Finite Group Databasebeta

← C61×#21772 #29525205

Subgroups — C61×#21772 #29525205

Order 15616.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#537C211yesmaximal, characteristic
2C2×C61×#408C211yesmaximal, characteristic, complemented
3C61×#2311C211yesmaximal, characteristic, complemented
4C61×#1895C211yesmaximal, characteristic, complemented
5C61×#1894C211yesmaximal, characteristic, complemented
6C61×#1893C211yesmaximal, characteristic, complemented
7C61×#1892C211yesmaximal, characteristic, complemented
8C61×#1875C211yesmaximal, characteristic, complemented
9C61×#1874C211yesmaximal, characteristic, complemented
10C61×#1873C211yesmaximal, characteristic, complemented
11C61×#1872C211yesmaximal, characteristic, complemented
12C61×#1824C211yesmaximal, characteristic, complemented
13C61×#1823C211yesmaximal, characteristic, complemented
14C61×#1788C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×#41×C61C2211yescharacteristic
18C22×M16×C61C2211yescharacteristic
19C23×C8×C61C2211yescharacteristic
20C61×#537—24no—
21C61×#537C418yescomplemented
22C2×C22⋊Q8×C61—21no—
23C2×C22⋊Q8×C61C2211yescharacteristic
24C2×C22⋊Q8×C61C2211yescharacteristic
25C2×#121×C61—21no—
26C2×#121×C61—21no—
27C2×#121×C61—21no—
28C2×#121×C61C2211yescharacteristic
29C2×#121×C61C2211yescharacteristic
30C2×#117×C61C2211yescharacteristic
31C22×C4⋊C4×C61C2211yescharacteristic
32C22×C4⋊C4×C61C2211yescharacteristic
33C2×#103×C61C2211yescharacteristic
34C2×#103×C61C2211yescharacteristic
35C2×#103×C61C2211yescharacteristic
36C2×#103×C61C2211yescharacteristic
37C2×#102×C61C2211yescharacteristic
38C2×#102×C61C2211yescharacteristic
39C2×#102×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C61×#408—24no—
42C2×C22⋊C8×C61C2211yescharacteristic
43C2×C22⋊C8×C61C2211yescharacteristic
44C2×C22⋊C8×C61C2211yescharacteristic
45C2×C22⋊C8×C61C2211yescharacteristic
46C61×#391—21no—
47C61×#390—21no—
48C61×#386—21no—
49C61×#386—21no—
50C61×#380C2211yescharacteristic
51C61×#380C2211yescharacteristic
52C61×#380C2211yescharacteristic
53C61×#380C2211yescharacteristic
54C61×#340C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C2×#41×C61—22no—
63C2×#41×C61—41no—
64C2×#41×C61—41no—
65C2×#41×C61—41no—
66C2×#41×C61—41no—
67C2×#41×C61—41no—
68C2×#41×C61—41no—
69C2×#41×C61—41no—
70C2×#41×C61—41no—
71C2×#41×C61C2×C414yes—
72C2×#41×C61C2×C414yescomplemented
73C2×#41×C61D414yes—
74C22×Q8×C61D411yescharacteristic
75C22×Q8×C61C2311yescharacteristic
76C22×D4×C61—21no—
77C22×D4×C61—21no—
78C22×D4×C61—21no—
79C22×D4×C61D411yescharacteristic
80C22×D4×C61D411yescharacteristic
81C22×D4×C61D411yescharacteristic
82C22×D4×C61C2311yescharacteristic
83C23×C4×C61—21no—
84C23×C4×C61—21no—
85C23×C4×C61—21no—
86C23×C4×C61C2311yescharacteristic
87C23×C4×C61C2311yescharacteristic
88C23×C4×C61C2311yescharacteristic
89C2×M16×C61—22no—
90C2×M16×C61—41no—
91C2×M16×C61—41no—
92C22×C8×C61—22no—
93C22×C8×C61—41no—
94C22×C8×C61—41no—
95C22×C8×C61C2311yescharacteristic
96C22×C8×C61C2311yescharacteristic
97C22×C8×C61C2311yescharacteristic
98C22×C8×C61C2311yescharacteristic
99C22⋊Q8×C61—28no—
100C22⋊Q8×C61—22no—
101C22⋊Q8×C61—22no—
102C22⋊Q8×C61C2×C414yes—
103C22⋊Q8×C61C2×C414yescomplemented
104#121×C61—28no—
105#121×C61—28no—
106#121×C61—28no—
107#121×C61—22no—
108#121×C61—22no—
109#121×C61C2×C414yes—
110#121×C61C2×C414yescomplemented
111#117×C61—41no—
112#117×C61—41no—
113C2×C4⋊C4×C61—22no—
114C2×C4⋊C4×C61—21no—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61—41no—
119C2×C4⋊C4×C61—41no—
120C2×C4⋊C4×C61C2×C414yescomplemented
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61—21no—
136C2×C42×C61—21no—
137#103×C61—41no—
138#103×C61—41no—
139#103×C61—41no—
140#103×C61—41no—
141#102×C61—41no—
142#102×C61—41no—
143#102×C61—41no—
144#102×C61—41no—
145C22⋊C8×C61—22no—
146C22⋊C8×C61—22no—
147C22⋊C8×C61—22no—
148C22⋊C8×C61—22no—
149#95×C61—21no—
150#95×C61—21no—
151#95×C61—21no—
152#95×C61—21no—
153C24×C61—21no—
154C24×C61C2×D411yescharacteristic
155C24×C61C2×D411yescharacteristic
156C24×C61C2×D411yescharacteristic
157#41×C61—44no—
158#41×C61—44no—
159#41×C61—44no—
160#41×C61—44no—
161#41×C61—44no—
162#41×C61—44no—
163#41×C61—44no—
164#41×C61—44no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—41no—
171C2×Q8×C61—41no—
172C2×Q8×C61C22⋊C414yes—
173C2×Q8×C61C22×C412yes—
174C2×D4×C61—24no—
175C2×D4×C61—24no—
176C2×D4×C61—24no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—41no—
183C2×D4×C61—41no—
184C2×D4×C61—41no—
185C2×D4×C61—41no—
186C2×D4×C61—41no—
187C2×D4×C61—41no—
188C2×D4×C61—42no—
189C2×D4×C61—42no—
190C2×D4×C61—81no—
191C2×D4×C61—81no—
192C2×D4×C61—81no—
193C2×D4×C61—81no—
194C2×D4×C61C22⋊C414yes—
195C2×D4×C61C22⋊C414yes—
196C2×D4×C61C22⋊C414yes—
197C2×D4×C61C22×C412yes—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—24no—
214C22×C4×C61—24no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—42no—
220C22×C4×C61—42no—
221C22×C4×C61—42no—
222C22×C4×C61—81no—
223C22×C4×C61—81no—
224C22×C4×C61—81no—
225C22×C4×C61—81no—
226C22×C4×C61C22×C412yes—
227C22×C4×C61C22×C412yes—
228C22×C4×C61C22×C412yes—
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D412yes—
233C22×C4×C61C2×D412yes—
234C22×C4×C61C2×D412yes—
235C22×C4×C61C2411yescharacteristic
236M16×C61—44no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—44no—
250C4⋊C4×C61—24no—
251C4⋊C4×C61—24no—
252C4⋊C4×C61—24no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—42no—
264C4⋊C4×C61C22×C412yes—
265C4⋊C4×C61C22×C412yes—
266C22⋊C4×C61—24no—
267C22⋊C4×C61—24no—
268C22⋊C4×C61—24no—
269C22⋊C4×C61—24no—
270C22⋊C4×C61—42no—
271C22⋊C4×C61—81no—
272C22⋊C4×C61—81no—
273C22⋊C4×C61—81no—
274C22⋊C4×C61—81no—
275C42×C61—42no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—22no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61C2×C22⋊C412yes—
302C23×C61C2×C22⋊C412yes—
303C23×C61C2×C22⋊C412yes—
304C23×C61C22×D411yescharacteristic
305Q8×C61—22no—
306Q8×C61—22no—
307Q8×C61—44no—
308Q8×C61—41no—
309Q8×C61—41no—
310D4×C61—22no—
311D4×C61—22no—
312D4×C61—44no—
313D4×C61—44no—
314D4×C61—44no—
315D4×C61—48no—
316D4×C61—41no—
317D4×C61—41no—
318D4×C61—84no—
319D4×C61—84no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—48no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—84no—
361C2×C4×C61—84no—
362C2×C4×C61C2×C22⋊C412yes—
363C2×C4×C61C2×C22⋊C412yes—
364C2×C4×C61C2×C22⋊C412yes—
365C2×C4×C61C23×C411yescharacteristic
366C2×C4×C61C22×D411yescharacteristic
367C2×C4×C61H(5,𝔽2)11yescharacteristic
368C2×C4×C61H(5,𝔽2)11yescharacteristic
369C2×C4×C61H(5,𝔽2)11yescharacteristic
370C2×C4×C61H(5,𝔽2)11yescharacteristic
371C8×C61—41no—
372C8×C61—41no—
373C8×C61—41no—
374C8×C61—41no—
375#21772C6111yesmaximal, characteristic, direct product factor, Sylow
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—22no—
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—22no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—42no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—81no—
401C22×C61—81no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61C22×C22⋊C411yescharacteristic
405C22×C61#53411yescharacteristic
406C22×C61#53411yescharacteristic
407C22×C61#57611yescharacteristic
408C22×C61#57711yescharacteristic
409C22×C61#57711yescharacteristic
410C22×C61#57811yescharacteristic
411C4×C61—22no—
412C4×C61—22no—
413C4×C61—22no—
414C4×C61—42no—
415C4×C61—42no—
416C4×C61—42no—
417C4×C61—81no—
418C4×C61—81no—
419C4×C61—81no—
420C4×C61—81no—
421C4×C61#51811yescharacteristic
422C4×C61#51811yescharacteristic
423C4×C61#53411yescharacteristic
424C4×C61#53411yescharacteristic
425C2×#537C2×C6111yescharacteristic
426C2×#408C2×C6111yescharacteristic, complemented
427#2311C2×C6111yescharacteristic, complemented
428#1895C2×C6111yescharacteristic, complemented
429#1894C2×C6111yescharacteristic, complemented
430#1893C2×C6111yescharacteristic, complemented
431#1892C2×C6111yescharacteristic, complemented
432#1875C2×C6111yescharacteristic, complemented
433#1874C2×C6111yescharacteristic, complemented
434#1873C2×C6111yescharacteristic, complemented
435#1872C2×C6111yescharacteristic, complemented
436#1824C2×C6111yescharacteristic, complemented
437#1823C2×C6111yescharacteristic, complemented
438#1788C2×C6111yescharacteristic, complemented
439#1788C2×C6111yescharacteristic, complemented
440C2×C61—42no—
441C2×C61—42no—
442C2×C61—42no—
443C2×C61—82no—
444C2×C61#230811yescharacteristic
445C2×C61#289711yescharacteristic
446C2×C61#289811yescharacteristic
447C2×C61#319811yescharacteristic
448C2×C61#320111yescharacteristic
449C2×C61#320311yescharacteristic
450C2×C61#320411yescharacteristic
451C22×#41C22×C6111yescharacteristic
452C22×#41C22×C6111yescharacteristic
453C22×M16C22×C6111yescharacteristic
454C23×C8C22×C6111yescharacteristic
455#537—24no—
456#537C4×C6118yescomplemented
457C2×C22⋊Q8—21no—
458C2×C22⋊Q8C22×C6111yescharacteristic
459C2×C22⋊Q8C22×C6111yescharacteristic
460C2×#121—21no—
461C2×#121—21no—
462C2×#121—21no—
463C2×#121C22×C6111yescharacteristic
464C2×#121C22×C6111yescharacteristic
465C2×#117C22×C6111yescharacteristic
466C22×C4⋊C4C22×C6111yescharacteristic
467C22×C4⋊C4C22×C6111yescharacteristic
468C2×#103C22×C6111yescharacteristic
469C2×#103C22×C6111yescharacteristic
470C2×#103C22×C6111yescharacteristic
471C2×#103C22×C6111yescharacteristic
472C2×#102C22×C6111yescharacteristic
473C2×#102C22×C6111yescharacteristic
474C2×#102C22×C6111yescharacteristic
475C2×#102C22×C6111yescharacteristic
476#408—24no—
477C2×C22⋊C8C22×C6111yescharacteristic
478C2×C22⋊C8C22×C6111yescharacteristic
479C2×C22⋊C8C22×C6111yescharacteristic
480C2×C22⋊C8C22×C6111yescharacteristic
481#391—21no—
482#390—21no—
483#386—21no—
484#386—21no—
485#380C22×C6111yescharacteristic
486#380C22×C6111yescharacteristic
487#380C22×C6111yescharacteristic
488#380C22×C6111yescharacteristic
489#340C22×C6111yescharacteristic
490#340C22×C6111yescharacteristic
491#340C22×C6111yescharacteristic
492#340C22×C6111yescharacteristic
493#340C22×C6111yescharacteristic
494#340C22×C6111yescharacteristic
495#340C22×C6111yescharacteristic
496#340C22×C6111yescharacteristic
497C61#2177211yescharacteristic, direct product factor, Sylow
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41C2×C4×C6114yes—
508C2×#41C2×C4×C6114yescomplemented
509C2×#41D4×C6114yes—
510C22×Q8D4×C6111yescharacteristic
511C22×Q8C23×C6111yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4D4×C6111yescharacteristic
516C22×D4D4×C6111yescharacteristic
517C22×D4D4×C6111yescharacteristic
518C22×D4C23×C6111yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C6111yescharacteristic
523C23×C4C23×C6111yescharacteristic
524C23×C4C23×C6111yescharacteristic
525C2×M16—22no—
526C2×M16—41no—
527C2×M16—41no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8C23×C6111yescharacteristic
532C22×C8C23×C6111yescharacteristic
533C22×C8C23×C6111yescharacteristic
534C22×C8C23×C6111yescharacteristic
535C22⋊Q8—28no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8C2×C4×C6114yes—
539C22⋊Q8C2×C4×C6114yescomplemented
540#121—28no—
541#121—28no—
542#121—28no—
543#121—22no—
544#121—22no—
545#121C2×C4×C6114yes—
546#121C2×C4×C6114yescomplemented
547#117—41no—
548#117—41no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—41no—
556C2×C4⋊C4C2×C4×C6114yescomplemented
557C2×C4⋊C4C23×C6111yescharacteristic
558C2×C4⋊C4C23×C6111yescharacteristic
559C2×C4⋊C4C23×C6111yescharacteristic
560C2×C4⋊C4C23×C6111yescharacteristic
561C2×C4⋊C4C23×C6111yescharacteristic
562C2×C4⋊C4C23×C6111yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C42—21no—
573#103—41no—
574#103—41no—
575#103—41no—
576#103—41no—
577#102—41no—
578#102—41no—
579#102—41no—
580#102—41no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—22no—
584C22⋊C8—22no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24C2×D4×C6111yescharacteristic
591C24C2×D4×C6111yescharacteristic
592C24C2×D4×C6111yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—41no—
607C2×Q8—41no—
608C2×Q8C22⋊C4×C6114yes—
609C2×Q8C22×C4×C6112yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—81no—
627C2×D4—81no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4C22⋊C4×C6114yes—
631C2×D4C22⋊C4×C6114yes—
632C2×D4C22⋊C4×C6114yes—
633C2×D4C22×C4×C6112yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—81no—
659C22×C4—81no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4C22×C4×C6112yes—
663C22×C4C22×C4×C6112yes—
664C22×C4C22×C4×C6112yes—
665C22×C4C2×D4×C6111yescharacteristic
666C22×C4C2×D4×C6111yescharacteristic
667C22×C4C2×D4×C6111yescharacteristic
668C22×C4C2×D4×C6112yes—
669C22×C4C2×D4×C6112yes—
670C22×C4C2×D4×C6112yes—
671C22×C4C24×C6111yescharacteristic
672M16—44no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—44no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—42no—
700C4⋊C4C22×C4×C6112yes—
701C4⋊C4C22×C4×C6112yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—42no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C22⋊C4—81no—
710C22⋊C4—81no—
711C42—42no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23C2×C22⋊C4×C6112yes—
738C23C2×C22⋊C4×C6112yes—
739C23C2×C22⋊C4×C6112yes—
740C23C22×D4×C6111yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—44no—
744Q8—41no—
745Q8—41no—
746D4—22no—
747D4—22no—
748D4—44no—
749D4—44no—
750D4—44no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—48no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—84no—
797C2×C4—84no—
798C2×C4C2×C22⋊C4×C6112yes—
799C2×C4C2×C22⋊C4×C6112yes—
800C2×C4C2×C22⋊C4×C6112yes—
801C2×C4C23×C4×C6111yescharacteristic
802C2×C4C22×D4×C6111yescharacteristic
803C2×C4H(5,𝔽2)×C6111yescharacteristic
804C2×C4H(5,𝔽2)×C6111yescharacteristic
805C2×C4H(5,𝔽2)×C6111yescharacteristic
806C2×C4H(5,𝔽2)×C6111yescharacteristic
807C8—41no—
808C8—41no—
809C8—41no—
810C8—41no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C22×C22⋊C4×C6111yescharacteristic
840C22C61×#53411yescharacteristic
841C22C61×#53411yescharacteristic
842C22C61×#57611yescharacteristic
843C22C61×#57711yescharacteristic
844C22C61×#57711yescharacteristic
845C22C61×#57811yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4C61×#51811yescharacteristic
857C4C61×#51811yescharacteristic
858C4C61×#53411yescharacteristic
859C4C61×#53411yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—82no—
864C2C61×#230811yescharacteristic
865C2C61×#289711yescharacteristic
866C2C61×#289811yescharacteristic
867C2C61×#319811yescharacteristic
868C2C61×#320111yescharacteristic
869C2C61×#320311yescharacteristic
870C2C61×#320411yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutatorC2×C4C23×C4×C61
Frattini, cosocleC22×C4C24×C61
prime radicalC2×C61×#537C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C22×#41×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#408C2semidirect
3. C61×#2311C2semidirect
4. C61×#1895C2semidirect
5. C61×#1894C2semidirect
6. C61×#1893C2semidirect
7. C61×#1892C2semidirect
8. C61×#1875C2semidirect
9. C61×#1874C2semidirect
10. C61×#1873C2semidirect
11. C61×#1872C2semidirect
12. C61×#1824C2semidirect
13. C61×#1823C2semidirect
14. C61×#1788C2semidirect
15. C61×#1788C2semidirect
21. C61×#537C4semidirect
72. C2×#41×C61C2×C4semidirect
103. C22⋊Q8×C61C2×C4semidirect
110. #121×C61C2×C4semidirect
120. C2×C4⋊C4×C61C2×C4semidirect
375. #21772C61direct (N × H)
426. C2×#408C2×C61semidirect
427. #2311C2×C61semidirect
428. #1895C2×C61semidirect
429. #1894C2×C61semidirect
430. #1893C2×C61semidirect
431. #1892C2×C61semidirect
432. #1875C2×C61semidirect
433. #1874C2×C61semidirect
434. #1873C2×C61semidirect
435. #1872C2×C61semidirect
436. #1824C2×C61semidirect
437. #1823C2×C61semidirect
438. #1788C2×C61semidirect
439. #1788C2×C61semidirect
456. #537C4×C61semidirect
497. C61#21772direct (N × H)
508. C2×#41C2×C4×C61semidirect
539. C22⋊Q8C2×C4×C61semidirect
546. #121C2×C4×C61semidirect
556. C2×C4⋊C4C2×C4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5372
C2×C61×#4082
C61×#23112
C61×#18952
C61×#18942
C61×#18932
C61×#18922
C61×#18752
C61×#18742
C61×#18732
C61×#18722
C61×#18242
C61×#18232
C61×#17882
#2177261