Finite Group Databasebeta

← #29607219

Subgroups — #29607219

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×#14519739C211yesmaximal, characteristic
2C2×#16839624C211yesmaximal, characteristic, complemented
3C2×#16839619C211yesmaximal, characteristic, complemented
4#21444072C211yesmaximal, characteristic, complemented
5#21444067C212yesmaximal, complemented
6#21444065C211yesmaximal, characteristic, complemented
7#21444061C211yesmaximal, characteristic, complemented
8#21444059C212yesmaximal
9#21444044C212yesmaximal, complemented
10#21444040C212yesmaximal, complemented
11C61×#1441C211yesmaximal, characteristic, complemented
12C23×D244C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C23×C4×D61C2211yescharacteristic
15C2×#14519739—24no—
16C2×#14519739—24no—
17C2×#14519739C418yescomplemented
18C22×C4⋊Dic61C2211yescharacteristic
19C22×#11758198C2211yescharacteristic
20C22×#11758198C2211yescharacteristic
21C22×#11758198C2212yes—
22C22×#11758198C2212yes—
23C22×#11758198C2212yes—
24C22×#11758198C2212yes—
25C22×C4×Dic61C2211yescharacteristic
26#16839624—24no—
27#16839619—24no—
28C2×#14519684C2212yes—
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C22×C4⋊C4×C61C2211yescharacteristic
36C22×C4⋊C4×C61C2211yescharacteristic
37C2×#95×C61C2211yescharacteristic
38C2×#95×C61C2212yes—
39C2×#95×C61C2212yes—
40C24×D61C2311yescharacteristic
41C24×D61C2311yescharacteristic
42C22×D244—22no—
43C22×D244—22no—
44C22×D244—22no—
45C22×D244—22no—
46C22×D244—22no—
47C22×D244—22no—
48C22×D244C2×C414yes—
49C23×Dic61C2312yes—
50C23×Dic61C2312yes—
51C23×Dic61C2311yescharacteristic
52C23×Dic61C2311yescharacteristic
53C22×C4×D61—22no—
54C22×C4×D61—22no—
55C22×C4×D61—42no—
56C22×C4×D61—42no—
57C22×C4×D61—42no—
58C22×C4×D61—42no—
59C22×C4×D61C2×C414yes—
60C22×C4×D61C2×C414yes—
61C22×C4×D61D414yes—
62C22×C4×D61D414yes—
63#14519739—232no—
64C2×C4⋊Dic61—22no—
65C2×C4⋊Dic61—42no—
66C2×#11758198—22no—
67C2×#11758198—22no—
68C2×#11758198—22no—
69C2×#11758198—22no—
70C2×#11758198—24no—
71C2×#11758198—24no—
72C2×#11758198—24no—
73C2×#11758198—24no—
74C2×#11758198—42no—
75C2×#11758198—42no—
76C2×#11758198—42no—
77C2×#11758198—42no—
78C2×#11758198—42no—
79C2×#11758198—42no—
80C2×#11758198—42no—
81C2×#11758198—42no—
82C2×#11758198C2×C414yes—
83C2×#11758198C2×C414yes—
84C2×C4×Dic61—22no—
85C2×C4×Dic61—22no—
86C2×C4×Dic61C2×C414yes—
87#14519684—22no—
88#14519684—24no—
89#14519684—24no—
90#14519684—24no—
91#14519684—42no—
92#14519684—42no—
93#14519684—42no—
94C23×C4×C61C2312yes—
95C23×C4×C61C2312yes—
96C23×C4×C61C2311yescharacteristic
97C23×C4×C61C2311yescharacteristic
98C23×C4×C61C2311yescharacteristic
99C2×C4⋊C4×C61—22no—
100C2×C4⋊C4×C61—22no—
101C2×C4⋊C4×C61—22no—
102C2×C4⋊C4×C61—42no—
103C2×C4⋊C4×C61C2×C414yes—
104#95×C61—22no—
105#95×C61—24no—
106#95×C61—42no—
107C24×C61C2411yescharacteristic
108C23×D61—21no—
109C23×D61—21no—
110C23×D61—21no—
111C23×D61—21no—
112C23×D61—21no—
113C23×D61—21no—
114C23×D61—21no—
115C23×D61—21no—
116C23×D61—22no—
117C23×D61—22no—
118C23×D61—22no—
119C23×D61—22no—
120C23×D61—22no—
121C23×D61—22no—
122C23×D61—22no—
123C23×D61—22no—
124C23×D61C22×C412yes—
125C23×D61C22×C412yes—
126C23×D61C2×D412yes—
127C23×D61C2×D412yes—
128C23×D61#4112yes—
129C23×D61#4112yes—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
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×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61C22×C412yes—
155C22×C4×C61C22×C412yes—
156C22×C4×C61C22×C412yes—
157C22×C4×C61C2×D412yes—
158C22×C4×C61C2×D412yes—
159C22×C4×C61#4112yes—
160C22×C4×C61#4112yes—
161C22×Dic61—22no—
162C22×Dic61—22no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—22no—
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×Dic61C22×C412yes—
182C22×Dic61C22×C412yes—
183C22×Dic61C2×D412yes—
184C22×Dic61C2×D412yes—
185C2×D244—28no—
186C2×D244—28no—
187C2×D244—28no—
188C2×D244—28no—
189C2×D244—28no—
190C2×D244—28no—
191C2×D244—28no—
192C2×C4×D61—28no—
193C2×C4×D61—48no—
194C2×C4×D61—48no—
195C2×C4×D61—44no—
196C2×C4×D61—44no—
197C2×C4×D61—48no—
198C2×C4×D61—48no—
199C2×C4×D61—44no—
200C2×C4×D61—44no—
201C2×C4×D61C22⋊C4116yescomplemented
202C4⋊C4×C61—28no—
203C4⋊C4×C61—44no—
204#11758198—28no—
205#11758198—28no—
206#11758198—48no—
207#11758198—48no—
208#11758198—48no—
209#11758198—48no—
210C4⋊Dic61—44no—
211C4×Dic61—28no—
212C23×C61C23×C411yescharacteristic
213C23×C61C22×D411yescharacteristic
214C23×C61C22×D411yescharacteristic
215C23×C61C2×#4111yescharacteristic
216C23×C61C2×#4111yescharacteristic
217C23×C61C2×#4111yescharacteristic
218C23×C61C2×#4111yescharacteristic
219C23×C61H(5,𝔽2)12yes—
220C23×C61H(5,𝔽2)12yes—
221C23×C61H(5,𝔽2)12yes—
222C23×C612−1+412yes—
223C22×D61—22no—
224C22×D61—22no—
225C22×D61—22no—
226C22×D61—22no—
227C22×D61—24no—
228C22×D61—24no—
229C22×D61—24no—
230C22×D61—24no—
231C22×D61—22no—
232C22×D61—22no—
233C22×D61—22no—
234C22×D61—22no—
235C22×D61—22no—
236C22×D61—22no—
237C22×D61—22no—
238C22×D61—22no—
239C22×D61—24no—
240C22×D61—22no—
241C22×D61—22no—
242C22×D61—22no—
243C22×D61—22no—
244C22×D61—24no—
245C22×D61—24no—
246C22×D61—24no—
247C22×D61—24no—
248C22×D61—24no—
249C22×D61—42no—
250C22×D61—41no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—41no—
254C22×D61—42no—
255C22×D61—42no—
256C22×D61—42no—
257C22×D61—42no—
258C22×D61—42no—
259C22×D61—42no—
260C22×D61—42no—
261C22×D61—42no—
262C22×D61—42no—
263C22×D61—42no—
264C22×D61—42no—
265C22×D61—42no—
266C22×D61—42no—
267C22×D61C2×C22⋊C414yes—
268C22×D61#11714yes—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—24no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—24no—
279C2×C4×C61—22no—
280C2×C4×C61—24no—
281C2×C4×C61—42no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
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×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61C2×C22⋊C414yes—
299C2×C4×C61#11714yes—
300C2×Dic61—24no—
301C2×Dic61—24no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—24no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—42no—
309C2×Dic61—42no—
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×Dic61C2×C22⋊C414yes—
324D244—232no—
325C4×D61—416no—
326C4×D61—416no—
327#14344—611nomaximal, Sylow
328C22×C61C22×C22⋊C411yescharacteristic
329C22×C61C2×#11711yescharacteristic
330C22×C61C2×#11711yescharacteristic
331C22×C61#51812yes—
332C22×C61#52012yes—
333C22×C61#52511yescharacteristic
334C22×C61#52511yescharacteristic
335C22×C61#52511yescharacteristic
336C22×C61#52511yescharacteristic
337C22×C61#53412yes—
338C22×C61#53411yescharacteristic
339C22×C61#53411yescharacteristic
340C22×C61#53511yescharacteristic
341C22×C61#53611yescharacteristic
342C22×C61#53712yes—
343C22×C61#53812yes—
344C22×C61#53812yes—
345C22×C61#53912yes—
346C22×C61#53912yes—
347C22×C61#54012yes—
348C22×C61#54012yes—
349C22×C61#54212yes—
350C22×C61#54212yes—
351C2×D61—24no—
352C2×D61—24no—
353C2×D61—28no—
354C2×D61—24no—
355C2×D61—24no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—44no—
359C2×D61—44no—
360C2×D61—44no—
361C2×D61—44no—
362C2×D61—44no—
363C2×D61—44no—
364C2×D61—44no—
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—42no—
368C2×D61—42no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—42no—
373C4×C61—24no—
374C4×C61—24no—
375C4×C61—42no—
376C4×C61—82no—
377C4×C61—82no—
378Dic61—24no—
379Dic61—42no—
380Dic61—82no—
381Dic61—82no—
382C22×C4×D4—611no—
383C2×#381—611no—
384C2×#380—611no—
385#1441—611no—
386#1441D6111yescharacteristic, complemented
387#1440—612no—
388#1439—611no—
389#1439—611no—
390#1438—612no—
391#1434—612no—
392C22⋊#95—612no—
393C2×C61#228011yescharacteristic
394C2×C61#230811yescharacteristic
395C2×C61#231111yescharacteristic
396C2×C61#231812yes—
397C2×C61#231912yes—
398C2×C61#263012yes—
399C2×C61#263012yes—
400C2×C61#263511yescharacteristic
401C2×C61#263511yescharacteristic
402C2×C61#263811yescharacteristic
403C2×C61#263811yescharacteristic
404D61—44no—
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⋊C4C2×D6111yescharacteristic
414C22×C4⋊C4C2×D6111yescharacteristic
415C22×C22⋊C4—611no—
416C22×C22⋊C4—611no—
417C22×C22⋊C4—612no—
418C22×C22⋊C4—612no—
419C22×C22⋊C4—612no—
420C22×C22⋊C4—612no—
421C22×C42—611no—
422#381—1224no—
423#380—1224no—
424C2×#95—612no—
425C2×#95—612no—
426C2×#95—612no—
427C2×#95—611no—
428C2×#95—612no—
429C2×#95—612no—
430C2×#95—612no—
431C2×#95C2×D6112yes—
432C2×#95C2×D6111yescharacteristic
433C2×#95C2×D6112yes—
434C61#1434411yescharacteristic, complemented, Sylow
435C25—611no—
436C25—611no—
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—614no—
446C23×C4—614no—
447C23×C4—614no—
448C23×C4—611no—
449C23×C4—614no—
450C23×C4—612no—
451C23×C4—612no—
452C23×C4—1222no—
453C23×C4—1222no—
454C23×C4—2442no—
455C23×C4—2442no—
456C23×C4—2442no—
457C23×C4—2442no—
458C23×C4C22×D6112yes—
459C23×C4C22×D6112yes—
460C23×C4C22×D6111yescharacteristic
461C23×C4C22×D6111yescharacteristic
462C23×C4C22×D6111yescharacteristic
463C4×D4—12232no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—1222no—
469C2×C4⋊C4—2442no—
470C2×C4⋊C4C4×D6114yes—
471C2×C22⋊C4—614no—
472C2×C22⋊C4—614no—
473C2×C22⋊C4—1222no—
474C2×C22⋊C4—1222no—
475C2×C22⋊C4—1222no—
476C2×C22⋊C4—1222no—
477C2×C22⋊C4—1224no—
478C2×C22⋊C4—1224no—
479C2×C22⋊C4—1224no—
480C2×C22⋊C4—1224no—
481C2×C22⋊C4—2442no—
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⋊C4—2442no—
489C2×C42—614no—
490C2×C42—1222no—
491C2×C42—1222no—
492#95—22no—
493#95—24no—
494#95—42no—
495#95—1224no—
496#95—1224no—
497#95—1222no—
498#95—1224no—
499#95—2442no—
500#95—2442no—
501#95—2442no—
502C24—612no—
503C24—612no—
504C24—612no—
505C24—612no—
506C24—612no—
507C24—612no—
508C24—1221no—
509C24—1221no—
510C24—1221no—
511C24—1221no—
512C24—1221no—
513C24—1221no—
514C24—1221no—
515C24—1221no—
516C24—1222no—
517C24—1222no—
518C24—1222no—
519C24—1222no—
520C24—1222no—
521C24—1222no—
522C24—1222no—
523C24—1222no—
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—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
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—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—612no—
559C22×C4—6116no—
560C22×C4—612no—
561C22×C4—1228no—
562C22×C4—1222no—
563C22×C4—1222no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
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—2448no—
583C22×C4—2448no—
584C22×C4—2444no—
585C22×C4—2444no—
586C22×C4—2448no—
587C22×C4—2448no—
588C22×C4—2444no—
589C22×C4—2444no—
590C22×C4C2×C4×D6112yes—
591C22×C4C2×C4×D6112yes—
592C22×C4C2×C4×D6112yes—
593C22×C4D4×D6112yes—
594C22×C4D4×D6112yes—
595C22×C4#1175822412yes—
596C22×C4#1175822612yes—
597C4⋊C4—28no—
598C4⋊C4—44no—
599C4⋊C4—2444no—
600C22⋊C4—1228no—
601C22⋊C4—1228no—
602C22⋊C4—2448no—
603C22⋊C4—2448no—
604C22⋊C4—2448no—
605C22⋊C4—2448no—
606C42—1228no—
607C23—614no—
608C23—614no—
609C23—1222no—
610C23—1222no—
611C23—1222no—
612C23—1222no—
613C23—1224no—
614C23—1224no—
615C23—1224no—
616C23—1224no—
617C23—1222no—
618C23—1222no—
619C23—1222no—
620C23—1222no—
621C23—1222no—
622C23—1222no—
623C23—1222no—
624C23—1222no—
625C23—1224no—
626C23—1222no—
627C23—1222no—
628C23—1222no—
629C23—1222no—
630C23—1224no—
631C23—1224no—
632C23—1224no—
633C23—1224no—
634C23—1224no—
635C23—2442no—
636C23—2441no—
637C23—2441no—
638C23—2441no—
639C23—2441no—
640C23—2442no—
641C23—2442no—
642C23—2442no—
643C23—2442no—
644C23—2442no—
645C23—2442no—
646C23—2442no—
647C23—2442no—
648C23—2442no—
649C23—2442no—
650C23—2442no—
651C23—2442no—
652C23—2442no—
653C23C22×C4×D6111yescharacteristic
654C23C2×D4×D6111yescharacteristic
655C23C2×D4×D6111yescharacteristic
656C23#41×D6111yescharacteristic
657C23#41×D6111yescharacteristic
658C23C2×#1175822411yescharacteristic
659C23C2×#1175822611yescharacteristic
660C23#1451982212yes—
661C23#1451982312yes—
662C23#1451982312yes—
663C23#1451982512yes—
664D4—12232no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
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—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—614no—
695C2×C4—1224no—
696C2×C4—1224no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1224no—
701C2×C4—24416no—
702C2×C4—24416no—
703C2×C4—2442no—
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—2441no—
718C2×C4—2441no—
719C2×C4—2442no—
720C2×C4C22⋊C4×D6114yes—
721C2×C4#1451973514yes—
722C22—1228no—
723C22—1224no—
724C22—1224no—
725C22—1224no—
726C22—1224no—
727C22—2444no—
728C22—2444no—
729C22—2444no—
730C22—2444no—
731C22—2444no—
732C22—2444no—
733C22—2444no—
734C22—2442no—
735C22—2442no—
736C22—2442no—
737C22—2442no—
738C22—2442no—
739C22—2442no—
740C22—2442no—
741C22—2442no—
742C22—2442no—
743C22—2442no—
744C22C2×C22⋊C4×D6111yescharacteristic
745C22#117×D6111yescharacteristic
746C22C2×#1451973511yescharacteristic
747C22#1684023412yes—
748C22#1684024412yes—
749C22#1684027211yescharacteristic
750C22#1684027211yescharacteristic
751C22#1684027511yescharacteristic
752C22#1684027511yescharacteristic
753C22#1684032012yes—
754C22#1684032211yescharacteristic
755C22#1684032311yescharacteristic
756C22#1684033011yescharacteristic
757C22#1684033711yescharacteristic
758C22#1684034212yes—
759C22#1684034812yes—
760C22#1684035112yes—
761C22#1684035812yes—
762C22#1684036012yes—
763C22#1684036512yes—
764C22#1684036812yes—
765C22#1684038512yes—
766C22#1684038612yes—
767C4—24no—
768C4—24no—
769C4—42no—
770C4—82no—
771C4—82no—
772C4—1224no—
773C4—4882no—
774C4—4882no—
775C4—2442no—
776C2—2444no—
777C2—2444no—
778C2#2144820111yescharacteristic
779C2#2144839311yescharacteristic
780C2#2144841011yescharacteristic
781C2#2144845112yes—
782C2#2144845812yes—
783C2#2145166712yes—
784C2#2145166912yes—
785C2#2145171111yescharacteristic
786C2#2145171211yescharacteristic
787C2#2145174411yescharacteristic
788C2#2145174511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1441C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1441D61
hypocenterC61#14344
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C2×#16839624C2semidirect
3. C2×#16839619C2semidirect
4. #21444072C2semidirect
5. #21444067C2semidirect
6. #21444065C2semidirect
7. #21444061C2semidirect
9. #21444044C2semidirect
10. #21444040C2semidirect
11. C61×#1441C2semidirect
17. C2×#14519739C4semidirect
201. C2×C4×D61C22⋊C4semidirect
386. #1441D61semidirect
434. C61#14344semidirect

Maximal subgroups

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

subgroupindex
C22×#145197392
C2×#168396242
C2×#168396192
#214440722
#214440672
#214440652
#214440612
#214440592
#214440442
#214440402
C61×#14412
#1434461