Finite Group Databasebeta

← C61×#13995 #29517428

Subgroups — C61×#13995 #29517428

Order 15616.

4210 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C61C211yesmaximal, characteristic
2C23×C22⋊C4×C61C211yesmaximal, characteristic, complemented
3C2×C61×#390C212yesmaximal, complemented
4C2×C61×#386C211yesmaximal, characteristic, complemented
5C2×C61×#386C211yesmaximal, characteristic, complemented
6C2×C61×#385C211yesmaximal, characteristic, complemented
7C2×C61×#379C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
9C61×#1439C212yesmaximal, complemented
10C61×#1438C212yesmaximal, complemented
11C61×#1437C212yesmaximal, complemented
12C26×C61C2211yescharacteristic
13C23×D4×C61C2211yescharacteristic
14C23×D4×C61C2212yes—
15C24×C4×C61C2211yescharacteristic
16C24×C4×C61C2211yescharacteristic
17C2×#120×C61—24no—
18C2×#120×C61—24no—
19C2×#120×C61C418yescomplemented
20C22×C4⋊C4×C61C2212yescomplemented
21C22×C22⋊C4×C61—24no—
22C22×C22⋊C4×C61—28no—
23C22×C22⋊C4×C61C2211yescharacteristic
24C22×C22⋊C4×C61C2212yes—
25C22×C22⋊C4×C61C2212yes—
26C22×C22⋊C4×C61C2212yes—
27C22×C22⋊C4×C61C2212yes—
28C22×C22⋊C4×C61C2211yescharacteristic
29C22×C22⋊C4×C61C2212yes—
30C22×C22⋊C4×C61C2211yescharacteristic
31C22×C22⋊C4×C61C2211yescharacteristic, complemented
32C22×C22⋊C4×C61C2212yescomplemented
33C22×C22⋊C4×C61C2211yescharacteristic, complemented
34C22×C42×C61C2212yescomplemented
35C61×#390—28no—
36C61×#386—24no—
37C61×#386—24no—
38C61×#385—24no—
39C61×#379—24no—
40C4×C22⋊C4×C61—24no—
41C2×#95×C61C2212yescomplemented
42C2×#95×C61C2212yescomplemented
43C2×#95×C61C2211yescharacteristic, complemented
44C2×#95×C61C2212yescomplemented
45C2×#95×C61C2211yescharacteristic, complemented
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×C414yes—
57C25×C61C2311yescharacteristic
58C25×C61C2312yes—
59C25×C61C2311yescharacteristic
60C22×D4×C61—22no—
61C22×D4×C61—22no—
62C22×D4×C61—24no—
63C22×D4×C61—22no—
64C22×D4×C61—22no—
65C22×D4×C61—24no—
66C22×D4×C61—22no—
67C22×D4×C61—22no—
68C22×D4×C61—24no—
69C22×D4×C61—24no—
70C22×D4×C61—42no—
71C22×D4×C61—42no—
72C22×D4×C61C2×C414yes—
73C22×D4×C61C2×C418yescomplemented
74C23×C4×C61—22no—
75C23×C4×C61—22no—
76C23×C4×C61—22no—
77C23×C4×C61—24no—
78C23×C4×C61—24no—
79C23×C4×C61—22no—
80C23×C4×C61—22no—
81C23×C4×C61—42no—
82C23×C4×C61—42no—
83C23×C4×C61D414yescomplemented
84C23×C4×C61C2311yescharacteristic
85C23×C4×C61C2311yescharacteristic
86C23×C4×C61C2311yescharacteristic
87C23×C4×C61C2311yescharacteristic
88C23×C4×C61C2312yes—
89C23×C4×C61C2312yes—
90C23×C4×C61C2312yes—
91C23×C4×C61C2311yescharacteristic
92#120×C61—232no—
93C2×C4⋊C4×C61—24no—
94C2×C4⋊C4×C61—24no—
95C2×C4⋊C4×C61—42no—
96C2×C22⋊C4×C61—232no—
97C2×C22⋊C4×C61—22no—
98C2×C22⋊C4×C61—24no—
99C2×C22⋊C4×C61—22no—
100C2×C22⋊C4×C61—24no—
101C2×C22⋊C4×C61—24no—
102C2×C22⋊C4×C61—24no—
103C2×C22⋊C4×C61—24no—
104C2×C22⋊C4×C61—24no—
105C2×C22⋊C4×C61—24no—
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—22no—
115C2×C22⋊C4×C61—22no—
116C2×C22⋊C4×C61—24no—
117C2×C22⋊C4×C61—24no—
118C2×C22⋊C4×C61—42no—
119C2×C22⋊C4×C61—42no—
120C2×C22⋊C4×C61—42no—
121C2×C22⋊C4×C61—42no—
122C2×C22⋊C4×C61C2×C414yes—
123C2×C22⋊C4×C61C2×C418yescomplemented
124C2×C22⋊C4×C61D414yes—
125C2×C22⋊C4×C61D414yes—
126C2×C22⋊C4×C61D414yescomplemented
127C2×C22⋊C4×C61D418yescomplemented
128C2×C42×C61—24no—
129C2×C42×C61—24no—
130C2×C42×C61—42no—
131#95×C61—24no—
132#95×C61—24no—
133#95×C61—24no—
134#95×C61—22no—
135#95×C61—22no—
136C24×C61—22no—
137C24×C61—22no—
138C24×C61—22no—
139C24×C61—22no—
140C24×C61—28no—
141C24×C61—28no—
142C24×C61—216no—
143C24×C61—216no—
144C24×C61—28no—
145C24×C61—22no—
146C24×C61—22no—
147C24×C61—22no—
148C24×C61—22no—
149C24×C61—22no—
150C24×C61—22no—
151C24×C61—22no—
152C24×C61—22no—
153C24×C61—22no—
154C24×C61—22no—
155C24×C61—22no—
156C24×C61—22no—
157C24×C61—28no—
158C24×C61—28no—
159C24×C61—21no—
160C24×C61—22no—
161C24×C61—21no—
162C24×C61—21no—
163C24×C61—21no—
164C24×C61—21no—
165C24×C61—21no—
166C24×C61—22no—
167C24×C61—22no—
168C24×C61—22no—
169C24×C61—48no—
170C24×C61—48no—
171C24×C61—48no—
172C24×C61—48no—
173C24×C61—48no—
174C24×C61—48no—
175C24×C61—48no—
176C24×C61—48no—
177C24×C61—48no—
178C24×C61—44no—
179C24×C61—44no—
180C24×C61—48no—
181C24×C61—44no—
182C24×C61—44no—
183C24×C61—44no—
184C24×C61—44no—
185C24×C61C22×C412yes—
186C24×C61C22×C414yes—
187C24×C61C22×C412yes—
188C24×C61C2×D414yes—
189C24×C61C2×D412yes—
190C24×C61C2×D412yes—
191C24×C61C2×D412yes—
192C24×C61C2×D412yes—
193C24×C61#4114yes—
194C24×C61#4112yes—
195C24×C61#4112yes—
196C24×C61C2411yescharacteristic
197C2×D4×C61—28no—
198C2×D4×C61—28no—
199C2×D4×C61—28no—
200C2×D4×C61—216no—
201C2×D4×C61—216no—
202C2×D4×C61—48no—
203C2×D4×C61—48no—
204C2×D4×C61—48no—
205C2×D4×C61—48no—
206C2×D4×C61—48no—
207C2×D4×C61—44no—
208C2×D4×C61—44no—
209C2×D4×C61—44no—
210C2×D4×C61—44no—
211C22×C4×C61—21no—
212C22×C4×C61—22no—
213C22×C4×C61—21no—
214C22×C4×C61—22no—
215C22×C4×C61—22no—
216C22×C4×C61—22no—
217C22×C4×C61—22no—
218C22×C4×C61—28no—
219C22×C4×C61—28no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—22no—
224C22×C4×C61—22no—
225C22×C4×C61—22no—
226C22×C4×C61—22no—
227C22×C4×C61—22no—
228C22×C4×C61—22no—
229C22×C4×C61—22no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—22no—
233C22×C4×C61—22no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—22no—
238C22×C4×C61—22no—
239C22×C4×C61—22no—
240C22×C4×C61—22no—
241C22×C4×C61—22no—
242C22×C4×C61—28no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—22no—
249C22×C4×C61—21no—
250C22×C4×C61—22no—
251C22×C4×C61—22no—
252C22×C4×C61—22no—
253C22×C4×C61—44no—
254C22×C4×C61—48no—
255C22×C4×C61—48no—
256C22×C4×C61—48no—
257C22×C4×C61—48no—
258C22×C4×C61—44no—
259C22×C4×C61—44no—
260C22×C4×C61C22×C412yes—
261C22×C4×C61C22×C414yes—
262C22×C4×C61C2×D414yes—
263C22×C4×C61C2×D412yes—
264C22×C4×C61C2×D414yes—
265C22×C4×C61C2×D414yes—
266C22×C4×C61C2×D414yes—
267C22×C4×C61C2×D412yes—
268C22×C4×C61C2×D414yes—
269C4⋊C4×C61—48no—
270C22⋊C4×C61—216no—
271C22⋊C4×C61—28no—
272C22⋊C4×C61—216no—
273C22⋊C4×C61—216no—
274C22⋊C4×C61—48no—
275C22⋊C4×C61—48no—
276C22⋊C4×C61—48no—
277C22⋊C4×C61—44no—
278C22⋊C4×C61—44no—
279C22⋊C4×C61—44no—
280C22⋊C4×C61C22⋊C4116yescomplemented
281C42×C61—48no—
282C23×C61—24no—
283C23×C61—24no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—24no—
287C23×C61—22no—
288C23×C61—22no—
289C23×C61—24no—
290C23×C61—24no—
291C23×C61—24no—
292C23×C61—24no—
293C23×C61—24no—
294C23×C61—24no—
295C23×C61—24no—
296C23×C61—24no—
297C23×C61—24no—
298C23×C61—232no—
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—24no—
308C23×C61—24no—
309C23×C61—24no—
310C23×C61—24no—
311C23×C61—24no—
312C23×C61—24no—
313C23×C61—24no—
314C23×C61—24no—
315C23×C61—24no—
316C23×C61—24no—
317C23×C61—22no—
318C23×C61—22no—
319C23×C61—24no—
320C23×C61—22no—
321C23×C61—24no—
322C23×C61—432no—
323C23×C61—432no—
324C23×C61—416no—
325C23×C61—416no—
326C23×C61—416no—
327C23×C61—432no—
328C23×C61—416no—
329C23×C61—432no—
330C23×C61—416no—
331C23×C61—42no—
332C23×C61—42no—
333C23×C61—42no—
334C23×C61—42no—
335C23×C61—42no—
336C23×C61—42no—
337C23×C61—42no—
338C23×C61—42no—
339C23×C61—42no—
340C23×C61—42no—
341C23×C61—42no—
342C23×C61—42no—
343C23×C61—42no—
344C23×C61—42no—
345C23×C61—42no—
346C23×C61—42no—
347C23×C61—416no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61—42no—
353C23×C61—41no—
354C23×C61—41no—
355C23×C61—41no—
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×C61C2×C22⋊C414yes—
367C23×C61C4×D418yes—
368C23×C61C4×D414yes—
369C23×C61C4×D414yes—
370C23×C61#12114yes—
371C23×C61#12114yes—
372C23×C61#12414yes—
373C23×C61#12714yes—
374C23×C61C23×C411yescharacteristic
375C23×C61C22×D411yescharacteristic
376C23×C61C22×D411yescharacteristic
377C23×C61C22×D411yescharacteristic
378C23×C61C22×D412yes—
379C23×C61C22×D411yescharacteristic
380C23×C61C2×#4111yescharacteristic
381C23×C61C2×#4111yescharacteristic
382C23×C61C2×#4112yes—
383C23×C61H(5,𝔽2)12yes—
384C23×C61H(5,𝔽2)12yes—
385D4×C61—432no—
386D4×C61—416no—
387C2×C4×C61—24no—
388C2×C4×C61—24no—
389C2×C4×C61—22no—
390C2×C4×C61—22no—
391C2×C4×C61—24no—
392C2×C4×C61—24no—
393C2×C4×C61—24no—
394C2×C4×C61—24no—
395C2×C4×C61—24no—
396C2×C4×C61—24no—
397C2×C4×C61—22no—
398C2×C4×C61—22no—
399C2×C4×C61—22no—
400C2×C4×C61—22no—
401C2×C4×C61—24no—
402C2×C4×C61—24no—
403C2×C4×C61—22no—
404C2×C4×C61—22no—
405C2×C4×C61—24no—
406C2×C4×C61—24no—
407C2×C4×C61—24no—
408C2×C4×C61—24no—
409C2×C4×C61—416no—
410C2×C4×C61—416no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61—42no—
414C2×C4×C61—41no—
415C2×C4×C61—42no—
416C2×C4×C61—41no—
417C2×C4×C61—42no—
418C2×C4×C61—42no—
419C2×C4×C61—42no—
420C2×C4×C61—42no—
421C2×C4×C61—42no—
422C2×C4×C61—42no—
423C2×C4×C61—42no—
424C2×C4×C61—42no—
425C2×C4×C61—41no—
426C2×C4×C61—41no—
427C2×C4×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61—42no—
432C2×C4×C61—42no—
433C2×C4×C61—42no—
434C2×C4×C61—42no—
435C2×C4×C61C2×C22⋊C418yescomplemented
436C2×C4×C61#12014yescomplemented
437#13995C6111yesmaximal, characteristic, direct product factor, Sylow
438C22×C61—24no—
439C22×C61—28no—
440C22×C61—28no—
441C22×C61—24no—
442C22×C61—24no—
443C22×C61—28no—
444C22×C61—24no—
445C22×C61—28no—
446C22×C61—24no—
447C22×C61—24no—
448C22×C61—28no—
449C22×C61—28no—
450C22×C61—28no—
451C22×C61—464no—
452C22×C61—44no—
453C22×C61—44no—
454C22×C61—44no—
455C22×C61—44no—
456C22×C61—44no—
457C22×C61—44no—
458C22×C61—44no—
459C22×C61—44no—
460C22×C61—44no—
461C22×C61—44no—
462C22×C61—44no—
463C22×C61—44no—
464C22×C61—42no—
465C22×C61—44no—
466C22×C61—44no—
467C22×C61—42no—
468C22×C61—42no—
469C22×C61—81no—
470C22×C61—81no—
471C22×C61—82no—
472C22×C61—81no—
473C22×C61—82no—
474C22×C61—81no—
475C22×C61#39018yescomplemented
476C22×C61C22×C22⋊C411yescharacteristic
477C22×C61C2×C4×D411yescharacteristic
478C22×C61C2×C4×D412yes—
479C22×C61C2×C4×D411yescharacteristic
480C22×C61#51812yes—
481C22×C61C2×#12011yescharacteristic
482C22×C61C2×#12111yescharacteristic
483C22×C61C2×#12111yescharacteristic
484C22×C61#52511yescharacteristic
485C22×C61#52512yes—
486C22×C61C2×#12411yescharacteristic
487C22×C61C2×#12711yescharacteristic
488C22×C61#53411yescharacteristic
489C22×C61#53511yescharacteristic
490C22×C61#53812yes—
491C22×C61D4212yes—
492C22×C61D4212yes—
493C22×C61D4212yes—
494C22×C61#54612yes—
495C22×C61#54612yes—
496C22×C61#54612yes—
497C22×C61#54612yes—
498C22×C61#55112yes—
499C4×C61—28no—
500C4×C61—24no—
501C4×C61—42no—
502C4×C61—44no—
503C4×C61—44no—
504C4×C61—42no—
505C4×C61—81no—
506C4×C61—81no—
507C22×#120C2×C6111yescharacteristic
508C23×C22⋊C4C2×C6111yescharacteristic, complemented
509C2×#390C2×C6112yescomplemented
510C2×#386C2×C6111yescharacteristic, complemented
511C2×#386C2×C6111yescharacteristic, complemented
512C2×#385C2×C6111yescharacteristic, complemented
513C2×#379C2×C6111yescharacteristic, complemented
514C2×C4×C22⋊C4C2×C6111yescharacteristic, complemented
515#1439C2×C6112yescomplemented
516#1438C2×C6112yescomplemented
517#1437C2×C6112yescomplemented
518C2×C61—28no—
519C2×C61—48no—
520C2×C61—82no—
521C2×C61C2×#39011yescharacteristic
522C2×C61C4×#12011yescharacteristic
523C2×C61#232111yescharacteristic
524C2×C61D4×C22⋊C412yes—
525C2×C61#235812yes—
526C2×C61#241011yescharacteristic
527C2×C61#241111yescharacteristic
528C2×C61#242412yes—
529C2×C61#243311yescharacteristic
530C2×C61#247212yes—
531C2×C61#253911yescharacteristic
532C26C22×C6111yescharacteristic
533C23×D4C22×C6111yescharacteristic
534C23×D4C22×C6112yes—
535C24×C4C22×C6111yescharacteristic
536C24×C4C22×C6111yescharacteristic
537C2×#120—24no—
538C2×#120—24no—
539C2×#120C4×C6118yescomplemented
540C22×C4⋊C4C22×C6112yescomplemented
541C22×C22⋊C4—24no—
542C22×C22⋊C4—28no—
543C22×C22⋊C4C22×C6112yes—
544C22×C22⋊C4C22×C6111yescharacteristic
545C22×C22⋊C4C22×C6112yes—
546C22×C22⋊C4C22×C6112yes—
547C22×C22⋊C4C22×C6112yes—
548C22×C22⋊C4C22×C6112yes—
549C22×C22⋊C4C22×C6111yescharacteristic
550C22×C22⋊C4C22×C6111yescharacteristic
551C22×C22⋊C4C22×C6111yescharacteristic, complemented
552C22×C22⋊C4C22×C6112yescomplemented
553C22×C22⋊C4C22×C6111yescharacteristic, complemented
554C22×C42C22×C6112yescomplemented
555#390—28no—
556#386—24no—
557#386—24no—
558#385—24no—
559#379—24no—
560C4×C22⋊C4—24no—
561C2×#95C22×C6111yescharacteristic, complemented
562C2×#95C22×C6112yescomplemented
563C2×#95C22×C6112yescomplemented
564C2×#95C22×C6112yescomplemented
565C2×#95C22×C6111yescharacteristic, complemented
566C61#1399511yescharacteristic, direct product factor, Sylow
567C25—24no—
568C25—22no—
569C25—24no—
570C25—22no—
571C25—22no—
572C25—22no—
573C25—22no—
574C25—22no—
575C25—42no—
576C25—42no—
577C25C2×C4×C6114yes—
578C25C23×C6111yescharacteristic
579C25C23×C6112yes—
580C25C23×C6111yescharacteristic
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—22no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—24no—
590C22×D4—24no—
591C22×D4—42no—
592C22×D4—42no—
593C22×D4C2×C4×C6114yes—
594C22×D4C2×C4×C6118yescomplemented
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—24no—
599C23×C4—24no—
600C23×C4—22no—
601C23×C4—22no—
602C23×C4—42no—
603C23×C4—42no—
604C23×C4D4×C6114yescomplemented
605C23×C4C23×C6111yescharacteristic
606C23×C4C23×C6111yescharacteristic
607C23×C4C23×C6111yescharacteristic
608C23×C4C23×C6112yes—
609C23×C4C23×C6112yes—
610C23×C4C23×C6111yescharacteristic
611C23×C4C23×C6112yes—
612C23×C4C23×C6111yescharacteristic
613#120—232no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—42no—
617C2×C22⋊C4—232no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—24no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—24no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4—42no—
643C2×C22⋊C4C2×C4×C6114yes—
644C2×C22⋊C4C2×C4×C6118yescomplemented
645C2×C22⋊C4D4×C6114yes—
646C2×C22⋊C4D4×C6114yes—
647C2×C22⋊C4D4×C6118yescomplemented
648C2×C22⋊C4D4×C6114yescomplemented
649C2×C42—24no—
650C2×C42—24no—
651C2×C42—42no—
652#95—24no—
653#95—24no—
654#95—24no—
655#95—22no—
656#95—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—28no—
662C24—28no—
663C24—216no—
664C24—216no—
665C24—28no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—28no—
679C24—28no—
680C24—21no—
681C24—21no—
682C24—22no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—22no—
687C24—21no—
688C24—22no—
689C24—22no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—48no—
699C24—44no—
700C24—44no—
701C24—48no—
702C24—44no—
703C24—44no—
704C24—44no—
705C24—44no—
706C24C22×C4×C6112yes—
707C24C22×C4×C6114yes—
708C24C22×C4×C6112yes—
709C24C2×D4×C6114yes—
710C24C2×D4×C6112yes—
711C24C2×D4×C6112yes—
712C24C2×D4×C6112yes—
713C24C2×D4×C6112yes—
714C24#41×C6114yes—
715C24#41×C6112yes—
716C24#41×C6112yes—
717C24C24×C6111yescharacteristic
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—216no—
722C2×D4—216no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—28no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—44no—
775C22×C4—48no—
776C22×C4—48no—
777C22×C4—48no—
778C22×C4—48no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4C22×C4×C6112yes—
782C22×C4C22×C4×C6114yes—
783C22×C4C2×D4×C6114yes—
784C22×C4C2×D4×C6112yes—
785C22×C4C2×D4×C6114yes—
786C22×C4C2×D4×C6114yes—
787C22×C4C2×D4×C6114yes—
788C22×C4C2×D4×C6112yes—
789C22×C4C2×D4×C6114yes—
790C4⋊C4—48no—
791C22⋊C4—216no—
792C22⋊C4—28no—
793C22⋊C4—216no—
794C22⋊C4—216no—
795C22⋊C4—48no—
796C22⋊C4—48no—
797C22⋊C4—48no—
798C22⋊C4—44no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4C22⋊C4×C61116yescomplemented
802C42—48no—
803C23—22no—
804C23—22no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—22no—
817C23—22no—
818C23—24no—
819C23—232no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—24no—
842C23—24no—
843C23—432no—
844C23—432no—
845C23—416no—
846C23—416no—
847C23—416no—
848C23—416no—
849C23—432no—
850C23—416no—
851C23—432no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—416no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—42no—
886C23—41no—
887C23C2×C22⋊C4×C6114yes—
888C23C4×D4×C6118yes—
889C23C4×D4×C6114yes—
890C23C4×D4×C6114yes—
891C23#121×C6114yes—
892C23#121×C6114yes—
893C23#124×C6114yes—
894C23#127×C6114yes—
895C23C23×C4×C6111yescharacteristic
896C23C22×D4×C6111yescharacteristic
897C23C22×D4×C6111yescharacteristic
898C23C22×D4×C6111yescharacteristic
899C23C22×D4×C6112yes—
900C23C22×D4×C6111yescharacteristic
901C23C2×#41×C6111yescharacteristic
902C23C2×#41×C6112yes—
903C23C2×#41×C6111yescharacteristic
904C23H(5,𝔽2)×C6112yes—
905C23H(5,𝔽2)×C6112yes—
906D4—432no—
907D4—416no—
908C2×C4—22no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—22no—
930C2×C4—416no—
931C2×C4—416no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—42no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4C2×C22⋊C4×C6118yescomplemented
957C2×C4#120×C6114yescomplemented
958C22—24no—
959C22—24no—
960C22—24no—
961C22—28no—
962C22—28no—
963C22—24no—
964C22—24no—
965C22—28no—
966C22—24no—
967C22—28no—
968C22—28no—
969C22—28no—
970C22—28no—
971C22—464no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—44no—
977C22—44no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—44no—
982C22—44no—
983C22—44no—
984C22—42no—
985C22—42no—
986C22—42no—
987C22—44no—
988C22—44no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—82no—
993C22—81no—
994C22—82no—
995C22C61×#39018yescomplemented
996C22C22×C22⋊C4×C6111yescharacteristic
997C22C2×C4×D4×C6111yescharacteristic
998C22C2×C4×D4×C6111yescharacteristic
999C22C2×C4×D4×C6112yes—
1000C22C61×#51812yes—
1001C22C2×#120×C6111yescharacteristic
1002C22C2×#121×C6111yescharacteristic
1003C22C2×#121×C6111yescharacteristic
1004C22C61×#52511yescharacteristic
1005C22C61×#52512yes—
1006C22C2×#124×C6111yescharacteristic
1007C22C2×#127×C6111yescharacteristic
1008C22C61×#53411yescharacteristic
1009C22C61×#53511yescharacteristic
1010C22C61×#53812yes—
1011C22D42×C6112yes—
1012C22D42×C6112yes—
1013C22D42×C6112yes—
1014C22C61×#54612yes—
1015C22C61×#54612yes—
1016C22C61×#54612yes—
1017C22C61×#54612yes—
1018C22C61×#55112yes—
1019C4—28no—
1020C4—24no—
1021C4—42no—
1022C4—42no—
1023C4—44no—
1024C4—44no—
1025C4—81no—
1026C4—81no—
1027C2—28no—
1028C2—48no—
1029C2—82no—
1030C2C2×C61×#39011yescharacteristic
1031C2C4×#120×C6111yescharacteristic
1032C2C61×#232111yescharacteristic
1033C2D4×C22⋊C4×C6112yes—
1034C2C61×#235812yes—
1035C2C61×#241011yescharacteristic
1036C2C61×#241111yescharacteristic
1037C2C61×#242412yes—
1038C2C61×#243311yescharacteristic
1039C2C61×#247212yes—
1040C2C61×#253911yescharacteristic
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. C23×C22⋊C4×C61C2semidirect
3. C2×C61×#390C2semidirect
4. C2×C61×#386C2semidirect
5. C2×C61×#386C2semidirect
6. C2×C61×#385C2semidirect
7. C2×C61×#379C2semidirect
8. C2×C4×C22⋊C4×C61C2semidirect
9. C61×#1439C2semidirect
10. C61×#1438C2semidirect
11. C61×#1437C2semidirect
19. C2×#120×C61C4semidirect
20. C22×C4⋊C4×C61C22semidirect
31. C22×C22⋊C4×C61C22semidirect
32. C22×C22⋊C4×C61C22semidirect
33. C22×C22⋊C4×C61C22semidirect
34. C22×C42×C61C22semidirect
41. C2×#95×C61C22semidirect
42. C2×#95×C61C22semidirect
43. C2×#95×C61C22semidirect
44. C2×#95×C61C22semidirect
45. C2×#95×C61C22semidirect
73. C22×D4×C61C2×C4semidirect
83. C23×C4×C61D4semidirect
123. C2×C22⋊C4×C61C2×C4semidirect
126. C2×C22⋊C4×C61D4semidirect
127. C2×C22⋊C4×C61D4semidirect
280. C22⋊C4×C61C22⋊C4semidirect
435. C2×C4×C61C2×C22⋊C4semidirect
436. C2×C4×C61#120semidirect
437. #13995C61direct (N × H)
475. C22×C61#390semidirect
508. C23×C22⋊C4C2×C61semidirect
509. C2×#390C2×C61semidirect
510. C2×#386C2×C61semidirect
511. C2×#386C2×C61semidirect
512. C2×#385C2×C61semidirect
513. C2×#379C2×C61semidirect
514. C2×C4×C22⋊C4C2×C61semidirect
515. #1439C2×C61semidirect
516. #1438C2×C61semidirect
517. #1437C2×C61semidirect
539. C2×#120C4×C61semidirect
540. C22×C4⋊C4C22×C61semidirect
551. C22×C22⋊C4C22×C61semidirect
552. C22×C22⋊C4C22×C61semidirect
553. C22×C22⋊C4C22×C61semidirect
554. C22×C42C22×C61semidirect
561. C2×#95C22×C61semidirect
562. C2×#95C22×C61semidirect
563. C2×#95C22×C61semidirect
564. C2×#95C22×C61semidirect
565. C2×#95C22×C61semidirect
566. C61#13995direct (N × H)
594. C22×D4C2×C4×C61semidirect
604. C23×C4D4×C61semidirect
644. C2×C22⋊C4C2×C4×C61semidirect
647. C2×C22⋊C4D4×C61semidirect
648. C2×C22⋊C4D4×C61semidirect
801. C22⋊C4C22⋊C4×C61semidirect
956. C2×C4C2×C22⋊C4×C61semidirect
957. C2×C4#120×C61semidirect
995. C22C61×#390semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C612
C23×C22⋊C4×C612
C2×C61×#3902
C2×C61×#3862
C2×C61×#3852
C2×C61×#3792
C2×C4×C22⋊C4×C612
C61×#14392
C61×#14382
C61×#14372
#1399561