Finite Group Databasebeta

← C61×#18252 #29521685

Subgroups — C61×#18252 #29521685

Order 15616.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3534C211yesmaximal, characteristic, complemented
2C61×#3006C211yesmaximal, characteristic, complemented
3C61×#3002C211yesmaximal, characteristic, complemented
4C61×#2430C211yesmaximal, characteristic, complemented
5C61×#1606C211yesmaximal, characteristic, complemented
6C61×#1604C211yesmaximal, characteristic, complemented
7C61×#1603C211yesmaximal, characteristic, complemented
8C61×#1601C211yesmaximal, characteristic, complemented
9C61×#1600C211yesmaximal, characteristic, complemented
10C61×#1598C211yesmaximal, characteristic, complemented
11C61×#1597C211yesmaximal, characteristic, complemented
12C61×#1595C211yesmaximal, characteristic, complemented
13C61×#1504C211yesmaximal, characteristic, complemented
14C2×C61×#327C211yesmaximal, characteristic, complemented
15C61×#1468C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic, complemented
17C2×AGL(1,ℤ/8)×C61—21no—
18C2×#135×C61—21no—
19C61×#562—21no—
20C61×#560—21no—
21C61×#553—21no—
22C61×#551—21no—
23C61×#546—21no—
24C61×#546—21no—
25C61×#546—21no—
26D42×C61—21no—
27C61×#540—21no—
28C61×#539—21no—
29C61×#539C2211yescharacteristic
30C61×#538—21no—
31C61×#538C2211yescharacteristic
32C61×#537C2211yescharacteristic
33C61×#534—21no—
34C61×#534C2211yescharacteristic
35C61×#525C2211yescharacteristic
36C2×#123×C61C2211yescharacteristic
37C2×#121×C61—21no—
38C2×#121×C61C2211yescharacteristic
39C61×#452—21no—
40C61×#451C2211yescharacteristic, complemented
41C61×#450C2211yescharacteristic, complemented
42C61×#449—21no—
43C61×#449—21no—
44C61×#449—21no—
45C61×#448C2211yescharacteristic
46C61×#448C2211yescharacteristic, complemented
47C61×#448C2211yescharacteristic, complemented
48C61×#447C2211yescharacteristic
49C61×#447C2211yescharacteristic, complemented
50C61×#447C2211yescharacteristic, complemented
51C61×#417—21no—
52C61×#416—21no—
53C61×#407C2211yescharacteristic, complemented
54C2×C22⋊C8×C61C2211yescharacteristic, complemented
55C61×#395C2211yescharacteristic, complemented
56C61×#394C2211yescharacteristic, complemented
57C61×#393C2211yescharacteristic, complemented
58C61×#392C2211yescharacteristic, complemented
59C61×#386—21no—
60C61×#386—21no—
61C61×#385—21no—
62C2×#95×C61C2211yescharacteristic, complemented
63C61×#328C2211yescharacteristic, complemented
64C61×#328C2211yescharacteristic, complemented
65C61×#327C2211yescharacteristic
66C61×#327C2211yescharacteristic
67C61×#327C2211yescharacteristic, complemented
68C61×#327C2211yescharacteristic, complemented
69C61×#327C2211yescharacteristic, complemented
70C61×#327C2211yescharacteristic, complemented
71C61×#324C2211yescharacteristic, complemented
72C61×#324C2211yescharacteristic, complemented
73C61×#323C2211yescharacteristic, complemented
74C61×#323C2211yescharacteristic, complemented
75C2×#41×C61—21no—
76C2×#41×C61—21no—
77C2×#41×C61—21no—
78C2×#41×C61—21no—
79C2×#41×C61—21no—
80C2×#41×C61—44no—
81C2×#41×C61D411yescharacteristic, complemented
82C22×Q8×C61C2311yescharacteristic
83C22×D4×C61—21no—
84C22×D4×C61—21no—
85C22×D4×C61—21no—
86C22×D4×C61—21no—
87C22×D4×C61—21no—
88C22×D4×C61D411yescharacteristic
89C22×D4×C61D411yescharacteristic, complemented
90C22×D4×C61C2311yescharacteristic
91C23×C4×C61—21no—
92C23×C4×C61—21no—
93C23×C4×C61C2311yescharacteristic
94AGL(1,ℤ/8)×C61—44no—
95#135×C61—44no—
96C2×Q16×C61—21no—
97C2×SD16×C61—21no—
98C2×SD16×C61—21no—
99C2×SD16×C61—21no—
100C2×SD16×C61—21no—
101C2×D8×C61—21no—
102C2×D8×C61—21no—
103C2×D8×C61—21no—
104C2×M16×C61—21no—
105C22×C8×C61—21no—
106#127×C61—21no—
107#126×C61—21no—
108#126×C61—21no—
109#126×C61—21no—
110#126×C61—21no—
111#125×C61—21no—
112#125×C61—21no—
113#124×C61—21no—
114#124×C61—21no—
115#124×C61—21no—
116#123×C61—21no—
117#123×C61—21no—
118#123×C61—21no—
119#123×C61—21no—
120#123×C61—21no—
121#123×C61—21no—
122#123×C61—21no—
123#123×C61—21no—
124#123×C61—21no—
125#123×C61—21no—
126#123×C61—21no—
127#123×C61—21no—
128#123×C61—21no—
129#123×C61—21no—
130C22⋊Q8×C61—21no—
131C22⋊Q8×C61—21no—
132C22⋊Q8×C61—21no—
133C22⋊Q8×C61—21no—
134C22⋊Q8×C61—21no—
135C22⋊Q8×C61D411yescharacteristic, complemented
136C22⋊Q8×C61C2311yescharacteristic
137#121×C61—21no—
138#121×C61—21no—
139#121×C61—21no—
140#121×C61—21no—
141#121×C61—21no—
142#121×C61—21no—
143#121×C61—21no—
144#121×C61—21no—
145#121×C61—21no—
146#121×C61—21no—
147#121×C61—21no—
148#121×C61—21no—
149#121×C61—21no—
150#121×C61—21no—
151#121×C61—21no—
152#121×C61—44no—
153#121×C61D411yescharacteristic, complemented
154#121×C61D411yescharacteristic, complemented
155#121×C61D411yescharacteristic, complemented
156#121×C61C2311yescharacteristic
157#121×C61C2311yescharacteristic
158#121×C61C2311yescharacteristic
159#120×C61—21no—
160#120×C61—21no—
161#120×C61—21no—
162#120×C61—21no—
163#120×C61—21no—
164#120×C61—21no—
165#120×C61—21no—
166#120×C61—21no—
167C4×D4×C61—21no—
168C4×D4×C61—21no—
169C4×D4×C61—21no—
170C4×D4×C61—21no—
171C4×D4×C61—21no—
172C4×D4×C61—21no—
173C4×D4×C61—21no—
174C4×D4×C61—21no—
175#117×C61—21no—
176#117×C61D411yescharacteristic, complemented
177C2×C4⋊C4×C61—21no—
178C2×C4⋊C4×C61D411yescharacteristic
179C2×C4⋊C4×C61D411yescharacteristic, complemented
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C22⋊C4×C61—21no—
182C2×C22⋊C4×C61—21no—
183C2×C22⋊C4×C61—21no—
184C2×C22⋊C4×C61—21no—
185C2×C22⋊C4×C61—21no—
186C2×C22⋊C4×C61—21no—
187C2×C22⋊C4×C61—21no—
188C2×C22⋊C4×C61D411yescharacteristic
189C2×C22⋊C4×C61D411yescharacteristic
190C2×C22⋊C4×C61C2311yescharacteristic
191#103×C61—21no—
192#103×C61—21no—
193#103×C61—21no—
194#103×C61—21no—
195#102×C61—21no—
196#102×C61—21no—
197#102×C61—21no—
198#102×C61—21no—
199C22⋊C8×C61—21no—
200C22⋊C8×C61—21no—
201C22⋊C8×C61C2311yescharacteristic
202C22⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61C2311yescharacteristic
204C22⋊C8×C61C2311yescharacteristic
205#95×C61—21no—
206#95×C61—21no—
207#95×C61—21no—
208#95×C61C2311yescharacteristic
209#95×C61C2311yescharacteristic
210C24×C61—21no—
211C24×C61—21no—
212C24×C61—21no—
213C24×C61C2×D411yescharacteristic
214C24×C61C2×D411yescharacteristic
215#41×C61—24no—
216#41×C61—24no—
217#41×C61—42no—
218#41×C61—42no—
219#41×C61—42no—
220#41×C61—42no—
221#41×C61—42no—
222#41×C61—42no—
223#41×C61—42no—
224#41×C61—81no—
225#41×C61—81no—
226C2×Q8×C61—21no—
227C2×Q8×C61—21no—
228C2×Q8×C61—21no—
229C2×Q8×C61—42no—
230C2×Q8×C61C2×D411yescharacteristic
231C2×D4×C61—24no—
232C2×D4×C61—21no—
233C2×D4×C61—21no—
234C2×D4×C61—21no—
235C2×D4×C61—21no—
236C2×D4×C61—21no—
237C2×D4×C61—21no—
238C2×D4×C61—21no—
239C2×D4×C61—21no—
240C2×D4×C61—21no—
241C2×D4×C61—21no—
242C2×D4×C61—21no—
243C2×D4×C61—21no—
244C2×D4×C61—21no—
245C2×D4×C61—21no—
246C2×D4×C61—21no—
247C2×D4×C61—21no—
248C2×D4×C61—21no—
249C2×D4×C61—21no—
250C2×D4×C61—21no—
251C2×D4×C61—42no—
252C2×D4×C61—42no—
253C2×D4×C61—42no—
254C2×D4×C61—42no—
255C2×D4×C61—41no—
256C2×D4×C61—41no—
257C2×D4×C61—42no—
258C2×D4×C61—42no—
259C2×D4×C61—81no—
260C2×D4×C61—81no—
261C2×D4×C61—81no—
262C2×D4×C61—81no—
263C2×D4×C61—81no—
264C2×D4×C61—82no—
265C2×D4×C61C2×D411yescharacteristic
266C2×D4×C61C2×D411yescharacteristic
267C2×D4×C61C2×D411yescharacteristic
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—42no—
279C22×C4×C61—42no—
280C22×C4×C61—42no—
281C22×C4×C61—42no—
282C22×C4×C61—41no—
283C22×C4×C61—41no—
284C22×C4×C61—42no—
285C22×C4×C61—81no—
286C22×C4×C61C2×D411yescharacteristic
287C22×C4×C61C2×D411yescharacteristic
288C22×C4×C61C2×D411yescharacteristic
289C22×C4×C61C2×D411yescharacteristic
290C22×C4×C61C2×D411yescharacteristic
291C22×C4×C61C2×D411yescharacteristic
292C22×C4×C61C2×D411yescharacteristic
293C22×C4×C61C2×D411yescharacteristic
294C22×C4×C61C2411yescharacteristic
295Q16×C61—42no—
296SD16×C61—42no—
297SD16×C61—42no—
298SD16×C61—42no—
299SD16×C61—42no—
300D8×C61—42no—
301D8×C61—42no—
302D8×C61—42no—
303M16×C61—42no—
304C2×C8×C61—21no—
305C2×C8×C61—21no—
306C2×C8×C61—21no—
307C2×C8×C61—21no—
308C2×C8×C61—42no—
309C4⋊C4×C61—21no—
310C4⋊C4×C61—21no—
311C4⋊C4×C61—21no—
312C4⋊C4×C61—21no—
313C4⋊C4×C61—21no—
314C4⋊C4×C61—21no—
315C4⋊C4×C61—21no—
316C4⋊C4×C61—21no—
317C4⋊C4×C61—21no—
318C4⋊C4×C61—21no—
319C4⋊C4×C61—21no—
320C4⋊C4×C61—21no—
321C4⋊C4×C61—21no—
322C4⋊C4×C61—42no—
323C4⋊C4×C61C2×D411yescharacteristic
324C4⋊C4×C61C2×D411yescharacteristic
325C4⋊C4×C61C2×D411yescharacteristic
326C4⋊C4×C61C2×D411yescharacteristic
327C22⋊C4×C61—21no—
328C22⋊C4×C61—21no—
329C22⋊C4×C61—21no—
330C22⋊C4×C61—21no—
331C22⋊C4×C61—21no—
332C22⋊C4×C61—21no—
333C22⋊C4×C61—21no—
334C22⋊C4×C61—21no—
335C22⋊C4×C61—21no—
336C22⋊C4×C61—21no—
337C22⋊C4×C61—21no—
338C22⋊C4×C61—21no—
339C22⋊C4×C61—21no—
340C22⋊C4×C61—21no—
341C22⋊C4×C61—21no—
342C22⋊C4×C61—21no—
343C22⋊C4×C61—21no—
344C22⋊C4×C61—21no—
345C22⋊C4×C61—21no—
346C22⋊C4×C61—21no—
347C22⋊C4×C61—21no—
348C22⋊C4×C61—21no—
349C22⋊C4×C61—21no—
350C22⋊C4×C61—21no—
351C22⋊C4×C61—21no—
352C22⋊C4×C61—42no—
353C22⋊C4×C61—42no—
354C22⋊C4×C61—42no—
355C22⋊C4×C61—81no—
356C42×C61—21no—
357C42×C61—21no—
358C42×C61—21no—
359C23×C61—21no—
360C23×C61—21no—
361C23×C61—22no—
362C23×C61—22no—
363C23×C61—21no—
364C23×C61—21no—
365C23×C61—21no—
366C23×C61—21no—
367C23×C61—21no—
368C23×C61—21no—
369C23×C61—41no—
370C23×C61—41no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61—41no—
375C23×C61—41no—
376C23×C61—41no—
377C23×C61—41no—
378C23×C61—42no—
379C23×C61—81no—
380C23×C61—81no—
381C23×C61—81no—
382C23×C61—81no—
383C23×C61—81no—
384C23×C61#12011yescharacteristic
385C23×C61#12011yescharacteristic
386C23×C61C22×D411yescharacteristic
387Q8×C61—22no—
388Q8×C61—22no—
389Q8×C61—41no—
390Q8×C61—41no—
391Q8×C61—41no—
392Q8×C61—81no—
393D4×C61—22no—
394D4×C61—22no—
395D4×C61—41no—
396D4×C61—41no—
397D4×C61—41no—
398D4×C61—41no—
399D4×C61—41no—
400D4×C61—44no—
401D4×C61—41no—
402D4×C61—41no—
403D4×C61—41no—
404D4×C61—41no—
405D4×C61—41no—
406D4×C61—41no—
407D4×C61—44no—
408D4×C61—42no—
409D4×C61—42no—
410D4×C61—81no—
411D4×C61—81no—
412D4×C61—81no—
413D4×C61—81no—
414D4×C61—81no—
415D4×C61—81no—
416D4×C61—81no—
417D4×C61—81no—
418D4×C61—81no—
419D4×C61—81no—
420D4×C61—81no—
421D4×C61—81no—
422D4×C61—84no—
423C2×C4×C61—22no—
424C2×C4×C61—22no—
425C2×C4×C61—22no—
426C2×C4×C61—22no—
427C2×C4×C61—21no—
428C2×C4×C61—21no—
429C2×C4×C61—21no—
430C2×C4×C61—21no—
431C2×C4×C61—21no—
432C2×C4×C61—21no—
433C2×C4×C61—21no—
434C2×C4×C61—21no—
435C2×C4×C61—21no—
436C2×C4×C61—21no—
437C2×C4×C61—41no—
438C2×C4×C61—41no—
439C2×C4×C61—41no—
440C2×C4×C61—41no—
441C2×C4×C61—44no—
442C2×C4×C61—44no—
443C2×C4×C61—41no—
444C2×C4×C61—41no—
445C2×C4×C61—41no—
446C2×C4×C61—41no—
447C2×C4×C61—41no—
448C2×C4×C61—41no—
449C2×C4×C61—41no—
450C2×C4×C61—41no—
451C2×C4×C61—41no—
452C2×C4×C61—81no—
453C2×C4×C61—81no—
454C2×C4×C61—81no—
455C2×C4×C61—81no—
456C2×C4×C61—81no—
457C2×C4×C61—81no—
458C2×C4×C61—81no—
459C2×C4×C61—84no—
460C2×C4×C61#12011yescharacteristic
461C2×C4×C61#12011yescharacteristic
462C2×C4×C61C22×D411yescharacteristic
463C2×C4×C61C22×D411yescharacteristic
464C8×C61—41no—
465C8×C61—41no—
466C8×C61—41no—
467C8×C61—41no—
468#18252C6111yesmaximal, characteristic, direct product factor, Sylow
469C22×C61—21no—
470C22×C61—21no—
471C22×C61—21no—
472C22×C61—21no—
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—42no—
477C22×C61—42no—
478C22×C61—42no—
479C22×C61—42no—
480C22×C61—41no—
481C22×C61—41no—
482C22×C61—41no—
483C22×C61—41no—
484C22×C61—41no—
485C22×C61—41no—
486C22×C61—41no—
487C22×C61—41no—
488C22×C61—42no—
489C22×C61—41no—
490C22×C61—41no—
491C22×C61—41no—
492C22×C61—41no—
493C22×C61—81no—
494C22×C61—81no—
495C22×C61—81no—
496C22×C61—81no—
497C22×C61—81no—
498C22×C61—81no—
499C22×C61—162no—
500C22×C61—162no—
501C22×C61B(4,𝔽2)12yes—
502C22×C61C2×#12011yescharacteristic
503C22×C61#57611yescharacteristic
504C22×C61#57711yescharacteristic
505C4×C61—21no—
506C4×C61—21no—
507C4×C61—21no—
508C4×C61—21no—
509C4×C61—42no—
510C4×C61—41no—
511C4×C61—41no—
512C4×C61—41no—
513C4×C61—41no—
514C4×C61—41no—
515C4×C61—41no—
516C4×C61—42no—
517C4×C61—41no—
518C4×C61—41no—
519C4×C61—81no—
520#3534C2×C6111yescharacteristic, complemented
521#3006C2×C6111yescharacteristic, complemented
522#3002C2×C6111yescharacteristic, complemented
523#2430C2×C6111yescharacteristic, complemented
524#1606C2×C6111yescharacteristic, complemented
525#1604C2×C6111yescharacteristic, complemented
526#1603C2×C6111yescharacteristic, complemented
527#1601C2×C6111yescharacteristic, complemented
528#1600C2×C6111yescharacteristic, complemented
529#1598C2×C6111yescharacteristic, complemented
530#1597C2×C6111yescharacteristic, complemented
531#1595C2×C6111yescharacteristic, complemented
532#1504C2×C6111yescharacteristic, complemented
533C2×#327C2×C6111yescharacteristic, complemented
534#1468C2×C6111yescharacteristic, complemented
535C2×C61—21no—
536C2×C61—21no—
537C2×C61—22no—
538C2×C61—41no—
539C2×C61—82no—
540C2×C61—81no—
541C2×C61—81no—
542C2×C61—81no—
543C2×C61—81no—
544C2×C61#301211yescharacteristic
545C2×C61#301811yescharacteristic
546C2×C61C2×B(4,𝔽2)11yescharacteristic
547C22×#41C22×C6111yescharacteristic, complemented
548C2×AGL(1,ℤ/8)—21no—
549C2×#135—21no—
550#562—21no—
551#560—21no—
552#553—21no—
553#551—21no—
554#546—21no—
555#546—21no—
556#546—21no—
557D42—21no—
558#540—21no—
559#539—21no—
560#539C22×C6111yescharacteristic
561#538—21no—
562#538C22×C6111yescharacteristic
563#537C22×C6111yescharacteristic
564#534—21no—
565#534C22×C6111yescharacteristic
566#525C22×C6111yescharacteristic
567C2×#123C22×C6111yescharacteristic
568C2×#121—21no—
569C2×#121C22×C6111yescharacteristic
570#452—21no—
571#451C22×C6111yescharacteristic, complemented
572#450C22×C6111yescharacteristic, complemented
573#449—21no—
574#449—21no—
575#449—21no—
576#448C22×C6111yescharacteristic
577#448C22×C6111yescharacteristic, complemented
578#448C22×C6111yescharacteristic, complemented
579#447C22×C6111yescharacteristic
580#447C22×C6111yescharacteristic, complemented
581#447C22×C6111yescharacteristic, complemented
582#417—21no—
583#416—21no—
584#407C22×C6111yescharacteristic, complemented
585C2×C22⋊C8C22×C6111yescharacteristic, complemented
586#395C22×C6111yescharacteristic, complemented
587#394C22×C6111yescharacteristic, complemented
588#393C22×C6111yescharacteristic, complemented
589#392C22×C6111yescharacteristic, complemented
590#386—21no—
591#386—21no—
592#385—21no—
593C2×#95C22×C6111yescharacteristic, complemented
594#328C22×C6111yescharacteristic, complemented
595#328C22×C6111yescharacteristic, complemented
596#327C22×C6111yescharacteristic
597#327C22×C6111yescharacteristic
598#327C22×C6111yescharacteristic, complemented
599#327C22×C6111yescharacteristic, complemented
600#327C22×C6111yescharacteristic, complemented
601#327C22×C6111yescharacteristic, complemented
602#324C22×C6111yescharacteristic, complemented
603#324C22×C6111yescharacteristic, complemented
604#323C22×C6111yescharacteristic, complemented
605#323C22×C6111yescharacteristic, complemented
606C61#1825211yescharacteristic, direct product factor, Sylow
607C2×#41—21no—
608C2×#41—21no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—44no—
613C2×#41D4×C6111yescharacteristic, complemented
614C22×Q8C23×C6111yescharacteristic
615C22×D4—21no—
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4D4×C6111yescharacteristic
621C22×D4D4×C6111yescharacteristic, complemented
622C22×D4C23×C6111yescharacteristic
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C6111yescharacteristic
626AGL(1,ℤ/8)—44no—
627#135—44no—
628C2×Q16—21no—
629C2×SD16—21no—
630C2×SD16—21no—
631C2×SD16—21no—
632C2×SD16—21no—
633C2×D8—21no—
634C2×D8—21no—
635C2×D8—21no—
636C2×M16—21no—
637C22×C8—21no—
638#127—21no—
639#126—21no—
640#126—21no—
641#126—21no—
642#126—21no—
643#125—21no—
644#125—21no—
645#124—21no—
646#124—21no—
647#124—21no—
648#123—21no—
649#123—21no—
650#123—21no—
651#123—21no—
652#123—21no—
653#123—21no—
654#123—21no—
655#123—21no—
656#123—21no—
657#123—21no—
658#123—21no—
659#123—21no—
660#123—21no—
661#123—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8D4×C6111yescharacteristic, complemented
668C22⋊Q8C23×C6111yescharacteristic
669#121—21no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—44no—
685#121D4×C6111yescharacteristic, complemented
686#121D4×C6111yescharacteristic, complemented
687#121D4×C6111yescharacteristic, complemented
688#121C23×C6111yescharacteristic
689#121C23×C6111yescharacteristic
690#121C23×C6111yescharacteristic
691#120—21no—
692#120—21no—
693#120—21no—
694#120—21no—
695#120—21no—
696#120—21no—
697#120—21no—
698#120—21no—
699C4×D4—21no—
700C4×D4—21no—
701C4×D4—21no—
702C4×D4—21no—
703C4×D4—21no—
704C4×D4—21no—
705C4×D4—21no—
706C4×D4—21no—
707#117—21no—
708#117D4×C6111yescharacteristic, complemented
709C2×C4⋊C4—21no—
710C2×C4⋊C4D4×C6111yescharacteristic
711C2×C4⋊C4D4×C6111yescharacteristic, complemented
712C2×C4⋊C4C23×C6111yescharacteristic
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4D4×C6111yescharacteristic
721C2×C22⋊C4D4×C6111yescharacteristic
722C2×C22⋊C4C23×C6111yescharacteristic
723#103—21no—
724#103—21no—
725#103—21no—
726#103—21no—
727#102—21no—
728#102—21no—
729#102—21no—
730#102—21no—
731C22⋊C8—21no—
732C22⋊C8—21no—
733C22⋊C8C23×C6111yescharacteristic
734C22⋊C8C23×C6111yescharacteristic
735C22⋊C8C23×C6111yescharacteristic
736C22⋊C8C23×C6111yescharacteristic
737#95—21no—
738#95—21no—
739#95—21no—
740#95C23×C6111yescharacteristic
741#95C23×C6111yescharacteristic
742C24—21no—
743C24—21no—
744C24—21no—
745C24C2×D4×C6111yescharacteristic
746C24C2×D4×C6111yescharacteristic
747#41—24no—
748#41—24no—
749#41—42no—
750#41—42no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—42no—
756#41—81no—
757#41—81no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8C2×D4×C6111yescharacteristic
763C2×D4—24no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—82no—
797C2×D4C2×D4×C6111yescharacteristic
798C2×D4C2×D4×C6111yescharacteristic
799C2×D4C2×D4×C6111yescharacteristic
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—42no—
817C22×C4—81no—
818C22×C4C2×D4×C6111yescharacteristic
819C22×C4C2×D4×C6111yescharacteristic
820C22×C4C2×D4×C6111yescharacteristic
821C22×C4C2×D4×C6111yescharacteristic
822C22×C4C2×D4×C6111yescharacteristic
823C22×C4C2×D4×C6111yescharacteristic
824C22×C4C2×D4×C6111yescharacteristic
825C22×C4C2×D4×C6111yescharacteristic
826C22×C4C24×C6111yescharacteristic
827Q16—42no—
828SD16—42no—
829SD16—42no—
830SD16—42no—
831SD16—42no—
832D8—42no—
833D8—42no—
834D8—42no—
835M16—42no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—42no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—42no—
855C4⋊C4C2×D4×C6111yescharacteristic
856C4⋊C4C2×D4×C6111yescharacteristic
857C4⋊C4C2×D4×C6111yescharacteristic
858C4⋊C4C2×D4×C6111yescharacteristic
859C22⋊C4—21no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—21no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—81no—
888C42—21no—
889C42—21no—
890C42—21no—
891C23—21no—
892C23—21no—
893C23—22no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—42no—
911C23—81no—
912C23—81no—
913C23—81no—
914C23—81no—
915C23—81no—
916C23#120×C6111yescharacteristic
917C23#120×C6111yescharacteristic
918C23C22×D4×C6111yescharacteristic
919Q8—22no—
920Q8—22no—
921Q8—41no—
922Q8—41no—
923Q8—41no—
924Q8—81no—
925D4—22no—
926D4—22no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—44no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—44no—
940D4—42no—
941D4—42no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—81no—
951D4—81no—
952D4—81no—
953D4—81no—
954D4—84no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—84no—
992C2×C4#120×C6111yescharacteristic
993C2×C4#120×C6111yescharacteristic
994C2×C4C22×D4×C6111yescharacteristic
995C2×C4C22×D4×C6111yescharacteristic
996C8—41no—
997C8—41no—
998C8—41no—
999C8—41no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—162no—
1031C22—162no—
1032C22C61×B(4,𝔽2)12yes—
1033C22C2×#120×C6111yescharacteristic
1034C22C61×#57611yescharacteristic
1035C22C61×#57711yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C2—21no—
1052C2—21no—
1053C2—22no—
1054C2—41no—
1055C2—82no—
1056C2—81no—
1057C2—81no—
1058C2—81no—
1059C2—81no—
1060C2C61×#301211yescharacteristic
1061C2C61×#301811yescharacteristic
1062C2C2×C61×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3534C2semidirect
2. C61×#3006C2semidirect
3. C61×#3002C2semidirect
4. C61×#2430C2semidirect
5. C61×#1606C2semidirect
6. C61×#1604C2semidirect
7. C61×#1603C2semidirect
8. C61×#1601C2semidirect
9. C61×#1600C2semidirect
10. C61×#1598C2semidirect
11. C61×#1597C2semidirect
12. C61×#1595C2semidirect
13. C61×#1504C2semidirect
14. C2×C61×#327C2semidirect
15. C61×#1468C2semidirect
16. C22×#41×C61C22semidirect
40. C61×#451C22semidirect
41. C61×#450C22semidirect
46. C61×#448C22semidirect
47. C61×#448C22semidirect
49. C61×#447C22semidirect
50. C61×#447C22semidirect
53. C61×#407C22semidirect
54. C2×C22⋊C8×C61C22semidirect
55. C61×#395C22semidirect
56. C61×#394C22semidirect
57. C61×#393C22semidirect
58. C61×#392C22semidirect
62. C2×#95×C61C22semidirect
63. C61×#328C22semidirect
64. C61×#328C22semidirect
67. C61×#327C22semidirect
68. C61×#327C22semidirect
69. C61×#327C22semidirect
70. C61×#327C22semidirect
71. C61×#324C22semidirect
72. C61×#324C22semidirect
73. C61×#323C22semidirect
74. C61×#323C22semidirect
81. C2×#41×C61D4semidirect
89. C22×D4×C61D4semidirect
135. C22⋊Q8×C61D4semidirect
153. #121×C61D4semidirect
154. #121×C61D4semidirect
155. #121×C61D4semidirect
176. #117×C61D4semidirect
179. C2×C4⋊C4×C61D4semidirect
468. #18252C61direct (N × H)
520. #3534C2×C61semidirect
521. #3006C2×C61semidirect
522. #3002C2×C61semidirect
523. #2430C2×C61semidirect
524. #1606C2×C61semidirect
525. #1604C2×C61semidirect
526. #1603C2×C61semidirect
527. #1601C2×C61semidirect
528. #1600C2×C61semidirect
529. #1598C2×C61semidirect
530. #1597C2×C61semidirect
531. #1595C2×C61semidirect
532. #1504C2×C61semidirect
533. C2×#327C2×C61semidirect
534. #1468C2×C61semidirect
547. C22×#41C22×C61semidirect
571. #451C22×C61semidirect
572. #450C22×C61semidirect
577. #448C22×C61semidirect
578. #448C22×C61semidirect
580. #447C22×C61semidirect
581. #447C22×C61semidirect
584. #407C22×C61semidirect
585. C2×C22⋊C8C22×C61semidirect
586. #395C22×C61semidirect
587. #394C22×C61semidirect
588. #393C22×C61semidirect
589. #392C22×C61semidirect
593. C2×#95C22×C61semidirect
594. #328C22×C61semidirect
595. #328C22×C61semidirect
598. #327C22×C61semidirect
599. #327C22×C61semidirect
600. #327C22×C61semidirect
601. #327C22×C61semidirect
602. #324C22×C61semidirect
603. #324C22×C61semidirect
604. #323C22×C61semidirect
605. #323C22×C61semidirect
606. C61#18252direct (N × H)
613. C2×#41D4×C61semidirect
621. C22×D4D4×C61semidirect
667. C22⋊Q8D4×C61semidirect
685. #121D4×C61semidirect
686. #121D4×C61semidirect
687. #121D4×C61semidirect
708. #117D4×C61semidirect
711. C2×C4⋊C4D4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#35342
C61×#30062
C61×#30022
C61×#24302
C61×#16062
C61×#16042
C61×#16032
C61×#16012
C61×#16002
C61×#15982
C61×#15972
C61×#15952
C61×#15042
C2×C61×#3272
C61×#14682
#1825261