharacteristic
463C23×C61C2×#4111yescharacteristic
464C23×C61C2×#4111yescharacteristic
465C23×C61C2×#4111yescharacteristic
466C23×C61H(5,𝔽2)11yescharacteristic
467C23×C61H(5,𝔽2)11yescharacteristic
468C23×C61H(5,𝔽2)11yescharacteristic
469C23×C61H(5,𝔽2)11yescharacteristic
470C23×C61H(5,𝔽2)11yescharacteristic
471C23×C612−1+411yescharacteristic
472D4×C61—416no—
473D4×C61—416no—
474D4×C61—416no—
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—416no—
503C2×C4×C61—416no—
504C2×C4×C61—41no—
505C2×C4×C61—41no—
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—41no—
555C2×C4×C61—41no—
556C2×C4×C61—41no—
557C2×C4×C61—41no—
558C2×C4×C61—41no—
559C2×C4×C61—41no—
560C2×C4×C61#12114yes—
561#15376C6111yesmaximal, characteristic, direct product factor, Sylow
562C22×C61—24no—
563C22×C61—24no—
564C22×C61—24no—
565C22×C61—24no—
566C22×C61—24no—
567C22×C61—24no—
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—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—42no—
596C22×C61—42no—
597C22×C61—42no—
598C22×C61—42no—
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×C61C2×#12111yescharacteristic
608C22×C61C2×#12111yescharacteristic
609C22×C61C2×#12311yescharacteristic
610C22×C61#52511yescharacteristic
611C22×C61#52511yescharacteristic
612C22×C61#52511yescharacteristic
613C22×C61#53411yescharacteristic
614C22×C61#53511yescharacteristic
615C22×C61#53511yescharacteristic
616C22×C61#53711yescharacteristic
617C22×C61#53811yescharacteristic
618C22×C61#53811yescharacteristic
619C22×C61#53811yescharacteristic
620C22×C61#53911yescharacteristic
621C22×C61#53911yescharacteristic
622C22×C61D4211yescharacteristic
623C22×C61D4211yescharacteristic
624C22×C61D4211yescharacteristic
625C22×C61D4211yescharacteristic
626C22×C61#54611yescharacteristic
627C22×C61#54611yescharacteristic
628C22×C61#54611yescharacteristic
629C22×C61#54611yescharacteristic
630C22×C61#54611yescharacteristic
631C22×C61#54711yescharacteristic
632C22×C61#54811yescharacteristic
633C22×C61#54811yescharacteristic
634C22×C61#55111yescharacteristic
635C22×C61#55111yescharacteristic
636C22×C61#55111yescharacteristic
637C22×C61#55311yescharacteristic
638C22×C61#55311yescharacteristic
639C22×C61#55311yescharacteristic
640C22×C61#56011yescharacteristic
641C22×C61#56211yescharacteristic
642C4×C61—24no—
643C4×C61—42no—
644C4×C61—42no—
645C4×C61—42no—
646C4×C61—42no—
647C4×C61—42no—
648C4×C61—42no—
649C4×C61—42no—
650C4×C61—81no—
651C4×C61—81no—
652C4×C61—81no—
653C4×C61—81no—
654C2×#394C2×C6111yescharacteristic, complemented
655C2×#392C2×C6111yescharacteristic
656C2×#386C2×C6111yescharacteristic, complemented
657C2×#386C2×C6111yescharacteristic, complemented
658C2×#386C2×C6111yescharacteristic, complemented
659C2×#386C2×C6111yescharacteristic, complemented
660C2×#385C2×C6111yescharacteristic, complemented
661C2×#380C2×C6111yescharacteristic, complemented
662#1443C2×C6111yescharacteristic, complemented
663#1442C2×C6111yescharacteristic, complemented
664#1440C2×C6111yescharacteristic, complemented
665#1439C2×C6111yescharacteristic, complemented
666#1439C2×C6111yescharacteristic, complemented
667#1439C2×C6111yescharacteristic, complemented
668#1438C2×C6111yescharacteristic, complemented
669C2×C61—44no—
670C2×C61—44no—
671C2×C61—82no—
672C2×C61#241211yescharacteristic
673C2×C61#241611yescharacteristic
674C2×C61#241811yescharacteristic
675C2×C61#242411yescharacteristic
676C2×C61#242411yescharacteristic
677C2×C61#244311yescharacteristic
678C2×C61#246311yescharacteristic
679C2×C61#253511yescharacteristic
680C2×C61#259811yescharacteristic
681C2×C61#266911yescharacteristic
682C2×C61#267611yescharacteristic
683C2×C61#269311yescharacteristic
684C2×C61#269611yescharacteristic
685C2×C61#270811yescharacteristic
686C2×C61#277811yescharacteristic
687C23×D4C22×C6111yescharacteristic
688C23×D4C22×C6111yescharacteristic
689C23×D4C22×C6111yescharacteristic
690C24×C4C22×C6111yescharacteristic
691C24×C4C22×C6111yescharacteristic
692C22×C4⋊C4C22×C6111yescharacteristic
693C22×C4⋊C4C22×C6111yescharacteristic
694C22×C4⋊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×C22⋊C4C22×C6111yescharacteristic
708#394—24no—
709#392—24no—
710#386—24no—
711#386—24no—
712#386—24no—
713#386—24no—
714#385—24no—
715#380—24no—
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
726C2×#95C22×C6111yescharacteristic
727C2×#95C22×C6111yescharacteristic
728C2×#95C22×C6111yescharacteristic
729C2×#95C22×C6111yescharacteristic
730C61#1537611yescharacteristic, direct product factor, Sylow
731C25C23×C6111yescharacteristic
732C25C23×C6111yescharacteristic
733C25C23×C6111yescharacteristic
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
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—41no—
749C22×D4—41no—
750C22×D4—41no—
751C22×D4—41no—
752C22×D4—41no—
753C22×D4—41no—
754C22×D4D4×C6114yes—
755C23×C4—22no—
756C23×C4—22no—
757C23×C4—22no—
758C23×C4—22no—
759C23×C4—22no—
760C23×C4—22no—
761C23×C4—22no—
762C23×C4—22no—
763C23×C4—41no—
764C23×C4—41no—
765C23×C4—41no—
766C23×C4—41no—
767C23×C4—41no—
768C23×C4—41no—
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
780C23×C4C23×C6111yescharacteristic
781C2×C4⋊C4—22no—
782C2×C4⋊C4—22no—
783C2×C4⋊C4—22no—
784C2×C4⋊C4—22no—
785C2×C4⋊C4—22no—
786C2×C4⋊C4—41no—
787C2×C4⋊C4—41no—
788C2×C4⋊C4—41no—
789C2×C4⋊C4—41no—
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—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—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4—41no—
821C2×C22⋊C4—41no—
822C2×C22⋊C4—41no—
823C2×C22⋊C4—41no—
824C2×C22⋊C4—41no—
825C2×C22⋊C4—41no—
826C2×C22⋊C4—41no—
827C2×C22⋊C4—41no—
828C2×C22⋊C4D4×C6114yescomplemented
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—22no—
837#95—22no—
838#95—22no—
839#95—41no—
840#95—41no—
841#95D4×C6114yescomplemented
842#95D4×C6114yescomplemented
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—
881C24C2×D4×C6112yes—
882C24C2×D4×C6112yes—
883C24C2×D4×C6112yes—
884C24#41×C6112yes—
885C24#41×C6112yes—
886C24#41×C6112yes—
887C24#41×C6112yes—
888C24C24×C6111yescharacteristic
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—28no—
893C2×D4—44no—
894C2×D4—44no—
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—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—28no—
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×C4—21no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
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×C4#41×C6112yes—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C22⋊C4—28no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
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—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—22no—
1066C23—22no—
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#121×C6114yes—
1128C23#123×C6114yes—
1129C23C22×D4×C6111yescharacteristic
1130C23C22×D4×C6111yescharacteristic
1131C23C22×D4×C6111yescharacteristic
1132C23C22×D4×C6111yescharacteristic
1133C23C2×#41×C6111yescharacteristic
1134C23C2×#41×C6111yescharacteristic
1135C23C2×#41×C6111yescharacteristic
1136C23C2×#41×C6111yescharacteristic
1137C23C2×#41×C6111yescharacteristic
1138C23H(5,𝔽2)×C6111yescharacteristic
1139C23H(5,𝔽2)×C6111yescharacteristic
1140C23H(5,𝔽2)×C6111yescharacteristic
1141C23H(5,𝔽2)×C6111yescharacteristic
1142C23H(5,𝔽2)×C6111yescharacteristic
1143C232−1+4×C6111yescharacteristic
1144D4—416no—
1145D4—416no—
1146D4—416no—
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—416no—
1175C2×C4—416no—
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—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#121×C6114yes—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
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—
1278C22C2×#121×C6111yescharacteristic
1279C22C2×#121×C6111yescharacteristic
1280C22C2×#123×C6111yescharacteristic
1281C22C61×#52511yescharacteristic
1282C22C61×#52511yescharacteristic
1283C22C61×#52511yescharacteristic
1284C22C61×#53411yescharacteristic
1285C22C61×#53511yescharacteristic
1286C22C61×#53511yescharacteristic
1287C22C61×#53711yescharacteristic
1288C22C61×#53811yescharacteristic
1289C22C61×#53811yescharacteristic
1290C22C61×#53811yescharacteristic
1291C22C61×#53911yescharacteristic
1292C22C61×#53911yescharacteristic
1293C22D42×C6111yescharacteristic
1294C22D42×C6111yescharacteristic
1295C22D42×C6111yescharacteristic
1296C22D42×C6111yescharacteristic
1297C22C61×#54611yescharacteristic
1298C22C61×#54611yescharacteristic
1299C22C61×#54611yescharacteristic
1300C22C61×#54611yescharacteristic
1301C22C61×#54611yescharacteristic
1302C22C61×#54711yescharacteristic
1303C22C61×#54811yescharacteristic
1304C22C61×#54811yescharacteristic
1305C22C61×#55111yescharacteristic
1306C22C61×#55111yescharacteristic
1307C22C61×#55111yescharacteristic
1308C22C61×#55311yescharacteristic
1309C22C61×#55311yescharacteristic
1310C22C61×#55311yescharacteristic
1311C22C61×#56011yescharacteristic
1312C22C61×#56211yescharacteristic
1313C4—24no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C2—44no—
1326C2—44no—
1327C2—82no—
1328C2C61×#241211yescharacteristic
1329C2C61×#241611yescharacteristic
1330C2C61×#241811yescharacteristic
1331C2C61×#242411yescharacteristic
1332C2C61×#242411yescharacteristic
1333C2C61×#244311yescharacteristic
1334C2C61×#246311yescharacteristic
1335C2C61×#253511yescharacteristic
1336C2C61×#259811yescharacteristic
1337C2C61×#266911yescharacteristic
1338C2C61×#267611yescharacteristic
1339C2C61×#269311yescharacteristic
1340C2C61×#269611yescharacteristic
1341C2C61×#270811yescharacteristic
1342C2C61×#277811yescharacteristic
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. C2×C61×#394C2semidirect
3. C2×C61×#386C2semidirect
4. C2×C61×#386C2semidirect
5. C2×C61×#386C2semidirect
6. C2×C61×#386C2semidirect
7. C2×C61×#385C2semidirect
8. C2×C61×#380C2semidirect
9. C61×#1443C2semidirect
10. C61×#1442C2semidirect
11. C61×#1440C2semidirect
12. C61×#1439C2semidirect
13. C61×#1439C2semidirect
14. C61×#1439C2semidirect
15. C61×#1438C2semidirect
156. C2×C22⋊C4×C61D4semidirect
169. #95×C61D4semidirect
170. #95×C61D4semidirect
561. #15376C61direct (N × H)
654. C2×#394C2×C61semidirect
656. C2×#386C2×C61semidirect
657. C2×#386C2×C61semidirect
658. C2×#386C2×C61semidirect
659. C2×#386C2×C61semidirect
660. C2×#385C2×C61semidirect
661. C2×#380C2×C61semidirect
662. #1443C2×C61semidirect
663. #1442C2×C61semidirect
664. #1440C2×C61semidirect
665. #1439C2×C61semidirect
666. #1439C2×C61semidirect
667. #1439C2×C61semidirect
668. #1438C2×C61semidirect
730. C61#15376direct (N × H)
828. C2×C22⋊C4D4×C61semidirect
841. #95D4×C61semidirect
842. #95D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#3942
C2×C61×#3922
C2×C61×#3862
C2×C61×#3852
C2×C61×#3802
C61×#14432
C61×#14422
C61×#14402
C61×#14392
C61×#14382
#1537661