Finite Group Databasebeta

← C2×C61×#2424 #29538083

Subgroups — C2×C61×#2424 #29538083

Order 15616.

5898 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C61C211yesmaximal, characteristic, complemented
2C22×#121×C61C211yesmaximal, characteristic, complemented
3C22×#120×C61C211yesmaximal, characteristic, complemented
4C22×#120×C61C211yesmaximal, characteristic, complemented
5C22×C4×D4×C61C211yesmaximal, characteristic, complemented
6C23×C22⋊C4×C61C211yesmaximal, characteristic, complemented
7C61×#2424C2116yesmaximal, direct product factor
8C2×C61×#396C211yesmaximal, characteristic, complemented
9C2×C61×#394C211yesmaximal, characteristic, complemented
10C2×C61×#394C211yesmaximal, characteristic, complemented
11C2×C61×#392C211yesmaximal, characteristic, complemented
12C2×C61×#390C211yesmaximal, characteristic, complemented
13C2×C61×#388C211yesmaximal, characteristic, complemented
14C2×C61×#386C211yesmaximal, characteristic, complemented
15C2×C61×#386C211yesmaximal, characteristic, complemented
16C2×C61×#385C211yesmaximal, characteristic, complemented
17C26×C61C2211yescharacteristic
18C23×D4×C61C2211yescharacteristic
19C23×D4×C61C2211yescharacteristic
20C23×D4×C61C2211yescharacteristic
21C23×D4×C61C2211yescharacteristic
22C23×D4×C61C2211yescharacteristic
23C23×D4×C61C2211yescharacteristic
24C23×D4×C61C2211yescharacteristic, complemented
25C24×C4×C61C2211yescharacteristic
26C24×C4×C61C2211yescharacteristic
27C24×C4×C61C2211yescharacteristic, complemented
28C2×#121×C61—28no—
29C2×#121×C61—28no—
30C2×#121×C61C2218yescomplemented
31C2×#121×C61C2218yescomplemented
32C2×#120×C61—28no—
33C2×#120×C61—28no—
34C2×#120×C61C2218yescomplemented
35C2×#120×C61C2218yescomplemented
36C2×C4×D4×C61—28no—
37C2×C4×D4×C61C2218yescomplemented
38C22×C4⋊C4×C61C2211yescharacteristic, complemented
39C22×C4⋊C4×C61C2211yescharacteristic, complemented
40C22×C4⋊C4×C61C2211yescharacteristic, complemented
41C22×C4⋊C4×C61C2211yescharacteristic, complemented
42C22×C22⋊C4×C61—28no—
43C22×C22⋊C4×C61C2211yescharacteristic
44C22×C22⋊C4×C61C2211yescharacteristic
45C22×C22⋊C4×C61C2211yescharacteristic
46C22×C22⋊C4×C61C2211yescharacteristic
47C22×C22⋊C4×C61C2211yescharacteristic
48C22×C22⋊C4×C61C2211yescharacteristic
49C22×C22⋊C4×C61C2211yescharacteristic
50C22×C22⋊C4×C61C2211yescharacteristic
51C22×C22⋊C4×C61C2211yescharacteristic
52C22×C22⋊C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2218yescomplemented
54C22×C22⋊C4×C61C2211yescharacteristic, complemented
55C22×C22⋊C4×C61C2211yescharacteristic, complemented
56C22×C22⋊C4×C61C2211yescharacteristic, complemented
57C22×C22⋊C4×C61C2211yescharacteristic, complemented
58C22×C22⋊C4×C61C2211yescharacteristic, complemented
59C22×C42×C61C2211yescharacteristic, complemented
60C61×#396C2218yescomplemented
61C61×#394C2218yescomplemented
62C61×#394C2218yescomplemented
63C61×#392C2218yescomplemented
64C61×#390C2218yescomplemented
65C61×#388C2218yescomplemented
66C61×#386C2218yescomplemented
67C61×#386C2218yescomplemented
68C61×#385C2218yescomplemented
69C2×#95×C61C2211yescharacteristic, complemented
70C2×#95×C61C2211yescharacteristic, complemented
71C2×#95×C61C2211yescharacteristic, complemented
72C2×#95×C61C2211yescharacteristic, complemented
73C25×C61—24no—
74C25×C61—24no—
75C25×C61—24no—
76C25×C61—24no—
77C25×C61—24no—
78C25×C61—42no—
79C25×C61—42no—
80C25×C61C2311yescharacteristic
81C25×C61C2311yescharacteristic
82C25×C61C2311yescharacteristic
83C25×C61C2311yescharacteristic
84C25×C61C2314yes—
85C25×C61C2311yescharacteristic
86C22×D4×C61—24no—
87C22×D4×C61—24no—
88C22×D4×C61—24no—
89C22×D4×C61—24no—
90C22×D4×C61—24no—
91C22×D4×C61—24no—
92C22×D4×C61—24no—
93C22×D4×C61—24no—
94C22×D4×C61—24no—
95C22×D4×C61—24no—
96C22×D4×C61—24no—
97C22×D4×C61—24no—
98C22×D4×C61—24no—
99C22×D4×C61—24no—
100C22×D4×C61—24no—
101C22×D4×C61—42no—
102C22×D4×C61—42no—
103C22×D4×C61—42no—
104C22×D4×C61—42no—
105C22×D4×C61—42no—
106C22×D4×C61D418yescomplemented
107C22×D4×C61C2314yes—
108C22×D4×C61C2314yes—
109C22×D4×C61C2314yes—
110C22×D4×C61C2314yes—
111C22×D4×C61C2314yes—
112C22×D4×C61C2314yes—
113C22×D4×C61C2314yescomplemented
114C23×C4×C61—24no—
115C23×C4×C61—24no—
116C23×C4×C61—24no—
117C23×C4×C61—24no—
118C23×C4×C61—24no—
119C23×C4×C61—24no—
120C23×C4×C61—42no—
121C23×C4×C61—42no—
122C23×C4×C61—42no—
123C23×C4×C61C2311yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C23×C4×C61C2311yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2314yes—
129C23×C4×C61C2314yes—
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2314yescomplemented
136#121×C61—232no—
137#121×C61—232no—
138#120×C61—232no—
139#120×C61—232no—
140C4×D4×C61—232no—
141C2×C4⋊C4×C61—24no—
142C2×C4⋊C4×C61—24no—
143C2×C4⋊C4×C61—24no—
144C2×C4⋊C4×C61—42no—
145C2×C4⋊C4×C61C2314yescomplemented
146C2×C4⋊C4×C61C2314yescomplemented
147C2×C4⋊C4×C61C2314yescomplemented
148C2×C4⋊C4×C61C2314yescomplemented
149C2×C22⋊C4×C61—24no—
150C2×C22⋊C4×C61—24no—
151C2×C22⋊C4×C61—24no—
152C2×C22⋊C4×C61—24no—
153C2×C22⋊C4×C61—24no—
154C2×C22⋊C4×C61—24no—
155C2×C22⋊C4×C61—24no—
156C2×C22⋊C4×C61—24no—
157C2×C22⋊C4×C61—24no—
158C2×C22⋊C4×C61—24no—
159C2×C22⋊C4×C61—24no—
160C2×C22⋊C4×C61—24no—
161C2×C22⋊C4×C61—232no—
162C2×C22⋊C4×C61—42no—
163C2×C22⋊C4×C61D418yescomplemented
164C2×C22⋊C4×C61D418yescomplemented
165C2×C22⋊C4×C61C2314yes—
166C2×C22⋊C4×C61C2314yes—
167C2×C22⋊C4×C61C2314yes—
168C2×C22⋊C4×C61C2314yes—
169C2×C22⋊C4×C61C2314yes—
170C2×C22⋊C4×C61C2314yes—
171C2×C22⋊C4×C61C2314yes—
172C2×C22⋊C4×C61C2314yes—
173C2×C22⋊C4×C61C2314yes—
174C2×C22⋊C4×C61C2314yes—
175C2×C22⋊C4×C61C2314yescomplemented
176C2×C22⋊C4×C61C2314yescomplemented
177C2×C22⋊C4×C61C2314yescomplemented
178C2×C22⋊C4×C61C2314yescomplemented
179C2×C22⋊C4×C61C2314yescomplemented
180C2×C42×C61—24no—
181C2×C42×C61C2314yescomplemented
182#95×C61C2314yescomplemented
183#95×C61C2314yescomplemented
184#95×C61C2314yescomplemented
185#95×C61C2314yescomplemented
186C24×C61—22no—
187C24×C61—22no—
188C24×C61—22no—
189C24×C61—22no—
190C24×C61—232no—
191C24×C61—28no—
192C24×C61—22no—
193C24×C61—22no—
194C24×C61—22no—
195C24×C61—22no—
196C24×C61—22no—
197C24×C61—22no—
198C24×C61—22no—
199C24×C61—22no—
200C24×C61—22no—
201C24×C61—28no—
202C24×C61—28no—
203C24×C61—22no—
204C24×C61—22no—
205C24×C61—22no—
206C24×C61—22no—
207C24×C61—22no—
208C24×C61—22no—
209C24×C61—22no—
210C24×C61—22no—
211C24×C61—22no—
212C24×C61—22no—
213C24×C61—22no—
214C24×C61—28no—
215C24×C61—28no—
216C24×C61—22no—
217C24×C61—22no—
218C24×C61—22no—
219C24×C61—22no—
220C24×C61—22no—
221C24×C61—44no—
222C24×C61—44no—
223C24×C61—416no—
224C24×C61—416no—
225C24×C61—416no—
226C24×C61—416no—
227C24×C61—416no—
228C24×C61—416no—
229C24×C61C2×D414yes—
230C24×C61C2×D414yes—
231C24×C61C2×D414yes—
232C24×C61C2×D414yes—
233C24×C61#4114yes—
234C24×C61#4114yes—
235C24×C61C2412yes—
236C24×C61C2412yes—
237C24×C61C2412yes—
238C24×C61C2412yes—
239C24×C61C2412yes—
240C24×C61C2411yescharacteristic
241C2×D4×C61—232no—
242C2×D4×C61—28no—
243C2×D4×C61—28no—
244C2×D4×C61—28no—
245C2×D4×C61—28no—
246C2×D4×C61—28no—
247C2×D4×C61—28no—
248C2×D4×C61—28no—
249C2×D4×C61—28no—
250C2×D4×C61—28no—
251C2×D4×C61—28no—
252C2×D4×C61—28no—
253C2×D4×C61—28no—
254C2×D4×C61—28no—
255C2×D4×C61—28no—
256C2×D4×C61—28no—
257C2×D4×C61—44no—
258C2×D4×C61—44no—
259C2×D4×C61—44no—
260C2×D4×C61—44no—
261C2×D4×C61—44no—
262C2×D4×C61—416no—
263C2×D4×C61—416no—
264C2×D4×C61—416no—
265C2×D4×C61—416no—
266C2×D4×C61—416no—
267C2×D4×C61—416no—
268C2×D4×C61C2×D4116yescomplemented
269C22×C4×C61—22no—
270C22×C4×C61—22no—
271C22×C4×C61—22no—
272C22×C4×C61—22no—
273C22×C4×C61—22no—
274C22×C4×C61—22no—
275C22×C4×C61—22no—
276C22×C4×C61—22no—
277C22×C4×C61—22no—
278C22×C4×C61—22no—
279C22×C4×C61—22no—
280C22×C4×C61—22no—
281C22×C4×C61—22no—
282C22×C4×C61—22no—
283C22×C4×C61—22no—
284C22×C4×C61—22no—
285C22×C4×C61—22no—
286C22×C4×C61—22no—
287C22×C4×C61—22no—
288C22×C4×C61—28no—
289C22×C4×C61—28no—
290C22×C4×C61—22no—
291C22×C4×C61—22no—
292C22×C4×C61—22no—
293C22×C4×C61—22no—
294C22×C4×C61—22no—
295C22×C4×C61—22no—
296C22×C4×C61—28no—
297C22×C4×C61—28no—
298C22×C4×C61—28no—
299C22×C4×C61—28no—
300C22×C4×C61—44no—
301C22×C4×C61—44no—
302C22×C4×C61—44no—
303C22×C4×C61—416no—
304C22×C4×C61—416no—
305C22×C4×C61—416no—
306C22×C4×C61C2×D414yes—
307C22×C4×C61C2×D414yes—
308C22×C4×C61C2×D414yes—
309C22×C4×C61C2×D414yes—
310C22×C4×C61C2×D414yes—
311C22×C4×C61C2412yes—
312C22×C4×C61C2412yes—
313C22×C4×C61C2412yes—
314C22×C4×C61C2412yes—
315C22×C4×C61C2412yes—
316C22×C4×C61C2412yes—
317C22×C4×C61C2412yes—
318C22×C4×C61C2412yes—
319C22×C4×C61C2412yes—
320C22×C4×C61C2412yes—
321C4⋊C4×C61—28no—
322C4⋊C4×C61—28no—
323C4⋊C4×C61—28no—
324C4⋊C4×C61—44no—
325C22⋊C4×C61—28no—
326C22⋊C4×C61—28no—
327C22⋊C4×C61—28no—
328C22⋊C4×C61—28no—
329C22⋊C4×C61—28no—
330C22⋊C4×C61—28no—
331C22⋊C4×C61—28no—
332C22⋊C4×C61—28no—
333C22⋊C4×C61—28no—
334C22⋊C4×C61—28no—
335C22⋊C4×C61—28no—
336C22⋊C4×C61—28no—
337C22⋊C4×C61—44no—
338C22⋊C4×C61C2×D4116yescomplemented
339C22⋊C4×C61C2×D4116yescomplemented
340C42×C61—28no—
341C23×C61—28no—
342C23×C61—28no—
343C23×C61—28no—
344C23×C61—28no—
345C23×C61—28no—
346C23×C61—28no—
347C23×C61—22no—
348C23×C61—22no—
349C23×C61—22no—
350C23×C61—22no—
351C23×C61—232no—
352C23×C61—28no—
353C23×C61—28no—
354C23×C61—28no—
355C23×C61—28no—
356C23×C61—28no—
357C23×C61—28no—
358C23×C61—28no—
359C23×C61—28no—
360C23×C61—28no—
361C23×C61—22no—
362C23×C61—22no—
363C23×C61—22no—
364C23×C61—22no—
365C23×C61—22no—
366C23×C61—22no—
367C23×C61—22no—
368C23×C61—22no—
369C23×C61—22no—
370C23×C61—22no—
371C23×C61—22no—
372C23×C61—22no—
373C23×C61—22no—
374C23×C61—22no—
375C23×C61—22no—
376C23×C61—22no—
377C23×C61—22no—
378C23×C61—22no—
379C23×C61—22no—
380C23×C61—22no—
381C23×C61—22no—
382C23×C61—22no—
383C23×C61—22no—
384C23×C61—22no—
385C23×C61—22no—
386C23×C61—416no—
387C23×C61—416no—
388C23×C61—416no—
389C23×C61—416no—
390C23×C61—4128no—
391C23×C61—416no—
392C23×C61—44no—
393C23×C61—44no—
394C23×C61—416no—
395C23×C61—44no—
396C23×C61—44no—
397C23×C61—44no—
398C23×C61—44no—
399C23×C61—44no—
400C23×C61—44no—
401C23×C61—44no—
402C23×C61—44no—
403C23×C61—44no—
404C23×C61—44no—
405C23×C61—44no—
406C23×C61—44no—
407C23×C61—44no—
408C23×C61—44no—
409C23×C61—44no—
410C23×C61—44no—
411C23×C61—44no—
412C23×C61#121116yescomplemented
413C23×C61C22×D414yes—
414C23×C61C22×D414yes—
415C23×C61C22×D414yes—
416C23×C61C22×D414yes—
417C23×C61C22×D412yes—
418C23×C61C22×D412yes—
419C23×C61C22×D412yes—
420C23×C61C2×#4114yes—
421C23×C61C2×#4114yes—
422C23×C61C2×#4112yes—
423C23×C61C2×#4112yes—
424C23×C61H(5,𝔽2)12yes—
425C23×C61H(5,𝔽2)12yes—
426C23×C61C2511yescharacteristic
427D4×C61—232no—
428D4×C61—416no—
429D4×C61—416no—
430D4×C61—416no—
431D4×C61—416no—
432D4×C61—416no—
433D4×C61—416no—
434C2×C4×C61—28no—
435C2×C4×C61—28no—
436C2×C4×C61—28no—
437C2×C4×C61—28no—
438C2×C4×C61—28no—
439C2×C4×C61—22no—
440C2×C4×C61—22no—
441C2×C4×C61—22no—
442C2×C4×C61—22no—
443C2×C4×C61—22no—
444C2×C4×C61—22no—
445C2×C4×C61—22no—
446C2×C4×C61—22no—
447C2×C4×C61—22no—
448C2×C4×C61—22no—
449C2×C4×C61—22no—
450C2×C4×C61—22no—
451C2×C4×C61—22no—
452C2×C4×C61—22no—
453C2×C4×C61—22no—
454C2×C4×C61—22no—
455C2×C4×C61—22no—
456C2×C4×C61—22no—
457C2×C4×C61—22no—
458C2×C4×C61—22no—
459C2×C4×C61—22no—
460C2×C4×C61—22no—
461C2×C4×C61—22no—
462C2×C4×C61—22no—
463C2×C4×C61—22no—
464C2×C4×C61—416no—
465C2×C4×C61—416no—
466C2×C4×C61—416no—
467C2×C4×C61—44no—
468C2×C4×C61—44no—
469C2×C4×C61—44no—
470C2×C4×C61—44no—
471C2×C4×C61—44no—
472C2×C4×C61C22×D414yes—
473C2×C4×C61C22×D414yes—
474C2×C4×C61C22×D414yes—
475C2×C4×C61C22×D414yes—
476C2×C4×C61C22×D414yes—
477C2×#2424C6111yesmaximal, characteristic, direct product factor, Sylow
478C22×C61—24no—
479C22×C61—232no—
480C22×C61—24no—
481C22×C61—24no—
482C22×C61—24no—
483C22×C61—24no—
484C22×C61—24no—
485C22×C61—24no—
486C22×C61—24no—
487C22×C61—24no—
488C22×C61—24no—
489C22×C61—24no—
490C22×C61—24no—
491C22×C61—24no—
492C22×C61—24no—
493C22×C61—24no—
494C22×C61—464no—
495C22×C61—42no—
496C22×C61—42no—
497C22×C61—42no—
498C22×C61—416no—
499C22×C61—416no—
500C22×C61—416no—
501C22×C61—42no—
502C22×C61—42no—
503C22×C61—42no—
504C22×C61—42no—
505C22×C61—42no—
506C22×C61—42no—
507C22×C61—42no—
508C22×C61—42no—
509C22×C61—42no—
510C22×C61—42no—
511C22×C61—42no—
512C22×C61—42no—
513C22×C61—42no—
514C22×C61—42no—
515C22×C61—42no—
516C22×C61—42no—
517C22×C61—88no—
518C22×C61C2×#12114yes—
519C22×C61C2×#12118yescomplemented
520C22×C61#52514yes—
521C22×C61#53814yes—
522C22×C61D4214yes—
523C22×C61D4214yes—
524C22×C61#54614yes—
525C22×C61#54614yes—
526C22×C61C23×D411yescharacteristic
527C22×C61C23×D411yescharacteristic
528C22×C61C23×D411yescharacteristic
529C22×C61C22×#4111yescharacteristic
530C22×C61C22×#4111yescharacteristic
531C22×C61C2×H(5,𝔽2)11yescharacteristic
532C22×C61C2×H(5,𝔽2)11yescharacteristic
533C4×C61—24no—
534C4×C61—24no—
535C4×C61—24no—
536C4×C61—24no—
537C4×C61—24no—
538C4×C61—42no—
539C4×C61—42no—
540C4×C61—42no—
541C4×C61—42no—
542C4×C61—42no—
543C22×#121C2×C6111yescharacteristic, complemented
544C22×#121C2×C6111yescharacteristic, complemented
545C22×#120C2×C6111yescharacteristic, complemented
546C22×#120C2×C6111yescharacteristic, complemented
547C22×C4×D4C2×C6111yescharacteristic, complemented
548C23×C22⋊C4C2×C6111yescharacteristic, complemented
549#2424C2×C61116yesdirect product factor
550C2×#396C2×C6111yescharacteristic, complemented
551C2×#394C2×C6111yescharacteristic, complemented
552C2×#394C2×C6111yescharacteristic, complemented
553C2×#392C2×C6111yescharacteristic, complemented
554C2×#390C2×C6111yescharacteristic, complemented
555C2×#388C2×C6111yescharacteristic, complemented
556C2×#386C2×C6111yescharacteristic, complemented
557C2×#386C2×C6111yescharacteristic, complemented
558C2×#385C2×C6111yescharacteristic, complemented
559C2×C61—28no—
560C2×C61—44no—
561C2×C61—44no—
562C2×C61—44no—
563C2×C61—82no—
564C2×C61#242418yesdirect product factor
565C2×C61C22×#12111yescharacteristic
566C2×C61C2×#52511yescharacteristic
567C2×C61C2×#53811yescharacteristic
568C2×C61C2×D4211yescharacteristic
569C2×C61C2×D4211yescharacteristic
570C2×C61C2×#54611yescharacteristic
571C2×C61C2×#54611yescharacteristic
572C26C22×C6111yescharacteristic
573C23×D4C22×C6111yescharacteristic
574C23×D4C22×C6111yescharacteristic
575C23×D4C22×C6111yescharacteristic
576C23×D4C22×C6111yescharacteristic
577C23×D4C22×C6111yescharacteristic
578C23×D4C22×C6111yescharacteristic
579C23×D4C22×C6111yescharacteristic, complemented
580C24×C4C22×C6111yescharacteristic
581C24×C4C22×C6111yescharacteristic
582C24×C4C22×C6111yescharacteristic, complemented
583C2×#121—28no—
584C2×#121—28no—
585C2×#121C22×C6118yescomplemented
586C2×#121C22×C6118yescomplemented
587C2×#120—28no—
588C2×#120—28no—
589C2×#120C22×C6118yescomplemented
590C2×#120C22×C6118yescomplemented
591C2×C4×D4—28no—
592C2×C4×D4C22×C6118yescomplemented
593C22×C4⋊C4C22×C6111yescharacteristic, complemented
594C22×C4⋊C4C22×C6111yescharacteristic, complemented
595C22×C4⋊C4C22×C6111yescharacteristic, complemented
596C22×C4⋊C4C22×C6111yescharacteristic, complemented
597C22×C22⋊C4—28no—
598C22×C22⋊C4C22×C6111yescharacteristic
599C22×C22⋊C4C22×C6111yescharacteristic
600C22×C22⋊C4C22×C6111yescharacteristic
601C22×C22⋊C4C22×C6111yescharacteristic
602C22×C22⋊C4C22×C6111yescharacteristic
603C22×C22⋊C4C22×C6111yescharacteristic
604C22×C22⋊C4C22×C6111yescharacteristic
605C22×C22⋊C4C22×C6111yescharacteristic
606C22×C22⋊C4C22×C6111yescharacteristic
607C22×C22⋊C4C22×C6111yescharacteristic
608C22×C22⋊C4C22×C6118yescomplemented
609C22×C22⋊C4C22×C6111yescharacteristic, complemented
610C22×C22⋊C4C22×C6111yescharacteristic, complemented
611C22×C22⋊C4C22×C6111yescharacteristic, complemented
612C22×C22⋊C4C22×C6111yescharacteristic, complemented
613C22×C22⋊C4C22×C6111yescharacteristic, complemented
614C22×C42C22×C6111yescharacteristic, complemented
615#396C22×C6118yescomplemented
616#394C22×C6118yescomplemented
617#394C22×C6118yescomplemented
618#392C22×C6118yescomplemented
619#390C22×C6118yescomplemented
620#388C22×C6118yescomplemented
621#386C22×C6118yescomplemented
622#386C22×C6118yescomplemented
623#385C22×C6118yescomplemented
624C2×#95C22×C6111yescharacteristic, complemented
625C2×#95C22×C6111yescharacteristic, complemented
626C2×#95C22×C6111yescharacteristic, complemented
627C2×#95C22×C6111yescharacteristic, complemented
628C61C2×#242411yescharacteristic, direct product factor, Sylow
629C25—24no—
630C25—24no—
631C25—24no—
632C25—24no—
633C25—24no—
634C25—42no—
635C25—42no—
636C25C23×C6111yescharacteristic
637C25C23×C6111yescharacteristic
638C25C23×C6111yescharacteristic
639C25C23×C6111yescharacteristic
640C25C23×C6114yes—
641C25C23×C6111yescharacteristic
642C22×D4—24no—
643C22×D4—24no—
644C22×D4—24no—
645C22×D4—24no—
646C22×D4—24no—
647C22×D4—24no—
648C22×D4—24no—
649C22×D4—24no—
650C22×D4—24no—
651C22×D4—24no—
652C22×D4—24no—
653C22×D4—24no—
654C22×D4—24no—
655C22×D4—24no—
656C22×D4—24no—
657C22×D4—42no—
658C22×D4—42no—
659C22×D4—42no—
660C22×D4—42no—
661C22×D4—42no—
662C22×D4D4×C6118yescomplemented
663C22×D4C23×C6114yes—
664C22×D4C23×C6114yes—
665C22×D4C23×C6114yes—
666C22×D4C23×C6114yes—
667C22×D4C23×C6114yes—
668C22×D4C23×C6114yes—
669C22×D4C23×C6114yescomplemented
670C23×C4—24no—
671C23×C4—24no—
672C23×C4—24no—
673C23×C4—24no—
674C23×C4—24no—
675C23×C4—24no—
676C23×C4—42no—
677C23×C4—42no—
678C23×C4—42no—
679C23×C4C23×C6111yescharacteristic
680C23×C4C23×C6111yescharacteristic
681C23×C4C23×C6111yescharacteristic
682C23×C4C23×C6111yescharacteristic
683C23×C4C23×C6111yescharacteristic
684C23×C4C23×C6114yes—
685C23×C4C23×C6114yes—
686C23×C4C23×C6111yescharacteristic
687C23×C4C23×C6111yescharacteristic
688C23×C4C23×C6111yescharacteristic
689C23×C4C23×C6111yescharacteristic
690C23×C4C23×C6111yescharacteristic
691C23×C4C23×C6114yescomplemented
692#121—232no—
693#121—232no—
694#120—232no—
695#120—232no—
696C4×D4—232no—
697C2×C4⋊C4—24no—
698C2×C4⋊C4—24no—
699C2×C4⋊C4—24no—
700C2×C4⋊C4—42no—
701C2×C4⋊C4C23×C6114yescomplemented
702C2×C4⋊C4C23×C6114yescomplemented
703C2×C4⋊C4C23×C6114yescomplemented
704C2×C4⋊C4C23×C6114yescomplemented
705C2×C22⋊C4—24no—
706C2×C22⋊C4—24no—
707C2×C22⋊C4—24no—
708C2×C22⋊C4—24no—
709C2×C22⋊C4—24no—
710C2×C22⋊C4—24no—
711C2×C22⋊C4—24no—
712C2×C22⋊C4—24no—
713C2×C22⋊C4—24no—
714C2×C22⋊C4—24no—
715C2×C22⋊C4—24no—
716C2×C22⋊C4—24no—
717C2×C22⋊C4—232no—
718C2×C22⋊C4—42no—
719C2×C22⋊C4D4×C6118yescomplemented
720C2×C22⋊C4D4×C6118yescomplemented
721C2×C22⋊C4C23×C6114yes—
722C2×C22⋊C4C23×C6114yes—
723C2×C22⋊C4C23×C6114yes—
724C2×C22⋊C4C23×C6114yes—
725C2×C22⋊C4C23×C6114yes—
726C2×C22⋊C4C23×C6114yes—
727C2×C22⋊C4C23×C6114yes—
728C2×C22⋊C4C23×C6114yes—
729C2×C22⋊C4C23×C6114yes—
730C2×C22⋊C4C23×C6114yes—
731C2×C22⋊C4C23×C6114yescomplemented
732C2×C22⋊C4C23×C6114yescomplemented
733C2×C22⋊C4C23×C6114yescomplemented
734C2×C22⋊C4C23×C6114yescomplemented
735C2×C22⋊C4C23×C6114yescomplemented
736C2×C42—24no—
737C2×C42C23×C6114yescomplemented
738#95C23×C6114yescomplemented
739#95C23×C6114yescomplemented
740#95C23×C6114yescomplemented
741#95C23×C6114yescomplemented
742C24—22no—
743C24—22no—
744C24—22no—
745C24—22no—
746C24—232no—
747C24—28no—
748C24—22no—
749C24—22no—
750C24—22no—
751C24—22no—
752C24—22no—
753C24—22no—
754C24—22no—
755C24—22no—
756C24—22no—
757C24—28no—
758C24—28no—
759C24—22no—
760C24—22no—
761C24—22no—
762C24—22no—
763C24—22no—
764C24—22no—
765C24—22no—
766C24—22no—
767C24—22no—
768C24—22no—
769C24—22no—
770C24—28no—
771C24—28no—
772C24—22no—
773C24—22no—
774C24—22no—
775C24—22no—
776C24—22no—
777C24—44no—
778C24—44no—
779C24—416no—
780C24—416no—
781C24—416no—
782C24—416no—
783C24—416no—
784C24—416no—
785C24C2×D4×C6114yes—
786C24C2×D4×C6114yes—
787C24C2×D4×C6114yes—
788C24C2×D4×C6114yes—
789C24#41×C6114yes—
790C24#41×C6114yes—
791C24C24×C6112yes—
792C24C24×C6112yes—
793C24C24×C6112yes—
794C24C24×C6112yes—
795C24C24×C6112yes—
796C24C24×C6111yescharacteristic
797C2×D4—232no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—28no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—28no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—44no—
818C2×D4—416no—
819C2×D4—416no—
820C2×D4—416no—
821C2×D4—416no—
822C2×D4—416no—
823C2×D4—416no—
824C2×D4C2×D4×C61116yescomplemented
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—28no—
845C22×C4—28no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—28no—
853C22×C4—28no—
854C22×C4—28no—
855C22×C4—28no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—416no—
860C22×C4—416no—
861C22×C4—416no—
862C22×C4C2×D4×C6114yes—
863C22×C4C2×D4×C6114yes—
864C22×C4C2×D4×C6114yes—
865C22×C4C2×D4×C6114yes—
866C22×C4C2×D4×C6114yes—
867C22×C4C24×C6112yes—
868C22×C4C24×C6112yes—
869C22×C4C24×C6112yes—
870C22×C4C24×C6112yes—
871C22×C4C24×C6112yes—
872C22×C4C24×C6112yes—
873C22×C4C24×C6112yes—
874C22×C4C24×C6112yes—
875C22×C4C24×C6112yes—
876C22×C4C24×C6112yes—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—44no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—44no—
894C22⋊C4C2×D4×C61116yescomplemented
895C22⋊C4C2×D4×C61116yescomplemented
896C42—28no—
897C23—28no—
898C23—28no—
899C23—28no—
900C23—28no—
901C23—28no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—28no—
907C23—232no—
908C23—28no—
909C23—28no—
910C23—28no—
911C23—28no—
912C23—28no—
913C23—28no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—28no—
933C23—28no—
934C23—28no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—416no—
943C23—416no—
944C23—416no—
945C23—416no—
946C23—4128no—
947C23—416no—
948C23—44no—
949C23—44no—
950C23—44no—
951C23—44no—
952C23—44no—
953C23—44no—
954C23—44no—
955C23—44no—
956C23—44no—
957C23—44no—
958C23—44no—
959C23—416no—
960C23—44no—
961C23—44no—
962C23—44no—
963C23—44no—
964C23—44no—
965C23—44no—
966C23—44no—
967C23—44no—
968C23#121×C61116yescomplemented
969C23C22×D4×C6114yes—
970C23C22×D4×C6114yes—
971C23C22×D4×C6114yes—
972C23C22×D4×C6114yes—
973C23C22×D4×C6112yes—
974C23C22×D4×C6112yes—
975C23C22×D4×C6112yes—
976C23C2×#41×C6114yes—
977C23C2×#41×C6114yes—
978C23C2×#41×C6112yes—
979C23C2×#41×C6112yes—
980C23H(5,𝔽2)×C6112yes—
981C23H(5,𝔽2)×C6112yes—
982C23C25×C6111yescharacteristic
983D4—232no—
984D4—416no—
985D4—416no—
986D4—416no—
987D4—416no—
988D4—416no—
989D4—416no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—28no—
993C2×C4—28no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—28no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—416no—
1021C2×C4—416no—
1022C2×C4—416no—
1023C2×C4—44no—
1024C2×C4—44no—
1025C2×C4—44no—
1026C2×C4—44no—
1027C2×C4—44no—
1028C2×C4C22×D4×C6114yes—
1029C2×C4C22×D4×C6114yes—
1030C2×C4C22×D4×C6114yes—
1031C2×C4C22×D4×C6114yes—
1032C2×C4C22×D4×C6114yes—
1033C22—24no—
1034C22—232no—
1035C22—24no—
1036C22—24no—
1037C22—24no—
1038C22—24no—
1039C22—24no—
1040C22—24no—
1041C22—24no—
1042C22—24no—
1043C22—24no—
1044C22—24no—
1045C22—24no—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—464no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—416no—
1054C22—416no—
1055C22—416no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—88no—
1073C22C2×#121×C6114yes—
1074C22C2×#121×C6118yescomplemented
1075C22C61×#52514yes—
1076C22C61×#53814yes—
1077C22D42×C6114yes—
1078C22D42×C6114yes—
1079C22C61×#54614yes—
1080C22C61×#54614yes—
1081C22C23×D4×C6111yescharacteristic
1082C22C23×D4×C6111yescharacteristic
1083C22C23×D4×C6111yescharacteristic
1084C22C22×#41×C6111yescharacteristic
1085C22C22×#41×C6111yescharacteristic
1086C22C2×H(5,𝔽2)×C6111yescharacteristic
1087C22C2×H(5,𝔽2)×C6111yescharacteristic
1088C4—24no—
1089C4—24no—
1090C4—24no—
1091C4—24no—
1092C4—24no—
1093C4—42no—
1094C4—42no—
1095C4—42no—
1096C4—42no—
1097C4—42no—
1098C2—28no—
1099C2—44no—
1100C2—44no—
1101C2—44no—
1102C2—82no—
1103C2C61×#242418yesdirect product factor
1104C2C22×#121×C6111yescharacteristic
1105C2C2×C61×#52511yescharacteristic
1106C2C2×C61×#53811yescharacteristic
1107C2C2×D42×C6111yescharacteristic
1108C2C2×D42×C6111yescharacteristic
1109C2C2×C61×#54611yescharacteristic
1110C2C2×C61×#54611yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutator, Frattini, cosocleC23C25×C61
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#121×C61C2semidirect
2. C22×#121×C61C2semidirect
3. C22×#120×C61C2semidirect
4. C22×#120×C61C2semidirect
5. C22×C4×D4×C61C2semidirect
6. C23×C22⋊C4×C61C2semidirect
7. C61×#2424C2direct (N × H)
8. C2×C61×#396C2semidirect
9. C2×C61×#394C2semidirect
10. C2×C61×#394C2semidirect
11. C2×C61×#392C2semidirect
12. C2×C61×#390C2semidirect
13. C2×C61×#388C2semidirect
14. C2×C61×#386C2semidirect
15. C2×C61×#386C2semidirect
16. C2×C61×#385C2semidirect
24. C23×D4×C61C22semidirect
27. C24×C4×C61C22semidirect
30. C2×#121×C61C22semidirect
31. C2×#121×C61C22semidirect
34. C2×#120×C61C22semidirect
35. C2×#120×C61C22semidirect
37. C2×C4×D4×C61C22semidirect
38. C22×C4⋊C4×C61C22semidirect
39. C22×C4⋊C4×C61C22semidirect
40. C22×C4⋊C4×C61C22semidirect
41. C22×C4⋊C4×C61C22semidirect
53. C22×C22⋊C4×C61C22semidirect
54. C22×C22⋊C4×C61C22semidirect
55. C22×C22⋊C4×C61C22semidirect
56. C22×C22⋊C4×C61C22semidirect
57. C22×C22⋊C4×C61C22semidirect
58. C22×C22⋊C4×C61C22semidirect
59. C22×C42×C61C22semidirect
60. C61×#396C22semidirect
61. C61×#394C22semidirect
62. C61×#394C22semidirect
63. C61×#392C22semidirect
64. C61×#390C22semidirect
65. C61×#388C22semidirect
66. C61×#386C22semidirect
67. C61×#386C22semidirect
68. C61×#385C22semidirect
69. C2×#95×C61C22semidirect
70. C2×#95×C61C22semidirect
71. C2×#95×C61C22semidirect
72. C2×#95×C61C22semidirect
106. C22×D4×C61D4semidirect
113. C22×D4×C61C23semidirect
135. C23×C4×C61C23semidirect
145. C2×C4⋊C4×C61C23semidirect
146. C2×C4⋊C4×C61C23semidirect
147. C2×C4⋊C4×C61C23semidirect
148. C2×C4⋊C4×C61C23semidirect
163. C2×C22⋊C4×C61D4semidirect
164. C2×C22⋊C4×C61D4semidirect
175. C2×C22⋊C4×C61C23semidirect
176. C2×C22⋊C4×C61C23semidirect
177. C2×C22⋊C4×C61C23semidirect
178. C2×C22⋊C4×C61C23semidirect
179. C2×C22⋊C4×C61C23semidirect
181. C2×C42×C61C23semidirect
182. #95×C61C23semidirect
183. #95×C61C23semidirect
184. #95×C61C23semidirect
185. #95×C61C23semidirect
268. C2×D4×C61C2×D4semidirect
338. C22⋊C4×C61C2×D4semidirect
339. C22⋊C4×C61C2×D4semidirect
412. C23×C61#121semidirect
477. C2×#2424C61direct (N × H)
519. C22×C61C2×#121semidirect
543. C22×#121C2×C61semidirect
544. C22×#121C2×C61semidirect
545. C22×#120C2×C61semidirect
546. C22×#120C2×C61semidirect
547. C22×C4×D4C2×C61semidirect
548. C23×C22⋊C4C2×C61semidirect
549. #2424C2×C61direct (N × H)
550. C2×#396C2×C61semidirect
551. C2×#394C2×C61semidirect
552. C2×#394C2×C61semidirect
553. C2×#392C2×C61semidirect
554. C2×#390C2×C61semidirect
555. C2×#388C2×C61semidirect
556. C2×#386C2×C61semidirect
557. C2×#386C2×C61semidirect
558. C2×#385C2×C61semidirect
564. C2×C61#2424direct (N × H)
579. C23×D4C22×C61semidirect
582. C24×C4C22×C61semidirect
585. C2×#121C22×C61semidirect
586. C2×#121C22×C61semidirect
589. C2×#120C22×C61semidirect
590. C2×#120C22×C61semidirect
592. C2×C4×D4C22×C61semidirect
593. C22×C4⋊C4C22×C61semidirect
594. C22×C4⋊C4C22×C61semidirect
595. C22×C4⋊C4C22×C61semidirect
596. C22×C4⋊C4C22×C61semidirect
608. C22×C22⋊C4C22×C61semidirect
609. C22×C22⋊C4C22×C61semidirect
610. C22×C22⋊C4C22×C61semidirect
611. C22×C22⋊C4C22×C61semidirect
612. C22×C22⋊C4C22×C61semidirect
613. C22×C22⋊C4C22×C61semidirect
614. C22×C42C22×C61semidirect
615. #396C22×C61semidirect
616. #394C22×C61semidirect
617. #394C22×C61semidirect
618. #392C22×C61semidirect
619. #390C22×C61semidirect
620. #388C22×C61semidirect
621. #386C22×C61semidirect
622. #386C22×C61semidirect
623. #385C22×C61semidirect
624. C2×#95C22×C61semidirect
625. C2×#95C22×C61semidirect
626. C2×#95C22×C61semidirect
627. C2×#95C22×C61semidirect
628. C61C2×#2424direct (N × H)
662. C22×D4D4×C61semidirect
669. C22×D4C23×C61semidirect
691. C23×C4C23×C61semidirect
701. C2×C4⋊C4C23×C61semidirect
702. C2×C4⋊C4C23×C61semidirect
703. C2×C4⋊C4C23×C61semidirect
704. C2×C4⋊C4C23×C61semidirect
719. C2×C22⋊C4D4×C61semidirect
720. C2×C22⋊C4D4×C61semidirect
731. C2×C22⋊C4C23×C61semidirect
732. C2×C22⋊C4C23×C61semidirect
733. C2×C22⋊C4C23×C61semidirect
734. C2×C22⋊C4C23×C61semidirect
735. C2×C22⋊C4C23×C61semidirect
737. C2×C42C23×C61semidirect
738. #95C23×C61semidirect
739. #95C23×C61semidirect
740. #95C23×C61semidirect
741. #95C23×C61semidirect
824. C2×D4C2×D4×C61semidirect
894. C22⋊C4C2×D4×C61semidirect
895. C22⋊C4C2×D4×C61semidirect
968. C23#121×C61semidirect
1074. C22C2×#121×C61semidirect
1103. C2C61×#2424direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#121×C612
C22×#120×C612
C22×C4×D4×C612
C23×C22⋊C4×C612
C61×#24242
C2×C61×#3962
C2×C61×#3942
C2×C61×#3922
C2×C61×#3902
C2×C61×#3882
C2×C61×#3862
C2×C61×#3852
C2×#242461