Finite Group Databasebeta

← C61×#26146 #29529579

Subgroups — C61×#26146 #29529579

Order 15616.

954 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#481C211yesmaximal, characteristic, complemented
2C2×C61×#428C211yesmaximal, characteristic, complemented
3C61×#2414C211yesmaximal, characteristic
4D4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
5C61×#2093C211yesmaximal, characteristic, complemented
6C61×#2084C211yesmaximal, characteristic, complemented
7C61×#2076C211yesmaximal, characteristic, complemented
8C61×#2034C211yesmaximal, characteristic, complemented
9C61×#1925C211yesmaximal, characteristic, complemented
10C61×#1920C211yesmaximal, characteristic, complemented
11C61×#1895C211yesmaximal, characteristic, complemented
12C61×#1874C211yesmaximal, characteristic, complemented
13C61×#1870C211yesmaximal, characteristic, complemented
14C61×#1854C211yesmaximal, characteristic, complemented
15C61×#1852C211yesmaximal, characteristic, complemented
16C22×M16×C61C2211yescharacteristic
17C2×#121×C61C2211yescharacteristic
18C2×#121×C61C2211yescharacteristic
19C2×C4×D4×C61—21no—
20C2×C4×D4×C61C2211yescharacteristic
21C2×#117×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2211yescharacteristic
23C22×C4⋊C4×C61C2211yescharacteristic
24C61×#481—24no—
25C61×#428—24no—
26C2×#107×C61C2211yescharacteristic
27C2×#107×C61C2211yescharacteristic
28C2×#107×C61C2211yescharacteristic
29C2×#106×C61C2211yescharacteristic
30C2×#106×C61C2211yescharacteristic
31C2×#106×C61C2211yescharacteristic
32C2×#102×C61C2211yescharacteristic
33C2×#102×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic
35C2×#102×C61C2211yescharacteristic
36C2×C22⋊C8×C61C2211yescharacteristic
37C2×C22⋊C8×C61C2211yescharacteristic
38C2×C22⋊C8×C61C2211yescharacteristic
39C61×#394—21no—
40C61×#392—21no—
41C61×#390—21no—
42C61×#390C2211yescharacteristic
43C61×#389—21no—
44C61×#389C2211yescharacteristic
45C61×#388—21no—
46C61×#385—21no—
47C61×#385—21no—
48C61×#384C2211yescharacteristic
49C61×#380C2211yescharacteristic
50C61×#380C2211yescharacteristic
51C61×#380C2211yescharacteristic
52C4×C4⋊C4×C61C2211yescharacteristic
53C61×#340C2211yescharacteristic
54C61×#340C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×D4×C61—21no—
62C22×D4×C61—21no—
63C22×D4×C61D411yescharacteristic
64C22×D4×C61C2311yescharacteristic
65C23×C4×C61—21no—
66C23×C4×C61—21no—
67C23×C4×C61C2311yescharacteristic
68C23×C4×C61C2311yescharacteristic
69C2×M16×C61—22no—
70C2×M16×C61—22no—
71C2×M16×C61—22no—
72C22×C8×C61C2311yescharacteristic
73C22×C8×C61C2311yescharacteristic
74C22×C8×C61C2311yescharacteristic
75C22×C8×C61C2311yescharacteristic
76#121×C61—22no—
77#121×C61—22no—
78#121×C61—22no—
79#121×C61—41no—
80C4×D4×C61—22no—
81C4×D4×C61—22no—
82C4×D4×C61—44no—
83#117×C61—22no—
84#117×C61—41no—
85C2×C4⋊C4×C61—22no—
86C2×C4⋊C4×C61—22no—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—41no—
93C2×C4⋊C4×C61—41no—
94C2×C4⋊C4×C61D411yescharacteristic
95C2×C4⋊C4×C61C2311yescharacteristic
96C2×C4⋊C4×C61C2311yescharacteristic
97C2×C4⋊C4×C61C2311yescharacteristic
98C2×C4⋊C4×C61C2311yescharacteristic
99C2×C4⋊C4×C61C2311yescharacteristic
100C2×C4⋊C4×C61C2311yescharacteristic
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C22⋊C4×C61—21no—
103C2×C22⋊C4×C61—21no—
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
115#107×C61—22no—
116#107×C61—22no—
117#107×C61—41no—
118#106×C61—22no—
119#106×C61—22no—
120#106×C61D414yescomplemented
121#102×C61—22no—
122#102×C61—22no—
123#102×C61—22no—
124#102×C61—41no—
125C22⋊C8×C61—22no—
126C22⋊C8×C61—22no—
127C22⋊C8×C61—22no—
128#95×C61—21no—
129#95×C61—21no—
130#95×C61—21no—
131#95×C61—21no—
132#95×C61—21no—
133C24×C61—21no—
134C24×C61C2×D411yescharacteristic
135C24×C61C2×D411yescharacteristic
136C2×D4×C61—22no—
137C2×D4×C61—22no—
138C2×D4×C61—22no—
139C2×D4×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—42no—
146C2×D4×C61—42no—
147C2×D4×C61—42no—
148C2×D4×C61—81no—
149C2×D4×C61—81no—
150C2×D4×C61—81no—
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—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—42no—
169C22×C4×C61—42no—
170C22×C4×C61—42no—
171C22×C4×C61—42no—
172C22×C4×C61—81no—
173C22×C4×C61—81no—
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61#4112yes—
179C22×C4×C61#4112yes—
180C22×C4×C61C2411yescharacteristic
181M16×C61—28no—
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—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61C2×D412yes—
193C2×C8×C61#4112yes—
194C4⋊C4×C61—22no—
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—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—42no—
208C4⋊C4×C61—42no—
209C4⋊C4×C61—42no—
210C4⋊C4×C61—81no—
211C4⋊C4×C61—81no—
212C4⋊C4×C61C2×D412yes—
213C4⋊C4×C61C2×D412yes—
214C22⋊C4×C61—22no—
215C22⋊C4×C61—22no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—42no—
218C22⋊C4×C61—42no—
219C22⋊C4×C61—42no—
220C22⋊C4×C61—42no—
221C22⋊C4×C61—42no—
222C22⋊C4×C61—81no—
223C22⋊C4×C61—81no—
224C42×C61—21no—
225C42×C61—21no—
226C42×C61—42no—
227C42×C61—42no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61#12312yes—
248C23×C61#13712yes—
249C23×C61C22×D411yescharacteristic
250D4×C61—28no—
251D4×C61—41no—
252D4×C61—41no—
253D4×C61—41no—
254D4×C61—41no—
255D4×C61—84no—
256D4×C61—84no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—22no—
268C2×C4×C61—21no—
269C2×C4×C61—22no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
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—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—84no—
297C2×C4×C61—84no—
298C2×C4×C61#12312yes—
299C2×C4×C61AGL(1,ℤ/8)12yes—
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×C4×C61H(5,𝔽2)11yescharacteristic
305C2×C4×C612−1+411yescharacteristic
306C8×C61—22no—
307C8×C61—22no—
308C8×C61—41no—
309C8×C61—41no—
310#26146C6111yesmaximal, characteristic, direct product factor, Sylow
311C22×C61—22no—
312C22×C61—22no—
313C22×C61—22no—
314C22×C61—22no—
315C22×C61—22no—
316C22×C61—22no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61—81no—
326C22×C61—81no—
327C22×C61—81no—
328C22×C61—81no—
329C22×C61—81no—
330C22×C61—81no—
331C22×C61—81no—
332C22×C61C2×#12311yescharacteristic
333C22×C61D4211yescharacteristic
334C22×C61#54711yescharacteristic
335C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
336C22×C61C2×#13711yescharacteristic
337C22×C61#57611yescharacteristic
338C22×C61#57711yescharacteristic
339C4×C61—22no—
340C4×C61—22no—
341C4×C61—41no—
342C4×C61—41no—
343C4×C61—42no—
344C4×C61—42no—
345C4×C61—81no—
346C4×C61—81no—
347C4×C61—81no—
348C4×C61—81no—
349C4×C61—81no—
350C4×C61#52511yescharacteristic
351C4×C61#53911yescharacteristic
352C4×C61#54811yescharacteristic
353C4×C61#55311yescharacteristic
354C2×#481C2×C6111yescharacteristic, complemented
355C2×#428C2×C6111yescharacteristic, complemented
356#2414C2×C6111yescharacteristic
357D4×C4⋊C4C2×C6111yescharacteristic, complemented
358#2093C2×C6111yescharacteristic, complemented
359#2084C2×C6111yescharacteristic, complemented
360#2076C2×C6111yescharacteristic, complemented
361#2034C2×C6111yescharacteristic, complemented
362#1925C2×C6111yescharacteristic, complemented
363#1920C2×C6111yescharacteristic, complemented
364#1895C2×C6111yescharacteristic, complemented
365#1874C2×C6111yescharacteristic, complemented
366#1870C2×C6111yescharacteristic, complemented
367#1854C2×C6111yescharacteristic, complemented
368#1852C2×C6111yescharacteristic, complemented
369C2×C61—42no—
370C2×C61—42no—
371C2×C61—161no—
372C2×C61#244311yescharacteristic
373C2×C61#309211yescharacteristic
374C2×C61#309611yescharacteristic
375C2×C61#326611yescharacteristic
376C2×C61#327411yescharacteristic
377C2×C61#334611yescharacteristic
378C2×C61#335411yescharacteristic
379C22×M16C22×C6111yescharacteristic
380C2×#121C22×C6111yescharacteristic
381C2×#121C22×C6111yescharacteristic
382C2×C4×D4—21no—
383C2×C4×D4C22×C6111yescharacteristic
384C2×#117C22×C6111yescharacteristic
385C22×C4⋊C4C22×C6111yescharacteristic
386C22×C4⋊C4C22×C6111yescharacteristic
387#481—24no—
388#428—24no—
389C2×#107C22×C6111yescharacteristic
390C2×#107C22×C6111yescharacteristic
391C2×#107C22×C6111yescharacteristic
392C2×#106C22×C6111yescharacteristic
393C2×#106C22×C6111yescharacteristic
394C2×#106C22×C6111yescharacteristic
395C2×#102C22×C6111yescharacteristic
396C2×#102C22×C6111yescharacteristic
397C2×#102C22×C6111yescharacteristic
398C2×#102C22×C6111yescharacteristic
399C2×C22⋊C8C22×C6111yescharacteristic
400C2×C22⋊C8C22×C6111yescharacteristic
401C2×C22⋊C8C22×C6111yescharacteristic
402#394—21no—
403#392—21no—
404#390—21no—
405#390C22×C6111yescharacteristic
406#389—21no—
407#389C22×C6111yescharacteristic
408#388—21no—
409#385—21no—
410#385—21no—
411#384C22×C6111yescharacteristic
412#380C22×C6111yescharacteristic
413#380C22×C6111yescharacteristic
414#380C22×C6111yescharacteristic
415C4×C4⋊C4C22×C6111yescharacteristic
416#340C22×C6111yescharacteristic
417#340C22×C6111yescharacteristic
418#340C22×C6111yescharacteristic
419#340C22×C6111yescharacteristic
420#340C22×C6111yescharacteristic
421#340C22×C6111yescharacteristic
422#336C22×C6111yescharacteristic
423#336C22×C6111yescharacteristic
424C61#2614611yescharacteristic, direct product factor, Sylow
425C22×D4—21no—
426C22×D4—21no—
427C22×D4D4×C6111yescharacteristic
428C22×D4C23×C6111yescharacteristic
429C23×C4—21no—
430C23×C4—21no—
431C23×C4C23×C6111yescharacteristic
432C23×C4C23×C6111yescharacteristic
433C2×M16—22no—
434C2×M16—22no—
435C2×M16—22no—
436C22×C8C23×C6111yescharacteristic
437C22×C8C23×C6111yescharacteristic
438C22×C8C23×C6111yescharacteristic
439C22×C8C23×C6111yescharacteristic
440#121—22no—
441#121—22no—
442#121—22no—
443#121—41no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—44no—
447#117—22no—
448#117—41no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4—41no—
458C2×C4⋊C4D4×C6111yescharacteristic
459C2×C4⋊C4C23×C6111yescharacteristic
460C2×C4⋊C4C23×C6111yescharacteristic
461C2×C4⋊C4C23×C6111yescharacteristic
462C2×C4⋊C4C23×C6111yescharacteristic
463C2×C4⋊C4C23×C6111yescharacteristic
464C2×C4⋊C4C23×C6111yescharacteristic
465C2×C4⋊C4C23×C6111yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4D4×C6111yescharacteristic
475C2×C22⋊C4D4×C6111yescharacteristic
476C2×C42—21no—
477C2×C42—21no—
478C2×C42C23×C6111yescharacteristic
479#107—22no—
480#107—22no—
481#107—41no—
482#106—22no—
483#106—22no—
484#106D4×C6114yescomplemented
485#102—22no—
486#102—22no—
487#102—22no—
488#102—41no—
489C22⋊C8—22no—
490C22⋊C8—22no—
491C22⋊C8—22no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497C24—21no—
498C24C2×D4×C6111yescharacteristic
499C24C2×D4×C6111yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4—81no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—81no—
537C22×C4—81no—
538C22×C4C2×D4×C6111yescharacteristic
539C22×C4C2×D4×C6111yescharacteristic
540C22×C4C2×D4×C6111yescharacteristic
541C22×C4C2×D4×C6111yescharacteristic
542C22×C4#41×C6112yes—
543C22×C4#41×C6112yes—
544C22×C4C24×C6111yescharacteristic
545M16—28no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8C2×D4×C6112yes—
557C2×C8#41×C6112yes—
558C4⋊C4—22no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—81no—
575C4⋊C4—81no—
576C4⋊C4C2×D4×C6112yes—
577C4⋊C4C2×D4×C6112yes—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—81no—
587C22⋊C4—81no—
588C42—21no—
589C42—21no—
590C42—42no—
591C42—42no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23#123×C6112yes—
612C23#137×C6112yes—
613C23C22×D4×C6111yescharacteristic
614D4—28no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—84no—
620D4—84no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—84no—
661C2×C4—84no—
662C2×C4#123×C6112yes—
663C2×C4AGL(1,ℤ/8)×C6112yes—
664C2×C4C22×D4×C6111yescharacteristic
665C2×C4C2×#41×C6111yescharacteristic
666C2×C4C2×#41×C6111yescharacteristic
667C2×C4C2×#41×C6111yescharacteristic
668C2×C4H(5,𝔽2)×C6111yescharacteristic
669C2×C42−1+4×C6111yescharacteristic
670C8—22no—
671C8—22no—
672C8—41no—
673C8—41no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22C2×#123×C6111yescharacteristic
696C22D42×C6111yescharacteristic
697C22C61×#54711yescharacteristic
698C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
699C22C2×#137×C6111yescharacteristic
700C22C61×#57611yescharacteristic
701C22C61×#57711yescharacteristic
702C4—22no—
703C4—22no—
704C4—41no—
705C4—41no—
706C4—42no—
707C4—42no—
708C4—81no—
709C4—81no—
710C4—81no—
711C4—81no—
712C4—81no—
713C4C61×#52511yescharacteristic
714C4C61×#53911yescharacteristic
715C4C61×#54811yescharacteristic
716C4C61×#55311yescharacteristic
717C2—42no—
718C2—42no—
719C2—161no—
720C2C61×#244311yescharacteristic
721C2C61×#309211yescharacteristic
722C2C61×#309611yescharacteristic
723C2C61×#326611yescharacteristic
724C2C61×#327411yescharacteristic
725C2C61×#334611yescharacteristic
726C2C61×#335411yescharacteristic
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
1. C2×C61×#481C2semidirect
2. C2×C61×#428C2semidirect
4. D4×C4⋊C4×C61C2semidirect
5. C61×#2093C2semidirect
6. C61×#2084C2semidirect
7. C61×#2076C2semidirect
8. C61×#2034C2semidirect
9. C61×#1925C2semidirect
10. C61×#1920C2semidirect
11. C61×#1895C2semidirect
12. C61×#1874C2semidirect
13. C61×#1870C2semidirect
14. C61×#1854C2semidirect
15. C61×#1852C2semidirect
120. #106×C61D4semidirect
310. #26146C61direct (N × H)
354. C2×#481C2×C61semidirect
355. C2×#428C2×C61semidirect
357. D4×C4⋊C4C2×C61semidirect
358. #2093C2×C61semidirect
359. #2084C2×C61semidirect
360. #2076C2×C61semidirect
361. #2034C2×C61semidirect
362. #1925C2×C61semidirect
363. #1920C2×C61semidirect
364. #1895C2×C61semidirect
365. #1874C2×C61semidirect
366. #1870C2×C61semidirect
367. #1854C2×C61semidirect
368. #1852C2×C61semidirect
424. C61#26146direct (N × H)
484. #106D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4812
C2×C61×#4282
C61×#24142
D4×C4⋊C4×C612
C61×#20932
C61×#20842
C61×#20762
C61×#20342
C61×#19252
C61×#19202
C61×#18952
C61×#18742
C61×#18702
C61×#18542
C61×#18522
#2614661