Finite Group Databasebeta

← #29611443

Subgroups — #29611443

Order 15616.

2774 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519760C211yesmaximal, characteristic, complemented
2C2×#16839677C211yesmaximal, characteristic, complemented
3C2×#16839670C211yesmaximal, characteristic
4C2×#16839641C211yesmaximal, characteristic, complemented
5C2×#16839635C211yesmaximal, characteristic, complemented
6#21444082C211yesmaximal, characteristic, complemented
7#21444068C211yesmaximal, characteristic, complemented
8#21444062C211yesmaximal, characteristic, complemented
9#21444061C211yesmaximal, characteristic, complemented
10#21444060C211yesmaximal, characteristic, complemented
11#21444058C211yesmaximal, characteristic, complemented
12#21444057C211yesmaximal, characteristic, complemented
13#21444052C211yesmaximal, characteristic, complemented
14#21444042C211yesmaximal, characteristic, complemented
15C22×C4×D4×C61C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C2×#14519760—24no—
19C2×#14519760—24no—
20C2×#14519760—24no—
21C22×#11758196C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35#16839677—24no—
36#16839670—24no—
37#16839641—24no—
38#16839635—24no—
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C23×D4×C61C2211yescharacteristic
52C24×C4×C61C2211yescharacteristic
53C24×C4×C61C2211yescharacteristic
54C2×C4×D4×C61—24no—
55C2×C4×D4×C61—24no—
56C2×C4×D4×C61—24no—
57C22×C4⋊C4×C61C2211yescharacteristic
58C22×C22⋊C4×C61C2211yescharacteristic
59C22×C22⋊C4×C61C2211yescharacteristic
60C22×C42×C61C2211yescharacteristic
61C24×D61C2311yescharacteristic
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—22no—
70C22×C22⋊D61—22no—
71C22×C22⋊D61—22no—
72C22×C22⋊D61—41no—
73C22×C22⋊D61—41no—
74C22×C22⋊D61—41no—
75C22×C22⋊D61—41no—
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83#14519760—232no—
84C2×#11758196—22no—
85C2×#11758196—22no—
86C2×#11758196—22no—
87C2×#11758196—22no—
88C2×#11758196—22no—
89C2×#11758196—22no—
90C2×#11758196—22no—
91C2×#11758196—41no—
92C2×#11758196D414yescomplemented
93C2×C22⋊Dic61—22no—
94C2×C22⋊Dic61—22no—
95C2×C22⋊Dic61—22no—
96C2×C22⋊Dic61—22no—
97C2×C22⋊Dic61—22no—
98C2×C22⋊Dic61—22no—
99C2×C22⋊Dic61—22no—
100C2×C22⋊Dic61—22no—
101C2×C22⋊Dic61—22no—
102C2×C22⋊Dic61—22no—
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×C22⋊Dic61—41no—
110C2×C22⋊Dic61—41no—
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×#11758198D414yescomplemented
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—22no—
131#14519684—22no—
132#14519684—22no—
133#14519684—22no—
134#14519684—22no—
135#14519684—41no—
136#14519684—41no—
137#14519684—41no—
138C25×C61C2311yescharacteristic
139C25×C61C2311yescharacteristic
140C22×D4×C61—22no—
141C22×D4×C61—22no—
142C22×D4×C61—22no—
143C22×D4×C61—22no—
144C22×D4×C61—22no—
145C22×D4×C61—22no—
146C22×D4×C61D414yes—
147C23×C4×C61—22no—
148C23×C4×C61—22no—
149C23×C4×C61—22no—
150C23×C4×C61—22no—
151C23×C4×C61—22no—
152C23×C4×C61—22no—
153C23×C4×C61—22no—
154C23×C4×C61—22no—
155C23×C4×C61—22no—
156C23×C4×C61—41no—
157C23×C4×C61—41no—
158C23×C4×C61—41no—
159C23×C4×C61—41no—
160C23×C4×C61D414yescomplemented
161C23×C4×C61C2311yescharacteristic
162C23×C4×C61C2311yescharacteristic
163C23×C4×C61C2311yescharacteristic
164C23×C4×C61C2311yescharacteristic
165C23×C4×C61C2311yescharacteristic
166C4×D4×C61—232no—
167C2×C4⋊C4×C61—22no—
168C2×C4⋊C4×C61—22no—
169C2×C4⋊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×C61D414yescomplemented
176C2×C42×C61—22no—
177C2×C42×C61—22no—
178C2×C42×C61—22no—
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×C61—21no—
202C24×C61—21no—
203C24×C61C2×D412yes—
204C24×C61C2×D412yes—
205C24×C61C2×D412yes—
206C24×C61C2×D412yes—
207C24×C61#4112yes—
208C24×C61#4112yes—
209C24×C61C2411yescharacteristic
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×D61—21no—
223C23×D61—21no—
224C23×D61C2×D412yes—
225C2×D4×C61—28no—
226C2×D4×C61—28no—
227C2×D4×C61—28no—
228C2×D4×C61—28no—
229C2×D4×C61—28no—
230C2×D4×C61—28no—
231C2×D4×C61—28no—
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—28no—
241C22×C4×C61—28no—
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—28no—
261C22×C4×C61—44no—
262C22×C4×C61—44no—
263C22×C4×C61—44no—
264C22×C4×C61—44no—
265C22×C4×C61—44no—
266C22×C4×C61—44no—
267C22×C4×C61—44no—
268C22×C4×C61—44no—
269C22×C4×C61—44no—
270C22×C4×C61—44no—
271C22×C4×C61—44no—
272C22×C4×C61C2×D412yes—
273C22×C4×C61C2×D412yes—
274C22×C4×C61C2×D412yes—
275C22×C4×C61C2×D412yes—
276C22×C4×C61C2×D412yes—
277C22×C4×C61C2×D412yes—
278C22×C4×C61C2×D412yes—
279C22×C4×C61#4112yes—
280C22×C4×C61#4112yes—
281C2×C22⋊D61—28no—
282C2×C22⋊D61—28no—
283C2×C22⋊D61—44no—
284C2×C22⋊D61—44no—
285C2×C22⋊D61—44no—
286C2×C22⋊D61—44no—
287C2×C22⋊D61—44no—
288C2×C22⋊D61—44no—
289C2×C22⋊D61—44no—
290C2×C22⋊D61—44no—
291C2×C22⋊D61—44no—
292C2×C22⋊D61—44no—
293C2×C22⋊D61—44no—
294C2×C22⋊D61—44no—
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×Dic61—21no—
323C22×Dic61—21no—
324C22×Dic61—21no—
325C22×Dic61—21no—
326C22×Dic61—21no—
327C22×Dic61—21no—
328C22×Dic61—21no—
329C22×Dic61—21no—
330C22×Dic61—21no—
331C22×Dic61—21no—
332C22×Dic61—21no—
333C22×Dic61—21no—
334C22×Dic61—21no—
335C22×Dic61—21no—
336C22×Dic61—21no—
337C22×Dic61—21no—
338C22×Dic61—21no—
339C22×Dic61C2×D412yes—
340C22×Dic61C2×D412yes—
341C22×Dic61C2×D412yes—
342C22×Dic61#4112yes—
343C22×Dic61#4112yes—
344C4⋊C4×C61—28no—
345C22⋊C4×C61—28no—
346C22⋊C4×C61—28no—
347C42×C61—28no—
348C22⋊Dic61—28no—
349C22⋊Dic61—28no—
350C22⋊Dic61—44no—
351C22⋊Dic61—44no—
352C22⋊Dic61—44no—
353C22⋊Dic61—44no—
354#11758198—28no—
355#11758198—28no—
356#11758198—44no—
357#11758198—44no—
358#11758198—44no—
359#11758196—28no—
360#11758196—28no—
361#11758196—44no—
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—22no—
397C23×C61—22no—
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#12014yes—
431C23×C61#12314yescomplemented
432C23×C61C22×D411yescharacteristic
433C23×C61C22×D411yescharacteristic
434C23×C61C22×D411yescharacteristic
435C23×C61C22×D411yescharacteristic
436C23×C61C22×D411yescharacteristic
437C23×C61C2×#4111yescharacteristic
438C23×C61C2×#4111yescharacteristic
439C23×C61C2×#4111yescharacteristic
440C23×C61C2×#4111yescharacteristic
441C23×C61C2×#4111yescharacteristic
442C23×C61C2×#4111yescharacteristic
443C23×C61H(5,𝔽2)11yescharacteristic
444C23×C61H(5,𝔽2)11yescharacteristic
445C23×C61H(5,𝔽2)11yescharacteristic
446C23×C612−1+411yescharacteristic
447C22×D61—22no—
448C22×D61—22no—
449C22×D61—22no—
450C22×D61—22no—
451C22×D61—22no—
452C22×D61—22no—
453C22×D61—22no—
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—
480C22×D61—41no—
481C22×D61—41no—
482D4×C61—232no—
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—22no—
499C2×C4×C61—22no—
500C2×C4×C61—22no—
501C2×C4×C61—22no—
502C2×C4×C61—22no—
503C2×C4×C61—22no—
504C2×C4×C61—416no—
505C2×C4×C61—416no—
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#12014yes—
519C2×C4×C61#12314yescomplemented
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—41no—
538C2×Dic61—41no—
539C2×Dic61—41no—
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×Dic61—41no—
567C2×Dic61—41no—
568C2×Dic61—41no—
569C2×Dic61—41no—
570C2×Dic61—41no—
571#14721—611nomaximal, Sylow
572C22×C61—24no—
573C22×C61—24no—
574C22×C61—24no—
575C22×C61—24no—
576C22×C61—24no—
577C22×C61—24no—
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×C61—42no—
601C22×C61—42no—
602C22×C61C2×#12011yescharacteristic
603C22×C61C2×#12011yescharacteristic
604C22×C61C2×#12311yescharacteristic
605C22×C61C2×#12311yescharacteristic
606C22×C61#52511yescharacteristic
607C22×C61#52511yescharacteristic
608C22×C61#52511yescharacteristic
609C22×C61#52511yescharacteristic
610C22×C61#52511yescharacteristic
611C22×C61#52511yescharacteristic
612C22×C61#53211yescharacteristic
613C22×C61#53211yescharacteristic
614C22×C61#53211yescharacteristic
615C22×C61#53411yescharacteristic
616C22×C61#53711yescharacteristic
617C22×C61#53811yescharacteristic
618C22×C61#53911yescharacteristic
619C22×C61#54011yescharacteristic
620C22×C61#54211yescharacteristic
621C22×C61D4211yescharacteristic
622C22×C61D4211yescharacteristic
623C22×C61D4211yescharacteristic
624C22×C61D4211yescharacteristic
625C22×C61#54611yescharacteristic
626C22×C61#54611yescharacteristic
627C22×C61#54611yescharacteristic
628C22×C61#54711yescharacteristic
629C22×C61#54711yescharacteristic
630C22×C61#54711yescharacteristic
631C22×C61#54811yescharacteristic
632C22×C61#55011yescharacteristic
633C22×C61#55111yescharacteristic
634C22×C61#55311yescharacteristic
635C22×C61#55311yescharacteristic
636C22×C61#55911yescharacteristic
637C2×D61—42no—
638C2×D61—42no—
639C2×D61—42no—
640C2×D61—42no—
641C2×D61—42no—
642C2×D61—42no—
643C2×D61—42no—
644C2×D61—81no—
645C2×D61—81no—
646C2×D61—81no—
647C2×D61—81no—
648C2×D61—81no—
649C2×D61—81no—
650C2×D61—81no—
651C2×D61—81no—
652C4×C61—24no—
653C4×C61—24no—
654C4×C61—42no—
655C4×C61—42no—
656C4×C61—42no—
657Dic61—42no—
658Dic61—42no—
659Dic61—42no—
660Dic61—42no—
661Dic61—42no—
662Dic61—81no—
663Dic61—81no—
664C22×#123—611no—
665C22×C4×D4D6111yescharacteristic, complemented
666C2×#394—611no—
667C2×#392—611no—
668C2×#386—611no—
669C2×#385—611no—
670#1444—611no—
671#1440—611no—
672#1439—611no—
673#1439—611no—
674#1438—611no—
675#1438—611no—
676#1437—611no—
677#1436—611no—
678C22⋊#95—611no—
679C2×C61—44no—
680C2×C61—44no—
681C2×C61#238811yescharacteristic
682C2×C61#240311yescharacteristic
683C2×C61#240711yescharacteristic
684C2×C61#241811yescharacteristic
685C2×C61#242211yescharacteristic
686C2×C61#243011yescharacteristic
687C2×C61#244311yescharacteristic
688C2×C61#244511yescharacteristic
689C2×C61#245511yescharacteristic
690C2×C61#245611yescharacteristic
691C2×C61#246111yescharacteristic
692C2×C61#246411yescharacteristic
693C2×C61#260211yescharacteristic
694C2×C61#263011yescharacteristic
695C2×C61#284911yescharacteristic
696D61—82no—
697C23×D4—611no—
698C23×D4—611no—
699C23×D4C2×D6111yescharacteristic
700C24×C4C2×D6111yescharacteristic
701C24×C4C2×D6111yescharacteristic
702C2×#123—1224no—
703C2×#123—1224no—
704C2×#123—1224no—
705C2×C4×D4—24no—
706C2×C4×D4—24no—
707C2×C4×D4—24no—
708C22×C4⋊C4—611no—
709C22×C4⋊C4—611no—
710C22×C4⋊C4—611no—
711C22×C4⋊C4C2×D6111yescharacteristic
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⋊C4—611no—
721C22×C22⋊C4—611no—
722C22×C22⋊C4—611no—
723C22×C22⋊C4C2×D6111yescharacteristic
724C22×C22⋊C4C2×D6111yescharacteristic
725C22×C42C2×D6111yescharacteristic
726#394—1224no—
727#392—1224no—
728#386—1224no—
729#385—1224no—
730C2×#95—611no—
731C2×#95—611no—
732C2×#95—611no—
733C2×#95—611no—
734C2×#95—611no—
735C2×#95—611no—
736C2×#95—611no—
737C2×#95—611no—
738C2×#95—611no—
739C2×#95—611no—
740C2×#95—611no—
741C2×#95—611no—
742C61#1472111yescharacteristic, complemented, Sylow
743C25—611no—
744C25C22×D6111yescharacteristic
745C25C22×D6111yescharacteristic
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—1222no—
753C22×D4—1222no—
754C22×D4—1222no—
755C22×D4—1222no—
756C22×D4—1222no—
757C22×D4—1222no—
758C22×D4—1222no—
759C22×D4—1222no—
760C22×D4—1222no—
761C22×D4—1222no—
762C22×D4—2441no—
763C22×D4—2441no—
764C22×D4—2441no—
765C22×D4—2441no—
766C22×D4C22⋊D6114yes—
767C23×C4—22no—
768C23×C4—22no—
769C23×C4—22no—
770C23×C4—22no—
771C23×C4—22no—
772C23×C4—22no—
773C23×C4—22no—
774C23×C4—22no—
775C23×C4—22no—
776C23×C4—41no—
777C23×C4—41no—
778C23×C4—41no—
779C23×C4—41no—
780C23×C4—611no—
781C23×C4—611no—
782C23×C4—611no—
783C23×C4—611no—
784C23×C4—611no—
785C23×C4—611no—
786C23×C4—611no—
787C23×C4C22⋊D6114yescomplemented
788C23×C4C22×D6111yescharacteristic
789C23×C4C22×D6111yescharacteristic
790C23×C4C22×D6111yescharacteristic
791C23×C4C22×D6111yescharacteristic
792C23×C4C22×D6111yescharacteristic
793#123—12232no—
794C4×D4—232no—
795C2×C4⋊C4—22no—
796C2×C4⋊C4—22no—
797C2×C4⋊C4—22no—
798C2×C4⋊C4—614no—
799C2×C4⋊C4—1222no—
800C2×C4⋊C4—1222no—
801C2×C4⋊C4—1222no—
802C2×C4⋊C4—1222no—
803C2×C4⋊C4—1222no—
804C2×C4⋊C4—1222no—
805C2×C4⋊C4—1222no—
806C2×C4⋊C4—2441no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—614no—
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—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—2441no—
840C2×C22⋊C4—2441no—
841C2×C22⋊C4—2441no—
842C2×C22⋊C4—2441no—
843C2×C22⋊C4—2441no—
844C2×C22⋊C4—2441no—
845C2×C22⋊C4C22⋊D6114yescomplemented
846C2×C42—22no—
847C2×C42—22no—
848C2×C42—22no—
849#95—1222no—
850#95—1222no—
851#95—1222no—
852#95—1222no—
853#95—1222no—
854#95—1222no—
855#95—1222no—
856#95—1222no—
857#95—1222no—
858#95—2441no—
859#95—2441no—
860#95—2441no—
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—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—612no—
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—
899C24—1221no—
900C24#1175822212yes—
901C24#1175822212yes—
902C24C2×C22⋊D6112yes—
903C24C2×C22⋊D6112yes—
904C24C2×C22⋊D6112yes—
905C24C2×C22⋊D6112yes—
906C24C23×D6111yescharacteristic
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—28no—
910C2×D4—28no—
911C2×D4—28no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—1228no—
915C2×D4—1228no—
916C2×D4—2444no—
917C2×D4—2444no—
918C2×D4—2444no—
919C2×D4—2444no—
920C2×D4—2444no—
921C2×D4—2444no—
922C2×D4—2444no—
923C2×D4—2444no—
924C2×D4—2444no—
925C2×D4—2444no—
926C2×D4—2444no—
927C2×D4—2444no—
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—28no—
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—28no—
956C22×C4—28no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—612no—
969C22×C4—612no—
970C22×C4—612no—
971C22×C4—612no—
972C22×C4—612no—
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—1221no—
1009C22×C4—1221no—
1010C22×C4—1221no—
1011C22×C4—1221no—
1012C22×C4—1221no—
1013C22×C4—1221no—
1014C22×C4—1221no—
1015C22×C4—1221no—
1016C22×C4—1221no—
1017C22×C4#1175822212yes—
1018C22×C4#1175822212yes—
1019C22×C4D4×D6112yes—
1020C22×C4D4×D6112yes—
1021C22×C4C2×C22⋊D6112yes—
1022C22×C4C2×C22⋊D6112yes—
1023C22×C4C2×C22⋊D6112yes—
1024C22×C4C2×C22⋊D6112yes—
1025C22×C4C2×C22⋊D6112yes—
1026C4⋊C4—28no—
1027C4⋊C4—1228no—
1028C4⋊C4—1228no—
1029C4⋊C4—2444no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—1228no—
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—28no—
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—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
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—1222no—
1113C23—1222no—
1114C23—1222no—
1115C23—1222no—
1116C23—1222no—
1117C23—1222no—
1118C23—1222no—
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—
1144C23—2441no—
1145C23—2441no—
1146C23—2441no—
1147C23#1451974614yes—
1148C23#1451976014yescomplemented
1149C23C2×D4×D6111yescharacteristic
1150C23C2×D4×D6111yescharacteristic
1151C23C22×C22⋊D6111yescharacteristic
1152C23C22×C22⋊D6111yescharacteristic
1153C23C22×C22⋊D6111yescharacteristic
1154C23#41×D6111yescharacteristic
1155C23#41×D6111yescharacteristic
1156C23C2×#1175822211yescharacteristic
1157C23C2×#1175822211yescharacteristic
1158C23C2×#1175822211yescharacteristic
1159C23C2×#1175822211yescharacteristic
1160C23#1451982211yescharacteristic
1161C23#1451982211yescharacteristic
1162C23#1451982311yescharacteristic
1163C23#1451982411yescharacteristic
1164D4—232no—
1165D4—24416no—
1166D4—24416no—
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—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—416no—
1189C2×C4—416no—
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—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—2441no—
1218C2×C4—2441no—
1219C2×C4—2441no—
1220C2×C4—2441no—
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×C4—2441no—
1248C2×C4—2441no—
1249C2×C4—2441no—
1250C2×C4—2441no—
1251C2×C4#1451974514yes—
1252C2×C4#1451976014yescomplemented
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—24no—
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—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—4881no—
1284C22—4881no—
1285C22—4881no—
1286C22—4881no—
1287C22—4881no—
1288C22—4881no—
1289C22—4881no—
1290C22—4881no—
1291C22—2442no—
1292C22—2442no—
1293C22—2442no—
1294C22—2442no—
1295C22—2442no—
1296C22—2442no—
1297C22—2442no—
1298C22C2×#1451974511yescharacteristic
1299C22C2×#1451974611yescharacteristic
1300C22C2×#1451976011yescharacteristic
1301C22C2×#1451976011yescharacteristic
1302C22#1684027111yescharacteristic
1303C22#1684027111yescharacteristic
1304C22#1684027311yescharacteristic
1305C22#1684027311yescharacteristic
1306C22#1684027311yescharacteristic
1307C22#1684027311yescharacteristic
1308C22#1684030811yescharacteristic
1309C22#1684030911yescharacteristic
1310C22#1684030911yescharacteristic
1311C22#1684032111yescharacteristic
1312C22#1684034011yescharacteristic
1313C22#1684034511yescharacteristic
1314C22#1684035411yescharacteristic
1315C22#1684036311yescharacteristic
1316C22#1684037711yescharacteristic
1317C22D4×C22⋊D6111yescharacteristic
1318C22D4×C22⋊D6111yescharacteristic
1319C22D4×C22⋊D6111yescharacteristic
1320C22D4×C22⋊D6111yescharacteristic
1321C22#1684040011yescharacteristic
1322C22#1684040011yescharacteristic
1323C22#1684040811yescharacteristic
1324C22#1684041111yescharacteristic
1325C22#1684041111yescharacteristic
1326C22#1684041711yescharacteristic
1327C22#1684042111yescharacteristic
1328C22#1684043311yescharacteristic
1329C22#1684044111yescharacteristic
1330C22#1684046111yescharacteristic
1331C22#1684046211yescharacteristic
1332C22#1684049511yescharacteristic
1333C4—24no—
1334C4—24no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—4881no—
1339C4—4881no—
1340C4—2442no—
1341C4—2442no—
1342C4—2442no—
1343C4—2442no—
1344C4—2442no—
1345C2—44no—
1346C2—44no—
1347C2—4882no—
1348C2#2144903411yescharacteristic
1349C2#2144912911yescharacteristic
1350C2#2144916411yescharacteristic
1351C2#2144927511yescharacteristic
1352C2#2144932711yescharacteristic
1353C2#2144942311yescharacteristic
1354C2#2144954811yescharacteristic
1355C2#2144957811yescharacteristic
1356C2#2144969611yescharacteristic
1357C2#2144971111yescharacteristic
1358C2#2144978011yescharacteristic
1359C2#2144981911yescharacteristic
1360C2#2145143111yescharacteristic
1361C2#2145165611yescharacteristic
1362C2#2145411111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutator, socle, cosocleC24×C61C24
FittingC22×C4×D4×C61C2
prime radicalC2×#16839670C2
hypercenterC22×C4×D4D61
hypocenterC61#14721
LCSG ▷ C24×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#14519760C2semidirect
2. C2×#16839677C2semidirect
4. C2×#16839641C2semidirect
5. C2×#16839635C2semidirect
6. #21444082C2semidirect
7. #21444068C2semidirect
8. #21444062C2semidirect
9. #21444061C2semidirect
10. #21444060C2semidirect
11. #21444058C2semidirect
12. #21444057C2semidirect
13. #21444052C2semidirect
14. #21444042C2semidirect
15. C22×C4×D4×C61C2semidirect
92. C2×#11758196D4semidirect
125. C2×#11758198D4semidirect
160. C23×C4×C61D4semidirect
175. C2×C22⋊C4×C61D4semidirect
431. C23×C61#123semidirect
519. C2×C4×C61#123semidirect
665. C22×C4×D4D61semidirect
742. C61#14721semidirect
787. C23×C4C22⋊D61semidirect
845. C2×C22⋊C4C22⋊D61semidirect
1148. C23#14519760semidirect
1252. C2×C4#14519760semidirect

Maximal subgroups

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

subgroupindex
C22×#145197602
C2×#168396772
C2×#168396702
C2×#168396412
C2×#168396352
#214440822
#214440682
#214440622
#214440612
#214440602
#214440582
#214440572
#214440522
#214440422
C22×C4×D4×C612
#1472161