Finite Group Databasebeta

← C61×#21543 #29524976

Subgroups — C61×#21543 #29524976

Order 15616.

1010 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#468C211yesmaximal, characteristic
2C2×C61×#440C211yesmaximal, characteristic, complemented
3C2×C61×#405C211yesmaximal, characteristic, complemented
4C61×#2324C211yesmaximal, characteristic
5C61×#2323C211yesmaximal, characteristic, complemented
6C61×#1968C211yesmaximal, characteristic, complemented
7C61×#1942C211yesmaximal, characteristic, complemented
8C61×#1936C211yesmaximal, characteristic, complemented
9C61×#1935C211yesmaximal, characteristic, complemented
10C61×#1893C211yesmaximal, characteristic
11C61×#1892C211yesmaximal, characteristic, complemented
12C61×#1809C211yesmaximal, characteristic, complemented
13C61×#1776C211yesmaximal, characteristic, complemented
14C4×#103×C61C211yesmaximal, characteristic, complemented
15C4×#102×C61C211yesmaximal, characteristic, complemented
16C22×SD16×C61C2211yescharacteristic
17C22×M16×C61C2211yescharacteristic
18C23×C8×C61C2211yescharacteristic
19C2×C22⋊Q8×C61C2211yescharacteristic
20C2×#121×C61C2211yescharacteristic
21C2×C4×Q8×C61C2211yescharacteristic
22C2×C4×D4×C61C2211yescharacteristic
23C2×#117×C61C2211yescharacteristic
24C61×#468C418yescomplemented
25C61×#440—24no—
26C2×#107×C61C2211yescharacteristic
27C2×#107×C61C2211yescharacteristic
28C2×#106×C61C2211yescharacteristic
29C2×#103×C61C2211yescharacteristic
30C2×#103×C61C2211yescharacteristic
31C2×#103×C61C2211yescharacteristic
32C2×#102×C61C2211yescharacteristic
33C2×#102×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic
35C61×#405—24no—
36C2×#97×C61C2211yescharacteristic
37C2×#97×C61C2211yescharacteristic
38C2×C4×C8×C61C2211yescharacteristic
39C2×C4×C8×C61C2211yescharacteristic
40C61×#391C2211yescharacteristic
41C61×#390—21no—
42C61×#390C2211yescharacteristic
43C61×#389—21no—
44C61×#389C2211yescharacteristic
45C61×#389C2211yescharacteristic
46C61×#388—21no—
47C61×#388—21no—
48C61×#388—21no—
49C61×#387—21no—
50C61×#386—21no—
51C61×#385—21no—
52C61×#380C2211yescharacteristic
53C61×#380C2211yescharacteristic
54C4×C4⋊C4×C61C2211yescharacteristic
55C4×C4⋊C4×C61C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×Q8×C61C2311yescharacteristic
63C22×D4×C61—21no—
64C22×D4×C61C2311yescharacteristic
65C23×C4×C61—21no—
66C23×C4×C61C2311yescharacteristic
67C2×SD16×C61—22no—
68C2×SD16×C61—22no—
69C2×SD16×C61C2×C414yes—
70C2×M16×C61—22no—
71C2×M16×C61—22no—
72C2×M16×C61C2×C414yescomplemented
73C22×C8×C61—22no—
74C22×C8×C61—22no—
75C22×C8×C61—22no—
76C22×C8×C61C2311yescharacteristic
77C22×C8×C61C2311yescharacteristic
78C22×C8×C61C2311yescharacteristic
79C22×C8×C61C2311yescharacteristic
80C22⋊Q8×C61—22no—
81C22⋊Q8×C61C2×C414yescomplemented
82#121×C61—22no—
83#121×C61C2×C414yes—
84C4×Q8×C61—22no—
85C4×Q8×C61—22no—
86C4×D4×C61—22no—
87C4×D4×C61—22no—
88#117×C61—22no—
89#117×C61—22no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61D411yescharacteristic
95C2×C4⋊C4×C61D411yescharacteristic
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×C61D411yescharacteristic
110C2×C22⋊C4×C61D411yescharacteristic
111C2×C42×C61—21no—
112C2×C42×C61—21no—
113C2×C42×C61—21no—
114C2×C42×C61C2311yescharacteristic
115C2×C42×C61C2311yescharacteristic
116#107×C61—22no—
117#107×C61C2×C414yescomplemented
118#106×C61—22no—
119#103×C61—22no—
120#103×C61—22no—
121#103×C61C2×C414yescomplemented
122#102×C61—22no—
123#102×C61—22no—
124#102×C61C2×C414yes—
125#97×C61—22no—
126#97×C61D414yescomplemented
127C4×C8×C61—22no—
128C4×C8×C61—22no—
129#95×C61—21no—
130#95×C61—21no—
131#95×C61—21no—
132#95×C61—21no—
133#95×C61—21no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61—21no—
137C24×C61—21no—
138C24×C61C2×D411yescharacteristic
139C2×Q8×C61—21no—
140C2×Q8×C61—21no—
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61C22×C412yes—
145C2×D4×C61—24no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—81no—
152C2×D4×C61—81no—
153C2×D4×C61C22×C412yes—
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—42no—
166C22×C4×C61—81no—
167C22×C4×C61—81no—
168C22×C4×C61C22×C412yes—
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61#4112yes—
175C22×C4×C61C2411yescharacteristic
176SD16×C61—28no—
177M16×C61—28no—
178C2×C8×C61—28no—
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×C61C22×C412yes—
186C2×C8×C61C22×C412yes—
187C2×C8×C61C2×D412yes—
188C2×C8×C61C2×D412yes—
189C2×C8×C61#4112yes—
190C2×C8×C61#4112yes—
191C4⋊C4×C61—24no—
192C4⋊C4×C61—22no—
193C4⋊C4×C61—22no—
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—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—42no—
205C4⋊C4×C61—81no—
206C4⋊C4×C61—81no—
207C4⋊C4×C61C22×C412yes—
208C4⋊C4×C61C22×C412yes—
209C22⋊C4×C61—24no—
210C22⋊C4×C61—24no—
211C22⋊C4×C61—22no—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—42no—
214C22⋊C4×C61—81no—
215C22⋊C4×C61—81no—
216C22⋊C4×C61—81no—
217C22⋊C4×C61—81no—
218C42×C61—21no—
219C42×C61—21no—
220C42×C61—42no—
221C42×C61—81no—
222C42×C61—81no—
223C42×C61C2×D412yes—
224C42×C61#4112yes—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—21no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—22no—
232C23×C61—41no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61C4×D412yes—
239C23×C61C22×D411yescharacteristic
240Q8×C61—22no—
241Q8×C61—22no—
242Q8×C61—41no—
243Q8×C61—41no—
244D4×C61—22no—
245D4×C61—22no—
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—22no—
262C2×C4×C61—21no—
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×C61C4×D412yes—
288C2×C4×C61#12112yes—
289C2×C4×C61#12112yes—
290C2×C4×C61C23×C411yescharacteristic
291C2×C4×C61C22×D411yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C8×C61—22no—
297C8×C61—22no—
298C8×C61—22no—
299C8×C61C4×D414yes—
300#21543C6111yesmaximal, characteristic, direct product factor, Sylow
301C22×C61—22no—
302C22×C61—22no—
303C22×C61—22no—
304C22×C61—41no—
305C22×C61—41no—
306C22×C61—41no—
307C22×C61—41no—
308C22×C61—42no—
309C22×C61—42no—
310C22×C61—42no—
311C22×C61—81no—
312C22×C61—81no—
313C22×C61—81no—
314C22×C61—81no—
315C22×C61C2×C4×D411yescharacteristic
316C22×C61C2×#12111yescharacteristic
317C22×C61#53211yescharacteristic
318C22×C61#57611yescharacteristic
319C22×C61#57711yescharacteristic
320C22×C61#57711yescharacteristic
321C22×C61#57811yescharacteristic
322C4×C61—22no—
323C4×C61—22no—
324C4×C61—22no—
325C4×C61—42no—
326C4×C61—42no—
327C4×C61—41no—
328C4×C61—41no—
329C4×C61—42no—
330C4×C61—81no—
331C4×C61—81no—
332C4×C61—81no—
333C4×C61—81no—
334C4×C61C2×C4×D411yescharacteristic
335C4×C61C4×#4111yescharacteristic
336C4×C61#52511yescharacteristic
337C4×C61#52911yescharacteristic
338C2×#468C2×C6111yescharacteristic
339C2×#440C2×C6111yescharacteristic, complemented
340C2×#405C2×C6111yescharacteristic, complemented
341#2324C2×C6111yescharacteristic
342#2323C2×C6111yescharacteristic, complemented
343#1968C2×C6111yescharacteristic, complemented
344#1942C2×C6111yescharacteristic, complemented
345#1936C2×C6111yescharacteristic, complemented
346#1935C2×C6111yescharacteristic, complemented
347#1893C2×C6111yescharacteristic
348#1892C2×C6111yescharacteristic, complemented
349#1809C2×C6111yescharacteristic, complemented
350#1776C2×C6111yescharacteristic, complemented
351C4×#103C2×C6111yescharacteristic, complemented
352C4×#102C2×C6111yescharacteristic, complemented
353C2×C61—42no—
354C2×C61—82no—
355C2×C61C4×#12111yescharacteristic
356C2×C61#294611yescharacteristic
357C2×C61#294711yescharacteristic
358C2×C61#306211yescharacteristic
359C2×C61#306311yescharacteristic
360C2×C61#317411yescharacteristic
361C2×C61#317511yescharacteristic
362C22×SD16C22×C6111yescharacteristic
363C22×M16C22×C6111yescharacteristic
364C23×C8C22×C6111yescharacteristic
365C2×C22⋊Q8C22×C6111yescharacteristic
366C2×#121C22×C6111yescharacteristic
367C2×C4×Q8C22×C6111yescharacteristic
368C2×C4×D4C22×C6111yescharacteristic
369C2×#117C22×C6111yescharacteristic
370#468C4×C6118yescomplemented
371#440—24no—
372C2×#107C22×C6111yescharacteristic
373C2×#107C22×C6111yescharacteristic
374C2×#106C22×C6111yescharacteristic
375C2×#103C22×C6111yescharacteristic
376C2×#103C22×C6111yescharacteristic
377C2×#103C22×C6111yescharacteristic
378C2×#102C22×C6111yescharacteristic
379C2×#102C22×C6111yescharacteristic
380C2×#102C22×C6111yescharacteristic
381#405—24no—
382C2×#97C22×C6111yescharacteristic
383C2×#97C22×C6111yescharacteristic
384C2×C4×C8C22×C6111yescharacteristic
385C2×C4×C8C22×C6111yescharacteristic
386#391C22×C6111yescharacteristic
387#390—21no—
388#390C22×C6111yescharacteristic
389#389—21no—
390#389C22×C6111yescharacteristic
391#389C22×C6111yescharacteristic
392#388—21no—
393#388—21no—
394#388—21no—
395#387—21no—
396#386—21no—
397#385—21no—
398#380C22×C6111yescharacteristic
399#380C22×C6111yescharacteristic
400C4×C4⋊C4C22×C6111yescharacteristic
401C4×C4⋊C4C22×C6111yescharacteristic
402#340C22×C6111yescharacteristic
403#340C22×C6111yescharacteristic
404#340C22×C6111yescharacteristic
405#340C22×C6111yescharacteristic
406#340C22×C6111yescharacteristic
407#340C22×C6111yescharacteristic
408C61#2154311yescharacteristic, direct product factor, Sylow
409C22×Q8C23×C6111yescharacteristic
410C22×D4—21no—
411C22×D4C23×C6111yescharacteristic
412C23×C4—21no—
413C23×C4C23×C6111yescharacteristic
414C2×SD16—22no—
415C2×SD16—22no—
416C2×SD16C2×C4×C6114yes—
417C2×M16—22no—
418C2×M16—22no—
419C2×M16C2×C4×C6114yescomplemented
420C22×C8—22no—
421C22×C8—22no—
422C22×C8—22no—
423C22×C8C23×C6111yescharacteristic
424C22×C8C23×C6111yescharacteristic
425C22×C8C23×C6111yescharacteristic
426C22×C8C23×C6111yescharacteristic
427C22⋊Q8—22no—
428C22⋊Q8C2×C4×C6114yescomplemented
429#121—22no—
430#121C2×C4×C6114yes—
431C4×Q8—22no—
432C4×Q8—22no—
433C4×D4—22no—
434C4×D4—22no—
435#117—22no—
436#117—22no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4D4×C6111yescharacteristic
442C2×C4⋊C4D4×C6111yescharacteristic
443C2×C4⋊C4C23×C6111yescharacteristic
444C2×C4⋊C4C23×C6111yescharacteristic
445C2×C4⋊C4C23×C6111yescharacteristic
446C2×C4⋊C4C23×C6111yescharacteristic
447C2×C4⋊C4C23×C6111yescharacteristic
448C2×C4⋊C4C23×C6111yescharacteristic
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
462C2×C42C23×C6111yescharacteristic
463#107—22no—
464#107C2×C4×C6114yescomplemented
465#106—22no—
466#103—22no—
467#103—22no—
468#103C2×C4×C6114yescomplemented
469#102—22no—
470#102—22no—
471#102C2×C4×C6114yes—
472#97—22no—
473#97D4×C6114yescomplemented
474C4×C8—22no—
475C4×C8—22no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484C24—21no—
485C24C2×D4×C6111yescharacteristic
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8C22×C4×C6112yes—
492C2×D4—24no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—81no—
499C2×D4—81no—
500C2×D4C22×C4×C6112yes—
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—42no—
513C22×C4—81no—
514C22×C4—81no—
515C22×C4C22×C4×C6112yes—
516C22×C4C2×D4×C6111yescharacteristic
517C22×C4C2×D4×C6111yescharacteristic
518C22×C4C2×D4×C6111yescharacteristic
519C22×C4C2×D4×C6111yescharacteristic
520C22×C4C2×D4×C6111yescharacteristic
521C22×C4#41×C6112yes—
522C22×C4C24×C6111yescharacteristic
523SD16—28no—
524M16—28no—
525C2×C8—28no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8C22×C4×C6112yes—
533C2×C8C22×C4×C6112yes—
534C2×C8C2×D4×C6112yes—
535C2×C8C2×D4×C6112yes—
536C2×C8#41×C6112yes—
537C2×C8#41×C6112yes—
538C4⋊C4—24no—
539C4⋊C4—22no—
540C4⋊C4—22no—
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—21no—
550C4⋊C4—21no—
551C4⋊C4—42no—
552C4⋊C4—81no—
553C4⋊C4—81no—
554C4⋊C4C22×C4×C6112yes—
555C4⋊C4C22×C4×C6112yes—
556C22⋊C4—24no—
557C22⋊C4—24no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—42no—
561C22⋊C4—81no—
562C22⋊C4—81no—
563C22⋊C4—81no—
564C22⋊C4—81no—
565C42—21no—
566C42—21no—
567C42—42no—
568C42—81no—
569C42—81no—
570C42C2×D4×C6112yes—
571C42#41×C6112yes—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—22no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23C4×D4×C6112yes—
586C23C22×D4×C6111yescharacteristic
587Q8—22no—
588Q8—22no—
589Q8—41no—
590Q8—41no—
591D4—22no—
592D4—22no—
593D4—41no—
594D4—41no—
595D4—84no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
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—22no—
611C2×C4—22no—
612C2×C4—22no—
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—84no—
634C2×C4C4×D4×C6112yes—
635C2×C4#121×C6112yes—
636C2×C4#121×C6112yes—
637C2×C4C23×C4×C6111yescharacteristic
638C2×C4C22×D4×C6111yescharacteristic
639C2×C4C2×#41×C6111yescharacteristic
640C2×C4C2×#41×C6111yescharacteristic
641C2×C4C2×#41×C6111yescharacteristic
642C2×C4C2×#41×C6111yescharacteristic
643C8—22no—
644C8—22no—
645C8—22no—
646C8C4×D4×C6114yes—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22C2×C4×D4×C6111yescharacteristic
662C22C2×#121×C6111yescharacteristic
663C22C61×#53211yescharacteristic
664C22C61×#57611yescharacteristic
665C22C61×#57711yescharacteristic
666C22C61×#57711yescharacteristic
667C22C61×#57811yescharacteristic
668C4—22no—
669C4—22no—
670C4—22no—
671C4—41no—
672C4—41no—
673C4—42no—
674C4—42no—
675C4—42no—
676C4—81no—
677C4—81no—
678C4—81no—
679C4—81no—
680C4C2×C4×D4×C6111yescharacteristic
681C4C4×#41×C6111yescharacteristic
682C4C61×#52511yescharacteristic
683C4C61×#52911yescharacteristic
684C2—42no—
685C2—82no—
686C2C4×#121×C6111yescharacteristic
687C2C61×#294611yescharacteristic
688C2C61×#294711yescharacteristic
689C2C61×#306211yescharacteristic
690C2C61×#306311yescharacteristic
691C2C61×#317411yescharacteristic
692C2C61×#317511yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutatorC2×C4C23×C4×C61
Frattini, cosocleC22×C4C24×C61
prime radicalC2×#121×C61C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×#117×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#440C2semidirect
3. C2×C61×#405C2semidirect
5. C61×#2323C2semidirect
6. C61×#1968C2semidirect
7. C61×#1942C2semidirect
8. C61×#1936C2semidirect
9. C61×#1935C2semidirect
11. C61×#1892C2semidirect
12. C61×#1809C2semidirect
13. C61×#1776C2semidirect
14. C4×#103×C61C2semidirect
15. C4×#102×C61C2semidirect
24. C61×#468C4semidirect
72. C2×M16×C61C2×C4semidirect
81. C22⋊Q8×C61C2×C4semidirect
117. #107×C61C2×C4semidirect
121. #103×C61C2×C4semidirect
126. #97×C61D4semidirect
300. #21543C61direct (N × H)
339. C2×#440C2×C61semidirect
340. C2×#405C2×C61semidirect
342. #2323C2×C61semidirect
343. #1968C2×C61semidirect
344. #1942C2×C61semidirect
345. #1936C2×C61semidirect
346. #1935C2×C61semidirect
348. #1892C2×C61semidirect
349. #1809C2×C61semidirect
350. #1776C2×C61semidirect
351. C4×#103C2×C61semidirect
352. C4×#102C2×C61semidirect
370. #468C4×C61semidirect
408. C61#21543direct (N × H)
419. C2×M16C2×C4×C61semidirect
428. C22⋊Q8C2×C4×C61semidirect
464. #107C2×C4×C61semidirect
468. #103C2×C4×C61semidirect
473. #97D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4682
C2×C61×#4402
C2×C61×#4052
C61×#23242
C61×#23232
C61×#19682
C61×#19422
C61×#19362
C61×#19352
C61×#18932
C61×#18922
C61×#18092
C61×#17762
C4×#103×C612
C4×#102×C612
#2154361