Finite Group Databasebeta

← #29605354

Subgroups — #29605354

Order 15616.

2854 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic61C211yesmaximal, characteristic, complemented
2C2×#16839670C211yesmaximal, characteristic
3C2×#16839639C212yesmaximal, complemented
4C2×#16839638C212yesmaximal, complemented
5C2×#16839609C211yesmaximal, characteristic, complemented
6#21444075C211yesmaximal, characteristic, complemented
7#21444065C211yesmaximal, characteristic, complemented
8#21444056C212yesmaximal, complemented
9#21444044C211yesmaximal, characteristic, complemented
10#21444041C212yesmaximal, complemented
11C61×#1438C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2212yes—
13C24×Dic61C2212yes—
14C23×C4×D61C2211yescharacteristic
15C2×D4×Dic61—28no—
16C2×D4×Dic61—24no—
17C22×C4⋊Dic61C2211yescharacteristic
18C22×C22⋊Dic61C2212yes—
19C22×C22⋊Dic61C2212yes—
20C22×#11758198C2212yes—
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×C4×Dic61C2211yescharacteristic
24C22×C4×Dic61C2211yescharacteristic
25#16839670C418yescomplemented
26#16839639—28no—
27#16839638—28no—
28#16839609—24no—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2212yes—
35C2×#14519684C2211yescharacteristic
36C23×D4×C61C2211yescharacteristic
37C22×C22⋊C4×C61C2212yes—
38C22×C22⋊C4×C61C2212yes—
39C2×#95×C61C2211yescharacteristic
40C2×#95×C61C2211yescharacteristic
41C24×D61C2311yescharacteristic
42C22×C22⋊D61—24no—
43C22×C22⋊D61—24no—
44C22×C22⋊D61—24no—
45C22×C22⋊D61—24no—
46C22×C22⋊D61—42no—
47C22×C22⋊D61—42no—
48C22×C22⋊D61C2×C418yescomplemented
49C23×Dic61—24no—
50C23×Dic61—24no—
51C23×Dic61—24no—
52C23×Dic61—24no—
53C23×Dic61—24no—
54C23×Dic61—42no—
55C23×Dic61—42no—
56C23×Dic61C2311yescharacteristic
57C23×Dic61C2312yes—
58C23×Dic61C2312yes—
59C23×Dic61C2311yescharacteristic
60C23×Dic61C2311yescharacteristic
61C22×C4×D61—22no—
62C22×C4×D61—22no—
63C22×C4×D61—22no—
64C22×C4×D61—24no—
65C22×C4×D61—42no—
66D4×Dic61—232no—
67C2×C4⋊Dic61—22no—
68C2×C4⋊Dic61—24no—
69C2×C22⋊Dic61—24no—
70C2×C22⋊Dic61—24no—
71C2×C22⋊Dic61—42no—
72C2×C22⋊Dic61—42no—
73C2×C22⋊Dic61C2×C418yescomplemented
74C2×C22⋊Dic61D418yescomplemented
75C2×#11758198—22no—
76C2×#11758198—22no—
77C2×#11758198—22no—
78C2×#11758198—22no—
79C2×#11758198—24no—
80C2×#11758198—24no—
81C2×#11758198—42no—
82C2×#11758198C2×C414yescomplemented
83C2×#11758198D414yescomplemented
84C2×C4×Dic61—24no—
85C2×C4×Dic61—22no—
86C2×C4×Dic61—42no—
87C2×C4×Dic61D414yescomplemented
88#14519684—24no—
89#14519684—22no—
90#14519684—24no—
91#14519684—24no—
92#14519684—24no—
93#14519684—42no—
94#14519684C2×C414yescomplemented
95C25×C61C2312yes—
96C22×D4×C61—24no—
97C22×D4×C61—24no—
98C22×D4×C61—22no—
99C22×D4×C61—22no—
100C22×D4×C61C2×C414yescomplemented
101C23×C4×C61C2312yes—
102C23×C4×C61C2311yescharacteristic
103C23×C4×C61C2311yescharacteristic
104C23×C4×C61C2311yescharacteristic
105C2×C22⋊C4×C61—24no—
106C2×C22⋊C4×C61—24no—
107C2×C22⋊C4×C61—24no—
108C2×C22⋊C4×C61—24no—
109C2×C22⋊C4×C61—42no—
110C2×C22⋊C4×C61—42no—
111#95×C61—22no—
112#95×C61—22no—
113C24×C61—22no—
114C24×C61—22no—
115C24×C61—22no—
116C24×C61—22no—
117C24×C61—22no—
118C24×C61—22no—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61—22no—
122C24×C61—22no—
123C24×C61—22no—
124C24×C61—22no—
125C24×C61C22×C414yes—
126C24×C61C2×D414yes—
127C24×C61#4114yes—
128C24×C61C2411yescharacteristic
129C23×D61—22no—
130C23×D61—21no—
131C23×D61—21no—
132C23×D61—22no—
133C23×D61—21no—
134C23×D61—21no—
135C23×D61—22no—
136C23×D61—22no—
137C23×D61C22×C412yes—
138C23×D61C2×D412yes—
139C23×D61#4112yes—
140C2×D4×C61—28no—
141C2×D4×C61—216no—
142C2×D4×C61—28no—
143C2×D4×C61—216no—
144C2×D4×C61—28no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—21no—
148C22×C4×C61—22no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—22no—
152C22×C4×C61—21no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61C22×C412yes—
163C22×C4×C61C2×D412yes—
164C22×C4×C61C2×D412yes—
165C22×C4×C61#4112yes—
166C22×C4×C61#4112yes—
167C2×C22⋊D61—216no—
168C2×C22⋊D61—216no—
169C2×C22⋊D61—48no—
170C2×C22⋊D61—48no—
171C2×C22⋊D61—48no—
172C2×C22⋊D61—48no—
173C2×C22⋊D61—48no—
174C22×Dic61—22no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—216no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—21no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—21no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—48no—
197C22×Dic61—48no—
198C22×Dic61—48no—
199C22×Dic61—48no—
200C22×Dic61—48no—
201C22×Dic61—48no—
202C22×Dic61C22×C414yes—
203C22×Dic61C22×C412yes—
204C22×Dic61C2×D414yes—
205C22×Dic61C2×D414yes—
206C22×Dic61C2×D412yes—
207C22×Dic61C2×D412yes—
208C22×Dic61C2×D412yes—
209C22×Dic61#4112yes—
210C2×C4×D61—28no—
211C2×C4×D61—48no—
212C2×C4×D61—48no—
213C2×C4×D61—44no—
214C2×C4×D61—44no—
215C22⋊C4×C61—48no—
216C22⋊C4×C61—48no—
217C22⋊Dic61—216no—
218C22⋊Dic61—48no—
219#11758198—28no—
220#11758198—28no—
221#11758198—48no—
222C4⋊Dic61—28no—
223C4×Dic61—28no—
224C4×Dic61—44no—
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—24no—
235C23×C61—24no—
236C23×C61—24no—
237C23×C61—24no—
238C23×C61—24no—
239C23×C61—24no—
240C23×C61—24no—
241C23×C61—24no—
242C23×C61—24no—
243C23×C61—42no—
244C23×C61—42no—
245C23×C61—42no—
246C23×C61—42no—
247C23×C61—42no—
248C23×C61—42no—
249C23×C61—42no—
250C23×C61—42no—
251C23×C61—42no—
252C23×C61—42no—
253C23×C61—42no—
254C23×C61—42no—
255C23×C61—42no—
256C23×C61—42no—
257C23×C61—42no—
258C23×C61—42no—
259C23×C61C4×D418yes—
260C23×C61C23×C411yescharacteristic
261C23×C61C22×D411yescharacteristic
262C23×C61C22×D412yes—
263C23×C61C22×D411yescharacteristic
264C23×C61C2×#4111yescharacteristic
265C23×C61C2×#4112yes—
266C23×C61C2×#4111yescharacteristic
267C23×C61C2×#4111yescharacteristic
268C23×C61C2×#4111yescharacteristic
269C23×C61H(5,𝔽2)12yes—
270C23×C61H(5,𝔽2)12yes—
271C22×D61—22no—
272C22×D61—24no—
273C22×D61—22no—
274C22×D61—24no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—24no—
280C22×D61—24no—
281C22×D61—24no—
282C22×D61—24no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—42no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—42no—
289C22×D61—42no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61—42no—
293C22×D61C4×D414yescomplemented
294D4×C61—232no—
295C2×C4×C61—24no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—24no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—24no—
302C2×C4×C61—24no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61C4×D414yes—
317C22⋊D61—432no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—24no—
323C2×Dic61—24no—
324C2×Dic61—24no—
325C2×Dic61—24no—
326C2×Dic61—22no—
327C2×Dic61—24no—
328C2×Dic61—24no—
329C2×Dic61—24no—
330C2×Dic61—24no—
331C2×Dic61—24no—
332C2×Dic61—24no—
333C2×Dic61—24no—
334C2×Dic61—432no—
335C2×Dic61—42no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61#12014yes—
347C2×Dic61#12114yes—
348C4×D61—416no—
349#14175—611nomaximal, Sylow
350C22×C61—28no—
351C22×C61—28no—
352C22×C61—28no—
353C22×C61—44no—
354C22×C61—44no—
355C22×C61—44no—
356C22×C61—44no—
357C22×C61—44no—
358C22×C61—44no—
359C22×C61—44no—
360C22×C61—44no—
361C22×C61—44no—
362C22×C61—44no—
363C22×C61—44no—
364C22×C61—44no—
365C22×C61C2×C4×D411yescharacteristic
366C22×C61C2×C4×D411yescharacteristic
367C22×C61C2×C4×D412yes—
368C22×C61C4×#4111yescharacteristic
369C22×C61#51812yes—
370C22×C61C2×#12011yescharacteristic
371C22×C61C2×#12111yescharacteristic
372C22×C61#52511yescharacteristic
373C22×C61#52512yes—
374C22×C61#52511yescharacteristic
375C22×C61#52911yescharacteristic
376C22×C61#53211yescharacteristic
377C22×C61#53511yescharacteristic
378C22×C61#53511yescharacteristic
379C22×C61#54012yes—
380C22×C61D4212yes—
381C22×C61#54612yes—
382C22×C61#54612yes—
383C22×C61#54612yes—
384C22×C61#54612yes—
385C22×C61#55112yes—
386C22×C61#55312yes—
387C22×C61#55312yes—
388C2×D61—28no—
389C2×D61—24no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61—44no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—44no—
396C2×D61—44no—
397C2×D61—42no—
398C2×D61—42no—
399C4×C61—24no—
400C4×C61—42no—
401C4×C61—42no—
402C4×C61—82no—
403Dic61—24no—
404Dic61—24no—
405Dic61—42no—
406Dic61—44no—
407Dic61—44no—
408C22×C4×D4—611no—
409C2×#392—611no—
410C2×#386—612no—
411C2×#386—612no—
412C2×C4×C22⋊C4—611no—
413#1442—611no—
414#1439—611no—
415#1438D6111yescharacteristic, complemented
416#1437—612no—
417#1434—611no—
418C22⋊#95—612no—
419C2×C61—48no—
420C2×C61C4×#12011yescharacteristic
421C2×C61C4×#12111yescharacteristic
422C2×C61#232811yescharacteristic
423C2×C61#235812yes—
424C2×C61#236412yes—
425C2×C61#240411yescharacteristic
426C2×C61#240811yescharacteristic
427C2×C61#245712yes—
428C2×C61#246412yes—
429C2×C61#253511yescharacteristic
430C2×C61#259811yescharacteristic
431D61—44no—
432C23×D4—612no—
433C23×D4C2×D6111yescharacteristic
434C24×C4—612no—
435C24×C4—611no—
436C2×C4×D4—1224no—
437C2×C4×D4—1228no—
438C22×C4⋊C4—611no—
439C22×C22⋊C4—612no—
440C22×C22⋊C4—611no—
441C22×C22⋊C4—611no—
442C22×C22⋊C4—612no—
443C22×C22⋊C4—612no—
444C22×C22⋊C4C2×D6112yes—
445C22×C22⋊C4C2×D6112yes—
446C22×C42—611no—
447C22×C42—611no—
448#392—618no—
449#386—1228no—
450#386—1228no—
451C4×C22⋊C4—1224no—
452C2×#95—611no—
453C2×#95—611no—
454C2×#95—612no—
455C2×#95—612no—
456C2×#95—612no—
457C2×#95—612no—
458C2×#95—612no—
459C2×#95C2×D6111yescharacteristic
460C2×#95C2×D6111yescharacteristic
461C61#1417511yescharacteristic, complemented, Sylow
462C25—611no—
463C25C22×D6112yes—
464C22×D4—24no—
465C22×D4—24no—
466C22×D4—22no—
467C22×D4—22no—
468C22×D4—618no—
469C22×D4—1224no—
470C22×D4—1224no—
471C22×D4—1224no—
472C22×D4—1224no—
473C22×D4—2442no—
474C22×D4—2442no—
475C22×D4C4×D6114yescomplemented
476C23×C4—611no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—612no—
480C23×C4—612no—
481C23×C4—1222no—
482C23×C4—1224no—
483C23×C4—1222no—
484C23×C4—1224no—
485C23×C4—1224no—
486C23×C4—1224no—
487C23×C4—1224no—
488C23×C4—1224no—
489C23×C4—1222no—
490C23×C4—2442no—
491C23×C4—2442no—
492C23×C4—2442no—
493C23×C4C22×D6112yes—
494C23×C4C22×D6111yescharacteristic
495C23×C4C22×D6111yescharacteristic
496C23×C4C22×D6111yescharacteristic
497C4×D4—12232no—
498C2×C4⋊C4—1224no—
499C2×C4⋊C4—1222no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—618no—
507C2×C22⋊C4—614no—
508C2×C22⋊C4—614no—
509C2×C22⋊C4—618no—
510C2×C22⋊C4—1222no—
511C2×C22⋊C4—1222no—
512C2×C22⋊C4—1224no—
513C2×C22⋊C4—1224no—
514C2×C22⋊C4—1222no—
515C2×C22⋊C4—1222no—
516C2×C22⋊C4—1224no—
517C2×C22⋊C4—1224no—
518C2×C22⋊C4—2442no—
519C2×C22⋊C4—2442no—
520C2×C22⋊C4—2442no—
521C2×C42—614no—
522C2×C42—1224no—
523C2×C42—1222no—
524C2×C42—2442no—
525#95—22no—
526#95—22no—
527#95—614no—
528#95—1222no—
529#95—1224no—
530#95—1224no—
531#95—1224no—
532#95—1224no—
533#95—2442no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—612no—
547C24—612no—
548C24—612no—
549C24—1221no—
550C24—1222no—
551C24—1221no—
552C24—1221no—
553C24—1221no—
554C24—1222no—
555C24—1222no—
556C24—1222no—
557C24C2×C4×D6114yes—
558C24D4×D6114yes—
559C24#1175822414yes—
560C24C23×D6111yescharacteristic
561C2×D4—28no—
562C2×D4—28no—
563C2×D4—216no—
564C2×D4—216no—
565C2×D4—28no—
566C2×D4—12216no—
567C2×D4—12216no—
568C2×D4—2448no—
569C2×D4—2448no—
570C2×D4—2448no—
571C2×D4—2448no—
572C2×D4—2448no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—612no—
591C22×C4—612no—
592C22×C4—614no—
593C22×C4—612no—
594C22×C4—612no—
595C22×C4—614no—
596C22×C4—612no—
597C22×C4—614no—
598C22×C4—1228no—
599C22×C4—1222no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—12216no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—1221no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1221no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—2448no—
622C22×C4—2444no—
623C22×C4—2448no—
624C22×C4—2444no—
625C22×C4—2448no—
626C22×C4—2448no—
627C22×C4—2448no—
628C22×C4—2448no—
629C22×C4—2448no—
630C22×C4—2448no—
631C22×C4C2×C4×D6112yes—
632C22×C4D4×D6112yes—
633C22×C4D4×D6112yes—
634C22×C4#1175822412yes—
635C22×C4#1175822412yes—
636C4⋊C4—1228no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—1228no—
640C22⋊C4—12216no—
641C22⋊C4—1228no—
642C22⋊C4—2448no—
643C22⋊C4—2448no—
644C42—1228no—
645C42—2444no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—614no—
681C23—1222no—
682C23—1224no—
683C23—1222no—
684C23—1224no—
685C23—1222no—
686C23—1222no—
687C23—1222no—
688C23—1222no—
689C23—1224no—
690C23—1224no—
691C23—1224no—
692C23—1224no—
693C23—2442no—
694C23—2442no—
695C23—2441no—
696C23—2442no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2442no—
701C23—2442no—
702C23—2442no—
703C23#1451973718yes—
704C23C22×C4×D6111yescharacteristic
705C23C2×D4×D6111yescharacteristic
706C23C2×D4×D6111yescharacteristic
707C23C2×D4×D6112yes—
708C23#41×D6111yescharacteristic
709C23#41×D6111yescharacteristic
710C23C2×#1175822412yes—
711C23C2×#1175822411yescharacteristic
712C23C2×#1175822411yescharacteristic
713C23#1451982212yes—
714C23#1451982312yes—
715D4—232no—
716D4—24432no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—614no—
739C2×C4—614no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1224no—
745C2×C4—1224no—
746C2×C4—1224no—
747C2×C4—1224no—
748C2×C4—1224no—
749C2×C4—1222no—
750C2×C4—1224no—
751C2×C4—1224no—
752C2×C4—1224no—
753C2×C4—1224no—
754C2×C4—1224no—
755C2×C4—1224no—
756C2×C4—24416no—
757C2×C4—24432no—
758C2×C4—2442no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4—2442no—
764C2×C4—2442no—
765C2×C4—2442no—
766C2×C4—2442no—
767C2×C4—2442no—
768C2×C4—2442no—
769C2×C4#1451973714yes—
770C22—28no—
771C22—28no—
772C22—28no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—1228no—
786C22—1224no—
787C22—2444no—
788C22—2442no—
789C22—2442no—
790C22—2442no—
791C22—2444no—
792C22—2442no—
793C22—2442no—
794C22—2442no—
795C22—2444no—
796C22C4×D4×D6111yescharacteristic
797C22C2×#1451973711yescharacteristic
798C22C2×#1451973712yes—
799C22C4×#1175822411yescharacteristic
800C22#1684023412yes—
801C22#120×D6111yescharacteristic
802C22#121×D6111yescharacteristic
803C22#1684026812yes—
804C22#1684026811yescharacteristic
805C22#1684027211yescharacteristic
806C22#1684029111yescharacteristic
807C22#1684031011yescharacteristic
808C22#1684032511yescharacteristic
809C22#1684033011yescharacteristic
810C22#1684036512yes—
811C22#1684039612yes—
812C22#1684039912yes—
813C22#1684039912yes—
814C22#1684040112yes—
815C22#1684040412yes—
816C22#1684043512yes—
817C22#1684045512yes—
818C22#1684046412yes—
819C4—24no—
820C4—42no—
821C4—42no—
822C4—82no—
823C4—1224no—
824C4—1224no—
825C4—2442no—
826C4—2444no—
827C4—2444no—
828C2—48no—
829C2—2444no—
830C2#2144831811yescharacteristic
831C2#2144833511yescharacteristic
832C2#2144854311yescharacteristic
833C2#2144879912yes—
834C2#2144886712yes—
835C2#2144913311yescharacteristic
836C2#2144917011yescharacteristic
837C2#2144972112yes—
838C2#2144982012yes—
839C2#2145071511yescharacteristic
840C2#2145138011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1438C2
socle, cosocleC24×C61C24
prime radicalC2×#16839670C2
hypercenter#1438D61
hypocenterC61#14175
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic61C2semidirect
3. C2×#16839639C2semidirect
4. C2×#16839638C2semidirect
5. C2×#16839609C2semidirect
6. #21444075C2semidirect
7. #21444065C2semidirect
8. #21444056C2semidirect
9. #21444044C2semidirect
10. #21444041C2semidirect
11. C61×#1438C2semidirect
25. #16839670C4semidirect
48. C22×C22⋊D61C2×C4semidirect
73. C2×C22⋊Dic61C2×C4semidirect
74. C2×C22⋊Dic61D4semidirect
82. C2×#11758198C2×C4semidirect
83. C2×#11758198D4semidirect
87. C2×C4×Dic61D4semidirect
94. #14519684C2×C4semidirect
100. C22×D4×C61C2×C4semidirect
293. C22×D61C4×D4semidirect
415. #1438D61semidirect
461. C61#14175semidirect
475. C22×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic612
C2×#168396702
C2×#168396392
C2×#168396382
C2×#168396092
#214440752
#214440652
#214440562
#214440442
#214440412
C61×#14382
#1417561