Finite Group Databasebeta

← C61×#21519 #29524952

Subgroups — C61×#21519 #29524952

Order 15616.

902 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3035C211yesmaximal, characteristic
2C2×C61×#444C211yesmaximal, characteristic, complemented
3C2×C61×#443C211yesmaximal, characteristic, complemented
4C61×#2932C211yesmaximal, characteristic, complemented
5C61×#2875C211yesmaximal, characteristic, complemented
6C61×#1980C211yesmaximal, characteristic, complemented
7C61×#1950C211yesmaximal, characteristic, complemented
8C61×#1929C211yesmaximal, characteristic, complemented
9C61×#1929C211yesmaximal, characteristic, complemented
10C61×#1876C211yesmaximal, characteristic, complemented
11C61×#1876C211yesmaximal, characteristic, complemented
12C61×#1806C211yesmaximal, characteristic, complemented
13C61×#1771C211yesmaximal, characteristic, complemented
14C61×#1765C211yesmaximal, characteristic, complemented
15C61×#1764C211yesmaximal, characteristic, complemented
16C2×#135×C61C2211yescharacteristic
17C2×#135×C61C2211yescharacteristic
18C2×#131×C61C2211yescharacteristic
19C2×#131×C61C2211yescharacteristic
20C2×#131×C61C2211yescharacteristic
21C2×#131×C61C2211yescharacteristic
22C61×#532C2211yescharacteristic
23C4×#41×C61C2211yescharacteristic
24C61×#464C411yescharacteristic, complemented
25C61×#464C411yescharacteristic, complemented
26C61×#463C411yescharacteristic, complemented
27C61×#463C411yescharacteristic, complemented
28C61×#462C411yescharacteristic, complemented
29C61×#461C411yescharacteristic, complemented
30C61×#460C411yescharacteristic, complemented
31C61×#459C411yescharacteristic, complemented
32C61×#444—24no—
33C61×#443—24no—
34C61×#435—21no—
35C61×#435—21no—
36C61×#435—21no—
37C61×#435—21no—
38C2×#108×C61C2211yescharacteristic
39C2×#108×C61C2211yescharacteristic
40C61×#423C2211yescharacteristic
41C2×C4⋊C8×C61C2211yescharacteristic
42C2×#104×C61C2211yescharacteristic
43C2×#104×C61C2211yescharacteristic
44C2×#104×C61C2211yescharacteristic
45C2×#104×C61C2211yescharacteristic
46C2×#104×C61C2211yescharacteristic
47C2×#104×C61C2211yescharacteristic
48C61×#416C2211yescharacteristic
49C61×#416C2211yescharacteristic
50C61×#408C2211yescharacteristic
51C61×#408C2211yescharacteristic
52C61×#405—21no—
53C61×#405—21no—
54C61×#405C2211yescharacteristic
55C61×#405C2211yescharacteristic
56C4×M16×C61—21no—
57C4×M16×C61C2211yescharacteristic
58C2×#97×C61—21no—
59C2×#97×C61C2211yescharacteristic
60C2×#97×C61C2211yescharacteristic
61C2×C4×C8×C61C2211yescharacteristic
62C4×C4⋊C4×C61C2211yescharacteristic
63C61×#341C2211yescharacteristic
64C61×#341C2211yescharacteristic
65C61×#339C2211yescharacteristic
66C61×#339C2211yescharacteristic
67C61×#336C2211yescharacteristic
68C61×#336C2211yescharacteristic
69C2×#41×C61C2311yescharacteristic
70C2×#41×C61C2311yescharacteristic
71C2×#41×C61C2311yescharacteristic
72#135×C61—22no—
73#135×C61—22no—
74#135×C61—22no—
75#135×C61—22no—
76C2×Q16×C61C2×C411yescharacteristic
77C2×Q16×C61C2×C411yescharacteristic
78C2×SD16×C61C2×C411yescharacteristic
79C2×SD16×C61C2×C411yescharacteristic
80C2×SD16×C61C2×C411yescharacteristic
81C2×SD16×C61C2×C411yescharacteristic
82C2×D8×C61C2×C411yescharacteristic
83C2×D8×C61C2×C411yescharacteristic
84#131×C61—22no—
85#131×C61—22no—
86#131×C61—22no—
87#131×C61—22no—
88#131×C61—22no—
89#131×C61—22no—
90#131×C61—22no—
91#131×C61D414yescomplemented
92C2×M16×C61—21no—
93C2×M16×C61—21no—
94C2×M16×C61—21no—
95C2×M16×C61—21no—
96C2×M16×C61C2311yescharacteristic
97C2×M16×C61C2311yescharacteristic
98C2×M16×C61C2311yescharacteristic
99C2×M16×C61C2311yescharacteristic
100C22×C8×C61—21no—
101C22×C8×C61—21no—
102C22×C8×C61—21no—
103C22×C8×C61—21no—
104C22×C8×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C4⋊Q8×C61C2×C411yescharacteristic
109#127×C61C2×C411yescharacteristic
110#124×C61C2×C411yescharacteristic
111#124×C61C2×C411yescharacteristic
112#121×C61—21no—
113#121×C61—21no—
114C4×Q8×C61C2×C411yescharacteristic
115C4×Q8×C61C2×C411yescharacteristic
116C4×D4×C61—21no—
117C4×D4×C61—21no—
118C4×D4×C61—21no—
119C4×D4×C61—21no—
120C4×D4×C61C2×C411yescharacteristic
121C4×D4×C61C2×C411yescharacteristic
122#117×C61—21no—
123#117×C61C2311yescharacteristic
124C2×C4⋊C4×C61—21no—
125C2×C42×C61—21no—
126C2×C42×C61C2311yescharacteristic
127C2×C42×C61C2311yescharacteristic
128C2×C42×C61C2311yescharacteristic
129#108×C61—22no—
130#108×C61—22no—
131C4⋊C8×C61—21no—
132C4⋊C8×C61—21no—
133C4⋊C8×C61C2×C411yescharacteristic
134C4⋊C8×C61C2×C411yescharacteristic
135C4⋊C8×C61C2×C411yescharacteristic
136C4⋊C8×C61C2×C411yescharacteristic
137#104×C61—22no—
138#104×C61—22no—
139#104×C61—22no—
140#104×C61—22no—
141#104×C61—22no—
142#104×C61—22no—
143#103×C61C2×C411yescharacteristic
144#103×C61C2×C411yescharacteristic
145#103×C61C2×C411yescharacteristic
146#103×C61C2×C411yescharacteristic
147#102×C61C2×C411yescharacteristic
148#102×C61C2×C411yescharacteristic
149#102×C61C2×C411yescharacteristic
150#102×C61C2×C411yescharacteristic
151C22⋊C8×C61—21no—
152C22⋊C8×C61—21no—
153C22⋊C8×C61—21no—
154C22⋊C8×C61—21no—
155#97×C61—21no—
156#97×C61—21no—
157#97×C61—22no—
158#97×C61—21no—
159#97×C61D411yescharacteristic
160#97×C61D411yescharacteristic
161#97×C61D411yescharacteristic
162#97×C61D411yescharacteristic
163C4×C8×C61—22no—
164C4×C8×C61—21no—
165C4×C8×C61—21no—
166C4×C8×C61—21no—
167#95×C61—21no—
168#41×C61—21no—
169#41×C61—21no—
170#41×C61—21no—
171#41×C61—21no—
172#41×C61—21no—
173#41×C61—21no—
174#41×C61—21no—
175#41×C61—21no—
176#41×C61—21no—
177#41×C61—21no—
178#41×C61C2×D412yes—
179#41×C61#4112yes—
180C2×Q8×C61C22×C411yescharacteristic
181C2×Q8×C61C22×C411yescharacteristic
182C2×Q8×C61C22×C411yescharacteristic
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61C22×C411yescharacteristic
189C2×D4×C61C22×C411yescharacteristic
190C2×D4×C61C22×C411yescharacteristic
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61#4111yescharacteristic
199C22×C4×C61#4111yescharacteristic
200C22×C4×C61C2411yescharacteristic
201Q16×C61—22no—
202Q16×C61—22no—
203SD16×C61—22no—
204SD16×C61—22no—
205SD16×C61—22no—
206SD16×C61—22no—
207D8×C61—22no—
208D8×C61—22no—
209M16×C61—24no—
210M16×C61—21no—
211M16×C61—21no—
212M16×C61—24no—
213M16×C61—21no—
214M16×C61—21no—
215M16×C61—21no—
216M16×C61—21no—
217M16×C61—42no—
218M16×C61—42no—
219M16×C61C2×D412yes—
220M16×C61#4112yes—
221C2×C8×C61—24no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—24no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—42no—
234C2×C8×C61—42no—
235C2×C8×C61C22×C411yescharacteristic
236C2×C8×C61C22×C411yescharacteristic
237C2×C8×C61C22×C411yescharacteristic
238C2×C8×C61C22×C411yescharacteristic
239C2×C8×C61C2×D411yescharacteristic
240C2×C8×C61C2×D411yescharacteristic
241C2×C8×C61C2×D412yes—
242C2×C8×C61C2×D411yescharacteristic
243C2×C8×C61C2×D411yescharacteristic
244C2×C8×C61#4112yes—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—42no—
250C4⋊C4×C61C22×C411yescharacteristic
251C4⋊C4×C61C22×C411yescharacteristic
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—
259C42×C61—21no—
260C42×C61—21no—
261C42×C61—21no—
262C42×C61—21no—
263C42×C61—21no—
264C42×C61—21no—
265C42×C61—21no—
266C42×C61C22×C411yescharacteristic
267C42×C61C22×C411yescharacteristic
268C42×C61C2×D411yescharacteristic
269C42×C61C2×D411yescharacteristic
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61C2×#4111yescharacteristic
274Q8×C61—21no—
275Q8×C61—21no—
276Q8×C61—21no—
277Q8×C61—21no—
278Q8×C61—21no—
279Q8×C61C4×D412yes—
280D4×C61—22no—
281D4×C61—22no—
282D4×C61—21no—
283D4×C61—21no—
284D4×C61—21no—
285D4×C61—21no—
286D4×C61—21no—
287D4×C61—41no—
288D4×C61—41no—
289D4×C61—41no—
290D4×C61—41no—
291D4×C61—81no—
292D4×C61—81no—
293D4×C61C4×D412yes—
294C2×C4×C61—21no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—81no—
314C2×C4×C61—81no—
315C2×C4×C61C4×D411yescharacteristic
316C2×C4×C61C4×D411yescharacteristic
317C2×C4×C61C4×D411yescharacteristic
318C2×C4×C61C4×D411yescharacteristic
319C2×C4×C61C23×C411yescharacteristic
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61C22×D411yescharacteristic
322C2×C4×C61C2×#4111yescharacteristic
323C2×C4×C61C2×#4111yescharacteristic
324C2×C4×C61C2×#4111yescharacteristic
325C8×C61—21no—
326C8×C61—21no—
327C8×C61—21no—
328C8×C61—21no—
329C8×C61—22no—
330C8×C61—21no—
331C8×C61—22no—
332C8×C61—21no—
333C8×C61—41no—
334C8×C61—41no—
335C8×C61#12112yes—
336C8×C61#12112yes—
337#21519C6111yesmaximal, characteristic, direct product factor, Sylow
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—22no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61C2×C4×D411yescharacteristic
350C22×C61#52911yescharacteristic
351C22×C61#53211yescharacteristic
352C4×C61—21no—
353C4×C61—21no—
354C4×C61—21no—
355C4×C61—21no—
356C4×C61—22no—
357C4×C61—42no—
358C4×C61—41no—
359C4×C61—41no—
360C4×C61—41no—
361C4×C61—41no—
362C4×C61—81no—
363C4×C61C2×C4×D411yescharacteristic
364C4×C61C4×#4111yescharacteristic
365C4×C61C2×#12111yescharacteristic
366C4×C61#52511yescharacteristic
367#3035C2×C6111yescharacteristic
368C2×#444C2×C6111yescharacteristic, complemented
369C2×#443C2×C6111yescharacteristic, complemented
370#2932C2×C6111yescharacteristic, complemented
371#2875C2×C6111yescharacteristic, complemented
372#1980C2×C6111yescharacteristic, complemented
373#1950C2×C6111yescharacteristic, complemented
374#1929C2×C6111yescharacteristic, complemented
375#1929C2×C6111yescharacteristic, complemented
376#1876C2×C6111yescharacteristic, complemented
377#1876C2×C6111yescharacteristic, complemented
378#1806C2×C6111yescharacteristic, complemented
379#1771C2×C6111yescharacteristic, complemented
380#1765C2×C6111yescharacteristic, complemented
381#1764C2×C6111yescharacteristic, complemented
382C2×C61—21no—
383C2×C61—21no—
384C2×C61—42no—
385C2×C61—81no—
386C2×C61—81no—
387C2×C61C4×#12111yescharacteristic
388C2×C61#295611yescharacteristic
389C2×C61#295711yescharacteristic
390C2×#135C22×C6111yescharacteristic
391C2×#135C22×C6111yescharacteristic
392C2×#131C22×C6111yescharacteristic
393C2×#131C22×C6111yescharacteristic
394C2×#131C22×C6111yescharacteristic
395C2×#131C22×C6111yescharacteristic
396#532C22×C6111yescharacteristic
397C4×#41C22×C6111yescharacteristic
398#464C4×C6111yescharacteristic, complemented
399#464C4×C6111yescharacteristic, complemented
400#463C4×C6111yescharacteristic, complemented
401#463C4×C6111yescharacteristic, complemented
402#462C4×C6111yescharacteristic, complemented
403#461C4×C6111yescharacteristic, complemented
404#460C4×C6111yescharacteristic, complemented
405#459C4×C6111yescharacteristic, complemented
406#444—24no—
407#443—24no—
408#435—21no—
409#435—21no—
410#435—21no—
411#435—21no—
412C2×#108C22×C6111yescharacteristic
413C2×#108C22×C6111yescharacteristic
414#423C22×C6111yescharacteristic
415C2×C4⋊C8C22×C6111yescharacteristic
416C2×#104C22×C6111yescharacteristic
417C2×#104C22×C6111yescharacteristic
418C2×#104C22×C6111yescharacteristic
419C2×#104C22×C6111yescharacteristic
420C2×#104C22×C6111yescharacteristic
421C2×#104C22×C6111yescharacteristic
422#416C22×C6111yescharacteristic
423#416C22×C6111yescharacteristic
424#408C22×C6111yescharacteristic
425#408C22×C6111yescharacteristic
426#405—21no—
427#405—21no—
428#405C22×C6111yescharacteristic
429#405C22×C6111yescharacteristic
430C4×M16—21no—
431C4×M16C22×C6111yescharacteristic
432C2×#97—21no—
433C2×#97C22×C6111yescharacteristic
434C2×#97C22×C6111yescharacteristic
435C2×C4×C8C22×C6111yescharacteristic
436C4×C4⋊C4C22×C6111yescharacteristic
437#341C22×C6111yescharacteristic
438#341C22×C6111yescharacteristic
439#339C22×C6111yescharacteristic
440#339C22×C6111yescharacteristic
441#336C22×C6111yescharacteristic
442#336C22×C6111yescharacteristic
443C61#2151911yescharacteristic, direct product factor, Sylow
444C2×#41C23×C6111yescharacteristic
445C2×#41C23×C6111yescharacteristic
446C2×#41C23×C6111yescharacteristic
447#135—22no—
448#135—22no—
449#135—22no—
450#135—22no—
451C2×Q16C2×C4×C6111yescharacteristic
452C2×Q16C2×C4×C6111yescharacteristic
453C2×SD16C2×C4×C6111yescharacteristic
454C2×SD16C2×C4×C6111yescharacteristic
455C2×SD16C2×C4×C6111yescharacteristic
456C2×SD16C2×C4×C6111yescharacteristic
457C2×D8C2×C4×C6111yescharacteristic
458C2×D8C2×C4×C6111yescharacteristic
459#131—22no—
460#131—22no—
461#131—22no—
462#131—22no—
463#131—22no—
464#131—22no—
465#131—22no—
466#131D4×C6114yescomplemented
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—21no—
470C2×M16—21no—
471C2×M16C23×C6111yescharacteristic
472C2×M16C23×C6111yescharacteristic
473C2×M16C23×C6111yescharacteristic
474C2×M16C23×C6111yescharacteristic
475C22×C8—21no—
476C22×C8—21no—
477C22×C8—21no—
478C22×C8—21no—
479C22×C8C23×C6111yescharacteristic
480C22×C8C23×C6111yescharacteristic
481C22×C8C23×C6111yescharacteristic
482C22×C8C23×C6111yescharacteristic
483C4⋊Q8C2×C4×C6111yescharacteristic
484#127C2×C4×C6111yescharacteristic
485#124C2×C4×C6111yescharacteristic
486#124C2×C4×C6111yescharacteristic
487#121—21no—
488#121—21no—
489C4×Q8C2×C4×C6111yescharacteristic
490C4×Q8C2×C4×C6111yescharacteristic
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4C2×C4×C6111yescharacteristic
496C4×D4C2×C4×C6111yescharacteristic
497#117—21no—
498#117C23×C6111yescharacteristic
499C2×C4⋊C4—21no—
500C2×C42—21no—
501C2×C42C23×C6111yescharacteristic
502C2×C42C23×C6111yescharacteristic
503C2×C42C23×C6111yescharacteristic
504#108—22no—
505#108—22no—
506C4⋊C8—21no—
507C4⋊C8—21no—
508C4⋊C8C2×C4×C6111yescharacteristic
509C4⋊C8C2×C4×C6111yescharacteristic
510C4⋊C8C2×C4×C6111yescharacteristic
511C4⋊C8C2×C4×C6111yescharacteristic
512#104—22no—
513#104—22no—
514#104—22no—
515#104—22no—
516#104—22no—
517#104—22no—
518#103C2×C4×C6111yescharacteristic
519#103C2×C4×C6111yescharacteristic
520#103C2×C4×C6111yescharacteristic
521#103C2×C4×C6111yescharacteristic
522#102C2×C4×C6111yescharacteristic
523#102C2×C4×C6111yescharacteristic
524#102C2×C4×C6111yescharacteristic
525#102C2×C4×C6111yescharacteristic
526C22⋊C8—21no—
527C22⋊C8—21no—
528C22⋊C8—21no—
529C22⋊C8—21no—
530#97—21no—
531#97—21no—
532#97—22no—
533#97—21no—
534#97D4×C6111yescharacteristic
535#97D4×C6111yescharacteristic
536#97D4×C6111yescharacteristic
537#97D4×C6111yescharacteristic
538C4×C8—22no—
539C4×C8—21no—
540C4×C8—21no—
541C4×C8—21no—
542#95—21no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41—21no—
552#41—21no—
553#41C2×D4×C6112yes—
554#41#41×C6112yes—
555C2×Q8C22×C4×C6111yescharacteristic
556C2×Q8C22×C4×C6111yescharacteristic
557C2×Q8C22×C4×C6111yescharacteristic
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4C22×C4×C6111yescharacteristic
564C2×D4C22×C4×C6111yescharacteristic
565C2×D4C22×C4×C6111yescharacteristic
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4#41×C6111yescharacteristic
574C22×C4#41×C6111yescharacteristic
575C22×C4C24×C6111yescharacteristic
576Q16—22no—
577Q16—22no—
578SD16—22no—
579SD16—22no—
580SD16—22no—
581SD16—22no—
582D8—22no—
583D8—22no—
584M16—24no—
585M16—21no—
586M16—21no—
587M16—24no—
588M16—21no—
589M16—21no—
590M16—21no—
591M16—21no—
592M16—42no—
593M16—42no—
594M16C2×D4×C6112yes—
595M16#41×C6112yes—
596C2×C8—24no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—24no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—42no—
609C2×C8—42no—
610C2×C8C22×C4×C6111yescharacteristic
611C2×C8C22×C4×C6111yescharacteristic
612C2×C8C22×C4×C6111yescharacteristic
613C2×C8C22×C4×C6111yescharacteristic
614C2×C8C2×D4×C6111yescharacteristic
615C2×C8C2×D4×C6111yescharacteristic
616C2×C8C2×D4×C6112yes—
617C2×C8C2×D4×C6111yescharacteristic
618C2×C8C2×D4×C6111yescharacteristic
619C2×C8#41×C6112yes—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—42no—
625C4⋊C4C22×C4×C6111yescharacteristic
626C4⋊C4C22×C4×C6111yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42C22×C4×C6111yescharacteristic
642C42C22×C4×C6111yescharacteristic
643C42C2×D4×C6111yescharacteristic
644C42C2×D4×C6111yescharacteristic
645C23—21no—
646C23—21no—
647C23—21no—
648C23C2×#41×C6111yescharacteristic
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8C4×D4×C6112yes—
655D4—22no—
656D4—22no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—81no—
667D4—81no—
668D4C4×D4×C6112yes—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—81no—
689C2×C4—81no—
690C2×C4C4×D4×C6111yescharacteristic
691C2×C4C4×D4×C6111yescharacteristic
692C2×C4C4×D4×C6111yescharacteristic
693C2×C4C4×D4×C6111yescharacteristic
694C2×C4C23×C4×C6111yescharacteristic
695C2×C4C22×D4×C6111yescharacteristic
696C2×C4C22×D4×C6111yescharacteristic
697C2×C4C2×#41×C6111yescharacteristic
698C2×C4C2×#41×C6111yescharacteristic
699C2×C4C2×#41×C6111yescharacteristic
700C8—21no—
701C8—21no—
702C8—21no—
703C8—21no—
704C8—22no—
705C8—21no—
706C8—22no—
707C8—21no—
708C8—41no—
709C8—41no—
710C8#121×C6112yes—
711C8#121×C6112yes—
712C22—21no—
713C22—21no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22C2×C4×D4×C6111yescharacteristic
724C22C61×#52911yescharacteristic
725C22C61×#53211yescharacteristic
726C4—22no—
727C4—21no—
728C4—21no—
729C4—21no—
730C4—21no—
731C4—42no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—81no—
737C4C2×C4×D4×C6111yescharacteristic
738C4C4×#41×C6111yescharacteristic
739C4C2×#121×C6111yescharacteristic
740C4C61×#52511yescharacteristic
741C2—21no—
742C2—21no—
743C2—42no—
744C2—81no—
745C2—81no—
746C2C4×#121×C6111yescharacteristic
747C2C61×#295611yescharacteristic
748C2C61×#295711yescharacteristic
subgroupG/H
centerC2×C4×C61C22×D4
commutatorC2×C4C23×C4×C61
Frattini, cosocleC22×C4C24×C61
socleC22×C61C2×C4×D4
prime radicalC61×#3035C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C61 ◁ C2×#97×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#444C2semidirect
3. C2×C61×#443C2semidirect
4. C61×#2932C2semidirect
5. C61×#2875C2semidirect
6. C61×#1980C2semidirect
7. C61×#1950C2semidirect
8. C61×#1929C2semidirect
9. C61×#1929C2semidirect
10. C61×#1876C2semidirect
11. C61×#1876C2semidirect
12. C61×#1806C2semidirect
13. C61×#1771C2semidirect
14. C61×#1765C2semidirect
15. C61×#1764C2semidirect
24. C61×#464C4semidirect
25. C61×#464C4semidirect
26. C61×#463C4semidirect
27. C61×#463C4semidirect
28. C61×#462C4semidirect
29. C61×#461C4semidirect
30. C61×#460C4semidirect
31. C61×#459C4semidirect
91. #131×C61D4semidirect
337. #21519C61direct (N × H)
368. C2×#444C2×C61semidirect
369. C2×#443C2×C61semidirect
370. #2932C2×C61semidirect
371. #2875C2×C61semidirect
372. #1980C2×C61semidirect
373. #1950C2×C61semidirect
374. #1929C2×C61semidirect
375. #1929C2×C61semidirect
376. #1876C2×C61semidirect
377. #1876C2×C61semidirect
378. #1806C2×C61semidirect
379. #1771C2×C61semidirect
380. #1765C2×C61semidirect
381. #1764C2×C61semidirect
398. #464C4×C61semidirect
399. #464C4×C61semidirect
400. #463C4×C61semidirect
401. #463C4×C61semidirect
402. #462C4×C61semidirect
403. #461C4×C61semidirect
404. #460C4×C61semidirect
405. #459C4×C61semidirect
443. C61#21519direct (N × H)
466. #131D4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#30352
C2×C61×#4442
C2×C61×#4432
C61×#29322
C61×#28752
C61×#19802
C61×#19502
C61×#19292
C61×#18762
C61×#18062
C61×#17712
C61×#17652
C61×#17642
#2151961