Finite Group Databasebeta

← C61×#13970 #29517403

Subgroups — C61×#13970 #29517403

Order 15616.

3058 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C61C211yesmaximal, characteristic
2C22×C4×D4×C61C211yesmaximal, characteristic, complemented
3C2×C61×#390C211yesmaximal, characteristic, complemented
4C2×C61×#386C212yesmaximal, complemented
5C2×C61×#380C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
7C61×#1440C212yesmaximal, complemented
8C61×#1438C212yesmaximal, complemented
9C61×C4⋊#95C211yesmaximal, characteristic, complemented
10C61×C4⋊#95C211yesmaximal, characteristic, complemented
11C61×C22⋊#95C212yesmaximal, complemented
12C23×D4×C61C2212yes—
13C23×D4×C61C2211yescharacteristic
14C24×C4×C61C2211yescharacteristic
15C24×C4×C61C2212yes—
16C2×#121×C61—24no—
17C2×#121×C61—24no—
18C2×#121×C61C418yescomplemented
19C2×C4×D4×C61—24no—
20C2×C4×D4×C61—24no—
21C2×C4×D4×C61—24no—
22C22×C4⋊C4×C61C2211yescharacteristic
23C22×C4⋊C4×C61C2211yescharacteristic
24C22×C4⋊C4×C61C2211yescharacteristic
25C22×C22⋊C4×C61C2211yescharacteristic
26C22×C22⋊C4×C61C2212yes—
27C22×C22⋊C4×C61C2212yes—
28C22×C22⋊C4×C61C2212yes—
29C22×C22⋊C4×C61C2212yes—
30C22×C22⋊C4×C61C2212yes—
31C22×C22⋊C4×C61C2211yescharacteristic
32C22×C42×C61C2211yescharacteristic
33C22×C42×C61C2211yescharacteristic
34C61×#390—24no—
35C61×#386—28no—
36C61×#380—24no—
37C4×C22⋊C4×C61—24no—
38C2×#95×C61C2211yescharacteristic
39C2×#95×C61C2211yescharacteristic
40C2×#95×C61C2212yes—
41C2×#95×C61C2212yes—
42C2×#95×C61C2212yes—
43C2×#95×C61C2212yes—
44C2×#95×C61C2212yes—
45C25×C61C2312yes—
46C25×C61C2311yescharacteristic
47C22×D4×C61—24no—
48C22×D4×C61—24no—
49C22×D4×C61—24no—
50C22×D4×C61—24no—
51C22×D4×C61—22no—
52C22×D4×C61—22no—
53C22×D4×C61—22no—
54C22×D4×C61—22no—
55C22×D4×C61—42no—
56C22×D4×C61—42no—
57C22×D4×C61C2×C414yes—
58C22×D4×C61C2×C418yescomplemented
59C22×D4×C61D414yes—
60C22×D4×C61D414yes—
61C23×C4×C61—24no—
62C23×C4×C61—22no—
63C23×C4×C61—22no—
64C23×C4×C61—24no—
65C23×C4×C61—24no—
66C23×C4×C61—22no—
67C23×C4×C61—22no—
68C23×C4×C61—22no—
69C23×C4×C61—22no—
70C23×C4×C61—24no—
71C23×C4×C61—24no—
72C23×C4×C61—42no—
73C23×C4×C61—42no—
74C23×C4×C61C2×C414yescomplemented
75C23×C4×C61C2312yes—
76C23×C4×C61C2311yescharacteristic
77C23×C4×C61C2312yes—
78C23×C4×C61C2312yes—
79C23×C4×C61C2311yescharacteristic
80C23×C4×C61C2311yescharacteristic
81C23×C4×C61C2311yescharacteristic
82C23×C4×C61C2311yescharacteristic
83C23×C4×C61C2311yescharacteristic
84#121×C61—232no—
85C4×D4×C61—232no—
86C2×C4⋊C4×C61—22no—
87C2×C4⋊C4×C61—22no—
88C2×C4⋊C4×C61—22no—
89C2×C4⋊C4×C61—22no—
90C2×C4⋊C4×C61—22no—
91C2×C4⋊C4×C61—22no—
92C2×C4⋊C4×C61—22no—
93C2×C4⋊C4×C61C2×C414yescomplemented
94C2×C4⋊C4×C61D414yescomplemented
95C2×C22⋊C4×C61—24no—
96C2×C22⋊C4×C61—24no—
97C2×C22⋊C4×C61—24no—
98C2×C22⋊C4×C61—22no—
99C2×C22⋊C4×C61—22no—
100C2×C22⋊C4×C61—22no—
101C2×C22⋊C4×C61—24no—
102C2×C22⋊C4×C61—24no—
103C2×C22⋊C4×C61—22no—
104C2×C22⋊C4×C61—22no—
105C2×C22⋊C4×C61—24no—
106C2×C22⋊C4×C61—24no—
107C2×C22⋊C4×C61—24no—
108C2×C22⋊C4×C61—24no—
109C2×C22⋊C4×C61—24no—
110C2×C22⋊C4×C61—24no—
111C2×C22⋊C4×C61—42no—
112C2×C22⋊C4×C61—42no—
113C2×C22⋊C4×C61—42no—
114C2×C22⋊C4×C61C2×C418yescomplemented
115C2×C22⋊C4×C61D414yescomplemented
116C2×C42×C61—22no—
117C2×C42×C61—22no—
118C2×C42×C61—22no—
119C2×C42×C61—22no—
120C2×C42×C61—22no—
121C2×C42×C61D414yescomplemented
122#95×C61—22no—
123#95×C61—22no—
124#95×C61—24no—
125#95×C61—24no—
126#95×C61—24no—
127#95×C61—42no—
128#95×C61—42no—
129C24×C61—21no—
130C24×C61—21no—
131C24×C61—22no—
132C24×C61—22no—
133C24×C61—22no—
134C24×C61—21no—
135C24×C61—21no—
136C24×C61—21no—
137C24×C61—21no—
138C24×C61—22no—
139C24×C61—21no—
140C24×C61—21no—
141C24×C61—22no—
142C24×C61—22no—
143C24×C61—22no—
144C24×C61—22no—
145C24×C61—21no—
146C24×C61—22no—
147C24×C61—22no—
148C24×C61—22no—
149C24×C61—21no—
150C24×C61—21no—
151C24×C61—22no—
152C24×C61—21no—
153C24×C61C22×C414yes—
154C24×C61C22×C412yes—
155C24×C61C2×D414yes—
156C24×C61C2×D414yes—
157C24×C61C2×D412yes—
158C24×C61#4112yes—
159C24×C61C2411yescharacteristic
160C2×D4×C61—216no—
161C2×D4×C61—216no—
162C2×D4×C61—28no—
163C2×D4×C61—28no—
164C2×D4×C61—28no—
165C2×D4×C61—28no—
166C2×D4×C61—28no—
167C2×D4×C61—28no—
168C2×D4×C61—48no—
169C2×D4×C61—48no—
170C2×D4×C61—48no—
171C2×D4×C61—48no—
172C2×D4×C61—48no—
173C2×D4×C61C22⋊C4116yescomplemented
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—216no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—22no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—22no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—22no—
204C22×C4×C61—22no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—22no—
208C22×C4×C61—22no—
209C22×C4×C61—22no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—22no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—28no—
216C22×C4×C61—28no—
217C22×C4×C61—28no—
218C22×C4×C61—22no—
219C22×C4×C61—22no—
220C22×C4×C61—22no—
221C22×C4×C61—22no—
222C22×C4×C61—22no—
223C22×C4×C61—22no—
224C22×C4×C61—22no—
225C22×C4×C61—48no—
226C22×C4×C61—48no—
227C22×C4×C61—48no—
228C22×C4×C61—48no—
229C22×C4×C61—48no—
230C22×C4×C61—44no—
231C22×C4×C61—44no—
232C22×C4×C61—44no—
233C22×C4×C61—48no—
234C22×C4×C61—44no—
235C22×C4×C61C22×C412yes—
236C22×C4×C61C22×C414yes—
237C22×C4×C61C22×C412yes—
238C22×C4×C61C2×D412yes—
239C22×C4×C61C2×D412yes—
240C22×C4×C61C2×D414yes—
241C22×C4×C61C2×D412yes—
242C22×C4×C61C2×D412yes—
243C22×C4×C61C2×D412yes—
244C22×C4×C61C2×D412yes—
245C22×C4×C61C2×D412yes—
246C22×C4×C61C2×D412yes—
247C22×C4×C61#4112yes—
248C22×C4×C61#4112yes—
249C22×C4×C61#4112yes—
250C22×C4×C61#4112yes—
251C4⋊C4×C61—28no—
252C4⋊C4×C61—28no—
253C4⋊C4×C61—44no—
254C22⋊C4×C61—28no—
255C22⋊C4×C61—216no—
256C22⋊C4×C61—216no—
257C22⋊C4×C61—28no—
258C22⋊C4×C61—48no—
259C22⋊C4×C61—48no—
260C22⋊C4×C61—48no—
261C42×C61—28no—
262C42×C61—44no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—24no—
267C23×C61—24no—
268C23×C61—24no—
269C23×C61—24no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—24no—
273C23×C61—24no—
274C23×C61—22no—
275C23×C61—24no—
276C23×C61—22no—
277C23×C61—24no—
278C23×C61—24no—
279C23×C61—24no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—24no—
285C23×C61—24no—
286C23×C61—22no—
287C23×C61—22no—
288C23×C61—24no—
289C23×C61—24no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—24no—
293C23×C61—24no—
294C23×C61—24no—
295C23×C61—24no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61—41no—
300C23×C61—42no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—42no—
305C23×C61—42no—
306C23×C61—42no—
307C23×C61—42no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—42no—
311C23×C61—41no—
312C23×C61—42no—
313C23×C61—41no—
314C23×C61—42no—
315C23×C61—42no—
316C23×C61—42no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61—42no—
323C23×C61—42no—
324C23×C61—41no—
325C23×C61—42no—
326C23×C61—42no—
327C23×C61—41no—
328C23×C61—42no—
329C23×C61—41no—
330C23×C61—42no—
331C23×C61C2×C22⋊C418yes—
332C23×C61C4×D414yescomplemented
333C23×C61C23×C411yescharacteristic
334C23×C61C22×D411yescharacteristic
335C23×C61C22×D411yescharacteristic
336C23×C61C22×D411yescharacteristic
337C23×C61C22×D411yescharacteristic
338C23×C61C22×D411yescharacteristic
339C23×C61C2×#4111yescharacteristic
340C23×C61C2×#4111yescharacteristic
341C23×C61C2×#4111yescharacteristic
342C23×C61C2×#4111yescharacteristic
343C23×C61C2×#4111yescharacteristic
344C23×C61H(5,𝔽2)11yescharacteristic
345C23×C61H(5,𝔽2)11yescharacteristic
346C23×C61H(5,𝔽2)11yescharacteristic
347C23×C612−1+411yescharacteristic
348D4×C61—232no—
349D4×C61—432no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—24no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—24no—
361C2×C4×C61—24no—
362C2×C4×C61—22no—
363C2×C4×C61—24no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—24no—
370C2×C4×C61—22no—
371C2×C4×C61—24no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—432no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—42no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—42no—
384C2×C4×C61—41no—
385C2×C4×C61—42no—
386C2×C4×C61—42no—
387C2×C4×C61—42no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—42no—
391C2×C4×C61—42no—
392C2×C4×C61—42no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—416no—
400C2×C4×C61—42no—
401C2×C4×C61—42no—
402C2×C4×C61—42no—
403C2×C4×C61—42no—
404C2×C4×C61—42no—
405C2×C4×C61—42no—
406C2×C4×C61—42no—
407C2×C4×C61C2×C22⋊C414yes—
408C2×C4×C61C4×D414yes—
409C2×C4×C61C4×D414yes—
410C2×C4×C61#12014yes—
411C2×C4×C61#12114yes—
412C2×C4×C61#12114yes—
413C2×C4×C61#12114yescomplemented
414C2×C4×C61#12314yes—
415#13970C6111yesmaximal, characteristic, direct product factor, Sylow
416C22×C61—24no—
417C22×C61—28no—
418C22×C61—28no—
419C22×C61—24no—
420C22×C61—28no—
421C22×C61—24no—
422C22×C61—42no—
423C22×C61—44no—
424C22×C61—42no—
425C22×C61—44no—
426C22×C61—42no—
427C22×C61—44no—
428C22×C61—44no—
429C22×C61—42no—
430C22×C61—44no—
431C22×C61—42no—
432C22×C61—44no—
433C22×C61—42no—
434C22×C61—44no—
435C22×C61—42no—
436C22×C61—44no—
437C22×C61—42no—
438C22×C61—44no—
439C22×C61—42no—
440C22×C61—44no—
441C22×C61—42no—
442C22×C61—42no—
443C22×C61—44no—
444C22×C61—42no—
445C22×C61—44no—
446C22×C61C22×C22⋊C411yescharacteristic
447C22×C61C2×C4×D411yescharacteristic
448C22×C61C2×C4×D411yescharacteristic
449C22×C61C2×C4×D411yescharacteristic
450C22×C61C4×#4111yescharacteristic
451C22×C61#51811yescharacteristic
452C22×C61#52011yescharacteristic
453C22×C61C2×#12011yescharacteristic
454C22×C61C2×#12111yescharacteristic
455C22×C61C2×#12111yescharacteristic
456C22×C61C2×#12111yescharacteristic
457C22×C61C2×#12311yescharacteristic
458C22×C61#52511yescharacteristic
459C22×C61#52911yescharacteristic
460C22×C61#53211yescharacteristic
461C22×C61#53511yescharacteristic
462C22×C61#53711yescharacteristic
463C22×C61#54011yescharacteristic
464C22×C61#54211yescharacteristic
465C22×C61D4211yescharacteristic
466C22×C61D4211yescharacteristic
467C22×C61D4211yescharacteristic
468C22×C61#54611yescharacteristic
469C22×C61#54611yescharacteristic
470C22×C61#54611yescharacteristic
471C22×C61#54611yescharacteristic
472C22×C61#54611yescharacteristic
473C22×C61#54711yescharacteristic
474C22×C61#54711yescharacteristic
475C22×C61#54711yescharacteristic
476C22×C61#54811yescharacteristic
477C22×C61#55011yescharacteristic
478C22×C61#55311yescharacteristic
479C22×C61#55311yescharacteristic
480C22×C61#55511yescharacteristic
481C4×C61—24no—
482C4×C61—44no—
483C4×C61—42no—
484C4×C61—44no—
485C4×C61—42no—
486C4×C61—42no—
487C4×C61—42no—
488C4×C61—82no—
489C4×C61#38618yescomplemented
490C22×#121C2×C6111yescharacteristic
491C22×C4×D4C2×C6111yescharacteristic, complemented
492C2×#390C2×C6111yescharacteristic, complemented
493C2×#386C2×C6112yescomplemented
494C2×#380C2×C6111yescharacteristic, complemented
495C2×C4×C22⋊C4C2×C6111yescharacteristic, complemented
496#1440C2×C6112yescomplemented
497#1438C2×C6112yescomplemented
498C4⋊#95C2×C6111yescharacteristic, complemented
499C4⋊#95C2×C6111yescharacteristic, complemented
500C22⋊#95C2×C6112yescomplemented
501C2×C61—44no—
502C2×C61—48no—
503C2×C61C2×#38611yescharacteristic
504C2×C61C4×#12111yescharacteristic
505C2×C61#232411yescharacteristic
506C2×C61D4×C22⋊C411yescharacteristic
507C2×C61#233911yescharacteristic
508C2×C61#236111yescharacteristic
509C2×C61#236311yescharacteristic
510C2×C61#240711yescharacteristic
511C2×C61#240811yescharacteristic
512C2×C61#242011yescharacteristic
513C2×C61#242211yescharacteristic
514C2×C61#242711yescharacteristic
515C2×C61#242811yescharacteristic
516C2×C61#253511yescharacteristic
517C2×C61#253711yescharacteristic
518C23×D4C22×C6112yes—
519C23×D4C22×C6111yescharacteristic
520C24×C4C22×C6111yescharacteristic
521C24×C4C22×C6112yes—
522C2×#121—24no—
523C2×#121—24no—
524C2×#121C4×C6118yescomplemented
525C2×C4×D4—24no—
526C2×C4×D4—24no—
527C2×C4×D4—24no—
528C22×C4⋊C4C22×C6111yescharacteristic
529C22×C4⋊C4C22×C6111yescharacteristic
530C22×C4⋊C4C22×C6111yescharacteristic
531C22×C22⋊C4C22×C6112yes—
532C22×C22⋊C4C22×C6111yescharacteristic
533C22×C22⋊C4C22×C6112yes—
534C22×C22⋊C4C22×C6112yes—
535C22×C22⋊C4C22×C6112yes—
536C22×C22⋊C4C22×C6112yes—
537C22×C22⋊C4C22×C6111yescharacteristic
538C22×C42C22×C6111yescharacteristic
539C22×C42C22×C6111yescharacteristic
540#390—24no—
541#386—28no—
542#380—24no—
543C4×C22⋊C4—24no—
544C2×#95C22×C6111yescharacteristic
545C2×#95C22×C6112yes—
546C2×#95C22×C6112yes—
547C2×#95C22×C6112yes—
548C2×#95C22×C6111yescharacteristic
549C2×#95C22×C6112yes—
550C2×#95C22×C6112yes—
551C61#1397011yescharacteristic, direct product factor, Sylow
552C25C23×C6112yes—
553C25C23×C6111yescharacteristic
554C22×D4—24no—
555C22×D4—24no—
556C22×D4—24no—
557C22×D4—24no—
558C22×D4—22no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—42no—
563C22×D4—42no—
564C22×D4C2×C4×C6114yes—
565C22×D4C2×C4×C6118yescomplemented
566C22×D4D4×C6114yes—
567C22×D4D4×C6114yes—
568C23×C4—24no—
569C23×C4—24no—
570C23×C4—24no—
571C23×C4—22no—
572C23×C4—22no—
573C23×C4—22no—
574C23×C4—22no—
575C23×C4—22no—
576C23×C4—22no—
577C23×C4—24no—
578C23×C4—24no—
579C23×C4—42no—
580C23×C4—42no—
581C23×C4C2×C4×C6114yescomplemented
582C23×C4C23×C6112yes—
583C23×C4C23×C6111yescharacteristic
584C23×C4C23×C6112yes—
585C23×C4C23×C6111yescharacteristic
586C23×C4C23×C6111yescharacteristic
587C23×C4C23×C6112yes—
588C23×C4C23×C6111yescharacteristic
589C23×C4C23×C6111yescharacteristic
590C23×C4C23×C6111yescharacteristic
591#121—232no—
592C4×D4—232no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4C2×C4×C6114yescomplemented
601C2×C4⋊C4D4×C6114yescomplemented
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—24no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—24no—
615C2×C22⋊C4—24no—
616C2×C22⋊C4—24no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—42no—
619C2×C22⋊C4—42no—
620C2×C22⋊C4—42no—
621C2×C22⋊C4C2×C4×C6118yescomplemented
622C2×C22⋊C4D4×C6114yescomplemented
623C2×C42—22no—
624C2×C42—22no—
625C2×C42—22no—
626C2×C42—22no—
627C2×C42—22no—
628C2×C42D4×C6114yescomplemented
629#95—22no—
630#95—22no—
631#95—24no—
632#95—24no—
633#95—24no—
634#95—42no—
635#95—42no—
636C24—21no—
637C24—21no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—22no—
645C24—21no—
646C24—21no—
647C24—22no—
648C24—21no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—21no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—21no—
657C24—21no—
658C24—22no—
659C24—21no—
660C24C22×C4×C6114yes—
661C24C22×C4×C6112yes—
662C24C2×D4×C6114yes—
663C24C2×D4×C6114yes—
664C24C2×D4×C6112yes—
665C24#41×C6112yes—
666C24C24×C6111yescharacteristic
667C2×D4—216no—
668C2×D4—216no—
669C2×D4—28no—
670C2×D4—28no—
671C2×D4—28no—
672C2×D4—28no—
673C2×D4—28no—
674C2×D4—28no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—48no—
679C2×D4—48no—
680C2×D4C22⋊C4×C61116yescomplemented
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—216no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—22no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—22no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—22no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—22no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—28no—
723C22×C4—28no—
724C22×C4—28no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—48no—
733C22×C4—48no—
734C22×C4—48no—
735C22×C4—48no—
736C22×C4—48no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—48no—
741C22×C4—44no—
742C22×C4C22×C4×C6112yes—
743C22×C4C22×C4×C6114yes—
744C22×C4C22×C4×C6112yes—
745C22×C4C2×D4×C6112yes—
746C22×C4C2×D4×C6112yes—
747C22×C4C2×D4×C6114yes—
748C22×C4C2×D4×C6112yes—
749C22×C4C2×D4×C6112yes—
750C22×C4C2×D4×C6112yes—
751C22×C4C2×D4×C6112yes—
752C22×C4C2×D4×C6112yes—
753C22×C4C2×D4×C6112yes—
754C22×C4#41×C6112yes—
755C22×C4#41×C6112yes—
756C22×C4#41×C6112yes—
757C22×C4#41×C6112yes—
758C4⋊C4—28no—
759C4⋊C4—28no—
760C4⋊C4—44no—
761C22⋊C4—216no—
762C22⋊C4—28no—
763C22⋊C4—216no—
764C22⋊C4—28no—
765C22⋊C4—48no—
766C22⋊C4—48no—
767C22⋊C4—48no—
768C42—28no—
769C42—44no—
770C23—22no—
771C23—22no—
772C23—24no—
773C23—24no—
774C23—22no—
775C23—22no—
776C23—24no—
777C23—24no—
778C23—22no—
779C23—22no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—24no—
791C23—24no—
792C23—24no—
793C23—22no—
794C23—24no—
795C23—22no—
796C23—24no—
797C23—24no—
798C23—22no—
799C23—24no—
800C23—22no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—22no—
805C23—22no—
806C23—42no—
807C23—42no—
808C23—41no—
809C23—41no—
810C23—42no—
811C23—41no—
812C23—42no—
813C23—41no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—42no—
822C23—41no—
823C23—42no—
824C23—41no—
825C23—42no—
826C23—42no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—42no—
831C23—41no—
832C23—41no—
833C23—42no—
834C23—41no—
835C23—41no—
836C23—42no—
837C23—42no—
838C23C2×C22⋊C4×C6118yes—
839C23C4×D4×C6114yescomplemented
840C23C23×C4×C6111yescharacteristic
841C23C22×D4×C6111yescharacteristic
842C23C22×D4×C6111yescharacteristic
843C23C22×D4×C6111yescharacteristic
844C23C22×D4×C6111yescharacteristic
845C23C22×D4×C6111yescharacteristic
846C23C2×#41×C6111yescharacteristic
847C23C2×#41×C6111yescharacteristic
848C23C2×#41×C6111yescharacteristic
849C23C2×#41×C6111yescharacteristic
850C23C2×#41×C6111yescharacteristic
851C23H(5,𝔽2)×C6111yescharacteristic
852C23H(5,𝔽2)×C6111yescharacteristic
853C23H(5,𝔽2)×C6111yescharacteristic
854C232−1+4×C6111yescharacteristic
855D4—232no—
856D4—432no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—24no—
866C2×C4—22no—
867C2×C4—24no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—24no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—22no—
877C2×C4—24no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—432no—
882C2×C4—41no—
883C2×C4—42no—
884C2×C4—41no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—42no—
905C2×C4—41no—
906C2×C4—416no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4C2×C22⋊C4×C6114yes—
915C2×C4C4×D4×C6114yes—
916C2×C4C4×D4×C6114yes—
917C2×C4#120×C6114yes—
918C2×C4#121×C6114yes—
919C2×C4#121×C6114yes—
920C2×C4#121×C6114yescomplemented
921C2×C4#123×C6114yes—
922C22—28no—
923C22—24no—
924C22—24no—
925C22—28no—
926C22—28no—
927C22—24no—
928C22—44no—
929C22—42no—
930C22—44no—
931C22—42no—
932C22—42no—
933C22—44no—
934C22—42no—
935C22—44no—
936C22—42no—
937C22—44no—
938C22—42no—
939C22—44no—
940C22—42no—
941C22—44no—
942C22—44no—
943C22—42no—
944C22—44no—
945C22—42no—
946C22—42no—
947C22—44no—
948C22—42no—
949C22—44no—
950C22—42no—
951C22—44no—
952C22C22×C22⋊C4×C6111yescharacteristic
953C22C2×C4×D4×C6111yescharacteristic
954C22C2×C4×D4×C6111yescharacteristic
955C22C2×C4×D4×C6111yescharacteristic
956C22C4×#41×C6111yescharacteristic
957C22C61×#51811yescharacteristic
958C22C61×#52011yescharacteristic
959C22C2×#120×C6111yescharacteristic
960C22C2×#121×C6111yescharacteristic
961C22C2×#121×C6111yescharacteristic
962C22C2×#121×C6111yescharacteristic
963C22C2×#123×C6111yescharacteristic
964C22C61×#52511yescharacteristic
965C22C61×#52911yescharacteristic
966C22C61×#53211yescharacteristic
967C22C61×#53511yescharacteristic
968C22C61×#53711yescharacteristic
969C22C61×#54011yescharacteristic
970C22C61×#54211yescharacteristic
971C22D42×C6111yescharacteristic
972C22D42×C6111yescharacteristic
973C22D42×C6111yescharacteristic
974C22C61×#54611yescharacteristic
975C22C61×#54611yescharacteristic
976C22C61×#54611yescharacteristic
977C22C61×#54611yescharacteristic
978C22C61×#54611yescharacteristic
979C22C61×#54711yescharacteristic
980C22C61×#54711yescharacteristic
981C22C61×#54711yescharacteristic
982C22C61×#54811yescharacteristic
983C22C61×#55011yescharacteristic
984C22C61×#55311yescharacteristic
985C22C61×#55311yescharacteristic
986C22C61×#55511yescharacteristic
987C4—24no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—44no—
992C4—42no—
993C4—44no—
994C4—82no—
995C4C61×#38618yescomplemented
996C2—48no—
997C2—44no—
998C2C2×C61×#38611yescharacteristic
999C2C4×#121×C6111yescharacteristic
1000C2C61×#232411yescharacteristic
1001C2D4×C22⋊C4×C6111yescharacteristic
1002C2C61×#233911yescharacteristic
1003C2C61×#236111yescharacteristic
1004C2C61×#236311yescharacteristic
1005C2C61×#240711yescharacteristic
1006C2C61×#240811yescharacteristic
1007C2C61×#242011yescharacteristic
1008C2C61×#242211yescharacteristic
1009C2C61×#242711yescharacteristic
1010C2C61×#242811yescharacteristic
1011C2C61×#253511yescharacteristic
1012C2C61×#253711yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutatorC23C23×C4×C61
Frattini, cosocleC24C24×C61
prime radicalC22×#121×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. C2×C61×#390C2semidirect
4. C2×C61×#386C2semidirect
5. C2×C61×#380C2semidirect
6. C2×C4×C22⋊C4×C61C2semidirect
7. C61×#1440C2semidirect
8. C61×#1438C2semidirect
9. C61×C4⋊#95C2semidirect
10. C61×C4⋊#95C2semidirect
11. C61×C22⋊#95C2semidirect
18. C2×#121×C61C4semidirect
58. C22×D4×C61C2×C4semidirect
74. C23×C4×C61C2×C4semidirect
93. C2×C4⋊C4×C61C2×C4semidirect
94. C2×C4⋊C4×C61D4semidirect
114. C2×C22⋊C4×C61C2×C4semidirect
115. C2×C22⋊C4×C61D4semidirect
121. C2×C42×C61D4semidirect
173. C2×D4×C61C22⋊C4semidirect
332. C23×C61C4×D4semidirect
413. C2×C4×C61#121semidirect
415. #13970C61direct (N × H)
489. C4×C61#386semidirect
491. C22×C4×D4C2×C61semidirect
492. C2×#390C2×C61semidirect
493. C2×#386C2×C61semidirect
494. C2×#380C2×C61semidirect
495. C2×C4×C22⋊C4C2×C61semidirect
496. #1440C2×C61semidirect
497. #1438C2×C61semidirect
498. C4⋊#95C2×C61semidirect
499. C4⋊#95C2×C61semidirect
500. C22⋊#95C2×C61semidirect
524. C2×#121C4×C61semidirect
551. C61#13970direct (N × H)
565. C22×D4C2×C4×C61semidirect
581. C23×C4C2×C4×C61semidirect
600. C2×C4⋊C4C2×C4×C61semidirect
601. C2×C4⋊C4D4×C61semidirect
621. C2×C22⋊C4C2×C4×C61semidirect
622. C2×C22⋊C4D4×C61semidirect
628. C2×C42D4×C61semidirect
680. C2×D4C22⋊C4×C61semidirect
839. C23C4×D4×C61semidirect
920. C2×C4#121×C61semidirect
995. C4C61×#386semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C612
C22×C4×D4×C612
C2×C61×#3902
C2×C61×#3862
C2×C61×#3802
C2×C4×C22⋊C4×C612
C61×#14402
C61×#14382
C61×C4⋊#952
C61×C22⋊#952
#1397061