Finite Group Databasebeta

← #29602147

Subgroups — #29602147

Order 15616.

2546 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D61C211yesmaximal, characteristic
2C2×#16839639C212yesmaximal
3C2×#16839624C211yesmaximal, characteristic, complemented
4C22×#14519684C211yesmaximal, characteristic, complemented
5#21444085C212yesmaximal, complemented
6#21444067C212yesmaximal, complemented
7#21444045C211yesmaximal, characteristic, complemented
8#21444044C211yesmaximal, characteristic, complemented
9#21444041C212yesmaximal, complemented
10#21444040C211yesmaximal, characteristic, complemented
11C61×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C24×Dic61C2212yes—
14C23×C4×D61C2211yescharacteristic
15C2×C4×C22⋊D61—28no—
16C2×C4×C22⋊D61C418yescomplemented
17C22×#11758196C2211yescharacteristic
18C22×C22⋊Dic61C2211yescharacteristic
19C22×#11758198C2212yes—
20C22×#11758198C2212yes—
21C22×#11758198C2211yescharacteristic
22C22×C4×Dic61C2211yescharacteristic
23#16839639—28no—
24#16839624—24no—
25C2×#14519684—24no—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2211yescharacteristic
35C24×C4×C61C2211yescharacteristic
36C22×C22⋊C4×C61C2212yes—
37C2×#95×C61C2211yescharacteristic
38C2×#95×C61C2211yescharacteristic
39C2×#95×C61C2212yes—
40C24×D61C2311yescharacteristic
41C22×C22⋊D61—24no—
42C22×C22⋊D61—22no—
43C22×C22⋊D61—22no—
44C22×C22⋊D61C2×C414yes—
45C22×C22⋊D61D418yes—
46C23×Dic61—24no—
47C23×Dic61—24no—
48C23×Dic61—24no—
49C23×Dic61—24no—
50C23×Dic61—24no—
51C23×Dic61—42no—
52C23×Dic61—42no—
53C23×Dic61C2311yescharacteristic
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2312yes—
56C23×Dic61C2312yes—
57C23×Dic61C2311yescharacteristic
58C22×C4×D61—24no—
59C22×C4×D61—22no—
60C22×C4×D61—22no—
61C22×C4×D61—42no—
62C22×C4×D61C2×C414yescomplemented
63C4×C22⋊D61—232no—
64C2×#11758196—24no—
65C2×#11758196C2×C414yescomplemented
66C2×C22⋊Dic61—24no—
67C2×C22⋊Dic61C2×C414yes—
68C2×#11758198—24no—
69C2×#11758198—24no—
70C2×#11758198—24no—
71C2×#11758198—24no—
72C2×#11758198—24no—
73C2×#11758198—42no—
74C2×#11758198—42no—
75C2×#11758198C2×C414yescomplemented
76C2×C4×Dic61—24no—
77C2×C4×Dic61C2×C414yescomplemented
78#14519684—22no—
79#14519684—24no—
80#14519684—24no—
81#14519684—24no—
82#14519684—24no—
83#14519684—24no—
84#14519684—42no—
85#14519684—42no—
86#14519684D414yescomplemented
87C25×C61C2311yescharacteristic
88C23×C4×C61—24no—
89C23×C4×C61—22no—
90C23×C4×C61—22no—
91C23×C4×C61—42no—
92C23×C4×C61C2×C414yes—
93C23×C4×C61C2312yes—
94C23×C4×C61C2312yes—
95C23×C4×C61C2311yescharacteristic
96C23×C4×C61C2311yescharacteristic
97C2×C22⋊C4×C61—24no—
98C2×C22⋊C4×C61—24no—
99C2×C22⋊C4×C61—24no—
100#95×C61—22no—
101#95×C61—22no—
102#95×C61—42no—
103C24×C61—21no—
104C24×C61—22no—
105C24×C61—21no—
106C24×C61—21no—
107C24×C61—22no—
108C24×C61—21no—
109C24×C61C22×C412yes—
110C24×C61C2×D414yes—
111C24×C61#4114yes—
112C24×C61#4112yes—
113C24×C61#4112yes—
114C24×C61C2411yescharacteristic
115C23×D61—21no—
116C23×D61—21no—
117C23×D61—22no—
118C23×D61—21no—
119C23×D61—21no—
120C23×D61—22no—
121C23×D61—22no—
122C23×D61—21no—
123C23×D61—21no—
124C23×D61C22×C412yes—
125C23×D61C2×D414yes—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—28no—
129C22×C4×C61—21no—
130C22×C4×C61—22no—
131C22×C4×C61—21no—
132C22×C4×C61—22no—
133C22×C4×C61—28no—
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—44no—
149C22×C4×C61—48no—
150C22×C4×C61—48no—
151C22×C4×C61C22×C412yes—
152C22×C4×C61C22×C412yes—
153C22×C4×C61C2×D412yes—
154C22×C4×C61#4112yes—
155C2×C22⋊D61—28no—
156C2×C22⋊D61—28no—
157C2×C22⋊D61—216no—
158C2×C22⋊D61—216no—
159C2×C22⋊D61C22⋊C4116yes—
160C22×Dic61—22no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—216no—
164C22×Dic61—21no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—21no—
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×Dic61—22no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—48no—
185C22×Dic61—48no—
186C22×Dic61—48no—
187C22×Dic61—48no—
188C22×Dic61—48no—
189C22×Dic61—48no—
190C22×Dic61C22×C412yes—
191C22×Dic61C22×C412yes—
192C22×Dic61C22×C412yes—
193C22×Dic61C2×D414yes—
194C22×Dic61C2×D414yes—
195C22×Dic61#4114yes—
196C2×C4×D61—28no—
197C2×C4×D61—28no—
198C2×C4×D61—44no—
199C2×C4×D61—48no—
200C2×C4×D61—48no—
201C22⋊C4×C61—48no—
202C22⋊Dic61—28no—
203#11758198—28no—
204#11758198—48no—
205#11758198—48no—
206#11758196—28no—
207C4×Dic61—28no—
208C23×C61—22no—
209C23×C61—22no—
210C23×C61—22no—
211C23×C61—22no—
212C23×C61—24no—
213C23×C61—24no—
214C23×C61—24no—
215C23×C61—24no—
216C23×C61—24no—
217C23×C61—22no—
218C23×C61—24no—
219C23×C61—24no—
220C23×C61—24no—
221C23×C61—22no—
222C23×C61—24no—
223C23×C61—22no—
224C23×C61—22no—
225C23×C61—24no—
226C23×C61C2×C22⋊C414yes—
227C23×C61#11714yes—
228C23×C61#11714yes—
229C23×C61#12318yes—
230C23×C61#12318yes—
231C23×C61C23×C411yescharacteristic
232C23×C61C22×D412yes—
233C23×C61C22×D411yescharacteristic
234C23×C61C2×#4112yes—
235C23×C61C2×#4111yescharacteristic
236C23×C61C2×#4111yescharacteristic
237C23×C61C2×#4111yescharacteristic
238C23×C61C2×#4112yes—
239C23×C61H(5,𝔽2)12yes—
240C23×C61H(5,𝔽2)11yescharacteristic
241C23×C612−1+411yescharacteristic
242C22×D61—22no—
243C22×D61—22no—
244C22×D61—22no—
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—24no—
249C22×D61—24no—
250C22×D61—24no—
251C22×D61—24no—
252C22×D61—24no—
253C22×D61—24no—
254C22×D61—42no—
255C22×D61—42no—
256C22×D61—42no—
257C22×D61—42no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—42no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—42no—
264C22×D61C2×C22⋊C414yes—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—24no—
268C2×C4×C61—24no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—416no—
273C2×C4×C61—42no—
274C2×C4×C61—42no—
275C2×C4×C61—42no—
276C2×C4×C61—42no—
277C2×C4×C61—42no—
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×C61C4×D414yes—
290C22⋊D61—232no—
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—24no—
294C2×Dic61—24no—
295C2×Dic61—22no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—24no—
302C2×Dic61—24no—
303C2×Dic61—24no—
304C2×Dic61—24no—
305C2×Dic61—24no—
306C2×Dic61—24no—
307C2×Dic61—432no—
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×Dic61C2×C22⋊C414yes—
321C4×D61—416no—
322#13894—611nomaximal, Sylow
323C22×C61—24no—
324C22×C61—24no—
325C22×C61—24no—
326C22×C61—24no—
327C22×C61—24no—
328C22×C61—28no—
329C22×C61—28no—
330C22×C61—28no—
331C22×C61—28no—
332C22×C61—24no—
333C22×C61#38118yescomplemented
334C22×C61C22×C22⋊C411yescharacteristic
335C22×C61C2×#11711yescharacteristic
336C22×C61C2×#11711yescharacteristic
337C22×C61C2×C4×D411yescharacteristic
338C22×C61C4×#4111yescharacteristic
339C22×C61#51811yescharacteristic
340C22×C61#52011yescharacteristic
341C22×C61C2×#12312yes—
342C22×C61C2×#12312yes—
343C22×C61#52512yes—
344C22×C61#52912yes—
345C22×C61#53812yes—
346C22×C61#53912yes—
347C22×C61D4212yes—
348C22×C61#54612yes—
349C22×C61#54611yescharacteristic
350C22×C61#54612yes—
351C22×C61#54712yes—
352C22×C61#54811yescharacteristic
353C22×C61#55112yes—
354C22×C61#55211yescharacteristic
355C22×C61#55312yes—
356C22×C61#55311yescharacteristic
357C2×D61—24no—
358C2×D61—24no—
359C2×D61—24no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—44no—
364C2×D61—44no—
365C2×D61—44no—
366C2×D61—44no—
367C2×D61—42no—
368C4×C61—24no—
369C4×C61—42no—
370C4×C61—82no—
371C4×C61—82no—
372Dic61—24no—
373Dic61—42no—
374Dic61—42no—
375Dic61—44no—
376Dic61—44no—
377C22×C4×D4—611no—
378C2×#386—612no—
379C2×#381—611no—
380C22×#95—611no—
381#1445—612no—
382#1440—612no—
383#1434—611no—
384#1434—611no—
385C22⋊#95—611no—
386C22⋊#95—612no—
387C22⋊#95D6111yescharacteristic, complemented
388C2×C61—28no—
389C2×C61C2×#38111yescharacteristic
390C2×C61#229011yescharacteristic
391C2×C61#231811yescharacteristic
392C2×C61D4×C22⋊C411yescharacteristic
393C2×C61#233911yescharacteristic
394C2×C61#235211yescharacteristic
395C2×C61#235311yescharacteristic
396C2×C61#241812yes—
397C2×C61#241912yes—
398C2×C61#244312yes—
399C2×C61#244412yes—
400D61—44no—
401C23×D4—611no—
402C24×C4—611no—
403C24×C4—612no—
404C24×C4C2×D6111yescharacteristic
405C2×C4×D4—618no—
406C2×C4×D4—1228no—
407C22×C4⋊C4—611no—
408C22×C22⋊C4—611no—
409C22×C22⋊C4—611no—
410C22×C22⋊C4—612no—
411C22×C22⋊C4—612no—
412C22×C22⋊C4C2×D6112yes—
413C22×C42—611no—
414#386—1228no—
415#381—1224no—
416C2×#95—611no—
417C2×#95—612no—
418C2×#95—611no—
419C2×#95—612no—
420C2×#95—612no—
421C2×#95—612no—
422C2×#95—612no—
423C2×#95—612no—
424C2×#95—612no—
425C2×#95—1224no—
426C2×#95C2×D6111yescharacteristic
427C2×#95C2×D6111yescharacteristic
428C2×#95C2×D6112yes—
429C61#1389411yescharacteristic, complemented, Sylow
430C25—611no—
431C25C22×D6111yescharacteristic
432C22×D4—614no—
433C22×D4—618no—
434C22×D4—1224no—
435C22×D4—1222no—
436C22×D4—1222no—
437C23×C4—24no—
438C23×C4—22no—
439C23×C4—22no—
440C23×C4—42no—
441C23×C4—611no—
442C23×C4—611no—
443C23×C4—611no—
444C23×C4—612no—
445C23×C4—612no—
446C23×C4—614no—
447C23×C4—1224no—
448C23×C4—1224no—
449C23×C4—1224no—
450C23×C4—1224no—
451C23×C4—1222no—
452C23×C4—1222no—
453C23×C4—1224no—
454C23×C4—1224no—
455C23×C4—2442no—
456C23×C4—2442no—
457C23×C4—2442no—
458C23×C4C4×D6114yes—
459C23×C4C22×D6112yes—
460C23×C4C22×D6112yes—
461C23×C4C22×D6111yescharacteristic
462C23×C4C22×D6111yescharacteristic
463C4×D4—12232no—
464C2×C4⋊C4—614no—
465C2×C4⋊C4—1224no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—614no—
470C2×C22⋊C4—614no—
471C2×C22⋊C4—1224no—
472C2×C22⋊C4—1224no—
473C2×C22⋊C4—1224no—
474C2×C22⋊C4—1224no—
475C2×C22⋊C4—1224no—
476C2×C22⋊C4—1224no—
477C2×C22⋊C4—2442no—
478C2×C22⋊C4—2442no—
479C2×C42—614no—
480C2×C42—1224no—
481#95—22no—
482#95—22no—
483#95—42no—
484#95—614no—
485#95—1224no—
486#95—1224no—
487#95—1224no—
488#95—1224no—
489#95—1224no—
490#95—1222no—
491#95—2442no—
492#95—2442no—
493C24—21no—
494C24—22no—
495C24—21no—
496C24—22no—
497C24—21no—
498C24—21no—
499C24—612no—
500C24—614no—
501C24—1221no—
502C24—1222no—
503C24—1221no—
504C24—1221no—
505C24—1222no—
506C24—1221no—
507C24—1222no—
508C24—1221no—
509C24—1221no—
510C24C2×C4×D6112yes—
511C24#1175822214yes—
512C24D4×D6114yes—
513C24#1175822412yes—
514C24#1175822612yes—
515C24C23×D6111yescharacteristic
516C2×D4—6116no—
517C2×D4—1228no—
518C2×D4—1228no—
519C2×D4—12216no—
520C2×D4—12216no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—44no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—612no—
547C22×C4—614no—
548C22×C4—612no—
549C22×C4—612no—
550C22×C4—614no—
551C22×C4—614no—
552C22×C4—1228no—
553C22×C4—1221no—
554C22×C4—1222no—
555C22×C4—1221no—
556C22×C4—12216no—
557C22×C4—1221no—
558C22×C4—1222no—
559C22×C4—1222no—
560C22×C4—1222no—
561C22×C4—1222no—
562C22×C4—1222no—
563C22×C4—1222no—
564C22×C4—1222no—
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—1221no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4—1221no—
577C22×C4—1228no—
578C22×C4—2444no—
579C22×C4—2448no—
580C22×C4—2448no—
581C22×C4—2448no—
582C22×C4—2448no—
583C22×C4—2448no—
584C22×C4—2448no—
585C22×C4—2448no—
586C22×C4—2448no—
587C22×C4C2×C4×D6112yes—
588C22×C4C2×C4×D6112yes—
589C22×C4D4×D6112yes—
590C22×C4#1175822412yes—
591C4⋊C4—1228no—
592C22⋊C4—48no—
593C22⋊C4—1228no—
594C22⋊C4—1228no—
595C22⋊C4—2448no—
596C22⋊C4—2448no—
597C42—1228no—
598C23—22no—
599C23—24no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—24no—
613C23—24no—
614C23—22no—
615C23—24no—
616C23—614no—
617C23—1222no—
618C23—1222no—
619C23—1222no—
620C23—1222no—
621C23—1222no—
622C23—1222no—
623C23—1224no—
624C23—1224no—
625C23—1224no—
626C23—1224no—
627C23—1224no—
628C23—1224no—
629C23—2441no—
630C23—2442no—
631C23—2441no—
632C23—2442no—
633C23—2442no—
634C23—2442no—
635C23—2442no—
636C23—2441no—
637C23—2441no—
638C23—2442no—
639C23C22⋊C4×D6114yes—
640C23#1451973414yes—
641C23#1451973514yes—
642C23#1451975918yes—
643C23#1451976218yes—
644C23C22×C4×D6111yescharacteristic
645C23C2×D4×D6112yes—
646C23C2×D4×D6111yescharacteristic
647C23#41×D6112yes—
648C23C2×#1175822411yescharacteristic
649C23C2×#1175822411yescharacteristic
650C23C2×#1175822212yes—
651C23C2×#1175822611yescharacteristic
652C23#1451982212yes—
653C23#1451982311yescharacteristic
654C23#1451982411yescharacteristic
655D4—12232no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—416no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—614no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1224no—
684C2×C4—1224no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1224no—
692C2×C4—1224no—
693C2×C4—1224no—
694C2×C4—1224no—
695C2×C4—1224no—
696C2×C4—1224no—
697C2×C4—24416no—
698C2×C4—24432no—
699C2×C4—2442no—
700C2×C4—2442no—
701C2×C4—2442no—
702C2×C4—2442no—
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#1451973714yes—
712C22—24no—
713C22—24no—
714C22—24no—
715C22—28no—
716C22—28no—
717C22—28no—
718C22—28no—
719C22—24no—
720C22—24no—
721C22—24no—
722C22—1224no—
723C22—1224no—
724C22—1224no—
725C22—2442no—
726C22—2442no—
727C22—2442no—
728C22—2444no—
729C22—2444no—
730C22—2444no—
731C22—2444no—
732C22—2442no—
733C22#1683962418yescomplemented
734C22C2×C22⋊C4×D6111yescharacteristic
735C22C2×#1451973411yescharacteristic
736C22C2×#1451973511yescharacteristic
737C22C2×#1451973711yescharacteristic
738C22#1684023011yescharacteristic
739C22#1684023511yescharacteristic
740C22#1684024211yescharacteristic
741C22C2×#1451975912yes—
742C22C2×#1451976212yes—
743C22#1684027112yes—
744C22#1684029212yes—
745C22#1684034512yes—
746C22#1684035412yes—
747C22#1684039412yes—
748C22#1684039912yes—
749C22#1684040311yescharacteristic
750C22#1684040412yes—
751C22#1684041012yes—
752C22#1684041811yescharacteristic
753C22#1684043912yes—
754C22#1684045411yescharacteristic
755C22#1684045512yes—
756C22#1684046411yescharacteristic
757C4—24no—
758C4—42no—
759C4—82no—
760C4—82no—
761C4—1224no—
762C4—2444no—
763C4—2444no—
764C4—2442no—
765C4—2442no—
766C2—28no—
767C2—2444no—
768C2C2×#1683962411yescharacteristic
769C2#2144825811yescharacteristic
770C2#2144844611yescharacteristic
771C2#2144863511yescharacteristic
772C2#2144864311yescharacteristic
773C2#2144875011yescharacteristic
774C2#2144876111yescharacteristic
775C2#2144928312yes—
776C2#2144929812yes—
777C2#2144955612yes—
778C2#2144957112yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C22⋊#95C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC22⋊#95D61
hypocenterC61#13894
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#16839624C2semidirect
4. C22×#14519684C2semidirect
5. #21444085C2semidirect
6. #21444067C2semidirect
7. #21444045C2semidirect
8. #21444044C2semidirect
9. #21444041C2semidirect
10. #21444040C2semidirect
11. C61×C22⋊#95C2semidirect
16. C2×C4×C22⋊D61C4semidirect
62. C22×C4×D61C2×C4semidirect
65. C2×#11758196C2×C4semidirect
75. C2×#11758198C2×C4semidirect
77. C2×C4×Dic61C2×C4semidirect
86. #14519684D4semidirect
333. C22×C61#381semidirect
387. C22⋊#95D61semidirect
429. C61#13894semidirect
733. C22#16839624semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D612
C2×#168396392
C2×#168396242
C22×#145196842
#214440852
#214440672
#214440452
#214440442
#214440412
#214440402
C61×C22⋊#952
#1389461