Finite Group Databasebeta

← #29602869

Subgroups — #29602869

Order 15616.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519737C211yesmaximal, characteristic
2C2×#16839641C211yesmaximal, characteristic
3C2×#16839639C211yesmaximal, characteristic
4C2×#16839634C211yesmaximal, characteristic, complemented
5C2×#16839633C211yesmaximal, characteristic, complemented
6C22×#14519684C211yesmaximal, characteristic, complemented
7#21444082C211yesmaximal, characteristic, complemented
8#21444077C211yesmaximal, characteristic, complemented
9#21444063C211yesmaximal, characteristic, complemented
10#21444061C211yesmaximal, characteristic, complemented
11#21444051C211yesmaximal, characteristic, complemented
12#21444050C211yesmaximal, characteristic, complemented
13#21444041C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C2×C61×#380C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519737—24no—
21C2×#14519737—24no—
22C2×#14519737—24no—
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33#16839641C418yescomplemented
34#16839639—24no—
35#16839634—24no—
36#16839633—24no—
37C2×#14519684—24no—
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C24×C4×C61C2211yescharacteristic
53C22×C4⋊C4×C61C2211yescharacteristic
54C22×C4⋊C4×C61C2211yescharacteristic
55C22×C22⋊C4×C61C2211yescharacteristic
56C22×C22⋊C4×C61C2211yescharacteristic
57C61×#380—24no—
58C2×#95×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C24×D61C2311yescharacteristic
61C22×C22⋊D61—22no—
62C22×C22⋊D61—22no—
63C22×C22⋊D61—22no—
64C22×C22⋊D61—22no—
65C22×C22⋊D61C2×C414yes—
66C22×C22⋊D61D414yes—
67C22×C22⋊D61Q814yes—
68C23×Dic61—22no—
69C23×Dic61—22no—
70C23×Dic61—22no—
71C23×Dic61—22no—
72C23×Dic61—22no—
73C23×Dic61—22no—
74C23×Dic61—22no—
75C23×Dic61—22no—
76C23×Dic61—22no—
77C23×Dic61—41no—
78C23×Dic61—41no—
79C23×Dic61—41no—
80C23×Dic61—41no—
81C23×Dic61D414yes—
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C22×C4×D61—22no—
90C22×C4×D61—22no—
91C22×C4×D61—22no—
92C22×C4×D61—22no—
93C22×C4×D61—22no—
94C22×C4×D61—41no—
95C22×C4×D61—41no—
96#14519737—232no—
97C2×#11758196—22no—
98C2×#11758196—22no—
99C2×#11758196—22no—
100C2×#11758196—22no—
101C2×#11758196—22no—
102C2×#11758196—22no—
103C2×#11758196—22no—
104C2×#11758196—41no—
105C2×#11758196—41no—
106C2×C22⋊Dic61—22no—
107C2×C22⋊Dic61—22no—
108C2×C22⋊Dic61C2×C414yescomplemented
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—22no—
112C2×#11758198—22no—
113C2×#11758198—22no—
114C2×#11758198—22no—
115C2×#11758198—22no—
116C2×#11758198—22no—
117C2×#11758198—22no—
118C2×#11758198—41no—
119C2×#11758198—41no—
120C2×#11758198—41no—
121C2×#11758198—41no—
122C2×#11758198C2×C414yescomplemented
123C2×#11758198C2×C414yescomplemented
124C2×C4×Dic61—22no—
125C2×C4×Dic61—22no—
126C2×C4×Dic61—22no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—22no—
131#14519684—22no—
132#14519684—22no—
133#14519684—22no—
134#14519684—22no—
135#14519684—22no—
136#14519684—41no—
137#14519684—41no—
138#14519684C2×C414yescomplemented
139#14519684C2×C414yescomplemented
140#14519684D414yescomplemented
141C25×C61C2311yescharacteristic
142C23×C4×C61—22no—
143C23×C4×C61—22no—
144C23×C4×C61—22no—
145C23×C4×C61—22no—
146C23×C4×C61—41no—
147C23×C4×C61—41no—
148C23×C4×C61C2×C414yescomplemented
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C23×C4×C61C2311yescharacteristic
154C23×C4×C61C2311yescharacteristic
155C2×C4⋊C4×C61—22no—
156C2×C4⋊C4×C61—22no—
157C2×C4⋊C4×C61—22no—
158C2×C4⋊C4×C61—22no—
159C2×C4⋊C4×C61—41no—
160C2×C4⋊C4×C61—41no—
161C2×C22⋊C4×C61—22no—
162C2×C22⋊C4×C61—22no—
163C2×C22⋊C4×C61—22no—
164C2×C22⋊C4×C61—22no—
165C2×C22⋊C4×C61—22no—
166C2×C22⋊C4×C61D414yes—
167#95×C61—22no—
168#95×C61—22no—
169C24×C61—21no—
170C24×C61—21no—
171C24×C61—21no—
172C24×C61—21no—
173C24×C61—21no—
174C24×C61—21no—
175C24×C61—21no—
176C24×C61—21no—
177C24×C61C22×C412yes—
178C24×C61C2×D412yes—
179C24×C61C2×D412yes—
180C24×C61C2×D412yes—
181C24×C61C2×Q812yes—
182C24×C61#4112yes—
183C24×C61#4112yes—
184C24×C61C2411yescharacteristic
185C23×D61—21no—
186C23×D61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—21no—
194C23×D61—21no—
195C23×D61—21no—
196C23×D61—21no—
197C23×D61C22×C412yes—
198C23×D61C2×D412yes—
199C23×D61C2×Q812yes—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—28no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
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—21no—
223C22×C4×C61—28no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—44no—
239C22×C4×C61—44no—
240C22×C4×C61—44no—
241C22×C4×C61—44no—
242C22×C4×C61—44no—
243C22×C4×C61C22×C412yes—
244C22×C4×C61C22×C412yes—
245C22×C4×C61C2×D412yes—
246C22×C4×C61C2×D412yes—
247C22×C4×C61C2×D412yes—
248C22×C4×C61#4112yes—
249C2×C22⋊D61—28no—
250C2×C22⋊D61—28no—
251C2×C22⋊D61—28no—
252C2×C22⋊D61—28no—
253C2×C22⋊D61—28no—
254C2×C22⋊D61—28no—
255C2×C22⋊D61C4⋊C4116yescomplemented
256C22×Dic61—21no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61—28no—
265C22×Dic61—28no—
266C22×Dic61—21no—
267C22×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61—21no—
271C22×Dic61—21no—
272C22×Dic61—21no—
273C22×Dic61—21no—
274C22×Dic61—21no—
275C22×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61—21no—
279C22×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—21no—
284C22×Dic61—21no—
285C22×Dic61—21no—
286C22×Dic61—21no—
287C22×Dic61—21no—
288C22×Dic61—21no—
289C22×Dic61—21no—
290C22×Dic61—21no—
291C22×Dic61—21no—
292C22×Dic61—21no—
293C22×Dic61—21no—
294C22×Dic61—21no—
295C22×Dic61—21no—
296C22×Dic61—28no—
297C22×Dic61—44no—
298C22×Dic61—44no—
299C22×Dic61—44no—
300C22×Dic61—44no—
301C22×Dic61—44no—
302C22×Dic61—44no—
303C22×Dic61—44no—
304C22×Dic61—44no—
305C22×Dic61—44no—
306C22×Dic61—44no—
307C22×Dic61—44no—
308C22×Dic61C22×C412yes—
309C22×Dic61C22×C412yes—
310C22×Dic61C22×C412yes—
311C22×Dic61C2×D412yes—
312C22×Dic61C2×D412yes—
313C22×Dic61C2×D412yes—
314C22×Dic61C2×D412yes—
315C22×Dic61C2×D412yes—
316C22×Dic61C2×Q812yes—
317C22×Dic61#4112yes—
318C22×Dic61#4112yes—
319C2×C4×D61—28no—
320C2×C4×D61—44no—
321C2×C4×D61—44no—
322C2×C4×D61—44no—
323C2×C4×D61—44no—
324C2×C4×D61—44no—
325C2×C4×D61—44no—
326C4⋊C4×C61—44no—
327C4⋊C4×C61—44no—
328C22⋊C4×C61—28no—
329C22⋊C4×C61—44no—
330C22⋊Dic61—28no—
331#11758198—28no—
332#11758198—28no—
333#11758198—44no—
334#11758198—44no—
335#11758198—44no—
336#11758196—28no—
337#11758196—44no—
338#11758196—44no—
339C4×Dic61—28no—
340C23×C61—22no—
341C23×C61—22no—
342C23×C61—22no—
343C23×C61—22no—
344C23×C61—22no—
345C23×C61—22no—
346C23×C61—22no—
347C23×C61—22no—
348C23×C61—22no—
349C23×C61—22no—
350C23×C61—22no—
351C23×C61—22no—
352C23×C61—22no—
353C23×C61—22no—
354C23×C61—22no—
355C23×C61—22no—
356C23×C61—22no—
357C23×C61—22no—
358C23×C61—22no—
359C23×C61—22no—
360C23×C61—22no—
361C23×C61—22no—
362C23×C61—22no—
363C23×C61—22no—
364C23×C61—22no—
365C23×C61—22no—
366C23×C61—22no—
367C23×C61—22no—
368C23×C61C2×C4⋊C414yes—
369C23×C61C4×D414yes—
370C23×C61C4×D414yes—
371C23×C61#12014yes—
372C23×C61C22⋊Q814yes—
373C23×C61C22⋊Q814yes—
374C23×C61#12314yes—
375C23×C61C23×C411yescharacteristic
376C23×C61C22×D411yescharacteristic
377C23×C61C22×D411yescharacteristic
378C23×C61C22×D411yescharacteristic
379C23×C61C22×D411yescharacteristic
380C23×C61C22×Q811yescharacteristic
381C23×C61C2×#4111yescharacteristic
382C23×C61C2×#4111yescharacteristic
383C23×C61C2×#4111yescharacteristic
384C23×C61C2×#4111yescharacteristic
385C23×C61C2×#4111yescharacteristic
386C23×C61H(5,𝔽2)11yescharacteristic
387C23×C61H(5,𝔽2)11yescharacteristic
388C23×C61H(5,𝔽2)11yescharacteristic
389C23×C612−1+411yescharacteristic
390C22×D61—22no—
391C22×D61—22no—
392C22×D61—22no—
393C22×D61—22no—
394C22×D61—22no—
395C22×D61—22no—
396C22×D61—22no—
397C22×D61—22no—
398C22×D61—22no—
399C22×D61—22no—
400C22×D61—22no—
401C22×D61—22no—
402C22×D61—22no—
403C22×D61—22no—
404C22×D61—22no—
405C22×D61—22no—
406C22×D61—22no—
407C22×D61—22no—
408C22×D61—41no—
409C22×D61—41no—
410C22×D61—41no—
411C22×D61—41no—
412C22×D61—41no—
413C22×D61—41no—
414C22×D61—41no—
415C22×D61—41no—
416C22×D61—41no—
417C22×D61—41no—
418C22×D61—41no—
419C22×D61—41no—
420C22×D61—41no—
421C22×D61—41no—
422C22×D61—41no—
423C22×D61—41no—
424C22×D61C2×C4⋊C414yes—
425C2×C4×C61—22no—
426C2×C4×C61—22no—
427C2×C4×C61—22no—
428C2×C4×C61—22no—
429C2×C4×C61—22no—
430C2×C4×C61—22no—
431C2×C4×C61—22no—
432C2×C4×C61—22no—
433C2×C4×C61—22no—
434C2×C4×C61—22no—
435C2×C4×C61—22no—
436C2×C4×C61—22no—
437C2×C4×C61—22no—
438C2×C4×C61—22no—
439C2×C4×C61—22no—
440C2×C4×C61—416no—
441C2×C4×C61—41no—
442C2×C4×C61—41no—
443C2×C4×C61—41no—
444C2×C4×C61—41no—
445C2×C4×C61—41no—
446C2×C4×C61—41no—
447C2×C4×C61—41no—
448C2×C4×C61—41no—
449C2×C4×C61—41no—
450C2×C4×C61—41no—
451C2×C4×C61—41no—
452C2×C4×C61—41no—
453C2×C4×C61—41no—
454C2×C4×C61—41no—
455C2×C4×C61—41no—
456C2×C4×C61—41no—
457C2×C4×C61—41no—
458C2×C4×C61—41no—
459C2×C4×C61—41no—
460C2×C4×C61—41no—
461C2×C4×C61—41no—
462C2×C4×C61—41no—
463C2×C4×C61—41no—
464C2×C4×C61—41no—
465C2×C4×C61—41no—
466C2×C4×C61—41no—
467C2×C4×C61C4×D414yescomplemented
468C22⋊D61—232no—
469C2×Dic61—22no—
470C2×Dic61—22no—
471C2×Dic61—22no—
472C2×Dic61—22no—
473C2×Dic61—22no—
474C2×Dic61—22no—
475C2×Dic61—22no—
476C2×Dic61—22no—
477C2×Dic61—22no—
478C2×Dic61—22no—
479C2×Dic61—22no—
480C2×Dic61—22no—
481C2×Dic61—22no—
482C2×Dic61—22no—
483C2×Dic61—22no—
484C2×Dic61—22no—
485C2×Dic61—22no—
486C2×Dic61—22no—
487C2×Dic61—22no—
488C2×Dic61—22no—
489C2×Dic61—22no—
490C2×Dic61—22no—
491C2×Dic61—22no—
492C2×Dic61—22no—
493C2×Dic61—22no—
494C2×Dic61—22no—
495C2×Dic61—22no—
496C2×Dic61—416no—
497C2×Dic61—416no—
498C2×Dic61—41no—
499C2×Dic61—41no—
500C2×Dic61—41no—
501C2×Dic61—41no—
502C2×Dic61—41no—
503C2×Dic61—41no—
504C2×Dic61—41no—
505C2×Dic61—41no—
506C2×Dic61—41no—
507C2×Dic61—41no—
508C2×Dic61—41no—
509C2×Dic61—41no—
510C2×Dic61—41no—
511C2×Dic61—41no—
512C2×Dic61—41no—
513C2×Dic61—41no—
514C2×Dic61—41no—
515C2×Dic61—41no—
516C2×Dic61—41no—
517C2×Dic61—41no—
518C2×Dic61C2×C4⋊C414yes—
519C2×Dic61#12114yes—
520C4×D61—416no—
521#13975—611nomaximal, Sylow
522C22×C61—24no—
523C22×C61—24no—
524C22×C61—24no—
525C22×C61—24no—
526C22×C61—24no—
527C22×C61—24no—
528C22×C61—24no—
529C22×C61—24no—
530C22×C61—24no—
531C22×C61—24no—
532C22×C61—24no—
533C22×C61—24no—
534C22×C61—24no—
535C22×C61—24no—
536C22×C61#38518yescomplemented
537C22×C61C22×C4⋊C411yescharacteristic
538C22×C61C2×C4×D411yescharacteristic
539C22×C61C2×C4×D411yescharacteristic
540C22×C61C2×C4×D411yescharacteristic
541C22×C61C4×#4111yescharacteristic
542C22×C61#51811yescharacteristic
543C22×C61#52011yescharacteristic
544C22×C61C2×#12011yescharacteristic
545C22×C61C2×#12111yescharacteristic
546C22×C61C2×C22⋊Q811yescharacteristic
547C22×C61C2×C22⋊Q811yescharacteristic
548C22×C61C2×#12311yescharacteristic
549C22×C61#52511yescharacteristic
550C22×C61#52911yescharacteristic
551C22×C61#53211yescharacteristic
552C22×C61#53411yescharacteristic
553C22×C61#53711yescharacteristic
554C22×C61#53811yescharacteristic
555C22×C61#53911yescharacteristic
556C22×C61D4211yescharacteristic
557C22×C61D4211yescharacteristic
558C22×C61#54611yescharacteristic
559C22×C61#54611yescharacteristic
560C22×C61#54611yescharacteristic
561C22×C61#54611yescharacteristic
562C22×C61#54611yescharacteristic
563C22×C61#54711yescharacteristic
564C22×C61#54711yescharacteristic
565C22×C61D4×Q811yescharacteristic
566C22×C61#55111yescharacteristic
567C22×C61#55111yescharacteristic
568C22×C61#55211yescharacteristic
569C22×C61#55411yescharacteristic
570C22×C61#55411yescharacteristic
571C22×C61#55411yescharacteristic
572C2×D61—24no—
573C2×D61—24no—
574C2×D61—24no—
575C2×D61—42no—
576C2×D61—42no—
577C2×D61—42no—
578C2×D61—42no—
579C2×D61—42no—
580C2×D61—42no—
581C2×D61—42no—
582C2×D61—42no—
583C2×D61—42no—
584C2×D61—42no—
585C2×D61—42no—
586C2×D61—42no—
587C4×C61—24no—
588C4×C61—42no—
589C4×C61—42no—
590C4×C61—42no—
591C4×C61—81no—
592C4×C61—81no—
593Dic61—24no—
594Dic61—24no—
595Dic61—42no—
596Dic61—42no—
597Dic61—42no—
598Dic61—42no—
599Dic61—42no—
600C22×C4×D4—611no—
601C2×#386—611no—
602C2×#386—611no—
603C2×#385—611no—
604C2×#385—611no—
605C2×#380D6111yescharacteristic, complemented
606C22×#95—611no—
607#1444—611no—
608#1442—611no—
609#1439—611no—
610#1439—611no—
611#1436—611no—
612#1436—611no—
613C22⋊#95—611no—
614C22⋊#95—611no—
615C2×C61—28no—
616C2×C61C2×#38511yescharacteristic
617C2×C61C4×#12111yescharacteristic
618C2×C61#232511yescharacteristic
619C2×C61D4×C4⋊C411yescharacteristic
620C2×C61#234911yescharacteristic
621C2×C61#235811yescharacteristic
622C2×C61#235911yescharacteristic
623C2×C61#241011yescharacteristic
624C2×C61#241711yescharacteristic
625C2×C61#241811yescharacteristic
626C2×C61#241911yescharacteristic
627C2×C61#243011yescharacteristic
628C2×C61#244911yescharacteristic
629C2×C61#245011yescharacteristic
630C2×C61#256411yescharacteristic
631D61—44no—
632C23×D4—611no—
633C24×C4—611no—
634C24×C4—611no—
635C24×C4—611no—
636C24×C4C2×D6111yescharacteristic
637C2×C4×D4—1224no—
638C2×C4×D4—1224no—
639C2×C4×D4—1224no—
640C22×C4⋊C4—611no—
641C22×C4⋊C4—611no—
642C22×C4⋊C4—611no—
643C22×C4⋊C4C2×D6111yescharacteristic
644C22×C4⋊C4C2×D6111yescharacteristic
645C22×C22⋊C4—611no—
646C22×C22⋊C4—611no—
647C22×C22⋊C4—611no—
648C22×C22⋊C4—611no—
649C22×C22⋊C4—611no—
650C22×C22⋊C4—611no—
651C22×C22⋊C4C2×D6111yescharacteristic
652C22×C22⋊C4C2×D6111yescharacteristic
653C22×C42—611no—
654#386—618no—
655#386—1224no—
656#385—1224no—
657#385—1224no—
658#380—24no—
659C2×#95—611no—
660C2×#95—611no—
661C2×#95—611no—
662C2×#95—611no—
663C2×#95—611no—
664C2×#95—611no—
665C2×#95—611no—
666C2×#95—611no—
667C2×#95—611no—
668C2×#95—611no—
669C2×#95—611no—
670C2×#95—611no—
671C2×#95—611no—
672C2×#95—611no—
673C2×#95—1224no—
674C2×#95C2×D6111yescharacteristic
675C2×#95C2×D6111yescharacteristic
676C61#1397511yescharacteristic, complemented, Sylow
677C25—611no—
678C25C22×D6111yescharacteristic
679C22×D4—614no—
680C22×D4—614no—
681C22×D4—614no—
682C22×D4—1222no—
683C22×D4—1222no—
684C22×D4—1222no—
685C22×D4—1222no—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—22no—
690C23×C4—41no—
691C23×C4—41no—
692C23×C4—611no—
693C23×C4—611no—
694C23×C4—611no—
695C23×C4—611no—
696C23×C4—611no—
697C23×C4—611no—
698C23×C4—611no—
699C23×C4—614no—
700C23×C4—1222no—
701C23×C4—1222no—
702C23×C4—1222no—
703C23×C4—1222no—
704C23×C4—1222no—
705C23×C4—1222no—
706C23×C4—1222no—
707C23×C4—1222no—
708C23×C4—1222no—
709C23×C4—1222no—
710C23×C4—1222no—
711C23×C4—1222no—
712C23×C4—1222no—
713C23×C4—1222no—
714C23×C4—2441no—
715C23×C4—2441no—
716C23×C4—2441no—
717C23×C4—2441no—
718C23×C4—2441no—
719C23×C4—2441no—
720C23×C4C4×D6114yescomplemented
721C23×C4C22×D6111yescharacteristic
722C23×C4C22×D6111yescharacteristic
723C23×C4C22×D6111yescharacteristic
724C23×C4C22×D6111yescharacteristic
725C23×C4C22×D6111yescharacteristic
726C23×C4C22×D6111yescharacteristic
727C4×D4—12232no—
728C2×C4⋊C4—22no—
729C2×C4⋊C4—22no—
730C2×C4⋊C4—22no—
731C2×C4⋊C4—22no—
732C2×C4⋊C4—41no—
733C2×C4⋊C4—41no—
734C2×C4⋊C4—1222no—
735C2×C4⋊C4—1222no—
736C2×C4⋊C4—1222no—
737C2×C4⋊C4—1222no—
738C2×C4⋊C4—1222no—
739C2×C4⋊C4—1222no—
740C2×C4⋊C4—1222no—
741C2×C4⋊C4—2441no—
742C2×C4⋊C4—2441no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—614no—
749C2×C22⋊C4—614no—
750C2×C22⋊C4—614no—
751C2×C22⋊C4—1222no—
752C2×C22⋊C4—1222no—
753C2×C22⋊C4—1222no—
754C2×C22⋊C4—1222no—
755C2×C22⋊C4—1222no—
756C2×C22⋊C4—1222no—
757C2×C22⋊C4—1222no—
758C2×C22⋊C4—1222no—
759C2×C22⋊C4—1222no—
760C2×C22⋊C4—1222no—
761C2×C22⋊C4—1222no—
762C2×C22⋊C4—2441no—
763C2×C22⋊C4—2441no—
764C2×C22⋊C4—2441no—
765C2×C22⋊C4—2441no—
766C2×C22⋊C4C22⋊D6114yes—
767C2×C42—1222no—
768C2×C42—1222no—
769C2×C42—1222no—
770#95—22no—
771#95—22no—
772#95—614no—
773#95—614no—
774#95—614no—
775#95—1222no—
776#95—1222no—
777#95—1222no—
778#95—1222no—
779#95—1222no—
780#95—1222no—
781#95—1222no—
782#95—1222no—
783#95—1222no—
784#95—2441no—
785#95—2441no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—612no—
795C24—612no—
796C24—612no—
797C24—1221no—
798C24—1221no—
799C24—1221no—
800C24—1221no—
801C24—1221no—
802C24—1221no—
803C24—1221no—
804C24—1221no—
805C24—1221no—
806C24—1221no—
807C24—1221no—
808C24—1221no—
809C24C2×C4×D6112yes—
810C24#1175822212yes—
811C24D4×D6112yes—
812C24D4×D6112yes—
813C24Q8×D6112yes—
814C24#1175822612yes—
815C24C2×C22⋊D6112yes—
816C24C23×D6111yescharacteristic
817C2×D4—6116no—
818C2×D4—1228no—
819C2×D4—1228no—
820C2×D4—1228no—
821C2×D4—1228no—
822C2×D4—1228no—
823C2×D4—1228no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—28no—
847C22×C4—28no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—612no—
868C22×C4—612no—
869C22×C4—612no—
870C22×C4—612no—
871C22×C4—612no—
872C22×C4—612no—
873C22×C4—612no—
874C22×C4—612no—
875C22×C4—612no—
876C22×C4—612no—
877C22×C4—612no—
878C22×C4—1228no—
879C22×C4—1228no—
880C22×C4—1221no—
881C22×C4—1221no—
882C22×C4—1221no—
883C22×C4—1221no—
884C22×C4—1221no—
885C22×C4—1221no—
886C22×C4—1221no—
887C22×C4—1221no—
888C22×C4—1228no—
889C22×C4—1221no—
890C22×C4—1221no—
891C22×C4—1221no—
892C22×C4—1221no—
893C22×C4—1221no—
894C22×C4—1221no—
895C22×C4—1221no—
896C22×C4—1221no—
897C22×C4—1221no—
898C22×C4—1221no—
899C22×C4—1221no—
900C22×C4—1221no—
901C22×C4—1221no—
902C22×C4—1221no—
903C22×C4—1221no—
904C22×C4—1221no—
905C22×C4—1221no—
906C22×C4—1221no—
907C22×C4—1221no—
908C22×C4—1221no—
909C22×C4—1221no—
910C22×C4—1221no—
911C22×C4—1221no—
912C22×C4—1221no—
913C22×C4—1221no—
914C22×C4—1221no—
915C22×C4—1221no—
916C22×C4—1221no—
917C22×C4—1221no—
918C22×C4—1221no—
919C22×C4—1228no—
920C22×C4—2444no—
921C22×C4—2444no—
922C22×C4—2444no—
923C22×C4—2444no—
924C22×C4—2444no—
925C22×C4—2444no—
926C22×C4—2444no—
927C22×C4—2444no—
928C22×C4—2444no—
929C22×C4—2444no—
930C22×C4—2444no—
931C22×C4—2444no—
932C22×C4—2444no—
933C22×C4—2444no—
934C22×C4—2444no—
935C22×C4—2444no—
936C22×C4—2444no—
937C22×C4C2×C4×D6112yes—
938C22×C4C2×C4×D6112yes—
939C22×C4D4×D6112yes—
940C22×C4#1175822412yes—
941C22×C4C2×C22⋊D6112yes—
942C22×C4C2×C22⋊D6112yes—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—1228no—
946C4⋊C4—2444no—
947C4⋊C4—2444no—
948C22⋊C4—28no—
949C22⋊C4—44no—
950C22⋊C4—1228no—
951C22⋊C4—1228no—
952C22⋊C4—1228no—
953C22⋊C4—2444no—
954C22⋊C4—2444no—
955C22⋊C4—2444no—
956C42—1228no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—614no—
986C23—1222no—
987C23—1222no—
988C23—1222no—
989C23—1222no—
990C23—1222no—
991C23—1222no—
992C23—1222no—
993C23—1222no—
994C23—1222no—
995C23—1222no—
996C23—1222no—
997C23—1222no—
998C23—1222no—
999C23—1222no—
1000C23—1222no—
1001C23—1222no—
1002C23—1222no—
1003C23—1222no—
1004C23—2441no—
1005C23—2441no—
1006C23—2441no—
1007C23—2441no—
1008C23—2441no—
1009C23—2441no—
1010C23—2441no—
1011C23—2441no—
1012C23—2441no—
1013C23—2441no—
1014C23—2441no—
1015C23—2441no—
1016C23—2441no—
1017C23—2441no—
1018C23—2441no—
1019C23—2441no—
1020C23C4⋊C4×D6114yes—
1021C23C4×C22⋊D6114yes—
1022C23#1451973914yes—
1023C23#1451974514yes—
1024C23#1451975314yes—
1025C23#1451975514yes—
1026C23#1451976214yes—
1027C23C22×C4×D6111yescharacteristic
1028C23C2×D4×D6111yescharacteristic
1029C23C2×D4×D6111yescharacteristic
1030C23C2×D4×D6111yescharacteristic
1031C23C22×C22⋊D6111yescharacteristic
1032C23C2×Q8×D6111yescharacteristic
1033C23#41×D6111yescharacteristic
1034C23#41×D6111yescharacteristic
1035C23C2×#1175822411yescharacteristic
1036C23C2×#1175822211yescharacteristic
1037C23C2×#1175822611yescharacteristic
1038C23#1451982211yescharacteristic
1039C23#1451982211yescharacteristic
1040C23#1451982311yescharacteristic
1041C23#1451982411yescharacteristic
1042D4—12232no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—416no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—614no—
1086C2×C4—614no—
1087C2×C4—1222no—
1088C2×C4—1222no—
1089C2×C4—1222no—
1090C2×C4—1222no—
1091C2×C4—1222no—
1092C2×C4—1222no—
1093C2×C4—1222no—
1094C2×C4—1222no—
1095C2×C4—1222no—
1096C2×C4—1222no—
1097C2×C4—1222no—
1098C2×C4—1222no—
1099C2×C4—1222no—
1100C2×C4—1222no—
1101C2×C4—1222no—
1102C2×C4—1222no—
1103C2×C4—1222no—
1104C2×C4—1222no—
1105C2×C4—1222no—
1106C2×C4—1222no—
1107C2×C4—1222no—
1108C2×C4—1222no—
1109C2×C4—1222no—
1110C2×C4—1222no—
1111C2×C4—1222no—
1112C2×C4—1222no—
1113C2×C4—1222no—
1114C2×C4—24416no—
1115C2×C4—24416no—
1116C2×C4—24416no—
1117C2×C4—2441no—
1118C2×C4—2441no—
1119C2×C4—2441no—
1120C2×C4—2441no—
1121C2×C4—2441no—
1122C2×C4—2441no—
1123C2×C4—2441no—
1124C2×C4—2441no—
1125C2×C4—2441no—
1126C2×C4—2441no—
1127C2×C4—2441no—
1128C2×C4—2441no—
1129C2×C4—2441no—
1130C2×C4—2441no—
1131C2×C4—2441no—
1132C2×C4—2441no—
1133C2×C4—2441no—
1134C2×C4—2441no—
1135C2×C4—2441no—
1136C2×C4—2441no—
1137C2×C4#1451973714yescomplemented
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—1224no—
1153C22—1224no—
1154C22—1224no—
1155C22—2442no—
1156C22—2442no—
1157C22—2442no—
1158C22—2442no—
1159C22—2442no—
1160C22—2442no—
1161C22—2442no—
1162C22—2442no—
1163C22—2442no—
1164C22—2442no—
1165C22—2442no—
1166C22—2442no—
1167C22#1683963318yescomplemented
1168C22C2×C4⋊C4×D6111yescharacteristic
1169C22C2×#1451973711yescharacteristic
1170C22C2×C4×C22⋊D6111yescharacteristic
1171C22C2×#1451973911yescharacteristic
1172C22#1684023011yescharacteristic
1173C22#1684023511yescharacteristic
1174C22#1684024211yescharacteristic
1175C22C2×#1451974511yescharacteristic
1176C22#121×D6111yescharacteristic
1177C22C2×#1451975311yescharacteristic
1178C22C2×#1451975511yescharacteristic
1179C22C2×#1451976211yescharacteristic
1180C22#1684027511yescharacteristic
1181C22#1684029811yescharacteristic
1182C22#1684030711yescharacteristic
1183C22#1684032011yescharacteristic
1184C22#1684033911yescharacteristic
1185C22#1684035211yescharacteristic
1186C22#1684036111yescharacteristic
1187C22D4×C22⋊D6111yescharacteristic
1188C22#1684039611yescharacteristic
1189C22#1684040011yescharacteristic
1190C22#1684040111yescharacteristic
1191C22#1684040111yescharacteristic
1192C22#1684040211yescharacteristic
1193C22#1684040611yescharacteristic
1194C22#1684041111yescharacteristic
1195C22#1684041211yescharacteristic
1196C22#1684042511yescharacteristic
1197C22#1684043611yescharacteristic
1198C22#1684043811yescharacteristic
1199C22#1684044511yescharacteristic
1200C22#1684046611yescharacteristic
1201C22#1684046611yescharacteristic
1202C22#1684047011yescharacteristic
1203C4—24no—
1204C4—42no—
1205C4—42no—
1206C4—42no—
1207C4—81no—
1208C4—81no—
1209C4—1224no—
1210C4—1224no—
1211C4—2442no—
1212C4—2442no—
1213C4—2442no—
1214C4—2442no—
1215C4—2442no—
1216C2—28no—
1217C2—2444no—
1218C2C2×#1683963311yescharacteristic
1219C2#2144832511yescharacteristic
1220C2#2144851911yescharacteristic
1221C2#2144871511yescharacteristic
1222C2#2144872311yescharacteristic
1223C2#2144879811yescharacteristic
1224C2#2144881111yescharacteristic
1225C2#2144919011yescharacteristic
1226C2#2144926911yescharacteristic
1227C2#2144928711yescharacteristic
1228C2#2144930211yescharacteristic
1229C2#2144942511yescharacteristic
1230C2#2144962411yescharacteristic
1231C2#2144963911yescharacteristic
1232C2#2145099711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#380C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#380D61
hypocenterC61#13975
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
4. C2×#16839634C2semidirect
5. C2×#16839633C2semidirect
6. C22×#14519684C2semidirect
7. #21444082C2semidirect
8. #21444077C2semidirect
9. #21444063C2semidirect
10. #21444061C2semidirect
11. #21444051C2semidirect
12. #21444050C2semidirect
13. #21444041C2semidirect
14. #21444040C2semidirect
15. C2×C61×#380C2semidirect
33. #16839641C4semidirect
108. C2×C22⋊Dic61C2×C4semidirect
122. C2×#11758198C2×C4semidirect
123. C2×#11758198C2×C4semidirect
138. #14519684C2×C4semidirect
139. #14519684C2×C4semidirect
140. #14519684D4semidirect
148. C23×C4×C61C2×C4semidirect
255. C2×C22⋊D61C4⋊C4semidirect
467. C2×C4×C61C4×D4semidirect
536. C22×C61#385semidirect
605. C2×#380D61semidirect
676. C61#13975semidirect
720. C23×C4C4×D61semidirect
1137. C2×C4#14519737semidirect
1167. C22#16839633semidirect

Maximal subgroups

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

subgroupindex
C22×#145197372
C2×#168396412
C2×#168396392
C2×#168396342
C2×#168396332
C22×#145196842
#214440822
#214440772
#214440632
#214440612
#214440512
#214440502
#214440412
#214440402
C2×C61×#3802
#1397561