Finite Group Databasebeta

← #26122542

Subgroups — #26122542

Order 12032.

1334 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093945C211yesmaximal, characteristic
2C22×C8×Dic47C211yesmaximal, characteristic, complemented
3C2×#15689026C211yesmaximal, characteristic
4C2×#15688886C211yesmaximal, characteristic, complemented
5C2×#15688885C211yesmaximal, characteristic, complemented
6#20241617C211yesmaximal, characteristic, complemented
7C22×#102×C47C211yesmaximal, characteristic
8C23×C47⋊C8C2211yescharacteristic
9C22×C4⋊Dic47C2211yescharacteristic
10C22×C4⋊Dic47C2211yescharacteristic
11C22×C22⋊Dic47—22no—
12C22×C4×Dic47C2211yescharacteristic
13C2×#13093945—22no—
14C2×#13093945—22no—
15C2×#13093945C414yescomplemented
16C2×C8×Dic47—22no—
17C2×C8×Dic47—22no—
18C2×C8×Dic47—22no—
19#15689026—22no—
20#15689026C414yescomplemented
21C2×C47⋊#95—22no—
22#15688886—22no—
23#15688885—22no—
24C23×D4×C47C2211yescharacteristic
25C23×C8×C47C2211yescharacteristic
26C22×C4⋊C4×C47C2211yescharacteristic
27C2×#102×C47—22no—
28C2×#102×C47—22no—
29C2×#102×C47C414yescomplemented
30C23×Dic47—21no—
31C23×Dic47—21no—
32C23×Dic47D412yes—
33C22×C47⋊C8—21no—
34C22×C47⋊C8—21no—
35C22×C47⋊C8—21no—
36C22×C47⋊C8—21no—
37C22×C47⋊C8C2×C412yes—
38C22×C47⋊C8D412yes—
39C22×C47⋊C8D412yes—
40C2×C4⋊Dic47—21no—
41C2×C4⋊Dic47—21no—
42C2×C4⋊Dic47—21no—
43C2×C4⋊Dic47—21no—
44C2×C4⋊Dic47—21no—
45C2×C4⋊Dic47—21no—
46C2×C4⋊Dic47—21no—
47C2×C4⋊Dic47—21no—
48C2×C4⋊Dic47—21no—
49C2×C4⋊Dic47—21no—
50C2×C4⋊Dic47C2×C412yes—
51C2×C4⋊Dic47C2×C412yes—
52C2×C22⋊Dic47—28no—
53C2×C22⋊Dic47—44no—
54C2×C22⋊Dic47—44no—
55C2×C4×Dic47—21no—
56C2×C4×Dic47—21no—
57C2×C4×Dic47—21no—
58C2×C4×Dic47—21no—
59C2×C4×Dic47C2×C412yes—
60C2×C4×Dic47D412yes—
61#13093945—28no—
62C8×Dic47—28no—
63C47⋊#95—44no—
64C25×C47—21no—
65C22×D4×C47—21no—
66C22×D4×C47—21no—
67C22×D4×C47—21no—
68C22×D4×C47—21no—
69C22×D4×C47—21no—
70C22×D4×C47—21no—
71C22×D4×C47—21no—
72C22×D4×C47—21no—
73C22×D4×C47—21no—
74C22×D4×C47—21no—
75C22×D4×C47—21no—
76C22×D4×C47C2×C412yes—
77C22×D4×C47C2×C412yes—
78C22×D4×C47C2×C412yes—
79C23×C4×C47—21no—
80C23×C4×C47C2311yescharacteristic
81C22×C8×C47—21no—
82C22×C8×C47—21no—
83C22×C8×C47—21no—
84C22×C8×C47—21no—
85C22×C8×C47C2×C412yes—
86C22×C8×C47D412yes—
87C22×C8×C47D412yes—
88C2×C4⋊C4×C47—21no—
89C2×C4⋊C4×C47—21no—
90C2×C4⋊C4×C47—21no—
91C2×C4⋊C4×C47—21no—
92C2×C4⋊C4×C47—21no—
93C2×C4⋊C4×C47C2×C412yes—
94#102×C47—28no—
95C24×C47—22no—
96C24×C47—22no—
97C24×C47—22no—
98C24×C47—41no—
99C24×C47—41no—
100C24×C47—41no—
101C24×C47—41no—
102C24×C47—42no—
103C24×C47—42no—
104C24×C47—42no—
105C24×C47—42no—
106C24×C47C2×D411yescharacteristic
107C2×D4×C47—22no—
108C2×D4×C47—22no—
109C2×D4×C47—22no—
110C2×D4×C47—22no—
111C2×D4×C47—22no—
112C2×D4×C47—22no—
113C2×D4×C47—22no—
114C2×D4×C47—22no—
115C2×D4×C47—22no—
116C2×D4×C47—22no—
117C2×D4×C47—22no—
118C2×D4×C47—22no—
119C2×D4×C47—22no—
120C2×D4×C47—22no—
121C2×D4×C47—22no—
122C2×D4×C47—41no—
123C2×D4×C47—41no—
124C2×D4×C47—41no—
125C2×D4×C47—41no—
126C2×D4×C47—41no—
127C2×D4×C47—41no—
128C2×D4×C47—41no—
129C2×D4×C47—41no—
130C2×D4×C47—41no—
131C2×D4×C47—41no—
132C2×D4×C47—41no—
133C2×D4×C47—41no—
134C2×D4×C47C4214yes—
135C22×C4×C47—22no—
136C22×C4×C47—41no—
137C22×C4×C47—41no—
138C22×C4×C47—42no—
139C22×C4×C47—42no—
140C22×C4×C47C22×C411yescharacteristic
141C22×C4×C47C22×C411yescharacteristic
142C22×C4×C47C22×C411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47#4111yescharacteristic
149C22×C4×C47#4111yescharacteristic
150C22×C4×C47#4111yescharacteristic
151C22×C4×C47#4111yescharacteristic
152C22×C4×C47#4111yescharacteristic
153C22×C4×C47#4111yescharacteristic
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—22no—
160C22×Dic47—41no—
161C22×Dic47—41no—
162C22×Dic47—41no—
163C22×Dic47—41no—
164C22×Dic47—42no—
165C22×Dic47—42no—
166C22×Dic47—42no—
167C22×Dic47—42no—
168C22×Dic47C22⋊C414yes—
169C22×Dic47D814yes—
170C22×Dic47SD1614yes—
171C2×C8×C47—22no—
172C2×C8×C47—22no—
173C2×C8×C47—22no—
174C2×C8×C47—22no—
175C2×C8×C47—22no—
176C2×C8×C47—22no—
177C2×C8×C47C22⋊C414yescomplemented
178C4⋊C4×C47—22no—
179C4⋊C4×C47—22no—
180C4⋊C4×C47—41no—
181C4⋊C4×C47—41no—
182C22⋊Dic47—416no—
183C4⋊Dic47—22no—
184C4⋊Dic47—22no—
185C4⋊Dic47—22no—
186C4⋊Dic47—22no—
187C4⋊Dic47—41no—
188C4⋊Dic47—41no—
189C4⋊Dic47—41no—
190C4⋊Dic47—41no—
191C4×Dic47—22no—
192C4×Dic47—22no—
193C4×Dic47—22no—
194C4×Dic47—22no—
195C2×C47⋊C8—22no—
196C2×C47⋊C8—22no—
197C2×C47⋊C8—22no—
198C2×C47⋊C8—22no—
199C2×C47⋊C8—22no—
200C2×C47⋊C8—22no—
201C2×C47⋊C8C22⋊C414yescomplemented
202C23×C47—24no—
203C23×C47—42no—
204C23×C47—42no—
205C23×C47—42no—
206C23×C47—42no—
207C23×C47—42no—
208C23×C47—42no—
209C23×C47—44no—
210C23×C47—44no—
211C23×C47—44no—
212C23×C47—44no—
213C23×C47—44no—
214C23×C47—44no—
215C23×C47—82no—
216C23×C47—82no—
217C23×C47—82no—
218C23×C47—82no—
219C23×C47—82no—
220C23×C47—82no—
221C23×C47—81no—
222C23×C47—81no—
223C23×C47—81no—
224C23×C47—81no—
225C23×C47C2×C22⋊C411yescharacteristic
226C23×C47C4×D411yescharacteristic
227C23×C47C4×D411yescharacteristic
228C23×C47#12111yescharacteristic
229C23×C47#12111yescharacteristic
230C23×C47#12411yescharacteristic
231C23×C47#12711yescharacteristic
232C23×C47C2×D812yes—
233C23×C47C2×SD1612yes—
234C23×C47#13512yes—
235C23×C47#13512yes—
236D4×C47—24no—
237D4×C47—24no—
238D4×C47—42no—
239D4×C47—42no—
240D4×C47—42no—
241D4×C47—42no—
242D4×C47—42no—
243D4×C47—42no—
244C2×C4×C47—42no—
245C2×C4×C47—44no—
246C2×C4×C47—82no—
247C2×C4×C47—81no—
248C2×C4×C47—81no—
249C2×C4×C47C2×C4211yescharacteristic
250C2×C4×C47C2×C22⋊C411yescharacteristic
251C2×C4×C47C2×C22⋊C411yescharacteristic
252C2×C4×C47#11711yescharacteristic
253C2×C4×C47#11711yescharacteristic
254C2×C4×C47#11711yescharacteristic
255C2×C4×C47C4×D411yescharacteristic
256C2×C4×C47C4×D411yescharacteristic
257C2×C4×C47C4×D411yescharacteristic
258C2×C4×C47C4×D411yescharacteristic
259C2×C4×C47C4×D411yescharacteristic
260C2×C4×C47C4×D411yescharacteristic
261C2×C4×C47C4×D411yescharacteristic
262C2×C4×C47C4×D411yescharacteristic
263C2×C4×C47C4×D411yescharacteristic
264C2×C4×C47C4×D411yescharacteristic
265C2×C4×C47#12011yescharacteristic
266C2×C4×C47#12111yescharacteristic
267C2×C4×C47#12111yescharacteristic
268C2×C4×C47#12111yescharacteristic
269C2×C4×C47#12111yescharacteristic
270C2×C4×C47#12311yescharacteristic
271C2×C4×C47#12311yescharacteristic
272C2×C4×C47#12311yescharacteristic
273C2×C4×C47#12411yescharacteristic
274C2×C4×C47#12411yescharacteristic
275C2×C4×C47#12611yescharacteristic
276C2×C4×C47#12611yescharacteristic
277C2×Dic47—24no—
278C2×Dic47—24no—
279C2×Dic47—24no—
280C2×Dic47—24no—
281C2×Dic47—24no—
282C2×Dic47—24no—
283C2×Dic47—42no—
284C2×Dic47—42no—
285C2×Dic47—44no—
286C2×Dic47—44no—
287C2×Dic47—82no—
288C2×Dic47—82no—
289C2×Dic47—81no—
290C2×Dic47—81no—
291C2×Dic47—81no—
292C2×Dic47—81no—
293C2×Dic47#10218yescomplemented
294C8×C47—24no—
295C47⋊C8—24no—
296#10925—471nomaximal, Sylow
297C22×C47—44no—
298C22×C47—48no—
299C22×C47—84no—
300C22×C47—84no—
301C22×C47—84no—
302C22×C47—82no—
303C22×C47—82no—
304C22×C47—82no—
305C22×C47—82no—
306C22×C47—82no—
307C22×C47—82no—
308C22×C47C4×C22⋊C411yescharacteristic
309C22×C47#38611yescharacteristic
310C22×C47#38811yescharacteristic
311C22×C47#38811yescharacteristic
312C22×C47#39011yescharacteristic
313C22×C47#39011yescharacteristic
314C22×C47#39011yescharacteristic
315C22×C47C2×#10212yes—
316C22×C47#41612yes—
317C22×C47C4×D812yes—
318C22×C47C4×D812yes—
319C22×C47C4×SD1612yes—
320C22×C47C4×SD1612yes—
321C22×C47#46512yes—
322C22×C47#46512yes—
323C22×C47#46612yes—
324C22×C47#46612yes—
325C22×C47#48612yes—
326C22×C47#48812yes—
327C22×C47#49211yescharacteristic
328C22×C47#49311yescharacteristic
329C22×C47#49511yescharacteristic
330C22×C47#49511yescharacteristic
331C4×C47—82no—
332C4×C47C4×C22⋊C411yescharacteristic
333C4×C47C4×C22⋊C411yescharacteristic
334C4×C47#38611yescharacteristic
335C4×C47#38611yescharacteristic
336C4×C47#38811yescharacteristic
337C4×C47#38811yescharacteristic
338C4×C47#38811yescharacteristic
339C4×C47#38811yescharacteristic
340Dic47—28no—
341Dic47—82no—
342Dic47—82no—
343C22×#102—471no—
344C22×#102D4711yescharacteristic
345C22×C4×C8—471no—
346C2×#390—471no—
347C2×#340—471no—
348C2×#340—471no—
349C4⋊#95—471no—
350C2×C47—84no—
351C2×C47#143711yescharacteristic
352C2×C47C4×#10212yes—
353C2×C47#189312yes—
354C2×C47#193412yes—
355C2×C47#193412yes—
356C2×C47#195711yescharacteristic
357C2×C47#195811yescharacteristic
358C2×C47#196811yescharacteristic
359C2×C47#196811yescharacteristic
360C2×C47#197011yescharacteristic
361C2×C47#197011yescharacteristic
362C23×D4C2×D4711yescharacteristic
363C23×C8—471no—
364C23×C8C2×D4711yescharacteristic
365C22×C4⋊C4—471no—
366C22×C4⋊C4—471no—
367C22×C4⋊C4C2×D4711yescharacteristic
368C22×C22⋊C4—942no—
369C22×C42—471no—
370C2×#102—22no—
371C2×#102—22no—
372C2×#102—474no—
373C2×#102—942no—
374C2×#102—942no—
375C2×#102Dic4714yescomplemented
376C2×C4×C8—942no—
377C2×C4×C8—942no—
378C2×C4×C8—942no—
379#390—474no—
380#390—942no—
381C2×#95—942no—
382#340—942no—
383#340—942no—
384C47#1092511yescharacteristic, complemented, Sylow
385C25—21no—
386C22×D4—21no—
387C22×D4—21no—
388C22×D4—21no—
389C22×D4—21no—
390C22×D4—21no—
391C22×D4—21no—
392C22×D4—21no—
393C22×D4—21no—
394C22×D4—21no—
395C22×D4—21no—
396C22×D4—21no—
397C22×D4C4×D4712yes—
398C22×D4C4×D4712yes—
399C22×D4C2×Dic4712yes—
400C23×C4—21no—
401C23×C4—472no—
402C23×C4—941no—
403C23×C4—941no—
404C23×C4C22×D4711yescharacteristic
405C22×C8—21no—
406C22×C8—21no—
407C22×C8—21no—
408C22×C8—21no—
409C22×C8—472no—
410C22×C8—472no—
411C22×C8—472no—
412C22×C8—941no—
413C22×C8—941no—
414C22×C8—941no—
415C22×C8—941no—
416C22×C8C2×Dic4712yes—
417C22×C8C22⋊D4712yes—
418C22×C8C22⋊D4712yes—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—472no—
425C2×C4⋊C4—472no—
426C2×C4⋊C4—941no—
427C2×C4⋊C4—941no—
428C2×C4⋊C4—941no—
429C2×C4⋊C4—941no—
430C2×C4⋊C4—941no—
431C2×C4⋊C4—941no—
432C2×C4⋊C4—941no—
433C2×C4⋊C4—941no—
434C2×C4⋊C4—941no—
435C2×C4⋊C4—941no—
436C2×C4⋊C4C2×Dic4712yes—
437C2×C22⋊C4—948no—
438C2×C22⋊C4—1884no—
439C2×C22⋊C4—1884no—
440C2×C42—472no—
441C2×C42—472no—
442C2×C42—941no—
443C2×C42—941no—
444C2×C42—941no—
445C2×C42—941no—
446#102—28no—
447#102—948no—
448C4×C8—948no—
449#95—1884no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—41no—
454C24—41no—
455C24—41no—
456C24—41no—
457C24—42no—
458C24—42no—
459C24—42no—
460C24—42no—
461C24D4×D4711yescharacteristic
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4C4×Dic4714yes—
490C22×C4—22no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—474no—
496C22×C4—474no—
497C22×C4—474no—
498C22×C4—942no—
499C22×C4—942no—
500C22×C4—942no—
501C22×C4—942no—
502C22×C4—942no—
503C22×C4—942no—
504C22×C4—1881no—
505C22×C4—1881no—
506C22×C4—1881no—
507C22×C4—1881no—
508C22×C4—1882no—
509C22×C4—1882no—
510C22×C4—1882no—
511C22×C4—1882no—
512C22×C4C2×C4×D4711yescharacteristic
513C22×C4C2×C4×D4711yescharacteristic
514C22×C4#1062535011yescharacteristic
515C22×C4#1062535011yescharacteristic
516C22×C4D4×D4711yescharacteristic
517C22×C4D4×D4711yescharacteristic
518C22×C4D4×D4711yescharacteristic
519C22×C4#1062535211yescharacteristic
520C22×C4#1062535211yescharacteristic
521C22×C4#1062535211yescharacteristic
522C22×C4#1062535211yescharacteristic
523C22×C4C22×Dic4711yescharacteristic
524C22×C4C2×C22⋊D4711yescharacteristic
525C22×C4C2×C22⋊D4711yescharacteristic
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—474no—
533C2×C8—942no—
534C2×C8—942no—
535C2×C8—942no—
536C2×C8—942no—
537C2×C8—942no—
538C2×C8—942no—
539C2×C8C22⋊Dic4714yescomplemented
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—41no—
543C4⋊C4—41no—
544C4⋊C4—942no—
545C4⋊C4—942no—
546C4⋊C4—942no—
547C4⋊C4—942no—
548C4⋊C4—1881no—
549C4⋊C4—1881no—
550C4⋊C4—1881no—
551C4⋊C4—1881no—
552C22⋊C4—18816no—
553C42—942no—
554C42—942no—
555C42—942no—
556C42—942no—
557C23—24no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—44no—
565C23—44no—
566C23—44no—
567C23—44no—
568C23—44no—
569C23—44no—
570C23—82no—
571C23—81no—
572C23—81no—
573C23—81no—
574C23—81no—
575C23—82no—
576C23—82no—
577C23—82no—
578C23—82no—
579C23—82no—
580C23C22⋊C4×D4711yescharacteristic
581C23(C22⋊D47)⋊C411yescharacteristic
582C23D4×Dic4711yescharacteristic
583C23#1309399511yescharacteristic
584C23#1309399711yescharacteristic
585C23#1309401011yescharacteristic
586C23#1309402011yescharacteristic
587C23D8×D4712yes—
588C23SD16×D4712yes—
589C23#1309404312yes—
590C23#1309404512yes—
591D4—24no—
592D4—24no—
593D4—42no—
594D4—42no—
595D4—42no—
596D4—42no—
597D4—42no—
598D4—42no—
599C2×C4—42no—
600C2×C4—44no—
601C2×C4—81no—
602C2×C4—81no—
603C2×C4—82no—
604C2×C4—478no—
605C2×C4—944no—
606C2×C4—944no—
607C2×C4—944no—
608C2×C4—944no—
609C2×C4—944no—
610C2×C4—944no—
611C2×C4—3761no—
612C2×C4—3761no—
613C2×C4—3761no—
614C2×C4—3761no—
615C2×C4—3762no—
616C2×C4—3762no—
617C2×C4—1882no—
618C2×C4—1882no—
619C2×C4—1884no—
620C2×C4—1884no—
621C2×C4C2×C4×Dic4711yescharacteristic
622C2×C4C22⋊C4×D4711yescharacteristic
623C2×C4C2×C22⋊Dic4711yescharacteristic
624C2×C4#1309398011yescharacteristic
625C2×C4#1309398011yescharacteristic
626C2×C4#1309398311yescharacteristic
627C2×C4(C22⋊D47)⋊C411yescharacteristic
628C2×C4(C22⋊D47)⋊C411yescharacteristic
629C2×C4(C22⋊D47)⋊C411yescharacteristic
630C2×C4C4×C22⋊D4711yescharacteristic
631C2×C4C4×C22⋊D4711yescharacteristic
632C2×C4C4×C22⋊D4711yescharacteristic
633C2×C4C4×C22⋊D4711yescharacteristic
634C2×C4D4×Dic4711yescharacteristic
635C2×C4D4×Dic4711yescharacteristic
636C2×C4D4×Dic4711yescharacteristic
637C2×C4#1309399211yescharacteristic
638C2×C4#1309399511yescharacteristic
639C2×C4#1309399611yescharacteristic
640C2×C4#1309399611yescharacteristic
641C2×C4#1309399711yescharacteristic
642C2×C4#1309400511yescharacteristic
643C2×C4#1309400611yescharacteristic
644C2×C4#1309400611yescharacteristic
645C2×C4#1309401011yescharacteristic
646C2×C4#1309401111yescharacteristic
647C2×C4#1309401711yescharacteristic
648C2×C4#1309401711yescharacteristic
649C8—24no—
650C8—944no—
651C22—48no—
652C22—44no—
653C22—82no—
654C22—82no—
655C22—82no—
656C22—82no—
657C22—84no—
658C22—84no—
659C22—84no—
660C22—82no—
661C22—82no—
662C22C22⋊C4×Dic4711yescharacteristic
663C22#1568899911yescharacteristic
664C22#1568901111yescharacteristic
665C22#1568901611yescharacteristic
666C22#1568902311yescharacteristic
667C22#1568902311yescharacteristic
668C22#1568902611yescharacteristic
669C22#102×D4712yes—
670C22#1568911612yes—
671C22#1568920312yes—
672C22D8×Dic4712yes—
673C22SD16×Dic4712yes—
674C22#1568921412yes—
675C22#1568934912yes—
676C22#1568935112yes—
677C22#1568935612yes—
678C22#1568935812yes—
679C22#1568946812yes—
680C22#1568947612yes—
681C22#1568949411yescharacteristic
682C22#1568949811yescharacteristic
683C22#1568950411yescharacteristic
684C22#1568950611yescharacteristic
685C4—82no—
686C4—948no—
687C4—3762no—
688C4—3762no—
689C4C4×C22⋊Dic4711yescharacteristic
690C4C22⋊C4×Dic4711yescharacteristic
691C4#1568899911yescharacteristic
692C4#1568900311yescharacteristic
693C4#1568901111yescharacteristic
694C4#1568901611yescharacteristic
695C4#1568901711yescharacteristic
696C4#1568901711yescharacteristic
697C2—84no—
698C2#2024162511yescharacteristic
699C2#102×Dic4712yes—
700C2#2024381312yes—
701C2#2024406812yes—
702C2#2024407312yes—
703C2#2024419211yescharacteristic
704C2#2024419811yescharacteristic
705C2#2024424311yescharacteristic
706C2#2024424411yescharacteristic
707C2#2024425111yescharacteristic
708C2#2024425511yescharacteristic
subgroupG/H
centerC24D4×D47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC22×#102×C47C2
socleC24×C47C2×D4
prime radicalC23×D4×C47C22
cosocleC23×C4×C47C23
hypercenterC22×#102D47
hypocenterC47#10925
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×C8×Dic47C2semidirect
4. C2×#15688886C2semidirect
5. C2×#15688885C2semidirect
6. #20241617C2semidirect
15. C2×#13093945C4semidirect
20. #15689026C4semidirect
29. C2×#102×C47C4semidirect
177. C2×C8×C47C22⋊C4semidirect
201. C2×C47⋊C8C22⋊C4semidirect
293. C2×Dic47#102semidirect
375. C2×#102Dic47semidirect
384. C47#10925semidirect
539. C2×C8C22⋊Dic47semidirect

Maximal subgroups

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

subgroupindex
C22×#130939452
C22×C8×Dic472
C2×#156890262
C2×#156888862
C2×#156888852
#202416172
C22×#102×C472
#1092547