Finite Group Databasebeta

← C47×#25585 #26065283

Subgroups — C47×#25585 #26065283

Order 12032.

1636 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3505C211yesmaximal, characteristic, complemented
2C47×#2435C211yesmaximal, characteristic, complemented
3C47×#2433C211yesmaximal, characteristic, complemented
4C47×#2408C211yesmaximal, characteristic, complemented
5C47×#2021C214yesmaximal, complemented
6C47×#1996C211yesmaximal, characteristic, complemented
7C47×#1964C211yesmaximal, characteristic, complemented
8C47×#1889C214yesmaximal, complemented
9C4×#99×C47C211yesmaximal, characteristic, complemented
10C23×D4×C47C2211yescharacteristic
11C47×#553—21no—
12C47×#553—22no—
13C47×#552—21no—
14C47×#551—22no—
15C47×#548—21no—
16C47×#546—21no—
17C47×#539—21no—
18C47×#538—21no—
19C47×#534C2212yes—
20C2×#127×C47—21no—
21C47×#529—21no—
22C2×#124×C47—21no—
23C47×#525—21no—
24C2×C22⋊Q8×C47C2211yescharacteristic
25C2×#121×C47—21no—
26C2×#121×C47C2211yescharacteristic
27C2×#120×C47C2214yes—
28C2×#120×C47C2212yes—
29C47×#518C2212yes—
30C2×C4×D4×C47C2211yescharacteristic
31C2×#99×C47C2212yes—
32C2×#99×C47C2214yes—
33C47×#394—21no—
34C47×#394—22no—
35C47×#392—21no—
36C47×#392—22no—
37C47×#390—21no—
38C47×#390—21no—
39C47×#390—21no—
40C47×#380C2211yescharacteristic
41C47×#379C2214yes—
42C47×#379C2212yes—
43C4×C22⋊C4×C47C2211yescharacteristic
44C4×C22⋊C4×C47C2211yescharacteristic
45C47×#342C2212yes—
46C47×#342C2214yes—
47C25×C47C2312yes—
48C2×#41×C47—21no—
49C22×Q8×C47D411yescharacteristic, complemented
50C22×D4×C47—22no—
51C22×D4×C47—24no—
52C22×D4×C47—21no—
53C22×D4×C47—21no—
54C22×D4×C47—21no—
55C22×D4×C47—21no—
56C22×D4×C47—21no—
57C22×D4×C47—21no—
58C22×D4×C47—44no—
59C22×D4×C47D411yescharacteristic, complemented
60C22×D4×C47C2311yescharacteristic
61C22×D4×C47C2312yes—
62C23×C4×C47D411yescharacteristic, complemented
63C23×C4×C47C2311yescharacteristic
64#127×C47—44no—
65#126×C47—22no—
66#126×C47—22no—
67#126×C47—22no—
68#125×C47—21no—
69#125×C47—22no—
70#124×C47—21no—
71#124×C47—22no—
72#124×C47—44no—
73#123×C47—22no—
74#123×C47—22no—
75#123×C47—22no—
76#123×C47—22no—
77#123×C47—22no—
78C22⋊Q8×C47—21no—
79C22⋊Q8×C47—22no—
80C22⋊Q8×C47—21no—
81C22⋊Q8×C47—21no—
82C22⋊Q8×C47—21no—
83C22⋊Q8×C47—21no—
84#121×C47—21no—
85#121×C47—22no—
86#121×C47—21no—
87#121×C47—21no—
88#121×C47—21no—
89#121×C47—21no—
90#121×C47—22no—
91#121×C47—22no—
92#121×C47—44no—
93#120×C47—22no—
94#120×C47—22no—
95#120×C47—28no—
96#120×C47—44no—
97#120×C47—44no—
98C4×Q8×C47—21no—
99C4×D4×C47—22no—
100C4×D4×C47—21no—
101C4×D4×C47—21no—
102C4×D4×C47—21no—
103C4×D4×C47—21no—
104C4×D4×C47—21no—
105C4×D4×C47—22no—
106C4×D4×C47—22no—
107C4×D4×C47—22no—
108C4×D4×C47—22no—
109#117×C47—21no—
110#117×C47—22no—
111#117×C47—22no—
112C2×C4⋊C4×C47—21no—
113C2×C4⋊C4×C47D411yescharacteristic, complemented
114C2×C4⋊C4×C47D411yescharacteristic, complemented
115C2×C4⋊C4×C47D411yescharacteristic, complemented
116C2×C4⋊C4×C47D412yescomplemented
117C2×C22⋊C4×C47—22no—
118C2×C22⋊C4×C47—24no—
119C2×C22⋊C4×C47—22no—
120C2×C22⋊C4×C47—22no—
121C2×C22⋊C4×C47—24no—
122C2×C22⋊C4×C47—22no—
123C2×C22⋊C4×C47—24no—
124C2×C22⋊C4×C47D411yescharacteristic, complemented
125C2×C22⋊C4×C47D412yescomplemented
126C2×C22⋊C4×C47C2312yes—
127C2×C22⋊C4×C47C2312yes—
128C2×C22⋊C4×C47C2311yescharacteristic
129C2×C22⋊C4×C47C2312yes—
130C2×C22⋊C4×C47C2312yes—
131C2×C42×C47—21no—
132C2×C42×C47—21no—
133C2×C42×C47D411yescharacteristic, complemented
134#99×C47—24no—
135#99×C47—44no—
136#95×C47—21no—
137#95×C47—21no—
138#95×C47—21no—
139C24×C47—22no—
140C24×C47—22no—
141C24×C47—22no—
142C24×C47—24no—
143C24×C47—24no—
144C24×C47—44no—
145C24×C47—82no—
146C24×C47C2×D412yes—
147C24×C47C2×D411yescharacteristic
148C24×C47C2411yescharacteristic
149#41×C47—82no—
150C2×Q8×C47—21no—
151C2×Q8×C47—21no—
152C2×Q8×C47—42no—
153C2×D4×C47—24no—
154C2×D4×C47—24no—
155C2×D4×C47—24no—
156C2×D4×C47—21no—
157C2×D4×C47—22no—
158C2×D4×C47—21no—
159C2×D4×C47—22no—
160C2×D4×C47—24no—
161C2×D4×C47—22no—
162C2×D4×C47—22no—
163C2×D4×C47—24no—
164C2×D4×C47—22no—
165C2×D4×C47—22no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47—42no—
169C2×D4×C47—42no—
170C2×D4×C47—42no—
171C2×D4×C47—42no—
172C2×D4×C47—48no—
173C2×D4×C47—44no—
174C2×D4×C47—44no—
175C2×D4×C47—44no—
176C2×D4×C47—44no—
177C2×D4×C47—44no—
178C2×D4×C47—48no—
179C2×D4×C47—41no—
180C2×D4×C47—41no—
181C2×D4×C47—41no—
182C2×D4×C47—41no—
183C2×D4×C47—84no—
184C2×D4×C47—82no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—22no—
191C22×C4×C47—22no—
192C22×C4×C47—42no—
193C22×C4×C47—42no—
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D412yes—
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D412yes—
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D412yes—
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C4⋊C4×C47—22no—
207C4⋊C4×C47—22no—
208C4⋊C4×C47—22no—
209C4⋊C4×C47—22no—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—22no—
212C4⋊C4×C47—21no—
213C4⋊C4×C47—21no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—22no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—42no—
219C22⋊C4×C47—22no—
220C22⋊C4×C47—22no—
221C22⋊C4×C47—22no—
222C22⋊C4×C47—22no—
223C22⋊C4×C47—22no—
224C22⋊C4×C47—22no—
225C22⋊C4×C47—21no—
226C22⋊C4×C47—22no—
227C22⋊C4×C47—21no—
228C22⋊C4×C47—22no—
229C22⋊C4×C47—22no—
230C22⋊C4×C47—22no—
231C22⋊C4×C47—21no—
232C22⋊C4×C47—21no—
233C22⋊C4×C47—22no—
234C22⋊C4×C47—22no—
235C22⋊C4×C47—24no—
236C22⋊C4×C47—22no—
237C22⋊C4×C47—48no—
238C22⋊C4×C47—44no—
239C22⋊C4×C47—44no—
240C22⋊C4×C47—48no—
241C22⋊C4×C47—84no—
242C22⋊C4×C47—82no—
243C22⋊C4×C47#4114yescomplemented
244C42×C47—22no—
245C42×C47—22no—
246C42×C47—21no—
247C42×C47—21no—
248C42×C47—42no—
249C42×C47—42no—
250C23×C47—24no—
251C23×C47—24no—
252C23×C47—24no—
253C23×C47—21no—
254C23×C47—22no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—24no—
258C23×C47—41no—
259C23×C47—41no—
260C23×C47—41no—
261C23×C47—41no—
262C23×C47—44no—
263C23×C47—42no—
264C23×C47—42no—
265C23×C47—42no—
266C23×C47—42no—
267C23×C47—42no—
268C23×C47—44no—
269C23×C47—42no—
270C23×C47—42no—
271C23×C47—42no—
272C23×C47—42no—
273C23×C47—42no—
274C23×C47—44no—
275C23×C47—44no—
276C23×C47—88no—
277C23×C47—88no—
278C23×C47C22×D411yescharacteristic
279C23×C47C22×D411yescharacteristic
280C23×C47C22×D411yescharacteristic
281C23×C47C2×#4112yes—
282C23×C47H(5,𝔽2)12yes—
283Q8×C47—42no—
284Q8×C47—81no—
285D4×C47—44no—
286D4×C47—44no—
287D4×C47—44no—
288D4×C47—42no—
289D4×C47—42no—
290D4×C47—42no—
291D4×C47—44no—
292D4×C47—42no—
293D4×C47—44no—
294D4×C47—42no—
295D4×C47—81no—
296D4×C47—82no—
297D4×C47—82no—
298D4×C47—816no—
299D4×C47—88no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—21no—
304C2×C4×C47—22no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—24no—
312C2×C4×C47—24no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—42no—
317C2×C4×C47—42no—
318C2×C4×C47—42no—
319C2×C4×C47—41no—
320C2×C4×C47—42no—
321C2×C4×C47—41no—
322C2×C4×C47—42no—
323C2×C4×C47—42no—
324C2×C4×C47—42no—
325C2×C4×C47—42no—
326C2×C4×C47—42no—
327C2×C4×C47—42no—
328C2×C4×C47—42no—
329C2×C4×C47—81no—
330C2×C4×C47—82no—
331C2×C4×C47—82no—
332C2×C4×C47#12011yescharacteristic
333C2×C4×C47#12011yescharacteristic
334C2×C4×C47#12011yescharacteristic
335C2×C4×C47#12011yescharacteristic
336#25585C4711yesmaximal, characteristic, direct product factor, Sylow
337C22×C47—21no—
338C22×C47—21no—
339C22×C47—21no—
340C22×C47—21no—
341C22×C47—21no—
342C22×C47—21no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—48no—
347C22×C47—44no—
348C22×C47—48no—
349C22×C47—44no—
350C22×C47—41no—
351C22×C47—42no—
352C22×C47—41no—
353C22×C47—42no—
354C22×C47—44no—
355C22×C47—42no—
356C22×C47—41no—
357C22×C47—84no—
358C22×C47—81no—
359C22×C47—84no—
360C22×C47—82no—
361C22×C47—84no—
362C22×C47—82no—
363C22×C47—82no—
364C22×C47—82no—
365C22×C47C2×#12011yescharacteristic
366C22×C47#53211yescharacteristic
367C22×C47#53511yescharacteristic
368C22×C47#54612yes—
369C22×C47#55012yes—
370C4×C47—21no—
371C4×C47—21no—
372C4×C47—21no—
373C4×C47—44no—
374C4×C47—41no—
375C4×C47—42no—
376C4×C47—41no—
377C4×C47—42no—
378C4×C47—41no—
379C4×C47—42no—
380C4×C47—82no—
381C4×C47—82no—
382C4×C47B(4,𝔽2)12yes—
383#3505C2×C4711yescharacteristic, complemented
384#2435C2×C4711yescharacteristic, complemented
385#2433C2×C4711yescharacteristic, complemented
386#2408C2×C4711yescharacteristic, complemented
387#2021C2×C4714yescomplemented
388#1996C2×C4711yescharacteristic, complemented
389#1964C2×C4711yescharacteristic, complemented
390#1889C2×C4714yescomplemented
391C4×#99C2×C4711yescharacteristic, complemented
392C2×C47—22no—
393C2×C47—21no—
394C2×C47—22no—
395C2×C47—21no—
396C2×C47—84no—
397C2×C47—81no—
398C2×C47—82no—
399C2×C47#243111yescharacteristic
400C2×C47C2×B(4,𝔽2)11yescharacteristic
401C2×C47#302711yescharacteristic
402C23×D4C22×C4711yescharacteristic
403#553—21no—
404#553—22no—
405#552—21no—
406#551—22no—
407#548—21no—
408#546—21no—
409#539—21no—
410#538—21no—
411#534C22×C4712yes—
412C2×#127—21no—
413#529—21no—
414C2×#124—21no—
415#525—21no—
416C2×C22⋊Q8C22×C4711yescharacteristic
417C2×#121—21no—
418C2×#121C22×C4711yescharacteristic
419C2×#120C22×C4714yes—
420C2×#120C22×C4712yes—
421#518C22×C4712yes—
422C2×C4×D4C22×C4711yescharacteristic
423C2×#99C22×C4712yes—
424C2×#99C22×C4714yes—
425#394—21no—
426#394—22no—
427#392—21no—
428#392—22no—
429#390—21no—
430#390—21no—
431#390—21no—
432#380C22×C4711yescharacteristic
433#379C22×C4712yes—
434#379C22×C4714yes—
435C4×C22⋊C4C22×C4711yescharacteristic
436C4×C22⋊C4C22×C4711yescharacteristic
437#342C22×C4712yes—
438#342C22×C4714yes—
439C47#2558511yescharacteristic, direct product factor, Sylow
440C25C23×C4712yes—
441C2×#41—21no—
442C22×Q8D4×C4711yescharacteristic, complemented
443C22×D4—22no—
444C22×D4—24no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—44no—
452C22×D4D4×C4711yescharacteristic, complemented
453C22×D4C23×C4711yescharacteristic
454C22×D4C23×C4712yes—
455C23×C4D4×C4711yescharacteristic, complemented
456C23×C4C23×C4711yescharacteristic
457#127—44no—
458#126—22no—
459#126—22no—
460#126—22no—
461#125—21no—
462#125—22no—
463#124—21no—
464#124—22no—
465#124—44no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470#123—22no—
471C22⋊Q8—21no—
472C22⋊Q8—22no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477#121—21no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121—22no—
484#121—22no—
485#121—44no—
486#120—22no—
487#120—22no—
488#120—28no—
489#120—44no—
490#120—44no—
491C4×Q8—21no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—21no—
503#117—22no—
504#117—22no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4D4×C4711yescharacteristic, complemented
507C2×C4⋊C4D4×C4711yescharacteristic, complemented
508C2×C4⋊C4D4×C4711yescharacteristic, complemented
509C2×C4⋊C4D4×C4712yescomplemented
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4D4×C4711yescharacteristic, complemented
518C2×C22⋊C4D4×C4712yescomplemented
519C2×C22⋊C4C23×C4712yes—
520C2×C22⋊C4C23×C4712yes—
521C2×C22⋊C4C23×C4711yescharacteristic
522C2×C22⋊C4C23×C4712yes—
523C2×C22⋊C4C23×C4712yes—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42D4×C4711yescharacteristic, complemented
527#99—24no—
528#99—44no—
529#95—21no—
530#95—21no—
531#95—21no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—24no—
536C24—24no—
537C24—44no—
538C24—82no—
539C24C2×D4×C4712yes—
540C24C2×D4×C4711yescharacteristic
541C24C24×C4711yescharacteristic
542#41—82no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—42no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—48no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—48no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—84no—
577C2×D4—82no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4C2×D4×C4711yescharacteristic
588C22×C4C2×D4×C4712yes—
589C22×C4C2×D4×C4711yescharacteristic
590C22×C4C2×D4×C4711yescharacteristic
591C22×C4C2×D4×C4711yescharacteristic
592C22×C4C2×D4×C4711yescharacteristic
593C22×C4C2×D4×C4712yes—
594C22×C4C2×D4×C4711yescharacteristic
595C22×C4C2×D4×C4712yes—
596C22×C4C2×D4×C4711yescharacteristic
597C22×C4C2×D4×C4711yescharacteristic
598C22×C4C2×D4×C4711yescharacteristic
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—21no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—24no—
630C22⋊C4—48no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—48no—
634C22⋊C4—84no—
635C22⋊C4—82no—
636C22⋊C4#41×C4714yescomplemented
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—42no—
642C42—42no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—44no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—44no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—44no—
669C23—88no—
670C23—88no—
671C23C22×D4×C4711yescharacteristic
672C23C22×D4×C4711yescharacteristic
673C23C22×D4×C4711yescharacteristic
674C23C2×#41×C4712yes—
675C23H(5,𝔽2)×C4712yes—
676Q8—42no—
677Q8—81no—
678D4—44no—
679D4—44no—
680D4—44no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—44no—
686D4—44no—
687D4—42no—
688D4—81no—
689D4—82no—
690D4—82no—
691D4—816no—
692D4—88no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—81no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4#120×C4711yescharacteristic
726C2×C4#120×C4711yescharacteristic
727C2×C4#120×C4711yescharacteristic
728C2×C4#120×C4711yescharacteristic
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—48no—
739C22—44no—
740C22—48no—
741C22—44no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—44no—
747C22—42no—
748C22—41no—
749C22—84no—
750C22—81no—
751C22—84no—
752C22—82no—
753C22—84no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22C2×#120×C4711yescharacteristic
758C22C47×#53211yescharacteristic
759C22C47×#53511yescharacteristic
760C22C47×#54612yes—
761C22C47×#55012yes—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—44no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—42no—
772C4—82no—
773C4—82no—
774C4C47×B(4,𝔽2)12yes—
775C2—22no—
776C2—21no—
777C2—22no—
778C2—21no—
779C2—84no—
780C2—81no—
781C2—82no—
782C2C47×#243111yescharacteristic
783C2C2×C47×B(4,𝔽2)11yescharacteristic
784C2C47×#302711yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC24C24×C47
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3505C2semidirect
2. C47×#2435C2semidirect
3. C47×#2433C2semidirect
4. C47×#2408C2semidirect
5. C47×#2021C2semidirect
6. C47×#1996C2semidirect
7. C47×#1964C2semidirect
8. C47×#1889C2semidirect
9. C4×#99×C47C2semidirect
49. C22×Q8×C47D4semidirect
59. C22×D4×C47D4semidirect
62. C23×C4×C47D4semidirect
113. C2×C4⋊C4×C47D4semidirect
114. C2×C4⋊C4×C47D4semidirect
115. C2×C4⋊C4×C47D4semidirect
116. C2×C4⋊C4×C47D4semidirect
124. C2×C22⋊C4×C47D4semidirect
125. C2×C22⋊C4×C47D4semidirect
133. C2×C42×C47D4semidirect
243. C22⋊C4×C47#41semidirect
336. #25585C47direct (N × H)
383. #3505C2×C47semidirect
384. #2435C2×C47semidirect
385. #2433C2×C47semidirect
386. #2408C2×C47semidirect
387. #2021C2×C47semidirect
388. #1996C2×C47semidirect
389. #1964C2×C47semidirect
390. #1889C2×C47semidirect
391. C4×#99C2×C47semidirect
439. C47#25585direct (N × H)
442. C22×Q8D4×C47semidirect
452. C22×D4D4×C47semidirect
455. C23×C4D4×C47semidirect
506. C2×C4⋊C4D4×C47semidirect
507. C2×C4⋊C4D4×C47semidirect
508. C2×C4⋊C4D4×C47semidirect
509. C2×C4⋊C4D4×C47semidirect
517. C2×C22⋊C4D4×C47semidirect
518. C2×C22⋊C4D4×C47semidirect
526. C2×C42D4×C47semidirect
636. C22⋊C4#41×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#35052
C47×#24352
C47×#24332
C47×#24082
C47×#20212
C47×#19962
C47×#19642
C47×#18892
C4×#99×C472
#2558547