Finite Group Databasebeta

← #29603421

Subgroups — #29603421

Order 15616.

2538 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839652C212yesmaximal, complemented
2C2×#16839641C211yesmaximal, characteristic
3C2×#16839641C211yesmaximal, characteristic
4C2×#16839641C211yesmaximal, characteristic
5C2×C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
6#21444078C212yesmaximal, complemented
7#21444061C212yesmaximal, complemented
8#21444051C212yesmaximal, complemented
9#21444042C211yesmaximal, characteristic, complemented
10#21444042C211yesmaximal, characteristic, complemented
11C23×C4⋊C4×C61C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C22×C22⋊Dic61C2211yescharacteristic
14C22×C22⋊Dic61C2211yescharacteristic
15C22×C22⋊Dic61C2211yescharacteristic
16C22×#11758198C2211yescharacteristic
17C22×#11758198C2212yes—
18C22×#11758198C2212yes—
19C22×#11758198C2211yescharacteristic
20C22×C4×Dic61C2212yes—
21#16839652—28no—
22#16839641—24no—
23#16839641—24no—
24#16839641C418yescomplemented
25C4×C22⋊Dic61—24no—
26C2×#14519684C2211yescharacteristic
27C2×#14519684C2212yes—
28C2×#14519684C2211yescharacteristic
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C24×C4×C61C2211yescharacteristic
36C24×C4×C61C2211yescharacteristic
37C24×C4×C61C2211yescharacteristic
38C22×C4⋊C4×C61—24no—
39C22×C4⋊C4×C61—28no—
40C22×C4⋊C4×C61C2212yes—
41C22×C4⋊C4×C61C2212yes—
42C24×D61C2311yescharacteristic
43C22×C22⋊D61—22no—
44C22×C22⋊D61—22no—
45C22×C22⋊D61—22no—
46C22×C22⋊D61—22no—
47C22×C22⋊D61—22no—
48C22×C22⋊D61—22no—
49C22×C22⋊D61C2×C414yes—
50C23×Dic61C2311yescharacteristic
51C23×Dic61C2311yescharacteristic
52C23×Dic61C2312yes—
53C23×Dic61C2311yescharacteristic
54C23×Dic61C2312yes—
55C2×C22⋊Dic61—22no—
56C2×C22⋊Dic61—22no—
57C2×C22⋊Dic61—22no—
58C2×C22⋊Dic61—22no—
59C2×C22⋊Dic61—22no—
60C2×C22⋊Dic61—22no—
61C2×C22⋊Dic61—22no—
62C2×C22⋊Dic61C2×C414yes—
63C2×C22⋊Dic61D414yes—
64C2×#11758198—24no—
65C2×#11758198—24no—
66C2×#11758198—22no—
67C2×#11758198—22no—
68C2×#11758198—24no—
69C2×#11758198—24no—
70C2×#11758198—24no—
71C2×#11758198—42no—
72C2×#11758198—42no—
73C2×#11758198C2×C418yescomplemented
74C2×C4×Dic61—24no—
75C2×C4×Dic61—24no—
76C2×C4×Dic61—42no—
77#14519684—22no—
78#14519684—22no—
79#14519684—24no—
80#14519684—24no—
81#14519684—24no—
82#14519684—24no—
83#14519684—24no—
84#14519684—42no—
85#14519684C2×C418yescomplemented
86C25×C61C2311yescharacteristic
87C23×C4×C61—22no—
88C23×C4×C61—22no—
89C23×C4×C61—24no—
90C23×C4×C61—24no—
91C23×C4×C61—22no—
92C23×C4×C61—22no—
93C23×C4×C61—22no—
94C23×C4×C61—24no—
95C23×C4×C61—24no—
96C23×C4×C61—22no—
97C23×C4×C61—22no—
98C23×C4×C61—42no—
99C23×C4×C61—42no—
100C23×C4×C61C2×C414yes—
101C23×C4×C61D414yes—
102C23×C4×C61C2311yescharacteristic
103C23×C4×C61C2312yes—
104C23×C4×C61C2312yes—
105C23×C4×C61C2311yescharacteristic
106C2×C4⋊C4×C61—232no—
107C2×C4⋊C4×C61—24no—
108C2×C4⋊C4×C61—24no—
109C2×C4⋊C4×C61—24no—
110C2×C4⋊C4×C61—24no—
111C2×C4⋊C4×C61—24no—
112C2×C4⋊C4×C61D418yescomplemented
113C24×C61—22no—
114C24×C61—22no—
115C24×C61—22no—
116C24×C61—22no—
117C24×C61C22×C412yes—
118C24×C61C2×D412yes—
119C24×C61C2×D412yes—
120C24×C61#4112yes—
121C24×C61#4112yes—
122C24×C61#4112yes—
123C24×C61#4112yes—
124C24×C61C2411yescharacteristic
125C23×D61—21no—
126C23×D61—21no—
127C23×D61—22no—
128C23×D61—21no—
129C23×D61—21no—
130C23×D61—21no—
131C23×D61—21no—
132C23×D61—22no—
133C23×D61—22no—
134C23×D61—22no—
135C23×D61C22×C412yes—
136C22×C4×C61—28no—
137C22×C4×C61—216no—
138C22×C4×C61—28no—
139C22×C4×C61—28no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—21no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—21no—
146C22×C4×C61—22no—
147C22×C4×C61—216no—
148C22×C4×C61—28no—
149C22×C4×C61—28no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—21no—
154C22×C4×C61—22no—
155C22×C4×C61—21no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—28no—
161C22×C4×C61—44no—
162C22×C4×C61—48no—
163C22×C4×C61—48no—
164C22×C4×C61—48no—
165C22×C4×C61—48no—
166C22×C4×C61—44no—
167C22×C4×C61—44no—
168C22×C4×C61C22×C414yes—
169C22×C4×C61C2×D412yes—
170C22×C4×C61C2×D414yes—
171C22×C4×C61C2×D414yes—
172C22×C4×C61C2×D412yes—
173C22×C4×C61C2×D414yes—
174C22×C4×C61#4114yes—
175C2×C22⋊D61—28no—
176C2×C22⋊D61—28no—
177C2×C22⋊D61—28no—
178C2×C22⋊D61—44no—
179C2×C22⋊D61—44no—
180C2×C22⋊D61—44no—
181C2×C22⋊D61—44no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—22no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61C22×C412yes—
211C22×Dic61C22×C414yes—
212C22×Dic61C2×D414yes—
213C4⋊C4×C61—216no—
214C4⋊C4×C61—216no—
215C22⋊Dic61—28no—
216C22⋊Dic61—28no—
217C22⋊Dic61—44no—
218#11758198—216no—
219#11758198—48no—
220#11758198—44no—
221#11758198—44no—
222C4×Dic61—48no—
223C23×C61—24no—
224C23×C61—24no—
225C23×C61—22no—
226C23×C61—22no—
227C23×C61—24no—
228C23×C61—22no—
229C23×C61—22no—
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#11714yes—
240C23×C61C4×D414yes—
241C23×C61C4×D414yes—
242C23×C61#12114yes—
243C23×C61#12314yes—
244C23×C61#12414yes—
245C23×C61#12614yes—
246C23×C61C23×C411yescharacteristic
247C23×C61C22×D411yescharacteristic
248C23×C61C22×D412yes—
249C23×C61C22×D411yescharacteristic
250C23×C61C2×#4111yescharacteristic
251C23×C61C2×#4111yescharacteristic
252C23×C61C2×#4111yescharacteristic
253C23×C61C2×#4112yes—
254C23×C61C2×#4111yescharacteristic
255C23×C61H(5,𝔽2)12yes—
256C23×C612−1+412yes—
257C22×D61—22no—
258C22×D61—24no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—24no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—42no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—42no—
272C22×D61—42no—
273C22×D61—42no—
274C22×D61—42no—
275C22×D61—42no—
276C22×D61—42no—
277C22×D61—42no—
278C22×D61—42no—
279C22×D61—42no—
280C2×C4×C61—232no—
281C2×C4×C61—24no—
282C2×C4×C61—24no—
283C2×C4×C61—24no—
284C2×C4×C61—22no—
285C2×C4×C61—24no—
286C2×C4×C61—24no—
287C2×C4×C61—24no—
288C2×C4×C61—22no—
289C2×C4×C61—24no—
290C2×C4×C61—24no—
291C2×C4×C61—22no—
292C2×C4×C61—24no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—24no—
296C2×C4×C61—24no—
297C2×C4×C61—416no—
298C2×C4×C61—416no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61C4×D418yes—
306C2×C4×C61#12014yes—
307C22⋊D61—416no—
308C2×Dic61—22no—
309C2×Dic61—24no—
310C2×Dic61—24no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—24no—
314C2×Dic61—24no—
315C2×Dic61—24no—
316C2×Dic61—24no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—42no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339#14019—611nomaximal, Sylow
340C22×C61—24no—
341C22×C61—24no—
342C22×C61—28no—
343C22×C61—28no—
344C22×C61—24no—
345C22×C61—24no—
346C22×C61—24no—
347C22×C61—28no—
348C22×C61—28no—
349C22×C61—24no—
350C22×C61#38818yescomplemented
351C22×C61C2×#11711yescharacteristic
352C22×C61C2×C4×D411yescharacteristic
353C22×C61C2×C4×D412yes—
354C22×C61C2×C4×D411yescharacteristic
355C22×C61#52012yes—
356C22×C61C2×#12011yescharacteristic
357C22×C61C2×#12111yescharacteristic
358C22×C61C2×#12311yescharacteristic
359C22×C61#52511yescharacteristic
360C22×C61#52512yes—
361C22×C61C2×#12411yescharacteristic
362C22×C61C2×#12611yescharacteristic
363C22×C61#53411yescharacteristic
364C22×C61#53611yescharacteristic
365C22×C61#53912yes—
366C22×C61D4212yes—
367C22×C61#54612yes—
368C22×C61#54712yes—
369C22×C61#54812yes—
370C22×C61#54812yes—
371C22×C61#55212yes—
372C22×C61#55312yes—
373C22×C61#55312yes—
374C2×D61—42no—
375C2×D61—44no—
376C2×D61—44no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—81no—
380C2×D61—81no—
381C2×D61—81no—
382C2×D61—81no—
383C2×D61—82no—
384C2×D61—82no—
385C4×C61—24no—
386C4×C61—28no—
387C4×C61—42no—
388C4×C61—44no—
389Dic61—44no—
390Dic61—44no—
391Dic61—42no—
392Dic61—81no—
393Dic61—81no—
394C23×C4⋊C4D6111yescharacteristic, complemented
395C2×#388—612no—
396C2×#386—611no—
397C2×#386—611no—
398C2×#386—611no—
399C2×C4×C22⋊C4—611no—
400#1442—612no—
401#1439—612no—
402#1436—612no—
403C22⋊#95—611no—
404C22⋊#95—611no—
405C2×C61—28no—
406C2×C61C2×#38811yescharacteristic
407C2×C61C4×#12011yescharacteristic
408C2×C61#232211yescharacteristic
409C2×C61#235212yes—
410C2×C61#236112yes—
411C2×C61#241011yescharacteristic
412C2×C61#241311yescharacteristic
413C2×C61#243611yescharacteristic
414C2×C61#244312yes—
415C2×C61#248112yes—
416C2×C61#259111yescharacteristic
417D61—82no—
418C23×D4—611no—
419C24×C4C2×D6111yescharacteristic
420C24×C4C2×D6111yescharacteristic
421C24×C4C2×D6111yescharacteristic
422C22×C4⋊C4—24no—
423C22×C4⋊C4—28no—
424C22×C4⋊C4C2×D6112yes—
425C22×C4⋊C4C2×D6112yes—
426C22×C22⋊C4—611no—
427C22×C22⋊C4—611no—
428C22×C22⋊C4—612no—
429C22×C22⋊C4—611no—
430C22×C22⋊C4—611no—
431C22×C22⋊C4—612no—
432C22×C22⋊C4—611no—
433C22×C42—612no—
434#388—1228no—
435#386—618no—
436#386—1224no—
437#386—1224no—
438C4×C22⋊C4—1224no—
439C2×#95—612no—
440C2×#95—612no—
441C2×#95—612no—
442C2×#95—612no—
443C2×#95—611no—
444C2×#95—612no—
445C2×#95—612no—
446C2×#95—611no—
447C2×#95—612no—
448C61#1401911yescharacteristic, complemented, Sylow
449C25—611no—
450C25C22×D6111yescharacteristic
451C22×D4—614no—
452C22×D4—1222no—
453C22×D4—1222no—
454C22×D4—1222no—
455C22×D4—1222no—
456C22×D4—1222no—
457C22×D4—1222no—
458C23×C4—22no—
459C23×C4—22no—
460C23×C4—24no—
461C23×C4—24no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—24no—
466C23×C4—24no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—42no—
470C23×C4—42no—
471C23×C4—612no—
472C23×C4—612no—
473C23×C4—611no—
474C23×C4—611no—
475C23×C4—611no—
476C23×C4C4×D6114yes—
477C23×C4C22⋊D6114yes—
478C23×C4C22×D6111yescharacteristic
479C23×C4C22×D6112yes—
480C23×C4C22×D6112yes—
481C23×C4C22×D6111yescharacteristic
482C2×C4⋊C4—232no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4C22⋊D6118yescomplemented
489C2×C22⋊C4—614no—
490C2×C22⋊C4—614no—
491C2×C22⋊C4—618no—
492C2×C22⋊C4—1222no—
493C2×C22⋊C4—1222no—
494C2×C22⋊C4—1222no—
495C2×C22⋊C4—1222no—
496C2×C22⋊C4—1224no—
497C2×C22⋊C4—1224no—
498C2×C22⋊C4—1224no—
499C2×C22⋊C4—1222no—
500C2×C22⋊C4—1222no—
501C2×C22⋊C4—1222no—
502C2×C22⋊C4—1222no—
503C2×C22⋊C4—1222no—
504C2×C22⋊C4—1224no—
505C2×C22⋊C4—1224no—
506C2×C22⋊C4—2442no—
507C2×C22⋊C4—2442no—
508C2×C42—1224no—
509C2×C42—1224no—
510C2×C42—2442no—
511#95—618no—
512#95—1224no—
513#95—1224no—
514#95—1224no—
515#95—1222no—
516#95—1222no—
517#95—1224no—
518#95—1224no—
519#95—2442no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—612no—
525C24—1221no—
526C24—1222no—
527C24—1221no—
528C24—1221no—
529C24—1222no—
530C24—1221no—
531C24—1221no—
532C24—1221no—
533C24—1222no—
534C24—1222no—
535C24C2×C4×D6112yes—
536C24#1175822212yes—
537C24D4×D6112yes—
538C24#1175822412yes—
539C24#1175822612yes—
540C24#1175822612yes—
541C24C2×C22⋊D6112yes—
542C24C23×D6111yescharacteristic
543C2×D4—1228no—
544C2×D4—1228no—
545C2×D4—1228no—
546C2×D4—2444no—
547C2×D4—2444no—
548C2×D4—2444no—
549C2×D4—2444no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—216no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—28no—
561C22×C4—216no—
562C22×C4—28no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—44no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—612no—
583C22×C4—614no—
584C22×C4—614no—
585C22×C4—1221no—
586C22×C4—1222no—
587C22×C4—1221no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1221no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1221no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1222no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1222no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4C2×C4×D6114yes—
614C22×C4#1175822214yes—
615C22×C4C2×C22⋊D6112yes—
616C22×C4C2×C22⋊D6114yes—
617C22×C4C2×C22⋊D6114yes—
618C22×C4C2×C22⋊D6112yes—
619C22×C4C2×C22⋊D6114yes—
620C4⋊C4—216no—
621C4⋊C4—216no—
622C22⋊C4—1228no—
623C22⋊C4—1228no—
624C22⋊C4—12216no—
625C22⋊C4—2448no—
626C22⋊C4—2444no—
627C22⋊C4—2444no—
628C22⋊C4—2444no—
629C42—2448no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—22no—
635C23—24no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—1222no—
647C23—1224no—
648C23—1222no—
649C23—1222no—
650C23—1224no—
651C23—2442no—
652C23—2442no—
653C23—2441no—
654C23—2441no—
655C23—2441no—
656C23—2441no—
657C23—2442no—
658C23—2441no—
659C23—2441no—
660C23—2441no—
661C23—2441no—
662C23—2442no—
663C23—2442no—
664C23—2442no—
665C23—2442no—
666C23—2442no—
667C23—2442no—
668C23—2442no—
669C23#1451973514yes—
670C23C4×C22⋊D6114yes—
671C23#1451973914yes—
672C23#1451974914yes—
673C23#1451976214yes—
674C23#1451976614yes—
675C23#1451977214yes—
676C23C22×C4×D6111yescharacteristic
677C23C2×D4×D6111yescharacteristic
678C23C22×C22⋊D6111yescharacteristic
679C23C22×C22⋊D6112yes—
680C23C2×#1175822411yescharacteristic
681C23C2×#1175822212yes—
682C23C2×#1175822211yescharacteristic
683C23C2×#1175822611yescharacteristic
684C23C2×#1175822611yescharacteristic
685C23#1451982212yes—
686C23#1451982512yes—
687D4—24416no—
688C2×C4—232no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—416no—
706C2×C4—416no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—1222no—
714C2×C4—1224no—
715C2×C4—1222no—
716C2×C4—1224no—
717C2×C4—1222no—
718C2×C4—1224no—
719C2×C4—1224no—
720C2×C4—1224no—
721C2×C4—1224no—
722C2×C4—2442no—
723C2×C4—2442no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4—2442no—
733C2×C4—2442no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2442no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4C4×C22⋊D6118yes—
745C2×C4#1451974614yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—24no—
750C22—28no—
751C22—28no—
752C22—28no—
753C22—24no—
754C22—28no—
755C22—24no—
756C22—4881no—
757C22—4881no—
758C22—4881no—
759C22—4882no—
760C22—4882no—
761C22—4881no—
762C22—2442no—
763C22—2444no—
764C22—2442no—
765C22—2442no—
766C22—2444no—
767C22#1683965218yescomplemented
768C22C2×#1451973511yescharacteristic
769C22C2×C4×C22⋊D6111yescharacteristic
770C22C2×C4×C22⋊D6112yes—
771C22C2×#1451973911yescharacteristic
772C22#1684024312yes—
773C22C2×#1451974611yescharacteristic
774C22C2×#1451974911yescharacteristic
775C22C2×#1451976211yescharacteristic
776C22#1684027311yescharacteristic
777C22#1684027312yes—
778C22C2×#1451976611yescharacteristic
779C22C2×#1451977211yescharacteristic
780C22#1684032111yescharacteristic
781C22#1684033611yescharacteristic
782C22#1684035912yes—
783C22D4×C22⋊D6112yes—
784C22#1684040612yes—
785C22#1684041312yes—
786C22#1684042312yes—
787C22#1684042312yes—
788C22#1684044712yes—
789C22#1684046012yes—
790C22#1684046012yes—
791C4—28no—
792C4—24no—
793C4—42no—
794C4—44no—
795C4—4881no—
796C4—4881no—
797C4—2442no—
798C4—2444no—
799C4—2444no—
800C2—28no—
801C2—4882no—
802C2C2×#1683965211yescharacteristic
803C2C4×#1451974611yescharacteristic
804C2#2144848811yescharacteristic
805C2#2144874412yes—
806C2#2144883512yes—
807C2#2144919311yescharacteristic
808C2#2144922611yescharacteristic
809C2#2144947311yescharacteristic
810C2#2144955412yes—
811C2#2145007412yes—
812C2#2145129911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC23×C4⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC23×C4⋊C4D61
hypocenterC61#14019
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16839652C2semidirect
5. C2×C4×C22⋊Dic61C2semidirect
6. #21444078C2semidirect
7. #21444061C2semidirect
8. #21444051C2semidirect
9. #21444042C2semidirect
10. #21444042C2semidirect
11. C23×C4⋊C4×C61C2semidirect
24. #16839641C4semidirect
73. C2×#11758198C2×C4semidirect
85. #14519684C2×C4semidirect
112. C2×C4⋊C4×C61D4semidirect
350. C22×C61#388semidirect
394. C23×C4⋊C4D61semidirect
448. C61#14019semidirect
488. C2×C4⋊C4C22⋊D61semidirect
767. C22#16839652semidirect

Maximal subgroups

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

subgroupindex
C2×#168396522
C2×#168396412
C2×C4×C22⋊Dic612
#214440782
#214440612
#214440512
#214440422
C23×C4⋊C4×C612
#1401961