Finite Group Databasebeta

← #29605332

Subgroups — #29605332

Order 15616.

2322 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D244C211yesmaximal, characteristic
2C2×#16839680C211yesmaximal, characteristic
3C2×#16839652C211yesmaximal, characteristic, complemented
4C2×#16839649C211yesmaximal, characteristic, complemented
5C2×#16839609C211yesmaximal, characteristic, complemented
6#21444067C211yesmaximal, characteristic, complemented
7#21444061C211yesmaximal, characteristic, complemented
8#21444059C211yesmaximal, characteristic
9#21444055C211yesmaximal, characteristic, complemented
10#21444053C211yesmaximal, characteristic, complemented
11#21444052C211yesmaximal, characteristic, complemented
12#21444040C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1436C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C2×C4×D244—24no—
20C2×C4×D244—24no—
21C2×C4×D244—24no—
22C22×C4⋊Dic61C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36#16839680C418yescomplemented
37#16839652—24no—
38#16839649—24no—
39#16839609—24no—
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C22×C4⋊C4×C61C2211yescharacteristic
52C22×C42×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C24×D61C2311yescharacteristic
59C24×D61C2311yescharacteristic
60C22×D244—22no—
61C22×D244—22no—
62C22×D244—22no—
63C22×D244—22no—
64C22×D244—22no—
65C22×D244—22no—
66C22×D244C2×C414yes—
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C22×C4×D61—22no—
74C22×C4×D61—22no—
75C22×C4×D61—22no—
76C22×C4×D61—22no—
77C22×C4×D61—22no—
78C22×C4×D61—22no—
79C22×C4×D61—22no—
80C22×C4×D61—22no—
81C22×C4×D61—22no—
82C22×C4×D61—41no—
83C22×C4×D61—41no—
84C22×C4×D61—41no—
85C22×C4×D61—41no—
86C22×C4×D61D414yes—
87C4×D244—232no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61D414yes—
91C2×#11758196—22no—
92C2×#11758196—22no—
93C2×#11758196C2×C414yescomplemented
94C2×#11758198—22no—
95C2×#11758198—22no—
96C2×#11758198—22no—
97C2×#11758198—22no—
98C2×#11758198—22no—
99C2×#11758198—22no—
100C2×#11758198—22no—
101C2×#11758198—22no—
102C2×#11758198—22no—
103C2×#11758198—22no—
104C2×#11758198—22no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—41no—
112C2×#11758198—41no—
113C2×#11758198—41no—
114C2×#11758198—41no—
115C2×#11758198—41no—
116C2×#11758198—41no—
117C2×#11758198—41no—
118C2×#11758198—41no—
119C2×#11758198C2×C414yescomplemented
120C2×#11758198C2×C414yescomplemented
121C2×#11758198C2×C414yescomplemented
122C2×#11758198C2×C414yescomplemented
123C2×#11758198D414yes—
124C2×C4×Dic61—22no—
125C2×C4×Dic61—22no—
126C2×C4×Dic61—22no—
127C2×C4×Dic61—22no—
128C2×C4×Dic61—41no—
129C2×C4×Dic61—41no—
130#14519684—22no—
131#14519684—22no—
132#14519684—22no—
133#14519684—22no—
134#14519684—22no—
135#14519684—22no—
136#14519684—22no—
137#14519684—22no—
138#14519684—22no—
139#14519684—41no—
140#14519684—41no—
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61—22no—
149C2×C4⋊C4×C61—22no—
150C2×C4⋊C4×C61—41no—
151C2×C42×C61—22no—
152C2×C42×C61—22no—
153C2×C42×C61—22no—
154#95×C61—22no—
155#95×C61—22no—
156#95×C61—22no—
157#95×C61—41no—
158#95×C61C2×C414yescomplemented
159C24×C61C2411yescharacteristic
160C23×D61—21no—
161C23×D61—21no—
162C23×D61—21no—
163C23×D61—21no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—21no—
167C23×D61—21no—
168C23×D61—21no—
169C23×D61—21no—
170C23×D61—21no—
171C23×D61—21no—
172C23×D61—21no—
173C23×D61—21no—
174C23×D61—21no—
175C23×D61—21no—
176C23×D61—21no—
177C23×D61—21no—
178C23×D61—21no—
179C23×D61—21no—
180C23×D61—21no—
181C23×D61—21no—
182C23×D61—21no—
183C23×D61—21no—
184C23×D61C22×C412yes—
185C23×D61C22×C412yes—
186C23×D61C2×D412yes—
187C23×D61C2×D412yes—
188C23×D61#4112yes—
189C23×D61#4112yes—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
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—21no—
204C22×C4×C61—21no—
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—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61C22×C412yes—
230C22×C4×C61C22×C412yes—
231C22×C4×C61C22×C412yes—
232C22×C4×C61C2×D412yes—
233C22×C4×C61C2×D412yes—
234C22×C4×C61C2×D412yes—
235C22×C4×C61#4112yes—
236C22×C4×C61#4112yes—
237C22×C4×C61#4112yes—
238C22×C4×C61#4112yes—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—21no—
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—21no—
265C22×Dic61—21no—
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×Dic61C22×C412yes—
275C22×Dic61C22×C412yes—
276C22×Dic61C2×D412yes—
277C22×Dic61C2×D412yes—
278C22×Dic61C2×D412yes—
279C22×Dic61C2×D412yes—
280C22×Dic61#4112yes—
281C2×D244—28no—
282C2×D244—28no—
283C2×D244—28no—
284C2×D244—28no—
285C2×D244—28no—
286C2×D244—28no—
287C2×D244—28no—
288C2×C4×D61—28no—
289C2×C4×D61—28no—
290C2×C4×D61—28no—
291C2×C4×D61—44no—
292C2×C4×D61—44no—
293C2×C4×D61—44no—
294C2×C4×D61—44no—
295C2×C4×D61—44no—
296C2×C4×D61—44no—
297C2×C4×D61—44no—
298C2×C4×D61—44no—
299C2×C4×D61—44no—
300C2×C4×D61—44no—
301C2×C4×D61—44no—
302C4⋊C4×C61—44no—
303C42×C61—28no—
304#11758198—28no—
305#11758198—28no—
306#11758198—28no—
307#11758198—28no—
308#11758198—28no—
309#11758198—44no—
310#11758198—44no—
311#11758198—44no—
312#11758198—44no—
313#11758198—44no—
314C4⋊Dic61—28no—
315#11758196—28no—
316C4×Dic61—44no—
317C4×Dic61—44no—
318C23×C61C23×C411yescharacteristic
319C23×C61C22×D411yescharacteristic
320C23×C61C22×D411yescharacteristic
321C23×C61C22×D411yescharacteristic
322C23×C61C2×#4111yescharacteristic
323C23×C61C2×#4111yescharacteristic
324C23×C61C2×#4111yescharacteristic
325C23×C61C2×#4111yescharacteristic
326C23×C61C2×#4111yescharacteristic
327C23×C61C2×#4111yescharacteristic
328C23×C61C2×#4111yescharacteristic
329C23×C61H(5,𝔽2)11yescharacteristic
330C23×C61H(5,𝔽2)11yescharacteristic
331C23×C61H(5,𝔽2)11yescharacteristic
332C23×C612−1+411yescharacteristic
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—22no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—22no—
351C22×D61—22no—
352C22×D61—22no—
353C22×D61—22no—
354C22×D61—22no—
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—22no—
358C22×D61—22no—
359C22×D61—22no—
360C22×D61—22no—
361C22×D61—22no—
362C22×D61—22no—
363C22×D61—22no—
364C22×D61—22no—
365C22×D61—22no—
366C22×D61—22no—
367C22×D61—22no—
368C22×D61—22no—
369C22×D61—41no—
370C22×D61—41no—
371C22×D61—41no—
372C22×D61—41no—
373C22×D61—41no—
374C22×D61—41no—
375C22×D61—41no—
376C22×D61—41no—
377C22×D61—41no—
378C22×D61—41no—
379C22×D61—41no—
380C22×D61—41no—
381C22×D61—41no—
382C22×D61—41no—
383C22×D61—41no—
384C22×D61—41no—
385C22×D61—41no—
386C22×D61—41no—
387C22×D61—41no—
388C22×D61—41no—
389C22×D61—41no—
390C22×D61—41no—
391C22×D61—41no—
392C22×D61—41no—
393C22×D61—41no—
394C22×D61—41no—
395C22×D61—41no—
396C22×D61—41no—
397C22×D61—41no—
398C22×D61—41no—
399C22×D61—41no—
400C22×D61—41no—
401C22×D61C4×D414yes—
402C22×D61C4×D414yes—
403C2×C4×C61—22no—
404C2×C4×C61—22no—
405C2×C4×C61—22no—
406C2×C4×C61—22no—
407C2×C4×C61—22no—
408C2×C4×C61—22no—
409C2×C4×C61—22no—
410C2×C4×C61—22no—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—22no—
415C2×C4×C61—22no—
416C2×C4×C61—22no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
422C2×C4×C61—22no—
423C2×C4×C61—22no—
424C2×C4×C61—22no—
425C2×C4×C61—22no—
426C2×C4×C61—22no—
427C2×C4×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61—41no—
435C2×C4×C61—41no—
436C2×C4×C61—41no—
437C2×C4×C61—41no—
438C2×C4×C61—41no—
439C2×C4×C61—41no—
440C2×C4×C61—41no—
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×C61C4×D414yes—
451C2×C4×C61#12314yes—
452C2×Dic61—22no—
453C2×Dic61—22no—
454C2×Dic61—22no—
455C2×Dic61—22no—
456C2×Dic61—22no—
457C2×Dic61—22no—
458C2×Dic61—22no—
459C2×Dic61—22no—
460C2×Dic61—22no—
461C2×Dic61—22no—
462C2×Dic61—22no—
463C2×Dic61—22no—
464C2×Dic61—22no—
465C2×Dic61—22no—
466C2×Dic61—22no—
467C2×Dic61—22no—
468C2×Dic61—22no—
469C2×Dic61—22no—
470C2×Dic61—41no—
471C2×Dic61—41no—
472C2×Dic61—41no—
473C2×Dic61—41no—
474C2×Dic61—41no—
475C2×Dic61—41no—
476C2×Dic61—41no—
477C2×Dic61—41no—
478C2×Dic61—41no—
479C2×Dic61—41no—
480C2×Dic61—41no—
481C2×Dic61—41no—
482C2×Dic61—41no—
483C2×Dic61—41no—
484C2×Dic61—41no—
485C2×Dic61—41no—
486C2×Dic61—41no—
487C2×Dic61—41no—
488C2×Dic61—41no—
489C2×Dic61—41no—
490C2×Dic61—41no—
491C2×Dic61—41no—
492C2×Dic61—41no—
493C2×Dic61#12014yes—
494D244—232no—
495C4×D61—416no—
496C4×D61—416no—
497#14173—611nomaximal, Sylow
498C22×C61C2×C4×D411yescharacteristic
499C22×C61C2×C4×D411yescharacteristic
500C22×C61C2×C4×D411yescharacteristic
501C22×C61C4×#4111yescharacteristic
502C22×C61C4×#4111yescharacteristic
503C22×C61#51811yescharacteristic
504C22×C61#52011yescharacteristic
505C22×C61C2×#12011yescharacteristic
506C22×C61C2×#12311yescharacteristic
507C22×C61#52511yescharacteristic
508C22×C61#52511yescharacteristic
509C22×C61#52511yescharacteristic
510C22×C61#52511yescharacteristic
511C22×C61#52911yescharacteristic
512C22×C61#52911yescharacteristic
513C22×C61#53411yescharacteristic
514C22×C61#53711yescharacteristic
515C22×C61#53811yescharacteristic
516C22×C61#53911yescharacteristic
517C22×C61#54611yescharacteristic
518C22×C61#54611yescharacteristic
519C22×C61#54611yescharacteristic
520C22×C61#54611yescharacteristic
521C22×C61#54611yescharacteristic
522C22×C61#54711yescharacteristic
523C22×C61#54811yescharacteristic
524C22×C61#55011yescharacteristic
525C22×C61#55111yescharacteristic
526C22×C61#55211yescharacteristic
527C22×C61#55311yescharacteristic
528C22×C61#55311yescharacteristic
529C22×C61#55311yescharacteristic
530C22×C61#55511yescharacteristic
531C22×C61#55611yescharacteristic
532C22×C61#55911yescharacteristic
533C2×D61—24no—
534C2×D61—24no—
535C2×D61—24no—
536C2×D61—24no—
537C2×D61—24no—
538C2×D61—24no—
539C2×D61—42no—
540C2×D61—42no—
541C2×D61—42no—
542C2×D61—42no—
543C2×D61—42no—
544C2×D61—42no—
545C2×D61—42no—
546C2×D61—42no—
547C2×D61—42no—
548C2×D61—42no—
549C2×D61—42no—
550C2×D61—42no—
551C2×D61—42no—
552C2×D61—42no—
553C2×D61—42no—
554C2×D61—42no—
555C2×D61—42no—
556C2×D61—42no—
557C2×D61—42no—
558C2×D61—42no—
559C2×D61—42no—
560C2×D61—42no—
561C2×D61—42no—
562C2×D61—42no—
563C4×C61—24no—
564C4×C61—24no—
565C4×C61—42no—
566C4×C61—42no—
567C4×C61—42no—
568C4×C61—42no—
569C4×C61—81no—
570Dic61—24no—
571Dic61—42no—
572Dic61—42no—
573Dic61—42no—
574Dic61—42no—
575Dic61—81no—
576C22×C4×D4—611no—
577C2×#394—611no—
578C2×#388—611no—
579C2×#387—611no—
580C2×C4×C22⋊C4—611no—
581#1440—611no—
582#1439—611no—
583#1438—611no—
584#1437—611no—
585#1436—611no—
586#1436—611no—
587#1436D6111yescharacteristic, complemented
588C22⋊#95—611no—
589C22⋊#95—611no—
590C22⋊#95—611no—
591C2×C61C4×#12011yescharacteristic
592C2×C61C4×#12311yescharacteristic
593C2×C61#232511yescharacteristic
594C2×C61#235911yescharacteristic
595C2×C61#236311yescharacteristic
596C2×C61#236411yescharacteristic
597C2×C61#236711yescharacteristic
598C2×C61#240511yescharacteristic
599C2×C61#240711yescharacteristic
600C2×C61#245911yescharacteristic
601C2×C61#246011yescharacteristic
602C2×C61#246611yescharacteristic
603C2×C61#246711yescharacteristic
604C2×C61#248511yescharacteristic
605C2×C61#260011yescharacteristic
606D61—44no—
607D61—44no—
608C23×D4—611no—
609C24×C4—611no—
610C24×C4—611no—
611C2×C4×D4—1224no—
612C2×C4×D4—1224no—
613C2×C4×D4—1224no—
614C22×C4⋊C4—611no—
615C22×C4⋊C4—611no—
616C22×C4⋊C4C2×D6111yescharacteristic
617C22×C22⋊C4—611no—
618C22×C22⋊C4—611no—
619C22×C22⋊C4—611no—
620C22×C22⋊C4—611no—
621C22×C22⋊C4—611no—
622C22×C22⋊C4—611no—
623C22×C22⋊C4—611no—
624C22×C22⋊C4—611no—
625C22×C22⋊C4—611no—
626C22×C22⋊C4—611no—
627C22×C42—611no—
628C22×C42—611no—
629C22×C42C2×D6111yescharacteristic
630#394—618no—
631#388—1224no—
632#387—1224no—
633C4×C22⋊C4—1224no—
634C2×#95—611no—
635C2×#95—611no—
636C2×#95—611no—
637C2×#95—611no—
638C2×#95—611no—
639C2×#95—611no—
640C2×#95—611no—
641C2×#95—611no—
642C2×#95—611no—
643C2×#95—611no—
644C2×#95—611no—
645C2×#95C2×D6111yescharacteristic
646C2×#95C2×D6111yescharacteristic
647C2×#95C2×D6111yescharacteristic
648C2×#95C2×D6111yescharacteristic
649C2×#95C2×D6111yescharacteristic
650C61#1417311yescharacteristic, complemented, Sylow
651C25—611no—
652C25—611no—
653C22×D4—614no—
654C22×D4—1222no—
655C22×D4—1222no—
656C22×D4—1222no—
657C22×D4—1222no—
658C22×D4—1222no—
659C22×D4—1222no—
660C23×C4—611no—
661C23×C4—611no—
662C23×C4—611no—
663C23×C4—611no—
664C23×C4—611no—
665C23×C4—614no—
666C23×C4—611no—
667C23×C4—1222no—
668C23×C4—1222no—
669C23×C4—1222no—
670C23×C4—1222no—
671C23×C4—1222no—
672C23×C4—1222no—
673C23×C4—1222no—
674C23×C4—1222no—
675C23×C4—1222no—
676C23×C4—2441no—
677C23×C4—2441no—
678C23×C4—2441no—
679C23×C4—2441no—
680C23×C4C22×D6111yescharacteristic
681C23×C4C22×D6111yescharacteristic
682C23×C4C22×D6111yescharacteristic
683C23×C4C22×D6111yescharacteristic
684C23×C4C22×D6111yescharacteristic
685C23×C4C22×D6111yescharacteristic
686C23×C4C22×D6111yescharacteristic
687C4×D4—12232no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—41no—
691C2×C4⋊C4—614no—
692C2×C4⋊C4—614no—
693C2×C4⋊C4—1222no—
694C2×C4⋊C4—1222no—
695C2×C4⋊C4—1222no—
696C2×C4⋊C4—1222no—
697C2×C22⋊C4—614no—
698C2×C22⋊C4—614no—
699C2×C22⋊C4—614no—
700C2×C22⋊C4—614no—
701C2×C22⋊C4—614no—
702C2×C22⋊C4—1222no—
703C2×C22⋊C4—1222no—
704C2×C22⋊C4—1222no—
705C2×C22⋊C4—1222no—
706C2×C22⋊C4—1222no—
707C2×C22⋊C4—1222no—
708C2×C22⋊C4—1222no—
709C2×C22⋊C4—1222no—
710C2×C22⋊C4—1222no—
711C2×C22⋊C4—1222no—
712C2×C22⋊C4—1222no—
713C2×C22⋊C4—1222no—
714C2×C22⋊C4—1222no—
715C2×C22⋊C4—1222no—
716C2×C22⋊C4—1222no—
717C2×C22⋊C4—1222no—
718C2×C22⋊C4—1222no—
719C2×C22⋊C4—2441no—
720C2×C22⋊C4—2441no—
721C2×C22⋊C4—2441no—
722C2×C22⋊C4—2441no—
723C2×C22⋊C4—2441no—
724C2×C22⋊C4—2441no—
725C2×C22⋊C4—2441no—
726C2×C22⋊C4—2441no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—1222no—
731C2×C42—1222no—
732C2×C42—1222no—
733C2×C42—1222no—
734C2×C42—2441no—
735C2×C42—2441no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—41no—
740#95—1222no—
741#95—1222no—
742#95—1222no—
743#95—1222no—
744#95—1222no—
745#95—1222no—
746#95—1222no—
747#95—1222no—
748#95—1222no—
749#95—2441no—
750#95—2441no—
751#95C4×D6114yescomplemented
752C24—612no—
753C24—612no—
754C24—612no—
755C24—612no—
756C24—612no—
757C24—612no—
758C24—1221no—
759C24—1221no—
760C24—1221no—
761C24—1221no—
762C24—1221no—
763C24—1221no—
764C24—1221no—
765C24—1221no—
766C24—1221no—
767C24—1221no—
768C24—1221no—
769C24—1221no—
770C24—1221no—
771C24—1221no—
772C24—1221no—
773C24—1221no—
774C24—1221no—
775C24—1221no—
776C24—1221no—
777C24—1221no—
778C24—1221no—
779C24—1221no—
780C24—1221no—
781C24—1221no—
782C24C23×D6111yescharacteristic
783C2×D4—1228no—
784C2×D4—1228no—
785C2×D4—1228no—
786C2×D4—1228no—
787C2×D4—1228no—
788C2×D4—1228no—
789C2×D4—1228no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—612no—
830C22×C4—612no—
831C22×C4—612no—
832C22×C4—612no—
833C22×C4—612no—
834C22×C4—612no—
835C22×C4—612no—
836C22×C4—1228no—
837C22×C4—1228no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—1221no—
848C22×C4—1221no—
849C22×C4—1221no—
850C22×C4—1221no—
851C22×C4—1221no—
852C22×C4—1221no—
853C22×C4—1221no—
854C22×C4—1221no—
855C22×C4—1221no—
856C22×C4—1221no—
857C22×C4—1221no—
858C22×C4—1221no—
859C22×C4—1221no—
860C22×C4—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1228no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—1221no—
871C22×C4—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—2444no—
875C22×C4—2444no—
876C22×C4—2444no—
877C22×C4—2444no—
878C22×C4—2444no—
879C22×C4—2444no—
880C22×C4—2444no—
881C22×C4—2444no—
882C22×C4—2444no—
883C22×C4—2444no—
884C22×C4—2444no—
885C22×C4C2×C4×D6112yes—
886C22×C4C2×C4×D6112yes—
887C22×C4C2×C4×D6112yes—
888C22×C4#1175822212yes—
889C22×C4#1175822212yes—
890C22×C4D4×D6112yes—
891C22×C4D4×D6112yes—
892C22×C4D4×D6112yes—
893C22×C4#1175822612yes—
894C22×C4#1175822612yes—
895C4⋊C4—44no—
896C4⋊C4—1228no—
897C4⋊C4—1228no—
898C22⋊C4—1228no—
899C22⋊C4—1228no—
900C22⋊C4—1228no—
901C22⋊C4—1228no—
902C22⋊C4—1228no—
903C22⋊C4—2444no—
904C22⋊C4—2444no—
905C22⋊C4—2444no—
906C22⋊C4—2444no—
907C22⋊C4—2444no—
908C42—28no—
909C42—2444no—
910C42—2444no—
911C23—614no—
912C23—614no—
913C23—1222no—
914C23—1222no—
915C23—1222no—
916C23—1222no—
917C23—1222no—
918C23—1222no—
919C23—1222no—
920C23—1222no—
921C23—1222no—
922C23—1222no—
923C23—1222no—
924C23—1222no—
925C23—1222no—
926C23—1222no—
927C23—1222no—
928C23—1222no—
929C23—1222no—
930C23—1222no—
931C23—1222no—
932C23—1222no—
933C23—1222no—
934C23—1222no—
935C23—1222no—
936C23—1222no—
937C23—1222no—
938C23—1222no—
939C23—1222no—
940C23—1222no—
941C23—1222no—
942C23—1222no—
943C23—1222no—
944C23—1222no—
945C23—1222no—
946C23—1222no—
947C23—1222no—
948C23—1222no—
949C23—2441no—
950C23—2441no—
951C23—2441no—
952C23—2441no—
953C23—2441no—
954C23—2441no—
955C23—2441no—
956C23—2441no—
957C23—2441no—
958C23—2441no—
959C23—2441no—
960C23—2441no—
961C23—2441no—
962C23—2441no—
963C23—2441no—
964C23—2441no—
965C23—2441no—
966C23—2441no—
967C23—2441no—
968C23—2441no—
969C23—2441no—
970C23—2441no—
971C23—2441no—
972C23—2441no—
973C23—2441no—
974C23—2441no—
975C23—2441no—
976C23—2441no—
977C23—2441no—
978C23—2441no—
979C23—2441no—
980C23—2441no—
981C23C22×C4×D6111yescharacteristic
982C23C2×D4×D6111yescharacteristic
983C23C2×D4×D6111yescharacteristic
984C23C2×D4×D6111yescharacteristic
985C23#41×D6111yescharacteristic
986C23#41×D6111yescharacteristic
987C23#41×D6111yescharacteristic
988C23C2×#1175822211yescharacteristic
989C23C2×#1175822211yescharacteristic
990C23C2×#1175822611yescharacteristic
991C23C2×#1175822611yescharacteristic
992C23#1451982211yescharacteristic
993C23#1451982311yescharacteristic
994C23#1451982311yescharacteristic
995C23#1451982411yescharacteristic
996D4—12232no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—614no—
1045C2×C4—1222no—
1046C2×C4—1222no—
1047C2×C4—1222no—
1048C2×C4—1222no—
1049C2×C4—1222no—
1050C2×C4—1222no—
1051C2×C4—1222no—
1052C2×C4—1222no—
1053C2×C4—1222no—
1054C2×C4—1222no—
1055C2×C4—1222no—
1056C2×C4—1222no—
1057C2×C4—1222no—
1058C2×C4—1222no—
1059C2×C4—1222no—
1060C2×C4—1222no—
1061C2×C4—1222no—
1062C2×C4—1222no—
1063C2×C4—24416no—
1064C2×C4—24416no—
1065C2×C4—2441no—
1066C2×C4—2441no—
1067C2×C4—2441no—
1068C2×C4—2441no—
1069C2×C4—2441no—
1070C2×C4—2441no—
1071C2×C4—2441no—
1072C2×C4—2441no—
1073C2×C4—2441no—
1074C2×C4—2441no—
1075C2×C4—2441no—
1076C2×C4—2441no—
1077C2×C4—2441no—
1078C2×C4—2441no—
1079C2×C4—2441no—
1080C2×C4—2441no—
1081C2×C4—2441no—
1082C2×C4—2441no—
1083C2×C4—2441no—
1084C2×C4—2441no—
1085C2×C4—2441no—
1086C2×C4—2441no—
1087C2×C4—2441no—
1088C2×C4#1451973914yes—
1089C2×C4#1451976214yes—
1090C22—1224no—
1091C22—1224no—
1092C22—1224no—
1093C22—1224no—
1094C22—1224no—
1095C22—1224no—
1096C22—2442no—
1097C22—2442no—
1098C22—2442no—
1099C22—2442no—
1100C22—2442no—
1101C22—2442no—
1102C22—2442no—
1103C22—2442no—
1104C22—2442no—
1105C22—2442no—
1106C22—2442no—
1107C22—2442no—
1108C22—2442no—
1109C22—2442no—
1110C22—2442no—
1111C22—2442no—
1112C22—2442no—
1113C22—2442no—
1114C22—2442no—
1115C22—2442no—
1116C22—2442no—
1117C22—2442no—
1118C22—2442no—
1119C22—2442no—
1120C22C4×D4×D6111yescharacteristic
1121C22C4×D4×D6111yescharacteristic
1122C22C2×#1451973911yescharacteristic
1123C22C4×#1175822211yescharacteristic
1124C22C4×#1175822611yescharacteristic
1125C22#1684023411yescharacteristic
1126C22#1684024211yescharacteristic
1127C22#120×D6111yescharacteristic
1128C22C2×#1451976211yescharacteristic
1129C22#1684027011yescharacteristic
1130C22#1684027111yescharacteristic
1131C22#1684027511yescharacteristic
1132C22#1684027511yescharacteristic
1133C22#1684029011yescharacteristic
1134C22#1684029911yescharacteristic
1135C22#1684032311yescharacteristic
1136C22#1684034111yescharacteristic
1137C22#1684034611yescharacteristic
1138C22#1684035311yescharacteristic
1139C22#1684040211yescharacteristic
1140C22#1684040311yescharacteristic
1141C22#1684040311yescharacteristic
1142C22#1684040811yescharacteristic
1143C22#1684040811yescharacteristic
1144C22#1684041011yescharacteristic
1145C22#1684042111yescharacteristic
1146C22#1684043011yescharacteristic
1147C22#1684043711yescharacteristic
1148C22#1684045011yescharacteristic
1149C22#1684045611yescharacteristic
1150C22#1684046211yescharacteristic
1151C22#1684046511yescharacteristic
1152C22#1684047811yescharacteristic
1153C22#1684048511yescharacteristic
1154C22#1684049711yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—81no—
1162C4—1224no—
1163C4—4881no—
1164C4—2442no—
1165C4—2442no—
1166C4—2442no—
1167C4—2442no—
1168C2—2444no—
1169C2—2444no—
1170C2#2144832011yescharacteristic
1171C2C4×#1451976211yescharacteristic
1172C2#2144852311yescharacteristic
1173C2#2144881811yescharacteristic
1174C2#2144885611yescharacteristic
1175C2#2144887011yescharacteristic
1176C2#2144888811yescharacteristic
1177C2#2144914811yescharacteristic
1178C2#2144916111yescharacteristic
1179C2#2144976311yescharacteristic
1180C2#2144977011yescharacteristic
1181C2#2144986211yescharacteristic
1182C2#2144986911yescharacteristic
1183C2#2145011911yescharacteristic
1184C2#2145140811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1436C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1436D61
hypocenterC61#14173
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×#16839652C2semidirect
4. C2×#16839649C2semidirect
5. C2×#16839609C2semidirect
6. #21444067C2semidirect
7. #21444061C2semidirect
9. #21444055C2semidirect
10. #21444053C2semidirect
11. #21444052C2semidirect
12. #21444040C2semidirect
13. #21444040C2semidirect
14. #21444040C2semidirect
15. C61×#1436C2semidirect
36. #16839680C4semidirect
93. C2×#11758196C2×C4semidirect
119. C2×#11758198C2×C4semidirect
120. C2×#11758198C2×C4semidirect
121. C2×#11758198C2×C4semidirect
122. C2×#11758198C2×C4semidirect
158. #95×C61C2×C4semidirect
587. #1436D61semidirect
650. C61#14173semidirect
751. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D2442
C2×#168396802
C2×#168396522
C2×#168396492
C2×#168396092
#214440672
#214440612
#214440592
#214440552
#214440532
#214440522
#214440402
C61×#14362
#1417361