Finite Group Databasebeta

← C61×#26199 #29529632

Subgroups — C61×#26199 #29529632

Order 15616.

844 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2414C211yesmaximal, characteristic
2C61×#2352C211yesmaximal, characteristic, complemented
3C61×#2101C211yesmaximal, characteristic, complemented
4C61×#2077C211yesmaximal, characteristic, complemented
5C61×#2073C211yesmaximal, characteristic, complemented
6C61×#2033C211yesmaximal, characteristic, complemented
7C61×#1926C211yesmaximal, characteristic, complemented
8C61×#1918C211yesmaximal, characteristic, complemented
9C61×#1893C211yesmaximal, characteristic, complemented
10C61×#1875C211yesmaximal, characteristic, complemented
11C61×#1874C211yesmaximal, characteristic, complemented
12C61×#1869C211yesmaximal, characteristic, complemented
13C61×#1854C211yesmaximal, characteristic, complemented
14C61×#1824C211yesmaximal, characteristic, complemented
15C61×#1735C211yesmaximal, characteristic, complemented
16C23×C8×C61C2211yescharacteristic
17C2×#121×C61C2211yescharacteristic
18C2×#121×C61C2211yescharacteristic
19C2×C4×D4×C61C2211yescharacteristic
20C2×#117×C61C2211yescharacteristic
21C2×#117×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2211yescharacteristic
23C2×#107×C61C2211yescharacteristic
24C2×#106×C61C2211yescharacteristic
25C2×#102×C61C2211yescharacteristic
26C2×#102×C61C2211yescharacteristic
27C2×#102×C61C2211yescharacteristic
28C2×#102×C61C2211yescharacteristic
29C2×C22⋊C8×C61C2211yescharacteristic
30C2×C22⋊C8×C61C2211yescharacteristic
31C2×C22⋊C8×C61C2211yescharacteristic
32C61×#394—21no—
33C61×#392—21no—
34C61×#390—21no—
35C61×#390C2211yescharacteristic
36C61×#389C2211yescharacteristic
37C61×#388—21no—
38C61×#388—21no—
39C61×#387—21no—
40C61×#386—21no—
41C61×#382C2211yescharacteristic
42C61×#380C2211yescharacteristic
43C61×#380C2211yescharacteristic
44C61×#380C2211yescharacteristic
45C4×C4⋊C4×C61C2211yescharacteristic
46C4×C22⋊C4×C61—21no—
47C61×#340C2211yescharacteristic
48C61×#340C2211yescharacteristic
49C61×#340C2211yescharacteristic
50C61×#340C2211yescharacteristic
51C61×#340C2211yescharacteristic
52C61×#340C2211yescharacteristic
53C61×#340C2211yescharacteristic
54C61×#340C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×D4×C61—21no—
60C22×D4×C61—21no—
61C22×D4×C61D411yescharacteristic
62C22×D4×C61C2311yescharacteristic
63C23×C4×C61—21no—
64C23×C4×C61C2311yescharacteristic
65C23×C4×C61C2311yescharacteristic
66C22×C8×C61—22no—
67C22×C8×C61—41no—
68C22×C8×C61—41no—
69C22×C8×C61C2311yescharacteristic
70C22×C8×C61C2311yescharacteristic
71C22×C8×C61C2311yescharacteristic
72C22×C8×C61C2311yescharacteristic
73#121×C61—22no—
74#121×C61—22no—
75#121×C61—22no—
76#121×C61—41no—
77C4×D4×C61—22no—
78C4×D4×C61—22no—
79#117×C61—22no—
80#117×C61—22no—
81#117×C61—41no—
82#117×C61—41no—
83C2×C4⋊C4×C61—22no—
84C2×C4⋊C4×C61—21no—
85C2×C4⋊C4×C61—21no—
86C2×C4⋊C4×C61—41no—
87C2×C4⋊C4×C61D411yescharacteristic
88C2×C4⋊C4×C61C2311yescharacteristic
89C2×C4⋊C4×C61C2311yescharacteristic
90C2×C4⋊C4×C61C2311yescharacteristic
91C2×C4⋊C4×C61C2311yescharacteristic
92C2×C4⋊C4×C61C2311yescharacteristic
93C2×C4⋊C4×C61C2311yescharacteristic
94C2×C4⋊C4×C61C2311yescharacteristic
95C2×C22⋊C4×C61—21no—
96C2×C22⋊C4×C61—21no—
97C2×C22⋊C4×C61—21no—
98C2×C22⋊C4×C61—21no—
99C2×C22⋊C4×C61—21no—
100C2×C22⋊C4×C61—21no—
101C2×C22⋊C4×C61—21no—
102C2×C22⋊C4×C61—21no—
103C2×C22⋊C4×C61—21no—
104C2×C22⋊C4×C61D411yescharacteristic
105C2×C22⋊C4×C61D411yescharacteristic
106C2×C42×C61—21no—
107C2×C42×C61—21no—
108C2×C42×C61—21no—
109C2×C42×C61C2311yescharacteristic
110#107×C61—22no—
111#106×C61—41no—
112#102×C61—22no—
113#102×C61—41no—
114#102×C61—41no—
115#102×C61—41no—
116C22⋊C8×C61—22no—
117C22⋊C8×C61—41no—
118C22⋊C8×C61—41no—
119#95×C61—21no—
120#95×C61—21no—
121#95×C61—21no—
122#95×C61—21no—
123#95×C61—21no—
124#95×C61—21no—
125#95×C61—21no—
126C24×C61—21no—
127C24×C61C2×D411yescharacteristic
128C24×C61C2×D411yescharacteristic
129C2×D4×C61—22no—
130C2×D4×C61—22no—
131C2×D4×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61—41no—
138C2×D4×C61—42no—
139C2×D4×C61—42no—
140C2×D4×C61—42no—
141C2×D4×C61—81no—
142C2×D4×C61—81no—
143C2×D4×C61—81no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—42no—
162C22×C4×C61—42no—
163C22×C4×C61—81no—
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61#4112yes—
169C22×C4×C61#4112yes—
170C22×C4×C61C2411yescharacteristic
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—44no—
184C4⋊C4×C61—22no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—42no—
198C4⋊C4×C61—81no—
199C4⋊C4×C61#4112yes—
200C4⋊C4×C61#4112yes—
201C22⋊C4×C61—22no—
202C22⋊C4×C61—22no—
203C22⋊C4×C61—42no—
204C22⋊C4×C61—42no—
205C22⋊C4×C61—42no—
206C22⋊C4×C61—42no—
207C22⋊C4×C61—42no—
208C22⋊C4×C61—42no—
209C22⋊C4×C61—81no—
210C22⋊C4×C61—81no—
211C22⋊C4×C61—81no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—42no—
215C42×C61—42no—
216C42×C61—81no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—21no—
228C23×C61—21no—
229C23×C61—41no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61—41no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61—41no—
236C23×C61#12312yes—
237C23×C61#13512yes—
238C23×C61C22×D411yescharacteristic
239D4×C61—44no—
240D4×C61—41no—
241D4×C61—41no—
242D4×C61—41no—
243D4×C61—41no—
244D4×C61—84no—
245D4×C61—84no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—22no—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—84no—
287C2×C4×C61#12312yes—
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61H(5,𝔽2)11yescharacteristic
293C2×C4×C61H(5,𝔽2)11yescharacteristic
294C8×C61—41no—
295C8×C61—41no—
296C8×C61—41no—
297C8×C61—41no—
298#26199C6111yesmaximal, characteristic, direct product factor, Sylow
299C22×C61—22no—
300C22×C61—22no—
301C22×C61—22no—
302C22×C61—22no—
303C22×C61—22no—
304C22×C61—22no—
305C22×C61—41no—
306C22×C61—41no—
307C22×C61—41no—
308C22×C61—41no—
309C22×C61—41no—
310C22×C61—41no—
311C22×C61—41no—
312C22×C61—41no—
313C22×C61—81no—
314C22×C61—81no—
315C22×C61—81no—
316C22×C61—81no—
317C22×C61—81no—
318C22×C61—81no—
319C22×C61—81no—
320C22×C61C2×#12311yescharacteristic
321C22×C61#54611yescharacteristic
322C22×C61#54611yescharacteristic
323C22×C61C2×#13511yescharacteristic
324C22×C61#57511yescharacteristic
325C22×C61#57611yescharacteristic
326C22×C61#57711yescharacteristic
327C4×C61—22no—
328C4×C61—41no—
329C4×C61—41no—
330C4×C61—41no—
331C4×C61—42no—
332C4×C61—42no—
333C4×C61—81no—
334C4×C61—81no—
335C4×C61—81no—
336C4×C61—81no—
337C4×C61—81no—
338C4×C61#52911yescharacteristic
339C4×C61#53811yescharacteristic
340C4×C61#55311yescharacteristic
341C4×C61#55311yescharacteristic
342#2414C2×C6111yescharacteristic
343#2352C2×C6111yescharacteristic, complemented
344#2101C2×C6111yescharacteristic, complemented
345#2077C2×C6111yescharacteristic, complemented
346#2073C2×C6111yescharacteristic, complemented
347#2033C2×C6111yescharacteristic, complemented
348#1926C2×C6111yescharacteristic, complemented
349#1918C2×C6111yescharacteristic, complemented
350#1893C2×C6111yescharacteristic, complemented
351#1875C2×C6111yescharacteristic, complemented
352#1874C2×C6111yescharacteristic, complemented
353#1869C2×C6111yescharacteristic, complemented
354#1854C2×C6111yescharacteristic, complemented
355#1824C2×C6111yescharacteristic, complemented
356#1735C2×C6111yescharacteristic, complemented
357C2×C61—42no—
358C2×C61—42no—
359C2×C61—161no—
360C2×C61#244411yescharacteristic
361C2×C61#309111yescharacteristic
362C2×C61#309611yescharacteristic
363C2×C61#329711yescharacteristic
364C2×C61#330111yescharacteristic
365C2×C61#331711yescharacteristic
366C2×C61#331911yescharacteristic
367C23×C8C22×C6111yescharacteristic
368C2×#121C22×C6111yescharacteristic
369C2×#121C22×C6111yescharacteristic
370C2×C4×D4C22×C6111yescharacteristic
371C2×#117C22×C6111yescharacteristic
372C2×#117C22×C6111yescharacteristic
373C22×C4⋊C4C22×C6111yescharacteristic
374C2×#107C22×C6111yescharacteristic
375C2×#106C22×C6111yescharacteristic
376C2×#102C22×C6111yescharacteristic
377C2×#102C22×C6111yescharacteristic
378C2×#102C22×C6111yescharacteristic
379C2×#102C22×C6111yescharacteristic
380C2×C22⋊C8C22×C6111yescharacteristic
381C2×C22⋊C8C22×C6111yescharacteristic
382C2×C22⋊C8C22×C6111yescharacteristic
383#394—21no—
384#392—21no—
385#390—21no—
386#390C22×C6111yescharacteristic
387#389C22×C6111yescharacteristic
388#388—21no—
389#388—21no—
390#387—21no—
391#386—21no—
392#382C22×C6111yescharacteristic
393#380C22×C6111yescharacteristic
394#380C22×C6111yescharacteristic
395#380C22×C6111yescharacteristic
396C4×C4⋊C4C22×C6111yescharacteristic
397C4×C22⋊C4—21no—
398#340C22×C6111yescharacteristic
399#340C22×C6111yescharacteristic
400#340C22×C6111yescharacteristic
401#340C22×C6111yescharacteristic
402#340C22×C6111yescharacteristic
403#340C22×C6111yescharacteristic
404#340C22×C6111yescharacteristic
405#340C22×C6111yescharacteristic
406#340C22×C6111yescharacteristic
407#340C22×C6111yescharacteristic
408#336C22×C6111yescharacteristic
409#336C22×C6111yescharacteristic
410C61#2619911yescharacteristic, direct product factor, Sylow
411C22×D4—21no—
412C22×D4—21no—
413C22×D4D4×C6111yescharacteristic
414C22×D4C23×C6111yescharacteristic
415C23×C4—21no—
416C23×C4C23×C6111yescharacteristic
417C23×C4C23×C6111yescharacteristic
418C22×C8—22no—
419C22×C8—41no—
420C22×C8—41no—
421C22×C8C23×C6111yescharacteristic
422C22×C8C23×C6111yescharacteristic
423C22×C8C23×C6111yescharacteristic
424C22×C8C23×C6111yescharacteristic
425#121—22no—
426#121—22no—
427#121—22no—
428#121—41no—
429C4×D4—22no—
430C4×D4—22no—
431#117—22no—
432#117—22no—
433#117—41no—
434#117—41no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—41no—
439C2×C4⋊C4D4×C6111yescharacteristic
440C2×C4⋊C4C23×C6111yescharacteristic
441C2×C4⋊C4C23×C6111yescharacteristic
442C2×C4⋊C4C23×C6111yescharacteristic
443C2×C4⋊C4C23×C6111yescharacteristic
444C2×C4⋊C4C23×C6111yescharacteristic
445C2×C4⋊C4C23×C6111yescharacteristic
446C2×C4⋊C4C23×C6111yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4D4×C6111yescharacteristic
457C2×C22⋊C4D4×C6111yescharacteristic
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42C23×C6111yescharacteristic
462#107—22no—
463#106—41no—
464#102—22no—
465#102—41no—
466#102—41no—
467#102—41no—
468C22⋊C8—22no—
469C22⋊C8—41no—
470C22⋊C8—41no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478C24—21no—
479C24C2×D4×C6111yescharacteristic
480C24C2×D4×C6111yescharacteristic
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—41no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—81no—
494C2×D4—81no—
495C2×D4—81no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—81no—
516C22×C4C2×D4×C6111yescharacteristic
517C22×C4C2×D4×C6111yescharacteristic
518C22×C4C2×D4×C6111yescharacteristic
519C22×C4C2×D4×C6111yescharacteristic
520C22×C4#41×C6112yes—
521C22×C4#41×C6112yes—
522C22×C4C24×C6111yescharacteristic
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—44no—
536C4⋊C4—22no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—42no—
550C4⋊C4—81no—
551C4⋊C4#41×C6112yes—
552C4⋊C4#41×C6112yes—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—81no—
562C22⋊C4—81no—
563C22⋊C4—81no—
564C42—21no—
565C42—21no—
566C42—42no—
567C42—42no—
568C42—81no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23#123×C6112yes—
589C23#135×C6112yes—
590C23C22×D4×C6111yescharacteristic
591D4—44no—
592D4—41no—
593D4—41no—
594D4—41no—
595D4—41no—
596D4—84no—
597D4—84no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—84no—
639C2×C4#123×C6112yes—
640C2×C4C2×#41×C6111yescharacteristic
641C2×C4C2×#41×C6111yescharacteristic
642C2×C4C2×#41×C6111yescharacteristic
643C2×C4C2×#41×C6111yescharacteristic
644C2×C4H(5,𝔽2)×C6111yescharacteristic
645C2×C4H(5,𝔽2)×C6111yescharacteristic
646C8—41no—
647C8—41no—
648C8—41no—
649C8—41no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22C2×#123×C6111yescharacteristic
672C22C61×#54611yescharacteristic
673C22C61×#54611yescharacteristic
674C22C2×#135×C6111yescharacteristic
675C22C61×#57511yescharacteristic
676C22C61×#57611yescharacteristic
677C22C61×#57711yescharacteristic
678C4—22no—
679C4—42no—
680C4—42no—
681C4—41no—
682C4—41no—
683C4—41no—
684C4—81no—
685C4—81no—
686C4—81no—
687C4—81no—
688C4—81no—
689C4C61×#52911yescharacteristic
690C4C61×#53811yescharacteristic
691C4C61×#55311yescharacteristic
692C4C61×#55311yescharacteristic
693C2—42no—
694C2—42no—
695C2—161no—
696C2C61×#244411yescharacteristic
697C2C61×#309111yescharacteristic
698C2C61×#309611yescharacteristic
699C2C61×#329711yescharacteristic
700C2C61×#330111yescharacteristic
701C2C61×#331711yescharacteristic
702C2C61×#331911yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#2414C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×C4×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2352C2semidirect
3. C61×#2101C2semidirect
4. C61×#2077C2semidirect
5. C61×#2073C2semidirect
6. C61×#2033C2semidirect
7. C61×#1926C2semidirect
8. C61×#1918C2semidirect
9. C61×#1893C2semidirect
10. C61×#1875C2semidirect
11. C61×#1874C2semidirect
12. C61×#1869C2semidirect
13. C61×#1854C2semidirect
14. C61×#1824C2semidirect
15. C61×#1735C2semidirect
298. #26199C61direct (N × H)
343. #2352C2×C61semidirect
344. #2101C2×C61semidirect
345. #2077C2×C61semidirect
346. #2073C2×C61semidirect
347. #2033C2×C61semidirect
348. #1926C2×C61semidirect
349. #1918C2×C61semidirect
350. #1893C2×C61semidirect
351. #1875C2×C61semidirect
352. #1874C2×C61semidirect
353. #1869C2×C61semidirect
354. #1854C2×C61semidirect
355. #1824C2×C61semidirect
356. #1735C2×C61semidirect
410. C61#26199direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#24142
C61×#23522
C61×#21012
C61×#20772
C61×#20732
C61×#20332
C61×#19262
C61×#19182
C61×#18932
C61×#18752
C61×#18742
C61×#18692
C61×#18542
C61×#18242
C61×#17352
#2619961