Finite Group Databasebeta

← C61×#13996 #29517429

Subgroups — C61×#13996 #29517429

Order 15616.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C61C211yesmaximal, characteristic
2C2×C61×#386C211yesmaximal, characteristic
3C2×C61×#386C211yesmaximal, characteristic
4C2×C61×#385C211yesmaximal, characteristic, complemented
5C2×C61×#381C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
7C22×#95×C61C211yesmaximal, characteristic, complemented
8C61×#1445C212yesmaximal, complemented
9C61×#1439C212yesmaximal, complemented
10C61×#1437C212yesmaximal, complemented
11C61×C4⋊#95C212yesmaximal, complemented
12C23×D4×C61C2211yescharacteristic
13C24×C4×C61C2211yescharacteristic
14C24×C4×C61C2211yescharacteristic
15C24×C4×C61C2211yescharacteristic
16C2×#123×C61—24no—
17C2×#123×C61—24no—
18C2×#123×C61C418yescomplemented
19C22×C4⋊C4×C61C2212yes—
20C22×C4⋊C4×C61C2212yes—
21C22×C22⋊C4×C61C2211yescharacteristic
22C22×C22⋊C4×C61C2211yescharacteristic
23C22×C22⋊C4×C61C2212yes—
24C22×C22⋊C4×C61C2212yes—
25C22×C22⋊C4×C61C2211yescharacteristic
26C22×C22⋊C4×C61C2211yescharacteristic
27C22×C22⋊C4×C61C2211yescharacteristic
28C22×C42×C61C2212yes—
29C61×#386—24no—
30C61×#386—24no—
31C61×#385—24no—
32C61×#381—24no—
33C4×C22⋊C4×C61—24no—
34C2×#95×C61—24no—
35C2×#95×C61C2212yes—
36C2×#95×C61C2212yes—
37C2×#95×C61C2212yes—
38C2×#95×C61C2212yes—
39C2×#95×C61C2212yes—
40C2×#95×C61C2212yes—
41C2×#95×C61C2211yescharacteristic
42C2×#95×C61C2212yes—
43C2×#95×C61C2211yescharacteristic
44C25×C61C2311yescharacteristic
45C25×C61C2311yescharacteristic
46C22×D4×C61—22no—
47C22×D4×C61—22no—
48C22×D4×C61—22no—
49C22×D4×C61—22no—
50C22×D4×C61—22no—
51C22×D4×C61—22no—
52C22×D4×C61C2×C414yes—
53C23×C4×C61—22no—
54C23×C4×C61—22no—
55C23×C4×C61—22no—
56C23×C4×C61—22no—
57C23×C4×C61—22no—
58C23×C4×C61—22no—
59C23×C4×C61—22no—
60C23×C4×C61—22no—
61C23×C4×C61—22no—
62C23×C4×C61—24no—
63C23×C4×C61—24no—
64C23×C4×C61—22no—
65C23×C4×C61—22no—
66C23×C4×C61—42no—
67C23×C4×C61—42no—
68C23×C4×C61C2×C414yes—
69C23×C4×C61D414yes—
70C23×C4×C61C2311yescharacteristic
71C23×C4×C61C2311yescharacteristic
72C23×C4×C61C2312yes—
73C23×C4×C61C2311yescharacteristic
74C23×C4×C61C2311yescharacteristic
75C23×C4×C61C2312yes—
76C23×C4×C61C2312yes—
77C23×C4×C61C2312yes—
78C23×C4×C61C2311yescharacteristic
79#123×C61—232no—
80C2×C4⋊C4×C61—24no—
81C2×C4⋊C4×C61—24no—
82C2×C4⋊C4×C61—24no—
83C2×C4⋊C4×C61—24no—
84C2×C4⋊C4×C61—42no—
85C2×C4⋊C4×C61C2×C418yescomplemented
86C2×C22⋊C4×C61—22no—
87C2×C22⋊C4×C61—22no—
88C2×C22⋊C4×C61—24no—
89C2×C22⋊C4×C61—24no—
90C2×C22⋊C4×C61—22no—
91C2×C22⋊C4×C61—22no—
92C2×C22⋊C4×C61—22no—
93C2×C22⋊C4×C61—24no—
94C2×C22⋊C4×C61—22no—
95C2×C22⋊C4×C61—22no—
96C2×C22⋊C4×C61—24no—
97C2×C22⋊C4×C61—24no—
98C2×C22⋊C4×C61—42no—
99C2×C22⋊C4×C61—42no—
100C2×C22⋊C4×C61C2×C414yes—
101C2×C22⋊C4×C61C2×C418yescomplemented
102C2×C22⋊C4×C61D414yes—
103C2×C22⋊C4×C61D414yes—
104C2×C22⋊C4×C61D414yes—
105C2×C42×C61—24no—
106C2×C42×C61—24no—
107C2×C42×C61—42no—
108#95×C61—24no—
109#95×C61—24no—
110#95×C61—24no—
111#95×C61—24no—
112#95×C61—24no—
113#95×C61—24no—
114#95×C61—24no—
115#95×C61—22no—
116#95×C61—22no—
117C24×C61—22no—
118C24×C61—22no—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61—21no—
122C24×C61—21no—
123C24×C61—21no—
124C24×C61—21no—
125C24×C61—22no—
126C24×C61—22no—
127C24×C61—21no—
128C24×C61—21no—
129C24×C61—22no—
130C24×C61—22no—
131C24×C61C22×C412yes—
132C24×C61C22×C412yes—
133C24×C61C2×D412yes—
134C24×C61C2×D412yes—
135C24×C61C2×D412yes—
136C24×C61C2×D412yes—
137C24×C61#4112yes—
138C24×C61#4112yes—
139C24×C61C2411yescharacteristic
140C2×D4×C61—28no—
141C2×D4×C61—28no—
142C2×D4×C61—28no—
143C2×D4×C61—44no—
144C2×D4×C61—44no—
145C2×D4×C61—44no—
146C2×D4×C61—44no—
147C22×C4×C61—21no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—21no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—28no—
155C22×C4×C61—28no—
156C22×C4×C61—28no—
157C22×C4×C61—28no—
158C22×C4×C61—28no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—21no—
162C22×C4×C61—22no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—22no—
166C22×C4×C61—22no—
167C22×C4×C61—22no—
168C22×C4×C61—22no—
169C22×C4×C61—22no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—22no—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—21no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—28no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—22no—
195C22×C4×C61—22no—
196C22×C4×C61—22no—
197C22×C4×C61—22no—
198C22×C4×C61—44no—
199C22×C4×C61—48no—
200C22×C4×C61—48no—
201C22×C4×C61—48no—
202C22×C4×C61—48no—
203C22×C4×C61—44no—
204C22×C4×C61—44no—
205C22×C4×C61—44no—
206C22×C4×C61—44no—
207C22×C4×C61—44no—
208C22×C4×C61—44no—
209C22×C4×C61C22×C414yes—
210C22×C4×C61C22×C412yes—
211C22×C4×C61C22×C414yes—
212C22×C4×C61C2×D414yes—
213C22×C4×C61C2×D412yes—
214C22×C4×C61C2×D414yes—
215C22×C4×C61C2×D414yes—
216C22×C4×C61C2×D412yes—
217C22×C4×C61#4114yes—
218C22×C4×C61#4114yes—
219C4⋊C4×C61—216no—
220C4⋊C4×C61—48no—
221C22⋊C4×C61—28no—
222C22⋊C4×C61—216no—
223C22⋊C4×C61—48no—
224C22⋊C4×C61—44no—
225C22⋊C4×C61—44no—
226C22⋊C4×C61—44no—
227C22⋊C4×C61C22⋊C4116yescomplemented
228C42×C61—48no—
229C23×C61—24no—
230C23×C61—24no—
231C23×C61—22no—
232C23×C61—22no—
233C23×C61—24no—
234C23×C61—22no—
235C23×C61—22no—
236C23×C61—24no—
237C23×C61—24no—
238C23×C61—24no—
239C23×C61—24no—
240C23×C61—24no—
241C23×C61—24no—
242C23×C61—24no—
243C23×C61—24no—
244C23×C61—24no—
245C23×C61—22no—
246C23×C61—22no—
247C23×C61—22no—
248C23×C61—24no—
249C23×C61—24no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—42no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—42no—
260C23×C61—42no—
261C23×C61—42no—
262C23×C61—42no—
263C23×C61—42no—
264C23×C61—42no—
265C23×C61—42no—
266C23×C61—42no—
267C23×C61—42no—
268C23×C61C2×C22⋊C414yes—
269C23×C61C4×D414yes—
270C23×C61C4×D414yes—
271C23×C61#12114yes—
272C23×C61#12114yes—
273C23×C61#12414yes—
274C23×C61#12714yes—
275C23×C61C23×C411yescharacteristic
276C23×C61C22×D411yescharacteristic
277C23×C61C22×D411yescharacteristic
278C23×C61C22×D411yescharacteristic
279C23×C61C22×D411yescharacteristic
280C23×C61C2×#4111yescharacteristic
281C23×C61C2×#4111yescharacteristic
282C23×C61C2×#4112yes—
283C23×C61C2×#4112yes—
284C23×C61H(5,𝔽2)12yes—
285C23×C612−1+412yes—
286D4×C61—416no—
287C2×C4×C61—24no—
288C2×C4×C61—24no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—24no—
292C2×C4×C61—24no—
293C2×C4×C61—24no—
294C2×C4×C61—24no—
295C2×C4×C61—24no—
296C2×C4×C61—24no—
297C2×C4×C61—24no—
298C2×C4×C61—22no—
299C2×C4×C61—24no—
300C2×C4×C61—24no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—24no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—24no—
307C2×C4×C61—22no—
308C2×C4×C61—24no—
309C2×C4×C61—24no—
310C2×C4×C61—24no—
311C2×C4×C61—24no—
312C2×C4×C61—416no—
313C2×C4×C61—416no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—42no—
319C2×C4×C61—41no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61—41no—
324C2×C4×C61—42no—
325C2×C4×C61—42no—
326C2×C4×C61—42no—
327C2×C4×C61—42no—
328C2×C4×C61—42no—
329C2×C4×C61—42no—
330C2×C4×C61—42no—
331C2×C4×C61—42no—
332C2×C4×C61—416no—
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—42no—
340C2×C4×C61—42no—
341C2×C4×C61—42no—
342C2×C4×C61—42no—
343C2×C4×C61C2×C22⋊C418yes—
344C2×C4×C61#12314yescomplemented
345#13996C6111yesmaximal, characteristic, direct product factor, Sylow
346C22×C61—24no—
347C22×C61—28no—
348C22×C61—28no—
349C22×C61—24no—
350C22×C61—24no—
351C22×C61—28no—
352C22×C61—28no—
353C22×C61—24no—
354C22×C61—24no—
355C22×C61—24no—
356C22×C61—42no—
357C22×C61—44no—
358C22×C61—44no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—81no—
362C22×C61—81no—
363C22×C61—82no—
364C22×C61—82no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61#39018yes—
368C22×C61C22×C22⋊C411yescharacteristic
369C22×C61C2×C4×D411yescharacteristic
370C22×C61C2×C4×D411yescharacteristic
371C22×C61C4×#4112yes—
372C22×C61#52012yes—
373C22×C61C2×#12111yescharacteristic
374C22×C61C2×#12111yescharacteristic
375C22×C61C2×#12311yescharacteristic
376C22×C61#52511yescharacteristic
377C22×C61C2×#12411yescharacteristic
378C22×C61#52912yes—
379C22×C61C2×#12711yescharacteristic
380C22×C61#53411yescharacteristic
381C22×C61#53611yescharacteristic
382C22×C61#53912yes—
383C22×C61#54612yes—
384C22×C61#54612yes—
385C22×C61#54612yes—
386C22×C61#54712yes—
387C22×C61#54712yes—
388C22×C61#54712yes—
389C22×C61#55112yes—
390C22×C61#55212yes—
391C4×C61—28no—
392C4×C61—24no—
393C4×C61—42no—
394C4×C61—44no—
395C4×C61—44no—
396C4×C61—44no—
397C4×C61—42no—
398C4×C61—81no—
399C4×C61—81no—
400C22×#123C2×C6111yescharacteristic
401C2×#386C2×C6111yescharacteristic
402C2×#386C2×C6111yescharacteristic
403C2×#385C2×C6111yescharacteristic, complemented
404C2×#381C2×C6111yescharacteristic, complemented
405C2×C4×C22⋊C4C2×C6111yescharacteristic, complemented
406C22×#95C2×C6111yescharacteristic, complemented
407#1445C2×C6112yescomplemented
408#1439C2×C6112yescomplemented
409#1437C2×C6112yescomplemented
410C4⋊#95C2×C6112yescomplemented
411C2×C61—28no—
412C2×C61—82no—
413C2×C61C2×#39011yescharacteristic
414C2×C61C4×#12311yescharacteristic
415C2×C61#232211yescharacteristic
416C2×C61#233912yes—
417C2×C61#235912yes—
418C2×C61#241211yescharacteristic
419C2×C61#241311yescharacteristic
420C2×C61#242512yes—
421C2×C61#248812yes—
422C2×C61#250111yescharacteristic
423C2×C61#253911yescharacteristic
424C23×D4C22×C6111yescharacteristic
425C24×C4C22×C6111yescharacteristic
426C24×C4C22×C6111yescharacteristic
427C24×C4C22×C6111yescharacteristic
428C2×#123—24no—
429C2×#123—24no—
430C2×#123C4×C6118yescomplemented
431C22×C4⋊C4C22×C6112yes—
432C22×C4⋊C4C22×C6112yes—
433C22×C22⋊C4C22×C6111yescharacteristic
434C22×C22⋊C4C22×C6111yescharacteristic
435C22×C22⋊C4C22×C6112yes—
436C22×C22⋊C4C22×C6112yes—
437C22×C22⋊C4C22×C6111yescharacteristic
438C22×C22⋊C4C22×C6111yescharacteristic
439C22×C22⋊C4C22×C6111yescharacteristic
440C22×C42C22×C6112yes—
441#386—24no—
442#386—24no—
443#385—24no—
444#381—24no—
445C4×C22⋊C4—24no—
446C2×#95—24no—
447C2×#95C22×C6111yescharacteristic
448C2×#95C22×C6112yes—
449C2×#95C22×C6112yes—
450C2×#95C22×C6112yes—
451C2×#95C22×C6112yes—
452C2×#95C22×C6112yes—
453C2×#95C22×C6112yes—
454C2×#95C22×C6112yes—
455C2×#95C22×C6111yescharacteristic
456C61#1399611yescharacteristic, direct product factor, Sylow
457C25C23×C6111yescharacteristic
458C25C23×C6111yescharacteristic
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4C2×C4×C6114yes—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—42no—
480C23×C4—42no—
481C23×C4C2×C4×C6114yes—
482C23×C4D4×C6114yes—
483C23×C4C23×C6111yescharacteristic
484C23×C4C23×C6111yescharacteristic
485C23×C4C23×C6112yes—
486C23×C4C23×C6111yescharacteristic
487C23×C4C23×C6112yes—
488C23×C4C23×C6111yescharacteristic
489C23×C4C23×C6112yes—
490C23×C4C23×C6112yes—
491C23×C4C23×C6111yescharacteristic
492#123—232no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—42no—
498C2×C4⋊C4C2×C4×C6118yescomplemented
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4C2×C4×C6114yes—
514C2×C22⋊C4C2×C4×C6118yescomplemented
515C2×C22⋊C4D4×C6114yes—
516C2×C22⋊C4D4×C6114yes—
517C2×C22⋊C4D4×C6114yes—
518C2×C42—24no—
519C2×C42—24no—
520C2×C42—42no—
521#95—24no—
522#95—24no—
523#95—24no—
524#95—24no—
525#95—24no—
526#95—24no—
527#95—24no—
528#95—22no—
529#95—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—22no—
544C24C22×C4×C6112yes—
545C24C22×C4×C6112yes—
546C24C2×D4×C6112yes—
547C24C2×D4×C6112yes—
548C24C2×D4×C6112yes—
549C24C2×D4×C6112yes—
550C24#41×C6112yes—
551C24#41×C6112yes—
552C24C24×C6111yescharacteristic
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—28no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4C22×C4×C6114yes—
623C22×C4C22×C4×C6112yes—
624C22×C4C22×C4×C6114yes—
625C22×C4C2×D4×C6114yes—
626C22×C4C2×D4×C6112yes—
627C22×C4C2×D4×C6114yes—
628C22×C4C2×D4×C6114yes—
629C22×C4C2×D4×C6112yes—
630C22×C4#41×C6114yes—
631C22×C4#41×C6114yes—
632C4⋊C4—216no—
633C4⋊C4—48no—
634C22⋊C4—28no—
635C22⋊C4—216no—
636C22⋊C4—48no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4C22⋊C4×C61116yescomplemented
641C42—48no—
642C23—22no—
643C23—22no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23C2×C22⋊C4×C6114yes—
682C23C4×D4×C6114yes—
683C23C4×D4×C6114yes—
684C23#121×C6114yes—
685C23#121×C6114yes—
686C23#124×C6114yes—
687C23#127×C6114yes—
688C23C23×C4×C6111yescharacteristic
689C23C22×D4×C6111yescharacteristic
690C23C22×D4×C6111yescharacteristic
691C23C22×D4×C6111yescharacteristic
692C23C22×D4×C6111yescharacteristic
693C23C2×#41×C6111yescharacteristic
694C23C2×#41×C6112yes—
695C23C2×#41×C6112yes—
696C23C2×#41×C6111yescharacteristic
697C23H(5,𝔽2)×C6112yes—
698C232−1+4×C6112yes—
699D4—416no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—416no—
726C2×C4—416no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—416no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4C2×C22⋊C4×C6118yes—
757C2×C4#123×C6114yescomplemented
758C22—24no—
759C22—24no—
760C22—24no—
761C22—28no—
762C22—28no—
763C22—24no—
764C22—24no—
765C22—28no—
766C22—28no—
767C22—24no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—44no—
772C22—44no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—82no—
777C22—82no—
778C22—81no—
779C22C61×#39018yes—
780C22C22×C22⋊C4×C6111yescharacteristic
781C22C2×C4×D4×C6111yescharacteristic
782C22C2×C4×D4×C6111yescharacteristic
783C22C4×#41×C6112yes—
784C22C61×#52012yes—
785C22C2×#121×C6111yescharacteristic
786C22C2×#121×C6111yescharacteristic
787C22C2×#123×C6111yescharacteristic
788C22C61×#52511yescharacteristic
789C22C2×#124×C6111yescharacteristic
790C22C61×#52912yes—
791C22C2×#127×C6111yescharacteristic
792C22C61×#53411yescharacteristic
793C22C61×#53611yescharacteristic
794C22C61×#53912yes—
795C22C61×#54612yes—
796C22C61×#54612yes—
797C22C61×#54612yes—
798C22C61×#54712yes—
799C22C61×#54712yes—
800C22C61×#54712yes—
801C22C61×#55112yes—
802C22C61×#55212yes—
803C4—28no—
804C4—24no—
805C4—44no—
806C4—44no—
807C4—42no—
808C4—42no—
809C4—44no—
810C4—81no—
811C4—81no—
812C2—28no—
813C2—82no—
814C2C2×C61×#39011yescharacteristic
815C2C4×#123×C6111yescharacteristic
816C2C61×#232211yescharacteristic
817C2C61×#233912yes—
818C2C61×#235912yes—
819C2C61×#241211yescharacteristic
820C2C61×#241311yescharacteristic
821C2C61×#242512yes—
822C2C61×#248812yes—
823C2C61×#250111yescharacteristic
824C2C61×#253911yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutatorC23C23×C4×C61
Frattini, cosocleC24C24×C61
prime radicalC23×D4×C61C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C61×#385C2semidirect
5. C2×C61×#381C2semidirect
6. C2×C4×C22⋊C4×C61C2semidirect
7. C22×#95×C61C2semidirect
8. C61×#1445C2semidirect
9. C61×#1439C2semidirect
10. C61×#1437C2semidirect
11. C61×C4⋊#95C2semidirect
18. C2×#123×C61C4semidirect
85. C2×C4⋊C4×C61C2×C4semidirect
101. C2×C22⋊C4×C61C2×C4semidirect
227. C22⋊C4×C61C22⋊C4semidirect
344. C2×C4×C61#123semidirect
345. #13996C61direct (N × H)
403. C2×#385C2×C61semidirect
404. C2×#381C2×C61semidirect
405. C2×C4×C22⋊C4C2×C61semidirect
406. C22×#95C2×C61semidirect
407. #1445C2×C61semidirect
408. #1439C2×C61semidirect
409. #1437C2×C61semidirect
410. C4⋊#95C2×C61semidirect
430. C2×#123C4×C61semidirect
456. C61#13996direct (N × H)
498. C2×C4⋊C4C2×C4×C61semidirect
514. C2×C22⋊C4C2×C4×C61semidirect
640. C22⋊C4C22⋊C4×C61semidirect
757. C2×C4#123×C61semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C612
C2×C61×#3862
C2×C61×#3852
C2×C61×#3812
C2×C4×C22⋊C4×C612
C22×#95×C612
C61×#14452
C61×#14392
C61×#14372
C61×C4⋊#952
#1399661