Finite Group Databasebeta

← C2×#20241631 #26137939

Subgroups — C2×#20241631 #26137939

Order 12032.

4926 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic47⋊C4C211yesmaximal, characteristic, complemented
2C23×C22⋊Dic47C211yesmaximal, characteristic
3C23×C22⋊Dic47C211yesmaximal, characteristic
4C22×C47⋊#95C211yesmaximal, characteristic, complemented
5C22×C47⋊#95C211yesmaximal, characteristic, complemented
6C22×C47⋊#95C211yesmaximal, characteristic, complemented
7#20241631C218yesmaximal, direct product factor
8C23×C22⋊C4×C47C211yesmaximal, characteristic
9C24×Dic47C2211yescharacteristic
10C24×Dic47C2211yescharacteristic
11C24×Dic47C2211yescharacteristic
12C24×Dic47C2211yescharacteristic
13C22×Dic47⋊C4—24no—
14C22×Dic47⋊C4—24no—
15C22×Dic47⋊C4—24no—
16C22×Dic47⋊C4C2214yescomplemented
17C22×C22⋊Dic47—24no—
18C22×C22⋊Dic47—24no—
19C22×C22⋊Dic47—24no—
20C22×C22⋊Dic47—24no—
21C22×C22⋊Dic47—24no—
22C22×C22⋊Dic47C418yescomplemented
23C22×C22⋊Dic47C2214yes—
24C22×C22⋊Dic47C2214yes—
25C2×C47⋊#95—24no—
26C2×C47⋊#95—24no—
27C2×C47⋊#95—24no—
28C2×C47⋊#95C2214yescomplemented
29C2×C47⋊#95C2214yescomplemented
30C2×C47⋊#95C2214yescomplemented
31C26×C47C2211yescharacteristic
32C24×C4×C47C2211yescharacteristic
33C24×C4×C47C2211yescharacteristic
34C22×C22⋊C4×C47—24no—
35C22×C22⋊C4×C47—24no—
36C22×C22⋊C4×C47—24no—
37C22×C22⋊C4×C47C2214yes—
38C23×Dic47—22no—
39C23×Dic47—22no—
40C23×Dic47—22no—
41C23×Dic47—22no—
42C23×Dic47—22no—
43C23×Dic47—22no—
44C23×Dic47—22no—
45C23×Dic47—22no—
46C23×Dic47—22no—
47C23×Dic47—22no—
48C23×Dic47—22no—
49C23×Dic47—22no—
50C23×Dic47—22no—
51C23×Dic47—22no—
52C23×Dic47—22no—
53C23×Dic47—22no—
54C23×Dic47—22no—
55C23×Dic47—22no—
56C23×Dic47—22no—
57C23×Dic47—22no—
58C23×Dic47—22no—
59C23×Dic47—22no—
60C23×Dic47C2×C414yes—
61C23×Dic47C2×C414yes—
62C23×Dic47D414yes—
63C23×Dic47D414yes—
64C23×Dic47D414yes—
65C23×Dic47D414yes—
66C23×Dic47C2312yes—
67C23×Dic47C2312yes—
68C23×Dic47C2312yes—
69C23×Dic47C2312yes—
70C2×Dic47⋊C4—232no—
71C2×Dic47⋊C4—28no—
72C2×Dic47⋊C4—28no—
73C2×Dic47⋊C4—28no—
74C2×C22⋊Dic47—232no—
75C2×C22⋊Dic47—28no—
76C2×C22⋊Dic47—232no—
77C2×C22⋊Dic47—28no—
78C2×C22⋊Dic47—28no—
79C2×C22⋊Dic47—28no—
80C2×C22⋊Dic47—28no—
81C2×C22⋊Dic47C2×C4116yescomplemented
82C47⋊#95—28no—
83C47⋊#95—28no—
84C47⋊#95—28no—
85C25×C47—22no—
86C25×C47—22no—
87C25×C47—22no—
88C25×C47—22no—
89C25×C47—22no—
90C25×C47—22no—
91C25×C47—22no—
92C25×C47—22no—
93C25×C47—22no—
94C25×C47—22no—
95C25×C47—22no—
96C25×C47—22no—
97C25×C47C2×C414yes—
98C25×C47D414yes—
99C25×C47Q814yes—
100C25×C47C2312yes—
101C25×C47C2311yescharacteristic
102C23×C4×C47—22no—
103C23×C4×C47—22no—
104C23×C4×C47—22no—
105C23×C4×C47—22no—
106C23×C4×C47—22no—
107C23×C4×C47—22no—
108C23×C4×C47—22no—
109C23×C4×C47—22no—
110C23×C4×C47—22no—
111C23×C4×C47—22no—
112C23×C4×C47—22no—
113C23×C4×C47—22no—
114C23×C4×C47D414yes—
115C23×C4×C47D414yes—
116C23×C4×C47C2312yes—
117C23×C4×C47C2312yes—
118C2×C22⋊C4×C47—232no—
119C2×C22⋊C4×C47—28no—
120C2×C22⋊C4×C47—28no—
121C2×C22⋊C4×C47—28no—
122C24×C47—28no—
123C24×C47—28no—
124C24×C47—28no—
125C24×C47—28no—
126C24×C47—28no—
127C24×C47—28no—
128C24×C47—28no—
129C24×C47—28no—
130C24×C47—28no—
131C24×C47—28no—
132C24×C47—28no—
133C24×C47—28no—
134C24×C47—28no—
135C24×C47—28no—
136C24×C47—28no—
137C24×C47—28no—
138C24×C47—28no—
139C24×C47—28no—
140C24×C47—22no—
141C24×C47—22no—
142C24×C47—22no—
143C24×C47—22no—
144C24×C47—22no—
145C24×C47—22no—
146C24×C47—22no—
147C24×C47—22no—
148C24×C47—22no—
149C24×C47—22no—
150C24×C47—22no—
151C24×C47—22no—
152C24×C47—44no—
153C24×C47—44no—
154C24×C47—44no—
155C24×C47—44no—
156C24×C47—44no—
157C24×C47—44no—
158C24×C47—44no—
159C24×C47—44no—
160C24×C47—44no—
161C24×C47—44no—
162C24×C47—44no—
163C24×C47—44no—
164C24×C47—44no—
165C24×C47—44no—
166C24×C47—44no—
167C24×C47—44no—
168C24×C47C4⋊C4116yescomplemented
169C24×C47C22×C414yes—
170C24×C47C22×C412yes—
171C24×C47C2×D414yes—
172C24×C47C2×D412yes—
173C24×C47C2×D412yes—
174C24×C47C2×D412yes—
175C24×C47C2×D412yes—
176C24×C47C2×D412yes—
177C24×C47C2×D412yes—
178C24×C47C2×D412yes—
179C24×C47C2×Q814yes—
180C24×C47C2×Q812yes—
181C24×C47#4112yes—
182C24×C47#4112yes—
183C24×C47#4112yes—
184C24×C47#4112yes—
185C24×C47#4112yes—
186C24×C47#4112yes—
187C24×C47C2411yescharacteristic
188C22×C4×C47—28no—
189C22×C4×C47—28no—
190C22×C4×C47—28no—
191C22×C4×C47—28no—
192C22×C4×C47—28no—
193C22×C4×C47—28no—
194C22×C4×C47—22no—
195C22×C4×C47—22no—
196C22×C4×C47—22no—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47—22no—
200C22×C4×C47—22no—
201C22×C4×C47—22no—
202C22×C4×C47—22no—
203C22×C4×C47—22no—
204C22×C4×C47—22no—
205C22×C4×C47—22no—
206C22×C4×C47—44no—
207C22×C4×C47—44no—
208C22×C4×C47—44no—
209C22×C4×C47—44no—
210C22×C4×C47—44no—
211C22×C4×C47—44no—
212C22×C4×C47—44no—
213C22×C4×C47—44no—
214C22×C4×C47C2×D414yes—
215C22×C4×C47C2×D414yes—
216C22×Dic47—28no—
217C22×Dic47—28no—
218C22×Dic47—28no—
219C22×Dic47—28no—
220C22×Dic47—28no—
221C22×Dic47—28no—
222C22×Dic47—22no—
223C22×Dic47—22no—
224C22×Dic47—22no—
225C22×Dic47—22no—
226C22×Dic47—28no—
227C22×Dic47—28no—
228C22×Dic47—28no—
229C22×Dic47—28no—
230C22×Dic47—28no—
231C22×Dic47—28no—
232C22×Dic47—28no—
233C22×Dic47—28no—
234C22×Dic47—28no—
235C22×Dic47—22no—
236C22×Dic47—22no—
237C22×Dic47—22no—
238C22×Dic47—22no—
239C22×Dic47—22no—
240C22×Dic47—22no—
241C22×Dic47—22no—
242C22×Dic47—22no—
243C22×Dic47—22no—
244C22×Dic47—22no—
245C22×Dic47—22no—
246C22×Dic47—22no—
247C22×Dic47—22no—
248C22×Dic47—22no—
249C22×Dic47—22no—
250C22×Dic47—22no—
251C22×Dic47—22no—
252C22×Dic47—22no—
253C22×Dic47—44no—
254C22×Dic47—44no—
255C22×Dic47—44no—
256C22×Dic47—44no—
257C22×Dic47—44no—
258C22×Dic47—44no—
259C22×Dic47—44no—
260C22×Dic47—44no—
261C22×Dic47—44no—
262C22×Dic47—44no—
263C22×Dic47—44no—
264C22×Dic47—44no—
265C22×Dic47C22⋊C4116yescomplemented
266C22×Dic47C22×C414yes—
267C22×Dic47C22×C414yes—
268C22×Dic47C2×D414yes—
269C22×Dic47C2×D414yes—
270C22×Dic47C2×D414yes—
271C22×Dic47C2×D414yes—
272C22⋊C4×C47—232no—
273C22⋊Dic47—232no—
274C22⋊Dic47—232no—
275Dic47⋊C4—232no—
276C23×C47—24no—
277C23×C47—24no—
278C23×C47—24no—
279C23×C47—24no—
280C23×C47—24no—
281C23×C47—24no—
282C23×C47—24no—
283C23×C47—24no—
284C23×C47—24no—
285C23×C47—24no—
286C23×C47—24no—
287C23×C47—24no—
288C23×C47—24no—
289C23×C47—24no—
290C23×C47—24no—
291C23×C47—24no—
292C23×C47—24no—
293C23×C47—24no—
294C23×C47—232no—
295C23×C47—232no—
296C23×C47—232no—
297C23×C47—42no—
298C23×C47—42no—
299C23×C47—42no—
300C23×C47—42no—
301C23×C47—42no—
302C23×C47—42no—
303C23×C47—42no—
304C23×C47—42no—
305C23×C47—42no—
306C23×C47—42no—
307C23×C47—42no—
308C23×C47—42no—
309C23×C47—42no—
310C23×C47—42no—
311C23×C47—42no—
312C23×C47—42no—
313C23×C47—416no—
314C23×C47—416no—
315C23×C47—416no—
316C23×C47—416no—
317C23×C47—416no—
318C23×C47—416no—
319C23×C47—416no—
320C23×C47—416no—
321C23×C47—416no—
322C23×C47—416no—
323C23×C47—416no—
324C23×C47—416no—
325C23×C47C2×C22⋊C414yes—
326C23×C47C2×C4⋊C414yes—
327C23×C47C2×C4⋊C418yescomplemented
328C23×C47#11714yes—
329C23×C47C4×D414yes—
330C23×C47C4×D414yes—
331C23×C47C4×D414yes—
332C23×C47C4×D414yes—
333C23×C47#12014yes—
334C23×C47#12014yes—
335C23×C47#12014yes—
336C23×C47#12114yes—
337C23×C47#12114yes—
338C23×C47#12114yes—
339C23×C47#12114yes—
340C23×C47#12114yes—
341C23×C47#12114yes—
342C23×C47#12114yes—
343C23×C47#12114yes—
344C23×C47C22⋊Q814yes—
345C23×C47C22⋊Q814yes—
346C23×C47C22⋊Q814yes—
347C23×C47C22⋊Q814yes—
348C23×C47C22⋊Q814yes—
349C23×C47C22⋊Q814yes—
350C23×C47#12314yes—
351C23×C47#12314yes—
352C23×C47#12314yes—
353C23×C47#12314yes—
354C23×C47#12314yes—
355C23×C47#12414yes—
356C23×C47#12414yes—
357C23×C47#12414yes—
358C23×C47#12614yes—
359C23×C47#12614yes—
360C23×C47#12714yes—
361C23×C47C23×C411yescharacteristic
362C23×C47C22×D411yescharacteristic
363C23×C47C22×D411yescharacteristic
364C23×C47C22×D411yescharacteristic
365C23×C47C22×D411yescharacteristic
366C23×C47C22×D411yescharacteristic
367C23×C47C22×D411yescharacteristic
368C23×C47C22×D411yescharacteristic
369C23×C47C22×Q811yescharacteristic
370C23×C47C2×#4111yescharacteristic
371C23×C47C2×#4111yescharacteristic
372C23×C47C2×#4111yescharacteristic
373C23×C47C2×#4111yescharacteristic
374C23×C47C2×#4111yescharacteristic
375C23×C47C2×#4111yescharacteristic
376C2×C4×C47—24no—
377C2×C4×C47—24no—
378C2×C4×C47—24no—
379C2×C4×C47—24no—
380C2×C4×C47—24no—
381C2×C4×C47—24no—
382C2×C4×C47—42no—
383C2×C4×C47—42no—
384C2×C4×C47—42no—
385C2×C4×C47—42no—
386C2×C4×C47—42no—
387C2×C4×C47—42no—
388C2×C4×C47—42no—
389C2×C4×C47—42no—
390C2×C4×C47—416no—
391C2×C4×C47—416no—
392C2×Dic47—24no—
393C2×Dic47—24no—
394C2×Dic47—24no—
395C2×Dic47—24no—
396C2×Dic47—24no—
397C2×Dic47—24no—
398C2×Dic47—232no—
399C2×Dic47—24no—
400C2×Dic47—24no—
401C2×Dic47—24no—
402C2×Dic47—24no—
403C2×Dic47—24no—
404C2×Dic47—24no—
405C2×Dic47—24no—
406C2×Dic47—24no—
407C2×Dic47—24no—
408C2×Dic47—42no—
409C2×Dic47—42no—
410C2×Dic47—42no—
411C2×Dic47—42no—
412C2×Dic47—42no—
413C2×Dic47—42no—
414C2×Dic47—42no—
415C2×Dic47—42no—
416C2×Dic47—42no—
417C2×Dic47—42no—
418C2×Dic47—42no—
419C2×Dic47—42no—
420C2×Dic47—416no—
421C2×Dic47—416no—
422C2×Dic47—416no—
423C2×Dic47C2×C22⋊C418yescomplemented
424C2×#1439—471nomaximal, Sylow
425C22×C47—28no—
426C22×C47—28no—
427C22×C47—28no—
428C22×C47—44no—
429C22×C47—44no—
430C22×C47—44no—
431C22×C47—44no—
432C22×C47—44no—
433C22×C47—44no—
434C22×C47—44no—
435C22×C47—44no—
436C22×C47—464no—
437C22×C47—44no—
438C22×C47—44no—
439C22×C47—44no—
440C22×C47—44no—
441C22×C47#38018yes—
442C22×C47#38518yes—
443C22×C47#38518yes—
444C22×C47#38618yes—
445C22×C47#38818yes—
446C22×C47#38818yes—
447C22×C47#39018yes—
448C22×C47#39218yes—
449C22×C47#39318yes—
450C22×C47#39418yes—
451C22×C47#39418yes—
452C22×C47#39618yes—
453C22×C47#39618yes—
454C22×C47#39718yes—
455C22×C47#39918yes—
456C22×C47C22×C22⋊C411yescharacteristic
457C22×C47C22×C4⋊C411yescharacteristic
458C22×C47C2×#11711yescharacteristic
459C22×C47C2×C4×D411yescharacteristic
460C22×C47C2×C4×D411yescharacteristic
461C22×C47C2×C4×D411yescharacteristic
462C22×C47C2×C4×D411yescharacteristic
463C22×C47C2×#12011yescharacteristic
464C22×C47C2×#12011yescharacteristic
465C22×C47C2×#12011yescharacteristic
466C22×C47C2×#12111yescharacteristic
467C22×C47C2×#12111yescharacteristic
468C22×C47C2×#12111yescharacteristic
469C22×C47C2×#12111yescharacteristic
470C22×C47C2×#12111yescharacteristic
471C22×C47C2×#12111yescharacteristic
472C22×C47C2×#12111yescharacteristic
473C22×C47C2×#12111yescharacteristic
474C22×C47C2×C22⋊Q811yescharacteristic
475C22×C47C2×C22⋊Q811yescharacteristic
476C22×C47C2×C22⋊Q811yescharacteristic
477C22×C47C2×C22⋊Q811yescharacteristic
478C22×C47C2×C22⋊Q811yescharacteristic
479C22×C47C2×C22⋊Q811yescharacteristic
480C22×C47C2×#12311yescharacteristic
481C22×C47C2×#12311yescharacteristic
482C22×C47C2×#12311yescharacteristic
483C22×C47C2×#12311yescharacteristic
484C22×C47C2×#12311yescharacteristic
485C22×C47C2×#12411yescharacteristic
486C22×C47C2×#12411yescharacteristic
487C22×C47C2×#12411yescharacteristic
488C22×C47C2×#12611yescharacteristic
489C22×C47C2×#12611yescharacteristic
490C22×C47C2×#12711yescharacteristic
491C4×C47—44no—
492C4×C47—44no—
493Dic47—28no—
494Dic47—44no—
495Dic47—44no—
496Dic47—44no—
497C23×C4⋊C4—471no—
498C23×C22⋊C4—471no—
499C23×C22⋊C4—471no—
500C23×C22⋊C4D4711yescharacteristic
501C22×#95—471no—
502C22×#95—471no—
503C22×#95—471no—
504#1439—478no—
505C2×C47—48no—
506C2×C47#1439116yescomplemented
507C2×C47C2×#38011yescharacteristic
508C2×C47C2×#38511yescharacteristic
509C2×C47C2×#38511yescharacteristic
510C2×C47C2×#38611yescharacteristic
511C2×C47C2×#38811yescharacteristic
512C2×C47C2×#38811yescharacteristic
513C2×C47C2×#39011yescharacteristic
514C2×C47C2×#39211yescharacteristic
515C2×C47C2×#39311yescharacteristic
516C2×C47C2×#39411yescharacteristic
517C2×C47C2×#39411yescharacteristic
518C2×C47C2×#39611yescharacteristic
519C2×C47C2×#39611yescharacteristic
520C2×C47C2×#39711yescharacteristic
521C2×C47C2×#39911yescharacteristic
522C26C2×D4711yescharacteristic
523C24×C4—471no—
524C24×C4—471no—
525C24×C4—471no—
526C24×C4—471no—
527C24×C4C2×D4711yescharacteristic
528C24×C4C2×D4711yescharacteristic
529C22×C4⋊C4—474no—
530C22×C4⋊C4—944no—
531C22×C4⋊C4—944no—
532C22×C4⋊C4—944no—
533C22×C22⋊C4—24no—
534C22×C22⋊C4—24no—
535C22×C22⋊C4—24no—
536C22×C22⋊C4—478no—
537C22×C22⋊C4—474no—
538C22×C22⋊C4—474no—
539C22×C22⋊C4—944no—
540C22×C22⋊C4—944no—
541C22×C22⋊C4—944no—
542C22×C22⋊C4—944no—
543C22×C22⋊C4—944no—
544C22×C22⋊C4C2×D4714yes—
545C2×#95—474no—
546C2×#95—474no—
547C2×#95—474no—
548C2×#95—944no—
549C2×#95—944no—
550C2×#95—944no—
551C47C2×#143911yescharacteristic, complemented, Sylow
552C25—22no—
553C25—22no—
554C25—22no—
555C25—22no—
556C25—22no—
557C25—22no—
558C25—22no—
559C25—22no—
560C25—22no—
561C25—22no—
562C25—22no—
563C25—22no—
564C25Dic9414yes—
565C25C4×D4714yes—
566C25C22⋊D4714yes—
567C25C22×D4712yes—
568C25C22×D4711yescharacteristic
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—22no—
573C23×C4—22no—
574C23×C4—22no—
575C23×C4—22no—
576C23×C4—22no—
577C23×C4—22no—
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—474no—
582C23×C4—474no—
583C23×C4—474no—
584C23×C4—472no—
585C23×C4—474no—
586C23×C4—474no—
587C23×C4—474no—
588C23×C4—472no—
589C23×C4—472no—
590C23×C4—472no—
591C23×C4—942no—
592C23×C4—942no—
593C23×C4—942no—
594C23×C4—942no—
595C23×C4—942no—
596C23×C4—942no—
597C23×C4—942no—
598C23×C4—942no—
599C23×C4—942no—
600C23×C4—942no—
601C23×C4—942no—
602C23×C4—942no—
603C23×C4—942no—
604C23×C4—942no—
605C23×C4—942no—
606C23×C4—942no—
607C23×C4—942no—
608C23×C4—942no—
609C23×C4—942no—
610C23×C4—942no—
611C23×C4—942no—
612C23×C4—942no—
613C23×C4C22⋊D4714yes—
614C23×C4C22⋊D4714yes—
615C23×C4C22×D4712yes—
616C23×C4C22×D4712yes—
617C2×C4⋊C4—948no—
618C2×C4⋊C4—948no—
619C2×C4⋊C4—9432no—
620C2×C4⋊C4—948no—
621C2×C22⋊C4—232no—
622C2×C22⋊C4—28no—
623C2×C22⋊C4—28no—
624C2×C22⋊C4—28no—
625C2×C22⋊C4—4716no—
626C2×C22⋊C4—9432no—
627C2×C22⋊C4—948no—
628C2×C22⋊C4—948no—
629C2×C22⋊C4—948no—
630C2×C22⋊C4—948no—
631C2×C22⋊C4—9432no—
632C2×C22⋊C4—948no—
633#95—948no—
634#95—948no—
635#95—948no—
636C24—28no—
637C24—28no—
638C24—28no—
639C24—28no—
640C24—28no—
641C24—28no—
642C24—28no—
643C24—28no—
644C24—28no—
645C24—28no—
646C24—28no—
647C24—28no—
648C24—28no—
649C24—28no—
650C24—28no—
651C24—28no—
652C24—28no—
653C24—28no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—44no—
667C24—44no—
668C24—44no—
669C24—44no—
670C24—44no—
671C24—44no—
672C24—44no—
673C24—44no—
674C24—44no—
675C24—44no—
676C24—44no—
677C24—44no—
678C24—44no—
679C24—44no—
680C24—44no—
681C24—44no—
682C24Dic47⋊C4116yescomplemented
683C24C2×Dic9414yes—
684C24C2×Dic9412yes—
685C24C2×C4×D4714yes—
686C24C2×C4×D4712yes—
687C24#1062535012yes—
688C24#1062535012yes—
689C24D4×D4712yes—
690C24D4×D4712yes—
691C24D4×D4712yes—
692C24D4×D4712yes—
693C24#1062535212yes—
694C24#1062535212yes—
695C24#1062535212yes—
696C24#1062535212yes—
697C24C2×C22⋊D4714yes—
698C24C2×C22⋊D4712yes—
699C24C2×C22⋊D4712yes—
700C24C2×C22⋊D4712yes—
701C24C23×D4711yescharacteristic
702C22×C4—28no—
703C22×C4—28no—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—28no—
707C22×C4—28no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—44no—
728C22×C4—4716no—
729C22×C4—474no—
730C22×C4—474no—
731C22×C4—474no—
732C22×C4—474no—
733C22×C4—474no—
734C22×C4—474no—
735C22×C4—948no—
736C22×C4—948no—
737C22×C4—948no—
738C22×C4—948no—
739C22×C4—948no—
740C22×C4—948no—
741C22×C4—942no—
742C22×C4—942no—
743C22×C4—942no—
744C22×C4—942no—
745C22×C4—948no—
746C22×C4—948no—
747C22×C4—948no—
748C22×C4—948no—
749C22×C4—948no—
750C22×C4—948no—
751C22×C4—948no—
752C22×C4—948no—
753C22×C4—948no—
754C22×C4—942no—
755C22×C4—942no—
756C22×C4—942no—
757C22×C4—942no—
758C22×C4—942no—
759C22×C4—942no—
760C22×C4—942no—
761C22×C4—942no—
762C22×C4—942no—
763C22×C4—942no—
764C22×C4—942no—
765C22×C4—942no—
766C22×C4—942no—
767C22×C4—942no—
768C22×C4—942no—
769C22×C4—942no—
770C22×C4—942no—
771C22×C4—942no—
772C22×C4—1884no—
773C22×C4—1884no—
774C22×C4—1884no—
775C22×C4—1884no—
776C22×C4—1884no—
777C22×C4—1884no—
778C22×C4—1884no—
779C22×C4—1884no—
780C22×C4—1884no—
781C22×C4—1884no—
782C22×C4—1884no—
783C22×C4—1884no—
784C22×C4C2×C22⋊D4714yes—
785C22×C4C2×C22⋊D4714yes—
786C4⋊C4—9432no—
787C22⋊C4—232no—
788C22⋊C4—9432no—
789C22⋊C4—9432no—
790C23—232no—
791C23—232no—
792C23—232no—
793C23—24no—
794C23—24no—
795C23—24no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—416no—
812C23—416no—
813C23—416no—
814C23—416no—
815C23—416no—
816C23—416no—
817C23—416no—
818C23—416no—
819C23—416no—
820C23—416no—
821C23—416no—
822C23—416no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23C22⋊C4×D4714yes—
840C23C2×Dic47⋊C414yes—
841C23C2×Dic47⋊C418yescomplemented
842C23#1309398014yes—
843C23(C22⋊D47)⋊C414yes—
844C23(C22⋊D47)⋊C414yes—
845C23C4×C22⋊D4714yes—
846C23C4×C22⋊D4714yes—
847C23#1309399214yes—
848C23#1309399214yes—
849C23#1309399314yes—
850C23#1309399514yes—
851C23#1309399514yes—
852C23#1309399614yes—
853C23#1309399614yes—
854C23#1309399614yes—
855C23#1309399614yes—
856C23#1309399714yes—
857C23#1309399714yes—
858C23#1309400114yes—
859C23#1309400114yes—
860C23#1309400114yes—
861C23#1309400114yes—
862C23#1309400314yes—
863C23#1309400314yes—
864C23#1309400514yes—
865C23#1309400514yes—
866C23#1309400614yes—
867C23#1309400614yes—
868C23#1309400714yes—
869C23#1309401014yes—
870C23#1309401014yes—
871C23#1309401114yes—
872C23#1309401714yes—
873C23#1309401714yes—
874C23#1309402014yes—
875C23C22×C4×D4711yescharacteristic
876C23C2×D4×D4711yescharacteristic
877C23C2×D4×D4711yescharacteristic
878C23C2×D4×D4711yescharacteristic
879C23C2×D4×D4711yescharacteristic
880C23C22×C22⋊D4711yescharacteristic
881C23C22×C22⋊D4711yescharacteristic
882C23C22×C22⋊D4711yescharacteristic
883C23C22×Dic9411yescharacteristic
884C23C2×#1062535211yescharacteristic
885C23C2×#1062535211yescharacteristic
886C23C2×#1062535211yescharacteristic
887C23C2×#1062535211yescharacteristic
888C23C2×#1062535011yescharacteristic
889C23C2×#1062535011yescharacteristic
890C2×C4—24no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—416no—
897C2×C4—416no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—478no—
907C2×C4—9432no—
908C2×C4—944no—
909C2×C4—944no—
910C2×C4—944no—
911C2×C4—944no—
912C2×C4—944no—
913C2×C4—944no—
914C2×C4—944no—
915C2×C4—944no—
916C2×C4—944no—
917C2×C4—944no—
918C2×C4—944no—
919C2×C4—944no—
920C2×C4—944no—
921C2×C4—944no—
922C2×C4—944no—
923C2×C4—18816no—
924C2×C4—18816no—
925C2×C4—18816no—
926C2×C4—1882no—
927C2×C4—1882no—
928C2×C4—1882no—
929C2×C4—1882no—
930C2×C4—1882no—
931C2×C4—1882no—
932C2×C4—1882no—
933C2×C4—1882no—
934C2×C4—1882no—
935C2×C4—1882no—
936C2×C4—1882no—
937C2×C4—1882no—
938C22—28no—
939C22—28no—
940C22—28no—
941C22—44no—
942C22—44no—
943C22—44no—
944C22—44no—
945C22—44no—
946C22—44no—
947C22—44no—
948C22—44no—
949C22—44no—
950C22—44no—
951C22—44no—
952C22—44no—
953C22—464no—
954C22#1568898118yes—
955C22#1568899518yes—
956C22#1568899618yes—
957C22#1568899918yes—
958C22#1568901118yes—
959C22#1568901718yes—
960C22#1568902318yes—
961C22#1568903118yes—
962C22#1568903518yes—
963C22#1568903718yes—
964C22#1568903818yes—
965C22#1568904618yes—
966C22#1568904618yes—
967C22#1568905118yes—
968C22#1568905918yes—
969C22C2×C22⋊C4×D4711yescharacteristic
970C22C22×Dic47⋊C411yescharacteristic
971C22C2×#1309398011yescharacteristic
972C22C2×(C22⋊D47)⋊C411yescharacteristic
973C22C2×(C22⋊D47)⋊C411yescharacteristic
974C22C2×C4×C22⋊D4711yescharacteristic
975C22C2×C4×C22⋊D4711yescharacteristic
976C22C2×#1309399211yescharacteristic
977C22C2×#1309399211yescharacteristic
978C22C2×#1309399311yescharacteristic
979C22C2×#1309399511yescharacteristic
980C22C2×#1309399511yescharacteristic
981C22C2×#1309399611yescharacteristic
982C22C2×#1309399611yescharacteristic
983C22C2×#1309399611yescharacteristic
984C22C2×#1309399611yescharacteristic
985C22C2×#1309399711yescharacteristic
986C22C2×#1309399711yescharacteristic
987C22C2×#1309400111yescharacteristic
988C22C2×#1309400111yescharacteristic
989C22C2×#1309400111yescharacteristic
990C22C2×#1309400111yescharacteristic
991C22C2×#1309400311yescharacteristic
992C22C2×#1309400311yescharacteristic
993C22C2×#1309400511yescharacteristic
994C22C2×#1309400511yescharacteristic
995C22C2×#1309400611yescharacteristic
996C22C2×#1309400611yescharacteristic
997C22C2×#1309400711yescharacteristic
998C22C2×#1309401011yescharacteristic
999C22C2×#1309401011yescharacteristic
1000C22C2×#1309401111yescharacteristic
1001C22C2×#1309401711yescharacteristic
1002C22C2×#1309401711yescharacteristic
1003C22C2×#1309402011yescharacteristic
1004C4—44no—
1005C4—44no—
1006C4—948no—
1007C4—1884no—
1008C4—1884no—
1009C4—1884no—
1010C2—48no—
1011C2#20241631116yesdirect product factor
1012C2C2×#1568898111yescharacteristic
1013C2C2×#1568899511yescharacteristic
1014C2C2×#1568899611yescharacteristic
1015C2C2×#1568899911yescharacteristic
1016C2C2×#1568901111yescharacteristic
1017C2C2×#1568901711yescharacteristic
1018C2C2×#1568902311yescharacteristic
1019C2C2×#1568903111yescharacteristic
1020C2C2×#1568903511yescharacteristic
1021C2C2×#1568903711yescharacteristic
1022C2C2×#1568903811yescharacteristic
1023C2C2×#1568904611yescharacteristic
1024C2C2×#1568904611yescharacteristic
1025C2C2×#1568905111yescharacteristic
1026C2C2×#1568905911yescharacteristic
subgroupG/H
centerC25C22×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC23×C22⋊C4×C47C2
socleC25×C47C23
prime radicalC26×C47C22
cosocleC24×C47C24
hypercenterC23×C22⋊C4D47
hypocenterC47C2×#1439
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C25 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×Dic47⋊C4C2semidirect
4. C22×C47⋊#95C2semidirect
5. C22×C47⋊#95C2semidirect
6. C22×C47⋊#95C2semidirect
7. #20241631C2direct (N × H)
16. C22×Dic47⋊C4C22semidirect
22. C22×C22⋊Dic47C4semidirect
28. C2×C47⋊#95C22semidirect
29. C2×C47⋊#95C22semidirect
30. C2×C47⋊#95C22semidirect
81. C2×C22⋊Dic47C2×C4semidirect
168. C24×C47C4⋊C4semidirect
265. C22×Dic47C22⋊C4semidirect
327. C23×C47C2×C4⋊C4semidirect
423. C2×Dic47C2×C22⋊C4semidirect
506. C2×C47#1439semidirect
551. C47C2×#1439semidirect
682. C24Dic47⋊C4semidirect
841. C23C2×Dic47⋊C4semidirect
1011. C2#20241631direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Dic47⋊C42
C23×C22⋊Dic472
C22×C47⋊#952
#202416312
C23×C22⋊C4×C472
C2×#143947