Finite Group Databasebeta

← C61×#25210 #29528643

Subgroups — C61×#25210 #29528643

Order 15616.

884 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#484C211yesmaximal, characteristic, complemented
2C2×C61×#465C211yesmaximal, characteristic
3C61×#2504C211yesmaximal, characteristic
4C61×#2360C211yesmaximal, characteristic, complemented
5C61×#2085C211yesmaximal, characteristic, complemented
6C61×#2074C211yesmaximal, characteristic, complemented
7C61×#2067C211yesmaximal, characteristic, complemented
8C61×#2055C211yesmaximal, characteristic, complemented
9C61×#1949C211yesmaximal, characteristic, complemented
10C61×#1925C211yesmaximal, characteristic, complemented
11C61×#1880C211yesmaximal, characteristic, complemented
12C61×#1874C211yesmaximal, characteristic
13C61×#1850C211yesmaximal, characteristic, complemented
14C61×#1805C211yesmaximal, characteristic, complemented
15C2×C61×#340C211yesmaximal, characteristic, complemented
16C22×SD16×C61C2211yescharacteristic
17C23×C8×C61C2211yescharacteristic
18C2×C22⋊Q8×C61C2211yescharacteristic
19C2×#121×C61C2211yescharacteristic
20C2×C4×Q8×C61C2211yescharacteristic
21C22×C4⋊C4×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2211yescharacteristic
23C61×#484—24no—
24C61×#465—24no—
25C2×#107×C61C2211yescharacteristic
26C2×#107×C61C2211yescharacteristic
27C2×#106×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×C4⋊C8×C61C2211yescharacteristic
30C2×#103×C61C2211yescharacteristic
31C2×#103×C61C2211yescharacteristic
32C2×#103×C61C2211yescharacteristic
33C2×#102×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic
35C2×#102×C61C2211yescharacteristic
36C2×C22⋊C8×C61C2211yescharacteristic
37C61×#397—21no—
38C61×#397—21no—
39C61×#391C2211yescharacteristic
40C61×#390C2211yescharacteristic
41C61×#390C2211yescharacteristic
42C61×#389—21no—
43C61×#389C2211yescharacteristic
44C61×#387—21no—
45C61×#386—21no—
46C61×#386—21no—
47C61×#385—21no—
48C61×#382C2211yescharacteristic
49C61×#382C2211yescharacteristic
50C4×C4⋊C4×C61C2211yescharacteristic
51C4×C22⋊C4×C61—21no—
52C4×C22⋊C4×C61C2211yescharacteristic
53C61×#340C2211yescharacteristic
54C61×#340C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×Q8×C61C2311yescharacteristic
62C22×D4×C61—21no—
63C22×D4×C61C2311yescharacteristic
64C23×C4×C61—21no—
65C23×C4×C61—21no—
66C23×C4×C61C2311yescharacteristic
67C2×SD16×C61—22no—
68C2×SD16×C61—22no—
69C2×SD16×C61—41no—
70C22×C8×C61—22no—
71C22×C8×C61—22no—
72C22×C8×C61—41no—
73C22×C8×C61C2311yescharacteristic
74C22×C8×C61C2311yescharacteristic
75C22×C8×C61C2311yescharacteristic
76C22×C8×C61C2311yescharacteristic
77C22⋊Q8×C61—22no—
78C22⋊Q8×C61D414yes—
79#121×C61—22no—
80#121×C61—22no—
81C4×Q8×C61—22no—
82C4×Q8×C61—41no—
83C2×C4⋊C4×C61—21no—
84C2×C4⋊C4×C61—22no—
85C2×C4⋊C4×C61—22no—
86C2×C4⋊C4×C61—22no—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—41no—
92C2×C4⋊C4×C61C2311yescharacteristic
93C2×C4⋊C4×C61C2311yescharacteristic
94C2×C4⋊C4×C61C2311yescharacteristic
95C2×C4⋊C4×C61C2311yescharacteristic
96C2×C4⋊C4×C61C2311yescharacteristic
97C2×C4⋊C4×C61C2311yescharacteristic
98C2×C22⋊C4×C61—21no—
99C2×C22⋊C4×C61—21no—
100C2×C22⋊C4×C61—21no—
101C2×C22⋊C4×C61—21no—
102C2×C22⋊C4×C61—21no—
103C2×C22⋊C4×C61—21no—
104C2×C22⋊C4×C61D411yescharacteristic
105C2×C22⋊C4×C61D411yescharacteristic
106C2×C42×C61—21no—
107C2×C42×C61—21no—
108C2×C42×C61C2311yescharacteristic
109C2×C42×C61C2311yescharacteristic
110#107×C61—22no—
111#107×C61—22no—
112#106×C61—22no—
113C4⋊C8×C61—22no—
114C4⋊C8×C61—41no—
115#103×C61—22no—
116#103×C61—22no—
117#103×C61—22no—
118#102×C61—22no—
119#102×C61—22no—
120#102×C61—41no—
121C22⋊C8×C61—22no—
122#95×C61—21no—
123#95×C61—21no—
124#95×C61—21no—
125#95×C61—21no—
126#95×C61—21no—
127#95×C61—21no—
128#95×C61—21no—
129#95×C61—21no—
130#95×C61D411yescharacteristic
131#95×C61D411yescharacteristic
132C24×C61—21no—
133C24×C61C2×D411yescharacteristic
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61C2×D412yes—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—42no—
147C2×D4×C61—42no—
148C2×D4×C61—42no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—42no—
161C22×C4×C61—42no—
162C22×C4×C61—42no—
163C22×C4×C61—81no—
164C22×C4×C61—81no—
165C22×C4×C61—81no—
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D412yes—
172C22×C4×C61#4112yes—
173C22×C4×C61C2411yescharacteristic
174SD16×C61—44no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—44no—
187C2×C8×C61#4112yes—
188C4⋊C4×C61—24no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—42no—
200C4⋊C4×C61—42no—
201C4⋊C4×C61—42no—
202C4⋊C4×C61—81no—
203C4⋊C4×C61C2×D412yes—
204C4⋊C4×C61#4112yes—
205C22⋊C4×C61—24no—
206C22⋊C4×C61—22no—
207C22⋊C4×C61—22no—
208C22⋊C4×C61—42no—
209C22⋊C4×C61—81no—
210C22⋊C4×C61—81no—
211C22⋊C4×C61—81no—
212C22⋊C4×C61—81no—
213C42×C61—21no—
214C42×C61—21no—
215C42×C61—21no—
216C42×C61—21no—
217C42×C61—42no—
218C42×C61—81no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61#12112yes—
231C23×C61#13512yes—
232C23×C61#13712yes—
233C23×C61C22×D411yescharacteristic
234Q8×C61—22no—
235Q8×C61—22no—
236Q8×C61—41no—
237Q8×C61—41no—
238D4×C61—41no—
239D4×C61—41no—
240D4×C61—41no—
241D4×C61—41no—
242D4×C61—84no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—22no—
248C2×C4×C61—22no—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—22no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—84no—
283C2×C4×C61—84no—
284C2×C4×C61#12112yes—
285C2×C4×C61C22×D411yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61H(5,𝔽2)11yescharacteristic
290C2×C4×C612−1+411yescharacteristic
291C8×C61—22no—
292C8×C61—41no—
293C8×C61—41no—
294C8×C61—41no—
295#25210C6111yesmaximal, characteristic, direct product factor, Sylow
296C22×C61—22no—
297C22×C61—22no—
298C22×C61—22no—
299C22×C61—22no—
300C22×C61—22no—
301C22×C61—22no—
302C22×C61—81no—
303C22×C61—81no—
304C22×C61—81no—
305C22×C61—81no—
306C22×C61—81no—
307C22×C61—81no—
308C22×C61—81no—
309C22×C61#46414yes—
310C22×C61C2×#12111yescharacteristic
311C22×C61#54611yescharacteristic
312C22×C61#54711yescharacteristic
313C22×C61C2×#13511yescharacteristic
314C22×C61C2×#13711yescharacteristic
315C22×C61#57611yescharacteristic
316C22×C61#57711yescharacteristic
317C4×C61—22no—
318C4×C61—41no—
319C4×C61—41no—
320C4×C61—42no—
321C4×C61—41no—
322C4×C61—42no—
323C4×C61—42no—
324C4×C61—41no—
325C4×C61—81no—
326C4×C61—81no—
327C4×C61—81no—
328C4×C61—81no—
329C4×C61#52911yescharacteristic
330C4×C61#53911yescharacteristic
331C4×C61#54611yescharacteristic
332C4×C61#54711yescharacteristic
333C2×#484C2×C6111yescharacteristic, complemented
334C2×#465C2×C6111yescharacteristic
335#2504C2×C6111yescharacteristic
336#2360C2×C6111yescharacteristic, complemented
337#2085C2×C6111yescharacteristic, complemented
338#2074C2×C6111yescharacteristic, complemented
339#2067C2×C6111yescharacteristic, complemented
340#2055C2×C6111yescharacteristic, complemented
341#1949C2×C6111yescharacteristic, complemented
342#1925C2×C6111yescharacteristic, complemented
343#1880C2×C6111yescharacteristic, complemented
344#1874C2×C6111yescharacteristic
345#1850C2×C6111yescharacteristic, complemented
346#1805C2×C6111yescharacteristic, complemented
347C2×#340C2×C6111yescharacteristic, complemented
348C2×C61—24no—
349C2×C61—161no—
350C2×C61#242511yescharacteristic
351C2×C61C2×#46411yescharacteristic
352C2×C61#304511yescharacteristic
353C2×C61#329711yescharacteristic
354C2×C61#332011yescharacteristic
355C2×C61#333711yescharacteristic
356C2×C61#334611yescharacteristic
357C22×SD16C22×C6111yescharacteristic
358C23×C8C22×C6111yescharacteristic
359C2×C22⋊Q8C22×C6111yescharacteristic
360C2×#121C22×C6111yescharacteristic
361C2×C4×Q8C22×C6111yescharacteristic
362C22×C4⋊C4C22×C6111yescharacteristic
363C22×C4⋊C4C22×C6111yescharacteristic
364#484—24no—
365#465—24no—
366C2×#107C22×C6111yescharacteristic
367C2×#107C22×C6111yescharacteristic
368C2×#106C22×C6111yescharacteristic
369C2×C4⋊C8C22×C6111yescharacteristic
370C2×C4⋊C8C22×C6111yescharacteristic
371C2×#103C22×C6111yescharacteristic
372C2×#103C22×C6111yescharacteristic
373C2×#103C22×C6111yescharacteristic
374C2×#102C22×C6111yescharacteristic
375C2×#102C22×C6111yescharacteristic
376C2×#102C22×C6111yescharacteristic
377C2×C22⋊C8C22×C6111yescharacteristic
378#397—21no—
379#397—21no—
380#391C22×C6111yescharacteristic
381#390C22×C6111yescharacteristic
382#390C22×C6111yescharacteristic
383#389—21no—
384#389C22×C6111yescharacteristic
385#387—21no—
386#386—21no—
387#386—21no—
388#385—21no—
389#382C22×C6111yescharacteristic
390#382C22×C6111yescharacteristic
391C4×C4⋊C4C22×C6111yescharacteristic
392C4×C22⋊C4—21no—
393C4×C22⋊C4C22×C6111yescharacteristic
394#340C22×C6111yescharacteristic
395#340C22×C6111yescharacteristic
396#340C22×C6111yescharacteristic
397#340C22×C6111yescharacteristic
398#340C22×C6111yescharacteristic
399#340C22×C6111yescharacteristic
400#336C22×C6111yescharacteristic
401#336C22×C6111yescharacteristic
402C61#2521011yescharacteristic, direct product factor, Sylow
403C22×Q8C23×C6111yescharacteristic
404C22×D4—21no—
405C22×D4C23×C6111yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408C23×C4C23×C6111yescharacteristic
409C2×SD16—22no—
410C2×SD16—22no—
411C2×SD16—41no—
412C22×C8—22no—
413C22×C8—22no—
414C22×C8—41no—
415C22×C8C23×C6111yescharacteristic
416C22×C8C23×C6111yescharacteristic
417C22×C8C23×C6111yescharacteristic
418C22×C8C23×C6111yescharacteristic
419C22⋊Q8—22no—
420C22⋊Q8D4×C6114yes—
421#121—22no—
422#121—22no—
423C4×Q8—22no—
424C4×Q8—41no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—41no—
434C2×C4⋊C4C23×C6111yescharacteristic
435C2×C4⋊C4C23×C6111yescharacteristic
436C2×C4⋊C4C23×C6111yescharacteristic
437C2×C4⋊C4C23×C6111yescharacteristic
438C2×C4⋊C4C23×C6111yescharacteristic
439C2×C4⋊C4C23×C6111yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4D4×C6111yescharacteristic
447C2×C22⋊C4D4×C6111yescharacteristic
448C2×C42—21no—
449C2×C42—21no—
450C2×C42C23×C6111yescharacteristic
451C2×C42C23×C6111yescharacteristic
452#107—22no—
453#107—22no—
454#106—22no—
455C4⋊C8—22no—
456C4⋊C8—41no—
457#103—22no—
458#103—22no—
459#103—22no—
460#102—22no—
461#102—22no—
462#102—41no—
463C22⋊C8—22no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95D4×C6111yescharacteristic
473#95D4×C6111yescharacteristic
474C24—21no—
475C24C2×D4×C6111yescharacteristic
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8C2×D4×C6112yes—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—42no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4C2×D4×C6111yescharacteristic
509C22×C4C2×D4×C6111yescharacteristic
510C22×C4C2×D4×C6111yescharacteristic
511C22×C4C2×D4×C6111yescharacteristic
512C22×C4C2×D4×C6111yescharacteristic
513C22×C4C2×D4×C6112yes—
514C22×C4#41×C6112yes—
515C22×C4C24×C6111yescharacteristic
516SD16—44no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—44no—
529C2×C8#41×C6112yes—
530C4⋊C4—24no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—81no—
545C4⋊C4C2×D4×C6112yes—
546C4⋊C4#41×C6112yes—
547C22⋊C4—24no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—42no—
551C22⋊C4—81no—
552C22⋊C4—81no—
553C22⋊C4—81no—
554C22⋊C4—81no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—42no—
560C42—81no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23#121×C6112yes—
573C23#135×C6112yes—
574C23#137×C6112yes—
575C23C22×D4×C6111yescharacteristic
576Q8—22no—
577Q8—22no—
578Q8—41no—
579Q8—41no—
580D4—41no—
581D4—41no—
582D4—41no—
583D4—41no—
584D4—84no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—84no—
625C2×C4—84no—
626C2×C4#121×C6112yes—
627C2×C4C22×D4×C6111yescharacteristic
628C2×C4C2×#41×C6111yescharacteristic
629C2×C4C2×#41×C6111yescharacteristic
630C2×C4C2×#41×C6111yescharacteristic
631C2×C4H(5,𝔽2)×C6111yescharacteristic
632C2×C42−1+4×C6111yescharacteristic
633C8—22no—
634C8—41no—
635C8—41no—
636C8—41no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22C61×#46414yes—
651C22C2×#121×C6111yescharacteristic
652C22C61×#54611yescharacteristic
653C22C61×#54711yescharacteristic
654C22C2×#135×C6111yescharacteristic
655C22C2×#137×C6111yescharacteristic
656C22C61×#57611yescharacteristic
657C22C61×#57711yescharacteristic
658C4—22no—
659C4—41no—
660C4—42no—
661C4—42no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—42no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4C61×#52911yescharacteristic
671C4C61×#53911yescharacteristic
672C4C61×#54611yescharacteristic
673C4C61×#54711yescharacteristic
674C2—24no—
675C2—161no—
676C2C61×#242511yescharacteristic
677C2C2×C61×#46411yescharacteristic
678C2C61×#304511yescharacteristic
679C2C61×#329711yescharacteristic
680C2C61×#332011yescharacteristic
681C2C61×#333711yescharacteristic
682C2C61×#334611yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×#121×C61C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C4×C22⋊C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#484C2semidirect
4. C61×#2360C2semidirect
5. C61×#2085C2semidirect
6. C61×#2074C2semidirect
7. C61×#2067C2semidirect
8. C61×#2055C2semidirect
9. C61×#1949C2semidirect
10. C61×#1925C2semidirect
11. C61×#1880C2semidirect
13. C61×#1850C2semidirect
14. C61×#1805C2semidirect
15. C2×C61×#340C2semidirect
295. #25210C61direct (N × H)
333. C2×#484C2×C61semidirect
336. #2360C2×C61semidirect
337. #2085C2×C61semidirect
338. #2074C2×C61semidirect
339. #2067C2×C61semidirect
340. #2055C2×C61semidirect
341. #1949C2×C61semidirect
342. #1925C2×C61semidirect
343. #1880C2×C61semidirect
345. #1850C2×C61semidirect
346. #1805C2×C61semidirect
347. C2×#340C2×C61semidirect
402. C61#25210direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#4842
C2×C61×#4652
C61×#25042
C61×#23602
C61×#20852
C61×#20742
C61×#20672
C61×#20552
C61×#19492
C61×#19252
C61×#18802
C61×#18742
C61×#18502
C61×#18052
C2×C61×#3402
#2521061