Finite Group Databasebeta

← C4×#15689037 #26138069

Subgroups — C4×#15689037 #26138069

Order 12032.

2550 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689037C211yesmaximal, characteristic
2C2×C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic47C212yesmaximal, complemented
4C2×C4×C22⋊Dic47C212yesmaximal, complemented
5#20241647C211yesmaximal, characteristic, complemented
6#20241638C211yesmaximal, characteristic, complemented
7#20241635C212yesmaximal, complemented
8#20241631C212yesmaximal, complemented
9#20241629C211yesmaximal, characteristic
10C4×C47⋊#95C211yesmaximal, characteristic, complemented
11C22×C4×D4×C47C211yesmaximal, characteristic
12C22×Dic47⋊C4C2211yescharacteristic
13C22×Dic47⋊C4C2211yescharacteristic
14C22×C22⋊Dic47C2212yes—
15C22×C22⋊Dic47C2212yes—
16C22×C22⋊Dic47C2212yes—
17C22×C22⋊Dic47C2212yes—
18C22×C4×Dic47C2212yes—
19C22×C4×Dic47C2211yescharacteristic
20C22×C4×Dic47C2211yescharacteristic
21#15689037C418yesdirect product factor
22C4×Dic47⋊C4—24no—
23C4×C22⋊Dic47—28no—
24C4×C22⋊Dic47—28no—
25C2×C47⋊#95C2211yescharacteristic
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2211yescharacteristic
34C23×D4×C47C2211yescharacteristic
35C24×C4×C47C2212yes—
36C2×C4×D4×C47—28no—
37C2×C4×D4×C47—24no—
38C22×C4⋊C4×C47C2211yescharacteristic
39C22×C22⋊C4×C47C2212yes—
40C22×C42×C47C2211yescharacteristic
41C23×Dic47C2312yes—
42C23×Dic47C2311yescharacteristic
43C23×Dic47C2311yescharacteristic
44C23×Dic47C2312yes—
45C23×Dic47C2311yescharacteristic
46C23×Dic47C2311yescharacteristic
47C2×Dic47⋊C4—22no—
48C2×Dic47⋊C4—22no—
49C2×Dic47⋊C4—22no—
50C2×Dic47⋊C4—22no—
51C2×Dic47⋊C4—22no—
52C2×Dic47⋊C4C2×C414yescomplemented
53C2×C22⋊Dic47—24no—
54C2×C22⋊Dic47—24no—
55C2×C22⋊Dic47—24no—
56C2×C22⋊Dic47—24no—
57C2×C22⋊Dic47—24no—
58C2×C22⋊Dic47—24no—
59C2×C22⋊Dic47—24no—
60C2×C22⋊Dic47—24no—
61C2×C22⋊Dic47—24no—
62C2×C22⋊Dic47—24no—
63C2×C22⋊Dic47C2×C418yescomplemented
64C2×C22⋊Dic47C2×C418yescomplemented
65C2×C4×Dic47—22no—
66C2×C4×Dic47—22no—
67C2×C4×Dic47—24no—
68C2×C4×Dic47—24no—
69C2×C4×Dic47—24no—
70C2×C4×Dic47—22no—
71C2×C4×Dic47—24no—
72C2×C4×Dic47D414yescomplemented
73C47⋊#95—24no—
74C47⋊#95—24no—
75C47⋊#95—22no—
76C47⋊#95—22no—
77C47⋊#95—22no—
78C47⋊#95—24no—
79C47⋊#95—24no—
80C47⋊#95—24no—
81C47⋊#95C2×C414yescomplemented
82C25×C47C2312yes—
83C22×D4×C47—24no—
84C22×D4×C47—24no—
85C22×D4×C47—22no—
86C22×D4×C47—22no—
87C22×D4×C47C2×C414yes—
88C23×C4×C47—24no—
89C23×C4×C47—24no—
90C23×C4×C47—24no—
91C23×C4×C47—24no—
92C23×C4×C47—24no—
93C23×C4×C47—24no—
94C23×C4×C47D418yes—
95C23×C4×C47C2312yes—
96C23×C4×C47C2311yescharacteristic
97C23×C4×C47C2311yescharacteristic
98C23×C4×C47C2311yescharacteristic
99C4×D4×C47—232no—
100C2×C4⋊C4×C47—24no—
101C2×C4⋊C4×C47—22no—
102C2×C22⋊C4×C47—24no—
103C2×C22⋊C4×C47—24no—
104C2×C22⋊C4×C47—24no—
105C2×C42×C47—24no—
106C2×C42×C47D414yes—
107C24×C47—22no—
108C24×C47—22no—
109C24×C47—22no—
110C24×C47—22no—
111C24×C47—22no—
112C24×C47—22no—
113C24×C47—22no—
114C24×C47—22no—
115C24×C47—22no—
116C24×C47—22no—
117C24×C47—22no—
118C24×C47—22no—
119C24×C47C22×C414yes—
120C24×C47C2×D414yes—
121C24×C47#4114yes—
122C24×C47C2411yescharacteristic
123C2×D4×C47—28no—
124C2×D4×C47—28no—
125C2×D4×C47—216no—
126C2×D4×C47—216no—
127C2×D4×C47—28no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—216no—
141C22×C4×C47—216no—
142C22×C4×C47—216no—
143C22×C4×C47—48no—
144C22×C4×C47—48no—
145C22×C4×C47—48no—
146C22×C4×C47—48no—
147C22×C4×C47C22×C412yes—
148C22×C4×C47C2×D412yes—
149C22×C4×C47C2×D414yes—
150C22×C4×C47C2×D412yes—
151C22×C4×C47C2×D414yes—
152C22×C4×C47C2×D412yes—
153C22×C4×C47C2×D412yes—
154C22×C4×C47#4112yes—
155C22×C4×C47#4112yes—
156C22×C4×C47#4114yes—
157C22×Dic47—21no—
158C22×Dic47—21no—
159C22×Dic47—21no—
160C22×Dic47—21no—
161C22×Dic47—21no—
162C22×Dic47—22no—
163C22×Dic47—22no—
164C22×Dic47—22no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—21no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—21no—
184C22×Dic47—21no—
185C22×Dic47C22×C414yes—
186C22×Dic47C22×C412yes—
187C22×Dic47C22×C412yes—
188C22×Dic47C2×D412yes—
189C22×Dic47C2×D412yes—
190C22×Dic47#4114yes—
191C22×Dic47#4112yes—
192C22×Dic47#4112yes—
193C4⋊C4×C47—28no—
194C22⋊C4×C47—216no—
195C42×C47—28no—
196C22⋊Dic47—216no—
197C22⋊Dic47—216no—
198C22⋊Dic47—216no—
199C22⋊Dic47—216no—
200Dic47⋊C4—28no—
201Dic47⋊C4—28no—
202C4×Dic47—28no—
203C4×Dic47—44no—
204C4×Dic47—48no—
205C23×C47—24no—
206C23×C47—24no—
207C23×C47—24no—
208C23×C47—24no—
209C23×C47—24no—
210C23×C47—24no—
211C23×C47—24no—
212C23×C47—24no—
213C23×C47—24no—
214C23×C47—24no—
215C23×C47—24no—
216C23×C47—24no—
217C23×C47—24no—
218C23×C47—24no—
219C23×C47—24no—
220C23×C47—24no—
221C23×C47—24no—
222C23×C47—24no—
223C23×C47—42no—
224C23×C47—42no—
225C23×C47—42no—
226C23×C47—42no—
227C23×C47—42no—
228C23×C47—42no—
229C23×C47—42no—
230C23×C47—42no—
231C23×C47—42no—
232C23×C47—42no—
233C23×C47—42no—
234C23×C47—42no—
235C23×C47—42no—
236C23×C47—42no—
237C23×C47—42no—
238C23×C47—42no—
239C23×C47C4×D418yes—
240C23×C47C23×C411yescharacteristic
241C23×C47C22×D411yescharacteristic
242C23×C47C22×D412yes—
243C23×C47C22×D411yescharacteristic
244C23×C47C2×#4111yescharacteristic
245C23×C47C2×#4111yescharacteristic
246C23×C47C2×#4112yes—
247C23×C47C2×#4111yescharacteristic
248C23×C47C2×#4112yes—
249C23×C47C2×#4112yes—
250C23×C47C2×#4111yescharacteristic
251D4×C47—232no—
252C2×C4×C47—24no—
253C2×C4×C47—22no—
254C2×C4×C47—22no—
255C2×C4×C47—24no—
256C2×C4×C47—22no—
257C2×C4×C47—24no—
258C2×C4×C47—24no—
259C2×C4×C47—24no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—42no—
263C2×C4×C47—42no—
264C2×C4×C47—42no—
265C2×C4×C47—42no—
266C2×C4×C47—42no—
267C2×C4×C47—42no—
268C2×C4×C47—432no—
269C2×C4×C47C4×D414yes—
270C2×C4×C47#12014yes—
271C2×C4×C47#12114yes—
272C2×C4×C47#12118yes—
273C2×C4×C47#12318yes—
274C2×C4×C47#12414yes—
275C2×Dic47—22no—
276C2×Dic47—22no—
277C2×Dic47—22no—
278C2×Dic47—22no—
279C2×Dic47—22no—
280C2×Dic47—22no—
281C2×Dic47—22no—
282C2×Dic47—24no—
283C2×Dic47—24no—
284C2×Dic47—24no—
285C2×Dic47—24no—
286C2×Dic47—22no—
287C2×Dic47—22no—
288C2×Dic47—24no—
289C2×Dic47—24no—
290C2×Dic47—24no—
291C2×Dic47—24no—
292C2×Dic47—24no—
293C2×Dic47—41no—
294C2×Dic47—41no—
295C2×Dic47—42no—
296C2×Dic47—42no—
297C2×Dic47—42no—
298C2×Dic47—42no—
299C2×Dic47—41no—
300C2×Dic47—42no—
301C2×Dic47—41no—
302C2×Dic47—42no—
303C2×Dic47—42no—
304C2×Dic47—42no—
305C2×Dic47—41no—
306C2×Dic47—42no—
307C2×Dic47—41no—
308C2×Dic47—42no—
309C2×Dic47—42no—
310C2×Dic47C4×D414yescomplemented
311C4×#394—471nomaximal, Sylow
312C22×C47—28no—
313C22×C47—28no—
314C22×C47—28no—
315C22×C47—44no—
316C22×C47—44no—
317C22×C47—44no—
318C22×C47—44no—
319C22×C47—44no—
320C22×C47—44no—
321C22×C47—44no—
322C22×C47—44no—
323C22×C47—44no—
324C22×C47—44no—
325C22×C47—44no—
326C22×C47—44no—
327C22×C47C2×C4×D411yescharacteristic
328C22×C47C2×C4×D412yes—
329C22×C47C2×C4×D411yescharacteristic
330C22×C47C4×#4111yescharacteristic
331C22×C47C4×#4112yes—
332C22×C47C2×#12011yescharacteristic
333C22×C47C2×#12111yescharacteristic
334C22×C47C2×#12112yes—
335C22×C47C2×#12312yes—
336C22×C47#52512yes—
337C22×C47#52511yescharacteristic
338C22×C47#52512yes—
339C22×C47#52512yes—
340C22×C47#52511yescharacteristic
341C22×C47C2×#12411yescharacteristic
342C22×C47#52912yes—
343C22×C47#52912yes—
344C22×C47#52912yes—
345C22×C47#52912yes—
346C22×C47#52911yescharacteristic
347C22×C47#53211yescharacteristic
348C22×C47#53212yes—
349C22×C47#53211yescharacteristic
350C4×C47—24no—
351C4×C47—44no—
352C4×C47—42no—
353C4×C47#39418yescomplemented
354Dic47—24no—
355Dic47—42no—
356Dic47—42no—
357Dic47—44no—
358Dic47—42no—
359Dic47—44no—
360C22×C4×D4D4711yescharacteristic
361C2×#394—471no—
362C2×C4×C4⋊C4—471no—
363C2×C4×C22⋊C4—472no—
364C2×C4×C22⋊C4—472no—
365#1442—471no—
366#1441—471no—
367#1440—472no—
368#1439—472no—
369#1438—471no—
370C4×#95—471no—
371C2×C47—48no—
372C2×C47C4×#12011yescharacteristic
373C2×C47C4×#12111yescharacteristic
374C2×C47C4×#12112yes—
375C2×C47C4×#12312yes—
376C2×C47C4×#12411yescharacteristic
377C2×C47C2×#39411yescharacteristic
378C2×C47#238811yescharacteristic
379C2×C47#239211yescharacteristic
380C2×C47#239212yes—
381C2×C47#239512yes—
382C2×C47#239811yescharacteristic
383C23×D4C2×D4711yescharacteristic
384C24×C4C2×D4712yes—
385C2×C4×D4—28no—
386C2×C4×D4—24no—
387C22×C4⋊C4—471no—
388C22×C4⋊C4—471no—
389C22×C4⋊C4C2×D4711yescharacteristic
390C22×C22⋊C4—472no—
391C22×C22⋊C4—472no—
392C22×C22⋊C4—472no—
393C22×C22⋊C4—472no—
394C22×C22⋊C4C2×D4712yes—
395C22×C42—471no—
396C22×C42—472no—
397C22×C42—471no—
398C22×C42C2×D4711yescharacteristic
399#394—478no—
400C4×C4⋊C4—944no—
401C4×C22⋊C4—948no—
402C4×C22⋊C4—948no—
403C2×#95—471no—
404C2×#95—471no—
405C2×#95—472no—
406C2×#95—471no—
407C2×#95—472no—
408C2×#95—472no—
409C2×#95—471no—
410C2×#95—472no—
411C2×#95—472no—
412C47C4×#39411yescharacteristic, complemented, Sylow
413C25C22×D4712yes—
414C22×D4—24no—
415C22×D4—24no—
416C22×D4—22no—
417C22×D4—22no—
418C22×D4C4×D4714yes—
419C23×C4—24no—
420C23×C4—24no—
421C23×C4—24no—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—24no—
425C23×C4—471no—
426C23×C4—471no—
427C23×C4—471no—
428C23×C4—472no—
429C23×C4—471no—
430C23×C4—472no—
431C23×C4C22⋊D4718yes—
432C23×C4C22×D4711yescharacteristic
433C23×C4C22×D4712yes—
434C23×C4C22×D4711yescharacteristic
435C23×C4C22×D4711yescharacteristic
436C4×D4—232no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—474no—
440C2×C4⋊C4—942no—
441C2×C4⋊C4—942no—
442C2×C4⋊C4—942no—
443C2×C4⋊C4—942no—
444C2×C4⋊C4—942no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—478no—
449C2×C22⋊C4—478no—
450C2×C22⋊C4—944no—
451C2×C22⋊C4—944no—
452C2×C22⋊C4—944no—
453C2×C22⋊C4—944no—
454C2×C22⋊C4—944no—
455C2×C22⋊C4—944no—
456C2×C22⋊C4—944no—
457C2×C22⋊C4—944no—
458C2×C22⋊C4—944no—
459C2×C22⋊C4—944no—
460C2×C42—24no—
461C2×C42—474no—
462C2×C42—942no—
463C2×C42—942no—
464C2×C42—944no—
465C2×C42—944no—
466C2×C42—944no—
467C2×C42—944no—
468C2×C42—942no—
469C2×C42C22⋊D4714yes—
470#95—474no—
471#95—944no—
472#95—944no—
473#95—944no—
474#95—942no—
475#95—944no—
476#95—944no—
477#95—942no—
478#95—942no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24C2×C4×D4714yes—
492C24#1062535014yes—
493C24C2×C22⋊D4714yes—
494C24C23×D4711yescharacteristic
495C2×D4—28no—
496C2×D4—216no—
497C2×D4—28no—
498C2×D4—216no—
499C2×D4—28no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—216no—
513C22×C4—216no—
514C22×C4—216no—
515C22×C4—48no—
516C22×C4—48no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4—472no—
520C22×C4—472no—
521C22×C4—472no—
522C22×C4—474no—
523C22×C4—472no—
524C22×C4—472no—
525C22×C4—474no—
526C22×C4—472no—
527C22×C4—941no—
528C22×C4—941no—
529C22×C4—941no—
530C22×C4—941no—
531C22×C4—942no—
532C22×C4—942no—
533C22×C4—941no—
534C22×C4—942no—
535C22×C4—942no—
536C22×C4—942no—
537C22×C4—942no—
538C22×C4—941no—
539C22×C4—941no—
540C22×C4—942no—
541C22×C4—942no—
542C22×C4—942no—
543C22×C4—942no—
544C22×C4—942no—
545C22×C4—941no—
546C22×C4—942no—
547C22×C4—941no—
548C22×C4—942no—
549C22×C4—942no—
550C22×C4—942no—
551C22×C4—942no—
552C22×C4—942no—
553C22×C4—942no—
554C22×C4—941no—
555C22×C4C2×C4×D4712yes—
556C22×C4#1062535012yes—
557C22×C4D4×D4712yes—
558C22×C4#1062535212yes—
559C22×C4#1062535214yes—
560C22×C4C2×C22⋊D4714yes—
561C22×C4C2×C22⋊D4712yes—
562C22×C4C2×C22⋊D4712yes—
563C22×C4C2×C22⋊D4712yes—
564C22×C4C2×C22⋊D4714yes—
565C4⋊C4—28no—
566C4⋊C4—948no—
567C4⋊C4—948no—
568C22⋊C4—216no—
569C22⋊C4—9416no—
570C22⋊C4—9416no—
571C22⋊C4—9416no—
572C22⋊C4—9416no—
573C42—28no—
574C42—948no—
575C42—1884no—
576C42—1888no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23C4×C22⋊D4718yes—
612C23C22×C4×D4711yescharacteristic
613C23C2×D4×D4711yescharacteristic
614C23C22×C22⋊D4711yescharacteristic
615C23C22×C22⋊D4712yes—
616C23#41×D4711yescharacteristic
617C23#41×D4711yescharacteristic
618C23#41×D4712yes—
619C23C2×#1062535211yescharacteristic
620C23C2×#1062535212yes—
621C23C2×#1062535012yes—
622C23C2×#1062535011yescharacteristic
623D4—232no—
624C2×C4—24no—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—432no—
641C2×C4—474no—
642C2×C4—942no—
643C2×C4—942no—
644C2×C4—942no—
645C2×C4—942no—
646C2×C4—942no—
647C2×C4—942no—
648C2×C4—944no—
649C2×C4—944no—
650C2×C4—944no—
651C2×C4—942no—
652C2×C4—944no—
653C2×C4—942no—
654C2×C4—944no—
655C2×C4—944no—
656C2×C4—942no—
657C2×C4—944no—
658C2×C4—944no—
659C2×C4—944no—
660C2×C4—1881no—
661C2×C4—1881no—
662C2×C4—1882no—
663C2×C4—1882no—
664C2×C4—1882no—
665C2×C4—1881no—
666C2×C4—1882no—
667C2×C4—1881no—
668C2×C4—1882no—
669C2×C4—1882no—
670C2×C4—1882no—
671C2×C4—1882no—
672C2×C4—1881no—
673C2×C4—1882no—
674C2×C4—1881no—
675C2×C4—1882no—
676C2×C4—1882no—
677C2×C4C4×C22⋊D4714yes—
678C2×C4#1309399314yes—
679C2×C4#1309399514yes—
680C2×C4#1309399618yes—
681C2×C4#1309400518yes—
682C2×C4#1309401114yes—
683C22—28no—
684C22—28no—
685C22—28no—
686C22—44no—
687C22—44no—
688C22—44no—
689C22—44no—
690C22—44no—
691C22—44no—
692C22—44no—
693C22—44no—
694C22—44no—
695C22—44no—
696C22—44no—
697C22—44no—
698C22C4×D4×D4711yescharacteristic
699C22C2×C4×C22⋊D4711yescharacteristic
700C22C2×C4×C22⋊D4712yes—
701C22C4×#1062535211yescharacteristic
702C22C4×#1062535212yes—
703C22C2×#1309399311yescharacteristic
704C22C2×#1309399511yescharacteristic
705C22C2×#1309399612yes—
706C22C2×#1309400512yes—
707C22#1568963012yes—
708C22#1568963011yescharacteristic
709C22#1568963212yes—
710C22#1568963411yescharacteristic
711C22#1568963412yes—
712C22C2×#1309401111yescharacteristic
713C22#1568965312yes—
714C22#1568965312yes—
715C22#1568965312yes—
716C22#1568965512yes—
717C22#1568965511yescharacteristic
718C22#1568966911yescharacteristic
719C22#1568966912yes—
720C22#1568967011yescharacteristic
721C4—24no—
722C4—44no—
723C4—42no—
724C4—944no—
725C4—1882no—
726C4—1882no—
727C4—1884no—
728C4—1882no—
729C4—1884no—
730C4#1568903718yesdirect product factor
731C2—48no—
732C2C4×#1309399311yescharacteristic
733C2C4×#1309399511yescharacteristic
734C2C4×#1309399612yes—
735C2C4×#1309400512yes—
736C2C4×#1309401111yescharacteristic
737C2C2×#1568903711yescharacteristic
738C2#2024660111yescharacteristic
739C2#2024662611yescharacteristic
740C2#2024663012yes—
741C2#2024664712yes—
742C2#2024667211yescharacteristic
subgroupG/H
centerC23×C4C22×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC22×C4×D4×C47C2
socle, cosocleC24×C47C24
prime radicalC23×D4×C47C22
hypercenterC22×C4×D4D47
hypocenterC47C4×#394
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic47⋊C4C2semidirect
3. C2×C4×C22⋊Dic47C2semidirect
4. C2×C4×C22⋊Dic47C2semidirect
5. #20241647C2semidirect
6. #20241638C2semidirect
7. #20241635C2semidirect
8. #20241631C2semidirect
10. C4×C47⋊#95C2semidirect
21. #15689037C4direct (N × H)
52. C2×Dic47⋊C4C2×C4semidirect
63. C2×C22⋊Dic47C2×C4semidirect
64. C2×C22⋊Dic47C2×C4semidirect
72. C2×C4×Dic47D4semidirect
81. C47⋊#95C2×C4semidirect
310. C2×Dic47C4×D4semidirect
353. C4×C47#394semidirect
412. C47C4×#394semidirect
730. C4#15689037direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156890372
C2×C4×Dic47⋊C42
C2×C4×C22⋊Dic472
#202416472
#202416382
#202416352
#202416312
#202416292
C4×C47⋊#952
C22×C4×D4×C472
C4×#39447