Finite Group Databasebeta

← #29603151

Subgroups — #29603151

Order 15616.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519749C211yesmaximal, characteristic
2C2×#16839665C211yesmaximal, characteristic, complemented
3C2×#16839662C211yesmaximal, characteristic, complemented
4C2×#16839662C211yesmaximal, characteristic, complemented
5C2×#16839662C211yesmaximal, characteristic, complemented
6C2×#16839659C211yesmaximal, characteristic, complemented
7C2×#16839620C211yesmaximal, characteristic, complemented
8C2×#16839613C211yesmaximal, characteristic, complemented
9C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
10#21444065C211yesmaximal, characteristic, complemented
11#21444062C211yesmaximal, characteristic, complemented
12#21444058C211yesmaximal, characteristic, complemented
13#21444056C211yesmaximal, characteristic, complemented
14#21444055C211yesmaximal, characteristic, complemented
15C61×#1438C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C2×#14519749—24no—
20C2×#14519749—24no—
21C2×#14519749C418yescomplemented
22C22×C4⋊Dic61C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41#16839665—24no—
42#16839662—24no—
43#16839662—24no—
44#16839662—24no—
45#16839659—24no—
46#16839620—24no—
47#16839613—24no—
48C22⋊C4×Dic61—24no—
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C23×D4×C61C2211yescharacteristic
56C22×C22⋊C4×C61C2211yescharacteristic
57C22×C22⋊C4×C61C2211yescharacteristic
58C22×C22⋊C4×C61C2211yescharacteristic
59C22×C22⋊C4×C61C2211yescharacteristic
60C2×#95×C61C2211yescharacteristic
61C2×#95×C61C2211yescharacteristic
62C24×D61C2311yescharacteristic
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—22no—
70C22×C22⋊D61—22no—
71C22×C22⋊D61—22no—
72C22×C22⋊D61—22no—
73C22×C22⋊D61—41no—
74C22×C22⋊D61—41no—
75C22×C22⋊D61C2×C414yes—
76C22×C22⋊D61C2×C414yes—
77C23×Dic61—22no—
78C23×Dic61—22no—
79C23×Dic61—22no—
80C23×Dic61—22no—
81C23×Dic61—22no—
82C23×Dic61—22no—
83C23×Dic61C2×C414yes—
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C23×Dic61C2311yescharacteristic
90C23×Dic61C2311yescharacteristic
91#14519749—232no—
92C2×C4⋊Dic61—22no—
93C2×C4⋊Dic61—22no—
94C2×C4⋊Dic61—41no—
95C2×#11758196—22no—
96C2×#11758196—22no—
97C2×#11758196—22no—
98C2×#11758196—22no—
99C2×#11758196—22no—
100C2×#11758196—22no—
101C2×#11758196—22no—
102C2×#11758196—41no—
103C2×#11758196C2×C414yes—
104C2×#11758196D414yes—
105C2×#11758196D414yes—
106C2×#11758196D414yescomplemented
107C2×C22⋊Dic61—22no—
108C2×C22⋊Dic61—22no—
109C2×C22⋊Dic61—22no—
110C2×C22⋊Dic61—22no—
111C2×C22⋊Dic61—22no—
112C2×C22⋊Dic61—22no—
113C2×C22⋊Dic61—22no—
114C2×C22⋊Dic61—22no—
115C2×C22⋊Dic61—22no—
116C2×C22⋊Dic61—22no—
117C2×C22⋊Dic61—22no—
118C2×C22⋊Dic61—41no—
119C2×C22⋊Dic61—41no—
120C2×C22⋊Dic61C2×C414yes—
121C2×C22⋊Dic61D414yescomplemented
122C2×#11758198—22no—
123C2×#11758198—22no—
124C2×#11758198—22no—
125C2×#11758198—22no—
126C2×#11758198—22no—
127C2×#11758198—22no—
128C2×#11758198—22no—
129C2×#11758198—22no—
130C2×#11758198—22no—
131C2×#11758198—22no—
132C2×#11758198—41no—
133C2×#11758198—41no—
134C2×#11758198—41no—
135C2×#11758198—41no—
136C2×#11758198C2×C414yes—
137C2×C4×Dic61—22no—
138C2×C4×Dic61—22no—
139C2×C4×Dic61—22no—
140C2×C4×Dic61—22no—
141C2×C4×Dic61—22no—
142C2×C4×Dic61—22no—
143C2×C4×Dic61—22no—
144C2×C4×Dic61—22no—
145C2×C4×Dic61—22no—
146C2×C4×Dic61—41no—
147C2×C4×Dic61—41no—
148C2×C4×Dic61D414yescomplemented
149#14519684—22no—
150#14519684—22no—
151#14519684—22no—
152#14519684—22no—
153#14519684—22no—
154#14519684—22no—
155C25×C61C2311yescharacteristic
156C25×C61C2311yescharacteristic
157C22×D4×C61—22no—
158C22×D4×C61—22no—
159C22×D4×C61—22no—
160C22×D4×C61—22no—
161C22×D4×C61—41no—
162C22×D4×C61—41no—
163C22×D4×C61C2×C414yes—
164C23×C4×C61C2311yescharacteristic
165C23×C4×C61C2311yescharacteristic
166C23×C4×C61C2311yescharacteristic
167C23×C4×C61C2311yescharacteristic
168C23×C4×C61C2311yescharacteristic
169C2×C22⋊C4×C61—22no—
170C2×C22⋊C4×C61—22no—
171C2×C22⋊C4×C61—22no—
172C2×C22⋊C4×C61—22no—
173C2×C22⋊C4×C61—22no—
174C2×C22⋊C4×C61—22no—
175C2×C22⋊C4×C61—22no—
176C2×C22⋊C4×C61—22no—
177C2×C22⋊C4×C61—41no—
178C2×C22⋊C4×C61—41no—
179C2×C22⋊C4×C61—41no—
180C2×C22⋊C4×C61—41no—
181#95×C61—22no—
182#95×C61—22no—
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×C61—21no—
202C24×C61—21no—
203C24×C61—21no—
204C24×C61—21no—
205C24×C61—21no—
206C24×C61—21no—
207C24×C61—21no—
208C24×C61—21no—
209C24×C61C22×C412yes—
210C24×C61C22×C412yes—
211C24×C61C2×D412yes—
212C24×C61#4112yes—
213C24×C61C2411yescharacteristic
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×D61—21no—
223C23×D61—21no—
224C23×D61—21no—
225C23×D61—21no—
226C23×D61—21no—
227C23×D61—21no—
228C23×D61C22×C412yes—
229C2×D4×C61—28no—
230C2×D4×C61—28no—
231C2×D4×C61—44no—
232C2×D4×C61—44no—
233C2×D4×C61—44no—
234C2×D4×C61—44no—
235C2×D4×C61—44no—
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×C61—21no—
264C22×C4×C61—21no—
265C22×C4×C61C22×C412yes—
266C22×C4×C61C2×D412yes—
267C22×C4×C61C2×D412yes—
268C22×C4×C61C2×D412yes—
269C22×C4×C61C2×D412yes—
270C22×C4×C61#4112yes—
271C2×C22⋊D61—28no—
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—
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—21no—
310C22×Dic61—21no—
311C22×Dic61—28no—
312C22×Dic61—28no—
313C22×Dic61—28no—
314C22×Dic61—21no—
315C22×Dic61—21no—
316C22×Dic61—21no—
317C22×Dic61—21no—
318C22×Dic61—21no—
319C22×Dic61—21no—
320C22×Dic61—21no—
321C22×Dic61—44no—
322C22×Dic61—44no—
323C22×Dic61—44no—
324C22×Dic61—44no—
325C22×Dic61C22×C412yes—
326C22×Dic61C22×C412yes—
327C22×Dic61C22×C412yes—
328C22×Dic61C2×D412yes—
329C22×Dic61C2×D412yes—
330C22×Dic61C2×D412yes—
331C22×Dic61C2×D412yes—
332C22×Dic61C2×D412yes—
333C22×Dic61C2×D412yes—
334C22×Dic61C2×D412yes—
335C22×Dic61C2×D412yes—
336C22×Dic61C2×D412yes—
337C22×Dic61C2×D412yes—
338C22×Dic61#4112yes—
339C22×Dic61#4112yes—
340C22×Dic61#4112yes—
341C22⋊C4×C61—28no—
342C22⋊C4×C61—44no—
343C22⋊C4×C61—44no—
344C22⋊C4×C61—44no—
345C22⋊Dic61—28no—
346C22⋊Dic61—28no—
347C22⋊Dic61—44no—
348C22⋊Dic61—44no—
349C22⋊Dic61—44no—
350#11758198—28no—
351#11758198—44no—
352#11758198—44no—
353#11758198—44no—
354#11758198—44no—
355C4⋊Dic61—44no—
356#11758196—28no—
357#11758196—44no—
358#11758196—44no—
359#11758196C22⋊C4116yescomplemented
360C4×Dic61—28no—
361C4×Dic61—44no—
362C4×Dic61—44no—
363C4×Dic61—44no—
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—41no—
390C23×C61—41no—
391C23×C61—41no—
392C23×C61—41no—
393C23×C61—41no—
394C23×C61—41no—
395C23×C61—41no—
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×C61—41no—
429C23×C61—41no—
430C23×C61—41no—
431C23×C61—41no—
432C23×C61—41no—
433C23×C61C4×D414yes—
434C23×C61C23×C411yescharacteristic
435C23×C61C22×D411yescharacteristic
436C23×C61C22×D411yescharacteristic
437C23×C61C22×D411yescharacteristic
438C23×C61C22×D411yescharacteristic
439C23×C61C22×D411yescharacteristic
440C23×C61C2×#4111yescharacteristic
441C23×C61C2×#4111yescharacteristic
442C23×C61C2×#4111yescharacteristic
443C23×C61C2×#4111yescharacteristic
444C23×C61C2×#4111yescharacteristic
445C23×C61H(5,𝔽2)11yescharacteristic
446C23×C61H(5,𝔽2)11yescharacteristic
447C23×C61H(5,𝔽2)11yescharacteristic
448C23×C612−1+411yescharacteristic
449C22×D61—22no—
450C22×D61—22no—
451C22×D61—22no—
452C22×D61—22no—
453C22×D61—22no—
454C22×D61—22no—
455C22×D61—22no—
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—
480C22×D61—41no—
481C22×D61—41no—
482C22×D61—41no—
483C22×D61—41no—
484D4×C61—416no—
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—22no—
499C2×C4×C61—22no—
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×C61C2×C22⋊C414yes—
520C22⋊D61—416no—
521C22⋊D61—416no—
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—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—416no—
556C2×Dic61—41no—
557C2×Dic61—41no—
558C2×Dic61—41no—
559C2×Dic61—41no—
560C2×Dic61—41no—
561C2×Dic61—41no—
562C2×Dic61—41no—
563C2×Dic61C2×C22⋊C414yes—
564C2×Dic61C2×C22⋊C414yes—
565C2×Dic61C4×D414yes—
566C2×Dic61C4×D414yes—
567C2×Dic61#12114yes—
568C2×Dic61#12114yes—
569C2×Dic61#12114yescomplemented
570C2×Dic61#12414yes—
571C2×Dic61#12714yes—
572#13998—611nomaximal, Sylow
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—81no—
596C22×C61—81no—
597C22×C61—81no—
598C22×C61—81no—
599C22×C61—81no—
600C22×C61—81no—
601C22×C61—81no—
602C22×C61—81no—
603C22×C61C22×C22⋊C411yescharacteristic
604C22×C61C2×C4×D411yescharacteristic
605C22×C61C2×C4×D411yescharacteristic
606C22×C61C2×C4×D411yescharacteristic
607C22×C61C4×#4111yescharacteristic
608C22×C61#51811yescharacteristic
609C22×C61#52011yescharacteristic
610C22×C61C2×#12111yescharacteristic
611C22×C61C2×#12111yescharacteristic
612C22×C61C2×#12111yescharacteristic
613C22×C61#52511yescharacteristic
614C22×C61C2×#12411yescharacteristic
615C22×C61#52911yescharacteristic
616C22×C61C2×#12711yescharacteristic
617C22×C61#53211yescharacteristic
618C22×C61#53511yescharacteristic
619C22×C61#53711yescharacteristic
620C22×C61#54011yescharacteristic
621C22×C61#54211yescharacteristic
622C22×C61D4211yescharacteristic
623C22×C61D4211yescharacteristic
624C22×C61D4211yescharacteristic
625C22×C61#54611yescharacteristic
626C22×C61#54611yescharacteristic
627C22×C61#54611yescharacteristic
628C22×C61#54711yescharacteristic
629C22×C61#54811yescharacteristic
630C22×C61#54811yescharacteristic
631C22×C61#54811yescharacteristic
632C22×C61#55011yescharacteristic
633C22×C61#55011yescharacteristic
634C22×C61#55011yescharacteristic
635C22×C61#55311yescharacteristic
636C22×C61#55311yescharacteristic
637C22×C61#55511yescharacteristic
638C2×D61—42no—
639C2×D61—42no—
640C2×D61—42no—
641C2×D61—42no—
642C2×D61—42no—
643C2×D61—42no—
644C2×D61—42no—
645C2×D61—81no—
646C2×D61—81no—
647C2×D61—81no—
648C2×D61—81no—
649C2×D61—81no—
650C2×D61—81no—
651C2×D61—81no—
652C2×D61—81no—
653C4×C61—24no—
654C4×C61—42no—
655C4×C61—42no—
656C4×C61—42no—
657C4×C61—81no—
658Dic61—24no—
659Dic61—24no—
660Dic61—42no—
661Dic61—42no—
662Dic61—42no—
663Dic61—81no—
664Dic61#39018yescomplemented
665C22×#121—611no—
666C2×#390—611no—
667C2×#390—611no—
668C2×#390—611no—
669C2×#390—611no—
670C2×#389—611no—
671C2×#380—611no—
672C2×C4×C4⋊C4—611no—
673C2×C4×C22⋊C4—611no—
674#1439—611no—
675#1439—611no—
676#1438—611no—
677#1438D6111yescharacteristic, complemented
678#1437—611no—
679#1437—611no—
680C2×C61—44no—
681C2×C61—82no—
682C2×C61C2×#39011yescharacteristic
683C2×C61C4×#12111yescharacteristic
684C2×C61#232411yescharacteristic
685C2×C61D4×C22⋊C411yescharacteristic
686C2×C61#234111yescharacteristic
687C2×C61#236111yescharacteristic
688C2×C61#236311yescharacteristic
689C2×C61#241411yescharacteristic
690C2×C61#241611yescharacteristic
691C2×C61#242611yescharacteristic
692C2×C61#242811yescharacteristic
693C2×C61#249011yescharacteristic
694C2×C61#249111yescharacteristic
695C2×C61#254011yescharacteristic
696C2×C61#254111yescharacteristic
697D61—82no—
698C23×D4—611no—
699C23×D4—611no—
700C23×D4C2×D6111yescharacteristic
701C24×C4—611no—
702C2×#121—618no—
703C2×#121—1224no—
704C2×#121—1224no—
705C22×C4⋊C4—611no—
706C22×C4⋊C4—611no—
707C22×C4⋊C4—611no—
708C22×C4⋊C4—611no—
709C22×C4⋊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⋊C4—611no—
719C22×C22⋊C4—611no—
720C22×C22⋊C4C2×D6111yescharacteristic
721C22×C22⋊C4C2×D6111yescharacteristic
722C22×C22⋊C4C2×D6111yescharacteristic
723C22×C22⋊C4C2×D6111yescharacteristic
724C22×C42—611no—
725C22×C42—611no—
726C22×C42—611no—
727C22×C42—611no—
728#390—1224no—
729#390—1224no—
730#390—1224no—
731#390—1224no—
732#389—1224no—
733#380—1224no—
734C4×C4⋊C4—1224no—
735C4×C22⋊C4—1224no—
736C2×#95—611no—
737C2×#95—611no—
738C2×#95—611no—
739C2×#95—611no—
740C2×#95—611no—
741C2×#95—611no—
742C2×#95C2×D6111yescharacteristic
743C2×#95C2×D6111yescharacteristic
744C61#1399811yescharacteristic, complemented, Sylow
745C25—611no—
746C25C22×D6111yescharacteristic
747C25C22×D6111yescharacteristic
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—41no—
753C22×D4—41no—
754C22×D4—614no—
755C22×D4—614no—
756C22×D4—1222no—
757C22×D4—1222no—
758C22×D4—1222no—
759C22×D4—1222no—
760C22×D4—1222no—
761C22×D4—1222no—
762C22×D4—1222no—
763C22×D4—1222no—
764C22×D4—1222no—
765C22×D4—1222no—
766C22×D4—2441no—
767C22×D4—2441no—
768C22×D4C4×D6114yes—
769C23×C4—611no—
770C23×C4—611no—
771C23×C4—611no—
772C23×C4—614no—
773C23×C4—611no—
774C23×C4—611no—
775C23×C4—611no—
776C23×C4—611no—
777C23×C4—1222no—
778C23×C4—1222no—
779C23×C4—1222no—
780C23×C4—1222no—
781C23×C4—1222no—
782C23×C4—1222no—
783C23×C4C22×D6111yescharacteristic
784C23×C4C22×D6111yescharacteristic
785C23×C4C22×D6111yescharacteristic
786C23×C4C22×D6111yescharacteristic
787C23×C4C22×D6111yescharacteristic
788#121—12232no—
789C2×C4⋊C4—614no—
790C2×C4⋊C4—614no—
791C2×C4⋊C4—614no—
792C2×C4⋊C4—614no—
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—1222no—
801C2×C4⋊C4—1222no—
802C2×C4⋊C4—2441no—
803C2×C4⋊C4—2441no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—614no—
817C2×C22⋊C4—614no—
818C2×C22⋊C4—614no—
819C2×C22⋊C4—1222no—
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—1222no—
831C2×C22⋊C4—1222no—
832C2×C22⋊C4—1222no—
833C2×C22⋊C4—1222no—
834C2×C22⋊C4—1222no—
835C2×C22⋊C4—1222no—
836C2×C22⋊C4—1222no—
837C2×C22⋊C4—1222no—
838C2×C22⋊C4—1222no—
839C2×C22⋊C4—1222no—
840C2×C22⋊C4—2441no—
841C2×C22⋊C4—2441no—
842C2×C22⋊C4—2441no—
843C2×C22⋊C4—2441no—
844C2×C22⋊C4—2441no—
845C2×C22⋊C4—2441no—
846C2×C42—614no—
847C2×C42—1222no—
848C2×C42—1222no—
849C2×C42—1222no—
850C2×C42—1222no—
851C2×C42—1222no—
852C2×C42—1222no—
853C2×C42—1222no—
854C2×C42—1222no—
855C2×C42—1222no—
856C2×C42—2441no—
857C2×C42—2441no—
858#95—22no—
859#95—22no—
860#95—1222no—
861#95—1222no—
862#95—1222no—
863#95—1222no—
864#95—1222no—
865#95—1222no—
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—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—612no—
893C24—1221no—
894C24—1221no—
895C24—1221no—
896C24—1221no—
897C24—1221no—
898C24—1221no—
899C24—1221no—
900C24—1221no—
901C24—1221no—
902C24—1221no—
903C24—1221no—
904C24—1221no—
905C24—1221no—
906C24—1221no—
907C24C2×C4×D6112yes—
908C24C2×C4×D6112yes—
909C24D4×D6112yes—
910C24#1175822412yes—
911C24C23×D6111yescharacteristic
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—1228no—
920C2×D4—1228no—
921C2×D4—1228no—
922C2×D4—1228no—
923C2×D4—1228no—
924C2×D4—2444no—
925C2×D4—2444no—
926C2×D4—2444no—
927C2×D4—2444no—
928C2×D4—2444no—
929C2×D4—2444no—
930C2×D4—2444no—
931C2×D4—2444no—
932C2×D4—2444no—
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—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—612no—
963C22×C4—612no—
964C22×C4—612no—
965C22×C4—612no—
966C22×C4—612no—
967C22×C4—612no—
968C22×C4—612no—
969C22×C4—612no—
970C22×C4—612no—
971C22×C4—612no—
972C22×C4—612no—
973C22×C4—612no—
974C22×C4—612no—
975C22×C4—612no—
976C22×C4—612no—
977C22×C4—612no—
978C22×C4—1228no—
979C22×C4—1228no—
980C22×C4—1228no—
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—1221no—
1009C22×C4—1221no—
1010C22×C4—1221no—
1011C22×C4—1221no—
1012C22×C4—1221no—
1013C22×C4—1221no—
1014C22×C4—2444no—
1015C22×C4—2444no—
1016C22×C4—2444no—
1017C22×C4—2444no—
1018C22×C4C2×C4×D6112yes—
1019C22×C4D4×D6112yes—
1020C22×C4D4×D6112yes—
1021C22×C4D4×D6112yes—
1022C22×C4D4×D6112yes—
1023C22×C4#1175822412yes—
1024C4⋊C4—6116no—
1025C4⋊C4—1228no—
1026C4⋊C4—2444no—
1027C4⋊C4—2444no—
1028C4⋊C4—2444no—
1029C22⋊C4—28no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—1228no—
1034C22⋊C4—1228no—
1035C22⋊C4—1228no—
1036C22⋊C4—2444no—
1037C22⋊C4—2444no—
1038C22⋊C4—2444no—
1039C22⋊C4—2444no—
1040C22⋊C4—2444no—
1041C22⋊C4—2444no—
1042C22⋊C4—2444no—
1043C42—1228no—
1044C42—2444no—
1045C42—2444no—
1046C42—2444no—
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—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
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—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—1222no—
1117C23—1222no—
1118C23—1222no—
1119C23—1222no—
1120C23—1222no—
1121C23—1222no—
1122C23—1222no—
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—
1144C23—2441no—
1145C23—2441no—
1146C23—2441no—
1147C23—2441no—
1148C23—2441no—
1149C23—2441no—
1150C23—2441no—
1151C23#1451973714yes—
1152C23C22×C4×D6111yescharacteristic
1153C23C2×D4×D6111yescharacteristic
1154C23C2×D4×D6111yescharacteristic
1155C23C2×D4×D6111yescharacteristic
1156C23C2×D4×D6111yescharacteristic
1157C23C2×D4×D6111yescharacteristic
1158C23#41×D6111yescharacteristic
1159C23#41×D6111yescharacteristic
1160C23#41×D6111yescharacteristic
1161C23C2×#1175822411yescharacteristic
1162C23C2×#1175822411yescharacteristic
1163C23#1451982211yescharacteristic
1164C23#1451982211yescharacteristic
1165C23#1451982211yescharacteristic
1166C23#1451982411yescharacteristic
1167D4—416no—
1168D4—24416no—
1169D4—24416no—
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—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
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—614no—
1206C2×C4—614no—
1207C2×C4—614no—
1208C2×C4—614no—
1209C2×C4—614no—
1210C2×C4—614no—
1211C2×C4—614no—
1212C2×C4—614no—
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—1222no—
1229C2×C4—1222no—
1230C2×C4—1222no—
1231C2×C4—1222no—
1232C2×C4—1222no—
1233C2×C4—1222no—
1234C2×C4—24416no—
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×C4—2441no—
1248C2×C4—2441no—
1249C2×C4—2441no—
1250C2×C4—2441no—
1251C2×C4—2441no—
1252C2×C4—2441no—
1253C2×C4—2441no—
1254C2×C4C22⋊C4×D6114yes—
1255C22—24no—
1256C22—24no—
1257C22—24no—
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—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—4881no—
1286C22—4881no—
1287C22—4881no—
1288C22—4881no—
1289C22—4881no—
1290C22—4881no—
1291C22—4881no—
1292C22—4881no—
1293C22—2442no—
1294C22—2442no—
1295C22—2442no—
1296C22—2442no—
1297C22—2442no—
1298C22—2442no—
1299C22—2442no—
1300C22C2×C22⋊C4×D6111yescharacteristic
1301C22C4×D4×D6111yescharacteristic
1302C22C4×D4×D6111yescharacteristic
1303C22C2×#1451973711yescharacteristic
1304C22C4×#1175822411yescharacteristic
1305C22#1684023511yescharacteristic
1306C22#1684024111yescharacteristic
1307C22#121×D6111yescharacteristic
1308C22#121×D6111yescharacteristic
1309C22#121×D6111yescharacteristic
1310C22#1684026811yescharacteristic
1311C22#124×D6111yescharacteristic
1312C22#1684028911yescharacteristic
1313C22#127×D6111yescharacteristic
1314C22#1684030711yescharacteristic
1315C22#1684032711yescharacteristic
1316C22#1684034111yescharacteristic
1317C22#1684036211yescharacteristic
1318C22#1684038011yescharacteristic
1319C22#1684039411yescharacteristic
1320C22#1684039411yescharacteristic
1321C22#1684039411yescharacteristic
1322C22#1684039911yescharacteristic
1323C22#1684039911yescharacteristic
1324C22#1684039911yescharacteristic
1325C22#1684041011yescharacteristic
1326C22#1684041811yescharacteristic
1327C22#1684041811yescharacteristic
1328C22#1684042011yescharacteristic
1329C22#1684043011yescharacteristic
1330C22#1684043011yescharacteristic
1331C22#1684043211yescharacteristic
1332C22#1684045511yescharacteristic
1333C22#1684045711yescharacteristic
1334C22#1684047611yescharacteristic
1335C4—24no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—81no—
1340C4—618no—
1341C4—1224no—
1342C4—1224no—
1343C4—4881no—
1344C4—2442no—
1345C4—2442no—
1346C4—2442no—
1347C2—44no—
1348C2—82no—
1349C2—4882no—
1350C2#390×D6111yescharacteristic
1351C2#2144832911yescharacteristic
1352C2#2144850911yescharacteristic
1353C2#2144863511yescharacteristic
1354C2#2144865811yescharacteristic
1355C2#2144883011yescharacteristic
1356C2#2144886011yescharacteristic
1357C2#2144923011yescharacteristic
1358C2#2144925211yescharacteristic
1359C2#2144937811yescharacteristic
1360C2#2144940011yescharacteristic
1361C2#2145016411yescharacteristic
1362C2#2145017511yescharacteristic
1363C2#2145075211yescharacteristic
1364C2#2145076011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1438C2
socle, cosocleC24×C61C24
prime radicalC22×#14519749C2
hypercenter#1438D61
hypocenterC61#13998
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#16839665C2semidirect
3. C2×#16839662C2semidirect
4. C2×#16839662C2semidirect
5. C2×#16839662C2semidirect
6. C2×#16839659C2semidirect
7. C2×#16839620C2semidirect
8. C2×#16839613C2semidirect
9. C2×C22⋊C4×Dic61C2semidirect
10. #21444065C2semidirect
11. #21444062C2semidirect
12. #21444058C2semidirect
13. #21444056C2semidirect
14. #21444055C2semidirect
15. C61×#1438C2semidirect
21. C2×#14519749C4semidirect
106. C2×#11758196D4semidirect
121. C2×C22⋊Dic61D4semidirect
148. C2×C4×Dic61D4semidirect
359. #11758196C22⋊C4semidirect
569. C2×Dic61#121semidirect
664. Dic61#390semidirect
677. #1438D61semidirect
744. C61#13998semidirect

Maximal subgroups

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

subgroupindex
C22×#145197492
C2×#168396652
C2×#168396622
C2×#168396592
C2×#168396202
C2×#168396132
C2×C22⋊C4×Dic612
#214440652
#214440622
#214440582
#214440562
#214440552
C61×#14382
#1399861