Finite Group Databasebeta

← C61×#25529 #29528962

Subgroups — C61×#25529 #29528962

Order 15616.

1014 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3495C211yesmaximal, characteristic
2C61×#3095C211yesmaximal, characteristic, complemented
3C61×#3056C211yesmaximal, characteristic
4C61×#2621C211yesmaximal, characteristic, complemented
5C61×#2061C211yesmaximal, characteristic, complemented
6C61×#2038C211yesmaximal, characteristic, complemented
7C61×#2028C211yesmaximal, characteristic, complemented
8C61×#2005C211yesmaximal, characteristic, complemented
9C61×#1901C211yesmaximal, characteristic, complemented
10C61×#1897C211yesmaximal, characteristic
11C61×#1886C211yesmaximal, characteristic, complemented
12C61×#1882C211yesmaximal, characteristic, complemented
13C61×#1860C211yesmaximal, characteristic, complemented
14C61×#1857C211yesmaximal, characteristic, complemented
15C61×#1733C211yesmaximal, characteristic, complemented
16C2×#137×C61C2211yescharacteristic
17C22×M16×C61C2211yescharacteristic
18C61×#556—21no—
19C61×#554—21no—
20C61×#552—21no—
21C61×#552—22no—
22C61×#552—21no—
23C61×#551—22no—
24C61×#544C2211yescharacteristic
25C61×#542—21no—
26C61×#541—21no—
27C61×#536C2211yescharacteristic
28C61×#533—21no—
29C2×C4⋊Q8×C61C2211yescharacteristic
30C61×#529—21no—
31C61×#525C2211yescharacteristic
32C2×C22⋊Q8×C61C2211yescharacteristic
33C2×C22⋊Q8×C61C2211yescharacteristic
34C61×#520C2211yescharacteristic
35C61×#519C2211yescharacteristic
36C2×#117×C61C2211yescharacteristic
37C2×#117×C61C2211yescharacteristic
38C61×#485—21no—
39C61×#485—21no—
40C61×#484—21no—
41C61×#483—21no—
42C61×#470—21no—
43C61×#468—21no—
44C61×#467—21no—
45C61×#465—21no—
46C61×#428C2211yescharacteristic
47C61×#428C2211yescharacteristic
48C61×#428C2211yescharacteristic
49C2×#104×C61C2211yescharacteristic
50C2×#104×C61C2211yescharacteristic
51C61×#419C2211yescharacteristic
52C61×#419C2211yescharacteristic
53C61×#419C2211yescharacteristic
54C61×#417C2211yescharacteristic
55C2×#101×C61C2211yescharacteristic
56C2×#101×C61C2211yescharacteristic
57C61×#407C2211yescharacteristic
58C61×#398—22no—
59C61×#397—22no—
60C61×#391C2211yescharacteristic
61C61×#391C2211yescharacteristic
62C61×#382C2211yescharacteristic
63C61×#343C2211yescharacteristic
64C61×#343C2211yescharacteristic
65C61×#339C2211yescharacteristic
66C61×#339C2211yescharacteristic
67C61×#339C2211yescharacteristic
68C61×#339C2211yescharacteristic
69C61×#339C2211yescharacteristic
70C61×#339C2211yescharacteristic
71C2×#41×C61C2311yescharacteristic
72C22×Q8×C61C2311yescharacteristic
73C22×Q8×C61C2311yescharacteristic
74C23×C4×C61C2311yescharacteristic
75#137×C61—22no—
76#137×C61—41no—
77C2×Q16×C61—21no—
78C2×SD16×C61—21no—
79C2×M16×C61—21no—
80C2×M16×C61—22no—
81C2×M16×C61—41no—
82C2×M16×C61C2311yescharacteristic
83C2×M16×C61C2311yescharacteristic
84C2×M16×C61C2311yescharacteristic
85C2×M16×C61C2311yescharacteristic
86C22×C8×C61—21no—
87C4⋊Q8×C61—21no—
88C4⋊Q8×C61—21no—
89C4⋊Q8×C61—21no—
90C4⋊Q8×C61—22no—
91C4⋊Q8×C61—41no—
92#126×C61—22no—
93#126×C61—22no—
94#126×C61—22no—
95#126×C61—22no—
96#125×C61—22no—
97#125×C61—22no—
98#125×C61—22no—
99#125×C61—21no—
100#125×C61—21no—
101#124×C61—22no—
102#124×C61—21no—
103#123×C61—22no—
104#123×C61—22no—
105#123×C61—22no—
106#123×C61—21no—
107C22⋊Q8×C61—22no—
108C22⋊Q8×C61—22no—
109C22⋊Q8×C61—21no—
110C22⋊Q8×C61—21no—
111C22⋊Q8×C61—22no—
112C22⋊Q8×C61—21no—
113C22⋊Q8×C61—21no—
114C22⋊Q8×C61—21no—
115C22⋊Q8×C61—21no—
116C22⋊Q8×C61—21no—
117C22⋊Q8×C61—21no—
118C22⋊Q8×C61—21no—
119C22⋊Q8×C61—21no—
120C22⋊Q8×C61D411yescharacteristic
121C22⋊Q8×C61D411yescharacteristic
122#121×C61D411yescharacteristic
123#121×C61D411yescharacteristic
124#120×C61—21no—
125C4×Q8×C61—22no—
126C4×Q8×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61—21no—
130C4×Q8×C61—21no—
131C4×D4×C61—22no—
132C4×D4×C61—21no—
133C4×D4×C61—22no—
134C4×D4×C61—21no—
135C4×D4×C61—21no—
136#117×C61—22no—
137#117×C61—22no—
138#117×C61—21no—
139#117×C61—22no—
140#117×C61—21no—
141#117×C61—21no—
142#117×C61—22no—
143#117×C61—41no—
144#117×C61D411yescharacteristic
145#117×C61D411yescharacteristic
146#117×C61C2311yescharacteristic
147#117×C61C2311yescharacteristic
148#117×C61C2311yescharacteristic
149C2×C4⋊C4×C61—21no—
150C2×C4⋊C4×C61—22no—
151C2×C4⋊C4×C61—21no—
152C2×C4⋊C4×C61—21no—
153C2×C4⋊C4×C61D412yes—
154C2×C4⋊C4×C61D411yescharacteristic
155C2×C4⋊C4×C61D411yescharacteristic
156C2×C4⋊C4×C61C2311yescharacteristic
157C2×C4⋊C4×C61C2311yescharacteristic
158C2×C22⋊C4×C61—21no—
159C2×C22⋊C4×C61—21no—
160C2×C22⋊C4×C61—21no—
161C2×C22⋊C4×C61D412yes—
162C2×C42×C61—21no—
163C2×C42×C61C2311yescharacteristic
164C2×C42×C61C2311yescharacteristic
165#107×C61—21no—
166#107×C61—21no—
167#107×C61—21no—
168#106×C61—21no—
169#106×C61—21no—
170#106×C61—21no—
171#104×C61—22no—
172#104×C61—41no—
173#103×C61—21no—
174#103×C61—21no—
175#103×C61—21no—
176#103×C61—21no—
177#103×C61—21no—
178#103×C61—21no—
179#103×C61—21no—
180#102×C61—21no—
181#101×C61—22no—
182#101×C61—41no—
183C22⋊C8×C61—21no—
184C22⋊C8×C61—21no—
185#95×C61—22no—
186#95×C61—22no—
187#95×C61—22no—
188C24×C61C2×D411yescharacteristic
189#41×C61—21no—
190#41×C61—21no—
191#41×C61—21no—
192#41×C61—21no—
193C2×Q8×C61—22no—
194C2×Q8×C61—21no—
195C2×Q8×C61—21no—
196C2×Q8×C61—21no—
197C2×Q8×C61—21no—
198C2×Q8×C61—21no—
199C2×Q8×C61—21no—
200C2×Q8×C61—21no—
201C2×Q8×C61—21no—
202C2×Q8×C61—21no—
203C2×Q8×C61—21no—
204C2×Q8×C61—21no—
205C2×Q8×C61—21no—
206C2×Q8×C61C2×D411yescharacteristic
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—21no—
210C2×D4×C61C2×D411yescharacteristic
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—22no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61C2×D412yes—
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D412yes—
230C22×C4×C61C2411yescharacteristic
231Q16×C61—42no—
232SD16×C61—42no—
233M16×C61—21no—
234M16×C61—21no—
235M16×C61—21no—
236M16×C61—21no—
237M16×C61—21no—
238M16×C61—21no—
239M16×C61—21no—
240M16×C61—42no—
241M16×C61#4112yes—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—42no—
247C4⋊C4×C61—22no—
248C4⋊C4×C61—22no—
249C4⋊C4×C61—22no—
250C4⋊C4×C61—22no—
251C4⋊C4×C61—22no—
252C4⋊C4×C61—22no—
253C4⋊C4×C61—22no—
254C4⋊C4×C61—22no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—22no—
258C4⋊C4×C61—22no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—42no—
266C4⋊C4×C61—44no—
267C4⋊C4×C61—41no—
268C4⋊C4×C61—41no—
269C4⋊C4×C61C2×D411yescharacteristic
270C4⋊C4×C61C2×D411yescharacteristic
271C4⋊C4×C61C2×D411yescharacteristic
272C4⋊C4×C61C2×D411yescharacteristic
273C4⋊C4×C61C2×D411yescharacteristic
274C4⋊C4×C61C2×D411yescharacteristic
275C22⋊C4×C61—22no—
276C22⋊C4×C61—22no—
277C22⋊C4×C61—22no—
278C22⋊C4×C61—21no—
279C22⋊C4×C61—21no—
280C22⋊C4×C61—22no—
281C22⋊C4×C61—22no—
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C22⋊C4×C61—42no—
290C22⋊C4×C61—41no—
291C22⋊C4×C61—41no—
292C42×C61—22no—
293C42×C61—22no—
294C42×C61—22no—
295C42×C61—21no—
296C42×C61—21no—
297C42×C61—21no—
298C42×C61—21no—
299C42×C61—21no—
300C42×C61—21no—
301C42×C61—21no—
302C42×C61—21no—
303C42×C61#4112yes—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61#12011yescharacteristic
310C23×C61#12011yescharacteristic
311C23×C61C22×D411yescharacteristic
312Q8×C61—21no—
313Q8×C61—21no—
314Q8×C61—41no—
315Q8×C61—41no—
316Q8×C61—41no—
317Q8×C61—41no—
318Q8×C61—41no—
319Q8×C61—41no—
320Q8×C61—41no—
321Q8×C61—41no—
322Q8×C61—82no—
323D4×C61—21no—
324D4×C61—21no—
325D4×C61—42no—
326D4×C61—41no—
327D4×C61—41no—
328D4×C61—81no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—22no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—42no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—42no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—42no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—81no—
366C2×C4×C61—82no—
367C2×C4×C61#12011yescharacteristic
368C2×C4×C61#12011yescharacteristic
369C2×C4×C61C22×D411yescharacteristic
370C2×C4×C61C22×D411yescharacteristic
371C2×C4×C61C2×#4111yescharacteristic
372C2×C4×C61C2×#4111yescharacteristic
373C2×C4×C61H(5,𝔽2)11yescharacteristic
374C2×C4×C612−1+411yescharacteristic
375C8×C61—22no—
376C8×C61—41no—
377C8×C61—41no—
378C8×C61—41no—
379#25529C6111yesmaximal, characteristic, direct product factor, Sylow
380C22×C61—21no—
381C22×C61—21no—
382C22×C61—21no—
383C22×C61—21no—
384C22×C61—21no—
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—21no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—81no—
392C22×C61—81no—
393C22×C61C2×#12011yescharacteristic
394C22×C61#54611yescharacteristic
395C22×C61#54711yescharacteristic
396C4×C61—21no—
397C4×C61—21no—
398C4×C61—42no—
399C4×C61—42no—
400C4×C61—41no—
401C4×C61—41no—
402C4×C61—41no—
403C4×C61—41no—
404C4×C61—42no—
405C4×C61—41no—
406C4×C61—41no—
407C4×C61—41no—
408C4×C61—81no—
409C4×C61—81no—
410C4×C61—81no—
411C4×C61#53211yescharacteristic
412C4×C61#53711yescharacteristic
413C4×C61#54611yescharacteristic
414C4×C61#54711yescharacteristic
415#3495C2×C6111yescharacteristic
416#3095C2×C6111yescharacteristic, complemented
417#3056C2×C6111yescharacteristic
418#2621C2×C6111yescharacteristic, complemented
419#2061C2×C6111yescharacteristic, complemented
420#2038C2×C6111yescharacteristic, complemented
421#2028C2×C6111yescharacteristic, complemented
422#2005C2×C6111yescharacteristic, complemented
423#1901C2×C6111yescharacteristic, complemented
424#1897C2×C6111yescharacteristic
425#1886C2×C6111yescharacteristic, complemented
426#1882C2×C6111yescharacteristic, complemented
427#1860C2×C6111yescharacteristic, complemented
428#1857C2×C6111yescharacteristic, complemented
429#1733C2×C6111yescharacteristic, complemented
430C2×C61—21no—
431C2×C61—21no—
432C2×C61—41no—
433C2×C61—41no—
434C2×C61—81no—
435C2×C61#243011yescharacteristic
436C2×C61#302011yescharacteristic
437C2×C61#302211yescharacteristic
438C2×#137C22×C6111yescharacteristic
439C22×M16C22×C6111yescharacteristic
440#556—21no—
441#554—21no—
442#552—21no—
443#552—22no—
444#552—21no—
445#551—22no—
446#544C22×C6111yescharacteristic
447#542—21no—
448#541—21no—
449#536C22×C6111yescharacteristic
450#533—21no—
451C2×C4⋊Q8C22×C6111yescharacteristic
452#529—21no—
453#525C22×C6111yescharacteristic
454C2×C22⋊Q8C22×C6111yescharacteristic
455C2×C22⋊Q8C22×C6111yescharacteristic
456#520C22×C6111yescharacteristic
457#519C22×C6111yescharacteristic
458C2×#117C22×C6111yescharacteristic
459C2×#117C22×C6111yescharacteristic
460#485—21no—
461#485—21no—
462#484—21no—
463#483—21no—
464#470—21no—
465#468—21no—
466#467—21no—
467#465—21no—
468#428C22×C6111yescharacteristic
469#428C22×C6111yescharacteristic
470#428C22×C6111yescharacteristic
471C2×#104C22×C6111yescharacteristic
472C2×#104C22×C6111yescharacteristic
473#419C22×C6111yescharacteristic
474#419C22×C6111yescharacteristic
475#419C22×C6111yescharacteristic
476#417C22×C6111yescharacteristic
477C2×#101C22×C6111yescharacteristic
478C2×#101C22×C6111yescharacteristic
479#407C22×C6111yescharacteristic
480#398—22no—
481#397—22no—
482#391C22×C6111yescharacteristic
483#391C22×C6111yescharacteristic
484#382C22×C6111yescharacteristic
485#343C22×C6111yescharacteristic
486#343C22×C6111yescharacteristic
487#339C22×C6111yescharacteristic
488#339C22×C6111yescharacteristic
489#339C22×C6111yescharacteristic
490#339C22×C6111yescharacteristic
491#339C22×C6111yescharacteristic
492#339C22×C6111yescharacteristic
493C61#2552911yescharacteristic, direct product factor, Sylow
494C2×#41C23×C6111yescharacteristic
495C22×Q8C23×C6111yescharacteristic
496C22×Q8C23×C6111yescharacteristic
497C23×C4C23×C6111yescharacteristic
498#137—22no—
499#137—41no—
500C2×Q16—21no—
501C2×SD16—21no—
502C2×M16—21no—
503C2×M16—22no—
504C2×M16—41no—
505C2×M16C23×C6111yescharacteristic
506C2×M16C23×C6111yescharacteristic
507C2×M16C23×C6111yescharacteristic
508C2×M16C23×C6111yescharacteristic
509C22×C8—21no—
510C4⋊Q8—21no—
511C4⋊Q8—21no—
512C4⋊Q8—21no—
513C4⋊Q8—22no—
514C4⋊Q8—41no—
515#126—22no—
516#126—22no—
517#126—22no—
518#126—22no—
519#125—22no—
520#125—22no—
521#125—22no—
522#125—21no—
523#125—21no—
524#124—22no—
525#124—21no—
526#123—22no—
527#123—22no—
528#123—21no—
529#123—22no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536C22⋊Q8—22no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540C22⋊Q8—21no—
541C22⋊Q8—21no—
542C22⋊Q8—21no—
543C22⋊Q8D4×C6111yescharacteristic
544C22⋊Q8D4×C6111yescharacteristic
545#121D4×C6111yescharacteristic
546#121D4×C6111yescharacteristic
547#120—21no—
548C4×Q8—22no—
549C4×Q8—21no—
550C4×Q8—21no—
551C4×Q8—21no—
552C4×Q8—21no—
553C4×Q8—21no—
554C4×D4—22no—
555C4×D4—21no—
556C4×D4—22no—
557C4×D4—21no—
558C4×D4—21no—
559#117—22no—
560#117—22no—
561#117—21no—
562#117—21no—
563#117—22no—
564#117—21no—
565#117—22no—
566#117—41no—
567#117D4×C6111yescharacteristic
568#117D4×C6111yescharacteristic
569#117C23×C6111yescharacteristic
570#117C23×C6111yescharacteristic
571#117C23×C6111yescharacteristic
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4D4×C6112yes—
577C2×C4⋊C4D4×C6111yescharacteristic
578C2×C4⋊C4D4×C6111yescharacteristic
579C2×C4⋊C4C23×C6111yescharacteristic
580C2×C4⋊C4C23×C6111yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4D4×C6112yes—
585C2×C42—21no—
586C2×C42C23×C6111yescharacteristic
587C2×C42C23×C6111yescharacteristic
588#107—21no—
589#107—21no—
590#107—21no—
591#106—21no—
592#106—21no—
593#106—21no—
594#104—22no—
595#104—41no—
596#103—21no—
597#103—21no—
598#103—21no—
599#103—21no—
600#103—21no—
601#103—21no—
602#103—21no—
603#102—21no—
604#101—22no—
605#101—41no—
606C22⋊C8—21no—
607C22⋊C8—21no—
608#95—22no—
609#95—22no—
610#95—22no—
611C24C2×D4×C6111yescharacteristic
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616C2×Q8—22no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8C2×D4×C6111yescharacteristic
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4C2×D4×C6111yescharacteristic
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4C2×D4×C6112yes—
647C22×C4C2×D4×C6111yescharacteristic
648C22×C4C2×D4×C6111yescharacteristic
649C22×C4C2×D4×C6111yescharacteristic
650C22×C4C2×D4×C6111yescharacteristic
651C22×C4C2×D4×C6111yescharacteristic
652C22×C4C2×D4×C6112yes—
653C22×C4C24×C6111yescharacteristic
654Q16—42no—
655SD16—42no—
656M16—21no—
657M16—21no—
658M16—21no—
659M16—21no—
660M16—21no—
661M16—21no—
662M16—21no—
663M16—42no—
664M16#41×C6112yes—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—42no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—42no—
689C4⋊C4—44no—
690C4⋊C4—41no—
691C4⋊C4—41no—
692C4⋊C4C2×D4×C6111yescharacteristic
693C4⋊C4C2×D4×C6111yescharacteristic
694C4⋊C4C2×D4×C6111yescharacteristic
695C4⋊C4C2×D4×C6111yescharacteristic
696C4⋊C4C2×D4×C6111yescharacteristic
697C4⋊C4C2×D4×C6111yescharacteristic
698C22⋊C4—22no—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—21no—
702C22⋊C4—21no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—42no—
713C22⋊C4—41no—
714C22⋊C4—41no—
715C42—22no—
716C42—22no—
717C42—22no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42#41×C6112yes—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—41no—
731C23—41no—
732C23#120×C6111yescharacteristic
733C23#120×C6111yescharacteristic
734C23C22×D4×C6111yescharacteristic
735Q8—21no—
736Q8—21no—
737Q8—41no—
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—41no—
743Q8—41no—
744Q8—41no—
745Q8—82no—
746D4—21no—
747D4—21no—
748D4—42no—
749D4—41no—
750D4—41no—
751D4—81no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—81no—
789C2×C4—82no—
790C2×C4#120×C6111yescharacteristic
791C2×C4#120×C6111yescharacteristic
792C2×C4C22×D4×C6111yescharacteristic
793C2×C4C22×D4×C6111yescharacteristic
794C2×C4C2×#41×C6111yescharacteristic
795C2×C4C2×#41×C6111yescharacteristic
796C2×C4H(5,𝔽2)×C6111yescharacteristic
797C2×C42−1+4×C6111yescharacteristic
798C8—22no—
799C8—41no—
800C8—41no—
801C8—41no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—81no—
814C22—81no—
815C22C2×#120×C6111yescharacteristic
816C22C61×#54611yescharacteristic
817C22C61×#54711yescharacteristic
818C4—21no—
819C4—21no—
820C4—42no—
821C4—42no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—81no—
831C4—81no—
832C4—81no—
833C4C61×#53211yescharacteristic
834C4C61×#53711yescharacteristic
835C4C61×#54611yescharacteristic
836C4C61×#54711yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2C61×#243011yescharacteristic
843C2C61×#302011yescharacteristic
844C2C61×#302211yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#525C22
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×#3095C2semidirect
4. C61×#2621C2semidirect
5. C61×#2061C2semidirect
6. C61×#2038C2semidirect
7. C61×#2028C2semidirect
8. C61×#2005C2semidirect
9. C61×#1901C2semidirect
11. C61×#1886C2semidirect
12. C61×#1882C2semidirect
13. C61×#1860C2semidirect
14. C61×#1857C2semidirect
15. C61×#1733C2semidirect
379. #25529C61direct (N × H)
416. #3095C2×C61semidirect
418. #2621C2×C61semidirect
419. #2061C2×C61semidirect
420. #2038C2×C61semidirect
421. #2028C2×C61semidirect
422. #2005C2×C61semidirect
423. #1901C2×C61semidirect
425. #1886C2×C61semidirect
426. #1882C2×C61semidirect
427. #1860C2×C61semidirect
428. #1857C2×C61semidirect
429. #1733C2×C61semidirect
493. C61#25529direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#34952
C61×#30952
C61×#30562
C61×#26212
C61×#20612
C61×#20382
C61×#20282
C61×#20052
C61×#19012
C61×#18972
C61×#18862
C61×#18822
C61×#18602
C61×#18572
C61×#17332
#2552961