Finite Group Databasebeta

← C61×#24467 #29527900

Subgroups — C61×#24467 #29527900

Order 15616.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 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
5C22×#104×C61C211yesmaximal, characteristic, complemented
6C61×#2850C211yesmaximal, characteristic, complemented
7C61×#2040C211yesmaximal, characteristic, complemented
8C61×#2037C211yesmaximal, characteristic, complemented
9C61×#2007C211yesmaximal, characteristic, complemented
10C61×#2004C211yesmaximal, characteristic, complemented
11C61×#1900C211yesmaximal, characteristic, complemented
12C61×#1896C211yesmaximal, characteristic, complemented
13C61×#1882C211yesmaximal, characteristic, complemented
14C61×#1860C211yesmaximal, 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
39C22×C42×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
50C2×#104×C61—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×#391C2211yescharacteristic, complemented
65C61×#390C2211yescharacteristic, complemented
66C61×#388—22no—
67C61×#386—22no—
68C61×#382C2211yescharacteristic, 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×C61—21no—
102C23×C4×C61C2311yescharacteristic
103#137×C61—22no—
104#137×C61—22no—
105#137×C61—22no—
106#137×C61—41no—
107#137×C61—41no—
108#137×C61—41no—
109C2×Q16×C61—21no—
110C2×Q16×C61—21no—
111C2×Q16×C61—21no—
112C2×SD16×C61—21no—
113C2×SD16×C61—21no—
114C2×SD16×C61—21no—
115C2×M16×C61—21no—
116C2×M16×C61—22no—
117C2×M16×C61—41no—
118C2×M16×C61C2311yescharacteristic
119C2×M16×C61C2311yescharacteristic
120C2×M16×C61C2311yescharacteristic
121C2×M16×C61C2311yescharacteristic
122C22×C8×C61—21no—
123#127×C61—22no—
124#127×C61—21no—
125#124×C61—22no—
126#124×C61—21no—
127#124×C61—22no—
128#124×C61—41no—
129#123×C61—22no—
130#123×C61—21no—
131C22⋊Q8×C61—22no—
132C22⋊Q8×C61—21no—
133C22⋊Q8×C61—21no—
134C22⋊Q8×C61—21no—
135C22⋊Q8×C61—21no—
136C22⋊Q8×C61—21no—
137C22⋊Q8×C61—21no—
138C22⋊Q8×C61D411yescharacteristic
139C22⋊Q8×C61D411yescharacteristic
140#121×C61—22no—
141#121×C61—22no—
142#121×C61—22no—
143#121×C61—22no—
144#121×C61—22no—
145#121×C61—21no—
146#121×C61—21no—
147#121×C61—21no—
148#121×C61—22no—
149#121×C61—21no—
150#121×C61—21no—
151#121×C61—21no—
152#121×C61—21no—
153#121×C61—21no—
154#121×C61D411yescharacteristic
155#121×C61D411yescharacteristic
156#120×C61—22no—
157#120×C61—22no—
158#120×C61—22no—
159#120×C61—22no—
160#120×C61—21no—
161C4×Q8×C61—21no—
162C4×D4×C61—22no—
163C4×D4×C61—22no—
164C4×D4×C61—21no—
165C4×D4×C61—22no—
166C4×D4×C61—21no—
167C4×D4×C61—21no—
168#117×C61—21no—
169#117×C61C2311yescharacteristic
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C22⋊C4×C61—22no—
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—22no—
177C2×C22⋊C4×C61—22no—
178C2×C22⋊C4×C61D412yes—
179C2×C42×C61—22no—
180C2×C42×C61—21no—
181C2×C42×C61—41no—
182C2×C42×C61C2311yescharacteristic
183C2×C42×C61C2311yescharacteristic
184#107×C61—21no—
185#106×C61—21no—
186#104×C61—22no—
187#104×C61—22no—
188#104×C61—22no—
189#104×C61—22no—
190#104×C61—41no—
191#104×C61D414yescomplemented
192#103×C61—21no—
193#103×C61—21no—
194#103×C61—21no—
195#103×C61—21no—
196#103×C61—21no—
197#102×C61—21no—
198#102×C61—21no—
199#102×C61—21no—
200#100×C61—22no—
201#100×C61—41no—
202C22⋊C8×C61—21no—
203C22⋊C8×C61—21no—
204#95×C61—22no—
205#95×C61—22no—
206C24×C61—22no—
207C24×C61—21no—
208C24×C61C2×D411yescharacteristic
209C24×C61C2×D412yes—
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—44no—
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—21no—
291C22×C4×C61—22no—
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×C61—42no—
301C22×C4×C61—42no—
302C22×C4×C61—42no—
303C22×C4×C61C2×D411yescharacteristic
304C22×C4×C61C2×D411yescharacteristic
305C22×C4×C61C2×D411yescharacteristic
306C22×C4×C61C2×D411yescharacteristic
307C22×C4×C61C2×D411yescharacteristic
308C22×C4×C61C2×D412yes—
309C22×C4×C61C2411yescharacteristic
310Q16×C61—42no—
311Q16×C61—42no—
312Q16×C61—42no—
313SD16×C61—42no—
314SD16×C61—42no—
315SD16×C61—42no—
316M16×C61—21no—
317M16×C61—21no—
318M16×C61—21no—
319M16×C61—21no—
320M16×C61—21no—
321M16×C61—21no—
322M16×C61—21no—
323M16×C61—42no—
324M16×C61C2×D412yescomplemented
325C2×C8×C61—21no—
326C2×C8×C61—21no—
327C2×C8×C61—21no—
328C2×C8×C61—21no—
329C2×C8×C61—42no—
330C4⋊C4×C61—22no—
331C4⋊C4×C61—22no—
332C4⋊C4×C61—21no—
333C4⋊C4×C61—21no—
334C4⋊C4×C61—21no—
335C4⋊C4×C61—21no—
336C4⋊C4×C61—21no—
337C4⋊C4×C61—21no—
338C4⋊C4×C61—41no—
339C4⋊C4×C61—41no—
340C4⋊C4×C61C2×D411yescharacteristic
341C4⋊C4×C61C2×D411yescharacteristic
342C22⋊C4×C61—22no—
343C22⋊C4×C61—22no—
344C22⋊C4×C61—22no—
345C22⋊C4×C61—22no—
346C22⋊C4×C61—22no—
347C22⋊C4×C61—21no—
348C22⋊C4×C61—21no—
349C22⋊C4×C61—21no—
350C22⋊C4×C61—21no—
351C22⋊C4×C61—22no—
352C22⋊C4×C61—22no—
353C22⋊C4×C61—21no—
354C22⋊C4×C61—44no—
355C22⋊C4×C61—44no—
356C22⋊C4×C61—41no—
357C22⋊C4×C61—41no—
358C42×C61—22no—
359C42×C61—21no—
360C42×C61—21no—
361C42×C61—21no—
362C42×C61—21no—
363C42×C61—42no—
364C42×C61C2×D412yescomplemented
365C23×C61—21no—
366C23×C61—21no—
367C23×C61—21no—
368C23×C61—22no—
369C23×C61—22no—
370C23×C61—21no—
371C23×C61—21no—
372C23×C61—22no—
373C23×C61—22no—
374C23×C61—41no—
375C23×C61—42no—
376C23×C61—44no—
377C23×C61—42no—
378C23×C61—42no—
379C23×C61—42no—
380C23×C61—81no—
381C23×C61—82no—
382C23×C61—82no—
383C23×C61#12011yescharacteristic
384C23×C61#12011yescharacteristic
385C23×C61C22×D411yescharacteristic
386Q8×C61—21no—
387Q8×C61—21no—
388Q8×C61—21no—
389Q8×C61—21no—
390Q8×C61—21no—
391Q8×C61—42no—
392Q8×C61—41no—
393Q8×C61—41no—
394Q8×C61—41no—
395Q8×C61—41no—
396Q8×C61#12112yes—
397D4×C61—22no—
398D4×C61—22no—
399D4×C61—21no—
400D4×C61—21no—
401D4×C61—21no—
402D4×C61—21no—
403D4×C61—21no—
404D4×C61—42no—
405D4×C61—42no—
406D4×C61—44no—
407D4×C61—42no—
408D4×C61—44no—
409D4×C61—41no—
410D4×C61—41no—
411D4×C61—41no—
412D4×C61—41no—
413D4×C61—44no—
414D4×C61—42no—
415D4×C61—41no—
416D4×C61—41no—
417D4×C61—41no—
418D4×C61—41no—
419D4×C61—81no—
420D4×C61—82no—
421D4×C61—82no—
422D4×C61—82no—
423D4×C61—82no—
424D4×C61#12112yes—
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—21no—
434C2×C4×C61—22no—
435C2×C4×C61—21no—
436C2×C4×C61—21no—
437C2×C4×C61—22no—
438C2×C4×C61—22no—
439C2×C4×C61—21no—
440C2×C4×C61—22no—
441C2×C4×C61—21no—
442C2×C4×C61—21no—
443C2×C4×C61—21no—
444C2×C4×C61—22no—
445C2×C4×C61—42no—
446C2×C4×C61—42no—
447C2×C4×C61—42no—
448C2×C4×C61—44no—
449C2×C4×C61—41no—
450C2×C4×C61—41no—
451C2×C4×C61—41no—
452C2×C4×C61—48no—
453C2×C4×C61—41no—
454C2×C4×C61—41no—
455C2×C4×C61—41no—
456C2×C4×C61—41no—
457C2×C4×C61—41no—
458C2×C4×C61—42no—
459C2×C4×C61—42no—
460C2×C4×C61—41no—
461C2×C4×C61—41no—
462C2×C4×C61—41no—
463C2×C4×C61—41no—
464C2×C4×C61—82no—
465C2×C4×C61#12011yescharacteristic
466C2×C4×C61#12011yescharacteristic
467C2×C4×C61C22×D411yescharacteristic
468C2×C4×C61C22×D411yescharacteristic
469C2×C4×C61C22×D411yescharacteristic
470C2×C4×C61C2×#4111yescharacteristic
471C2×C4×C61H(5,𝔽2)11yescharacteristic
472C2×C4×C61H(5,𝔽2)11yescharacteristic
473C8×C61—22no—
474C8×C61—41no—
475C8×C61—41no—
476C8×C61—41no—
477#24467C6111yesmaximal, characteristic, direct product factor, Sylow
478C22×C61—21no—
479C22×C61—21no—
480C22×C61—21no—
481C22×C61—21no—
482C22×C61—21no—
483C22×C61—22no—
484C22×C61—21no—
485C22×C61—21no—
486C22×C61—42no—
487C22×C61—42no—
488C22×C61—41no—
489C22×C61—41no—
490C22×C61—41no—
491C22×C61—41no—
492C22×C61—42no—
493C22×C61—42no—
494C22×C61—41no—
495C22×C61—41no—
496C22×C61—41no—
497C22×C61—42no—
498C22×C61—41no—
499C22×C61—84no—
500C22×C61—82no—
501C22×C61—82no—
502C22×C61—164no—
503C22×C61#45512yescomplemented
504C22×C61C2×#12011yescharacteristic
505C22×C61D4211yescharacteristic
506C22×C61#54611yescharacteristic
507C4×C61—21no—
508C4×C61—21no—
509C4×C61—22no—
510C4×C61—42no—
511C4×C61—42no—
512C4×C61—41no—
513C4×C61—41no—
514C4×C61—42no—
515C4×C61—41no—
516C4×C61—41no—
517C4×C61—81no—
518C4×C61—81no—
519C4×C61C2×#12111yescharacteristic
520C4×C61#53411yescharacteristic
521C4×C61D4211yescharacteristic
522C4×C61#54611yescharacteristic
523#3488C2×C6111yescharacteristic
524#3056C2×C6111yescharacteristic, complemented
525C2×#455C2×C6111yescharacteristic, complemented
526#3007C2×C6111yescharacteristic, complemented
527C22×#104C2×C6111yescharacteristic, complemented
528#2850C2×C6111yescharacteristic, complemented
529#2040C2×C6111yescharacteristic, complemented
530#2037C2×C6111yescharacteristic, complemented
531#2007C2×C6111yescharacteristic, complemented
532#2004C2×C6111yescharacteristic, complemented
533#1900C2×C6111yescharacteristic, complemented
534#1896C2×C6111yescharacteristic, complemented
535#1882C2×C6111yescharacteristic, complemented
536#1860C2×C6111yescharacteristic, complemented
537#1792C2×C6111yescharacteristic, complemented
538C2×C61—21no—
539C2×C61—21no—
540C2×C61—22no—
541C2×C61—41no—
542C2×C61—42no—
543C2×C61—81no—
544C2×C61—82no—
545C2×C61—81no—
546C2×C61#241011yescharacteristic
547C2×C61C2×#45511yescharacteristic
548C2×C61#301811yescharacteristic
549C2×H(5,𝔽2)C22×C6111yescharacteristic
550C22×#41C22×C6111yescharacteristic
551C2×#137C22×C6111yescharacteristic
552C2×#137C22×C6111yescharacteristic, complemented
553C2×#137C22×C6111yescharacteristic, complemented
554C22×M16C22×C6111yescharacteristic, complemented
555#550—21no—
556#548—21no—
557#546—21no—
558#546—22no—
559D42—22no—
560D42—21no—
561#537—21no—
562#537C22×C6111yescharacteristic
563#535—21no—
564#535C22×C6111yescharacteristic
565C2×#124C22×C6111yescharacteristic, complemented
566#525—21no—
567#525C22×C6111yescharacteristic
568C2×C22⋊Q8C22×C6111yescharacteristic, complemented
569C2×#121—21no—
570C2×#121C22×C6111yescharacteristic
571#520C22×C6111yescharacteristic
572C22×C42C22×C6111yescharacteristic, complemented
573#470—21no—
574#468—21no—
575#467—21no—
576#465—21no—
577#455—24no—
578#452—21no—
579#452—21no—
580#451—21no—
581#450—21no—
582#428C22×C6111yescharacteristic, complemented
583C2×#104—24no—
584C2×#104C22×C6111yescharacteristic
585C2×#104C22×C6111yescharacteristic
586C2×#104C22×C6111yescharacteristic, complemented
587C2×#104C22×C6111yescharacteristic, complemented
588C2×#104C22×C6111yescharacteristic, complemented
589C2×#104C22×C6111yescharacteristic, complemented
590#419C22×C6111yescharacteristic, complemented
591#417C22×C6111yescharacteristic
592#417C22×C6111yescharacteristic, complemented
593#417C22×C6111yescharacteristic, complemented
594C2×#100C22×C6111yescharacteristic, complemented
595C2×#100C22×C6111yescharacteristic, complemented
596#407C22×C6111yescharacteristic, complemented
597#391C22×C6111yescharacteristic, complemented
598#390C22×C6111yescharacteristic, complemented
599#388—22no—
600#386—22no—
601#382C22×C6111yescharacteristic, complemented
602#343C22×C6111yescharacteristic, complemented
603#343C22×C6111yescharacteristic, complemented
604#339C22×C6111yescharacteristic, complemented
605#339C22×C6111yescharacteristic, complemented
606C61#2446711yescharacteristic, direct product factor, Sylow
607H(5,𝔽2)—22no—
608H(5,𝔽2)—22no—
609H(5,𝔽2)—41no—
610H(5,𝔽2)—41no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—21no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C2×#41D4×C6111yescharacteristic
620C2×#41D4×C6111yescharacteristic
621C2×#41C23×C6111yescharacteristic
622C2×#41C23×C6111yescharacteristic
623C2×#41C23×C6111yescharacteristic
624C22×Q8D4×C6111yescharacteristic
625C22×Q8C23×C6111yescharacteristic
626C22×D4—21no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4D4×C6111yescharacteristic
632C22×D4D4×C6112yes—
633C22×D4C23×C6111yescharacteristic
634C23×C4—21no—
635C23×C4—21no—
636C23×C4C23×C6111yescharacteristic
637#137—22no—
638#137—22no—
639#137—22no—
640#137—41no—
641#137—41no—
642#137—41no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—21no—
646C2×SD16—21no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×M16—21no—
650C2×M16—22no—
651C2×M16—41no—
652C2×M16C23×C6111yescharacteristic
653C2×M16C23×C6111yescharacteristic
654C2×M16C23×C6111yescharacteristic
655C2×M16C23×C6111yescharacteristic
656C22×C8—21no—
657#127—22no—
658#127—21no—
659#124—22no—
660#124—21no—
661#124—22no—
662#124—41no—
663#123—22no—
664#123—21no—
665C22⋊Q8—22no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8—21no—
670C22⋊Q8—21no—
671C22⋊Q8—21no—
672C22⋊Q8D4×C6111yescharacteristic
673C22⋊Q8D4×C6111yescharacteristic
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—21no—
685#121—22no—
686#121—21no—
687#121—21no—
688#121D4×C6111yescharacteristic
689#121D4×C6111yescharacteristic
690#120—22no—
691#120—22no—
692#120—22no—
693#120—21no—
694#120—22no—
695C4×Q8—21no—
696C4×D4—22no—
697C4×D4—22no—
698C4×D4—21no—
699C4×D4—22no—
700C4×D4—21no—
701C4×D4—21no—
702#117—21no—
703#117C23×C6111yescharacteristic
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4C23×C6111yescharacteristic
707C2×C4⋊C4C23×C6111yescharacteristic
708C2×C22⋊C4—22no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4D4×C6112yes—
713C2×C42—22no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42C23×C6111yescharacteristic
717C2×C42C23×C6111yescharacteristic
718#107—21no—
719#106—21no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—22no—
724#104—41no—
725#104D4×C6114yescomplemented
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#103—21no—
731#102—21no—
732#102—21no—
733#102—21no—
734#100—22no—
735#100—41no—
736C22⋊C8—21no—
737C22⋊C8—21no—
738#95—22no—
739#95—22no—
740C24—22no—
741C24—21no—
742C24C2×D4×C6111yescharacteristic
743C24C2×D4×C6112yes—
744#41—21no—
745#41—21no—
746#41—22no—
747#41—22no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—21no—
756#41—42no—
757#41—42no—
758#41—41no—
759#41—41no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41—42no—
765#41—42no—
766#41C2×D4×C6112yes—
767#41#41×C6112yes—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—41no—
777C2×Q8C2×D4×C6111yescharacteristic
778C2×Q8C2×D4×C6111yescharacteristic
779C2×Q8C2×D4×C6111yescharacteristic
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—22no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—41no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—44no—
812C2×D4—84no—
813C2×D4C2×D4×C6111yescharacteristic
814C2×D4C2×D4×C6111yescharacteristic
815C2×D4C2×D4×C6111yescharacteristic
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4C2×D4×C6111yescharacteristic
838C22×C4C2×D4×C6111yescharacteristic
839C22×C4C2×D4×C6111yescharacteristic
840C22×C4C2×D4×C6111yescharacteristic
841C22×C4C2×D4×C6111yescharacteristic
842C22×C4C2×D4×C6112yes—
843C22×C4C24×C6111yescharacteristic
844Q16—42no—
845Q16—42no—
846Q16—42no—
847SD16—42no—
848SD16—42no—
849SD16—42no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16—21no—
857M16—42no—
858M16C2×D4×C6112yescomplemented
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—42no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4C2×D4×C6111yescharacteristic
875C4⋊C4C2×D4×C6111yescharacteristic
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—21no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—21no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—41no—
891C22⋊C4—41no—
892C42—22no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—42no—
898C42C2×D4×C6112yescomplemented
899C23—21no—
900C23—21no—
901C23—22no—
902C23—21no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—44no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—81no—
915C23—82no—
916C23—82no—
917C23#120×C6111yescharacteristic
918C23#120×C6111yescharacteristic
919C23C22×D4×C6111yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—21no—
924Q8—21no—
925Q8—42no—
926Q8—41no—
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8#121×C6112yes—
931D4—22no—
932D4—22no—
933D4—21no—
934D4—21no—
935D4—21no—
936D4—21no—
937D4—21no—
938D4—42no—
939D4—42no—
940D4—44no—
941D4—42no—
942D4—44no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—44no—
948D4—42no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—81no—
954D4—82no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4#121×C6112yes—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—22no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—22no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—21no—
975C2×C4—22no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—44no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—48no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—82no—
999C2×C4#120×C6111yescharacteristic
1000C2×C4#120×C6111yescharacteristic
1001C2×C4C22×D4×C6111yescharacteristic
1002C2×C4C22×D4×C6111yescharacteristic
1003C2×C4C22×D4×C6111yescharacteristic
1004C2×C4C2×#41×C6111yescharacteristic
1005C2×C4H(5,𝔽2)×C6111yescharacteristic
1006C2×C4H(5,𝔽2)×C6111yescharacteristic
1007C8—22no—
1008C8—41no—
1009C8—41no—
1010C8—41no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—22no—
1017C22—21no—
1018C22—21no—
1019C22—42no—
1020C22—42no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—42no—
1027C22—41no—
1028C22—41no—
1029C22—41no—
1030C22—42no—
1031C22—41no—
1032C22—84no—
1033C22—82no—
1034C22—82no—
1035C22—164no—
1036C22C61×#45512yescomplemented
1037C22C2×#120×C6111yescharacteristic
1038C22D42×C6111yescharacteristic
1039C22C61×#54611yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—22no—
1043C4—42no—
1044C4—42no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C4—81no—
1052C4C2×#121×C6111yescharacteristic
1053C4C61×#53411yescharacteristic
1054C4D42×C6111yescharacteristic
1055C4C61×#54611yescharacteristic
1056C2—21no—
1057C2—21no—
1058C2—22no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2C61×#241011yescharacteristic
1065C2C2×C61×#45511yescharacteristic
1066C2C61×#301811yescharacteristic
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. C22×#104×C61C2semidirect
6. C61×#2850C2semidirect
7. C61×#2040C2semidirect
8. C61×#2037C2semidirect
9. C61×#2007C2semidirect
10. C61×#2004C2semidirect
11. C61×#1900C2semidirect
12. C61×#1896C2semidirect
13. C61×#1882C2semidirect
14. C61×#1860C2semidirect
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. C22×C42×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
64. C61×#391C22semidirect
65. C61×#390C22semidirect
68. C61×#382C22semidirect
69. C61×#343C22semidirect
70. C61×#343C22semidirect
71. C61×#339C22semidirect
72. C61×#339C22semidirect
191. #104×C61D4semidirect
324. M16×C61C2×D4semidirect
364. C42×C61C2×D4semidirect
477. #24467C61direct (N × H)
503. C22×C61#455semidirect
524. #3056C2×C61semidirect
525. C2×#455C2×C61semidirect
526. #3007C2×C61semidirect
527. C22×#104C2×C61semidirect
528. #2850C2×C61semidirect
529. #2040C2×C61semidirect
530. #2037C2×C61semidirect
531. #2007C2×C61semidirect
532. #2004C2×C61semidirect
533. #1900C2×C61semidirect
534. #1896C2×C61semidirect
535. #1882C2×C61semidirect
536. #1860C2×C61semidirect
537. #1792C2×C61semidirect
552. C2×#137C22×C61semidirect
553. C2×#137C22×C61semidirect
554. C22×M16C22×C61semidirect
565. C2×#124C22×C61semidirect
568. C2×C22⋊Q8C22×C61semidirect
572. C22×C42C22×C61semidirect
582. #428C22×C61semidirect
586. C2×#104C22×C61semidirect
587. C2×#104C22×C61semidirect
588. C2×#104C22×C61semidirect
589. C2×#104C22×C61semidirect
590. #419C22×C61semidirect
592. #417C22×C61semidirect
593. #417C22×C61semidirect
594. C2×#100C22×C61semidirect
595. C2×#100C22×C61semidirect
596. #407C22×C61semidirect
597. #391C22×C61semidirect
598. #390C22×C61semidirect
601. #382C22×C61semidirect
602. #343C22×C61semidirect
603. #343C22×C61semidirect
604. #339C22×C61semidirect
605. #339C22×C61semidirect
606. C61#24467direct (N × H)
725. #104D4×C61semidirect
858. M16C2×D4×C61semidirect
898. C42C2×D4×C61semidirect
1036. C22C61×#455semidirect

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
C22×#104×C612
C61×#28502
C61×#20402
C61×#20372
C61×#20072
C61×#20042
C61×#19002
C61×#18962
C61×#18822
C61×#18602
C61×#17922
#2446761