Finite Group Databasebeta

← C61×#25162 #29528595

Subgroups — C61×#25162 #29528595

Order 15616.

1240 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#459C211yesmaximal, characteristic, complemented
2C2×C61×#449C211yesmaximal, characteristic, complemented
3C2×C61×#449C211yesmaximal, characteristic, complemented
4C2×C4×D8×C61C211yesmaximal, characteristic, complemented
5C61×#2428C211yesmaximal, characteristic, complemented
6C61×#2339C211yesmaximal, characteristic, complemented
7C61×#2068C211yesmaximal, characteristic, complemented
8C61×#2034C211yesmaximal, characteristic, complemented
9C61×#2033C211yesmaximal, characteristic, complemented
10C61×#2014C211yesmaximal, characteristic, complemented
11C61×#1968C211yesmaximal, characteristic, complemented
12C61×#1923C211yesmaximal, characteristic, complemented
13C61×#1879C211yesmaximal, characteristic, complemented
14C61×#1877C211yesmaximal, characteristic, complemented
15C61×#1864C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C22×SD16×C61C2211yescharacteristic
19C22×D8×C61C2211yescharacteristic
20C22×D8×C61C2211yescharacteristic
21C2×#127×C61C2211yescharacteristic
22C2×#121×C61—21no—
23C2×#121×C61C2211yescharacteristic
24C2×#121×C61C2211yescharacteristic
25C2×C4×D4×C61C2211yescharacteristic
26C2×C4×D4×C61C2211yescharacteristic
27C2×C4×D4×C61C2211yescharacteristic
28C61×#459—24no—
29C61×#449—24no—
30C61×#449—24no—
31C4×D8×C61—24no—
32C2×#107×C61C2211yescharacteristic
33C2×#106×C61C2211yescharacteristic
34C2×C4⋊C8×C61C2211yescharacteristic
35C2×#103×C61C2211yescharacteristic
36C2×#103×C61C2211yescharacteristic
37C2×#102×C61C2211yescharacteristic
38C2×#102×C61C2211yescharacteristic
39C2×#102×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic
42C2×#102×C61C2211yescharacteristic
43C2×C22⋊C8×C61C2211yescharacteristic
44C2×C22⋊C8×C61C2211yescharacteristic
45C2×C4×C8×C61C2211yescharacteristic
46C61×#394—21no—
47C61×#392—21no—
48C61×#391C2211yescharacteristic
49C61×#391C2211yescharacteristic
50C61×#390C2211yescharacteristic
51C61×#389C2211yescharacteristic
52C61×#386—21no—
53C61×#386—21no—
54C61×#386—21no—
55C61×#381—21no—
56C61×#380C2211yescharacteristic
57C4×C22⋊C4×C61C2211yescharacteristic
58C2×#95×C61—21no—
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C2×#41×C61—22no—
64C2×#41×C61—22no—
65C2×#41×C61—22no—
66C2×#41×C61—22no—
67C2×#41×C61—41no—
68C2×#41×C61—41no—
69C22×Q8×C61C2311yescharacteristic
70C22×D4×C61—21no—
71C22×D4×C61—21no—
72C22×D4×C61—21no—
73C22×D4×C61—21no—
74C22×D4×C61—21no—
75C22×D4×C61C2311yescharacteristic
76C22×D4×C61C2311yescharacteristic
77C22×D4×C61C2311yescharacteristic
78C23×C4×C61—21no—
79C23×C4×C61—21no—
80C23×C4×C61—21no—
81C23×C4×C61—21no—
82C23×C4×C61C2311yescharacteristic
83C2×SD16×C61—22no—
84C2×SD16×C61—22no—
85C2×SD16×C61—22no—
86C2×SD16×C61—22no—
87C2×SD16×C61—41no—
88C2×SD16×C61—41no—
89C2×D8×C61—22no—
90C2×D8×C61—22no—
91C2×D8×C61—22no—
92C2×D8×C61—22no—
93C2×D8×C61—22no—
94C2×D8×C61D414yescomplemented
95C22×C8×C61C2311yescharacteristic
96C22×C8×C61C2311yescharacteristic
97C22×C8×C61C2311yescharacteristic
98C22×C8×C61C2311yescharacteristic
99#127×C61—22no—
100#127×C61—41no—
101#121×C61—22no—
102#121×C61—22no—
103#121×C61—44no—
104#121×C61—41no—
105#121×C61—41no—
106C4×D4×C61—22no—
107C4×D4×C61—22no—
108C4×D4×C61—22no—
109C4×D4×C61—41no—
110C4×D4×C61—41no—
111C4×D4×C61—41no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—21no—
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61D411yescharacteristic
126C2×C22⋊C4×C61D411yescharacteristic
127C2×C42×C61C2311yescharacteristic
128C2×C42×C61C2311yescharacteristic
129#107×C61—22no—
130#106×C61—41no—
131C4⋊C8×C61—22no—
132#103×C61—22no—
133#103×C61—22no—
134#102×C61—22no—
135#102×C61—22no—
136#102×C61—22no—
137#102×C61—22no—
138#102×C61—41no—
139#102×C61D414yescomplemented
140C22⋊C8×C61—22no—
141C22⋊C8×C61—22no—
142C4×C8×C61—22no—
143#95×C61—21no—
144#95×C61—21no—
145#95×C61—21no—
146#95×C61—21no—
147#95×C61—21no—
148#95×C61—21no—
149#95×C61D411yescharacteristic
150#95×C61D411yescharacteristic
151C24×C61—21no—
152C24×C61—21no—
153C24×C61—21no—
154C24×C61C2×D411yescharacteristic
155#41×C61—44no—
156#41×C61—44no—
157#41×C61—44no—
158#41×C61—44no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61#4112yes—
165C2×D4×C61—24no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—42no—
181C2×D4×C61—42no—
182C2×D4×C61—42no—
183C2×D4×C61—42no—
184C2×D4×C61—42no—
185C2×D4×C61—42no—
186C2×D4×C61—42no—
187C2×D4×C61—42no—
188C2×D4×C61—42no—
189C2×D4×C61—42no—
190C2×D4×C61—81no—
191C2×D4×C61—81no—
192C2×D4×C61—81no—
193C2×D4×C61—81no—
194C2×D4×C61C2×D412yes—
195C2×D4×C61C2×D412yes—
196C2×D4×C61C2×D412yes—
197C2×D4×C61#4112yes—
198C22×C4×C61—24no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—42no—
211C22×C4×C61—42no—
212C22×C4×C61—42no—
213C22×C4×C61—42no—
214C22×C4×C61—42no—
215C22×C4×C61—42no—
216C22×C4×C61—42no—
217C22×C4×C61—42no—
218C22×C4×C61—81no—
219C22×C4×C61—81no—
220C22×C4×C61—81no—
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2411yescharacteristic
227SD16×C61—44no—
228SD16×C61—44no—
229D8×C61—28no—
230D8×C61—44no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61C2×D412yes—
242C2×C8×C61C2×D412yes—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—42no—
251C4⋊C4×C61C2×D412yes—
252C22⋊C4×C61—22no—
253C22⋊C4×C61—22no—
254C22⋊C4×C61—42no—
255C22⋊C4×C61—42no—
256C22⋊C4×C61—42no—
257C22⋊C4×C61—42no—
258C22⋊C4×C61—42no—
259C22⋊C4×C61—42no—
260C22⋊C4×C61—81no—
261C22⋊C4×C61—81no—
262C42×C61—21no—
263C42×C61—21no—
264C42×C61—21no—
265C42×C61—21no—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—22no—
269C23×C61—21no—
270C23×C61—22no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61C22×D411yescharacteristic
295Q8×C61—22no—
296Q8×C61—22no—
297Q8×C61—41no—
298Q8×C61—41no—
299D4×C61—22no—
300D4×C61—22no—
301D4×C61—22no—
302D4×C61—22no—
303D4×C61—22no—
304D4×C61—48no—
305D4×C61—41no—
306D4×C61—41no—
307D4×C61—41no—
308D4×C61—41no—
309D4×C61—41no—
310D4×C61—41no—
311D4×C61—84no—
312D4×C61—84no—
313D4×C61—84no—
314D4×C61—84no—
315D4×C61#12114yescomplemented
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—22no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—22no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—48no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—84no—
350C2×C4×C61—84no—
351C2×C4×C61—84no—
352C2×C4×C61#13512yes—
353C2×C4×C61AGL(1,ℤ/8)12yes—
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C2×#4111yescharacteristic
357C2×C4×C61C2×#4111yescharacteristic
358C2×C4×C61H(5,𝔽2)11yescharacteristic
359C2×C4×C61H(5,𝔽2)11yescharacteristic
360C8×C61—22no—
361C8×C61—22no—
362C8×C61—41no—
363C8×C61—41no—
364#25162C6111yesmaximal, characteristic, direct product factor, Sylow
365C22×C61—24no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—42no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—42no—
379C22×C61—42no—
380C22×C61—41no—
381C22×C61—41no—
382C22×C61—81no—
383C22×C61—81no—
384C22×C61—81no—
385C22×C61—81no—
386C22×C61—81no—
387C22×C61—81no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61—81no—
391C22×C61—81no—
392C22×C61—81no—
393C22×C61#52511yescharacteristic
394C22×C61D4211yescharacteristic
395C22×C61D4211yescharacteristic
396C22×C61C2×#13511yescharacteristic
397C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
398C22×C61#57611yescharacteristic
399C22×C61#57711yescharacteristic
400C4×C61—22no—
401C4×C61—22no—
402C4×C61—41no—
403C4×C61—42no—
404C4×C61—42no—
405C4×C61—41no—
406C4×C61—41no—
407C4×C61—81no—
408C4×C61—81no—
409C4×C61—81no—
410C4×C61C2×#12111yescharacteristic
411C4×C61#53811yescharacteristic
412C4×C61#54611yescharacteristic
413C4×C61#54611yescharacteristic
414C2×#459C2×C6111yescharacteristic, complemented
415C2×#449C2×C6111yescharacteristic, complemented
416C2×#449C2×C6111yescharacteristic, complemented
417C2×C4×D8C2×C6111yescharacteristic, complemented
418#2428C2×C6111yescharacteristic, complemented
419#2339C2×C6111yescharacteristic, complemented
420#2068C2×C6111yescharacteristic, complemented
421#2034C2×C6111yescharacteristic, complemented
422#2033C2×C6111yescharacteristic, complemented
423#2014C2×C6111yescharacteristic, complemented
424#1968C2×C6111yescharacteristic, complemented
425#1923C2×C6111yescharacteristic, complemented
426#1879C2×C6111yescharacteristic, complemented
427#1877C2×C6111yescharacteristic, complemented
428#1864C2×C6111yescharacteristic, complemented
429C2×C61—44no—
430C2×C61—81no—
431C2×C61—82no—
432C2×C61—161no—
433C2×C61#242411yescharacteristic
434C2×C61#310611yescharacteristic
435C2×C61#311911yescharacteristic
436C2×C61#326411yescharacteristic
437C2×C61#327211yescharacteristic
438C2×C61#328011yescharacteristic
439C2×C61#328411yescharacteristic
440C22×#41C22×C6111yescharacteristic
441C22×SD16C22×C6111yescharacteristic
442C22×SD16C22×C6111yescharacteristic
443C22×D8C22×C6111yescharacteristic
444C22×D8C22×C6111yescharacteristic
445C2×#127C22×C6111yescharacteristic
446C2×#121—21no—
447C2×#121C22×C6111yescharacteristic
448C2×#121C22×C6111yescharacteristic
449C2×C4×D4C22×C6111yescharacteristic
450C2×C4×D4C22×C6111yescharacteristic
451C2×C4×D4C22×C6111yescharacteristic
452#459—24no—
453#449—24no—
454#449—24no—
455C4×D8—24no—
456C2×#107C22×C6111yescharacteristic
457C2×#106C22×C6111yescharacteristic
458C2×C4⋊C8C22×C6111yescharacteristic
459C2×#103C22×C6111yescharacteristic
460C2×#103C22×C6111yescharacteristic
461C2×#102C22×C6111yescharacteristic
462C2×#102C22×C6111yescharacteristic
463C2×#102C22×C6111yescharacteristic
464C2×#102C22×C6111yescharacteristic
465C2×#102C22×C6111yescharacteristic
466C2×#102C22×C6111yescharacteristic
467C2×C22⋊C8C22×C6111yescharacteristic
468C2×C22⋊C8C22×C6111yescharacteristic
469C2×C4×C8C22×C6111yescharacteristic
470#394—21no—
471#392—21no—
472#391C22×C6111yescharacteristic
473#391C22×C6111yescharacteristic
474#390C22×C6111yescharacteristic
475#389C22×C6111yescharacteristic
476#386—21no—
477#386—21no—
478#386—21no—
479#381—21no—
480#380C22×C6111yescharacteristic
481C4×C22⋊C4C22×C6111yescharacteristic
482C2×#95—21no—
483#340C22×C6111yescharacteristic
484#340C22×C6111yescharacteristic
485#336C22×C6111yescharacteristic
486#336C22×C6111yescharacteristic
487C61#2516211yescharacteristic, direct product factor, Sylow
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C22×Q8C23×C6111yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C23×C6111yescharacteristic
501C22×D4C23×C6111yescharacteristic
502C22×D4C23×C6111yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4C23×C6111yescharacteristic
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—41no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8D4×C6114yescomplemented
520C22×C8C23×C6111yescharacteristic
521C22×C8C23×C6111yescharacteristic
522C22×C8C23×C6111yescharacteristic
523C22×C8C23×C6111yescharacteristic
524#127—22no—
525#127—41no—
526#121—22no—
527#121—22no—
528#121—44no—
529#121—41no—
530#121—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C6111yescharacteristic
539C2×C4⋊C4C23×C6111yescharacteristic
540C2×C4⋊C4C23×C6111yescharacteristic
541C2×C4⋊C4C23×C6111yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C6111yescharacteristic
551C2×C22⋊C4D4×C6111yescharacteristic
552C2×C42C23×C6111yescharacteristic
553C2×C42C23×C6111yescharacteristic
554#107—22no—
555#106—41no—
556C4⋊C8—22no—
557#103—22no—
558#103—22no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—22no—
563#102—41no—
564#102D4×C6114yescomplemented
565C22⋊C8—22no—
566C22⋊C8—22no—
567C4×C8—22no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95—21no—
574#95D4×C6111yescharacteristic
575#95D4×C6111yescharacteristic
576C24—21no—
577C24—21no—
578C24—21no—
579C24C2×D4×C6111yescharacteristic
580#41—44no—
581#41—44no—
582#41—44no—
583#41—44no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8#41×C6112yes—
590C2×D4—24no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4C2×D4×C6112yes—
620C2×D4C2×D4×C6112yes—
621C2×D4C2×D4×C6112yes—
622C2×D4#41×C6112yes—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4C2×D4×C6111yescharacteristic
647C22×C4C2×D4×C6111yescharacteristic
648C22×C4C2×D4×C6111yescharacteristic
649C22×C4C2×D4×C6111yescharacteristic
650C22×C4C2×D4×C6111yescharacteristic
651C22×C4C24×C6111yescharacteristic
652SD16—44no—
653SD16—44no—
654D8—28no—
655D8—44no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8C2×D4×C6112yes—
667C2×C8C2×D4×C6112yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—42no—
676C4⋊C4C2×D4×C6112yes—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—81no—
686C22⋊C4—81no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23C22×D4×C6111yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—84no—
737D4—84no—
738D4—84no—
739D4—84no—
740D4#121×C6114yescomplemented
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—48no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—84no—
775C2×C4—84no—
776C2×C4—84no—
777C2×C4#135×C6112yes—
778C2×C4AGL(1,ℤ/8)×C6112yes—
779C2×C4C22×D4×C6111yescharacteristic
780C2×C4C22×D4×C6111yescharacteristic
781C2×C4C2×#41×C6111yescharacteristic
782C2×C4C2×#41×C6111yescharacteristic
783C2×C4H(5,𝔽2)×C6111yescharacteristic
784C2×C4H(5,𝔽2)×C6111yescharacteristic
785C8—22no—
786C8—22no—
787C8—41no—
788C8—41no—
789C22—24no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—42no—
800C22—41no—
801C22—41no—
802C22—42no—
803C22—42no—
804C22—41no—
805C22—41no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22C61×#52511yescharacteristic
818C22D42×C6111yescharacteristic
819C22D42×C6111yescharacteristic
820C22C2×#135×C6111yescharacteristic
821C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
822C22C61×#57611yescharacteristic
823C22C61×#57711yescharacteristic
824C4—22no—
825C4—22no—
826C4—41no—
827C4—42no—
828C4—42no—
829C4—41no—
830C4—41no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4C2×#121×C6111yescharacteristic
835C4C61×#53811yescharacteristic
836C4C61×#54611yescharacteristic
837C4C61×#54611yescharacteristic
838C2—44no—
839C2—81no—
840C2—82no—
841C2—161no—
842C2C61×#242411yescharacteristic
843C2C61×#310611yescharacteristic
844C2C61×#311911yescharacteristic
845C2C61×#326411yescharacteristic
846C2C61×#327211yescharacteristic
847C2C61×#328011yescharacteristic
848C2C61×#328411yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
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×#459C2semidirect
2. C2×C61×#449C2semidirect
3. C2×C61×#449C2semidirect
4. C2×C4×D8×C61C2semidirect
5. C61×#2428C2semidirect
6. C61×#2339C2semidirect
7. C61×#2068C2semidirect
8. C61×#2034C2semidirect
9. C61×#2033C2semidirect
10. C61×#2014C2semidirect
11. C61×#1968C2semidirect
12. C61×#1923C2semidirect
13. C61×#1879C2semidirect
14. C61×#1877C2semidirect
15. C61×#1864C2semidirect
94. C2×D8×C61D4semidirect
139. #102×C61D4semidirect
315. D4×C61#121semidirect
364. #25162C61direct (N × H)
414. C2×#459C2×C61semidirect
415. C2×#449C2×C61semidirect
416. C2×#449C2×C61semidirect
417. C2×C4×D8C2×C61semidirect
418. #2428C2×C61semidirect
419. #2339C2×C61semidirect
420. #2068C2×C61semidirect
421. #2034C2×C61semidirect
422. #2033C2×C61semidirect
423. #2014C2×C61semidirect
424. #1968C2×C61semidirect
425. #1923C2×C61semidirect
426. #1879C2×C61semidirect
427. #1877C2×C61semidirect
428. #1864C2×C61semidirect
487. C61#25162direct (N × H)
519. C2×D8D4×C61semidirect
564. #102D4×C61semidirect
740. D4#121×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4592
C2×C61×#4492
C2×C4×D8×C612
C61×#24282
C61×#23392
C61×#20682
C61×#20342
C61×#20332
C61×#20142
C61×#19682
C61×#19232
C61×#18792
C61×#18772
C61×#18642
#2516261