Finite Group Databasebeta

← C61×#25204 #29528637

Subgroups — C61×#25204 #29528637

Order 15616.

940 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#483C211yesmaximal, characteristic, complemented
2C2×C61×#465C211yesmaximal, characteristic
3C61×#2501C211yesmaximal, characteristic
4C61×#2360C211yesmaximal, characteristic, complemented
5C61×#2084C211yesmaximal, characteristic, complemented
6C61×#2072C211yesmaximal, characteristic, complemented
7C61×#2065C211yesmaximal, characteristic, complemented
8C61×#2055C211yesmaximal, characteristic, complemented
9C61×#1948C211yesmaximal, characteristic, complemented
10C61×#1926C211yesmaximal, characteristic, complemented
11C61×#1880C211yesmaximal, characteristic, complemented
12C61×#1874C211yesmaximal, characteristic
13C61×#1850C211yesmaximal, characteristic, complemented
14C61×#1803C211yesmaximal, characteristic, complemented
15C2×C61×#340C211yesmaximal, characteristic, complemented
16C22×SD16×C61C2211yescharacteristic
17C23×C8×C61C2211yescharacteristic
18C2×#123×C61—21no—
19C2×#123×C61—21no—
20C2×C22⋊Q8×C61C2211yescharacteristic
21C2×#121×C61C2211yescharacteristic
22C2×C4×Q8×C61C2211yescharacteristic
23C22×C4⋊C4×C61C2211yescharacteristic
24C22×C4⋊C4×C61C2211yescharacteristic
25C61×#483—24no—
26C61×#465—24no—
27C2×#106×C61C2211yescharacteristic
28C2×#106×C61C2211yescharacteristic
29C2×#106×C61C2211yescharacteristic
30C2×C4⋊C8×C61C2211yescharacteristic
31C2×C4⋊C8×C61C2211yescharacteristic
32C2×#103×C61C2211yescharacteristic
33C2×#103×C61C2211yescharacteristic
34C2×#103×C61C2211yescharacteristic
35C2×#102×C61C2211yescharacteristic
36C2×#102×C61C2211yescharacteristic
37C2×#102×C61C2211yescharacteristic
38C2×C22⋊C8×C61C2211yescharacteristic
39C61×#399—21no—
40C61×#399—21no—
41C61×#391C2211yescharacteristic
42C61×#390C2211yescharacteristic
43C61×#390C2211yescharacteristic
44C61×#389—21no—
45C61×#389C2211yescharacteristic
46C61×#387—21no—
47C61×#385—21no—
48C61×#384C2211yescharacteristic
49C61×#384C2211yescharacteristic
50C4×C4⋊C4×C61C2211yescharacteristic
51C4×C22⋊C4×C61—21no—
52C4×C22⋊C4×C61C2211yescharacteristic
53C61×#340C2211yescharacteristic
54C61×#340C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×Q8×C61C2311yescharacteristic
62C22×D4×C61—21no—
63C22×D4×C61C2311yescharacteristic
64C23×C4×C61—21no—
65C23×C4×C61—21no—
66C23×C4×C61C2311yescharacteristic
67C2×SD16×C61—22no—
68C2×SD16×C61—22no—
69C2×SD16×C61—41no—
70C22×C8×C61—22no—
71C22×C8×C61—22no—
72C22×C8×C61—41no—
73C22×C8×C61C2311yescharacteristic
74C22×C8×C61C2311yescharacteristic
75C22×C8×C61C2311yescharacteristic
76C22×C8×C61C2311yescharacteristic
77#123×C61—44no—
78#123×C61—44no—
79C22⋊Q8×C61—22no—
80C22⋊Q8×C61D414yes—
81#121×C61—22no—
82#121×C61—22no—
83C4×Q8×C61—22no—
84C4×Q8×C61—41no—
85C2×C4⋊C4×C61—21no—
86C2×C4⋊C4×C61—22no—
87C2×C4⋊C4×C61—22no—
88C2×C4⋊C4×C61—22no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—41no—
98C2×C4⋊C4×C61C2311yescharacteristic
99C2×C4⋊C4×C61C2311yescharacteristic
100C2×C4⋊C4×C61C2311yescharacteristic
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C4⋊C4×C61C2311yescharacteristic
104C2×C22⋊C4×C61—21no—
105C2×C22⋊C4×C61—21no—
106C2×C22⋊C4×C61—21no—
107C2×C22⋊C4×C61—21no—
108C2×C22⋊C4×C61—21no—
109C2×C22⋊C4×C61—21no—
110C2×C22⋊C4×C61D411yescharacteristic
111C2×C22⋊C4×C61D411yescharacteristic
112C2×C42×C61—21no—
113C2×C42×C61—21no—
114C2×C42×C61C2311yescharacteristic
115C2×C42×C61C2311yescharacteristic
116#106×C61—22no—
117#106×C61—22no—
118#106×C61—22no—
119C4⋊C8×C61—22no—
120C4⋊C8×C61—41no—
121#103×C61—22no—
122#103×C61—22no—
123#103×C61—22no—
124#102×C61—22no—
125#102×C61—22no—
126#102×C61—41no—
127C22⋊C8×C61—22no—
128#95×C61—21no—
129#95×C61—21no—
130#95×C61—21no—
131#95×C61—21no—
132#95×C61D411yescharacteristic
133#95×C61D411yescharacteristic
134C24×C61—21no—
135C24×C61C2×D411yescharacteristic
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×Q8×C61—21no—
141C2×Q8×C61C2×D412yes—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—42no—
149C2×D4×C61—42no—
150C2×D4×C61—42no—
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—21no—
162C22×C4×C61—42no—
163C22×C4×C61—42no—
164C22×C4×C61—42no—
165C22×C4×C61—42no—
166C22×C4×C61—42no—
167C22×C4×C61—81no—
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D412yes—
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61#4112yes—
175C22×C4×C61C2411yescharacteristic
176SD16×C61—44no—
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—21no—
184C2×C8×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—44no—
189C2×C8×C61#4112yes—
190C4⋊C4×C61—24no—
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—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—42no—
202C4⋊C4×C61—42no—
203C4⋊C4×C61—42no—
204C4⋊C4×C61—42no—
205C4⋊C4×C61—42no—
206C4⋊C4×C61—42no—
207C4⋊C4×C61—42no—
208C4⋊C4×C61—81no—
209C4⋊C4×C61C2×D412yes—
210C4⋊C4×C61#4112yes—
211C22⋊C4×C61—24no—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—42no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—42no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—42no—
218C22⋊C4×C61SD1614yescomplemented
219C42×C61—21no—
220C42×C61—21no—
221C42×C61—21no—
222C42×C61—21no—
223C42×C61—42no—
224C42×C61—81no—
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#12112yes—
237C23×C61C2×SD1612yes—
238C23×C61AGL(1,ℤ/8)12yes—
239C23×C61C22×D411yescharacteristic
240Q8×C61—22no—
241Q8×C61—22no—
242Q8×C61—41no—
243Q8×C61—41no—
244D4×C61—41no—
245D4×C61—41no—
246D4×C61—41no—
247D4×C61—41no—
248D4×C61—84no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—21no—
262C2×C4×C61—22no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
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—84no—
288C2×C4×C61#12112yes—
289C2×C4×C61C2×SD1612yes—
290C2×C4×C61C2×SD1612yes—
291C2×C4×C61C22×D411yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61H(5,𝔽2)11yescharacteristic
296C2×C4×C612−1+411yescharacteristic
297C8×C61—22no—
298C8×C61—41no—
299C8×C61—41no—
300C8×C61—41no—
301#25204C6111yesmaximal, characteristic, direct product factor, Sylow
302C22×C61—22no—
303C22×C61—22no—
304C22×C61—22no—
305C22×C61—22no—
306C22×C61—22no—
307C22×C61—22no—
308C22×C61—81no—
309C22×C61—81no—
310C22×C61—81no—
311C22×C61—81no—
312C22×C61—81no—
313C22×C61—81no—
314C22×C61—81no—
315C22×C61#46014yes—
316C22×C61C2×#12111yescharacteristic
317C22×C61#54611yescharacteristic
318C22×C61#54711yescharacteristic
319C22×C61C22×SD1611yescharacteristic
320C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
321C22×C61#57711yescharacteristic
322C22×C61#57811yescharacteristic
323C4×C61—22no—
324C4×C61—22no—
325C4×C61—22no—
326C4×C61—41no—
327C4×C61—42no—
328C4×C61—42no—
329C4×C61—41no—
330C4×C61—42no—
331C4×C61—81no—
332C4×C61—81no—
333C4×C61—81no—
334C4×C61—81no—
335C4×C61#52911yescharacteristic
336C4×C61#53911yescharacteristic
337C4×C61#54611yescharacteristic
338C4×C61#54711yescharacteristic
339C2×#483C2×C6111yescharacteristic, complemented
340C2×#465C2×C6111yescharacteristic
341#2501C2×C6111yescharacteristic
342#2360C2×C6111yescharacteristic, complemented
343#2084C2×C6111yescharacteristic, complemented
344#2072C2×C6111yescharacteristic, complemented
345#2065C2×C6111yescharacteristic, complemented
346#2055C2×C6111yescharacteristic, complemented
347#1948C2×C6111yescharacteristic, complemented
348#1926C2×C6111yescharacteristic, complemented
349#1880C2×C6111yescharacteristic, complemented
350#1874C2×C6111yescharacteristic
351#1850C2×C6111yescharacteristic, complemented
352#1803C2×C6111yescharacteristic, complemented
353C2×#340C2×C6111yescharacteristic, complemented
354C2×C61—24no—
355C2×C61—161no—
356C2×C61#242511yescharacteristic
357C2×C61C2×#46011yescharacteristic
358C2×C61#304611yescharacteristic
359C2×C61#329811yescharacteristic
360C2×C61#330611yescharacteristic
361C2×C61#333511yescharacteristic
362C2×C61#334311yescharacteristic
363C22×SD16C22×C6111yescharacteristic
364C23×C8C22×C6111yescharacteristic
365C2×#123—21no—
366C2×#123—21no—
367C2×C22⋊Q8C22×C6111yescharacteristic
368C2×#121C22×C6111yescharacteristic
369C2×C4×Q8C22×C6111yescharacteristic
370C22×C4⋊C4C22×C6111yescharacteristic
371C22×C4⋊C4C22×C6111yescharacteristic
372#483—24no—
373#465—24no—
374C2×#106C22×C6111yescharacteristic
375C2×#106C22×C6111yescharacteristic
376C2×#106C22×C6111yescharacteristic
377C2×C4⋊C8C22×C6111yescharacteristic
378C2×C4⋊C8C22×C6111yescharacteristic
379C2×#103C22×C6111yescharacteristic
380C2×#103C22×C6111yescharacteristic
381C2×#103C22×C6111yescharacteristic
382C2×#102C22×C6111yescharacteristic
383C2×#102C22×C6111yescharacteristic
384C2×#102C22×C6111yescharacteristic
385C2×C22⋊C8C22×C6111yescharacteristic
386#399—21no—
387#399—21no—
388#391C22×C6111yescharacteristic
389#390C22×C6111yescharacteristic
390#390C22×C6111yescharacteristic
391#389—21no—
392#389C22×C6111yescharacteristic
393#387—21no—
394#385—21no—
395#384C22×C6111yescharacteristic
396#384C22×C6111yescharacteristic
397C4×C4⋊C4C22×C6111yescharacteristic
398C4×C22⋊C4—21no—
399C4×C22⋊C4C22×C6111yescharacteristic
400#340C22×C6111yescharacteristic
401#340C22×C6111yescharacteristic
402#340C22×C6111yescharacteristic
403#340C22×C6111yescharacteristic
404#340C22×C6111yescharacteristic
405#340C22×C6111yescharacteristic
406#336C22×C6111yescharacteristic
407#336C22×C6111yescharacteristic
408C61#2520411yescharacteristic, direct product factor, Sylow
409C22×Q8C23×C6111yescharacteristic
410C22×D4—21no—
411C22×D4C23×C6111yescharacteristic
412C23×C4—21no—
413C23×C4—21no—
414C23×C4C23×C6111yescharacteristic
415C2×SD16—22no—
416C2×SD16—22no—
417C2×SD16—41no—
418C22×C8—22no—
419C22×C8—22no—
420C22×C8—41no—
421C22×C8C23×C6111yescharacteristic
422C22×C8C23×C6111yescharacteristic
423C22×C8C23×C6111yescharacteristic
424C22×C8C23×C6111yescharacteristic
425#123—44no—
426#123—44no—
427C22⋊Q8—22no—
428C22⋊Q8D4×C6114yes—
429#121—22no—
430#121—22no—
431C4×Q8—22no—
432C4×Q8—41no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—41no—
446C2×C4⋊C4C23×C6111yescharacteristic
447C2×C4⋊C4C23×C6111yescharacteristic
448C2×C4⋊C4C23×C6111yescharacteristic
449C2×C4⋊C4C23×C6111yescharacteristic
450C2×C4⋊C4C23×C6111yescharacteristic
451C2×C4⋊C4C23×C6111yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4D4×C6111yescharacteristic
459C2×C22⋊C4D4×C6111yescharacteristic
460C2×C42—21no—
461C2×C42—21no—
462C2×C42C23×C6111yescharacteristic
463C2×C42C23×C6111yescharacteristic
464#106—22no—
465#106—22no—
466#106—22no—
467C4⋊C8—22no—
468C4⋊C8—41no—
469#103—22no—
470#103—22no—
471#103—22no—
472#102—22no—
473#102—22no—
474#102—41no—
475C22⋊C8—22no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95D4×C6111yescharacteristic
481#95D4×C6111yescharacteristic
482C24—21no—
483C24C2×D4×C6111yescharacteristic
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8C2×D4×C6112yes—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
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—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—81no—
516C22×C4C2×D4×C6111yescharacteristic
517C22×C4C2×D4×C6111yescharacteristic
518C22×C4C2×D4×C6111yescharacteristic
519C22×C4C2×D4×C6112yes—
520C22×C4C2×D4×C6111yescharacteristic
521C22×C4C2×D4×C6111yescharacteristic
522C22×C4#41×C6112yes—
523C22×C4C24×C6111yescharacteristic
524SD16—44no—
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—21no—
536C2×C8—44no—
537C2×C8#41×C6112yes—
538C4⋊C4—24no—
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—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—81no—
557C4⋊C4C2×D4×C6112yes—
558C4⋊C4#41×C6112yes—
559C22⋊C4—24no—
560C22⋊C4—22no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4SD16×C6114yescomplemented
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—42no—
572C42—81no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23#121×C6112yes—
585C23C2×SD16×C6112yes—
586C23AGL(1,ℤ/8)×C6112yes—
587C23C22×D4×C6111yescharacteristic
588Q8—22no—
589Q8—22no—
590Q8—41no—
591Q8—41no—
592D4—41no—
593D4—41no—
594D4—41no—
595D4—41no—
596D4—84no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
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—84no—
635C2×C4—84no—
636C2×C4#121×C6112yes—
637C2×C4C2×SD16×C6112yes—
638C2×C4C2×SD16×C6112yes—
639C2×C4C22×D4×C6111yescharacteristic
640C2×C4C2×#41×C6111yescharacteristic
641C2×C4C2×#41×C6111yescharacteristic
642C2×C4C2×#41×C6111yescharacteristic
643C2×C4H(5,𝔽2)×C6111yescharacteristic
644C2×C42−1+4×C6111yescharacteristic
645C8—22no—
646C8—41no—
647C8—41no—
648C8—41no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22C61×#46014yes—
663C22C2×#121×C6111yescharacteristic
664C22C61×#54611yescharacteristic
665C22C61×#54711yescharacteristic
666C22C22×SD16×C6111yescharacteristic
667C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
668C22C61×#57711yescharacteristic
669C22C61×#57811yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—42no—
674C4—41no—
675C4—42no—
676C4—41no—
677C4—42no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—81no—
682C4C61×#52911yescharacteristic
683C4C61×#53911yescharacteristic
684C4C61×#54611yescharacteristic
685C4C61×#54711yescharacteristic
686C2—24no—
687C2—161no—
688C2C61×#242511yescharacteristic
689C2C2×C61×#46011yescharacteristic
690C2C61×#304611yescharacteristic
691C2C61×#329811yescharacteristic
692C2C61×#330611yescharacteristic
693C2C61×#333511yescharacteristic
694C2C61×#334311yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×#121×C61C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C4×C22⋊C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#483C2semidirect
4. C61×#2360C2semidirect
5. C61×#2084C2semidirect
6. C61×#2072C2semidirect
7. C61×#2065C2semidirect
8. C61×#2055C2semidirect
9. C61×#1948C2semidirect
10. C61×#1926C2semidirect
11. C61×#1880C2semidirect
13. C61×#1850C2semidirect
14. C61×#1803C2semidirect
15. C2×C61×#340C2semidirect
218. C22⋊C4×C61SD16semidirect
301. #25204C61direct (N × H)
339. C2×#483C2×C61semidirect
342. #2360C2×C61semidirect
343. #2084C2×C61semidirect
344. #2072C2×C61semidirect
345. #2065C2×C61semidirect
346. #2055C2×C61semidirect
347. #1948C2×C61semidirect
348. #1926C2×C61semidirect
349. #1880C2×C61semidirect
351. #1850C2×C61semidirect
352. #1803C2×C61semidirect
353. C2×#340C2×C61semidirect
408. C61#25204direct (N × H)
566. C22⋊C4SD16×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4832
C2×C61×#4652
C61×#25012
C61×#23602
C61×#20842
C61×#20722
C61×#20652
C61×#20552
C61×#19482
C61×#19262
C61×#18802
C61×#18742
C61×#18502
C61×#18032
C2×C61×#3402
#2520461