Finite Group Databasebeta

← C61×#24471 #29527904

Subgroups — C61×#24471 #29527904

Order 15616.

1444 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×#3488C211yesmaximal, characteristic
2C61×#3056C211yesmaximal, characteristic, complemented
3C2×C61×#455C211yesmaximal, characteristic, complemented
4C61×#3007C211yesmaximal, characteristic, complemented
5C2×C61×#421C211yesmaximal, characteristic, complemented
6C61×#2620C211yesmaximal, characteristic, complemented
7C61×#2039C211yesmaximal, characteristic, complemented
8C61×#2037C211yesmaximal, characteristic, complemented
9C61×#2007C211yesmaximal, characteristic, complemented
10C61×#2004C211yesmaximal, characteristic, complemented
11C61×#1900C211yesmaximal, characteristic, complemented
12C61×#1897C211yesmaximal, characteristic, complemented
13C61×#1882C211yesmaximal, characteristic, complemented
14C61×#1859C211yesmaximal, characteristic, complemented
15C61×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C61C2211yescharacteristic
17C22×#41×C61C2211yescharacteristic
18C2×#137×C61C2211yescharacteristic
19C2×#137×C61C2211yescharacteristic, complemented
20C2×#137×C61C2211yescharacteristic, complemented
21C22×M16×C61C2211yescharacteristic, complemented
22C61×#550—21no—
23C61×#548—21no—
24C61×#546—21no—
25C61×#546—22no—
26D42×C61—22no—
27D42×C61—21no—
28C61×#537—21no—
29C61×#537C2211yescharacteristic
30C61×#535—21no—
31C61×#535C2211yescharacteristic
32C2×#124×C61C2211yescharacteristic, complemented
33C61×#525—21no—
34C61×#525C2211yescharacteristic
35C2×C22⋊Q8×C61C2211yescharacteristic, complemented
36C2×#121×C61—21no—
37C2×#121×C61C2211yescharacteristic
38C61×#520C2211yescharacteristic
39C2×#117×C61C2211yescharacteristic, complemented
40C61×#470—21no—
41C61×#468—21no—
42C61×#467—21no—
43C61×#465—21no—
44C61×#455—24no—
45C61×#452—21no—
46C61×#452—21no—
47C61×#451—21no—
48C61×#450—21no—
49C61×#428C2211yescharacteristic, complemented
50C61×#421—24no—
51C2×#104×C61C2211yescharacteristic
52C2×#104×C61C2211yescharacteristic
53C2×#104×C61C2211yescharacteristic, complemented
54C2×#104×C61C2211yescharacteristic, complemented
55C2×#104×C61C2211yescharacteristic, complemented
56C2×#104×C61C2211yescharacteristic, complemented
57C61×#419C2211yescharacteristic, complemented
58C61×#417C2211yescharacteristic
59C61×#417C2211yescharacteristic, complemented
60C61×#417C2211yescharacteristic, complemented
61C2×#100×C61C2211yescharacteristic, complemented
62C2×#100×C61C2211yescharacteristic, complemented
63C61×#407C2211yescharacteristic, complemented
64C61×#396—22no—
65C61×#394—22no—
66C61×#391C2211yescharacteristic, complemented
67C61×#390C2211yescharacteristic, complemented
68C61×#384C2211yescharacteristic, complemented
69C61×#343C2211yescharacteristic, complemented
70C61×#343C2211yescharacteristic, complemented
71C61×#339C2211yescharacteristic, complemented
72C61×#339C2211yescharacteristic, complemented
73H(5,𝔽2)×C61—22no—
74H(5,𝔽2)×C61—22no—
75H(5,𝔽2)×C61—41no—
76H(5,𝔽2)×C61—41no—
77C2×#41×C61—21no—
78C2×#41×C61—21no—
79C2×#41×C61—21no—
80C2×#41×C61—21no—
81C2×#41×C61—22no—
82C2×#41×C61—22no—
83C2×#41×C61—41no—
84C2×#41×C61—41no—
85C2×#41×C61D411yescharacteristic
86C2×#41×C61D411yescharacteristic
87C2×#41×C61C2311yescharacteristic
88C2×#41×C61C2311yescharacteristic
89C2×#41×C61C2311yescharacteristic
90C22×Q8×C61D411yescharacteristic
91C22×Q8×C61C2311yescharacteristic
92C22×D4×C61—21no—
93C22×D4×C61—22no—
94C22×D4×C61—22no—
95C22×D4×C61—21no—
96C22×D4×C61—21no—
97C22×D4×C61D411yescharacteristic
98C22×D4×C61D412yes—
99C22×D4×C61C2311yescharacteristic
100C23×C4×C61—21no—
101C23×C4×C61C2311yescharacteristic
102#137×C61—22no—
103#137×C61—22no—
104#137×C61—22no—
105#137×C61—41no—
106#137×C61—41no—
107#137×C61—41no—
108C2×Q16×C61—21no—
109C2×Q16×C61—21no—
110C2×Q16×C61—21no—
111C2×SD16×C61—21no—
112C2×SD16×C61—21no—
113C2×SD16×C61—21no—
114C2×M16×C61—21no—
115C2×M16×C61—22no—
116C2×M16×C61—41no—
117C2×M16×C61C2311yescharacteristic
118C2×M16×C61C2311yescharacteristic
119C2×M16×C61C2311yescharacteristic
120C2×M16×C61C2311yescharacteristic
121C22×C8×C61—21no—
122#127×C61—22no—
123#127×C61—21no—
124#124×C61—22no—
125#124×C61—21no—
126#124×C61—22no—
127#124×C61—41no—
128#123×C61—22no—
129#123×C61—21no—
130C22⋊Q8×C61—22no—
131C22⋊Q8×C61—21no—
132C22⋊Q8×C61—21no—
133C22⋊Q8×C61—21no—
134C22⋊Q8×C61—21no—
135C22⋊Q8×C61—21no—
136C22⋊Q8×C61—21no—
137C22⋊Q8×C61D411yescharacteristic
138C22⋊Q8×C61D411yescharacteristic
139#121×C61—22no—
140#121×C61—22no—
141#121×C61—22no—
142#121×C61—22no—
143#121×C61—22no—
144#121×C61—21no—
145#121×C61—21no—
146#121×C61—21no—
147#121×C61—22no—
148#121×C61—21no—
149#121×C61—21no—
150#121×C61—21no—
151#121×C61—21no—
152#121×C61—21no—
153#121×C61D411yescharacteristic
154#121×C61D411yescharacteristic
155#120×C61—22no—
156#120×C61—22no—
157#120×C61—22no—
158#120×C61—22no—
159#120×C61—21no—
160C4×Q8×C61—21no—
161C4×D4×C61—22no—
162C4×D4×C61—22no—
163C4×D4×C61—21no—
164C4×D4×C61—22no—
165C4×D4×C61—21no—
166C4×D4×C61—21no—
167#117×C61—21no—
168#117×C61—22no—
169#117×C61—41no—
170#117×C61C2311yescharacteristic
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61—22no—
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C22⋊C4×C61—22no—
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C22⋊C4×C61—22no—
181C2×C22⋊C4×C61—22no—
182C2×C22⋊C4×C61D412yes—
183C2×C42×C61C2311yescharacteristic
184C2×C42×C61C2311yescharacteristic
185#107×C61—21no—
186#106×C61—21no—
187#104×C61—22no—
188#104×C61—22no—
189#104×C61—22no—
190#104×C61—22no—
191#104×C61—41no—
192#104×C61D414yescomplemented
193#103×C61—21no—
194#103×C61—21no—
195#103×C61—21no—
196#103×C61—21no—
197#103×C61—21no—
198#102×C61—21no—
199#102×C61—21no—
200#102×C61—21no—
201#100×C61—22no—
202#100×C61—41no—
203C22⋊C8×C61—21no—
204C22⋊C8×C61—21no—
205#95×C61—22no—
206C24×C61—22no—
207C24×C61—21no—
208C24×C61C2×D412yes—
209C24×C61C2×D411yescharacteristic
210#41×C61—21no—
211#41×C61—21no—
212#41×C61—22no—
213#41×C61—22no—
214#41×C61—21no—
215#41×C61—21no—
216#41×C61—21no—
217#41×C61—21no—
218#41×C61—21no—
219#41×C61—21no—
220#41×C61—21no—
221#41×C61—21no—
222#41×C61—42no—
223#41×C61—42no—
224#41×C61—41no—
225#41×C61—41no—
226#41×C61—42no—
227#41×C61—42no—
228#41×C61—42no—
229#41×C61—42no—
230#41×C61—42no—
231#41×C61—42no—
232#41×C61C2×D412yes—
233#41×C61#4112yes—
234C2×Q8×C61—21no—
235C2×Q8×C61—22no—
236C2×Q8×C61—21no—
237C2×Q8×C61—21no—
238C2×Q8×C61—21no—
239C2×Q8×C61—21no—
240C2×Q8×C61—21no—
241C2×Q8×C61—21no—
242C2×Q8×C61—41no—
243C2×Q8×C61C2×D411yescharacteristic
244C2×Q8×C61C2×D411yescharacteristic
245C2×Q8×C61C2×D411yescharacteristic
246C2×D4×C61—21no—
247C2×D4×C61—22no—
248C2×D4×C61—22no—
249C2×D4×C61—22no—
250C2×D4×C61—22no—
251C2×D4×C61—21no—
252C2×D4×C61—21no—
253C2×D4×C61—21no—
254C2×D4×C61—21no—
255C2×D4×C61—21no—
256C2×D4×C61—22no—
257C2×D4×C61—22no—
258C2×D4×C61—22no—
259C2×D4×C61—21no—
260C2×D4×C61—22no—
261C2×D4×C61—21no—
262C2×D4×C61—21no—
263C2×D4×C61—21no—
264C2×D4×C61—21no—
265C2×D4×C61—21no—
266C2×D4×C61—21no—
267C2×D4×C61—21no—
268C2×D4×C61—41no—
269C2×D4×C61—42no—
270C2×D4×C61—42no—
271C2×D4×C61—42no—
272C2×D4×C61—42no—
273C2×D4×C61—44no—
274C2×D4×C61—44no—
275C2×D4×C61—42no—
276C2×D4×C61—42no—
277C2×D4×C61—82no—
278C2×D4×C61—84no—
279C2×D4×C61C2×D411yescharacteristic
280C2×D4×C61C2×D411yescharacteristic
281C2×D4×C61C2×D411yescharacteristic
282C22×C4×C61—21no—
283C22×C4×C61—21no—
284C22×C4×C61—21no—
285C22×C4×C61—21no—
286C22×C4×C61—21no—
287C22×C4×C61—22no—
288C22×C4×C61—21no—
289C22×C4×C61—21no—
290C22×C4×C61—22no—
291C22×C4×C61—21no—
292C22×C4×C61—21no—
293C22×C4×C61—21no—
294C22×C4×C61—21no—
295C22×C4×C61—21no—
296C22×C4×C61—21no—
297C22×C4×C61—21no—
298C22×C4×C61—42no—
299C22×C4×C61—42no—
300C22×C4×C61C2×D411yescharacteristic
301C22×C4×C61C2×D411yescharacteristic
302C22×C4×C61C2×D411yescharacteristic
303C22×C4×C61C2×D411yescharacteristic
304C22×C4×C61C2×D411yescharacteristic
305C22×C4×C61C2×D412yes—
306C22×C4×C61C2411yescharacteristic
307Q16×C61—42no—
308Q16×C61—42no—
309Q16×C61—42no—
310SD16×C61—42no—
311SD16×C61—42no—
312SD16×C61—42no—
313M16×C61—21no—
314M16×C61—21no—
315M16×C61—21no—
316M16×C61—21no—
317M16×C61—21no—
318M16×C61—21no—
319M16×C61—21no—
320M16×C61—42no—
321M16×C61C2×D412yescomplemented
322C2×C8×C61—21no—
323C2×C8×C61—21no—
324C2×C8×C61—21no—
325C2×C8×C61—21no—
326C2×C8×C61—42no—
327C4⋊C4×C61—22no—
328C4⋊C4×C61—22no—
329C4⋊C4×C61—21no—
330C4⋊C4×C61—21no—
331C4⋊C4×C61—21no—
332C4⋊C4×C61—21no—
333C4⋊C4×C61—21no—
334C4⋊C4×C61—21no—
335C4⋊C4×C61—42no—
336C4⋊C4×C61—41no—
337C4⋊C4×C61—41no—
338C4⋊C4×C61—82no—
339C4⋊C4×C61C2×D411yescharacteristic
340C4⋊C4×C61C2×D411yescharacteristic
341C22⋊C4×C61—22no—
342C22⋊C4×C61—22no—
343C22⋊C4×C61—22no—
344C22⋊C4×C61—22no—
345C22⋊C4×C61—22no—
346C22⋊C4×C61—21no—
347C22⋊C4×C61—21no—
348C22⋊C4×C61—21no—
349C22⋊C4×C61—21no—
350C22⋊C4×C61—22no—
351C22⋊C4×C61—22no—
352C22⋊C4×C61—21no—
353C22⋊C4×C61—42no—
354C22⋊C4×C61—44no—
355C22⋊C4×C61—41no—
356C22⋊C4×C61—41no—
357C22⋊C4×C61—82no—
358C42×C61—22no—
359C42×C61—21no—
360C42×C61—21no—
361C42×C61—21no—
362C42×C61—21no—
363C42×C61C2×D412yescomplemented
364C23×C61—21no—
365C23×C61—21no—
366C23×C61—21no—
367C23×C61—22no—
368C23×C61—21no—
369C23×C61—21no—
370C23×C61—22no—
371C23×C61—22no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61—42no—
375C23×C61—42no—
376C23×C61—44no—
377C23×C61—42no—
378C23×C61—42no—
379C23×C61—81no—
380C23×C61—82no—
381C23×C61—82no—
382C23×C61#12011yescharacteristic
383C23×C61#12011yescharacteristic
384C23×C61C22×D411yescharacteristic
385Q8×C61—21no—
386Q8×C61—21no—
387Q8×C61—21no—
388Q8×C61—21no—
389Q8×C61—21no—
390Q8×C61—42no—
391Q8×C61—41no—
392Q8×C61—41no—
393Q8×C61—41no—
394Q8×C61—41no—
395Q8×C61#12112yes—
396D4×C61—22no—
397D4×C61—22no—
398D4×C61—21no—
399D4×C61—21no—
400D4×C61—21no—
401D4×C61—21no—
402D4×C61—21no—
403D4×C61—42no—
404D4×C61—42no—
405D4×C61—44no—
406D4×C61—42no—
407D4×C61—44no—
408D4×C61—44no—
409D4×C61—42no—
410D4×C61—41no—
411D4×C61—41no—
412D4×C61—41no—
413D4×C61—41no—
414D4×C61—41no—
415D4×C61—41no—
416D4×C61—41no—
417D4×C61—41no—
418D4×C61—81no—
419D4×C61—82no—
420D4×C61—82no—
421D4×C61—82no—
422D4×C61—82no—
423D4×C61#12112yes—
424C2×C4×C61—21no—
425C2×C4×C61—21no—
426C2×C4×C61—21no—
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—22no—
434C2×C4×C61—21no—
435C2×C4×C61—21no—
436C2×C4×C61—22no—
437C2×C4×C61—21no—
438C2×C4×C61—22no—
439C2×C4×C61—21no—
440C2×C4×C61—21no—
441C2×C4×C61—21no—
442C2×C4×C61—22no—
443C2×C4×C61—42no—
444C2×C4×C61—42no—
445C2×C4×C61—42no—
446C2×C4×C61—44no—
447C2×C4×C61—41no—
448C2×C4×C61—41no—
449C2×C4×C61—41no—
450C2×C4×C61—41no—
451C2×C4×C61—41no—
452C2×C4×C61—41no—
453C2×C4×C61—42no—
454C2×C4×C61—41no—
455C2×C4×C61—42no—
456C2×C4×C61—41no—
457C2×C4×C61—41no—
458C2×C4×C61—41no—
459C2×C4×C61—41no—
460C2×C4×C61—41no—
461C2×C4×C61—41no—
462C2×C4×C61—82no—
463C2×C4×C61#12011yescharacteristic
464C2×C4×C61#12011yescharacteristic
465C2×C4×C61C22×D411yescharacteristic
466C2×C4×C61C22×D411yescharacteristic
467C2×C4×C61C22×D411yescharacteristic
468C2×C4×C61C2×#4111yescharacteristic
469C2×C4×C61H(5,𝔽2)11yescharacteristic
470C2×C4×C61H(5,𝔽2)11yescharacteristic
471C8×C61—22no—
472C8×C61—41no—
473C8×C61—41no—
474C8×C61—41no—
475#24471C6111yesmaximal, characteristic, direct product factor, Sylow
476C22×C61—21no—
477C22×C61—21no—
478C22×C61—21no—
479C22×C61—21no—
480C22×C61—22no—
481C22×C61—21no—
482C22×C61—21no—
483C22×C61—21no—
484C22×C61—21no—
485C22×C61—41no—
486C22×C61—41no—
487C22×C61—41no—
488C22×C61—41no—
489C22×C61—42no—
490C22×C61—42no—
491C22×C61—41no—
492C22×C61—41no—
493C22×C61—41no—
494C22×C61—42no—
495C22×C61—41no—
496C22×C61—81no—
497C22×C61—81no—
498C22×C61—82no—
499C22×C61—82no—
500C22×C61—84no—
501C22×C61—164no—
502C22×C61C2×#12011yescharacteristic
503C22×C61D4211yescharacteristic
504C22×C61#54611yescharacteristic
505C4×C61—21no—
506C4×C61—21no—
507C4×C61—22no—
508C4×C61—42no—
509C4×C61—41no—
510C4×C61—41no—
511C4×C61—42no—
512C4×C61—41no—
513C4×C61—41no—
514C4×C61—81no—
515C4×C61—81no—
516C4×C61—81no—
517C4×C61C2×#12111yescharacteristic
518C4×C61#53411yescharacteristic
519C4×C61D4211yescharacteristic
520C4×C61#54611yescharacteristic
521#3488C2×C6111yescharacteristic
522#3056C2×C6111yescharacteristic, complemented
523C2×#455C2×C6111yescharacteristic, complemented
524#3007C2×C6111yescharacteristic, complemented
525C2×#421C2×C6111yescharacteristic, complemented
526#2620C2×C6111yescharacteristic, complemented
527#2039C2×C6111yescharacteristic, complemented
528#2037C2×C6111yescharacteristic, complemented
529#2007C2×C6111yescharacteristic, complemented
530#2004C2×C6111yescharacteristic, complemented
531#1900C2×C6111yescharacteristic, complemented
532#1897C2×C6111yescharacteristic, complemented
533#1882C2×C6111yescharacteristic, complemented
534#1859C2×C6111yescharacteristic, complemented
535#1792C2×C6111yescharacteristic, complemented
536C2×C61—21no—
537C2×C61—21no—
538C2×C61—41no—
539C2×C61—41no—
540C2×C61—42no—
541C2×C61—81no—
542C2×C61—82no—
543C2×C61—81no—
544C2×C61#241011yescharacteristic
545C2×C61#301911yescharacteristic
546C2×C61#302211yescharacteristic
547C2×H(5,𝔽2)C22×C6111yescharacteristic
548C22×#41C22×C6111yescharacteristic
549C2×#137C22×C6111yescharacteristic
550C2×#137C22×C6111yescharacteristic, complemented
551C2×#137C22×C6111yescharacteristic, complemented
552C22×M16C22×C6111yescharacteristic, complemented
553#550—21no—
554#548—21no—
555#546—21no—
556#546—22no—
557D42—22no—
558D42—21no—
559#537—21no—
560#537C22×C6111yescharacteristic
561#535—21no—
562#535C22×C6111yescharacteristic
563C2×#124C22×C6111yescharacteristic, complemented
564#525—21no—
565#525C22×C6111yescharacteristic
566C2×C22⋊Q8C22×C6111yescharacteristic, complemented
567C2×#121—21no—
568C2×#121C22×C6111yescharacteristic
569#520C22×C6111yescharacteristic
570C2×#117C22×C6111yescharacteristic, complemented
571#470—21no—
572#468—21no—
573#467—21no—
574#465—21no—
575#455—24no—
576#452—21no—
577#452—21no—
578#451—21no—
579#450—21no—
580#428C22×C6111yescharacteristic, complemented
581#421—24no—
582C2×#104C22×C6111yescharacteristic
583C2×#104C22×C6111yescharacteristic
584C2×#104C22×C6111yescharacteristic, complemented
585C2×#104C22×C6111yescharacteristic, complemented
586C2×#104C22×C6111yescharacteristic, complemented
587C2×#104C22×C6111yescharacteristic, complemented
588#419C22×C6111yescharacteristic, complemented
589#417C22×C6111yescharacteristic
590#417C22×C6111yescharacteristic, complemented
591#417C22×C6111yescharacteristic, complemented
592C2×#100C22×C6111yescharacteristic, complemented
593C2×#100C22×C6111yescharacteristic, complemented
594#407C22×C6111yescharacteristic, complemented
595#396—22no—
596#394—22no—
597#391C22×C6111yescharacteristic, complemented
598#390C22×C6111yescharacteristic, complemented
599#384C22×C6111yescharacteristic, complemented
600#343C22×C6111yescharacteristic, complemented
601#343C22×C6111yescharacteristic, complemented
602#339C22×C6111yescharacteristic, complemented
603#339C22×C6111yescharacteristic, complemented
604C61#2447111yescharacteristic, direct product factor, Sylow
605H(5,𝔽2)—22no—
606H(5,𝔽2)—22no—
607H(5,𝔽2)—41no—
608H(5,𝔽2)—41no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—41no—
616C2×#41—41no—
617C2×#41D4×C6111yescharacteristic
618C2×#41D4×C6111yescharacteristic
619C2×#41C23×C6111yescharacteristic
620C2×#41C23×C6111yescharacteristic
621C2×#41C23×C6111yescharacteristic
622C22×Q8D4×C6111yescharacteristic
623C22×Q8C23×C6111yescharacteristic
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—21no—
628C22×D4—21no—
629C22×D4D4×C6111yescharacteristic
630C22×D4D4×C6112yes—
631C22×D4C23×C6111yescharacteristic
632C23×C4—21no—
633C23×C4C23×C6111yescharacteristic
634#137—22no—
635#137—22no—
636#137—22no—
637#137—41no—
638#137—41no—
639#137—41no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×SD16—21no—
646C2×M16—21no—
647C2×M16—22no—
648C2×M16—41no—
649C2×M16C23×C6111yescharacteristic
650C2×M16C23×C6111yescharacteristic
651C2×M16C23×C6111yescharacteristic
652C2×M16C23×C6111yescharacteristic
653C22×C8—21no—
654#127—22no—
655#127—21no—
656#124—22no—
657#124—21no—
658#124—22no—
659#124—41no—
660#123—22no—
661#123—21no—
662C22⋊Q8—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C6111yescharacteristic
670C22⋊Q8D4×C6111yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—22no—
683#121—21no—
684#121—21no—
685#121D4×C6111yescharacteristic
686#121D4×C6111yescharacteristic
687#120—22no—
688#120—22no—
689#120—22no—
690#120—21no—
691#120—22no—
692C4×Q8—21no—
693C4×D4—22no—
694C4×D4—22no—
695C4×D4—21no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—21no—
699#117—21no—
700#117—22no—
701#117—41no—
702#117C23×C6111yescharacteristic
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4C23×C6111yescharacteristic
708C2×C4⋊C4C23×C6111yescharacteristic
709C2×C22⋊C4—22no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4D4×C6112yes—
715C2×C42C23×C6111yescharacteristic
716C2×C42C23×C6111yescharacteristic
717#107—21no—
718#106—21no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104D4×C6114yescomplemented
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#102—21no—
731#102—21no—
732#102—21no—
733#100—22no—
734#100—41no—
735C22⋊C8—21no—
736C22⋊C8—21no—
737#95—22no—
738C24—22no—
739C24—21no—
740C24C2×D4×C6112yes—
741C24C2×D4×C6111yescharacteristic
742#41—21no—
743#41—21no—
744#41—22no—
745#41—22no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—42no—
755#41—42no—
756#41—41no—
757#41—41no—
758#41—42no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41C2×D4×C6112yes—
765#41#41×C6112yes—
766C2×Q8—21no—
767C2×Q8—22no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8C2×D4×C6111yescharacteristic
776C2×Q8C2×D4×C6111yescharacteristic
777C2×Q8C2×D4×C6111yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—41no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—82no—
810C2×D4—84no—
811C2×D4C2×D4×C6111yescharacteristic
812C2×D4C2×D4×C6111yescharacteristic
813C2×D4C2×D4×C6111yescharacteristic
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4C2×D4×C6111yescharacteristic
833C22×C4C2×D4×C6111yescharacteristic
834C22×C4C2×D4×C6111yescharacteristic
835C22×C4C2×D4×C6111yescharacteristic
836C22×C4C2×D4×C6111yescharacteristic
837C22×C4C2×D4×C6112yes—
838C22×C4C24×C6111yescharacteristic
839Q16—42no—
840Q16—42no—
841Q16—42no—
842SD16—42no—
843SD16—42no—
844SD16—42no—
845M16—21no—
846M16—21no—
847M16—21no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—42no—
853M16C2×D4×C6112yescomplemented
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—42no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—82no—
871C4⋊C4C2×D4×C6111yescharacteristic
872C4⋊C4C2×D4×C6111yescharacteristic
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—42no—
886C22⋊C4—44no—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—82no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42C2×D4×C6112yescomplemented
896C23—21no—
897C23—21no—
898C23—21no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—42no—
907C23—42no—
908C23—44no—
909C23—42no—
910C23—42no—
911C23—81no—
912C23—82no—
913C23—82no—
914C23#120×C6111yescharacteristic
915C23#120×C6111yescharacteristic
916C23C22×D4×C6111yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—21no—
920Q8—21no—
921Q8—21no—
922Q8—42no—
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—41no—
927Q8#121×C6112yes—
928D4—22no—
929D4—22no—
930D4—21no—
931D4—21no—
932D4—21no—
933D4—21no—
934D4—21no—
935D4—42no—
936D4—42no—
937D4—44no—
938D4—42no—
939D4—44no—
940D4—44no—
941D4—42no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—81no—
951D4—82no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4#121×C6112yes—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—22no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—22no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—44no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—42no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—82no—
995C2×C4#120×C6111yescharacteristic
996C2×C4#120×C6111yescharacteristic
997C2×C4C22×D4×C6111yescharacteristic
998C2×C4C22×D4×C6111yescharacteristic
999C2×C4C22×D4×C6111yescharacteristic
1000C2×C4C2×#41×C6111yescharacteristic
1001C2×C4H(5,𝔽2)×C6111yescharacteristic
1002C2×C4H(5,𝔽2)×C6111yescharacteristic
1003C8—22no—
1004C8—41no—
1005C8—41no—
1006C8—41no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—22no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—42no—
1021C22—42no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—81no—
1028C22—81no—
1029C22—82no—
1030C22—82no—
1031C22—84no—
1032C22—164no—
1033C22C2×#120×C6111yescharacteristic
1034C22D42×C6111yescharacteristic
1035C22C61×#54611yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—22no—
1039C4—42no—
1040C4—41no—
1041C4—41no—
1042C4—42no—
1043C4—41no—
1044C4—41no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4C2×#121×C6111yescharacteristic
1049C4C61×#53411yescharacteristic
1050C4D42×C6111yescharacteristic
1051C4C61×#54611yescharacteristic
1052C2—21no—
1053C2—21no—
1054C2—41no—
1055C2—41no—
1056C2—42no—
1057C2—81no—
1058C2—82no—
1059C2—81no—
1060C2C61×#241011yescharacteristic
1061C2C61×#301911yescharacteristic
1062C2C61×#302211yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#3488C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#3056C2semidirect
3. C2×C61×#455C2semidirect
4. C61×#3007C2semidirect
5. C2×C61×#421C2semidirect
6. C61×#2620C2semidirect
7. C61×#2039C2semidirect
8. C61×#2037C2semidirect
9. C61×#2007C2semidirect
10. C61×#2004C2semidirect
11. C61×#1900C2semidirect
12. C61×#1897C2semidirect
13. C61×#1882C2semidirect
14. C61×#1859C2semidirect
15. C61×#1792C2semidirect
19. C2×#137×C61C22semidirect
20. C2×#137×C61C22semidirect
21. C22×M16×C61C22semidirect
32. C2×#124×C61C22semidirect
35. C2×C22⋊Q8×C61C22semidirect
39. C2×#117×C61C22semidirect
49. C61×#428C22semidirect
53. C2×#104×C61C22semidirect
54. C2×#104×C61C22semidirect
55. C2×#104×C61C22semidirect
56. C2×#104×C61C22semidirect
57. C61×#419C22semidirect
59. C61×#417C22semidirect
60. C61×#417C22semidirect
61. C2×#100×C61C22semidirect
62. C2×#100×C61C22semidirect
63. C61×#407C22semidirect
66. C61×#391C22semidirect
67. C61×#390C22semidirect
68. C61×#384C22semidirect
69. C61×#343C22semidirect
70. C61×#343C22semidirect
71. C61×#339C22semidirect
72. C61×#339C22semidirect
192. #104×C61D4semidirect
321. M16×C61C2×D4semidirect
363. C42×C61C2×D4semidirect
475. #24471C61direct (N × H)
522. #3056C2×C61semidirect
523. C2×#455C2×C61semidirect
524. #3007C2×C61semidirect
525. C2×#421C2×C61semidirect
526. #2620C2×C61semidirect
527. #2039C2×C61semidirect
528. #2037C2×C61semidirect
529. #2007C2×C61semidirect
530. #2004C2×C61semidirect
531. #1900C2×C61semidirect
532. #1897C2×C61semidirect
533. #1882C2×C61semidirect
534. #1859C2×C61semidirect
535. #1792C2×C61semidirect
550. C2×#137C22×C61semidirect
551. C2×#137C22×C61semidirect
552. C22×M16C22×C61semidirect
563. C2×#124C22×C61semidirect
566. C2×C22⋊Q8C22×C61semidirect
570. C2×#117C22×C61semidirect
580. #428C22×C61semidirect
584. C2×#104C22×C61semidirect
585. C2×#104C22×C61semidirect
586. C2×#104C22×C61semidirect
587. C2×#104C22×C61semidirect
588. #419C22×C61semidirect
590. #417C22×C61semidirect
591. #417C22×C61semidirect
592. C2×#100C22×C61semidirect
593. C2×#100C22×C61semidirect
594. #407C22×C61semidirect
597. #391C22×C61semidirect
598. #390C22×C61semidirect
599. #384C22×C61semidirect
600. #343C22×C61semidirect
601. #343C22×C61semidirect
602. #339C22×C61semidirect
603. #339C22×C61semidirect
604. C61#24471direct (N × H)
724. #104D4×C61semidirect
853. M16C2×D4×C61semidirect
895. C42C2×D4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#34882
C61×#30562
C2×C61×#4552
C61×#30072
C2×C61×#4212
C61×#26202
C61×#20392
C61×#20372
C61×#20072
C61×#20042
C61×#19002
C61×#18972
C61×#18822
C61×#18592
C61×#17922
#2447161