Finite Group Databasebeta

← #29607342

Subgroups — #29607342

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×#14519749C211yesmaximal, characteristic
2C2×#16839662C211yesmaximal, characteristic, complemented
3C2×#16839656C211yesmaximal, characteristic, complemented
4C2×#16839642C211yesmaximal, characteristic, complemented
5C2×#16839639C211yesmaximal, characteristic, complemented
6C2×#16839634C211yesmaximal, characteristic, complemented
7C2×#16839620C211yesmaximal, characteristic, complemented
8#21444070C211yesmaximal, characteristic, complemented
9#21444063C211yesmaximal, characteristic, complemented
10#21444063C211yesmaximal, characteristic, complemented
11#21444058C211yesmaximal, characteristic, complemented
12#21444058C211yesmaximal, characteristic, complemented
13#21444050C211yesmaximal, characteristic, complemented
14#21444041C211yesmaximal, characteristic, complemented
15C61×#1438C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C24×Dic61C2211yescharacteristic
20C2×#14519749—24no—
21C2×#14519749—24no—
22C2×#14519749C418yescomplemented
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37#16839662—24no—
38#16839656—24no—
39#16839642—24no—
40#16839639—24no—
41#16839634—24no—
42#16839620—24no—
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C23×D4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C22×C22⋊C4×C61C2211yescharacteristic
56C22×C22⋊C4×C61C2211yescharacteristic
57C22×C22⋊C4×C61C2211yescharacteristic
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⋊D61—22no—
66C22×C22⋊D61—22no—
67C22×C22⋊D61—22no—
68C22×C22⋊D61—22no—
69C22×C22⋊D61—41no—
70C22×C22⋊D61—41no—
71C22×C22⋊D61—41no—
72C22×C22⋊D61—41no—
73C22×C22⋊D61C2×C414yes—
74C22×C22⋊D61C2×C414yescomplemented
75C23×Dic61—22no—
76C23×Dic61—22no—
77C23×Dic61—22no—
78C23×Dic61—22no—
79C23×Dic61—22no—
80C23×Dic61—22no—
81C23×Dic61—22no—
82C23×Dic61—41no—
83C23×Dic61—41no—
84C23×Dic61—41no—
85C23×Dic61—41no—
86C23×Dic61—41no—
87C23×Dic61—41no—
88C23×Dic61C2×C414yescomplemented
89C23×Dic61C2311yescharacteristic
90C23×Dic61C2311yescharacteristic
91C23×Dic61C2311yescharacteristic
92C23×Dic61C2311yescharacteristic
93C23×Dic61C2311yescharacteristic
94C23×Dic61C2311yescharacteristic
95C23×Dic61C2311yescharacteristic
96#14519749—232no—
97C2×#11758196—22no—
98C2×#11758196—22no—
99C2×#11758196—22no—
100C2×#11758196—22no—
101C2×#11758196—22no—
102C2×#11758196—22no—
103C2×#11758196—22no—
104C2×#11758196—22no—
105C2×#11758196—41no—
106C2×#11758196—41no—
107C2×#11758196—41no—
108C2×#11758196C2×C414yescomplemented
109C2×C22⋊Dic61—22no—
110C2×C22⋊Dic61—22no—
111C2×C22⋊Dic61—22no—
112C2×C22⋊Dic61—22no—
113C2×C22⋊Dic61—41no—
114C2×C22⋊Dic61—41no—
115C2×C22⋊Dic61—41no—
116C2×C22⋊Dic61—41no—
117C2×C22⋊Dic61C2×C414yes—
118C2×C22⋊Dic61D414yes—
119C2×C22⋊Dic61D414yes—
120C2×C22⋊Dic61D414yescomplemented
121C2×#11758198—22no—
122C2×#11758198—22no—
123C2×#11758198—22no—
124C2×#11758198—22no—
125C2×#11758198—22no—
126C2×#11758198—22no—
127C2×#11758198—41no—
128C2×#11758198—41no—
129C2×#11758198—41no—
130C2×#11758198—41no—
131C2×#11758198—41no—
132C2×#11758198—41no—
133C2×#11758198—41no—
134C2×#11758198—41no—
135C2×#11758198C2×C414yescomplemented
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—22no—
147#14519684—22no—
148#14519684D414yescomplemented
149C25×C61C2311yescharacteristic
150C25×C61C2311yescharacteristic
151C22×D4×C61—22no—
152C22×D4×C61—22no—
153C22×D4×C61—22no—
154C22×D4×C61—22no—
155C22×D4×C61—41no—
156C22×D4×C61—41no—
157C22×D4×C61C2×C414yes—
158C23×C4×C61C2311yescharacteristic
159C23×C4×C61C2311yescharacteristic
160C23×C4×C61C2311yescharacteristic
161C23×C4×C61C2311yescharacteristic
162C23×C4×C61C2311yescharacteristic
163C2×C22⋊C4×C61—22no—
164C2×C22⋊C4×C61—22no—
165C2×C22⋊C4×C61—22no—
166C2×C22⋊C4×C61—22no—
167C2×C22⋊C4×C61—22no—
168C2×C22⋊C4×C61—22no—
169C2×C22⋊C4×C61—41no—
170C2×C22⋊C4×C61—41no—
171C2×C22⋊C4×C61—41no—
172C2×C22⋊C4×C61—41no—
173C2×C22⋊C4×C61—41no—
174C2×C22⋊C4×C61—41no—
175#95×C61—41no—
176#95×C61—41no—
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×C61—21no—
190C24×C61—21no—
191C24×C61—21no—
192C24×C61—21no—
193C24×C61—21no—
194C24×C61—21no—
195C24×C61—21no—
196C24×C61—21no—
197C24×C61—21no—
198C24×C61—21no—
199C24×C61—21no—
200C24×C61—21no—
201C24×C61C22×C412yes—
202C24×C61C22×C412yes—
203C24×C61C2×D412yes—
204C24×C61C2×D412yes—
205C24×C61C2×D412yes—
206C24×C61#4112yes—
207C24×C61C2411yescharacteristic
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×D61—21no—
220C23×D61—21no—
221C23×D61—21no—
222C23×D61C22×C412yes—
223C2×D4×C61—28no—
224C2×D4×C61—28no—
225C2×D4×C61—44no—
226C2×D4×C61—44no—
227C2×D4×C61—44no—
228C2×D4×C61—44no—
229C2×D4×C61—44no—
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—21no—
258C22×C4×C61—21no—
259C22×C4×C61—21no—
260C22×C4×C61—21no—
261C22×C4×C61—21no—
262C22×C4×C61—21no—
263C22×C4×C61C22×C412yes—
264C22×C4×C61C2×D412yes—
265C2×C22⋊D61—28no—
266C2×C22⋊D61—28no—
267C2×C22⋊D61—28no—
268C2×C22⋊D61—28no—
269C2×C22⋊D61—44no—
270C2×C22⋊D61—44no—
271C2×C22⋊D61—44no—
272C2×C22⋊D61—44no—
273C2×C22⋊D61—44no—
274C2×C22⋊D61—44no—
275C2×C22⋊D61—44no—
276C2×C22⋊D61—44no—
277C2×C22⋊D61—44no—
278C2×C22⋊D61—44no—
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—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—28no—
310C22×Dic61—28no—
311C22×Dic61—21no—
312C22×Dic61—21no—
313C22×Dic61—21no—
314C22×Dic61—21no—
315C22×Dic61—21no—
316C22×Dic61—21no—
317C22×Dic61—21no—
318C22×Dic61—44no—
319C22×Dic61—44no—
320C22×Dic61—44no—
321C22×Dic61—44no—
322C22×Dic61—44no—
323C22×Dic61—44no—
324C22×Dic61—44no—
325C22×Dic61—44no—
326C22×Dic61—44no—
327C22×Dic61—44no—
328C22×Dic61—44no—
329C22×Dic61—44no—
330C22×Dic61C22×C412yes—
331C22×Dic61C22×C412yes—
332C22×Dic61C22×C412yes—
333C22×Dic61C2×D412yes—
334C22×Dic61C2×D412yes—
335C22×Dic61C2×D412yes—
336C22×Dic61C2×D412yes—
337C22×Dic61C2×D412yes—
338C22×Dic61C2×D412yes—
339C22×Dic61C2×D412yes—
340C22×Dic61C2×D412yes—
341C22×Dic61#4112yes—
342C22⋊C4×C61—44no—
343C22⋊C4×C61—44no—
344C22⋊C4×C61—44no—
345C22⋊C4×C61—44no—
346C22⋊Dic61—44no—
347C22⋊Dic61—44no—
348C22⋊Dic61—44no—
349C22⋊Dic61C22⋊C4116yescomplemented
350#11758198—28no—
351#11758198—44no—
352#11758198—44no—
353#11758198—44no—
354#11758198—44no—
355#11758196—28no—
356#11758196—44no—
357#11758196—44no—
358#11758196—44no—
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—22no—
379C23×C61—22no—
380C23×C61—22no—
381C23×C61—22no—
382C23×C61—22no—
383C23×C61—22no—
384C23×C61—22no—
385C23×C61—22no—
386C23×C61—22no—
387C23×C61—22no—
388C23×C61—22no—
389C23×C61—22no—
390C23×C61—22no—
391C23×C61—22no—
392C23×C61—22no—
393C23×C61—22no—
394C23×C61—22no—
395C23×C61—22no—
396C23×C61—41no—
397C23×C61—41no—
398C23×C61—41no—
399C23×C61—41no—
400C23×C61—41no—
401C23×C61—41no—
402C23×C61—41no—
403C23×C61—41no—
404C23×C61—41no—
405C23×C61—41no—
406C23×C61—41no—
407C23×C61—41no—
408C23×C61—41no—
409C23×C61—41no—
410C23×C61—41no—
411C23×C61—41no—
412C23×C61—41no—
413C23×C61—41no—
414C23×C61—41no—
415C23×C61—41no—
416C23×C61—41no—
417C23×C61—41no—
418C23×C61—41no—
419C23×C61—41no—
420C23×C61—41no—
421C23×C61—41no—
422C23×C61—41no—
423C23×C61—41no—
424C23×C61—41no—
425C23×C61—41no—
426C23×C61—41no—
427C23×C61—41no—
428C23×C61C2×C22⋊C414yes—
429C23×C61C4×D414yes—
430C23×C61C23×C411yescharacteristic
431C23×C61C22×D411yescharacteristic
432C23×C61C22×D411yescharacteristic
433C23×C61C22×D411yescharacteristic
434C23×C61C22×D411yescharacteristic
435C23×C61C2×#4111yescharacteristic
436C23×C61C2×#4111yescharacteristic
437C23×C61H(5,𝔽2)11yescharacteristic
438C23×C61H(5,𝔽2)11yescharacteristic
439C23×C61H(5,𝔽2)11yescharacteristic
440C23×C61H(5,𝔽2)11yescharacteristic
441C23×C61H(5,𝔽2)11yescharacteristic
442C23×C61H(5,𝔽2)11yescharacteristic
443C23×C612−1+411yescharacteristic
444C23×C612−1+411yescharacteristic
445C22×D61—22no—
446C22×D61—22no—
447C22×D61—22no—
448C22×D61—22no—
449C22×D61—22no—
450C22×D61—22no—
451C22×D61—22no—
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×D61—41no—
480D4×C61—416no—
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—41no—
488C2×C4×C61—41no—
489C2×C4×C61—41no—
490C2×C4×C61—41no—
491C2×C4×C61—41no—
492C2×C4×C61—41no—
493C2×C4×C61—41no—
494C2×C4×C61—41no—
495C2×C4×C61—41no—
496C2×C4×C61—41no—
497C2×C4×C61—41no—
498C2×C4×C61—41no—
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—
516C22⋊D61—416no—
517C22⋊D61—416no—
518C2×Dic61—22no—
519C2×Dic61—22no—
520C2×Dic61—22no—
521C2×Dic61—22no—
522C2×Dic61—22no—
523C2×Dic61—22no—
524C2×Dic61—22no—
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—22no—
541C2×Dic61—22no—
542C2×Dic61—22no—
543C2×Dic61—22no—
544C2×Dic61—22no—
545C2×Dic61—416no—
546C2×Dic61—416no—
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×Dic61C2×C22⋊C414yes—
567C2×Dic61C2×C22⋊C414yes—
568C2×Dic61C4×D414yes—
569#14361—611nomaximal, Sylow
570C22×C61—24no—
571C22×C61—24no—
572C22×C61—24no—
573C22×C61—24no—
574C22×C61—24no—
575C22×C61—24no—
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×C61—42no—
586C22×C61—42no—
587C22×C61—42no—
588C22×C61—42no—
589C22×C61—42no—
590C22×C61—42no—
591C22×C61—42no—
592C22×C61—42no—
593C22×C61—42no—
594C22×C61—42no—
595C22×C61—42no—
596C22×C61—42no—
597C22×C61—42no—
598C22×C61—42no—
599C22×C61—42no—
600C22×C61C22×C22⋊C411yescharacteristic
601C22×C61C2×C4×D411yescharacteristic
602C22×C61C2×C4×D411yescharacteristic
603C22×C61#51811yescharacteristic
604C22×C61#51811yescharacteristic
605C22×C61#52011yescharacteristic
606C22×C61#52011yescharacteristic
607C22×C61#53411yescharacteristic
608C22×C61#53511yescharacteristic
609C22×C61#53511yescharacteristic
610C22×C61#53611yescharacteristic
611C22×C61#53711yescharacteristic
612C22×C61#53711yescharacteristic
613C22×C61#53711yescharacteristic
614C22×C61#53711yescharacteristic
615C22×C61#53811yescharacteristic
616C22×C61#53911yescharacteristic
617C22×C61#54011yescharacteristic
618C22×C61#54211yescharacteristic
619C22×C61D4211yescharacteristic
620C22×C61D4211yescharacteristic
621C22×C61D4211yescharacteristic
622C22×C61D4211yescharacteristic
623C22×C61D4211yescharacteristic
624C22×C61#54611yescharacteristic
625C22×C61#54611yescharacteristic
626C22×C61#54611yescharacteristic
627C22×C61#54611yescharacteristic
628C22×C61#54711yescharacteristic
629C22×C61#54811yescharacteristic
630C22×C61#55311yescharacteristic
631C22×C61#56011yescharacteristic
632C22×C61#56011yescharacteristic
633C22×C61#56211yescharacteristic
634C22×C61#56211yescharacteristic
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—42no—
651C4×C61—42no—
652C4×C61—81no—
653C4×C61—81no—
654C4×C61—81no—
655Dic61—24no—
656Dic61—24no—
657Dic61—24no—
658Dic61—42no—
659Dic61—42no—
660Dic61—42no—
661Dic61—81no—
662C22×#121—611no—
663C2×#390—611no—
664C2×#388—611no—
665C2×#386—611no—
666C2×#386—611no—
667C2×#385—611no—
668C2×#380—611no—
669#1441—611no—
670#1439—611no—
671#1439—611no—
672#1438—611no—
673#1438—611no—
674#1438D6111yescharacteristic, complemented
675#1436—611no—
676C22⋊#95—611no—
677C2×C61—44no—
678C2×C61—44no—
679C2×C61#231111yescharacteristic
680C2×C61#232411yescharacteristic
681C2×C61#232511yescharacteristic
682C2×C61D4×C22⋊C411yescharacteristic
683C2×C61D4×C22⋊C411yescharacteristic
684C2×C61#236111yescharacteristic
685C2×C61#237711yescharacteristic
686C2×C61#266911yescharacteristic
687C2×C61#267111yescharacteristic
688C2×C61#267211yescharacteristic
689C2×C61#267511yescharacteristic
690C2×C61#267611yescharacteristic
691C2×C61#268111yescharacteristic
692C2×C61#269111yescharacteristic
693C2×C61#270311yescharacteristic
694D61—82no—
695C23×D4—611no—
696C23×D4—611no—
697C23×D4C2×D6111yescharacteristic
698C24×C4—611no—
699C24×C4—611no—
700C2×#121—618no—
701C2×#121—1224no—
702C2×#121—1224no—
703C22×C4⋊C4—611no—
704C22×C4⋊C4—611no—
705C22×C4⋊C4—611no—
706C22×C4⋊C4—611no—
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⋊C4C2×D6111yescharacteristic
717C22×C22⋊C4C2×D6111yescharacteristic
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—1224no—
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—
741C25C22×D6111yescharacteristic
742C25C22×D6111yescharacteristic
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4—614no—
750C22×D4—614no—
751C22×D4—1222no—
752C22×D4—1222no—
753C22×D4—1222no—
754C22×D4—1222no—
755C22×D4—1222no—
756C22×D4—1222no—
757C22×D4—1222no—
758C22×D4—1222no—
759C22×D4—2441no—
760C22×D4—2441no—
761C22×D4—2441no—
762C22×D4—2441no—
763C22×D4C4×D6114yes—
764C23×C4—611no—
765C23×C4—611no—
766C23×C4—611no—
767C23×C4—611no—
768C23×C4—611no—
769C23×C4—611no—
770C23×C4—614no—
771C23×C4—611no—
772C23×C4—1222no—
773C23×C4—1222no—
774C23×C4—1222no—
775C23×C4—1222no—
776C23×C4—1222no—
777C23×C4—1222no—
778C23×C4—1222no—
779C23×C4—2441no—
780C23×C4—2441no—
781C23×C4—2441no—
782C23×C4—2441no—
783C23×C4—2441no—
784C23×C4—2441no—
785C23×C4C22×D6111yescharacteristic
786C23×C4C22×D6111yescharacteristic
787C23×C4C22×D6111yescharacteristic
788C23×C4C22×D6111yescharacteristic
789C23×C4C22×D6111yescharacteristic
790#121—12232no—
791C2×C4⋊C4—614no—
792C2×C4⋊C4—1222no—
793C2×C4⋊C4—1222no—
794C2×C4⋊C4—1222no—
795C2×C4⋊C4—1222no—
796C2×C4⋊C4—1222no—
797C2×C4⋊C4—1222no—
798C2×C4⋊C4—1222no—
799C2×C4⋊C4—1222no—
800C2×C4⋊C4—2441no—
801C2×C4⋊C4—2441no—
802C2×C4⋊C4—2441no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—614no—
816C2×C22⋊C4—614no—
817C2×C22⋊C4—614no—
818C2×C22⋊C4—614no—
819C2×C22⋊C4—614no—
820C2×C22⋊C4—1222no—
821C2×C22⋊C4—1222no—
822C2×C22⋊C4—1222no—
823C2×C22⋊C4—1222no—
824C2×C22⋊C4—1222no—
825C2×C22⋊C4—1222no—
826C2×C22⋊C4—1222no—
827C2×C22⋊C4—1222no—
828C2×C22⋊C4—1222no—
829C2×C22⋊C4—1222no—
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⋊C4—2441no—
840C2×C22⋊C4—2441no—
841C2×C22⋊C4—2441no—
842C2×C42—1222no—
843C2×C42—1222no—
844C2×C42—2441no—
845#95—41no—
846#95—41no—
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—1222no—
856#95—1222no—
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—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—612no—
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—
896C24C2×C4×D6112yes—
897C24C2×C4×D6112yes—
898C24D4×D6112yes—
899C24D4×D6112yes—
900C24D4×D6112yes—
901C24#1175822412yes—
902C24C23×D6111yescharacteristic
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—1228no—
911C2×D4—1228no—
912C2×D4—1228no—
913C2×D4—1228no—
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—612no—
958C22×C4—612no—
959C22×C4—612no—
960C22×C4—612no—
961C22×C4—612no—
962C22×C4—612no—
963C22×C4—612no—
964C22×C4—612no—
965C22×C4—612no—
966C22×C4—612no—
967C22×C4—612no—
968C22×C4—612no—
969C22×C4—1228no—
970C22×C4—1228no—
971C22×C4—1221no—
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—1221no—
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—2444no—
1009C22×C4—2444no—
1010C22×C4—2444no—
1011C22×C4—2444no—
1012C22×C4—2444no—
1013C22×C4—2444no—
1014C22×C4—2444no—
1015C22×C4—2444no—
1016C22×C4—2444no—
1017C22×C4—2444no—
1018C22×C4—2444no—
1019C22×C4—2444no—
1020C22×C4C2×C4×D6112yes—
1021C22×C4D4×D6112yes—
1022C4⋊C4—1228no—
1023C4⋊C4—2444no—
1024C4⋊C4—2444no—
1025C4⋊C4—2444no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—6116no—
1031C22⋊C4—1228no—
1032C22⋊C4—2444no—
1033C22⋊C4—2444no—
1034C22⋊C4—2444no—
1035C22⋊C4—2444no—
1036C22⋊C4—2444no—
1037C22⋊C4—2444no—
1038C22⋊C4—2444no—
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—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—1222no—
1109C23—1222no—
1110C23—1222no—
1111C23—1222no—
1112C23—1222no—
1113C23—1222no—
1114C23—1222no—
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—
1143C23C22⋊C4×D6114yes—
1144C23#1451973714yes—
1145C23C22×C4×D6111yescharacteristic
1146C23C2×D4×D6111yescharacteristic
1147C23C2×D4×D6111yescharacteristic
1148C23C2×D4×D6111yescharacteristic
1149C23C2×D4×D6111yescharacteristic
1150C23#41×D6111yescharacteristic
1151C23C2×#1175822411yescharacteristic
1152C23#1451982211yescharacteristic
1153C23#1451982211yescharacteristic
1154C23#1451982211yescharacteristic
1155C23#1451982211yescharacteristic
1156C23#1451982211yescharacteristic
1157C23#1451982311yescharacteristic
1158C23#1451982411yescharacteristic
1159C23#1451982411yescharacteristic
1160D4—416no—
1161D4—24416no—
1162D4—24416no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
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—614no—
1199C2×C4—614no—
1200C2×C4—614no—
1201C2×C4—1222no—
1202C2×C4—1222no—
1203C2×C4—1222no—
1204C2×C4—1222no—
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—1222no—
1221C2×C4—1222no—
1222C2×C4—1222no—
1223C2×C4—1222no—
1224C2×C4—1222no—
1225C2×C4—1222no—
1226C2×C4—1222no—
1227C2×C4—1222no—
1228C2×C4—24416no—
1229C2×C4—2441no—
1230C2×C4—2441no—
1231C2×C4—2441no—
1232C2×C4—2441no—
1233C2×C4—2441no—
1234C2×C4—2441no—
1235C2×C4—2441no—
1236C2×C4—24416no—
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×C4—2441no—
1248C2×C4—2441no—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—4881no—
1280C22—4881no—
1281C22—4881no—
1282C22—4881no—
1283C22—4881no—
1284C22—4881no—
1285C22—4881no—
1286C22—4881no—
1287C22—2442no—
1288C22—2442no—
1289C22—2442no—
1290C22—2442no—
1291C22—2442no—
1292C22—2442no—
1293C22—2442no—
1294C22C2×C22⋊C4×D6111yescharacteristic
1295C22C4×D4×D6111yescharacteristic
1296C22C2×#1451973711yescharacteristic
1297C22#1684023411yescharacteristic
1298C22#1684023511yescharacteristic
1299C22#1684024111yescharacteristic
1300C22#1684024111yescharacteristic
1301C22#1684032011yescharacteristic
1302C22#1684032511yescharacteristic
1303C22#1684032711yescharacteristic
1304C22#1684033411yescharacteristic
1305C22#1684033911yescharacteristic
1306C22#1684033911yescharacteristic
1307C22#1684033911yescharacteristic
1308C22#1684033911yescharacteristic
1309C22#1684034711yescharacteristic
1310C22#1684035611yescharacteristic
1311C22#1684036211yescharacteristic
1312C22#1684037611yescharacteristic
1313C22#1684039411yescharacteristic
1314C22#1684039411yescharacteristic
1315C22#1684039411yescharacteristic
1316C22#1684039411yescharacteristic
1317C22#1684039611yescharacteristic
1318C22#1684039911yescharacteristic
1319C22#1684039911yescharacteristic
1320C22#1684040111yescharacteristic
1321C22#1684040411yescharacteristic
1322C22#1684041011yescharacteristic
1323C22#1684041811yescharacteristic
1324C22#1684045511yescharacteristic
1325C22#1684049911yescharacteristic
1326C22#1684050011yescharacteristic
1327C22#1684050611yescharacteristic
1328C22#1684050711yescharacteristic
1329C4—42no—
1330C4—42no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—1224no—
1335C4—1224no—
1336C4—1224no—
1337C4—4881no—
1338C4—2442no—
1339C4—2442no—
1340C4—2442no—
1341C2—44no—
1342C2—44no—
1343C2—4882no—
1344C2#2144840611yescharacteristic
1345C2#2144850511yescharacteristic
1346C2#2144852011yescharacteristic
1347C2#2144863511yescharacteristic
1348C2#2144863711yescharacteristic
1349C2#2144883011yescharacteristic
1350C2#2144897011yescharacteristic
1351C2#2145203011yescharacteristic
1352C2#2145204811yescharacteristic
1353C2#2145207211yescharacteristic
1354C2#2145210811yescharacteristic
1355C2#2145211311yescharacteristic
1356C2#2145217711yescharacteristic
1357C2#2145229311yescharacteristic
1358C2#2145246711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1438C2
socle, cosocleC24×C61C24
prime radicalC22×#14519749C2
hypercenter#1438D61
hypocenterC61#14361
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#16839662C2semidirect
3. C2×#16839656C2semidirect
4. C2×#16839642C2semidirect
5. C2×#16839639C2semidirect
6. C2×#16839634C2semidirect
7. C2×#16839620C2semidirect
8. #21444070C2semidirect
9. #21444063C2semidirect
10. #21444063C2semidirect
11. #21444058C2semidirect
12. #21444058C2semidirect
13. #21444050C2semidirect
14. #21444041C2semidirect
15. C61×#1438C2semidirect
22. C2×#14519749C4semidirect
74. C22×C22⋊D61C2×C4semidirect
88. C23×Dic61C2×C4semidirect
108. C2×#11758196C2×C4semidirect
120. C2×C22⋊Dic61D4semidirect
135. C2×#11758198C2×C4semidirect
148. #14519684D4semidirect
349. C22⋊Dic61C22⋊C4semidirect
674. #1438D61semidirect
739. C61#14361semidirect

Maximal subgroups

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

subgroupindex
C22×#145197492
C2×#168396622
C2×#168396562
C2×#168396422
C2×#168396392
C2×#168396342
C2×#168396202
#214440702
#214440632
#214440582
#214440502
#214440412
C61×#14382
#1436161