Finite Group Databasebeta

← C61×#15137 #29518570

Subgroups — C61×#15137 #29518570

Order 15616.

1438 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#398C212yesmaximal
2C2×C61×#389C211yesmaximal, characteristic
3C2×C61×#389C211yesmaximal, characteristic
4C2×C61×#389C211yesmaximal, characteristic
5C2×C61×#384C211yesmaximal, characteristic
6C61×#1444C212yesmaximal
7C61×#1442C212yesmaximal
8C61×#1441C212yesmaximal
9C61×C4⋊#95C211yesmaximal, characteristic
10C61×C4⋊#95C211yesmaximal, characteristic
11C4×#95×C61C211yesmaximal, characteristic
12C22×C4⋊C4×C61C2211yescharacteristic
13C22×C4⋊C4×C61C2212yes—
14C22×C4⋊C4×C61C2212yes—
15C22×C4⋊C4×C61C2212yes—
16C22×C4⋊C4×C61C2212yes—
17C22×C4⋊C4×C61C2212yes—
18C22×C4⋊C4×C61C2211yescharacteristic
19C22×C4⋊C4×C61C2211yescharacteristic
20C22×C4⋊C4×C61C2211yescharacteristic
21C22×C42×C61C2211yescharacteristic
22C22×C42×C61C2211yescharacteristic
23C22×C42×C61C2211yescharacteristic
24C61×#398—28no—
25C61×#389—24no—
26C61×#389—24no—
27C61×#389—24no—
28C61×#384—24no—
29C2×#95×C61C2212yes—
30C2×#95×C61C2212yes—
31C2×#95×C61C2212yes—
32C2×#95×C61C2212yes—
33C2×#95×C61C2212yes—
34C2×#95×C61C2211yescharacteristic
35C2×#95×C61C2211yescharacteristic
36C2×#95×C61C2212yes—
37C2×#95×C61C2212yes—
38C2×#95×C61C2211yescharacteristic
39C2×#95×C61C2211yescharacteristic
40C23×C4×C61C2312yes—
41C23×C4×C61C2311yescharacteristic
42C23×C4×C61C2312yes—
43C23×C4×C61C2311yescharacteristic
44C23×C4×C61C2312yes—
45C23×C4×C61C2311yescharacteristic
46C23×C4×C61C2311yescharacteristic
47C23×C4×C61C2312yes—
48C23×C4×C61C2311yescharacteristic
49C23×C4×C61C2311yescharacteristic
50C23×C4×C61C2311yescharacteristic
51C2×C4⋊C4×C61—22no—
52C2×C4⋊C4×C61—22no—
53C2×C4⋊C4×C61—22no—
54C2×C4⋊C4×C61—22no—
55C2×C4⋊C4×C61—22no—
56C2×C4⋊C4×C61—22no—
57C2×C4⋊C4×C61—24no—
58C2×C4⋊C4×C61—24no—
59C2×C4⋊C4×C61—22no—
60C2×C4⋊C4×C61—24no—
61C2×C4⋊C4×C61—24no—
62C2×C4⋊C4×C61—24no—
63C2×C4⋊C4×C61—22no—
64C2×C4⋊C4×C61—24no—
65C2×C4⋊C4×C61—24no—
66C2×C4⋊C4×C61—24no—
67C2×C4⋊C4×C61—24no—
68C2×C4⋊C4×C61—24no—
69C2×C4⋊C4×C61—22no—
70C2×C4⋊C4×C61—42no—
71C2×C4⋊C4×C61—42no—
72C2×C4⋊C4×C61—42no—
73C2×C4⋊C4×C61—42no—
74C2×C4⋊C4×C61—42no—
75C2×C4⋊C4×C61D414yes—
76C2×C4⋊C4×C61D414yes—
77C2×C4⋊C4×C61Q814yes—
78C2×C42×C61—22no—
79C2×C42×C61—22no—
80C2×C42×C61—22no—
81C2×C42×C61—22no—
82C2×C42×C61—22no—
83C2×C42×C61—22no—
84C2×C42×C61—22no—
85C2×C42×C61—22no—
86C2×C42×C61Q814yes—
87#95×C61—24no—
88#95×C61—24no—
89#95×C61—24no—
90#95×C61—24no—
91#95×C61—24no—
92#95×C61—22no—
93#95×C61—24no—
94#95×C61—22no—
95#95×C61—42no—
96#95×C61D414yes—
97#95×C61Q814yes—
98C24×C61C2411yescharacteristic
99C22×C4×C61—21no—
100C22×C4×C61—21no—
101C22×C4×C61—21no—
102C22×C4×C61—21no—
103C22×C4×C61—21no—
104C22×C4×C61—21no—
105C22×C4×C61—21no—
106C22×C4×C61—21no—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61—21no—
117C22×C4×C61—22no—
118C22×C4×C61—21no—
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—21no—
136C22×C4×C61—22no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—22no—
140C22×C4×C61—21no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—21no—
144C22×C4×C61—22no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—22no—
148C22×C4×C61—21no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61C2×D412yes—
157C22×C4×C61C2×D414yes—
158C22×C4×C61C2×D414yes—
159C22×C4×C61C2×D412yes—
160C22×C4×C61C2×D412yes—
161C22×C4×C61C2×D412yes—
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2×Q812yes—
164C22×C4×C61C2×Q812yes—
165C22×C4×C61C2×Q814yes—
166C22×C4×C61C2×Q812yes—
167C22×C4×C61C2×Q812yes—
168C22×C4×C61C2×Q812yes—
169C22×C4×C61C2×Q812yes—
170C22×C4×C61C2×Q812yes—
171C22×C4×C61#4112yes—
172C22×C4×C61#4112yes—
173C22×C4×C61#4112yes—
174C22×C4×C61#4112yes—
175C22×C4×C61#4112yes—
176C4⋊C4×C61—28no—
177C4⋊C4×C61—28no—
178C4⋊C4×C61—28no—
179C4⋊C4×C61—48no—
180C4⋊C4×C61—48no—
181C4⋊C4×C61—48no—
182C4⋊C4×C61—48no—
183C4⋊C4×C61—48no—
184C4⋊C4×C61—44no—
185C42×C61—28no—
186C42×C61—44no—
187C42×C61—44no—
188C23×C61C22×D411yescharacteristic
189C23×C61C22×D411yescharacteristic
190C23×C61C22×D411yescharacteristic
191C23×C61C22×Q811yescharacteristic
192C23×C61C22×Q811yescharacteristic
193C23×C61C22×Q811yescharacteristic
194C23×C61C2×#4111yescharacteristic
195C23×C61C2×#4111yescharacteristic
196C23×C61C2×#4111yescharacteristic
197C23×C61C2×#4111yescharacteristic
198C23×C61C2×#4111yescharacteristic
199C23×C61H(5,𝔽2)11yescharacteristic
200C23×C61H(5,𝔽2)11yescharacteristic
201C23×C612−1+411yescharacteristic
202C23×C612−1+411yescharacteristic
203C2×C4×C61—22no—
204C2×C4×C61—22no—
205C2×C4×C61—22no—
206C2×C4×C61—22no—
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—22no—
210C2×C4×C61—22no—
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—22no—
215C2×C4×C61—24no—
216C2×C4×C61—24no—
217C2×C4×C61—24no—
218C2×C4×C61—22no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—24no—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—24no—
227C2×C4×C61—24no—
228C2×C4×C61—24no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—24no—
234C2×C4×C61—22no—
235C2×C4×C61—24no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—42no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—41no—
244C2×C4×C61—42no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—42no—
248C2×C4×C61—41no—
249C2×C4×C61—42no—
250C2×C4×C61—42no—
251C2×C4×C61—42no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—42no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—42no—
258C2×C4×C61—41no—
259C2×C4×C61—42no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—42no—
264C2×C4×C61—42no—
265C2×C4×C61—42no—
266C2×C4×C61—42no—
267C2×C4×C61—42no—
268C2×C4×C61—42no—
269C2×C4×C61—42no—
270C2×C4×C61—42no—
271C2×C4×C61#12114yes—
272C2×C4×C61C22⋊Q814yes—
273C2×C4×C61C22⋊Q814yes—
274C2×C4×C61#12314yes—
275C2×C4×C61#12514yes—
276C2×C4×C61#12514yes—
277C2×C4×C61#12514yes—
278C2×C4×C61C4⋊Q814yes—
279C2×C4×C61C4⋊Q814yes—
280#15137C6111yesmaximal, characteristic, direct product factor, Sylow
281C22×C61C2×#12111yescharacteristic
282C22×C61C2×C22⋊Q811yescharacteristic
283C22×C61C2×C22⋊Q811yescharacteristic
284C22×C61C2×#12311yescharacteristic
285C22×C61C2×#12511yescharacteristic
286C22×C61C2×#12511yescharacteristic
287C22×C61C2×#12511yescharacteristic
288C22×C61C2×C4⋊Q811yescharacteristic
289C22×C61C2×C4⋊Q811yescharacteristic
290C22×C61#53211yescharacteristic
291C22×C61#53211yescharacteristic
292C22×C61#53311yescharacteristic
293C22×C61#53311yescharacteristic
294C22×C61#54011yescharacteristic
295C22×C61#54111yescharacteristic
296C22×C61#54211yescharacteristic
297C22×C61#54211yescharacteristic
298C22×C61#54411yescharacteristic
299C22×C61#54411yescharacteristic
300C22×C61D4211yescharacteristic
301C22×C61D4211yescharacteristic
302C22×C61#54611yescharacteristic
303C22×C61#54711yescharacteristic
304C22×C61#54711yescharacteristic
305C22×C61#54811yescharacteristic
306C22×C61D4×Q811yescharacteristic
307C22×C61D4×Q811yescharacteristic
308C22×C61D4×Q811yescharacteristic
309C22×C61#55011yescharacteristic
310C22×C61#55211yescharacteristic
311C22×C61#55311yescharacteristic
312C22×C61#55411yescharacteristic
313C22×C61#55411yescharacteristic
314C22×C61#55711yescharacteristic
315C22×C61Q8211yescharacteristic
316C4×C61—24no—
317C4×C61—24no—
318C4×C61—44no—
319C4×C61—42no—
320C4×C61—42no—
321C4×C61—44no—
322C4×C61—42no—
323C4×C61—42no—
324C4×C61—44no—
325C4×C61—82no—
326C4×C61#39818yescomplemented
327C2×#398C2×C6112yes—
328C2×#389C2×C6111yescharacteristic
329C2×#389C2×C6111yescharacteristic
330C2×#389C2×C6111yescharacteristic
331C2×#384C2×C6111yescharacteristic
332#1444C2×C6112yes—
333#1442C2×C6112yes—
334#1441C2×C6112yes—
335C4⋊#95C2×C6111yescharacteristic
336C4⋊#95C2×C6111yescharacteristic
337C4×#95C2×C6111yescharacteristic
338C2×C61C2×#39811yescharacteristic
339C2×C61#242211yescharacteristic
340C2×C61#242311yescharacteristic
341C2×C61#242811yescharacteristic
342C2×C61#242911yescharacteristic
343C2×C61#244011yescharacteristic
344C2×C61#244211yescharacteristic
345C2×C61#245111yescharacteristic
346C2×C61#245211yescharacteristic
347C2×C61#250611yescharacteristic
348C2×C61#250711yescharacteristic
349C2×C61#255111yescharacteristic
350C2×C61#255211yescharacteristic
351C2×C61#264711yescharacteristic
352C2×C61#285911yescharacteristic
353C22×C4⋊C4C22×C6111yescharacteristic
354C22×C4⋊C4C22×C6112yes—
355C22×C4⋊C4C22×C6112yes—
356C22×C4⋊C4C22×C6112yes—
357C22×C4⋊C4C22×C6112yes—
358C22×C4⋊C4C22×C6112yes—
359C22×C4⋊C4C22×C6111yescharacteristic
360C22×C4⋊C4C22×C6111yescharacteristic
361C22×C4⋊C4C22×C6111yescharacteristic
362C22×C42C22×C6111yescharacteristic
363C22×C42C22×C6111yescharacteristic
364C22×C42C22×C6111yescharacteristic
365#398—28no—
366#389—24no—
367#389—24no—
368#389—24no—
369#384—24no—
370C2×#95C22×C6112yes—
371C2×#95C22×C6112yes—
372C2×#95C22×C6111yescharacteristic
373C2×#95C22×C6111yescharacteristic
374C2×#95C22×C6112yes—
375C2×#95C22×C6112yes—
376C2×#95C22×C6112yes—
377C2×#95C22×C6112yes—
378C2×#95C22×C6112yes—
379C2×#95C22×C6111yescharacteristic
380C2×#95C22×C6111yescharacteristic
381C61#1513711yescharacteristic, direct product factor, Sylow
382C23×C4C23×C6112yes—
383C23×C4C23×C6112yes—
384C23×C4C23×C6111yescharacteristic
385C23×C4C23×C6112yes—
386C23×C4C23×C6111yescharacteristic
387C23×C4C23×C6112yes—
388C23×C4C23×C6111yescharacteristic
389C23×C4C23×C6111yescharacteristic
390C23×C4C23×C6111yescharacteristic
391C23×C4C23×C6111yescharacteristic
392C23×C4C23×C6111yescharacteristic
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—42no—
413C2×C4⋊C4—42no—
414C2×C4⋊C4—42no—
415C2×C4⋊C4—42no—
416C2×C4⋊C4—42no—
417C2×C4⋊C4D4×C6114yes—
418C2×C4⋊C4D4×C6114yes—
419C2×C4⋊C4Q8×C6114yes—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42Q8×C6114yes—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—22no—
435#95—24no—
436#95—22no—
437#95—42no—
438#95D4×C6114yes—
439#95Q8×C6114yes—
440C24C24×C6111yescharacteristic
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4C2×D4×C6112yes—
499C22×C4C2×D4×C6114yes—
500C22×C4C2×D4×C6114yes—
501C22×C4C2×D4×C6112yes—
502C22×C4C2×D4×C6112yes—
503C22×C4C2×D4×C6112yes—
504C22×C4C2×D4×C6112yes—
505C22×C4C2×Q8×C6112yes—
506C22×C4C2×Q8×C6112yes—
507C22×C4C2×Q8×C6114yes—
508C22×C4C2×Q8×C6112yes—
509C22×C4C2×Q8×C6112yes—
510C22×C4C2×Q8×C6112yes—
511C22×C4C2×Q8×C6112yes—
512C22×C4C2×Q8×C6112yes—
513C22×C4#41×C6112yes—
514C22×C4#41×C6112yes—
515C22×C4#41×C6112yes—
516C22×C4#41×C6112yes—
517C22×C4#41×C6112yes—
518C4⋊C4—28no—
519C4⋊C4—28no—
520C4⋊C4—28no—
521C4⋊C4—48no—
522C4⋊C4—48no—
523C4⋊C4—48no—
524C4⋊C4—48no—
525C4⋊C4—48no—
526C4⋊C4—44no—
527C42—28no—
528C42—44no—
529C42—44no—
530C23C22×D4×C6111yescharacteristic
531C23C22×D4×C6111yescharacteristic
532C23C22×D4×C6111yescharacteristic
533C23C22×Q8×C6111yescharacteristic
534C23C22×Q8×C6111yescharacteristic
535C23C22×Q8×C6111yescharacteristic
536C23C2×#41×C6111yescharacteristic
537C23C2×#41×C6111yescharacteristic
538C23C2×#41×C6111yescharacteristic
539C23C2×#41×C6111yescharacteristic
540C23C2×#41×C6111yescharacteristic
541C23H(5,𝔽2)×C6111yescharacteristic
542C23H(5,𝔽2)×C6111yescharacteristic
543C232−1+4×C6111yescharacteristic
544C232−1+4×C6111yescharacteristic
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4#121×C6114yes—
614C2×C4C22⋊Q8×C6114yes—
615C2×C4C22⋊Q8×C6114yes—
616C2×C4#123×C6114yes—
617C2×C4#125×C6114yes—
618C2×C4#125×C6114yes—
619C2×C4#125×C6114yes—
620C2×C4C4⋊Q8×C6114yes—
621C2×C4C4⋊Q8×C6114yes—
622C22C2×#121×C6111yescharacteristic
623C22C2×C22⋊Q8×C6111yescharacteristic
624C22C2×C22⋊Q8×C6111yescharacteristic
625C22C2×#123×C6111yescharacteristic
626C22C2×#125×C6111yescharacteristic
627C22C2×#125×C6111yescharacteristic
628C22C2×#125×C6111yescharacteristic
629C22C2×C4⋊Q8×C6111yescharacteristic
630C22C2×C4⋊Q8×C6111yescharacteristic
631C22C61×#53211yescharacteristic
632C22C61×#53211yescharacteristic
633C22C61×#53311yescharacteristic
634C22C61×#53311yescharacteristic
635C22C61×#54011yescharacteristic
636C22C61×#54111yescharacteristic
637C22C61×#54211yescharacteristic
638C22C61×#54211yescharacteristic
639C22C61×#54411yescharacteristic
640C22C61×#54411yescharacteristic
641C22D42×C6111yescharacteristic
642C22D42×C6111yescharacteristic
643C22C61×#54611yescharacteristic
644C22C61×#54711yescharacteristic
645C22C61×#54711yescharacteristic
646C22C61×#54811yescharacteristic
647C22D4×Q8×C6111yescharacteristic
648C22D4×Q8×C6111yescharacteristic
649C22D4×Q8×C6111yescharacteristic
650C22C61×#55011yescharacteristic
651C22C61×#55211yescharacteristic
652C22C61×#55311yescharacteristic
653C22C61×#55411yescharacteristic
654C22C61×#55411yescharacteristic
655C22C61×#55711yescharacteristic
656C22Q82×C6111yescharacteristic
657C4—24no—
658C4—24no—
659C4—42no—
660C4—44no—
661C4—42no—
662C4—42no—
663C4—44no—
664C4—42no—
665C4—44no—
666C4—82no—
667C4C61×#39818yescomplemented
668C2C2×C61×#39811yescharacteristic
669C2C61×#242211yescharacteristic
670C2C61×#242311yescharacteristic
671C2C61×#242811yescharacteristic
672C2C61×#242911yescharacteristic
673C2C61×#244011yescharacteristic
674C2C61×#244211yescharacteristic
675C2C61×#245111yescharacteristic
676C2C61×#245211yescharacteristic
677C2C61×#250611yescharacteristic
678C2C61×#250711yescharacteristic
679C2C61×#255111yescharacteristic
680C2C61×#255211yescharacteristic
681C2C61×#264711yescharacteristic
682C2C61×#285911yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C61C24
commutator, Frattini, cosocleC24C24×C61
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
280. #15137C61direct (N × H)
326. C4×C61#398semidirect
381. C61#15137direct (N × H)
667. C4C61×#398semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#3982
C2×C61×#3892
C2×C61×#3842
C61×#14442
C61×#14422
C61×#14412
C61×C4⋊#952
C4×#95×C612
#1513761