Finite Group Databasebeta

← #29606759

Subgroups — #29606759

Order 15616.

2566 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839670C211yesmaximal, characteristic
2C2×#16839653C211yesmaximal, characteristic, complemented
3C2×#16839641C212yesmaximal, complemented
4#21444078C211yesmaximal, characteristic, complemented
5#21444062C212yesmaximal, complemented
6#21444061C211yesmaximal, characteristic, complemented
7#21444060C211yesmaximal, characteristic, complemented
8#21444058C212yesmaximal, complemented
9#21444046C211yesmaximal, characteristic, complemented
10#21444042C212yesmaximal, complemented
11C22×C4×D4×C61C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2212yes—
13C22×#11758196C2211yescharacteristic
14C22×C22⋊Dic61C2212yes—
15C22×C22⋊Dic61C2212yes—
16C22×C22⋊Dic61C2212yes—
17C22×#11758198C2211yescharacteristic
18C22×#11758198C2211yescharacteristic
19C22×#11758198C2212yes—
20C22×#11758198C2211yescharacteristic
21#16839670C418yescomplemented
22#16839653—24no—
23#16839641—28no—
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2211yescharacteristic
27C2×#14519684C2211yescharacteristic
28C2×#14519684C2211yescharacteristic
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2211yescharacteristic
33C23×D4×C61C2211yescharacteristic
34C24×C4×C61C2212yes—
35C2×C4×D4×C61—28no—
36C2×C4×D4×C61—24no—
37C22×C4⋊C4×C61C2211yescharacteristic
38C22×C22⋊C4×C61C2212yes—
39C22×C42×C61C2211yescharacteristic
40C24×D61C2311yescharacteristic
41C22×C22⋊D61—24no—
42C22×C22⋊D61—24no—
43C22×C22⋊D61—42no—
44C22×C22⋊D61—42no—
45C22×C22⋊D61—42no—
46C22×C22⋊D61—42no—
47C22×C22⋊D61C2×C418yescomplemented
48C23×Dic61C2311yescharacteristic
49C23×Dic61C2311yescharacteristic
50C23×Dic61C2312yes—
51C23×Dic61C2311yescharacteristic
52C23×Dic61C2312yes—
53C2×#11758196—22no—
54C2×#11758196—42no—
55C2×C22⋊Dic61—24no—
56C2×C22⋊Dic61—24no—
57C2×C22⋊Dic61—42no—
58C2×C22⋊Dic61—42no—
59C2×C22⋊Dic61—42no—
60C2×C22⋊Dic61—42no—
61C2×C22⋊Dic61—42no—
62C2×C22⋊Dic61—42no—
63C2×C22⋊Dic61C2×C418yescomplemented
64C2×#11758198—22no—
65C2×#11758198—22no—
66C2×#11758198—24no—
67C2×#11758198—24no—
68C2×#11758198—22no—
69C2×#11758198—22no—
70C2×#11758198—42no—
71C2×#11758198—42no—
72C2×#11758198—42no—
73C2×#11758198C2×C414yescomplemented
74#14519684—24no—
75#14519684—24no—
76#14519684—22no—
77#14519684—22no—
78#14519684—22no—
79#14519684—42no—
80#14519684—42no—
81#14519684—42no—
82#14519684C2×C414yescomplemented
83C25×C61C2312yes—
84C22×D4×C61—24no—
85C22×D4×C61—24no—
86C22×D4×C61—22no—
87C22×D4×C61—22no—
88C22×D4×C61C2×C414yes—
89C23×C4×C61—24no—
90C23×C4×C61—24no—
91C23×C4×C61—42no—
92C23×C4×C61—42no—
93C23×C4×C61—42no—
94C23×C4×C61—42no—
95C23×C4×C61D418yescomplemented
96C23×C4×C61C2311yescharacteristic
97C23×C4×C61C2312yes—
98C23×C4×C61C2311yescharacteristic
99C23×C4×C61C2311yescharacteristic
100C4×D4×C61—232no—
101C2×C4⋊C4×C61—24no—
102C2×C4⋊C4×C61—22no—
103C2×C22⋊C4×C61—24no—
104C2×C22⋊C4×C61—24no—
105C2×C22⋊C4×C61—24no—
106C2×C42×C61—24no—
107C2×C42×C61D414yescomplemented
108C24×C61—22no—
109C24×C61—22no—
110C24×C61—22no—
111C24×C61—22no—
112C24×C61—22no—
113C24×C61—22no—
114C24×C61—22no—
115C24×C61—22no—
116C24×C61—22no—
117C24×C61—22no—
118C24×C61—22no—
119C24×C61—22no—
120C24×C61C22×C414yes—
121C24×C61C2×D414yes—
122C24×C61#4114yes—
123C24×C61C2411yescharacteristic
124C23×D61—22no—
125C23×D61—21no—
126C23×D61—22no—
127C23×D61—21no—
128C23×D61—21no—
129C23×D61—21no—
130C23×D61—22no—
131C23×D61—22no—
132C23×D61—21no—
133C23×D61—21no—
134C23×D61C22×C412yes—
135C2×D4×C61—28no—
136C2×D4×C61—28no—
137C2×D4×C61—216no—
138C2×D4×C61—216no—
139C2×D4×C61—28no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—21no—
143C22×C4×C61—22no—
144C22×C4×C61—21no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—21no—
153C22×C4×C61—22no—
154C22×C4×C61—21no—
155C22×C4×C61—216no—
156C22×C4×C61—48no—
157C22×C4×C61—48no—
158C22×C4×C61—48no—
159C22×C4×C61—48no—
160C22×C4×C61—48no—
161C22×C4×C61—48no—
162C22×C4×C61C22×C412yes—
163C22×C4×C61C2×D412yes—
164C22×C4×C61C2×D414yes—
165C22×C4×C61C2×D412yes—
166C22×C4×C61C2×D414yes—
167C22×C4×C61C2×D412yes—
168C22×C4×C61#4112yes—
169C2×C22⋊D61—216no—
170C2×C22⋊D61—48no—
171C2×C22⋊D61—48no—
172C2×C22⋊D61—48no—
173C2×C22⋊D61—48no—
174C2×C22⋊D61—48no—
175C2×C22⋊D61—48no—
176C22×Dic61—22no—
177C22×Dic61—21no—
178C22×Dic61—22no—
179C22×Dic61—21no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—21no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—21no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—21no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—21no—
199C22×Dic61—22no—
200C22×Dic61—21no—
201C22×Dic61—22no—
202C22×Dic61—21no—
203C22×Dic61C22×C414yes—
204C22×Dic61C22×C412yes—
205C4⋊C4×C61—28no—
206C22⋊C4×C61—216no—
207C42×C61—28no—
208C22⋊Dic61—48no—
209C22⋊Dic61—48no—
210C22⋊Dic61—48no—
211#11758198—28no—
212#11758198—48no—
213#11758198—44no—
214#11758198—44no—
215#11758196—44no—
216C23×C61—24no—
217C23×C61—24no—
218C23×C61—24no—
219C23×C61—24no—
220C23×C61—24no—
221C23×C61—24no—
222C23×C61—24no—
223C23×C61—24no—
224C23×C61—24no—
225C23×C61—24no—
226C23×C61—24no—
227C23×C61—24no—
228C23×C61—24no—
229C23×C61—24no—
230C23×C61—24no—
231C23×C61—24no—
232C23×C61—24no—
233C23×C61—24no—
234C23×C61—42no—
235C23×C61—42no—
236C23×C61—42no—
237C23×C61—42no—
238C23×C61—42no—
239C23×C61—42no—
240C23×C61—42no—
241C23×C61—42no—
242C23×C61—42no—
243C23×C61—42no—
244C23×C61—42no—
245C23×C61—42no—
246C23×C61—42no—
247C23×C61—42no—
248C23×C61—42no—
249C23×C61—42no—
250C23×C61C4×D418yes—
251C23×C61C23×C411yescharacteristic
252C23×C61C22×D412yes—
253C23×C61C22×D411yescharacteristic
254C23×C61C2×#4112yes—
255C23×C61C2×#4111yescharacteristic
256C23×C61H(5,𝔽2)11yescharacteristic
257C23×C61H(5,𝔽2)12yes—
258C23×C61H(5,𝔽2)11yescharacteristic
259C23×C61H(5,𝔽2)12yes—
260C23×C61H(5,𝔽2)11yescharacteristic
261C23×C612−1+411yescharacteristic
262C22×D61—22no—
263C22×D61—24no—
264C22×D61—22no—
265C22×D61—24no—
266C22×D61—22no—
267C22×D61—41no—
268C22×D61—42no—
269C22×D61—41no—
270C22×D61—42no—
271C22×D61—42no—
272C22×D61—41no—
273C22×D61—42no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—42no—
278C22×D61—42no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61—42no—
282C22×D61—41no—
283C22×D61—42no—
284C22×D61—41no—
285D4×C61—232no—
286C2×C4×C61—24no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—24no—
290C2×C4×C61—24no—
291C2×C4×C61—24no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—24no—
296C2×C4×C61—24no—
297C2×C4×C61—24no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—432no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61C4×D414yes—
308C2×C4×C61#12014yes—
309C22⋊D61—432no—
310C2×Dic61—22no—
311C2×Dic61—24no—
312C2×Dic61—24no—
313C2×Dic61—24no—
314C2×Dic61—24no—
315C2×Dic61—42no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339#14299—611nomaximal, Sylow
340C22×C61—28no—
341C22×C61—28no—
342C22×C61—28no—
343C22×C61—44no—
344C22×C61—44no—
345C22×C61—44no—
346C22×C61—44no—
347C22×C61—44no—
348C22×C61—44no—
349C22×C61—44no—
350C22×C61—44no—
351C22×C61—44no—
352C22×C61—44no—
353C22×C61—44no—
354C22×C61—44no—
355C22×C61C2×C4×D412yes—
356C22×C61C2×C4×D411yescharacteristic
357C22×C61#51811yescharacteristic
358C22×C61#51812yes—
359C22×C61#52011yescharacteristic
360C22×C61C2×#12011yescharacteristic
361C22×C61#52512yes—
362C22×C61#52511yescharacteristic
363C22×C61#53412yes—
364C22×C61#53412yes—
365C22×C61#53512yes—
366C22×C61#53511yescharacteristic
367C22×C61#53511yescharacteristic
368C22×C61#53511yescharacteristic
369C22×C61#53711yescharacteristic
370C22×C61#53712yes—
371C22×C61#53812yes—
372C22×C61#53812yes—
373C22×C61#53812yes—
374C22×C61#53912yes—
375C22×C61#54011yescharacteristic
376C22×C61#54012yes—
377C22×C61#54211yescharacteristic
378C2×D61—44no—
379C2×D61—42no—
380C2×D61—44no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—81no—
384C2×D61—81no—
385C2×D61—82no—
386C2×D61—81no—
387C2×D61—82no—
388C2×D61—81no—
389C4×C61—24no—
390C4×C61—24no—
391C4×C61—44no—
392C4×C61—42no—
393Dic61—44no—
394Dic61—42no—
395Dic61—81no—
396Dic61—81no—
397Dic61—82no—
398C22×C4×D4D6111yescharacteristic, complemented
399C2×#392—611no—
400C2×#388—611no—
401C2×#386—612no—
402#1442—611no—
403#1439—611no—
404#1439—612no—
405#1438—611no—
406#1438—612no—
407#1434—611no—
408C22⋊#95—612no—
409C2×C61—48no—
410C2×C61C4×#12011yescharacteristic
411C2×C61#232112yes—
412C2×C61#232411yescharacteristic
413C2×C61#232512yes—
414C2×C61#232811yescharacteristic
415C2×C61#261311yescharacteristic
416C2×C61#261511yescharacteristic
417C2×C61#263012yes—
418C2×C61#263111yescharacteristic
419C2×C61#263512yes—
420C2×C61#263611yescharacteristic
421D61—82no—
422C23×D4—612no—
423C23×D4C2×D6111yescharacteristic
424C24×C4C2×D6112yes—
425C2×C4×D4—28no—
426C2×C4×D4—24no—
427C22×C4⋊C4—611no—
428C22×C4⋊C4C2×D6111yescharacteristic
429C22×C22⋊C4—611no—
430C22×C22⋊C4—612no—
431C22×C22⋊C4—611no—
432C22×C22⋊C4—612no—
433C22×C22⋊C4—612no—
434C22×C22⋊C4—611no—
435C22×C22⋊C4—612no—
436C22×C22⋊C4C2×D6112yes—
437C22×C42C2×D6111yescharacteristic
438#392—618no—
439#388—1224no—
440#386—1228no—
441C2×#95—611no—
442C2×#95—611no—
443C2×#95—612no—
444C2×#95—611no—
445C2×#95—611no—
446C2×#95—612no—
447C2×#95—612no—
448C2×#95—612no—
449C2×#95—612no—
450C61#1429911yescharacteristic, complemented, Sylow
451C25—611no—
452C25C22×D6112yes—
453C22×D4—24no—
454C22×D4—24no—
455C22×D4—22no—
456C22×D4—22no—
457C22×D4—618no—
458C22×D4—1224no—
459C22×D4—1224no—
460C22×D4—2442no—
461C22×D4—2442no—
462C22×D4—2442no—
463C22×D4—2442no—
464C22×D4C4×D6114yes—
465C23×C4—24no—
466C23×C4—24no—
467C23×C4—42no—
468C23×C4—42no—
469C23×C4—42no—
470C23×C4—42no—
471C23×C4—611no—
472C23×C4—612no—
473C23×C4—611no—
474C23×C4—611no—
475C23×C4—612no—
476C23×C4C22⋊D6118yescomplemented
477C23×C4C22×D6111yescharacteristic
478C23×C4C22×D6112yes—
479C23×C4C22×D6111yescharacteristic
480C23×C4C22×D6111yescharacteristic
481C4×D4—232no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—1222no—
485C2×C4⋊C4—2442no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—614no—
490C2×C22⋊C4—618no—
491C2×C22⋊C4—1222no—
492C2×C22⋊C4—1222no—
493C2×C22⋊C4—1224no—
494C2×C22⋊C4—1224no—
495C2×C22⋊C4—1224no—
496C2×C22⋊C4—1224no—
497C2×C22⋊C4—1222no—
498C2×C22⋊C4—1222no—
499C2×C22⋊C4—2442no—
500C2×C22⋊C4—2442no—
501C2×C22⋊C4—2442no—
502C2×C22⋊C4—2442no—
503C2×C22⋊C4—2442no—
504C2×C22⋊C4—2442no—
505C2×C22⋊C4—2442no—
506C2×C22⋊C4—2442no—
507C2×C22⋊C4—2442no—
508C2×C42—24no—
509C2×C42C22⋊D6114yescomplemented
510#95—614no—
511#95—1222no—
512#95—1224no—
513#95—1224no—
514#95—1222no—
515#95—1222no—
516#95—2442no—
517#95—2442no—
518#95—2442no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—612no—
532C24—1221no—
533C24—1222no—
534C24—1221no—
535C24—1222no—
536C24—1221no—
537C24—1222no—
538C24—1221no—
539C24—1222no—
540C24—1221no—
541C24—1221no—
542C24C2×C4×D6114yes—
543C24#1175822214yes—
544C24C2×C22⋊D6114yes—
545C24C23×D6111yescharacteristic
546C2×D4—28no—
547C2×D4—216no—
548C2×D4—28no—
549C2×D4—216no—
550C2×D4—28no—
551C2×D4—12216no—
552C2×D4—2448no—
553C2×D4—2448no—
554C2×D4—2448no—
555C2×D4—2448no—
556C2×D4—2448no—
557C2×D4—2448no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—216no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—614no—
581C22×C4—612no—
582C22×C4—1222no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1221no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1221no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1221no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1221no—
603C22×C4—1222no—
604C22×C4—1221no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1221no—
609C22×C4C2×C4×D6112yes—
610C22×C4#1175822212yes—
611C22×C4C2×C22⋊D6114yes—
612C22×C4C2×C22⋊D6112yes—
613C22×C4C2×C22⋊D6112yes—
614C22×C4C2×C22⋊D6114yes—
615C22×C4C2×C22⋊D6112yes—
616C4⋊C4—28no—
617C4⋊C4—2444no—
618C22⋊C4—216no—
619C22⋊C4—1228no—
620C22⋊C4—2448no—
621C22⋊C4—2444no—
622C22⋊C4—2448no—
623C22⋊C4—2448no—
624C22⋊C4—2448no—
625C22⋊C4—2444no—
626C42—28no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—1222no—
662C23—1224no—
663C23—1222no—
664C23—1224no—
665C23—1222no—
666C23—2441no—
667C23—2442no—
668C23—2441no—
669C23—2442no—
670C23—2442no—
671C23—2441no—
672C23—2442no—
673C23—2441no—
674C23—2441no—
675C23—2442no—
676C23—2441no—
677C23—2442no—
678C23—2442no—
679C23—2442no—
680C23—2442no—
681C23—2442no—
682C23—2441no—
683C23—2441no—
684C23C4×C22⋊D6118yes—
685C23C22×C4×D6111yescharacteristic
686C23C22×C22⋊D6112yes—
687C23C22×C22⋊D6111yescharacteristic
688C23C2×#1175822212yes—
689C23C2×#1175822211yescharacteristic
690C23#1451982211yescharacteristic
691C23#1451982212yes—
692C23#1451982211yescharacteristic
693C23#1451982311yescharacteristic
694C23#1451982312yes—
695C23#1451982411yescharacteristic
696D4—232no—
697D4—24432no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—432no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—1222no—
720C2×C4—1224no—
721C2×C4—1224no—
722C2×C4—1224no—
723C2×C4—1224no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2442no—
727C2×C4—2442no—
728C2×C4—2442no—
729C2×C4—2441no—
730C2×C4—2442no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2442no—
735C2×C4—2442no—
736C2×C4—2442no—
737C2×C4—2442no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—2441no—
743C2×C4—2442no—
744C2×C4—2441no—
745C2×C4—2442no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4C4×C22⋊D6114yes—
749C2×C4#1451974614yes—
750C22—28no—
751C22—28no—
752C22—28no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—4881no—
766C22—4881no—
767C22—4882no—
768C22—4881no—
769C22—4882no—
770C22—4881no—
771C22—2444no—
772C22—2442no—
773C22—2444no—
774C22—2442no—
775C22—2442no—
776C22C2×C4×C22⋊D6112yes—
777C22C2×C4×C22⋊D6111yescharacteristic
778C22#1684023411yescharacteristic
779C22#1684023412yes—
780C22#1684024111yescharacteristic
781C22C2×#1451974611yescharacteristic
782C22#1684027312yes—
783C22#1684027311yescharacteristic
784C22#1684032112yes—
785C22#1684032112yes—
786C22#1684032612yes—
787C22#1684032611yescharacteristic
788C22#1684032911yescharacteristic
789C22#1684032911yescharacteristic
790C22#1684034011yescharacteristic
791C22#1684034012yes—
792C22#1684034512yes—
793C22#1684034512yes—
794C22#1684034512yes—
795C22#1684035412yes—
796C22#1684036311yescharacteristic
797C22#1684036312yes—
798C22#1684037711yescharacteristic
799C4—24no—
800C4—24no—
801C4—44no—
802C4—42no—
803C4—4881no—
804C4—4881no—
805C4—4882no—
806C4—2444no—
807C4—2442no—
808C2—48no—
809C2—4882no—
810C2C4×#1451974611yescharacteristic
811C2#2144847312yes—
812C2#2144850611yescharacteristic
813C2#2144851712yes—
814C2#2144854111yescharacteristic
815C2#2145153111yescharacteristic
816C2#2145154311yescharacteristic
817C2#2145165612yes—
818C2#2145167111yescharacteristic
819C2#2145170312yes—
820C2#2145171411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC22×C4×D4×C61C2
socle, cosocleC24×C61C24
prime radicalC2×#16839670C2
hypercenterC22×C4×D4D61
hypocenterC61#14299
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#16839653C2semidirect
3. C2×#16839641C2semidirect
4. #21444078C2semidirect
5. #21444062C2semidirect
6. #21444061C2semidirect
7. #21444060C2semidirect
8. #21444058C2semidirect
9. #21444046C2semidirect
10. #21444042C2semidirect
11. C22×C4×D4×C61C2semidirect
21. #16839670C4semidirect
47. C22×C22⋊D61C2×C4semidirect
63. C2×C22⋊Dic61C2×C4semidirect
73. C2×#11758198C2×C4semidirect
82. #14519684C2×C4semidirect
95. C23×C4×C61D4semidirect
107. C2×C42×C61D4semidirect
398. C22×C4×D4D61semidirect
450. C61#14299semidirect
476. C23×C4C22⋊D61semidirect
509. C2×C42C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396702
C2×#168396532
C2×#168396412
#214440782
#214440622
#214440612
#214440602
#214440582
#214440462
#214440422
C22×C4×D4×C612
#1429961