Finite Group Databasebeta

← C61×#13967 #29517400

Subgroups — C61×#13967 #29517400

Order 15616.

4478 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C61C211yesmaximal, characteristic
2C22×C4×D4×C61C211yesmaximal, characteristic, complemented
3C23×C22⋊C4×C61C211yesmaximal, characteristic, complemented
4C2×C61×#386C211yesmaximal, characteristic, complemented
5C2×C61×#386C212yesmaximal, complemented
6C2×C61×#379C211yesmaximal, characteristic, complemented
7C61×#1439C212yesmaximal, complemented
8C61×#1438C212yesmaximal, complemented
9C61×#1437C212yesmaximal, complemented
10C61×C22⋊#95C211yesmaximal, characteristic, complemented
11C61×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C61C2211yescharacteristic
13C23×D4×C61C2212yes—
14C23×D4×C61C2211yescharacteristic
15C24×C4×C61C2211yescharacteristic
16C24×C4×C61C2211yescharacteristic
17C24×C4×C61C2211yescharacteristic, complemented
18C2×#120×C61—24no—
19C2×#120×C61—24no—
20C2×#120×C61C418yescomplemented
21C2×C4×D4×C61—24no—
22C2×C4×D4×C61—24no—
23C2×C4×D4×C61—24no—
24C22×C4⋊C4×C61C2211yescharacteristic, complemented
25C22×C22⋊C4×C61—24no—
26C22×C22⋊C4×C61—28no—
27C22×C22⋊C4×C61C2211yescharacteristic
28C22×C22⋊C4×C61C2212yes—
29C22×C22⋊C4×C61C2212yes—
30C22×C22⋊C4×C61C2212yes—
31C22×C22⋊C4×C61C2211yescharacteristic
32C22×C22⋊C4×C61C2212yes—
33C22×C22⋊C4×C61C2211yescharacteristic
34C22×C22⋊C4×C61C2212yes—
35C22×C22⋊C4×C61C2211yescharacteristic, complemented
36C22×C22⋊C4×C61C2212yescomplemented
37C22×C42×C61C2211yescharacteristic, complemented
38C61×#386—24no—
39C61×#386—28no—
40C61×#379—24no—
41C2×#95×C61C2212yescomplemented
42C2×#95×C61C2212yescomplemented
43C2×#95×C61C2212yescomplemented
44C2×#95×C61C2212yescomplemented
45C2×#95×C61C2212yescomplemented
46C25×C61—24no—
47C25×C61—22no—
48C25×C61—24no—
49C25×C61—22no—
50C25×C61—22no—
51C25×C61—22no—
52C25×C61—22no—
53C25×C61—22no—
54C25×C61—42no—
55C25×C61—42no—
56C25×C61C2×C414yescomplemented
57C25×C61C2311yescharacteristic
58C25×C61C2312yes—
59C25×C61C2311yescharacteristic
60C22×D4×C61—22no—
61C22×D4×C61—22no—
62C22×D4×C61—22no—
63C22×D4×C61—22no—
64C22×D4×C61—24no—
65C22×D4×C61—24no—
66C22×D4×C61—24no—
67C22×D4×C61—24no—
68C22×D4×C61—42no—
69C22×D4×C61—42no—
70C22×D4×C61C2×C414yes—
71C22×D4×C61C2×C418yescomplemented
72C22×D4×C61D414yes—
73C22×D4×C61D414yes—
74C23×C4×C61—22no—
75C23×C4×C61—22no—
76C23×C4×C61—22no—
77C23×C4×C61—22no—
78C23×C4×C61—24no—
79C23×C4×C61—24no—
80C23×C4×C61—22no—
81C23×C4×C61—22no—
82C23×C4×C61—22no—
83C23×C4×C61—22no—
84C23×C4×C61—24no—
85C23×C4×C61—42no—
86C23×C4×C61—42no—
87C23×C4×C61—42no—
88C23×C4×C61D414yescomplemented
89C23×C4×C61C2312yes—
90C23×C4×C61C2312yes—
91C23×C4×C61C2312yes—
92C23×C4×C61C2311yescharacteristic
93C23×C4×C61C2311yescharacteristic
94C23×C4×C61C2311yescharacteristic
95C23×C4×C61C2311yescharacteristic
96C23×C4×C61C2311yescharacteristic
97#120×C61—232no—
98C4×D4×C61—232no—
99C2×C4⋊C4×C61—22no—
100C2×C4⋊C4×C61—22no—
101C2×C4⋊C4×C61—22no—
102C2×C22⋊C4×C61—232no—
103C2×C22⋊C4×C61—24no—
104C2×C22⋊C4×C61—22no—
105C2×C22⋊C4×C61—22no—
106C2×C22⋊C4×C61—22no—
107C2×C22⋊C4×C61—22no—
108C2×C22⋊C4×C61—22no—
109C2×C22⋊C4×C61—24no—
110C2×C22⋊C4×C61—24no—
111C2×C22⋊C4×C61—24no—
112C2×C22⋊C4×C61—24no—
113C2×C22⋊C4×C61—24no—
114C2×C22⋊C4×C61—24no—
115C2×C22⋊C4×C61—22no—
116C2×C22⋊C4×C61—22no—
117C2×C22⋊C4×C61—22no—
118C2×C22⋊C4×C61—24no—
119C2×C22⋊C4×C61—22no—
120C2×C22⋊C4×C61—24no—
121C2×C22⋊C4×C61—24no—
122C2×C22⋊C4×C61—22no—
123C2×C22⋊C4×C61—24no—
124C2×C22⋊C4×C61—24no—
125C2×C22⋊C4×C61—24no—
126C2×C22⋊C4×C61—42no—
127C2×C22⋊C4×C61—42no—
128C2×C22⋊C4×C61—42no—
129C2×C22⋊C4×C61C2×C414yescomplemented
130C2×C22⋊C4×C61C2×C418yescomplemented
131C2×C22⋊C4×C61D414yescomplemented
132C2×C22⋊C4×C61D418yescomplemented
133C2×C42×C61—22no—
134C2×C42×C61—22no—
135C2×C42×C61—22no—
136#95×C61—24no—
137#95×C61—24no—
138#95×C61—24no—
139#95×C61—42no—
140#95×C61—42no—
141C24×C61—22no—
142C24×C61—22no—
143C24×C61—22no—
144C24×C61—22no—
145C24×C61—28no—
146C24×C61—28no—
147C24×C61—216no—
148C24×C61—28no—
149C24×C61—216no—
150C24×C61—22no—
151C24×C61—22no—
152C24×C61—22no—
153C24×C61—21no—
154C24×C61—21no—
155C24×C61—22no—
156C24×C61—22no—
157C24×C61—22no—
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61—22no—
163C24×C61—22no—
164C24×C61—22no—
165C24×C61—22no—
166C24×C61—22no—
167C24×C61—22no—
168C24×C61—22no—
169C24×C61—22no—
170C24×C61—28no—
171C24×C61—28no—
172C24×C61—48no—
173C24×C61—48no—
174C24×C61—48no—
175C24×C61—48no—
176C24×C61—48no—
177C24×C61—48no—
178C24×C61—48no—
179C24×C61—48no—
180C24×C61—48no—
181C24×C61—44no—
182C24×C61—44no—
183C24×C61—48no—
184C24×C61—44no—
185C24×C61—44no—
186C24×C61—44no—
187C24×C61—44no—
188C24×C61C22×C412yes—
189C24×C61C22×C414yes—
190C24×C61C22×C412yes—
191C24×C61C2×D412yes—
192C24×C61C2×D412yes—
193C24×C61C2×D414yes—
194C24×C61C2×D412yes—
195C24×C61C2×D412yes—
196C24×C61C2×D412yes—
197C24×C61C2×D412yes—
198C24×C61#4114yes—
199C24×C61#4112yes—
200C24×C61#4112yes—
201C24×C61C2411yescharacteristic
202C2×D4×C61—28no—
203C2×D4×C61—28no—
204C2×D4×C61—28no—
205C2×D4×C61—28no—
206C2×D4×C61—28no—
207C2×D4×C61—28no—
208C2×D4×C61—216no—
209C2×D4×C61—216no—
210C2×D4×C61—48no—
211C2×D4×C61—48no—
212C2×D4×C61—48no—
213C2×D4×C61—48no—
214C2×D4×C61—48no—
215C2×D4×C61C22⋊C4116yescomplemented
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—22no—
223C22×C4×C61—28no—
224C22×C4×C61—28no—
225C22×C4×C61—28no—
226C22×C4×C61—22no—
227C22×C4×C61—22no—
228C22×C4×C61—22no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—22no—
232C22×C4×C61—22no—
233C22×C4×C61—22no—
234C22×C4×C61—22no—
235C22×C4×C61—22no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—22no—
241C22×C4×C61—22no—
242C22×C4×C61—22no—
243C22×C4×C61—22no—
244C22×C4×C61—22no—
245C22×C4×C61—22no—
246C22×C4×C61—22no—
247C22×C4×C61—22no—
248C22×C4×C61—22no—
249C22×C4×C61—22no—
250C22×C4×C61—28no—
251C22×C4×C61—22no—
252C22×C4×C61—22no—
253C22×C4×C61—22no—
254C22×C4×C61—22no—
255C22×C4×C61—22no—
256C22×C4×C61—22no—
257C22×C4×C61—22no—
258C22×C4×C61—44no—
259C22×C4×C61—48no—
260C22×C4×C61—48no—
261C22×C4×C61—48no—
262C22×C4×C61—48no—
263C22×C4×C61—48no—
264C22×C4×C61—48no—
265C22×C4×C61—44no—
266C22×C4×C61—44no—
267C22×C4×C61—44no—
268C22×C4×C61—44no—
269C22×C4×C61C22×C414yes—
270C22×C4×C61C22×C412yes—
271C22×C4×C61C2×D414yes—
272C22×C4×C61C2×D412yes—
273C22×C4×C61C2×D412yes—
274C22×C4×C61C2×D412yes—
275C22×C4×C61C2×D412yes—
276C22×C4×C61C2×D412yes—
277C22×C4×C61C2×D414yes—
278C22×C4×C61C2×D412yes—
279C4⋊C4×C61—28no—
280C22⋊C4×C61—216no—
281C22⋊C4×C61—28no—
282C22⋊C4×C61—28no—
283C22⋊C4×C61—28no—
284C22⋊C4×C61—216no—
285C22⋊C4×C61—216no—
286C22⋊C4×C61—48no—
287C22⋊C4×C61—48no—
288C22⋊C4×C61—48no—
289C22⋊C4×C61—44no—
290C42×C61—28no—
291C23×C61—24no—
292C23×C61—24no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—24no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—24no—
299C23×C61—24no—
300C23×C61—24no—
301C23×C61—24no—
302C23×C61—24no—
303C23×C61—24no—
304C23×C61—24no—
305C23×C61—24no—
306C23×C61—24no—
307C23×C61—232no—
308C23×C61—24no—
309C23×C61—24no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—24no—
313C23×C61—24no—
314C23×C61—24no—
315C23×C61—24no—
316C23×C61—24no—
317C23×C61—24no—
318C23×C61—24no—
319C23×C61—22no—
320C23×C61—22no—
321C23×C61—22no—
322C23×C61—22no—
323C23×C61—24no—
324C23×C61—24no—
325C23×C61—24no—
326C23×C61—24no—
327C23×C61—24no—
328C23×C61—24no—
329C23×C61—24no—
330C23×C61—24no—
331C23×C61—24no—
332C23×C61—24no—
333C23×C61—24no—
334C23×C61—24no—
335C23×C61—24no—
336C23×C61—24no—
337C23×C61—24no—
338C23×C61—432no—
339C23×C61—432no—
340C23×C61—416no—
341C23×C61—416no—
342C23×C61—416no—
343C23×C61—416no—
344C23×C61—432no—
345C23×C61—432no—
346C23×C61—416no—
347C23×C61—41no—
348C23×C61—42no—
349C23×C61—42no—
350C23×C61—42no—
351C23×C61—42no—
352C23×C61—41no—
353C23×C61—42no—
354C23×C61—41no—
355C23×C61—42no—
356C23×C61—41no—
357C23×C61—42no—
358C23×C61—42no—
359C23×C61—42no—
360C23×C61—42no—
361C23×C61—42no—
362C23×C61—42no—
363C23×C61—42no—
364C23×C61—42no—
365C23×C61—42no—
366C23×C61—42no—
367C23×C61—42no—
368C23×C61—42no—
369C23×C61—42no—
370C23×C61—42no—
371C23×C61—42no—
372C23×C61—42no—
373C23×C61—416no—
374C23×C61C2×C22⋊C414yes—
375C23×C61C2×C22⋊C414yescomplemented
376C23×C61C4×D414yes—
377C23×C61C4×D414yes—
378C23×C61C4×D418yescomplemented
379C23×C61#12014yes—
380C23×C61#12114yes—
381C23×C61#12114yes—
382C23×C61#12314yes—
383C23×C61C23×C411yescharacteristic
384C23×C61C22×D411yescharacteristic
385C23×C61C22×D411yescharacteristic
386C23×C61C22×D411yescharacteristic
387C23×C61C22×D411yescharacteristic
388C23×C61C22×D412yes—
389C23×C61C2×#4111yescharacteristic
390C23×C61C2×#4111yescharacteristic
391C23×C61C2×#4112yes—
392C23×C61H(5,𝔽2)12yes—
393C23×C61H(5,𝔽2)12yes—
394D4×C61—232no—
395D4×C61—432no—
396C2×C4×C61—22no—
397C2×C4×C61—22no—
398C2×C4×C61—22no—
399C2×C4×C61—22no—
400C2×C4×C61—22no—
401C2×C4×C61—22no—
402C2×C4×C61—22no—
403C2×C4×C61—22no—
404C2×C4×C61—24no—
405C2×C4×C61—24no—
406C2×C4×C61—24no—
407C2×C4×C61—24no—
408C2×C4×C61—24no—
409C2×C4×C61—22no—
410C2×C4×C61—22no—
411C2×C4×C61—24no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—22no—
415C2×C4×C61—24no—
416C2×C4×C61—24no—
417C2×C4×C61—24no—
418C2×C4×C61—24no—
419C2×C4×C61—416no—
420C2×C4×C61—416no—
421C2×C4×C61—416no—
422C2×C4×C61—41no—
423C2×C4×C61—42no—
424C2×C4×C61—41no—
425C2×C4×C61—41no—
426C2×C4×C61—41no—
427C2×C4×C61—42no—
428C2×C4×C61—42no—
429C2×C4×C61—42no—
430C2×C4×C61—42no—
431C2×C4×C61—42no—
432C2×C4×C61—42no—
433C2×C4×C61—42no—
434C2×C4×C61—42no—
435C2×C4×C61—42no—
436C2×C4×C61—42no—
437C2×C4×C61—42no—
438C2×C4×C61—42no—
439C2×C4×C61—42no—
440C2×C4×C61—42no—
441C2×C4×C61—42no—
442C2×C4×C61—42no—
443C2×C4×C61—42no—
444C2×C4×C61—42no—
445C2×C4×C61C2×C22⋊C414yescomplemented
446C2×C4×C61#12014yescomplemented
447#13967C6111yesmaximal, characteristic, direct product factor, Sylow
448C22×C61—24no—
449C22×C61—28no—
450C22×C61—28no—
451C22×C61—24no—
452C22×C61—24no—
453C22×C61—24no—
454C22×C61—28no—
455C22×C61—28no—
456C22×C61—24no—
457C22×C61—24no—
458C22×C61—28no—
459C22×C61—28no—
460C22×C61—28no—
461C22×C61—24no—
462C22×C61—28no—
463C22×C61—464no—
464C22×C61—42no—
465C22×C61—44no—
466C22×C61—44no—
467C22×C61—44no—
468C22×C61—44no—
469C22×C61—42no—
470C22×C61—44no—
471C22×C61—42no—
472C22×C61—44no—
473C22×C61—42no—
474C22×C61—44no—
475C22×C61—44no—
476C22×C61—44no—
477C22×C61—44no—
478C22×C61—44no—
479C22×C61—44no—
480C22×C61—44no—
481C22×C61—42no—
482C22×C61—44no—
483C22×C61—44no—
484C22×C61—42no—
485C22×C61#38618yescomplemented
486C22×C61C22×C22⋊C411yescharacteristic
487C22×C61C2×C4×D411yescharacteristic
488C22×C61C2×C4×D412yes—
489C22×C61C2×C4×D411yescharacteristic
490C22×C61#51812yes—
491C22×C61C2×#12011yescharacteristic
492C22×C61C2×#12011yescharacteristic
493C22×C61C2×#12111yescharacteristic
494C22×C61C2×#12111yescharacteristic
495C22×C61C2×#12311yescharacteristic
496C22×C61#52511yescharacteristic
497C22×C61#52512yes—
498C22×C61#53411yescharacteristic
499C22×C61#53511yescharacteristic
500C22×C61#53812yes—
501C22×C61D4212yes—
502C22×C61D4212yes—
503C22×C61D4212yes—
504C22×C61#54612yes—
505C22×C61#54612yes—
506C22×C61#54612yes—
507C22×C61#54612yes—
508C22×C61#55112yes—
509C4×C61—24no—
510C4×C61—24no—
511C4×C61—44no—
512C4×C61—42no—
513C4×C61—42no—
514C4×C61—42no—
515C4×C61—44no—
516C4×C61—82no—
517C22×#120C2×C6111yescharacteristic
518C22×C4×D4C2×C6111yescharacteristic, complemented
519C23×C22⋊C4C2×C6111yescharacteristic, complemented
520C2×#386C2×C6112yescomplemented
521C2×#386C2×C6111yescharacteristic, complemented
522C2×#379C2×C6111yescharacteristic, complemented
523#1439C2×C6112yescomplemented
524#1438C2×C6112yescomplemented
525#1437C2×C6112yescomplemented
526C22⋊#95C2×C6111yescharacteristic, complemented
527C22⋊#95C2×C6111yescharacteristic, complemented
528C2×C61—28no—
529C2×C61—44no—
530C2×C61—48no—
531C2×C61C2×#38611yescharacteristic
532C2×C61C4×#12011yescharacteristic
533C2×C61#232111yescharacteristic
534C2×C61D4×C22⋊C412yes—
535C2×C61#235812yes—
536C2×C61#240311yescharacteristic
537C2×C61#240411yescharacteristic
538C2×C61#240811yescharacteristic
539C2×C61#241812yes—
540C2×C61#242412yes—
541C2×C61#253411yescharacteristic
542C26C22×C6111yescharacteristic
543C23×D4C22×C6112yes—
544C23×D4C22×C6111yescharacteristic
545C24×C4C22×C6111yescharacteristic
546C24×C4C22×C6111yescharacteristic
547C24×C4C22×C6111yescharacteristic, complemented
548C2×#120—24no—
549C2×#120—24no—
550C2×#120C4×C6118yescomplemented
551C2×C4×D4—24no—
552C2×C4×D4—24no—
553C2×C4×D4—24no—
554C22×C4⋊C4C22×C6111yescharacteristic, complemented
555C22×C22⋊C4—24no—
556C22×C22⋊C4—28no—
557C22×C22⋊C4C22×C6112yes—
558C22×C22⋊C4C22×C6111yescharacteristic
559C22×C22⋊C4C22×C6112yes—
560C22×C22⋊C4C22×C6112yes—
561C22×C22⋊C4C22×C6111yescharacteristic
562C22×C22⋊C4C22×C6112yes—
563C22×C22⋊C4C22×C6112yes—
564C22×C22⋊C4C22×C6111yescharacteristic
565C22×C22⋊C4C22×C6111yescharacteristic, complemented
566C22×C22⋊C4C22×C6112yescomplemented
567C22×C42C22×C6111yescharacteristic, complemented
568#386—24no—
569#386—28no—
570#379—24no—
571C2×#95C22×C6112yescomplemented
572C2×#95C22×C6112yescomplemented
573C2×#95C22×C6112yescomplemented
574C2×#95C22×C6112yescomplemented
575C2×#95C22×C6112yescomplemented
576C61#1396711yescharacteristic, direct product factor, Sylow
577C25—24no—
578C25—22no—
579C25—24no—
580C25—22no—
581C25—22no—
582C25—22no—
583C25—22no—
584C25—22no—
585C25—42no—
586C25—42no—
587C25C2×C4×C6114yescomplemented
588C25C23×C6111yescharacteristic
589C25C23×C6112yes—
590C25C23×C6111yescharacteristic
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—22no—
595C22×D4—24no—
596C22×D4—24no—
597C22×D4—24no—
598C22×D4—24no—
599C22×D4—42no—
600C22×D4—42no—
601C22×D4C2×C4×C6114yes—
602C22×D4C2×C4×C6118yescomplemented
603C22×D4D4×C6114yes—
604C22×D4D4×C6114yes—
605C23×C4—22no—
606C23×C4—22no—
607C23×C4—22no—
608C23×C4—22no—
609C23×C4—24no—
610C23×C4—24no—
611C23×C4—22no—
612C23×C4—22no—
613C23×C4—22no—
614C23×C4—22no—
615C23×C4—24no—
616C23×C4—42no—
617C23×C4—42no—
618C23×C4—42no—
619C23×C4D4×C6114yescomplemented
620C23×C4C23×C6112yes—
621C23×C4C23×C6112yes—
622C23×C4C23×C6111yescharacteristic
623C23×C4C23×C6111yescharacteristic
624C23×C4C23×C6111yescharacteristic
625C23×C4C23×C6112yes—
626C23×C4C23×C6111yescharacteristic
627C23×C4C23×C6111yescharacteristic
628#120—232no—
629C4×D4—232no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C22⋊C4—232no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—22no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—24no—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—24no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—24no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—24no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—24no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—24no—
655C2×C22⋊C4—24no—
656C2×C22⋊C4—24no—
657C2×C22⋊C4—42no—
658C2×C22⋊C4—42no—
659C2×C22⋊C4—42no—
660C2×C22⋊C4C2×C4×C6114yescomplemented
661C2×C22⋊C4C2×C4×C6118yescomplemented
662C2×C22⋊C4D4×C6118yescomplemented
663C2×C22⋊C4D4×C6114yescomplemented
664C2×C42—22no—
665C2×C42—22no—
666C2×C42—22no—
667#95—24no—
668#95—24no—
669#95—24no—
670#95—42no—
671#95—42no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—28no—
677C24—28no—
678C24—216no—
679C24—28no—
680C24—216no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—21no—
691C24—21no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—28no—
702C24—28no—
703C24—48no—
704C24—48no—
705C24—48no—
706C24—48no—
707C24—48no—
708C24—48no—
709C24—48no—
710C24—48no—
711C24—48no—
712C24—44no—
713C24—44no—
714C24—48no—
715C24—44no—
716C24—44no—
717C24—44no—
718C24—44no—
719C24C22×C4×C6112yes—
720C24C22×C4×C6114yes—
721C24C22×C4×C6112yes—
722C24C2×D4×C6112yes—
723C24C2×D4×C6112yes—
724C24C2×D4×C6114yes—
725C24C2×D4×C6112yes—
726C24C2×D4×C6112yes—
727C24C2×D4×C6112yes—
728C24C2×D4×C6112yes—
729C24#41×C6114yes—
730C24#41×C6112yes—
731C24#41×C6112yes—
732C24C24×C6111yescharacteristic
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—28no—
739C2×D4—216no—
740C2×D4—216no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4C22⋊C4×C61116yescomplemented
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—28no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—44no—
790C22×C4—48no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—48no—
794C22×C4—48no—
795C22×C4—48no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4C22×C4×C6114yes—
801C22×C4C22×C4×C6112yes—
802C22×C4C2×D4×C6114yes—
803C22×C4C2×D4×C6112yes—
804C22×C4C2×D4×C6112yes—
805C22×C4C2×D4×C6112yes—
806C22×C4C2×D4×C6112yes—
807C22×C4C2×D4×C6112yes—
808C22×C4C2×D4×C6114yes—
809C22×C4C2×D4×C6112yes—
810C4⋊C4—28no—
811C22⋊C4—216no—
812C22⋊C4—28no—
813C22⋊C4—28no—
814C22⋊C4—28no—
815C22⋊C4—216no—
816C22⋊C4—216no—
817C22⋊C4—48no—
818C22⋊C4—48no—
819C22⋊C4—48no—
820C22⋊C4—44no—
821C42—28no—
822C23—22no—
823C23—22no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—22no—
836C23—22no—
837C23—24no—
838C23—232no—
839C23—24no—
840C23—24no—
841C23—24no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—24no—
851C23—24no—
852C23—22no—
853C23—22no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—24no—
867C23—24no—
868C23—24no—
869C23—432no—
870C23—432no—
871C23—416no—
872C23—416no—
873C23—416no—
874C23—416no—
875C23—416no—
876C23—432no—
877C23—432no—
878C23—41no—
879C23—42no—
880C23—41no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23—42no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—416no—
898C23—41no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—41no—
904C23—42no—
905C23C2×C22⋊C4×C6114yes—
906C23C2×C22⋊C4×C6114yescomplemented
907C23C4×D4×C6114yes—
908C23C4×D4×C6114yes—
909C23C4×D4×C6118yescomplemented
910C23#120×C6114yes—
911C23#121×C6114yes—
912C23#121×C6114yes—
913C23#123×C6114yes—
914C23C23×C4×C6111yescharacteristic
915C23C22×D4×C6111yescharacteristic
916C23C22×D4×C6112yes—
917C23C22×D4×C6111yescharacteristic
918C23C22×D4×C6111yescharacteristic
919C23C22×D4×C6111yescharacteristic
920C23C2×#41×C6111yescharacteristic
921C23C2×#41×C6112yes—
922C23C2×#41×C6111yescharacteristic
923C23H(5,𝔽2)×C6112yes—
924C23H(5,𝔽2)×C6112yes—
925D4—232no—
926D4—432no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—416no—
951C2×C4—416no—
952C2×C4—416no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—41no—
967C2×C4—42no—
968C2×C4—41no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4C2×C22⋊C4×C6114yescomplemented
977C2×C4#120×C6114yescomplemented
978C22—24no—
979C22—24no—
980C22—24no—
981C22—28no—
982C22—28no—
983C22—24no—
984C22—24no—
985C22—24no—
986C22—28no—
987C22—28no—
988C22—24no—
989C22—28no—
990C22—28no—
991C22—28no—
992C22—28no—
993C22—464no—
994C22—42no—
995C22—44no—
996C22—44no—
997C22—42no—
998C22—42no—
999C22—44no—
1000C22—44no—
1001C22—44no—
1002C22—44no—
1003C22—42no—
1004C22—44no—
1005C22—42no—
1006C22—44no—
1007C22—42no—
1008C22—44no—
1009C22—44no—
1010C22—44no—
1011C22—44no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22C61×#38618yescomplemented
1016C22C22×C22⋊C4×C6111yescharacteristic
1017C22C2×C4×D4×C6111yescharacteristic
1018C22C2×C4×D4×C6111yescharacteristic
1019C22C2×C4×D4×C6112yes—
1020C22C61×#51812yes—
1021C22C2×#120×C6111yescharacteristic
1022C22C2×#120×C6111yescharacteristic
1023C22C2×#121×C6111yescharacteristic
1024C22C2×#121×C6111yescharacteristic
1025C22C2×#123×C6111yescharacteristic
1026C22C61×#52511yescharacteristic
1027C22C61×#52512yes—
1028C22C61×#53411yescharacteristic
1029C22C61×#53511yescharacteristic
1030C22C61×#53812yes—
1031C22D42×C6112yes—
1032C22D42×C6112yes—
1033C22D42×C6112yes—
1034C22C61×#54612yes—
1035C22C61×#54612yes—
1036C22C61×#54612yes—
1037C22C61×#54612yes—
1038C22C61×#55112yes—
1039C4—24no—
1040C4—24no—
1041C4—44no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—44no—
1046C4—82no—
1047C2—28no—
1048C2—48no—
1049C2—44no—
1050C2C2×C61×#38611yescharacteristic
1051C2C4×#120×C6111yescharacteristic
1052C2C61×#232111yescharacteristic
1053C2D4×C22⋊C4×C6112yes—
1054C2C61×#235812yes—
1055C2C61×#240311yescharacteristic
1056C2C61×#240411yescharacteristic
1057C2C61×#240811yescharacteristic
1058C2C61×#241812yes—
1059C2C61×#242412yes—
1060C2C61×#253411yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutatorC23C23×C4×C61
Frattini, cosocleC24C24×C61
prime radicalC22×#120×C61C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×D4×C61C2semidirect
3. C23×C22⋊C4×C61C2semidirect
4. C2×C61×#386C2semidirect
5. C2×C61×#386C2semidirect
6. C2×C61×#379C2semidirect
7. C61×#1439C2semidirect
8. C61×#1438C2semidirect
9. C61×#1437C2semidirect
10. C61×C22⋊#95C2semidirect
11. C61×C22⋊#95C2semidirect
17. C24×C4×C61C22semidirect
20. C2×#120×C61C4semidirect
24. C22×C4⋊C4×C61C22semidirect
35. C22×C22⋊C4×C61C22semidirect
36. C22×C22⋊C4×C61C22semidirect
37. C22×C42×C61C22semidirect
41. C2×#95×C61C22semidirect
42. C2×#95×C61C22semidirect
43. C2×#95×C61C22semidirect
44. C2×#95×C61C22semidirect
45. C2×#95×C61C22semidirect
56. C25×C61C2×C4semidirect
71. C22×D4×C61C2×C4semidirect
88. C23×C4×C61D4semidirect
129. C2×C22⋊C4×C61C2×C4semidirect
130. C2×C22⋊C4×C61C2×C4semidirect
131. C2×C22⋊C4×C61D4semidirect
132. C2×C22⋊C4×C61D4semidirect
215. C2×D4×C61C22⋊C4semidirect
375. C23×C61C2×C22⋊C4semidirect
378. C23×C61C4×D4semidirect
445. C2×C4×C61C2×C22⋊C4semidirect
446. C2×C4×C61#120semidirect
447. #13967C61direct (N × H)
485. C22×C61#386semidirect
518. C22×C4×D4C2×C61semidirect
519. C23×C22⋊C4C2×C61semidirect
520. C2×#386C2×C61semidirect
521. C2×#386C2×C61semidirect
522. C2×#379C2×C61semidirect
523. #1439C2×C61semidirect
524. #1438C2×C61semidirect
525. #1437C2×C61semidirect
526. C22⋊#95C2×C61semidirect
527. C22⋊#95C2×C61semidirect
547. C24×C4C22×C61semidirect
550. C2×#120C4×C61semidirect
554. C22×C4⋊C4C22×C61semidirect
565. C22×C22⋊C4C22×C61semidirect
566. C22×C22⋊C4C22×C61semidirect
567. C22×C42C22×C61semidirect
571. C2×#95C22×C61semidirect
572. C2×#95C22×C61semidirect
573. C2×#95C22×C61semidirect
574. C2×#95C22×C61semidirect
575. C2×#95C22×C61semidirect
576. C61#13967direct (N × H)
587. C25C2×C4×C61semidirect
602. C22×D4C2×C4×C61semidirect
619. C23×C4D4×C61semidirect
660. C2×C22⋊C4C2×C4×C61semidirect
661. C2×C22⋊C4C2×C4×C61semidirect
662. C2×C22⋊C4D4×C61semidirect
663. C2×C22⋊C4D4×C61semidirect
746. C2×D4C22⋊C4×C61semidirect
906. C23C2×C22⋊C4×C61semidirect
909. C23C4×D4×C61semidirect
976. C2×C4C2×C22⋊C4×C61semidirect
977. C2×C4#120×C61semidirect
1015. C22C61×#386semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C612
C22×C4×D4×C612
C23×C22⋊C4×C612
C2×C61×#3862
C2×C61×#3792
C61×#14392
C61×#14382
C61×#14372
C61×C22⋊#952
#1396761