Finite Group Databasebeta

← #29607352

Subgroups — #29607352

Order 15616.

2594 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519750C211yesmaximal, characteristic
2C2×#16839663C211yesmaximal, characteristic, complemented
3C2×#16839655C211yesmaximal, characteristic, complemented
4C2×#16839641C211yesmaximal, characteristic, complemented
5C2×#16839641C211yesmaximal, characteristic, complemented
6C2×#16839619C211yesmaximal, characteristic, complemented
7#21444069C211yesmaximal, characteristic, complemented
8#21444065C211yesmaximal, characteristic, complemented
9#21444061C211yesmaximal, characteristic, complemented
10#21444059C211yesmaximal, characteristic, complemented
11#21444058C211yesmaximal, characteristic, complemented
12#21444058C211yesmaximal, characteristic, complemented
13#21444054C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C2×C61×#385C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519750—24no—
21C2×#14519750—24no—
22C2×#14519750C418yescomplemented
23C22×C4⋊Dic61C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37#16839663—24no—
38#16839655—24no—
39#16839641—24no—
40#16839641—24no—
41#16839619—24no—
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×#385—24no—
58C2×#95×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C24×D61C2311yescharacteristic
61C24×D61C2311yescharacteristic
62C22×D244—22no—
63C22×D244—22no—
64C22×D244—22no—
65C22×D244—22no—
66C22×D244—41no—
67C22×D244—41no—
68C22×D244C2×C414yescomplemented
69C22×C22⋊D61—22no—
70C22×C22⋊D61—22no—
71C22×C22⋊D61—22no—
72C22×C22⋊D61—22no—
73C22×C22⋊D61—22no—
74C22×C22⋊D61—22no—
75C22×C22⋊D61—22no—
76C22×C22⋊D61—22no—
77C22×C22⋊D61—41no—
78C22×C22⋊D61—41no—
79C22×C22⋊D61—41no—
80C22×C22⋊D61—41no—
81C22×C22⋊D61C2×C414yes—
82C22×C22⋊D61C2×C414yes—
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—41no—
94C22×C4×D61—41no—
95C22×C4×D61C2×C414yescomplemented
96#14519750—232no—
97C2×C4⋊Dic61—22no—
98C2×C4⋊Dic61—22no—
99C2×C4⋊Dic61—41no—
100C2×#11758196—22no—
101C2×#11758196—22no—
102C2×#11758196C2×C414yescomplemented
103C2×C22⋊Dic61—22no—
104C2×C22⋊Dic61—22no—
105C2×C22⋊Dic61—22no—
106C2×C22⋊Dic61—22no—
107C2×C22⋊Dic61—41no—
108C2×C22⋊Dic61—41no—
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—41no—
121C2×#11758198—41no—
122C2×#11758198—41no—
123C2×#11758198—41no—
124C2×#11758198—41no—
125C2×#11758198—41no—
126C2×#11758198—41no—
127C2×#11758198—41no—
128C2×#11758198—41no—
129C2×#11758198—41no—
130C2×#11758198—41no—
131C2×#11758198—41no—
132C2×#11758198—41no—
133C2×#11758198—41no—
134C2×#11758198C2×C414yescomplemented
135C2×#11758198D414yescomplemented
136C2×C4×Dic61—22no—
137C2×C4×Dic61—22no—
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—41no—
147#14519684—41no—
148#14519684D414yescomplemented
149C25×C61C2311yescharacteristic
150C23×C4×C61—22no—
151C23×C4×C61—22no—
152C23×C4×C61—22no—
153C23×C4×C61—41no—
154C23×C4×C61—41no—
155C23×C4×C61—41no—
156C23×C4×C61—41no—
157C23×C4×C61C2311yescharacteristic
158C23×C4×C61C2311yescharacteristic
159C23×C4×C61C2311yescharacteristic
160C23×C4×C61C2311yescharacteristic
161C23×C4×C61C2311yescharacteristic
162C23×C4×C61C2311yescharacteristic
163C2×C4⋊C4×C61—22no—
164C2×C4⋊C4×C61—22no—
165C2×C4⋊C4×C61—22no—
166C2×C4⋊C4×C61—22no—
167C2×C4⋊C4×C61—41no—
168C2×C4⋊C4×C61—41no—
169C2×C22⋊C4×C61—22no—
170C2×C22⋊C4×C61—41no—
171C2×C22⋊C4×C61—41no—
172C2×C22⋊C4×C61C2×C414yes—
173C2×C22⋊C4×C61D414yes—
174C2×C22⋊C4×C61D414yes—
175#95×C61—22no—
176#95×C61—22no—
177C24×C61—21no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61—21no—
181C24×C61—21no—
182C24×C61—21no—
183C24×C61—21no—
184C24×C61—21no—
185C24×C61—21no—
186C24×C61—21no—
187C24×C61—21no—
188C24×C61—21no—
189C24×C61C22×C412yes—
190C24×C61C2×D412yes—
191C24×C61C2×D412yes—
192C24×C61C2411yescharacteristic
193C23×D61—21no—
194C23×D61—21no—
195C23×D61—21no—
196C23×D61—21no—
197C23×D61—21no—
198C23×D61—21no—
199C23×D61—21no—
200C23×D61—21no—
201C23×D61—21no—
202C23×D61—21no—
203C23×D61—21no—
204C23×D61—21no—
205C23×D61—21no—
206C23×D61—21no—
207C23×D61—21no—
208C23×D61—21no—
209C23×D61—21no—
210C23×D61—21no—
211C23×D61—21no—
212C23×D61—21no—
213C23×D61—21no—
214C23×D61—21no—
215C23×D61—21no—
216C23×D61—21no—
217C23×D61—21no—
218C23×D61—21no—
219C23×D61C22×C412yes—
220C23×D61C22×C412yes—
221C23×D61C2×D412yes—
222C23×D61#4112yes—
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×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61—44no—
258C22×C4×C61—44no—
259C22×C4×C61—44no—
260C22×C4×C61—44no—
261C22×C4×C61—44no—
262C22×C4×C61—44no—
263C22×C4×C61—44no—
264C22×C4×C61C22×C412yes—
265C22×C4×C61C22×C412yes—
266C22×C4×C61C2×D412yes—
267C22×C4×C61C2×D412yes—
268C22×C4×C61C2×D412yes—
269C22×C4×C61C2×D412yes—
270C22×C4×C61C2×D412yes—
271C22×C4×C61C2×D412yes—
272C2×C22⋊D61—28no—
273C2×C22⋊D61—28no—
274C2×C22⋊D61—28no—
275C2×C22⋊D61—28no—
276C2×C22⋊D61—44no—
277C2×C22⋊D61—44no—
278C2×C22⋊D61—44no—
279C2×C22⋊D61—44no—
280C2×C22⋊D61—44no—
281C2×C22⋊D61—44no—
282C2×C22⋊D61—44no—
283C2×C22⋊D61—44no—
284C2×C22⋊D61—44no—
285C2×C22⋊D61—44no—
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—21no—
297C22×Dic61—21no—
298C22×Dic61—21no—
299C22×Dic61—21no—
300C22×Dic61—21no—
301C22×Dic61—21no—
302C22×Dic61—21no—
303C22×Dic61—21no—
304C22×Dic61—21no—
305C22×Dic61—21no—
306C22×Dic61—21no—
307C22×Dic61—21no—
308C22×Dic61—21no—
309C22×Dic61—21no—
310C22×Dic61—21no—
311C22×Dic61—21no—
312C22×Dic61—21no—
313C22×Dic61—21no—
314C22×Dic61—21no—
315C22×Dic61—21no—
316C22×Dic61—21no—
317C22×Dic61—21no—
318C22×Dic61—21no—
319C22×Dic61—21no—
320C22×Dic61—21no—
321C22×Dic61—21no—
322C22×Dic61C22×C412yes—
323C22×Dic61C22×C412yes—
324C22×Dic61C2×D412yes—
325C22×Dic61C2×D412yes—
326C22×Dic61C2×D412yes—
327C22×Dic61#4112yes—
328C2×D244—28no—
329C2×D244—28no—
330C2×D244—44no—
331C2×D244—44no—
332C2×D244—44no—
333C2×D244—44no—
334C2×D244—44no—
335C2×C4×D61—28no—
336C2×C4×D61—28no—
337C2×C4×D61—44no—
338C2×C4×D61—44no—
339C2×C4×D61—44no—
340C2×C4×D61—44no—
341C2×C4×D61—44no—
342C4⋊C4×C61—44no—
343C4⋊C4×C61—44no—
344C22⋊C4×C61—44no—
345C22⋊C4×C61C22⋊C4116yescomplemented
346C22⋊Dic61—44no—
347C22⋊Dic61—44no—
348#11758198—28no—
349#11758198—44no—
350#11758198—44no—
351#11758198—44no—
352#11758198—44no—
353#11758198—44no—
354#11758198—44no—
355#11758198—44no—
356#11758198—44no—
357C4⋊Dic61—44no—
358#11758196—28no—
359C4×Dic61—44no—
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×C61—22no—
369C23×C61—22no—
370C23×C61—22no—
371C23×C61—22no—
372C23×C61—22no—
373C23×C61—22no—
374C23×C61—22no—
375C23×C61—22no—
376C23×C61—22no—
377C23×C61—22no—
378C23×C61—41no—
379C23×C61—41no—
380C23×C61—41no—
381C23×C61—41no—
382C23×C61—41no—
383C23×C61—41no—
384C23×C61—41no—
385C23×C61—41no—
386C23×C61—41no—
387C23×C61—41no—
388C23×C61—41no—
389C23×C61—41no—
390C23×C61—41no—
391C23×C61—41no—
392C23×C61—41no—
393C23×C61—41no—
394C23×C61C2×C22⋊C414yes—
395C23×C61C23×C411yescharacteristic
396C23×C61C22×D411yescharacteristic
397C23×C61C22×D411yescharacteristic
398C23×C61C22×D411yescharacteristic
399C23×C61C22×D411yescharacteristic
400C23×C61C2×#4111yescharacteristic
401C23×C61C2×#4111yescharacteristic
402C23×C61H(5,𝔽2)11yescharacteristic
403C23×C61H(5,𝔽2)11yescharacteristic
404C23×C61H(5,𝔽2)11yescharacteristic
405C23×C61H(5,𝔽2)11yescharacteristic
406C23×C61H(5,𝔽2)11yescharacteristic
407C23×C61H(5,𝔽2)11yescharacteristic
408C23×C612−1+411yescharacteristic
409C23×C612−1+411yescharacteristic
410C22×D61—22no—
411C22×D61—22no—
412C22×D61—22no—
413C22×D61—22no—
414C22×D61—22no—
415C22×D61—22no—
416C22×D61—22no—
417C22×D61—22no—
418C22×D61—22no—
419C22×D61—22no—
420C22×D61—22no—
421C22×D61—22no—
422C22×D61—22no—
423C22×D61—22no—
424C22×D61—22no—
425C22×D61—22no—
426C22×D61—22no—
427C22×D61—22no—
428C22×D61—22no—
429C22×D61—22no—
430C22×D61—22no—
431C22×D61—22no—
432C22×D61—22no—
433C22×D61—22no—
434C22×D61—22no—
435C22×D61—41no—
436C22×D61—41no—
437C22×D61—41no—
438C22×D61—41no—
439C22×D61—41no—
440C22×D61—41no—
441C22×D61—41no—
442C22×D61—41no—
443C22×D61—41no—
444C22×D61—41no—
445C22×D61—41no—
446C22×D61—41no—
447C22×D61—41no—
448C22×D61—41no—
449C22×D61—41no—
450C22×D61—41no—
451C22×D61—41no—
452C22×D61—41no—
453C22×D61—41no—
454C22×D61—41no—
455C22×D61—41no—
456C22×D61—41no—
457C22×D61—41no—
458C22×D61—41no—
459C22×D61—41no—
460C22×D61—41no—
461C22×D61—41no—
462C22×D61—41no—
463C22×D61—41no—
464C22×D61—41no—
465C22×D61—41no—
466C22×D61—41no—
467C22×D61—41no—
468C22×D61—41no—
469C22×D61—41no—
470C22×D61—41no—
471C22×D61—41no—
472C22×D61—41no—
473C22×D61—41no—
474C22×D61—41no—
475C22×D61—41no—
476C22×D61—41no—
477C22×D61—41no—
478C22×D61—41no—
479C22×D61C4×D414yes—
480C2×C4×C61—22no—
481C2×C4×C61—22no—
482C2×C4×C61—22no—
483C2×C4×C61—22no—
484C2×C4×C61—22no—
485C2×C4×C61—22no—
486C2×C4×C61—22no—
487C2×C4×C61—22no—
488C2×C4×C61—22no—
489C2×C4×C61—22no—
490C2×C4×C61—22no—
491C2×C4×C61—22no—
492C2×C4×C61—22no—
493C2×C4×C61—22no—
494C2×C4×C61—22no—
495C2×C4×C61—22no—
496C2×C4×C61—22no—
497C2×C4×C61—22no—
498C2×C4×C61—416no—
499C2×C4×C61—41no—
500C2×C4×C61—41no—
501C2×C4×C61—41no—
502C2×C4×C61—41no—
503C2×C4×C61—41no—
504C2×C4×C61—41no—
505C2×C4×C61—41no—
506C2×C4×C61—41no—
507C2×C4×C61—41no—
508C2×C4×C61—41no—
509C2×C4×C61—41no—
510C2×C4×C61—41no—
511C2×C4×C61—41no—
512C2×C4×C61—41no—
513C2×C4×C61—41no—
514C2×C4×C61—41no—
515C2×C4×C61—41no—
516C2×C4×C61—41no—
517C2×C4×C61—41no—
518C2×C4×C61—41no—
519C2×C4×C61—41no—
520C2×C4×C61—41no—
521C2×C4×C61C2×C22⋊C414yes—
522C2×C4×C61C2×C22⋊C414yes—
523C22⋊D61—416no—
524C22⋊D61—416no—
525C2×Dic61—22no—
526C2×Dic61—22no—
527C2×Dic61—22no—
528C2×Dic61—22no—
529C2×Dic61—22no—
530C2×Dic61—22no—
531C2×Dic61—22no—
532C2×Dic61—22no—
533C2×Dic61—22no—
534C2×Dic61—22no—
535C2×Dic61—22no—
536C2×Dic61—22no—
537C2×Dic61—22no—
538C2×Dic61—22no—
539C2×Dic61—22no—
540C2×Dic61—41no—
541C2×Dic61—41no—
542C2×Dic61—41no—
543C2×Dic61—41no—
544C2×Dic61—41no—
545C2×Dic61—41no—
546C2×Dic61—41no—
547C2×Dic61—41no—
548C2×Dic61—41no—
549C2×Dic61—41no—
550C2×Dic61—41no—
551C2×Dic61—41no—
552C2×Dic61—41no—
553C2×Dic61—41no—
554C2×Dic61—41no—
555C2×Dic61—41no—
556C2×Dic61—41no—
557C2×Dic61—41no—
558C2×Dic61—41no—
559C2×Dic61—41no—
560C2×Dic61—41no—
561C2×Dic61—41no—
562C2×Dic61—41no—
563C2×Dic61—41no—
564C2×Dic61—41no—
565C2×Dic61—41no—
566C2×Dic61C4×D414yes—
567D244—416no—
568C4×D61—416no—
569#14361—611nomaximal, Sylow
570C22×C61—24no—
571C22×C61—24no—
572C22×C61—24no—
573C22×C61—42no—
574C22×C61—42no—
575C22×C61—42no—
576C22×C61—42no—
577C22×C61—42no—
578C22×C61—42no—
579C22×C61—42no—
580C22×C61—42no—
581C22×C61—42no—
582C22×C61—42no—
583C22×C61—42no—
584C22×C61—42no—
585C22×C61C22×C22⋊C411yescharacteristic
586C22×C61C2×C4×D411yescharacteristic
587C22×C61C2×C4×D411yescharacteristic
588C22×C61#51811yescharacteristic
589C22×C61#51811yescharacteristic
590C22×C61#52011yescharacteristic
591C22×C61#52011yescharacteristic
592C22×C61#53411yescharacteristic
593C22×C61#53511yescharacteristic
594C22×C61#53511yescharacteristic
595C22×C61#53611yescharacteristic
596C22×C61#53711yescharacteristic
597C22×C61#53711yescharacteristic
598C22×C61#53711yescharacteristic
599C22×C61#53711yescharacteristic
600C22×C61#53811yescharacteristic
601C22×C61#53911yescharacteristic
602C22×C61#54011yescharacteristic
603C22×C61#54211yescharacteristic
604C22×C61D4211yescharacteristic
605C22×C61D4211yescharacteristic
606C22×C61D4211yescharacteristic
607C22×C61D4211yescharacteristic
608C22×C61D4211yescharacteristic
609C22×C61#54611yescharacteristic
610C22×C61#54611yescharacteristic
611C22×C61#54611yescharacteristic
612C22×C61#54611yescharacteristic
613C22×C61#54711yescharacteristic
614C22×C61#54811yescharacteristic
615C22×C61#55311yescharacteristic
616C22×C61#56011yescharacteristic
617C22×C61#56011yescharacteristic
618C22×C61#56211yescharacteristic
619C22×C61#56211yescharacteristic
620C2×D61—24no—
621C2×D61—24no—
622C2×D61—24no—
623C2×D61—42no—
624C2×D61—42no—
625C2×D61—42no—
626C2×D61—42no—
627C2×D61—42no—
628C2×D61—42no—
629C2×D61—42no—
630C2×D61—42no—
631C2×D61—42no—
632C2×D61—42no—
633C2×D61—42no—
634C2×D61—42no—
635C2×D61—42no—
636C2×D61—42no—
637C2×D61—42no—
638C2×D61—42no—
639C2×D61—42no—
640C2×D61—42no—
641C2×D61—42no—
642C2×D61—81no—
643C2×D61—81no—
644C2×D61—81no—
645C2×D61—81no—
646C2×D61—81no—
647C2×D61—81no—
648C2×D61—81no—
649C2×D61—81no—
650C4×C61—24no—
651C4×C61—24no—
652C4×C61—42no—
653C4×C61—42no—
654C4×C61—81no—
655C4×C61—81no—
656Dic61—24no—
657Dic61—42no—
658Dic61—42no—
659Dic61—42no—
660Dic61—81no—
661Dic61—81no—
662C22×#121—611no—
663C2×#390—611no—
664C2×#388—611no—
665C2×#386—611no—
666C2×#386—611no—
667C2×#385D6111yescharacteristic, complemented
668C2×#380—611no—
669#1441—611no—
670#1439—611no—
671#1439—611no—
672#1438—611no—
673#1438—611no—
674#1438—611no—
675#1436—611no—
676C22⋊#95—611no—
677C2×C61—44no—
678C2×C61#231111yescharacteristic
679C2×C61#232411yescharacteristic
680C2×C61#232511yescharacteristic
681C2×C61D4×C22⋊C411yescharacteristic
682C2×C61D4×C22⋊C411yescharacteristic
683C2×C61#236111yescharacteristic
684C2×C61#237711yescharacteristic
685C2×C61#266911yescharacteristic
686C2×C61#267111yescharacteristic
687C2×C61#267211yescharacteristic
688C2×C61#267511yescharacteristic
689C2×C61#267611yescharacteristic
690C2×C61#268111yescharacteristic
691C2×C61#269111yescharacteristic
692C2×C61#270311yescharacteristic
693D61—44no—
694D61—82no—
695C23×D4—611no—
696C23×D4—611no—
697C23×D4—611no—
698C24×C4—611no—
699C24×C4C2×D6111yescharacteristic
700C2×#121—618no—
701C2×#121—1224no—
702C2×#121—1224no—
703C22×C4⋊C4—611no—
704C22×C4⋊C4—611no—
705C22×C4⋊C4C2×D6111yescharacteristic
706C22×C4⋊C4C2×D6111yescharacteristic
707C22×C22⋊C4—611no—
708C22×C22⋊C4—611no—
709C22×C22⋊C4—611no—
710C22×C22⋊C4—611no—
711C22×C22⋊C4—611no—
712C22×C22⋊C4—611no—
713C22×C22⋊C4—611no—
714C22×C22⋊C4—611no—
715C22×C22⋊C4—611no—
716C22×C22⋊C4—611no—
717C22×C22⋊C4—611no—
718C22×C22⋊C4C2×D6111yescharacteristic
719C22×C22⋊C4C2×D6111yescharacteristic
720C22×C42—611no—
721#390—1224no—
722#388—1224no—
723#386—1224no—
724#386—1224no—
725#385—24no—
726#380—1224no—
727C2×#95—611no—
728C2×#95—611no—
729C2×#95—611no—
730C2×#95—611no—
731C2×#95—611no—
732C2×#95—611no—
733C2×#95—611no—
734C2×#95—611no—
735C2×#95—611no—
736C2×#95—611no—
737C2×#95C2×D6111yescharacteristic
738C2×#95C2×D6111yescharacteristic
739C61#1436111yescharacteristic, complemented, Sylow
740C25—611no—
741C25—611no—
742C25C22×D6111yescharacteristic
743C22×D4—614no—
744C22×D4—614no—
745C22×D4—614no—
746C22×D4—1222no—
747C22×D4—1222no—
748C22×D4—1222no—
749C22×D4—1222no—
750C22×D4—1222no—
751C22×D4—1222no—
752C22×D4—1222no—
753C22×D4—1222no—
754C22×D4—1222no—
755C22×D4—1222no—
756C22×D4—1222no—
757C22×D4—1222no—
758C22×D4—2441no—
759C22×D4—2441no—
760C22×D4—2441no—
761C22×D4—2441no—
762C22×D4—2441no—
763C22×D4—2441no—
764C23×C4—22no—
765C23×C4—22no—
766C23×C4—22no—
767C23×C4—41no—
768C23×C4—41no—
769C23×C4—41no—
770C23×C4—41no—
771C23×C4—611no—
772C23×C4—611no—
773C23×C4—611no—
774C23×C4—611no—
775C23×C4—614no—
776C23×C4—611no—
777C23×C4—611no—
778C23×C4—1222no—
779C23×C4—1222no—
780C23×C4—1222no—
781C23×C4—1222no—
782C23×C4—2441no—
783C23×C4—2441no—
784C23×C4C22×D6111yescharacteristic
785C23×C4C22×D6111yescharacteristic
786C23×C4C22×D6111yescharacteristic
787C23×C4C22×D6111yescharacteristic
788C23×C4C22×D6111yescharacteristic
789C23×C4C22×D6111yescharacteristic
790#121—12232no—
791C2×C4⋊C4—22no—
792C2×C4⋊C4—22no—
793C2×C4⋊C4—22no—
794C2×C4⋊C4—22no—
795C2×C4⋊C4—41no—
796C2×C4⋊C4—41no—
797C2×C4⋊C4—614no—
798C2×C4⋊C4—1222no—
799C2×C4⋊C4—1222no—
800C2×C4⋊C4—1222no—
801C2×C4⋊C4—1222no—
802C2×C4⋊C4—2441no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—614no—
807C2×C22⋊C4—614no—
808C2×C22⋊C4—1222no—
809C2×C22⋊C4—1222no—
810C2×C22⋊C4—1222no—
811C2×C22⋊C4—1222no—
812C2×C22⋊C4—1222no—
813C2×C22⋊C4—1222no—
814C2×C22⋊C4—1222no—
815C2×C22⋊C4—1222no—
816C2×C22⋊C4—1222no—
817C2×C22⋊C4—1222no—
818C2×C22⋊C4—1222no—
819C2×C22⋊C4—1222no—
820C2×C22⋊C4—1222no—
821C2×C22⋊C4—1222no—
822C2×C22⋊C4—1222no—
823C2×C22⋊C4—2441no—
824C2×C22⋊C4—2441no—
825C2×C22⋊C4—2441no—
826C2×C22⋊C4—2441no—
827C2×C22⋊C4—2441no—
828C2×C22⋊C4—2441no—
829C2×C22⋊C4—2441no—
830C2×C22⋊C4—2441no—
831C2×C22⋊C4—2441no—
832C2×C22⋊C4—2441no—
833C2×C22⋊C4—2441no—
834C2×C22⋊C4—2441no—
835C2×C22⋊C4—2441no—
836C2×C22⋊C4—2441no—
837C2×C22⋊C4—2441no—
838C2×C22⋊C4—2441no—
839C2×C22⋊C4C4×D6114yes—
840C2×C22⋊C4D24414yes—
841C2×C22⋊C4C22⋊D6114yes—
842C2×C42—1222no—
843C2×C42—1222no—
844C2×C42—2441no—
845#95—22no—
846#95—22no—
847#95—614no—
848#95—1222no—
849#95—1222no—
850#95—1222no—
851#95—1222no—
852#95—1222no—
853#95—1222no—
854#95—1222no—
855#95—2441no—
856#95—2441no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—612no—
870C24—612no—
871C24—612no—
872C24—612no—
873C24—1221no—
874C24—1221no—
875C24—1221no—
876C24—1221no—
877C24—1221no—
878C24—1221no—
879C24—1221no—
880C24—1221no—
881C24—1221no—
882C24—1221no—
883C24—1221no—
884C24—1221no—
885C24—1221no—
886C24—1221no—
887C24—1221no—
888C24—1221no—
889C24—1221no—
890C24—1221no—
891C24—1221no—
892C24—1221no—
893C24—1221no—
894C24—1221no—
895C24—1221no—
896C24—1221no—
897C24—1221no—
898C24—1221no—
899C24C2×C4×D6112yes—
900C24C2×D24412yes—
901C24C2×C22⋊D6112yes—
902C24C23×D6111yescharacteristic
903C2×D4—1228no—
904C2×D4—1228no—
905C2×D4—1228no—
906C2×D4—1228no—
907C2×D4—1228no—
908C2×D4—1228no—
909C2×D4—2444no—
910C2×D4—2444no—
911C2×D4—2444no—
912C2×D4—2444no—
913C2×D4—2444no—
914C2×D4—2444no—
915C2×D4—2444no—
916C2×D4—2444no—
917C2×D4—2444no—
918C2×D4—2444no—
919C2×D4—2444no—
920C2×D4—2444no—
921C2×D4—2444no—
922C2×D4—2444no—
923C2×D4—2444no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—612no—
966C22×C4—612no—
967C22×C4—612no—
968C22×C4—612no—
969C22×C4—612no—
970C22×C4—612no—
971C22×C4—1228no—
972C22×C4—1221no—
973C22×C4—1221no—
974C22×C4—1221no—
975C22×C4—1221no—
976C22×C4—1221no—
977C22×C4—1221no—
978C22×C4—1221no—
979C22×C4—1221no—
980C22×C4—1221no—
981C22×C4—1221no—
982C22×C4—1221no—
983C22×C4—1221no—
984C22×C4—1221no—
985C22×C4—1221no—
986C22×C4—1221no—
987C22×C4—1221no—
988C22×C4—1221no—
989C22×C4—1221no—
990C22×C4—1221no—
991C22×C4—1221no—
992C22×C4—1221no—
993C22×C4—1221no—
994C22×C4—1228no—
995C22×C4—1221no—
996C22×C4—1221no—
997C22×C4—1221no—
998C22×C4—1221no—
999C22×C4—1221no—
1000C22×C4—1221no—
1001C22×C4—1221no—
1002C22×C4—1221no—
1003C22×C4—1221no—
1004C22×C4—1221no—
1005C22×C4—1221no—
1006C22×C4—1221no—
1007C22×C4—1221no—
1008C22×C4—1221no—
1009C22×C4—2444no—
1010C22×C4—2444no—
1011C22×C4—2444no—
1012C22×C4—2444no—
1013C22×C4—2444no—
1014C22×C4C2×C4×D6112yes—
1015C22×C4C2×C4×D6112yes—
1016C22×C4C2×D24412yes—
1017C22×C4C2×D24412yes—
1018C22×C4D4×D6112yes—
1019C22×C4D4×D6112yes—
1020C22×C4C2×C22⋊D6112yes—
1021C22×C4C2×C22⋊D6112yes—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—1228no—
1025C4⋊C4—2444no—
1026C22⋊C4—44no—
1027C22⋊C4—1228no—
1028C22⋊C4—2444no—
1029C22⋊C4—2444no—
1030C22⋊C4—2444no—
1031C22⋊C4—2444no—
1032C22⋊C4—2444no—
1033C22⋊C4—2444no—
1034C22⋊C4—2444no—
1035C22⋊C4—2444no—
1036C22⋊C4—2444no—
1037C22⋊C4—2444no—
1038C22⋊C4#11758198116yescomplemented
1039C42—2444no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—614no—
1075C23—1222no—
1076C23—1222no—
1077C23—1222no—
1078C23—1222no—
1079C23—1222no—
1080C23—1222no—
1081C23—1222no—
1082C23—1222no—
1083C23—1222no—
1084C23—1222no—
1085C23—1222no—
1086C23—1222no—
1087C23—1222no—
1088C23—1222no—
1089C23—1222no—
1090C23—1222no—
1091C23—1222no—
1092C23—1222no—
1093C23—1222no—
1094C23—1222no—
1095C23—1222no—
1096C23—1222no—
1097C23—1222no—
1098C23—1222no—
1099C23—1222no—
1100C23—2441no—
1101C23—2441no—
1102C23—2441no—
1103C23—2441no—
1104C23—2441no—
1105C23—2441no—
1106C23—2441no—
1107C23—2441no—
1108C23—2441no—
1109C23—2441no—
1110C23—2441no—
1111C23—2441no—
1112C23—2441no—
1113C23—2441no—
1114C23—2441no—
1115C23—2441no—
1116C23—2441no—
1117C23—2441no—
1118C23—2441no—
1119C23—2441no—
1120C23—2441no—
1121C23—2441no—
1122C23—2441no—
1123C23—2441no—
1124C23—2441no—
1125C23—2441no—
1126C23—2441no—
1127C23—2441no—
1128C23—2441no—
1129C23—2441no—
1130C23—2441no—
1131C23—2441no—
1132C23—2441no—
1133C23—2441no—
1134C23—2441no—
1135C23—2441no—
1136C23—2441no—
1137C23—2441no—
1138C23—2441no—
1139C23—2441no—
1140C23—2441no—
1141C23—2441no—
1142C23—2441no—
1143C23—2441no—
1144C23C2×#1175819814yes—
1145C23C22×C4×D6111yescharacteristic
1146C23C2×D4×D6111yescharacteristic
1147C23C2×D4×D6111yescharacteristic
1148C23C22×C22⋊D6111yescharacteristic
1149C23C22×D24411yescharacteristic
1150C23#41×D6111yescharacteristic
1151C23#41×D6111yescharacteristic
1152C23#1451982211yescharacteristic
1153C23#1451982211yescharacteristic
1154C23#1451982211yescharacteristic
1155C23#1451982211yescharacteristic
1156C23#1451982311yescharacteristic
1157C23#1451982311yescharacteristic
1158C23#1451982511yescharacteristic
1159C23#1451982511yescharacteristic
1160D4—24416no—
1161D4—24416no—
1162D4—24416no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—416no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—614no—
1205C2×C4—1222no—
1206C2×C4—1222no—
1207C2×C4—1222no—
1208C2×C4—1222no—
1209C2×C4—1222no—
1210C2×C4—1222no—
1211C2×C4—1222no—
1212C2×C4—1222no—
1213C2×C4—1222no—
1214C2×C4—1222no—
1215C2×C4—1222no—
1216C2×C4—1222no—
1217C2×C4—1222no—
1218C2×C4—1222no—
1219C2×C4—1222no—
1220C2×C4—24416no—
1221C2×C4—2441no—
1222C2×C4—2441no—
1223C2×C4—2441no—
1224C2×C4—2441no—
1225C2×C4—2441no—
1226C2×C4—2441no—
1227C2×C4—2441no—
1228C2×C4—2441no—
1229C2×C4—2441no—
1230C2×C4—2441no—
1231C2×C4—2441no—
1232C2×C4—2441no—
1233C2×C4—2441no—
1234C2×C4—2441no—
1235C2×C4—2441no—
1236C2×C4—2441no—
1237C2×C4—2441no—
1238C2×C4—2441no—
1239C2×C4—2441no—
1240C2×C4—2441no—
1241C2×C4—2441no—
1242C2×C4—2441no—
1243C2×C4—2441no—
1244C2×C4—2441no—
1245C2×C4—2441no—
1246C2×C4—2441no—
1247C2×C4C2×#1175819814yes—
1248C2×C4C2×#1175819814yes—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—1224no—
1265C22—1224no—
1266C22—1224no—
1267C22—4881no—
1268C22—4881no—
1269C22—4881no—
1270C22—4881no—
1271C22—4881no—
1272C22—4881no—
1273C22—4881no—
1274C22—4881no—
1275C22—2442no—
1276C22—2442no—
1277C22—2442no—
1278C22—2442no—
1279C22—2442no—
1280C22—2442no—
1281C22—2442no—
1282C22—2442no—
1283C22—2442no—
1284C22—2442no—
1285C22—2442no—
1286C22—2442no—
1287C22—2442no—
1288C22—2442no—
1289C22—2442no—
1290C22—2442no—
1291C22—2442no—
1292C22—2442no—
1293C22—2442no—
1294C22C22×#1175819811yescharacteristic
1295C22C4×D4×D6111yescharacteristic
1296C22C4×D4×D6111yescharacteristic
1297C22#1684023411yescharacteristic
1298C22#1684023411yescharacteristic
1299C22#1684024311yescharacteristic
1300C22#1684024311yescharacteristic
1301C22#1684032211yescharacteristic
1302C22#1684032711yescharacteristic
1303C22#1684032911yescharacteristic
1304C22#1684033611yescharacteristic
1305C22#1684034211yescharacteristic
1306C22#1684034211yescharacteristic
1307C22#1684034311yescharacteristic
1308C22#1684034311yescharacteristic
1309C22#1684034811yescharacteristic
1310C22#1684035811yescharacteristic
1311C22#1684036411yescharacteristic
1312C22#1684038211yescharacteristic
1313C22#1684039411yescharacteristic
1314C22D4×C22⋊D6111yescharacteristic
1315C22D4×C22⋊D6111yescharacteristic
1316C22D4×D24411yescharacteristic
1317C22D4×D24411yescharacteristic
1318C22#1684040011yescharacteristic
1319C22#1684040011yescharacteristic
1320C22#1684040711yescharacteristic
1321C22#1684040711yescharacteristic
1322C22#1684041411yescharacteristic
1323C22#1684042211yescharacteristic
1324C22#1684045711yescharacteristic
1325C22#1684050111yescharacteristic
1326C22#1684050211yescharacteristic
1327C22#1684050811yescharacteristic
1328C22#1684050811yescharacteristic
1329C4—24no—
1330C4—24no—
1331C4—42no—
1332C4—42no—
1333C4—81no—
1334C4—81no—
1335C4—1224no—
1336C4—4881no—
1337C4—4881no—
1338C4—2442no—
1339C4—2442no—
1340C4—2442no—
1341C2—44no—
1342C2—4882no—
1343C2—2444no—
1344C2#2144841211yescharacteristic
1345C2#2144851111yescharacteristic
1346C2#2144851611yescharacteristic
1347C2D4×#1175819811yescharacteristic
1348C2D4×#1175819811yescharacteristic
1349C2#2144883811yescharacteristic
1350C2#2144897511yescharacteristic
1351C2#2145203311yescharacteristic
1352C2#2145205811yescharacteristic
1353C2#2145206611yescharacteristic
1354C2#2145211011yescharacteristic
1355C2#2145212311yescharacteristic
1356C2#2145216711yescharacteristic
1357C2#2145229811yescharacteristic
1358C2#2145245611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#385C2
socle, cosocleC24×C61C24
prime radicalC22×#14519750C2
hypercenterC2×#385D61
hypocenterC61#14361
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×#16839663C2semidirect
3. C2×#16839655C2semidirect
4. C2×#16839641C2semidirect
5. C2×#16839641C2semidirect
6. C2×#16839619C2semidirect
7. #21444069C2semidirect
8. #21444065C2semidirect
9. #21444061C2semidirect
10. #21444059C2semidirect
11. #21444058C2semidirect
12. #21444058C2semidirect
13. #21444054C2semidirect
14. #21444040C2semidirect
15. C2×C61×#385C2semidirect
22. C2×#14519750C4semidirect
68. C22×D244C2×C4semidirect
95. C22×C4×D61C2×C4semidirect
102. C2×#11758196C2×C4semidirect
134. C2×#11758198C2×C4semidirect
135. C2×#11758198D4semidirect
148. #14519684D4semidirect
345. C22⋊C4×C61C22⋊C4semidirect
667. C2×#385D61semidirect
739. C61#14361semidirect
1038. C22⋊C4#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×#145197502
C2×#168396632
C2×#168396552
C2×#168396412
C2×#168396192
#214440692
#214440652
#214440612
#214440592
#214440582
#214440542
#214440402
C2×C61×#3852
#1436161