Finite Group Databasebeta

← C61×#24142 #29527575

Subgroups — C61×#24142 #29527575

Order 15616.

1292 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3505C211yesmaximal, characteristic, complemented
2C61×#2626C211yesmaximal, characteristic, complemented
3C61×#2617C211yesmaximal, characteristic, complemented
4C61×#2321C211yesmaximal, characteristic, complemented
5C61×#2044C212yesmaximal, complemented
6C61×#2021C212yesmaximal, complemented
7C61×#1996C211yesmaximal, characteristic, complemented
8C61×#1964C211yesmaximal, characteristic, complemented
9C61×#1889C212yesmaximal, complemented
10C61×#1867C212yesmaximal, complemented
11C61×#1799C211yesmaximal, characteristic, complemented
12C61×#553—22no—
13C61×#553—21no—
14C61×#552—21no—
15C61×#551—22no—
16C61×#548—21no—
17C61×#546—21no—
18C61×#539—21no—
19C61×#538—21no—
20C61×#534C2212yes—
21C61×#529—21no—
22C61×#525—21no—
23C2×C22⋊Q8×C61C2211yescharacteristic
24C2×#121×C61C2211yescharacteristic
25C2×#120×C61C2211yescharacteristic
26C2×#120×C61C2212yes—
27C61×#518C2212yes—
28C2×C4×D4×C61C2211yescharacteristic
29C22×C22⋊C4×C61C2211yescharacteristic
30C2×#99×C61C2212yes—
31C2×#99×C61C2212yes—
32C2×#99×C61C2212yes—
33C61×#399—21no—
34C61×#397—21no—
35C61×#396—22no—
36C61×#394—22no—
37C61×#393—21no—
38C61×#392—21no—
39C61×#390—21no—
40C61×#388—21no—
41C61×#388—21no—
42C61×#386—21no—
43C61×#386C2211yescharacteristic
44C61×#386C2212yes—
45C61×#385C2212yes—
46C61×#385C2211yescharacteristic
47C61×#380C2211yescharacteristic
48C61×#380C2211yescharacteristic
49C61×#379C2212yes—
50C61×#379C2211yescharacteristic
51C4×C22⋊C4×C61C2211yescharacteristic
52C61×#342C2212yes—
53C61×#342C2212yes—
54C61×#342C2212yes—
55C25×C61C2311yescharacteristic
56C2×#41×C61—21no—
57C22×Q8×C61D411yescharacteristic, complemented
58C22×D4×C61—21no—
59C22×D4×C61—22no—
60C22×D4×C61D411yescharacteristic, complemented
61C22×D4×C61C2311yescharacteristic
62C22×D4×C61C2312yes—
63C23×C4×C61D411yescharacteristic, complemented
64C23×C4×C61C2311yescharacteristic
65C23×C4×C61C2311yescharacteristic
66#126×C61—22no—
67#126×C61—22no—
68#126×C61—22no—
69#125×C61—22no—
70#125×C61—21no—
71#124×C61—22no—
72#124×C61—21no—
73#123×C61—22no—
74#123×C61—22no—
75#123×C61—22no—
76#123×C61—22no—
77#123×C61—22no—
78C22⋊Q8×C61—22no—
79C22⋊Q8×C61—21no—
80C22⋊Q8×C61—21no—
81C22⋊Q8×C61—21no—
82C22⋊Q8×C61—21no—
83C22⋊Q8×C61—21no—
84#121×C61—22no—
85#121×C61—21no—
86#121×C61—22no—
87#121×C61—22no—
88#121×C61—21no—
89#121×C61—21no—
90#121×C61—21no—
91#121×C61—21no—
92#120×C61—22no—
93#120×C61—22no—
94#120×C61—22no—
95#120×C61—22no—
96#120×C61—24no—
97#120×C61—42no—
98C4×Q8×C61—21no—
99C4×D4×C61—21no—
100C4×D4×C61—22no—
101C4×D4×C61—22no—
102C4×D4×C61—22no—
103C4×D4×C61—21no—
104C4×D4×C61—21no—
105C4×D4×C61—22no—
106C4×D4×C61—21no—
107C4×D4×C61—21no—
108C4×D4×C61—22no—
109#117×C61—22no—
110#117×C61—21no—
111#117×C61—22no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61—21no—
114C2×C4⋊C4×C61—21no—
115C2×C4⋊C4×C61—22no—
116C2×C4⋊C4×C61D411yescharacteristic, complemented
117C2×C4⋊C4×C61D411yescharacteristic, complemented
118C2×C4⋊C4×C61D412yescomplemented
119C2×C4⋊C4×C61D411yescharacteristic, complemented
120C2×C22⋊C4×C61—22no—
121C2×C22⋊C4×C61—21no—
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—22no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—22no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—22no—
134C2×C22⋊C4×C61—22no—
135C2×C22⋊C4×C61D411yescharacteristic, complemented
136C2×C22⋊C4×C61D412yescomplemented
137C2×C22⋊C4×C61C2312yes—
138C2×C22⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61C2312yes—
140C2×C22⋊C4×C61C2312yes—
141C2×C22⋊C4×C61C2311yescharacteristic
142C2×C22⋊C4×C61C2311yescharacteristic
143C2×C42×C61—21no—
144C2×C42×C61D411yescharacteristic, complemented
145#99×C61—24no—
146#99×C61—42no—
147#99×C61—42no—
148#95×C61—21no—
149#95×C61—21no—
150#95×C61—21no—
151#95×C61—21no—
152#95×C61—22no—
153#95×C61—21no—
154#95×C61—22no—
155C24×C61—21no—
156C24×C61—21no—
157C24×C61—21no—
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—81no—
162C24×C61—81no—
163C24×C61C2×D412yes—
164C24×C61C2×D411yescharacteristic
165C24×C61#4112yescomplemented
166C24×C61C2411yescharacteristic
167#41×C61—82no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—81no—
171C2×D4×C61—21no—
172C2×D4×C61—22no—
173C2×D4×C61—21no—
174C2×D4×C61—22no—
175C2×D4×C61—22no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—22no—
179C2×D4×C61—21no—
180C2×D4×C61—22no—
181C2×D4×C61—21no—
182C2×D4×C61—22no—
183C2×D4×C61—22no—
184C2×D4×C61—22no—
185C2×D4×C61—24no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—44no—
189C2×D4×C61—81no—
190C2×D4×C61—81no—
191C2×D4×C61—81no—
192C2×D4×C61—82no—
193C2×D4×C61—82no—
194C22×C4×C61—21no—
195C22×C4×C61—22no—
196C22×C4×C61—22no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—22no—
203C22×C4×C61—22no—
204C22×C4×C61—21no—
205C22×C4×C61—81no—
206C22×C4×C61—81no—
207C22×C4×C61—81no—
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D412yes—
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D412yes—
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D412yes—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C4⋊C4×C61—22no—
221C4⋊C4×C61—22no—
222C4⋊C4×C61—22no—
223C4⋊C4×C61—22no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—22no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—22no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—81no—
233C4⋊C4×C61—81no—
234C4⋊C4×C61—81no—
235C4⋊C4×C61—82no—
236C22⋊C4×C61—22no—
237C22⋊C4×C61—22no—
238C22⋊C4×C61—24no—
239C22⋊C4×C61—22no—
240C22⋊C4×C61—22no—
241C22⋊C4×C61—22no—
242C22⋊C4×C61—22no—
243C22⋊C4×C61—21no—
244C22⋊C4×C61—22no—
245C22⋊C4×C61—21no—
246C22⋊C4×C61—22no—
247C22⋊C4×C61—21no—
248C22⋊C4×C61—22no—
249C22⋊C4×C61—21no—
250C22⋊C4×C61—21no—
251C22⋊C4×C61—22no—
252C22⋊C4×C61—22no—
253C22⋊C4×C61—22no—
254C22⋊C4×C61—21no—
255C22⋊C4×C61—22no—
256C22⋊C4×C61—22no—
257C22⋊C4×C61—21no—
258C22⋊C4×C61—44no—
259C22⋊C4×C61—41no—
260C22⋊C4×C61—41no—
261C22⋊C4×C61—41no—
262C22⋊C4×C61—41no—
263C22⋊C4×C61—81no—
264C22⋊C4×C61—82no—
265C22⋊C4×C61—81no—
266C22⋊C4×C61—82no—
267C22⋊C4×C61—81no—
268C22⋊C4×C61—82no—
269C22⋊C4×C61#4112yescomplemented
270C42×C61—22no—
271C42×C61—22no—
272C42×C61—21no—
273C42×C61—21no—
274C42×C61—81no—
275C23×C61—21no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—21no—
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—21no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—42no—
289C23×C61—41no—
290C23×C61—42no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—42no—
294C23×C61—41no—
295C23×C61—42no—
296C23×C61—42no—
297C23×C61—42no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—82no—
303C23×C61—82no—
304C23×C61—82no—
305C23×C61—82no—
306C23×C61C22×D411yescharacteristic
307C23×C61C22×D411yescharacteristic
308C23×C61C22×D411yescharacteristic
309C23×C61C2×#4111yescharacteristic
310C23×C61C2×#4111yescharacteristic
311C23×C61H(5,𝔽2)11yescharacteristic
312C23×C612−1+411yescharacteristic
313Q8×C61—42no—
314Q8×C61—81no—
315D4×C61—42no—
316D4×C61—42no—
317D4×C61—42no—
318D4×C61—41no—
319D4×C61—41no—
320D4×C61—41no—
321D4×C61—42no—
322D4×C61—42no—
323D4×C61—41no—
324D4×C61—81no—
325D4×C61—82no—
326D4×C61—84no—
327D4×C61—82no—
328D4×C61—88no—
329C2×C4×C61—21no—
330C2×C4×C61—22no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—21no—
336C2×C4×C61—22no—
337C2×C4×C61—21no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
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—42no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—42no—
351C2×C4×C61—41no—
352C2×C4×C61—42no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—42no—
356C2×C4×C61—42no—
357C2×C4×C61—41no—
358C2×C4×C61—42no—
359C2×C4×C61—42no—
360C2×C4×C61—42no—
361C2×C4×C61—41no—
362C2×C4×C61—42no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—42no—
366C2×C4×C61—42no—
367C2×C4×C61—81no—
368C2×C4×C61—82no—
369C2×C4×C61—82no—
370C2×C4×C61#12011yescharacteristic
371C2×C4×C61#12011yescharacteristic
372C2×C4×C61#12011yescharacteristic
373C2×C4×C61#12011yescharacteristic
374#24142C6111yesmaximal, characteristic, direct product factor, Sylow
375C22×C61—21no—
376C22×C61—21no—
377C22×C61—21no—
378C22×C61—21no—
379C22×C61—21no—
380C22×C61—21no—
381C22×C61—41no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—44no—
388C22×C61—42no—
389C22×C61—44no—
390C22×C61—41no—
391C22×C61—42no—
392C22×C61—42no—
393C22×C61—41no—
394C22×C61—42no—
395C22×C61—42no—
396C22×C61—41no—
397C22×C61—82no—
398C22×C61—81no—
399C22×C61—82no—
400C22×C61—82no—
401C22×C61—81no—
402C22×C61—81no—
403C22×C61—82no—
404C22×C61—81no—
405C22×C61—81no—
406C22×C61C2×#12011yescharacteristic
407C22×C61#52511yescharacteristic
408C22×C61#53711yescharacteristic
409C22×C61#54611yescharacteristic
410C22×C61#54711yescharacteristic
411C22×C61#54811yescharacteristic
412C22×C61#55011yescharacteristic
413C4×C61—21no—
414C4×C61—21no—
415C4×C61—21no—
416C4×C61—21no—
417C4×C61—42no—
418C4×C61—41no—
419C4×C61—42no—
420C4×C61—41no—
421C4×C61—42no—
422C4×C61—41no—
423C4×C61—42no—
424C4×C61—82no—
425C4×C61—81no—
426C4×C61—82no—
427C4×C61—81no—
428#3505C2×C6111yescharacteristic, complemented
429#2626C2×C6111yescharacteristic, complemented
430#2617C2×C6111yescharacteristic, complemented
431#2321C2×C6111yescharacteristic, complemented
432#2044C2×C6112yescomplemented
433#2021C2×C6112yescomplemented
434#1996C2×C6111yescharacteristic, complemented
435#1964C2×C6111yescharacteristic, complemented
436#1889C2×C6112yescomplemented
437#1867C2×C6112yescomplemented
438#1799C2×C6111yescharacteristic, complemented
439C2×C61—21no—
440C2×C61—21no—
441C2×C61—21no—
442C2×C61—21no—
443C2×C61—21no—
444C2×C61—21no—
445C2×C61—82no—
446C2×C61—81no—
447C2×C61—82no—
448C2×C61#240711yescharacteristic
449C2×C61#302611yescharacteristic
450C2×C61#302711yescharacteristic
451#553—22no—
452#553—21no—
453#552—21no—
454#551—22no—
455#548—21no—
456#546—21no—
457#539—21no—
458#538—21no—
459#534C22×C6112yes—
460#529—21no—
461#525—21no—
462C2×C22⋊Q8C22×C6111yescharacteristic
463C2×#121C22×C6111yescharacteristic
464C2×#120C22×C6111yescharacteristic
465C2×#120C22×C6112yes—
466#518C22×C6112yes—
467C2×C4×D4C22×C6111yescharacteristic
468C22×C22⋊C4C22×C6111yescharacteristic
469C2×#99C22×C6112yes—
470C2×#99C22×C6112yes—
471C2×#99C22×C6112yes—
472#399—21no—
473#397—21no—
474#396—22no—
475#394—22no—
476#393—21no—
477#392—21no—
478#390—21no—
479#388—21no—
480#388—21no—
481#386—21no—
482#386C22×C6111yescharacteristic
483#386C22×C6112yes—
484#385C22×C6111yescharacteristic
485#385C22×C6112yes—
486#380C22×C6111yescharacteristic
487#380C22×C6111yescharacteristic
488#379C22×C6111yescharacteristic
489#379C22×C6112yes—
490C4×C22⋊C4C22×C6111yescharacteristic
491#342C22×C6112yes—
492#342C22×C6112yes—
493#342C22×C6112yes—
494C61#2414211yescharacteristic, direct product factor, Sylow
495C25C23×C6111yescharacteristic
496C2×#41—21no—
497C22×Q8D4×C6111yescharacteristic, complemented
498C22×D4—21no—
499C22×D4—22no—
500C22×D4D4×C6111yescharacteristic, complemented
501C22×D4C23×C6111yescharacteristic
502C22×D4C23×C6112yes—
503C23×C4D4×C6111yescharacteristic, complemented
504C23×C4C23×C6111yescharacteristic
505C23×C4C23×C6111yescharacteristic
506#126—22no—
507#126—22no—
508#126—22no—
509#125—21no—
510#125—22no—
511#124—21no—
512#124—22no—
513#123—22no—
514#123—22no—
515#123—22no—
516#123—22no—
517#123—22no—
518C22⋊Q8—21no—
519C22⋊Q8—22no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524#121—21no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—22no—
531#121—22no—
532#120—22no—
533#120—22no—
534#120—22no—
535#120—22no—
536#120—24no—
537#120—42no—
538C4×Q8—21no—
539C4×D4—22no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—22no—
549#117—21no—
550#117—22no—
551#117—22no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4D4×C6111yescharacteristic, complemented
557C2×C4⋊C4D4×C6111yescharacteristic, complemented
558C2×C4⋊C4D4×C6112yescomplemented
559C2×C4⋊C4D4×C6111yescharacteristic, complemented
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4D4×C6111yescharacteristic, complemented
576C2×C22⋊C4D4×C6112yescomplemented
577C2×C22⋊C4C23×C6112yes—
578C2×C22⋊C4C23×C6111yescharacteristic
579C2×C22⋊C4C23×C6112yes—
580C2×C22⋊C4C23×C6111yescharacteristic
581C2×C22⋊C4C23×C6112yes—
582C2×C22⋊C4C23×C6111yescharacteristic
583C2×C42—21no—
584C2×C42D4×C6111yescharacteristic, complemented
585#99—24no—
586#99—42no—
587#99—42no—
588#95—21no—
589#95—21no—
590#95—21no—
591#95—21no—
592#95—22no—
593#95—21no—
594#95—22no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—81no—
602C24—81no—
603C24C2×D4×C6112yes—
604C24C2×D4×C6111yescharacteristic
605C24#41×C6112yescomplemented
606C24C24×C6111yescharacteristic
607#41—82no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—81no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—44no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—82no—
633C2×D4—82no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4C2×D4×C6111yescharacteristic
649C22×C4C2×D4×C6112yes—
650C22×C4C2×D4×C6111yescharacteristic
651C22×C4C2×D4×C6112yes—
652C22×C4C2×D4×C6111yescharacteristic
653C22×C4C2×D4×C6112yes—
654C22×C4C2×D4×C6111yescharacteristic
655C22×C4C2×D4×C6111yescharacteristic
656C22×C4C2×D4×C6111yescharacteristic
657C22×C4C2×D4×C6111yescharacteristic
658C22×C4C2×D4×C6111yescharacteristic
659C22×C4C2×D4×C6111yescharacteristic
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—82no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—24no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—21no—
684C22⋊C4—22no—
685C22⋊C4—21no—
686C22⋊C4—22no—
687C22⋊C4—21no—
688C22⋊C4—22no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—21no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—21no—
698C22⋊C4—44no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C22⋊C4—41no—
702C22⋊C4—41no—
703C22⋊C4—81no—
704C22⋊C4—82no—
705C22⋊C4—81no—
706C22⋊C4—82no—
707C22⋊C4—81no—
708C22⋊C4—82no—
709C22⋊C4#41×C6112yescomplemented
710C42—22no—
711C42—22no—
712C42—21no—
713C42—21no—
714C42—81no—
715C23—22no—
716C23—22no—
717C23—21no—
718C23—22no—
719C23—22no—
720C23—21no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—82no—
743C23—82no—
744C23—82no—
745C23—82no—
746C23C22×D4×C6111yescharacteristic
747C23C22×D4×C6111yescharacteristic
748C23C22×D4×C6111yescharacteristic
749C23C2×#41×C6111yescharacteristic
750C23C2×#41×C6111yescharacteristic
751C23H(5,𝔽2)×C6111yescharacteristic
752C232−1+4×C6111yescharacteristic
753Q8—42no—
754Q8—81no—
755D4—42no—
756D4—42no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—42no—
761D4—42no—
762D4—41no—
763D4—42no—
764D4—81no—
765D4—82no—
766D4—84no—
767D4—82no—
768D4—88no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—81no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4#120×C6111yescharacteristic
811C2×C4#120×C6111yescharacteristic
812C2×C4#120×C6111yescharacteristic
813C2×C4#120×C6111yescharacteristic
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—42no—
826C22—44no—
827C22—42no—
828C22—44no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—41no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C2×#120×C6111yescharacteristic
846C22C61×#52511yescharacteristic
847C22C61×#53711yescharacteristic
848C22C61×#54611yescharacteristic
849C22C61×#54711yescharacteristic
850C22C61×#54811yescharacteristic
851C22C61×#55011yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—82no—
864C4—81no—
865C4—82no—
866C4—81no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—21no—
873C2—82no—
874C2—81no—
875C2—82no—
876C2C61×#240711yescharacteristic
877C2C61×#302611yescharacteristic
878C2C61×#302711yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC24C24×C61
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3505C2semidirect
2. C61×#2626C2semidirect
3. C61×#2617C2semidirect
4. C61×#2321C2semidirect
5. C61×#2044C2semidirect
6. C61×#2021C2semidirect
7. C61×#1996C2semidirect
8. C61×#1964C2semidirect
9. C61×#1889C2semidirect
10. C61×#1867C2semidirect
11. C61×#1799C2semidirect
57. C22×Q8×C61D4semidirect
60. C22×D4×C61D4semidirect
63. C23×C4×C61D4semidirect
116. C2×C4⋊C4×C61D4semidirect
117. C2×C4⋊C4×C61D4semidirect
118. C2×C4⋊C4×C61D4semidirect
119. C2×C4⋊C4×C61D4semidirect
135. C2×C22⋊C4×C61D4semidirect
136. C2×C22⋊C4×C61D4semidirect
144. C2×C42×C61D4semidirect
165. C24×C61#41semidirect
269. C22⋊C4×C61#41semidirect
374. #24142C61direct (N × H)
428. #3505C2×C61semidirect
429. #2626C2×C61semidirect
430. #2617C2×C61semidirect
431. #2321C2×C61semidirect
432. #2044C2×C61semidirect
433. #2021C2×C61semidirect
434. #1996C2×C61semidirect
435. #1964C2×C61semidirect
436. #1889C2×C61semidirect
437. #1867C2×C61semidirect
438. #1799C2×C61semidirect
494. C61#24142direct (N × H)
497. C22×Q8D4×C61semidirect
500. C22×D4D4×C61semidirect
503. C23×C4D4×C61semidirect
556. C2×C4⋊C4D4×C61semidirect
557. C2×C4⋊C4D4×C61semidirect
558. C2×C4⋊C4D4×C61semidirect
559. C2×C4⋊C4D4×C61semidirect
575. C2×C22⋊C4D4×C61semidirect
576. C2×C22⋊C4D4×C61semidirect
584. C2×C42D4×C61semidirect
605. C24#41×C61semidirect
709. C22⋊C4#41×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#35052
C61×#26262
C61×#26172
C61×#23212
C61×#20442
C61×#20212
C61×#19962
C61×#19642
C61×#18892
C61×#18672
C61×#17992
#2414261