Finite Group Databasebeta

← #29607226

Subgroups — #29607226

Order 15616.

2150 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519737C211yesmaximal, characteristic
2C2×#16839629C211yesmaximal, characteristic, complemented
3C2×#16839627C211yesmaximal, characteristic, complemented
4#21444085C212yesmaximal, complemented
5#21444065C211yesmaximal, characteristic, complemented
6#21444064C211yesmaximal, characteristic, complemented
7#21444061C211yesmaximal, characteristic, complemented
8#21444058C212yesmaximal
9#21444041C212yesmaximal, complemented
10#21444040C212yesmaximal, complemented
11C61×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C23×C4×D61C2211yescharacteristic
15C2×#14519737—24no—
16C2×#14519737—24no—
17C2×#14519737C418yescomplemented
18C22×C4⋊Dic61C2211yescharacteristic
19C22×#11758196C2211yescharacteristic
20C22×C22⋊Dic61C2212yes—
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2212yes—
23C22×#11758198C2212yes—
24C22×C4×Dic61C2211yescharacteristic
25#16839629—24no—
26#16839627—24no—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2211yescharacteristic
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C22×C4⋊C4×C61C2211yescharacteristic
36C22×C22⋊C4×C61C2211yescharacteristic
37C22×C22⋊C4×C61C2212yes—
38C2×#95×C61C2211yescharacteristic
39C2×#95×C61C2212yes—
40C24×D61C2311yescharacteristic
41C22×C22⋊D61—22no—
42C22×C22⋊D61—22no—
43C22×C22⋊D61—22no—
44C22×C22⋊D61—22no—
45C22×C22⋊D61—22no—
46C22×C22⋊D61—22no—
47C22×C22⋊D61C2×C414yes—
48C23×Dic61—22no—
49C23×Dic61—22no—
50C23×Dic61—42no—
51C23×Dic61—42no—
52C23×Dic61C2×C414yes—
53C23×Dic61C2312yes—
54C23×Dic61C2312yes—
55C23×Dic61C2311yescharacteristic
56C23×Dic61C2311yescharacteristic
57C23×Dic61C2311yescharacteristic
58C22×C4×D61—22no—
59C22×C4×D61—22no—
60C22×C4×D61—42no—
61C22×C4×D61—42no—
62C22×C4×D61C2×C414yes—
63#14519737—232no—
64C2×C4⋊Dic61—22no—
65C2×C4⋊Dic61—42no—
66C2×#11758196—22no—
67C2×#11758196—22no—
68C2×#11758196C2×C414yes—
69C2×C22⋊Dic61—24no—
70C2×C22⋊Dic61—42no—
71C2×C22⋊Dic61—42no—
72C2×#11758198—22no—
73C2×#11758198—22no—
74C2×#11758198—24no—
75C2×#11758198—24no—
76C2×#11758198—42no—
77C2×#11758198—42no—
78C2×#11758198—42no—
79C2×#11758198—42no—
80C2×#11758198C2×C414yes—
81C2×C4×Dic61C2×C414yes—
82C2×C4×Dic61D414yes—
83C2×C4×Dic61D414yes—
84#14519684—22no—
85#14519684—24no—
86#14519684—24no—
87#14519684—24no—
88#14519684—24no—
89#14519684—42no—
90#14519684—42no—
91#14519684—42no—
92C25×C61C2311yescharacteristic
93C23×C4×C61C2312yes—
94C23×C4×C61C2312yes—
95C23×C4×C61C2311yescharacteristic
96C23×C4×C61C2311yescharacteristic
97C2×C4⋊C4×C61—22no—
98C2×C4⋊C4×C61—42no—
99C2×C22⋊C4×C61—22no—
100C2×C22⋊C4×C61—22no—
101C2×C22⋊C4×C61—24no—
102C2×C22⋊C4×C61—42no—
103C2×C22⋊C4×C61—42no—
104C2×C22⋊C4×C61C2×C414yes—
105#95×C61—22no—
106#95×C61—42no—
107C24×C61—21no—
108C24×C61—21no—
109C24×C61—21no—
110C24×C61—21no—
111C24×C61—22no—
112C24×C61—22no—
113C24×C61—22no—
114C24×C61—22no—
115C24×C61C22×C412yes—
116C24×C61#4112yes—
117C24×C61#4112yes—
118C24×C61C2411yescharacteristic
119C23×D61—21no—
120C23×D61—21no—
121C23×D61—21no—
122C23×D61—21no—
123C23×D61—22no—
124C23×D61—22no—
125C23×D61—22no—
126C23×D61—22no—
127C23×D61C22×C412yes—
128C23×D61#4112yes—
129C23×D61#4112yes—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61C22×C412yes—
151C22×C4×C61C22×C412yes—
152C22×C4×C61C2×D412yes—
153C22×C4×C61C2×D412yes—
154C2×C22⋊D61—28no—
155C2×C22⋊D61—28no—
156C2×C22⋊D61—28no—
157C2×C22⋊D61—28no—
158C2×C22⋊D61—28no—
159C2×C22⋊D61—28no—
160C2×C22⋊D61—28no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—28no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—48no—
187C22×Dic61—44no—
188C22×Dic61—48no—
189C22×Dic61—44no—
190C22×Dic61C22×C412yes—
191C22×Dic61C22×C412yes—
192C22×Dic61C22×C412yes—
193C22×Dic61C2×D412yes—
194C22×Dic61C2×D412yes—
195C22×Dic61C2×D412yes—
196C22×Dic61C2×D412yes—
197C2×C4×D61—28no—
198C2×C4×D61—48no—
199C2×C4×D61—44no—
200C2×C4×D61—48no—
201C2×C4×D61—44no—
202C4⋊C4×C61—44no—
203C22⋊C4×C61—28no—
204C22⋊C4×C61—48no—
205C22⋊Dic61—48no—
206#11758198—28no—
207#11758198—48no—
208#11758198—48no—
209C4⋊Dic61—44no—
210#11758196—28no—
211C4×Dic61C22⋊C4116yescomplemented
212C23×C61—22no—
213C23×C61—22no—
214C23×C61—24no—
215C23×C61—24no—
216C23×C61—22no—
217C23×C61—22no—
218C23×C61—22no—
219C23×C61—22no—
220C23×C61—24no—
221C23×C61—24no—
222C23×C61—24no—
223C23×C61—24no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61—42no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61—42no—
230C23×C61—42no—
231C23×C61—42no—
232C23×C61—42no—
233C23×C61—42no—
234C23×C61#11714yes—
235C23×C61C23×C411yescharacteristic
236C23×C61C22×D411yescharacteristic
237C23×C61C22×D411yescharacteristic
238C23×C61C2×#4111yescharacteristic
239C23×C61C2×#4111yescharacteristic
240C23×C61C2×#4111yescharacteristic
241C23×C61C2×#4111yescharacteristic
242C23×C61H(5,𝔽2)12yes—
243C23×C61H(5,𝔽2)12yes—
244C23×C61H(5,𝔽2)12yes—
245C23×C612−1+412yes—
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—24no—
249C22×D61—24no—
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—24no—
255C22×D61—24no—
256C22×D61—24no—
257C22×D61—24no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—42no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—42no—
264C22×D61—42no—
265C22×D61—42no—
266C22×D61—42no—
267C22×D61—42no—
268C22×D61#11714yes—
269C2×C4×C61—24no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—24no—
273C2×C4×C61—22no—
274C2×C4×C61—24no—
275C2×C4×C61—41no—
276C2×C4×C61—42no—
277C2×C4×C61—41no—
278C2×C4×C61—42no—
279C2×C4×C61—42no—
280C2×C4×C61—42no—
281C2×C4×C61—42no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—42no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61C2×C22⋊C414yes—
293C22⋊D61—232no—
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—24no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—24no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—24no—
306C2×Dic61—416no—
307C2×Dic61—41no—
308C2×Dic61—42no—
309C2×Dic61—41no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61C2×C22⋊C414yes—
325C2×Dic61C2×C22⋊C414yes—
326C4×D61—416no—
327#14345—611nomaximal, Sylow
328C22×C61—28no—
329C22×C61—24no—
330C22×C61—42no—
331C22×C61—42no—
332C22×C61—44no—
333C22×C61—42no—
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—44no—
338C22×C61—44no—
339C22×C61C22×C22⋊C411yescharacteristic
340C22×C61C2×#11711yescharacteristic
341C22×C61C2×#11711yescharacteristic
342C22×C61#51812yes—
343C22×C61#52012yes—
344C22×C61#52511yescharacteristic
345C22×C61#52511yescharacteristic
346C22×C61#52511yescharacteristic
347C22×C61#52511yescharacteristic
348C22×C61#53511yescharacteristic
349C22×C61#53511yescharacteristic
350C22×C61#53512yes—
351C22×C61#53511yescharacteristic
352C22×C61#53611yescharacteristic
353C22×C61#53712yes—
354C22×C61#53812yes—
355C22×C61#53812yes—
356C22×C61#53812yes—
357C22×C61#53812yes—
358C22×C61#53912yes—
359C22×C61#53912yes—
360C22×C61#53912yes—
361C22×C61#53912yes—
362C2×D61—28no—
363C2×D61—24no—
364C2×D61—42no—
365C2×D61—42no—
366C2×D61—44no—
367C2×D61—42no—
368C2×D61—42no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—44no—
372C2×D61—44no—
373C4×C61—24no—
374C4×C61—42no—
375C4×C61—82no—
376C4×C61—82no—
377Dic61—24no—
378Dic61—24no—
379Dic61—42no—
380Dic61—82no—
381Dic61—82no—
382C22×C4×D4—611no—
383C2×#383—611no—
384C2×#382—611no—
385#1445—612no—
386#1439—611no—
387#1439—611no—
388#1439—611no—
389#1439D6111yescharacteristic, complemented
390#1438—612no—
391C22⋊#95—612no—
392C22⋊#95—612no—
393C2×C61—44no—
394C2×C61#228011yescharacteristic
395C2×C61#230911yescharacteristic
396C2×C61#231111yescharacteristic
397C2×C61#231812yes—
398C2×C61#231812yes—
399C2×C61#263111yescharacteristic
400C2×C61#263111yescharacteristic
401C2×C61#263311yescharacteristic
402C2×C61#263311yescharacteristic
403C2×C61#263612yes—
404C2×C61#263612yes—
405D61—44no—
406C23×D4—611no—
407C24×C4—611no—
408C24×C4—611no—
409C2×C4×D4—618no—
410C2×C4×D4—1224no—
411C2×C4×D4—1224no—
412C22×C4⋊C4—611no—
413C22×C4⋊C4—611no—
414C22×C4⋊C4C2×D6111yescharacteristic
415C22×C22⋊C4—611no—
416C22×C22⋊C4—612no—
417C22×C22⋊C4—612no—
418C22×C22⋊C4—612no—
419C22×C22⋊C4C2×D6111yescharacteristic
420C22×C22⋊C4C2×D6112yes—
421C22×C42—611no—
422#383—1224no—
423#382—1224no—
424C2×#95—612no—
425C2×#95—612no—
426C2×#95—612no—
427C2×#95—612no—
428C2×#95—611no—
429C2×#95—612no—
430C2×#95—612no—
431C2×#95—612no—
432C2×#95C2×D6111yescharacteristic
433C2×#95C2×D6112yes—
434C61#1434511yescharacteristic, complemented, Sylow
435C25—611no—
436C25C22×D6111yescharacteristic
437C22×D4—614no—
438C22×D4—1222no—
439C22×D4—1222no—
440C22×D4—1222no—
441C22×D4—1222no—
442C22×D4—1222no—
443C22×D4—1222no—
444C23×C4—611no—
445C23×C4—611no—
446C23×C4—611no—
447C23×C4—614no—
448C23×C4—614no—
449C23×C4—612no—
450C23×C4—612no—
451C23×C4—1222no—
452C23×C4—1222no—
453C23×C4—1222no—
454C23×C4—1222no—
455C23×C4—2442no—
456C23×C4—2442no—
457C23×C4—2442no—
458C23×C4—2442no—
459C23×C4C22×D6112yes—
460C23×C4C22×D6112yes—
461C23×C4C22×D6111yescharacteristic
462C23×C4C22×D6111yescharacteristic
463C4×D4—12232no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—614no—
467C2×C4⋊C4—1222no—
468C2×C4⋊C4—1222no—
469C2×C4⋊C4—1222no—
470C2×C4⋊C4—2442no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—42no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4—614no—
477C2×C22⋊C4—1222no—
478C2×C22⋊C4—1222no—
479C2×C22⋊C4—1224no—
480C2×C22⋊C4—1224no—
481C2×C22⋊C4—1224no—
482C2×C22⋊C4—2442no—
483C2×C22⋊C4—2442no—
484C2×C22⋊C4—2442no—
485C2×C22⋊C4—2442no—
486C2×C22⋊C4—2442no—
487C2×C22⋊C4—2442no—
488C2×C22⋊C4C4×D6114yes—
489C2×C42—614no—
490C2×C42—614no—
491C2×C42—614no—
492#95—22no—
493#95—42no—
494#95—1224no—
495#95—1224no—
496#95—1224no—
497#95—1224no—
498#95—1222no—
499#95—2442no—
500#95—2442no—
501#95—2442no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—612no—
511C24—612no—
512C24—612no—
513C24—1221no—
514C24—1221no—
515C24—1221no—
516C24—1221no—
517C24—1222no—
518C24—1222no—
519C24—1222no—
520C24—1222no—
521C24C2×C4×D6112yes—
522C24#1175822412yes—
523C24#1175822612yes—
524C24C23×D6111yescharacteristic
525C2×D4—1228no—
526C2×D4—1228no—
527C2×D4—1228no—
528C2×D4—1228no—
529C2×D4—1228no—
530C2×D4—1228no—
531C2×D4—1228no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—612no—
553C22×C4—612no—
554C22×C4—612no—
555C22×C4—612no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—612no—
559C22×C4—1228no—
560C22×C4—1228no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—2448no—
586C22×C4—2444no—
587C22×C4—2448no—
588C22×C4—2444no—
589C22×C4—2448no—
590C22×C4—2444no—
591C22×C4—2448no—
592C22×C4—2444no—
593C22×C4C2×C4×D6112yes—
594C22×C4C2×C4×D6112yes—
595C22×C4D4×D6112yes—
596C22×C4D4×D6112yes—
597C4⋊C4—44no—
598C4⋊C4—1228no—
599C4⋊C4—2444no—
600C22⋊C4—28no—
601C22⋊C4—48no—
602C22⋊C4—1228no—
603C22⋊C4—2448no—
604C22⋊C4—2448no—
605C22⋊C4—2448no—
606C42—6116no—
607C23—22no—
608C23—22no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—41no—
620C23—41no—
621C23—42no—
622C23—41no—
623C23—41no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—614no—
630C23—1222no—
631C23—1222no—
632C23—1224no—
633C23—1224no—
634C23—1222no—
635C23—1222no—
636C23—1222no—
637C23—1222no—
638C23—1224no—
639C23—1224no—
640C23—1224no—
641C23—1224no—
642C23—2441no—
643C23—2441no—
644C23—2442no—
645C23—2441no—
646C23—2441no—
647C23—2442no—
648C23—2442no—
649C23—2442no—
650C23—2442no—
651C23—2442no—
652C23#1451973514yes—
653C23C22×C4×D6111yescharacteristic
654C23C2×D4×D6111yescharacteristic
655C23C2×D4×D6111yescharacteristic
656C23#41×D6111yescharacteristic
657C23#41×D6111yescharacteristic
658C23C2×#1175822411yescharacteristic
659C23C2×#1175822611yescharacteristic
660C23#1451982212yes—
661C23#1451982212yes—
662C23#1451982312yes—
663C23#1451982412yes—
664D4—12232no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—614no—
689C2×C4—614no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1224no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1224no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1224no—
702C2×C4—24416no—
703C2×C4—24416no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4—2442no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4—2442no—
714C2×C4—2442no—
715C2×C4—2442no—
716C2×C4—2442no—
717C2×C4—2442no—
718C2×C4—2441no—
719C2×C4—2442no—
720C2×C4—2441no—
721C2×C4C22⋊C4×D6114yes—
722C22—24no—
723C22—28no—
724C22—44no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—44no—
730C22—44no—
731C22—42no—
732C22—42no—
733C22—1228no—
734C22—1224no—
735C22—2442no—
736C22—2442no—
737C22—2442no—
738C22—2442no—
739C22—2444no—
740C22—2444no—
741C22—2442no—
742C22—2442no—
743C22—2444no—
744C22C2×C22⋊C4×D6111yescharacteristic
745C22#117×D6111yescharacteristic
746C22C2×#1451973511yescharacteristic
747C22#1684023412yes—
748C22#1684024112yes—
749C22#1684027211yescharacteristic
750C22#1684027211yescharacteristic
751C22#1684027511yescharacteristic
752C22#1684027511yescharacteristic
753C22#1684032511yescharacteristic
754C22#1684032711yescharacteristic
755C22#1684032812yes—
756C22#1684033011yescharacteristic
757C22#1684033411yescharacteristic
758C22#1684033912yes—
759C22#1684034412yes—
760C22#1684034612yes—
761C22#1684034712yes—
762C22#1684035212yes—
763C22#1684035312yes—
764C22#1684035512yes—
765C22#1684035612yes—
766C22#1684036112yes—
767C4—24no—
768C4—42no—
769C4—82no—
770C4—82no—
771C4—1224no—
772C4—1224no—
773C4—4882no—
774C4—4882no—
775C4—2442no—
776C2—44no—
777C2—2444no—
778C2#2144820111yescharacteristic
779C2#2144839811yescharacteristic
780C2#2144840611yescharacteristic
781C2#2144844712yes—
782C2#2144844912yes—
783C2#2145167611yescharacteristic
784C2#2145167711yescharacteristic
785C2#2145169211yescharacteristic
786C2#2145169311yescharacteristic
787C2#2145172112yes—
788C2#2145172312yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1439C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenter#1439D61
hypocenterC61#14345
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#16839629C2semidirect
3. C2×#16839627C2semidirect
4. #21444085C2semidirect
5. #21444065C2semidirect
6. #21444064C2semidirect
7. #21444061C2semidirect
9. #21444041C2semidirect
10. #21444040C2semidirect
11. C61×#1439C2semidirect
17. C2×#14519737C4semidirect
211. C4×Dic61C22⋊C4semidirect
389. #1439D61semidirect
434. C61#14345semidirect

Maximal subgroups

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

subgroupindex
C22×#145197372
C2×#168396292
C2×#168396272
#214440852
#214440652
#214440642
#214440612
#214440582
#214440412
#214440402
C61×#14392
#1434561