Finite Group Databasebeta

← C61×#22950 #29526383

Subgroups — C61×#22950 #29526383

Order 15616.

768 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3091C211yesmaximal, characteristic
2C61×#2933C211yesmaximal, characteristic
3C61×#2924C211yesmaximal, characteristic, complemented
4C61×#1946C211yesmaximal, characteristic, complemented
5C61×#1938C211yesmaximal, characteristic, complemented
6C61×#1929C211yesmaximal, characteristic, complemented
7C61×#1922C211yesmaximal, characteristic, complemented
8C61×#1922C211yesmaximal, characteristic, complemented
9C61×#1896C211yesmaximal, characteristic
10C61×#1866C211yesmaximal, characteristic, complemented
11C61×#1855C211yesmaximal, characteristic, complemented
12C61×#1773C211yesmaximal, characteristic, complemented
13C61×#1765C211yesmaximal, characteristic, complemented
14C61×#1749C211yesmaximal, characteristic, complemented
15C2×C61×#339C211yesmaximal, characteristic, complemented
16C2×#131×C61C2211yescharacteristic
17C22×M16×C61C2211yescharacteristic
18C61×#525C2211yescharacteristic
19C2×#117×C61C2211yescharacteristic
20C22×C42×C61C2211yescharacteristic
21C61×#485C411yescharacteristic, complemented
22C61×#485C411yescharacteristic, complemented
23C61×#484C411yescharacteristic, complemented
24C61×#483C411yescharacteristic, complemented
25C61×#482C411yescharacteristic, complemented
26C61×#482C411yescharacteristic, complemented
27C61×#481C411yescharacteristic, complemented
28C61×#480C411yescharacteristic, complemented
29C61×#436—21no—
30C61×#435—21no—
31C61×#435—21no—
32C8×D4×C61—21no—
33C61×#433—21no—
34C61×#433—21no—
35C61×#432—21no—
36C61×#431—21no—
37C2×#108×C61C2211yescharacteristic
38C2×#108×C61C2211yescharacteristic
39C61×#427C2211yescharacteristic
40C61×#427C2211yescharacteristic
41C61×#424C2211yescharacteristic
42C61×#424C2211yescharacteristic
43C61×#424C2211yescharacteristic
44C2×#104×C61C2211yescharacteristic
45C2×#104×C61C2211yescharacteristic
46C61×#416C2211yescharacteristic
47C61×#416C2211yescharacteristic
48C61×#408C2211yescharacteristic
49C61×#407C2211yescharacteristic
50C2×C22⋊C8×C61C2211yescharacteristic
51C2×C22⋊C8×C61C2211yescharacteristic
52C61×#405C2211yescharacteristic
53C61×#405C2211yescharacteristic
54C61×#405C2211yescharacteristic
55C2×#97×C61C2211yescharacteristic
56C2×#97×C61C2211yescharacteristic
57C61×#341C2211yescharacteristic
58C61×#341C2211yescharacteristic
59C61×#339C2211yescharacteristic
60C61×#339C2211yescharacteristic
61C61×#339C2211yescharacteristic
62C61×#339C2211yescharacteristic
63C61×#339C2211yescharacteristic
64C61×#339C2211yescharacteristic
65C61×#336C2211yescharacteristic
66C61×#336C2211yescharacteristic
67C2×#41×C61C2311yescharacteristic
68C23×C4×C61—21no—
69C23×C4×C61C2311yescharacteristic
70#131×C61—22no—
71#131×C61—41no—
72C2×M16×C61—21no—
73C2×M16×C61—21no—
74C2×M16×C61—22no—
75C2×M16×C61—41no—
76C2×M16×C61C2311yescharacteristic
77C2×M16×C61C2311yescharacteristic
78C2×M16×C61C2311yescharacteristic
79C2×M16×C61C2311yescharacteristic
80C22×C8×C61—21no—
81C22×C8×C61—21no—
82C22×C8×C61C2311yescharacteristic
83C22×C8×C61C2311yescharacteristic
84C22×C8×C61C2311yescharacteristic
85C22×C8×C61C2311yescharacteristic
86#123×C61—21no—
87C22⋊Q8×C61C2×C411yescharacteristic
88C22⋊Q8×C61C2×C411yescharacteristic
89#121×C61C2×C411yescharacteristic
90#121×C61C2×C411yescharacteristic
91#120×C61—21no—
92C4×D4×C61—21no—
93C4×D4×C61—21no—
94#117×C61—21no—
95#117×C61—21no—
96#117×C61C2×C411yescharacteristic
97#117×C61C2×C411yescharacteristic
98#117×C61C2311yescharacteristic
99#117×C61C2311yescharacteristic
100#117×C61C2311yescharacteristic
101C2×C4⋊C4×C61C2×C411yescharacteristic
102C2×C4⋊C4×C61C2×C411yescharacteristic
103C2×C22⋊C4×C61—21no—
104C2×C42×C61—21no—
105C2×C42×C61—22no—
106C2×C42×C61—21no—
107C2×C42×C61—41no—
108C2×C42×C61C2311yescharacteristic
109C2×C42×C61C2311yescharacteristic
110#108×C61—22no—
111#108×C61—41no—
112#107×C61C2×C411yescharacteristic, complemented
113#107×C61C2×C411yescharacteristic, complemented
114#107×C61C2×C411yescharacteristic, complemented
115#107×C61C2×C411yescharacteristic, complemented
116#106×C61C2×C411yescharacteristic, complemented
117#106×C61C2×C411yescharacteristic, complemented
118#106×C61C2×C411yescharacteristic, complemented
119#106×C61C2×C411yescharacteristic, complemented
120C4⋊C8×C61—21no—
121C4⋊C8×C61—21no—
122C4⋊C8×C61—21no—
123C4⋊C8×C61—21no—
124C4⋊C8×C61—21no—
125C4⋊C8×C61—21no—
126#104×C61—22no—
127#104×C61—41no—
128#103×C61C2×C411yescharacteristic, complemented
129#103×C61C2×C411yescharacteristic, complemented
130#103×C61C2×C411yescharacteristic, complemented
131#103×C61C2×C411yescharacteristic, complemented
132#102×C61C2×C411yescharacteristic, complemented
133#102×C61C2×C411yescharacteristic, complemented
134#102×C61C2×C411yescharacteristic, complemented
135#102×C61C2×C411yescharacteristic, complemented
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C22⋊C8×C61—21no—
139C22⋊C8×C61—21no—
140C22⋊C8×C61C2×C411yescharacteristic
141C22⋊C8×C61C2×C411yescharacteristic
142C22⋊C8×C61C2×C411yescharacteristic
143C22⋊C8×C61C2×C411yescharacteristic
144C22⋊C8×C61D411yescharacteristic
145C22⋊C8×C61D411yescharacteristic
146C22⋊C8×C61D411yescharacteristic
147C22⋊C8×C61D411yescharacteristic
148#97×C61—21no—
149#97×C61—21no—
150#97×C61—21no—
151#97×C61—22no—
152#97×C61—41no—
153C4×C8×C61—21no—
154C4×C8×C61—21no—
155C4×C8×C61—21no—
156C24×C61#4111yescharacteristic
157#41×C61—21no—
158#41×C61—21no—
159#41×C61—21no—
160#41×C61—21no—
161C2×Q8×C61C22×C411yescharacteristic
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61C22×C411yescharacteristic
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—42no—
176C22×C4×C61—42no—
177C22×C4×C61—42no—
178C22×C4×C61C22×C411yescharacteristic
179C22×C4×C61C22×C411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61#4111yescharacteristic
183C22×C4×C61C2411yescharacteristic
184M16×C61—21no—
185M16×C61—21no—
186M16×C61—21no—
187M16×C61—21no—
188M16×C61—21no—
189M16×C61—21no—
190M16×C61—21no—
191M16×C61—42no—
192M16×C61—42no—
193M16×C61#4112yes—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—42no—
207C2×C8×C61—42no—
208C2×C8×C61C22×C411yescharacteristic
209C2×C8×C61C22×C411yescharacteristic
210C2×C8×C61C22×C411yescharacteristic
211C2×C8×C61C22×C411yescharacteristic
212C2×C8×C61C2×D411yescharacteristic
213C2×C8×C61C2×D411yescharacteristic
214C2×C8×C61C2×D411yescharacteristic
215C2×C8×C61C2×D411yescharacteristic
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61C22×C411yescharacteristic
221C4⋊C4×C61C22×C411yescharacteristic
222C4⋊C4×C61C22×C411yescharacteristic
223C4⋊C4×C61C22×C411yescharacteristic
224C4⋊C4×C61C22×C411yescharacteristic
225C4⋊C4×C61C22×C411yescharacteristic
226C22⋊C4×C61—21no—
227C22⋊C4×C61—21no—
228C22⋊C4×C61—21no—
229C22⋊C4×C61—21no—
230C22⋊C4×C61—21no—
231C22⋊C4×C61—21no—
232C22⋊C4×C61—21no—
233C22⋊C4×C61—21no—
234C22⋊C4×C61—21no—
235C42×C61—21no—
236C42×C61—21no—
237C42×C61—21no—
238C42×C61—21no—
239C42×C61—21no—
240C42×C61—21no—
241C42×C61—21no—
242C42×C61—21no—
243C42×C61—42no—
244C42×C61#4112yes—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—22no—
248C23×C61—21no—
249C23×C61—41no—
250C23×C61C4×D411yescharacteristic
251C23×C61C4×D411yescharacteristic
252C23×C61C2×#4111yescharacteristic
253Q8×C61—21no—
254Q8×C61—21no—
255D4×C61—21no—
256D4×C61—21no—
257D4×C61—41no—
258D4×C61—41no—
259D4×C61—42no—
260D4×C61—81no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—22no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—22no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—48no—
284C2×C4×C61—41no—
285C2×C4×C61—42no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—81no—
289C2×C4×C61C4×D411yescharacteristic
290C2×C4×C61C4×D411yescharacteristic
291C2×C4×C61C23×C411yescharacteristic
292C2×C4×C61C22×D411yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61H(5,𝔽2)11yescharacteristic
296C2×C4×C612−1+411yescharacteristic
297C8×C61—21no—
298C8×C61—21no—
299C8×C61—21no—
300C8×C61—21no—
301C8×C61—21no—
302C8×C61—21no—
303C8×C61—22no—
304C8×C61—21no—
305C8×C61—21no—
306C8×C61—41no—
307C8×C61—41no—
308C8×C61—41no—
309#22950C6111yesmaximal, characteristic, direct product factor, Sylow
310C22×C61—21no—
311C22×C61—21no—
312C22×C61—21no—
313C22×C61—21no—
314C22×C61—21no—
315C22×C61—21no—
316C22×C61—21no—
317C22×C61—42no—
318C22×C61—42no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61#44412yes—
323C22×C61C2×C4×D411yescharacteristic
324C22×C61#55111yescharacteristic
325C22×C61#55211yescharacteristic
326C4×C61—21no—
327C4×C61—21no—
328C4×C61—42no—
329C4×C61—42no—
330C4×C61—41no—
331C4×C61—41no—
332C4×C61—41no—
333C4×C61—41no—
334C4×C61—41no—
335C4×C61—41no—
336C4×C61—41no—
337C4×C61C4×#4111yescharacteristic
338C4×C61#52011yescharacteristic
339C4×C61#54611yescharacteristic
340C4×C61#54711yescharacteristic
341#3091C2×C6111yescharacteristic
342#2933C2×C6111yescharacteristic
343#2924C2×C6111yescharacteristic, complemented
344#1946C2×C6111yescharacteristic, complemented
345#1938C2×C6111yescharacteristic, complemented
346#1929C2×C6111yescharacteristic, complemented
347#1922C2×C6111yescharacteristic, complemented
348#1922C2×C6111yescharacteristic, complemented
349#1896C2×C6111yescharacteristic
350#1866C2×C6111yescharacteristic, complemented
351#1855C2×C6111yescharacteristic, complemented
352#1773C2×C6111yescharacteristic, complemented
353#1765C2×C6111yescharacteristic, complemented
354#1749C2×C6111yescharacteristic, complemented
355C2×#339C2×C6111yescharacteristic, complemented
356C2×C61—21no—
357C2×C61—21no—
358C2×C61—22no—
359C2×C61—41no—
360C2×C61—81no—
361C2×C61#235911yescharacteristic
362C2×C61C2×#44411yescharacteristic
363C2×C61#295611yescharacteristic
364C2×#131C22×C6111yescharacteristic
365C22×M16C22×C6111yescharacteristic
366#525C22×C6111yescharacteristic
367C2×#117C22×C6111yescharacteristic
368C22×C42C22×C6111yescharacteristic
369#485C4×C6111yescharacteristic, complemented
370#485C4×C6111yescharacteristic, complemented
371#484C4×C6111yescharacteristic, complemented
372#483C4×C6111yescharacteristic, complemented
373#482C4×C6111yescharacteristic, complemented
374#482C4×C6111yescharacteristic, complemented
375#481C4×C6111yescharacteristic, complemented
376#480C4×C6111yescharacteristic, complemented
377#436—21no—
378#435—21no—
379#435—21no—
380C8×D4—21no—
381#433—21no—
382#433—21no—
383#432—21no—
384#431—21no—
385C2×#108C22×C6111yescharacteristic
386C2×#108C22×C6111yescharacteristic
387#427C22×C6111yescharacteristic
388#427C22×C6111yescharacteristic
389#424C22×C6111yescharacteristic
390#424C22×C6111yescharacteristic
391#424C22×C6111yescharacteristic
392C2×#104C22×C6111yescharacteristic
393C2×#104C22×C6111yescharacteristic
394#416C22×C6111yescharacteristic
395#416C22×C6111yescharacteristic
396#408C22×C6111yescharacteristic
397#407C22×C6111yescharacteristic
398C2×C22⋊C8C22×C6111yescharacteristic
399C2×C22⋊C8C22×C6111yescharacteristic
400#405C22×C6111yescharacteristic
401#405C22×C6111yescharacteristic
402#405C22×C6111yescharacteristic
403C2×#97C22×C6111yescharacteristic
404C2×#97C22×C6111yescharacteristic
405#341C22×C6111yescharacteristic
406#341C22×C6111yescharacteristic
407#339C22×C6111yescharacteristic
408#339C22×C6111yescharacteristic
409#339C22×C6111yescharacteristic
410#339C22×C6111yescharacteristic
411#339C22×C6111yescharacteristic
412#339C22×C6111yescharacteristic
413#336C22×C6111yescharacteristic
414#336C22×C6111yescharacteristic
415C61#2295011yescharacteristic, direct product factor, Sylow
416C2×#41C23×C6111yescharacteristic
417C23×C4—21no—
418C23×C4C23×C6111yescharacteristic
419#131—22no—
420#131—41no—
421C2×M16—21no—
422C2×M16—21no—
423C2×M16—22no—
424C2×M16—41no—
425C2×M16C23×C6111yescharacteristic
426C2×M16C23×C6111yescharacteristic
427C2×M16C23×C6111yescharacteristic
428C2×M16C23×C6111yescharacteristic
429C22×C8—21no—
430C22×C8—21no—
431C22×C8C23×C6111yescharacteristic
432C22×C8C23×C6111yescharacteristic
433C22×C8C23×C6111yescharacteristic
434C22×C8C23×C6111yescharacteristic
435#123—21no—
436C22⋊Q8C2×C4×C6111yescharacteristic
437C22⋊Q8C2×C4×C6111yescharacteristic
438#121C2×C4×C6111yescharacteristic
439#121C2×C4×C6111yescharacteristic
440#120—21no—
441C4×D4—21no—
442C4×D4—21no—
443#117—21no—
444#117—21no—
445#117C2×C4×C6111yescharacteristic
446#117C2×C4×C6111yescharacteristic
447#117C23×C6111yescharacteristic
448#117C23×C6111yescharacteristic
449#117C23×C6111yescharacteristic
450C2×C4⋊C4C2×C4×C6111yescharacteristic
451C2×C4⋊C4C2×C4×C6111yescharacteristic
452C2×C22⋊C4—21no—
453C2×C42—21no—
454C2×C42—22no—
455C2×C42—21no—
456C2×C42—41no—
457C2×C42C23×C6111yescharacteristic
458C2×C42C23×C6111yescharacteristic
459#108—22no—
460#108—41no—
461#107C2×C4×C6111yescharacteristic, complemented
462#107C2×C4×C6111yescharacteristic, complemented
463#107C2×C4×C6111yescharacteristic, complemented
464#107C2×C4×C6111yescharacteristic, complemented
465#106C2×C4×C6111yescharacteristic, complemented
466#106C2×C4×C6111yescharacteristic, complemented
467#106C2×C4×C6111yescharacteristic, complemented
468#106C2×C4×C6111yescharacteristic, complemented
469C4⋊C8—21no—
470C4⋊C8—21no—
471C4⋊C8—21no—
472C4⋊C8—21no—
473C4⋊C8—21no—
474C4⋊C8—21no—
475#104—22no—
476#104—41no—
477#103C2×C4×C6111yescharacteristic, complemented
478#103C2×C4×C6111yescharacteristic, complemented
479#103C2×C4×C6111yescharacteristic, complemented
480#103C2×C4×C6111yescharacteristic, complemented
481#102C2×C4×C6111yescharacteristic, complemented
482#102C2×C4×C6111yescharacteristic, complemented
483#102C2×C4×C6111yescharacteristic, complemented
484#102C2×C4×C6111yescharacteristic, complemented
485C22⋊C8—21no—
486C22⋊C8—21no—
487C22⋊C8—21no—
488C22⋊C8—21no—
489C22⋊C8C2×C4×C6111yescharacteristic
490C22⋊C8C2×C4×C6111yescharacteristic
491C22⋊C8C2×C4×C6111yescharacteristic
492C22⋊C8C2×C4×C6111yescharacteristic
493C22⋊C8D4×C6111yescharacteristic
494C22⋊C8D4×C6111yescharacteristic
495C22⋊C8D4×C6111yescharacteristic
496C22⋊C8D4×C6111yescharacteristic
497#97—21no—
498#97—21no—
499#97—21no—
500#97—22no—
501#97—41no—
502C4×C8—21no—
503C4×C8—21no—
504C4×C8—21no—
505C24#41×C6111yescharacteristic
506#41—21no—
507#41—21no—
508#41—21no—
509#41—21no—
510C2×Q8C22×C4×C6111yescharacteristic
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4C22×C4×C6111yescharacteristic
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4C22×C4×C6111yescharacteristic
528C22×C4C22×C4×C6111yescharacteristic
529C22×C4C2×D4×C6111yescharacteristic
530C22×C4C2×D4×C6111yescharacteristic
531C22×C4#41×C6111yescharacteristic
532C22×C4C24×C6111yescharacteristic
533M16—21no—
534M16—21no—
535M16—21no—
536M16—21no—
537M16—21no—
538M16—21no—
539M16—21no—
540M16—42no—
541M16—42no—
542M16#41×C6112yes—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—42no—
556C2×C8—42no—
557C2×C8C22×C4×C6111yescharacteristic
558C2×C8C22×C4×C6111yescharacteristic
559C2×C8C22×C4×C6111yescharacteristic
560C2×C8C22×C4×C6111yescharacteristic
561C2×C8C2×D4×C6111yescharacteristic
562C2×C8C2×D4×C6111yescharacteristic
563C2×C8C2×D4×C6111yescharacteristic
564C2×C8C2×D4×C6111yescharacteristic
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4C22×C4×C6111yescharacteristic
570C4⋊C4C22×C4×C6111yescharacteristic
571C4⋊C4C22×C4×C6111yescharacteristic
572C4⋊C4C22×C4×C6111yescharacteristic
573C4⋊C4C22×C4×C6111yescharacteristic
574C4⋊C4C22×C4×C6111yescharacteristic
575C22⋊C4—21no—
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—21no—
581C22⋊C4—21no—
582C22⋊C4—21no—
583C22⋊C4—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—42no—
593C42#41×C6112yes—
594C23—21no—
595C23—21no—
596C23—22no—
597C23—21no—
598C23—41no—
599C23C4×D4×C6111yescharacteristic
600C23C4×D4×C6111yescharacteristic
601C23C2×#41×C6111yescharacteristic
602Q8—21no—
603Q8—21no—
604D4—21no—
605D4—21no—
606D4—41no—
607D4—41no—
608D4—42no—
609D4—81no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—48no—
633C2×C4—41no—
634C2×C4—42no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—81no—
638C2×C4C4×D4×C6111yescharacteristic
639C2×C4C4×D4×C6111yescharacteristic
640C2×C4C23×C4×C6111yescharacteristic
641C2×C4C22×D4×C6111yescharacteristic
642C2×C4C2×#41×C6111yescharacteristic
643C2×C4C2×#41×C6111yescharacteristic
644C2×C4H(5,𝔽2)×C6111yescharacteristic
645C2×C42−1+4×C6111yescharacteristic
646C8—21no—
647C8—21no—
648C8—22no—
649C8—21no—
650C8—21no—
651C8—21no—
652C8—21no—
653C8—21no—
654C8—21no—
655C8—41no—
656C8—41no—
657C8—41no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—42no—
666C22—42no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22C61×#44412yes—
671C22C2×C4×D4×C6111yescharacteristic
672C22C61×#55111yescharacteristic
673C22C61×#55211yescharacteristic
674C4—21no—
675C4—21no—
676C4—42no—
677C4—42no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4—41no—
682C4—41no—
683C4—41no—
684C4—41no—
685C4C4×#41×C6111yescharacteristic
686C4C61×#52011yescharacteristic
687C4C61×#54611yescharacteristic
688C4C61×#54711yescharacteristic
689C2—21no—
690C2—21no—
691C2—22no—
692C2—41no—
693C2—81no—
694C2C61×#235911yescharacteristic
695C2C2×C61×#44411yescharacteristic
696C2C61×#295611yescharacteristic
subgroupG/H
centerC2×C4×C61C22×D4
commutatorC2×C4C23×C4×C61
Frattini, cosocleC22×C4C24×C61
socleC22×C61C2×C4×D4
prime radicalC61×#525C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C61 ◁ C2×C22⋊C8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
3. C61×#2924C2semidirect
4. C61×#1946C2semidirect
5. C61×#1938C2semidirect
6. C61×#1929C2semidirect
7. C61×#1922C2semidirect
8. C61×#1922C2semidirect
10. C61×#1866C2semidirect
11. C61×#1855C2semidirect
12. C61×#1773C2semidirect
13. C61×#1765C2semidirect
14. C61×#1749C2semidirect
15. C2×C61×#339C2semidirect
21. C61×#485C4semidirect
22. C61×#485C4semidirect
23. C61×#484C4semidirect
24. C61×#483C4semidirect
25. C61×#482C4semidirect
26. C61×#482C4semidirect
27. C61×#481C4semidirect
28. C61×#480C4semidirect
112. #107×C61C2×C4semidirect
113. #107×C61C2×C4semidirect
114. #107×C61C2×C4semidirect
115. #107×C61C2×C4semidirect
116. #106×C61C2×C4semidirect
117. #106×C61C2×C4semidirect
118. #106×C61C2×C4semidirect
119. #106×C61C2×C4semidirect
128. #103×C61C2×C4semidirect
129. #103×C61C2×C4semidirect
130. #103×C61C2×C4semidirect
131. #103×C61C2×C4semidirect
132. #102×C61C2×C4semidirect
133. #102×C61C2×C4semidirect
134. #102×C61C2×C4semidirect
135. #102×C61C2×C4semidirect
309. #22950C61direct (N × H)
343. #2924C2×C61semidirect
344. #1946C2×C61semidirect
345. #1938C2×C61semidirect
346. #1929C2×C61semidirect
347. #1922C2×C61semidirect
348. #1922C2×C61semidirect
350. #1866C2×C61semidirect
351. #1855C2×C61semidirect
352. #1773C2×C61semidirect
353. #1765C2×C61semidirect
354. #1749C2×C61semidirect
355. C2×#339C2×C61semidirect
369. #485C4×C61semidirect
370. #485C4×C61semidirect
371. #484C4×C61semidirect
372. #483C4×C61semidirect
373. #482C4×C61semidirect
374. #482C4×C61semidirect
375. #481C4×C61semidirect
376. #480C4×C61semidirect
415. C61#22950direct (N × H)
461. #107C2×C4×C61semidirect
462. #107C2×C4×C61semidirect
463. #107C2×C4×C61semidirect
464. #107C2×C4×C61semidirect
465. #106C2×C4×C61semidirect
466. #106C2×C4×C61semidirect
467. #106C2×C4×C61semidirect
468. #106C2×C4×C61semidirect
477. #103C2×C4×C61semidirect
478. #103C2×C4×C61semidirect
479. #103C2×C4×C61semidirect
480. #103C2×C4×C61semidirect
481. #102C2×C4×C61semidirect
482. #102C2×C4×C61semidirect
483. #102C2×C4×C61semidirect
484. #102C2×C4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#30912
C61×#29332
C61×#29242
C61×#19462
C61×#19382
C61×#19292
C61×#19222
C61×#18962
C61×#18662
C61×#18552
C61×#17732
C61×#17652
C61×#17492
C2×C61×#3392
#2295061