Finite Group Databasebeta

← #29603131

Subgroups — #29603131

Order 15616.

2474 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519762C211yesmaximal, characteristic
2C2×#16839640C211yesmaximal, characteristic
3C2×#16839640C211yesmaximal, characteristic
4C2×#16839636C211yesmaximal, characteristic, complemented
5C2×#16839624C211yesmaximal, characteristic, complemented
6C2×#16839609C211yesmaximal, characteristic, complemented
7C2×#95×D61C211yesmaximal, characteristic, complemented
8#21444085C211yesmaximal, characteristic, complemented
9#21444065C211yesmaximal, characteristic, complemented
10#21444063C211yesmaximal, characteristic, complemented
11#21444055C211yesmaximal, characteristic, complemented
12#21444055C211yesmaximal, characteristic, complemented
13#21444048C211yesmaximal, characteristic, complemented
14#21444047C211yesmaximal, characteristic, complemented
15C61×#1445C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519762—24no—
21C2×#14519762—24no—
22C2×#14519762C418yescomplemented
23C22×C4⋊Dic61C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37#16839640—24no—
38#16839640—24no—
39#16839636—24no—
40#16839624—24no—
41#16839609—24no—
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52#95×D61—24no—
53C22×C4⋊C4×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C2×#95×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C24×D61C2311yescharacteristic
61C24×D61C2311yescharacteristic
62C22×D244—22no—
63C22×D244—22no—
64C22×D244—22no—
65C22×D244—22no—
66C22×D244—22no—
67C22×D244—22no—
68C22×D244C2×C414yes—
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
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—22no—
83C22×C4×D61—22no—
84C22×C4×D61—22no—
85C22×C4×D61—22no—
86C22×C4×D61—22no—
87C22×C4×D61—22no—
88C22×C4×D61—22no—
89C22×C4×D61—22no—
90C22×C4×D61—41no—
91C22×C4×D61—41no—
92C22×C4×D61—41no—
93C22×C4×D61—41no—
94C22×C4×D61C2×C414yes—
95C22×C4×D61D414yes—
96#14519762—232no—
97C2×C4⋊Dic61—22no—
98C2×C4⋊Dic61—22no—
99C2×C4⋊Dic61—41no—
100C2×#11758196—22no—
101C2×#11758196—22no—
102C2×#11758196—22no—
103C2×#11758196—22no—
104C2×#11758196—41no—
105C2×#11758196C2×C414yescomplemented
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
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—22no—
119C2×#11758198—22no—
120C2×#11758198—22no—
121C2×#11758198—22no—
122C2×#11758198—22no—
123C2×#11758198—41no—
124C2×#11758198—41no—
125C2×#11758198—41no—
126C2×#11758198—41no—
127C2×#11758198C2×C414yes—
128C2×#11758198C2×C414yescomplemented
129C2×#11758198C2×C414yescomplemented
130C2×#11758198D414yes—
131C2×#11758198D414yes—
132C2×#11758198D414yes—
133C2×C4×Dic61—22no—
134C2×C4×Dic61—22no—
135C2×C4×Dic61—22no—
136C2×C4×Dic61—22no—
137C2×C4×Dic61—41no—
138C2×C4×Dic61—41no—
139#14519684—22no—
140#14519684—22no—
141#14519684—22no—
142#14519684—22no—
143#14519684—22no—
144#14519684—22no—
145#14519684—22no—
146#14519684—22no—
147#14519684—22no—
148#14519684—22no—
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C23×C4×C61C2311yescharacteristic
154C23×C4×C61C2311yescharacteristic
155C23×C4×C61C2311yescharacteristic
156C2×C4⋊C4×C61—22no—
157C2×C4⋊C4×C61—22no—
158C2×C4⋊C4×C61C2×C414yescomplemented
159#95×C61—22no—
160#95×C61—22no—
161#95×C61—22no—
162#95×C61—22no—
163#95×C61—22no—
164#95×C61—22no—
165C24×C61C2411yescharacteristic
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×D61—21no—
185C23×D61—21no—
186C23×D61—21no—
187C23×D61—21no—
188C23×D61C22×C412yes—
189C23×D61C22×C412yes—
190C23×D61C2×D412yes—
191C23×D61C2×D412yes—
192C23×D61C2×D412yes—
193C23×D61C2×D412yes—
194C23×D61#4112yes—
195C23×D61#4112yes—
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×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×C61C22×C412yes—
238C22×C4×C61C22×C412yes—
239C22×C4×C61C22×C412yes—
240C22×C4×C61C2×D412yes—
241C22×C4×C61C2×D412yes—
242C22×C4×C61C2×D412yes—
243C22×C4×C61C2×D412yes—
244C22×C4×C61#4112yes—
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×Dic61—21no—
275C22×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61C22×C412yes—
279C22×Dic61C22×C412yes—
280C22×Dic61C2×D412yes—
281C22×Dic61C2×D412yes—
282C22×Dic61C2×D412yes—
283C22×Dic61C2×D412yes—
284C22×Dic61#4112yes—
285C22×Dic61#4112yes—
286C22×Dic61#4112yes—
287C2×D244—28no—
288C2×D244—28no—
289C2×D244—28no—
290C2×D244—44no—
291C2×D244—44no—
292C2×D244—44no—
293C2×D244—44no—
294C2×C4×D61—28no—
295C2×C4×D61—28no—
296C2×C4×D61—28no—
297C2×C4×D61—28no—
298C2×C4×D61—28no—
299C2×C4×D61—28no—
300C2×C4×D61—44no—
301C2×C4×D61—44no—
302C2×C4×D61—44no—
303C2×C4×D61—44no—
304C2×C4×D61—44no—
305C2×C4×D61—44no—
306C2×C4×D61—44no—
307C2×C4×D61—44no—
308C2×C4×D61—44no—
309C2×C4×D61—44no—
310C2×C4×D61—44no—
311C2×C4×D61—44no—
312C2×C4×D61—44no—
313C2×C4×D61—44no—
314C2×C4×D61—44no—
315C4⋊C4×C61—28no—
316#11758198—28no—
317#11758198—28no—
318#11758198—28no—
319#11758198—44no—
320#11758198—44no—
321#11758198—44no—
322#11758198—44no—
323#11758198—44no—
324#11758198C22⋊C4116yescomplemented
325C4⋊Dic61—44no—
326#11758196—28no—
327#11758196—44no—
328C4×Dic61—44no—
329C4×Dic61—44no—
330C23×C61C23×C411yescharacteristic
331C23×C61C22×D411yescharacteristic
332C23×C61C22×D411yescharacteristic
333C23×C61C22×D411yescharacteristic
334C23×C61C22×D411yescharacteristic
335C23×C61C2×#4111yescharacteristic
336C23×C61C2×#4111yescharacteristic
337C23×C61C2×#4111yescharacteristic
338C23×C61C2×#4111yescharacteristic
339C23×C61C2×#4111yescharacteristic
340C23×C61C2×#4111yescharacteristic
341C23×C61H(5,𝔽2)11yescharacteristic
342C23×C61H(5,𝔽2)11yescharacteristic
343C23×C612−1+411yescharacteristic
344C23×C612−1+411yescharacteristic
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—22no—
370C22×D61—22no—
371C22×D61—22no—
372C22×D61—22no—
373C22×D61—22no—
374C22×D61—22no—
375C22×D61—22no—
376C22×D61—22no—
377C22×D61—22no—
378C22×D61—22no—
379C22×D61—22no—
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×D61—41no—
402C22×D61—41no—
403C22×D61—41no—
404C22×D61—41no—
405C22×D61—41no—
406C22×D61—41no—
407C22×D61—41no—
408C22×D61C2×C22⋊C414yes—
409C22×D61C4×D414yes—
410C22×D61C4×D414yes—
411C22×D61#12114yes—
412C22×D61#12114yes—
413C22×D61#12414yes—
414C22×D61#12714yes—
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—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—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×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×C61C2×C22⋊C414yes—
464C2×Dic61—22no—
465C2×Dic61—22no—
466C2×Dic61—22no—
467C2×Dic61—22no—
468C2×Dic61—22no—
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—41no—
486C2×Dic61—41no—
487C2×Dic61—41no—
488C2×Dic61—41no—
489C2×Dic61—41no—
490C2×Dic61—41no—
491C2×Dic61—41no—
492C2×Dic61—41no—
493C2×Dic61—41no—
494C2×Dic61—41no—
495C2×Dic61—41no—
496C2×Dic61—41no—
497C2×Dic61—41no—
498C2×Dic61—41no—
499C2×Dic61—41no—
500C2×Dic61—41no—
501C2×Dic61—41no—
502C2×Dic61—41no—
503C2×Dic61—41no—
504C2×Dic61C2×C22⋊C414yes—
505C2×Dic61#12314yescomplemented
506D244—416no—
507C4×D61—416no—
508C4×D61—416no—
509C4×D61—416no—
510#13996—611nomaximal, Sylow
511C22×C61C22×C22⋊C411yescharacteristic
512C22×C61C2×C4×D411yescharacteristic
513C22×C61C2×C4×D411yescharacteristic
514C22×C61C4×#4111yescharacteristic
515C22×C61C4×#4111yescharacteristic
516C22×C61#52011yescharacteristic
517C22×C61#52011yescharacteristic
518C22×C61C2×#12111yescharacteristic
519C22×C61C2×#12111yescharacteristic
520C22×C61C2×#12311yescharacteristic
521C22×C61#52511yescharacteristic
522C22×C61C2×#12411yescharacteristic
523C22×C61#52911yescharacteristic
524C22×C61#52911yescharacteristic
525C22×C61C2×#12711yescharacteristic
526C22×C61#53411yescharacteristic
527C22×C61#53611yescharacteristic
528C22×C61#53911yescharacteristic
529C22×C61#53911yescharacteristic
530C22×C61#54611yescharacteristic
531C22×C61#54611yescharacteristic
532C22×C61#54611yescharacteristic
533C22×C61#54611yescharacteristic
534C22×C61#54611yescharacteristic
535C22×C61#54611yescharacteristic
536C22×C61#54711yescharacteristic
537C22×C61#54711yescharacteristic
538C22×C61#54711yescharacteristic
539C22×C61#54711yescharacteristic
540C22×C61#54711yescharacteristic
541C22×C61#54711yescharacteristic
542C22×C61#55111yescharacteristic
543C22×C61#55111yescharacteristic
544C22×C61#55211yescharacteristic
545C22×C61#55211yescharacteristic
546C2×D61—24no—
547C2×D61—24no—
548C2×D61—24no—
549C2×D61—24no—
550C2×D61—24no—
551C2×D61—24no—
552C2×D61—24no—
553C2×D61—24no—
554C2×D61—24no—
555C2×D61—24no—
556C2×D61—24no—
557C2×D61—24no—
558C2×D61—24no—
559C2×D61—24no—
560C2×D61—42no—
561C2×D61—42no—
562C2×D61—42no—
563C2×D61—42no—
564C2×D61—42no—
565C2×D61—42no—
566C2×D61—42no—
567C2×D61—81no—
568C2×D61—81no—
569C2×D61—81no—
570C2×D61—81no—
571C2×D61—81no—
572C2×D61—81no—
573C2×D61—81no—
574C2×D61—81no—
575C2×D61#39018yes—
576C4×C61—24no—
577C4×C61—42no—
578C4×C61—42no—
579C4×C61—42no—
580C4×C61—42no—
581C4×C61—42no—
582C4×C61—81no—
583Dic61—24no—
584Dic61—24no—
585Dic61—42no—
586Dic61—42no—
587Dic61—42no—
588Dic61—81no—
589C22×#123—611no—
590C2×#386—611no—
591C2×#386—611no—
592C2×#385—611no—
593C2×#381—611no—
594C2×C4×C22⋊C4—611no—
595C22×#95—611no—
596#1445—611no—
597#1445D6111yescharacteristic, complemented
598#1439—611no—
599#1439—611no—
600#1437—611no—
601#1437—611no—
602C4⋊#95—611no—
603C4⋊#95—611no—
604C2×C61C2×#39011yescharacteristic
605C2×C61C4×#12311yescharacteristic
606C2×C61#232211yescharacteristic
607C2×C61#233911yescharacteristic
608C2×C61#233911yescharacteristic
609C2×C61#235911yescharacteristic
610C2×C61#235911yescharacteristic
611C2×C61#241211yescharacteristic
612C2×C61#241311yescharacteristic
613C2×C61#242511yescharacteristic
614C2×C61#242511yescharacteristic
615C2×C61#248811yescharacteristic
616C2×C61#248811yescharacteristic
617C2×C61#250111yescharacteristic
618C2×C61#253911yescharacteristic
619D61—28no—
620D61—82no—
621C23×D4—611no—
622C24×C4—611no—
623C24×C4—611no—
624C24×C4—611no—
625C2×#123—618no—
626C2×#123—1224no—
627C2×#123—1224no—
628C22×C4⋊C4—611no—
629C22×C4⋊C4—611no—
630C22×C4⋊C4—611no—
631C22×C4⋊C4C2×D6111yescharacteristic
632C22×C22⋊C4—611no—
633C22×C22⋊C4—611no—
634C22×C22⋊C4—611no—
635C22×C22⋊C4—611no—
636C22×C22⋊C4—611no—
637C22×C22⋊C4—611no—
638C22×C22⋊C4—611no—
639C22×C22⋊C4—611no—
640C22×C22⋊C4—611no—
641C22×C42—611no—
642C22×C42—611no—
643#386—1224no—
644#386—1224no—
645#385—1224no—
646#381—1224no—
647C4×C22⋊C4—1224no—
648C2×#95—611no—
649C2×#95—611no—
650C2×#95—611no—
651C2×#95—611no—
652C2×#95—611no—
653C2×#95—611no—
654C2×#95—611no—
655C2×#95—611no—
656C2×#95—611no—
657C2×#95—611no—
658C2×#95—1224no—
659C2×#95C2×D6111yescharacteristic
660C2×#95C2×D6111yescharacteristic
661C2×#95C2×D6111yescharacteristic
662C2×#95C2×D6111yescharacteristic
663C2×#95C2×D6111yescharacteristic
664C2×#95C2×D6111yescharacteristic
665C61#1399611yescharacteristic, complemented, Sylow
666C25—611no—
667C25—611no—
668C22×D4—614no—
669C22×D4—1222no—
670C22×D4—1222no—
671C22×D4—1222no—
672C22×D4—1222no—
673C22×D4—1222no—
674C22×D4—1222no—
675C23×C4—611no—
676C23×C4—611no—
677C23×C4—611no—
678C23×C4—611no—
679C23×C4—611no—
680C23×C4—614no—
681C23×C4—614no—
682C23×C4—611no—
683C23×C4—1222no—
684C23×C4—1222no—
685C23×C4—1222no—
686C23×C4—1222no—
687C23×C4—1222no—
688C23×C4—1222no—
689C23×C4—1222no—
690C23×C4—1222no—
691C23×C4—1222no—
692C23×C4—1222no—
693C23×C4—1222no—
694C23×C4—1222no—
695C23×C4—1222no—
696C23×C4—1222no—
697C23×C4—1222no—
698C23×C4—2441no—
699C23×C4—2441no—
700C23×C4—2441no—
701C23×C4—2441no—
702C23×C4C22×D6111yescharacteristic
703C23×C4C22×D6111yescharacteristic
704C23×C4C22×D6111yescharacteristic
705C23×C4C22×D6111yescharacteristic
706C23×C4C22×D6111yescharacteristic
707C23×C4C22×D6111yescharacteristic
708C23×C4C22×D6111yescharacteristic
709#123—12232no—
710C2×C4⋊C4—22no—
711C2×C4⋊C4—22no—
712C2×C4⋊C4—614no—
713C2×C4⋊C4—1222no—
714C2×C4⋊C4—1222no—
715C2×C4⋊C4—1222no—
716C2×C4⋊C4—1222no—
717C2×C4⋊C4—1222no—
718C2×C4⋊C4—1222no—
719C2×C4⋊C4—2441no—
720C2×C4⋊C4—2441no—
721C2×C4⋊C4C4×D6114yescomplemented
722C2×C22⋊C4—614no—
723C2×C22⋊C4—614no—
724C2×C22⋊C4—614no—
725C2×C22⋊C4—614no—
726C2×C22⋊C4—614no—
727C2×C22⋊C4—614no—
728C2×C22⋊C4—1222no—
729C2×C22⋊C4—1222no—
730C2×C22⋊C4—1222no—
731C2×C22⋊C4—1222no—
732C2×C22⋊C4—1222no—
733C2×C22⋊C4—1222no—
734C2×C22⋊C4—1222no—
735C2×C22⋊C4—1222no—
736C2×C22⋊C4—1222no—
737C2×C22⋊C4—1222no—
738C2×C22⋊C4—1222no—
739C2×C22⋊C4—1222no—
740C2×C22⋊C4—1222no—
741C2×C22⋊C4—1222no—
742C2×C22⋊C4—1222no—
743C2×C22⋊C4—1222no—
744C2×C22⋊C4—1222no—
745C2×C22⋊C4—2441no—
746C2×C22⋊C4—2441no—
747C2×C22⋊C4—2441no—
748C2×C22⋊C4—2441no—
749C2×C42—1222no—
750C2×C42—1222no—
751C2×C42—1222no—
752C2×C42—1222no—
753C2×C42—2441no—
754C2×C42—2441no—
755#95—22no—
756#95—22no—
757#95—22no—
758#95—22no—
759#95—22no—
760#95—22no—
761#95—1222no—
762#95—1222no—
763#95—1222no—
764#95—1222no—
765#95—1222no—
766#95—1222no—
767#95—1222no—
768#95—1222no—
769#95—1222no—
770#95—1222no—
771C24—612no—
772C24—612no—
773C24—612no—
774C24—612no—
775C24—612no—
776C24—612no—
777C24—612no—
778C24—612no—
779C24—1221no—
780C24—1221no—
781C24—1221no—
782C24—1221no—
783C24—1221no—
784C24—1221no—
785C24—1221no—
786C24—1221no—
787C24—1221no—
788C24—1221no—
789C24—1221no—
790C24—1221no—
791C24—1221no—
792C24—1221no—
793C24—1221no—
794C24—1221no—
795C24—1221no—
796C24—1221no—
797C24—1221no—
798C24—1221no—
799C24—1221no—
800C24—1221no—
801C24C23×D6111yescharacteristic
802C2×D4—1228no—
803C2×D4—1228no—
804C2×D4—1228no—
805C2×D4—2444no—
806C2×D4—2444no—
807C2×D4—2444no—
808C2×D4—2444no—
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—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—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—612no—
851C22×C4—612no—
852C22×C4—612no—
853C22×C4—612no—
854C22×C4—612no—
855C22×C4—612no—
856C22×C4—612no—
857C22×C4—612no—
858C22×C4—612no—
859C22×C4—1228no—
860C22×C4—1228no—
861C22×C4—1228no—
862C22×C4—1228no—
863C22×C4—1228no—
864C22×C4—1228no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—1221no—
871C22×C4—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—1221no—
878C22×C4—1221no—
879C22×C4—1221no—
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—1221no—
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—2444no—
899C22×C4—2444no—
900C22×C4—2444no—
901C22×C4—2444no—
902C22×C4—2444no—
903C22×C4—2444no—
904C22×C4—2444no—
905C22×C4—2444no—
906C22×C4—2444no—
907C22×C4—2444no—
908C22×C4—2444no—
909C22×C4—2444no—
910C22×C4—2444no—
911C22×C4—2444no—
912C22×C4—2444no—
913C22×C4C2×C4×D6112yes—
914C22×C4C2×C4×D6112yes—
915C22×C4C2×C4×D6112yes—
916C22×C4D4×D6112yes—
917C22×C4D4×D6112yes—
918C22×C4D4×D6112yes—
919C22×C4D4×D6112yes—
920C22×C4#1175822612yes—
921C4⋊C4—28no—
922C4⋊C4—1228no—
923C4⋊C4—2444no—
924C4⋊C4—2444no—
925C22⋊C4—6116no—
926C22⋊C4—1228no—
927C22⋊C4—1228no—
928C22⋊C4—1228no—
929C22⋊C4—2444no—
930C22⋊C4—2444no—
931C22⋊C4—2444no—
932C22⋊C4—2444no—
933C22⋊C4—2444no—
934C42—2444no—
935C42—2444no—
936C23—614no—
937C23—614no—
938C23—614no—
939C23—614no—
940C23—614no—
941C23—614no—
942C23—614no—
943C23—1222no—
944C23—1222no—
945C23—1222no—
946C23—1222no—
947C23—1222no—
948C23—1222no—
949C23—1222no—
950C23—1222no—
951C23—1222no—
952C23—1222no—
953C23—1222no—
954C23—1222no—
955C23—1222no—
956C23—1222no—
957C23—1222no—
958C23—1222no—
959C23—1222no—
960C23—1222no—
961C23—1222no—
962C23—1222no—
963C23—1222no—
964C23—1222no—
965C23—1222no—
966C23—1222no—
967C23—1222no—
968C23—1222no—
969C23—1222no—
970C23—1222no—
971C23—1222no—
972C23—1222no—
973C23—1222no—
974C23—1222no—
975C23—1222no—
976C23—1222no—
977C23—1222no—
978C23—2441no—
979C23—2441no—
980C23—2441no—
981C23—2441no—
982C23—2441no—
983C23—2441no—
984C23—2441no—
985C23—2441no—
986C23—2441no—
987C23—2441no—
988C23—2441no—
989C23—2441no—
990C23—2441no—
991C23—2441no—
992C23—2441no—
993C23—2441no—
994C23—2441no—
995C23—2441no—
996C23—2441no—
997C23—2441no—
998C23—2441no—
999C23—2441no—
1000C23—2441no—
1001C23—2441no—
1002C23—2441no—
1003C23—2441no—
1004C23—2441no—
1005C23—2441no—
1006C23C22×C4×D6111yescharacteristic
1007C23C2×D4×D6111yescharacteristic
1008C23C2×D4×D6111yescharacteristic
1009C23C2×D4×D6111yescharacteristic
1010C23C2×D4×D6111yescharacteristic
1011C23#41×D6111yescharacteristic
1012C23#41×D6111yescharacteristic
1013C23#41×D6111yescharacteristic
1014C23#41×D6111yescharacteristic
1015C23#41×D6111yescharacteristic
1016C23C2×#1175822611yescharacteristic
1017C23#1451982311yescharacteristic
1018C23#1451982311yescharacteristic
1019C23#1451982411yescharacteristic
1020C23#1451982511yescharacteristic
1021D4—24416no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
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—614no—
1071C2×C4—614no—
1072C2×C4—1222no—
1073C2×C4—1222no—
1074C2×C4—1222no—
1075C2×C4—1222no—
1076C2×C4—1222no—
1077C2×C4—1222no—
1078C2×C4—1222no—
1079C2×C4—1222no—
1080C2×C4—1222no—
1081C2×C4—1222no—
1082C2×C4—1222no—
1083C2×C4—1222no—
1084C2×C4—1222no—
1085C2×C4—1222no—
1086C2×C4—1222no—
1087C2×C4—1222no—
1088C2×C4—1222no—
1089C2×C4—1222no—
1090C2×C4—1222no—
1091C2×C4—1222no—
1092C2×C4—1222no—
1093C2×C4—24416no—
1094C2×C4—24416no—
1095C2×C4—24416no—
1096C2×C4—2441no—
1097C2×C4—2441no—
1098C2×C4—2441no—
1099C2×C4—2441no—
1100C2×C4—2441no—
1101C2×C4—2441no—
1102C2×C4—2441no—
1103C2×C4—2441no—
1104C2×C4—2441no—
1105C2×C4—2441no—
1106C2×C4—2441no—
1107C2×C4—2441no—
1108C2×C4—2441no—
1109C2×C4—2441no—
1110C2×C4—2441no—
1111C2×C4—2441no—
1112C2×C4—2441no—
1113C2×C4—2441no—
1114C2×C4—2441no—
1115C2×C4C22⋊C4×D6114yes—
1116C22—618no—
1117C22—1224no—
1118C22—1224no—
1119C22—1224no—
1120C22—1224no—
1121C22—1224no—
1122C22—1224no—
1123C22—1224no—
1124C22—1224no—
1125C22—1224no—
1126C22—1224no—
1127C22—1224no—
1128C22—1224no—
1129C22—1224no—
1130C22—1224no—
1131C22—4881no—
1132C22—4881no—
1133C22—4881no—
1134C22—4881no—
1135C22—4881no—
1136C22—4881no—
1137C22—4881no—
1138C22—4881no—
1139C22—2442no—
1140C22—2442no—
1141C22—2442no—
1142C22—2442no—
1143C22—2442no—
1144C22—2442no—
1145C22—2442no—
1146C22C2×C22⋊C4×D6111yescharacteristic
1147C22C4×D4×D6111yescharacteristic
1148C22C4×D4×D6111yescharacteristic
1149C22#1684023011yescharacteristic
1150C22C4×#1175822611yescharacteristic
1151C22#1684024211yescharacteristic
1152C22#1684024411yescharacteristic
1153C22#121×D6111yescharacteristic
1154C22#121×D6111yescharacteristic
1155C22#123×D6111yescharacteristic
1156C22#1684027511yescharacteristic
1157C22#124×D6111yescharacteristic
1158C22#1684029511yescharacteristic
1159C22#1684029711yescharacteristic
1160C22#127×D6111yescharacteristic
1161C22#1684032311yescharacteristic
1162C22#1684033511yescharacteristic
1163C22#1684035311yescharacteristic
1164C22#1684036011yescharacteristic
1165C22#1684040311yescharacteristic
1166C22#1684040311yescharacteristic
1167C22#1684040411yescharacteristic
1168C22#1684040411yescharacteristic
1169C22#1684040411yescharacteristic
1170C22#1684040511yescharacteristic
1171C22#1684041011yescharacteristic
1172C22#1684041011yescharacteristic
1173C22#1684041011yescharacteristic
1174C22#1684041411yescharacteristic
1175C22#1684041411yescharacteristic
1176C22#1684041511yescharacteristic
1177C22#1684043711yescharacteristic
1178C22#1684043711yescharacteristic
1179C22#1684044411yescharacteristic
1180C22#1684045011yescharacteristic
1181C4—24no—
1182C4—42no—
1183C4—42no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—81no—
1188C4—1224no—
1189C4—1224no—
1190C4—4881no—
1191C4—2442no—
1192C4—2442no—
1193C4—2442no—
1194C2—1228no—
1195C2—4882no—
1196C2#390×D6111yescharacteristic
1197C2#2144834011yescharacteristic
1198C2#2144849211yescharacteristic
1199C2#2144864311yescharacteristic
1200C2#2144864811yescharacteristic
1201C2#2144880411yescharacteristic
1202C2#2144881811yescharacteristic
1203C2#2144920811yescharacteristic
1204C2#2144921911yescharacteristic
1205C2#2144936311yescharacteristic
1206C2#2144937311yescharacteristic
1207C2#2145014011yescharacteristic
1208C2#2145014611yescharacteristic
1209C2#2145028511yescharacteristic
1210C2#2145074611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1445C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1445D61
hypocenterC61#13996
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
4. C2×#16839636C2semidirect
5. C2×#16839624C2semidirect
6. C2×#16839609C2semidirect
7. C2×#95×D61C2semidirect
8. #21444085C2semidirect
9. #21444065C2semidirect
10. #21444063C2semidirect
11. #21444055C2semidirect
12. #21444055C2semidirect
13. #21444048C2semidirect
14. #21444047C2semidirect
15. C61×#1445C2semidirect
22. C2×#14519762C4semidirect
105. C2×#11758196C2×C4semidirect
128. C2×#11758198C2×C4semidirect
129. C2×#11758198C2×C4semidirect
158. C2×C4⋊C4×C61C2×C4semidirect
324. #11758198C22⋊C4semidirect
505. C2×Dic61#123semidirect
597. #1445D61semidirect
665. C61#13996semidirect
721. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197622
C2×#168396402
C2×#168396362
C2×#168396242
C2×#168396092
C2×#95×D612
#214440852
#214440652
#214440632
#214440552
#214440482
#214440472
C61×#14452
#1399661