Finite Group Databasebeta

← C61×#23680 #29527113

Subgroups — C61×#23680 #29527113

Order 15616.

956 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×SD16×C61C211yesmaximal, characteristic, complemented
2C2×C4×D8×C61C211yesmaximal, characteristic
3C4×#124×C61C211yesmaximal, characteristic, complemented
4C61×#2293C211yesmaximal, characteristic, complemented
5C61×#2085C211yesmaximal, characteristic, complemented
6C61×#2073C211yesmaximal, characteristic, complemented
7C61×#2068C211yesmaximal, characteristic, complemented
8C61×#2065C211yesmaximal, characteristic, complemented
9C61×#2055C211yesmaximal, characteristic, complemented
10C61×#2054C211yesmaximal, characteristic
11C61×#2042C211yesmaximal, characteristic, complemented
12C61×#2012C211yesmaximal, characteristic
13C4×C4⋊C8×C61C211yesmaximal, characteristic, complemented
14C4×#103×C61C211yesmaximal, characteristic, complemented
15C4×#102×C61C211yesmaximal, characteristic, complemented
16C22×SD16×C61C2211yescharacteristic
17C22×D8×C61C2211yescharacteristic
18C2×#124×C61C2211yescharacteristic
19C2×C4×Q8×C61C2211yescharacteristic
20C2×C4×D4×C61C2211yescharacteristic
21C2×C4×D4×C61C2211yescharacteristic
22C2×#117×C61—21no—
23C4×SD16×C61—24no—
24C4×D8×C61—24no—
25C2×#107×C61C2211yescharacteristic
26C2×#106×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×#103×C61C2211yescharacteristic
30C2×#103×C61C2211yescharacteristic
31C2×#103×C61C2211yescharacteristic
32C2×#102×C61C2211yescharacteristic
33C2×#102×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic
35C2×#102×C61C2211yescharacteristic
36C2×#102×C61C2211yescharacteristic
37C2×C4×C8×C61C2211yescharacteristic
38C2×C4×C8×C61C2211yescharacteristic
39C61×#391C2211yescharacteristic
40C61×#390C2211yescharacteristic
41C61×#390C2211yescharacteristic
42C61×#390C2211yescharacteristic
43C61×#389C2211yescharacteristic
44C61×#389C2211yescharacteristic
45C61×#388—21no—
46C61×#388—21no—
47C61×#388—21no—
48C61×#388—21no—
49C61×#382C2211yescharacteristic
50C4×C4⋊C4×C61C2211yescharacteristic
51C4×C22⋊C4×C61—21no—
52C4×C22⋊C4×C61—21no—
53C4×C22⋊C4×C61—21no—
54C43×C61C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×Q8×C61C2311yescharacteristic
62C22×D4×C61C2311yescharacteristic
63C22×D4×C61C2311yescharacteristic
64C23×C4×C61—21no—
65C23×C4×C61—21no—
66C2×SD16×C61—22no—
67C2×SD16×C61—22no—
68C2×SD16×C61—22no—
69C2×D8×C61—22no—
70C2×D8×C61—22no—
71C2×D8×C61—22no—
72C22×C8×C61C2311yescharacteristic
73C22×C8×C61C2311yescharacteristic
74C22×C8×C61C2311yescharacteristic
75C22×C8×C61C2311yescharacteristic
76#124×C61—22no—
77#124×C61—22no—
78C4×Q8×C61—22no—
79C4×Q8×C61—22no—
80C4×D4×C61—22no—
81C4×D4×C61—22no—
82C4×D4×C61—22no—
83C4×D4×C61D414yes—
84#117×C61—44no—
85C2×C4⋊C4×C61—21no—
86C2×C4⋊C4×C61—21no—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61C2311yescharacteristic
89C2×C4⋊C4×C61C2311yescharacteristic
90C2×C4⋊C4×C61C2311yescharacteristic
91C2×C4⋊C4×C61C2311yescharacteristic
92C2×C4⋊C4×C61C2311yescharacteristic
93C2×C22⋊C4×C61—21no—
94C2×C22⋊C4×C61—21no—
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×C42×C61—21no—
104C2×C42×C61—21no—
105C2×C42×C61D411yescharacteristic
106C2×C42×C61D411yescharacteristic
107C2×C42×C61D411yescharacteristic
108C2×C42×C61D411yescharacteristic
109C2×C42×C61C2311yescharacteristic
110C2×C42×C61C2311yescharacteristic
111C2×C42×C61C2311yescharacteristic
112#107×C61—22no—
113#106×C61—22no—
114C4⋊C8×C61—22no—
115C4⋊C8×C61—22no—
116#103×C61—22no—
117#103×C61—22no—
118#103×C61—22no—
119#102×C61—22no—
120#102×C61—22no—
121#102×C61—22no—
122#102×C61—22no—
123#102×C61—22no—
124C4×C8×C61—22no—
125C4×C8×C61—22no—
126#95×C61—21no—
127#95×C61—21no—
128#95×C61—21no—
129#95×C61—21no—
130#95×C61—21no—
131#95×C61—21no—
132#95×C61—21no—
133C24×C61—21no—
134C24×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×Q8×C61#4112yes—
141C2×D4×C61—21no—
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—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61C2×D412yes—
152C2×D4×C61#4112yes—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—24no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—42no—
161C22×C4×C61—42no—
162C22×C4×C61—42no—
163C22×C4×C61—42no—
164C22×C4×C61—42no—
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2411yescharacteristic
172SD16×C61—28no—
173D8×C61—28no—
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—21no—
184C2×C8×C61#4112yes—
185C2×C8×C61#4112yes—
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—42no—
196C4⋊C4×C61—42no—
197C4⋊C4×C61—42no—
198C4⋊C4×C61C2×D412yes—
199C22⋊C4×C61—24no—
200C22⋊C4×C61—24no—
201C22⋊C4×C61—24no—
202C22⋊C4×C61—42no—
203C22⋊C4×C61—42no—
204C22⋊C4×C61—42no—
205C22⋊C4×C61—42no—
206C22⋊C4×C61—42no—
207C22⋊C4×C61—42no—
208C22⋊C4×C61—42no—
209C42×C61—22no—
210C42×C61—22no—
211C42×C61—22no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—21no—
215C42×C61—21no—
216C42×C61—41no—
217C42×C61—42no—
218C42×C61—42no—
219C42×C61C2×D412yes—
220C42×C61#4112yes—
221C23×C61—22no—
222C23×C61—22no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61—41no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61C22×D411yescharacteristic
236Q8×C61—22no—
237Q8×C61—22no—
238Q8×C61—41no—
239Q8×C61—41no—
240D4×C61—22no—
241D4×C61—22no—
242D4×C61—22no—
243D4×C61—22no—
244D4×C61—41no—
245D4×C61—41no—
246D4×C61—41no—
247D4×C61—41no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—22no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—22no—
256C2×C4×C61—21no—
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—48no—
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—84no—
281C2×C4×C61#12112yes—
282C2×C4×C61#12112yes—
283C2×C4×C61#13512yes—
284C2×C4×C61#13512yes—
285C2×C4×C61AGL(1,ℤ/8)12yes—
286C2×C4×C61C22×D411yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C8×C61—22no—
293C8×C61—22no—
294C8×C61—41no—
295C8×C61—41no—
296#23680C6111yesmaximal, characteristic, direct product factor, Sylow
297C22×C61—42no—
298C22×C61—42no—
299C22×C61—42no—
300C22×C61—42no—
301C22×C61—42no—
302C22×C61—42no—
303C22×C61—81no—
304C22×C61—81no—
305C22×C61—81no—
306C22×C61—81no—
307C22×C61—81no—
308C22×C61—81no—
309C22×C61—81no—
310C22×C61—81no—
311C22×C61C2×#12111yescharacteristic
312C22×C61#52511yescharacteristic
313C22×C61#53211yescharacteristic
314C22×C61C2×#13511yescharacteristic
315C22×C61C2×#13511yescharacteristic
316C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
317C22×C61#57511yescharacteristic
318C4×C61—22no—
319C4×C61—22no—
320C4×C61—41no—
321C4×C61—41no—
322C4×C61—42no—
323C4×C61—41no—
324C4×C61—42no—
325C4×C61—81no—
326C4×C61—81no—
327C4×C61—81no—
328C4×C61—81no—
329C4×C61#46314yes—
330C4×C61#52511yescharacteristic
331C4×C61#52511yescharacteristic
332C4×C61#52911yescharacteristic
333C4×C61#52911yescharacteristic
334C2×C4×SD16C2×C6111yescharacteristic, complemented
335C2×C4×D8C2×C6111yescharacteristic
336C4×#124C2×C6111yescharacteristic, complemented
337#2293C2×C6111yescharacteristic, complemented
338#2085C2×C6111yescharacteristic, complemented
339#2073C2×C6111yescharacteristic, complemented
340#2068C2×C6111yescharacteristic, complemented
341#2065C2×C6111yescharacteristic, complemented
342#2055C2×C6111yescharacteristic, complemented
343#2054C2×C6111yescharacteristic
344#2042C2×C6111yescharacteristic, complemented
345#2012C2×C6111yescharacteristic
346C4×C4⋊C8C2×C6111yescharacteristic, complemented
347C4×#103C2×C6111yescharacteristic, complemented
348C4×#102C2×C6111yescharacteristic, complemented
349C2×C61—82no—
350C2×C61—82no—
351C2×C61#239211yescharacteristic
352C2×C61C2×#46311yescharacteristic
353C2×C61#303511yescharacteristic
354C2×C61#310211yescharacteristic
355C2×C61#310611yescharacteristic
356C2×C61#316811yescharacteristic
357C2×C61#317111yescharacteristic
358C22×SD16C22×C6111yescharacteristic
359C22×D8C22×C6111yescharacteristic
360C2×#124C22×C6111yescharacteristic
361C2×C4×Q8C22×C6111yescharacteristic
362C2×C4×D4C22×C6111yescharacteristic
363C2×C4×D4C22×C6111yescharacteristic
364C2×#117—21no—
365C4×SD16—24no—
366C4×D8—24no—
367C2×#107C22×C6111yescharacteristic
368C2×#106C22×C6111yescharacteristic
369C2×C4⋊C8C22×C6111yescharacteristic
370C2×C4⋊C8C22×C6111yescharacteristic
371C2×#103C22×C6111yescharacteristic
372C2×#103C22×C6111yescharacteristic
373C2×#103C22×C6111yescharacteristic
374C2×#102C22×C6111yescharacteristic
375C2×#102C22×C6111yescharacteristic
376C2×#102C22×C6111yescharacteristic
377C2×#102C22×C6111yescharacteristic
378C2×#102C22×C6111yescharacteristic
379C2×C4×C8C22×C6111yescharacteristic
380C2×C4×C8C22×C6111yescharacteristic
381#391C22×C6111yescharacteristic
382#390C22×C6111yescharacteristic
383#390C22×C6111yescharacteristic
384#390C22×C6111yescharacteristic
385#389C22×C6111yescharacteristic
386#389C22×C6111yescharacteristic
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#382C22×C6111yescharacteristic
392C4×C4⋊C4C22×C6111yescharacteristic
393C4×C22⋊C4—21no—
394C4×C22⋊C4—21no—
395C4×C22⋊C4—21no—
396C43C22×C6111yescharacteristic
397#340C22×C6111yescharacteristic
398#340C22×C6111yescharacteristic
399#340C22×C6111yescharacteristic
400#340C22×C6111yescharacteristic
401#336C22×C6111yescharacteristic
402#336C22×C6111yescharacteristic
403C61#2368011yescharacteristic, direct product factor, Sylow
404C22×Q8C23×C6111yescharacteristic
405C22×D4C23×C6111yescharacteristic
406C22×D4C23×C6111yescharacteristic
407C23×C4—21no—
408C23×C4—21no—
409C2×SD16—22no—
410C2×SD16—22no—
411C2×SD16—22no—
412C2×D8—22no—
413C2×D8—22no—
414C2×D8—22no—
415C22×C8C23×C6111yescharacteristic
416C22×C8C23×C6111yescharacteristic
417C22×C8C23×C6111yescharacteristic
418C22×C8C23×C6111yescharacteristic
419#124—22no—
420#124—22no—
421C4×Q8—22no—
422C4×Q8—22no—
423C4×D4—22no—
424C4×D4—22no—
425C4×D4—22no—
426C4×D4D4×C6114yes—
427#117—44no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4C23×C6111yescharacteristic
432C2×C4⋊C4C23×C6111yescharacteristic
433C2×C4⋊C4C23×C6111yescharacteristic
434C2×C4⋊C4C23×C6111yescharacteristic
435C2×C4⋊C4C23×C6111yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42D4×C6111yescharacteristic
449C2×C42D4×C6111yescharacteristic
450C2×C42D4×C6111yescharacteristic
451C2×C42D4×C6111yescharacteristic
452C2×C42C23×C6111yescharacteristic
453C2×C42C23×C6111yescharacteristic
454C2×C42C23×C6111yescharacteristic
455#107—22no—
456#106—22no—
457C4⋊C8—22no—
458C4⋊C8—22no—
459#103—22no—
460#103—22no—
461#103—22no—
462#102—22no—
463#102—22no—
464#102—22no—
465#102—22no—
466#102—22no—
467C4×C8—22no—
468C4×C8—22no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476C24—21no—
477C24—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8#41×C6112yes—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4C2×D4×C6112yes—
495C2×D4#41×C6112yes—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—24no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4C2×D4×C6111yescharacteristic
509C22×C4C2×D4×C6111yescharacteristic
510C22×C4C2×D4×C6111yescharacteristic
511C22×C4C2×D4×C6111yescharacteristic
512C22×C4C2×D4×C6111yescharacteristic
513C22×C4C2×D4×C6111yescharacteristic
514C22×C4C24×C6111yescharacteristic
515SD16—28no—
516D8—28no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8#41×C6112yes—
528C2×C8#41×C6112yes—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4C2×D4×C6112yes—
542C22⋊C4—24no—
543C22⋊C4—24no—
544C22⋊C4—24no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C42—22no—
553C42—22no—
554C42—22no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—41no—
560C42—42no—
561C42—42no—
562C42C2×D4×C6112yes—
563C42#41×C6112yes—
564C23—22no—
565C23—22no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23C22×D4×C6111yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—41no—
582Q8—41no—
583D4—22no—
584D4—22no—
585D4—22no—
586D4—22no—
587D4—41no—
588D4—41no—
589D4—41no—
590D4—41no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—48no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
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—84no—
624C2×C4#121×C6112yes—
625C2×C4#121×C6112yes—
626C2×C4#135×C6112yes—
627C2×C4#135×C6112yes—
628C2×C4AGL(1,ℤ/8)×C6112yes—
629C2×C4C22×D4×C6111yescharacteristic
630C2×C4C2×#41×C6111yescharacteristic
631C2×C4C2×#41×C6111yescharacteristic
632C2×C4C2×#41×C6111yescharacteristic
633C2×C4C2×#41×C6111yescharacteristic
634C2×C4C2×#41×C6111yescharacteristic
635C8—22no—
636C8—22no—
637C8—41no—
638C8—41no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22C2×#121×C6111yescharacteristic
654C22C61×#52511yescharacteristic
655C22C61×#53211yescharacteristic
656C22C2×#135×C6111yescharacteristic
657C22C2×#135×C6111yescharacteristic
658C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
659C22C61×#57511yescharacteristic
660C4—22no—
661C4—22no—
662C4—42no—
663C4—41no—
664C4—41no—
665C4—42no—
666C4—41no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4C61×#46314yes—
672C4C61×#52511yescharacteristic
673C4C61×#52511yescharacteristic
674C4C61×#52911yescharacteristic
675C4C61×#52911yescharacteristic
676C2—82no—
677C2—82no—
678C2C61×#239211yescharacteristic
679C2C2×C61×#46311yescharacteristic
680C2C61×#303511yescharacteristic
681C2C61×#310211yescharacteristic
682C2C61×#310611yescharacteristic
683C2C61×#316811yescharacteristic
684C2C61×#317111yescharacteristic
subgroupG/H
centerC22×C4×C61C2×D4
commutator, Frattini, cosocleC22×C4C24×C61
socleC23×C61C22×D4
prime radicalC22×D8×C61C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C61 ◁ C43×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C4×SD16×C61C2semidirect
3. C4×#124×C61C2semidirect
4. C61×#2293C2semidirect
5. C61×#2085C2semidirect
6. C61×#2073C2semidirect
7. C61×#2068C2semidirect
8. C61×#2065C2semidirect
9. C61×#2055C2semidirect
11. C61×#2042C2semidirect
13. C4×C4⋊C8×C61C2semidirect
14. C4×#103×C61C2semidirect
15. C4×#102×C61C2semidirect
296. #23680C61direct (N × H)
334. C2×C4×SD16C2×C61semidirect
336. C4×#124C2×C61semidirect
337. #2293C2×C61semidirect
338. #2085C2×C61semidirect
339. #2073C2×C61semidirect
340. #2068C2×C61semidirect
341. #2065C2×C61semidirect
342. #2055C2×C61semidirect
344. #2042C2×C61semidirect
346. C4×C4⋊C8C2×C61semidirect
347. C4×#103C2×C61semidirect
348. C4×#102C2×C61semidirect
403. C61#23680direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×SD16×C612
C2×C4×D8×C612
C4×#124×C612
C61×#22932
C61×#20852
C61×#20732
C61×#20682
C61×#20652
C61×#20552
C61×#20542
C61×#20422
C61×#20122
C4×C4⋊C8×C612
C4×#103×C612
C4×#102×C612
#2368061