Finite Group Databasebeta

← #26138182

Subgroups — #26138182

Order 12032.

2950 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093986C211yesmaximal, characteristic
2C22×C4⋊C4×D47C211yesmaximal, characteristic, complemented
3C2×#15689001C212yesmaximal
4C2×#15688982C212yesmaximal, complemented
5C2×#15688982C211yesmaximal, characteristic, complemented
6#20241641C211yesmaximal, characteristic, complemented
7#20241634C211yesmaximal, characteristic, complemented
8#20241630C211yesmaximal, characteristic, complemented
9Dic47⋊#95C212yesmaximal, complemented
10(C2×D47)⋊#95C212yesmaximal, complemented
11C47×#1441C211yesmaximal, characteristic, complemented
12C23×D188C2211yescharacteristic
13C23×C4×D47C2211yescharacteristic
14C23×C4×D47C2212yes—
15C23×C4×D47C2211yescharacteristic
16C2×#13093986—24no—
17C2×#13093986—24no—
18C2×#13093986C418yescomplemented
19C22×C4⋊Dic47C2211yescharacteristic
20C22×Dic47⋊C4C2212yes—
21C22×Dic47⋊C4C2212yes—
22C2×C4⋊C4×D47—24no—
23C2×C4⋊C4×D47—28no—
24C22×(C2×D47)⋊C4C2212yes—
25C22×(C2×D47)⋊C4C2212yes—
26C22×(C2×D47)⋊C4C2212yes—
27C22×(C2×D47)⋊C4C2211yescharacteristic
28C22×(C2×D47)⋊C4C2211yescharacteristic
29C22×C4×Dic47C2211yescharacteristic
30#15689001—28no—
31#15688982—24no—
32#15688982—28no—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2211yescharacteristic
35C2×C47⋊#95C2212yes—
36C2×C47⋊#95C2212yes—
37C2×C47⋊#95C2212yes—
38C22×C4⋊C4×C47C2211yescharacteristic
39C22×C4⋊C4×C47C2211yescharacteristic
40C2×#95×C47C2212yes—
41C2×#95×C47C2211yescharacteristic
42C2×#95×C47C2212yes—
43C24×D47C2311yescharacteristic
44C24×D47C2311yescharacteristic
45C22×D188—22no—
46C22×D188—22no—
47C22×D188—22no—
48C22×D188—22no—
49C22×D188C2×C414yes—
50C22×D188D414yes—
51C22×D188Q814yes—
52C23×Dic47C2312yes—
53C23×Dic47C2311yescharacteristic
54C23×Dic47C2312yes—
55C23×Dic47C2311yescharacteristic
56C22×C4×D47—24no—
57C22×C4×D47—24no—
58C22×C4×D47—24no—
59C22×C4×D47—24no—
60C22×C4×D47—24no—
61C22×C4×D47—24no—
62C22×C4×D47—22no—
63C22×C4×D47—22no—
64C22×C4×D47—24no—
65C22×C4×D47—24no—
66C22×C4×D47—24no—
67C22×C4×D47—42no—
68C22×C4×D47—42no—
69C22×C4×D47C2×C414yes—
70C22×C4×D47C2×C414yescomplemented
71C22×C4×D47D414yes—
72C22×C4×D47D414yes—
73#13093986—232no—
74C2×C4⋊Dic47—22no—
75C2×C4⋊Dic47—24no—
76C2×Dic47⋊C4—24no—
77C2×Dic47⋊C4—24no—
78C2×Dic47⋊C4—24no—
79C2×Dic47⋊C4—24no—
80C2×Dic47⋊C4—24no—
81C2×Dic47⋊C4D418yescomplemented
82C4⋊C4×D47—232no—
83C2×(C2×D47)⋊C4—22no—
84C2×(C2×D47)⋊C4—22no—
85C2×(C2×D47)⋊C4—22no—
86C2×(C2×D47)⋊C4—22no—
87C2×(C2×D47)⋊C4—24no—
88C2×(C2×D47)⋊C4—24no—
89C2×(C2×D47)⋊C4—24no—
90C2×(C2×D47)⋊C4—24no—
91C2×(C2×D47)⋊C4—24no—
92C2×(C2×D47)⋊C4—24no—
93C2×(C2×D47)⋊C4—24no—
94C2×(C2×D47)⋊C4—42no—
95C2×(C2×D47)⋊C4—42no—
96C2×(C2×D47)⋊C4C2×C414yes—
97C2×(C2×D47)⋊C4C2×C414yescomplemented
98C2×C4×Dic47—22no—
99C2×C4×Dic47—22no—
100C2×C4×Dic47C2×C414yescomplemented
101C47⋊#95—22no—
102C47⋊#95—24no—
103C47⋊#95—24no—
104C47⋊#95—42no—
105C47⋊#95—42no—
106C23×C4×C47C2312yes—
107C23×C4×C47C2311yescharacteristic
108C23×C4×C47C2312yes—
109C23×C4×C47C2311yescharacteristic
110C23×C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47—24no—
112C2×C4⋊C4×C47—22no—
113C2×C4⋊C4×C47—22no—
114C2×C4⋊C4×C47—22no—
115C2×C4⋊C4×C47C2×C414yescomplemented
116#95×C47—24no—
117#95×C47—22no—
118#95×C47—24no—
119C24×C47C2411yescharacteristic
120C23×D47—22no—
121C23×D47—22no—
122C23×D47—22no—
123C23×D47—22no—
124C23×D47—22no—
125C23×D47—21no—
126C23×D47—21no—
127C23×D47—22no—
128C23×D47—21no—
129C23×D47—21no—
130C23×D47—22no—
131C23×D47—22no—
132C23×D47C22×C412yes—
133C23×D47C22×C412yes—
134C23×D47C2×D412yes—
135C23×D47C2×D412yes—
136C23×D47C2×D412yes—
137C23×D47C2×D412yes—
138C23×D47C2×Q812yes—
139C23×D47C2×Q812yes—
140C23×D47#4112yes—
141C23×D47#4112yes—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—22no—
145C22×C4×C47—22no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—22no—
159C22×C4×C47—22no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47—22no—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
165C22×C4×C47C22×C412yes—
166C22×C4×C47C22×C412yes—
167C22×C4×C47C22×C412yes—
168C22×C4×C47C2×D414yes—
169C22×C4×C47C2×D412yes—
170C22×C4×C47C2×D412yes—
171C22×C4×C47C2×D412yes—
172C22×C4×C47C2×Q812yes—
173C22×Dic47—22no—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47C22×C412yes—
191C22×Dic47C22×C412yes—
192C22×Dic47C2×D414yes—
193C22×Dic47C2×D412yes—
194C22×Dic47C2×D412yes—
195C22×Dic47C2×D414yes—
196C22×Dic47#4114yes—
197C2×D188—28no—
198C2×D188—28no—
199C2×D188—28no—
200C2×D188—28no—
201C2×D188—28no—
202C2×D188—28no—
203C2×D188C4⋊C4116yescomplemented
204C2×C4×D47—216no—
205C2×C4×D47—28no—
206C2×C4×D47—216no—
207C2×C4×D47—28no—
208C2×C4×D47—216no—
209C2×C4×D47—28no—
210C2×C4×D47—216no—
211C2×C4×D47—48no—
212C2×C4×D47—48no—
213C2×C4×D47—48no—
214C2×C4×D47—48no—
215C2×C4×D47—48no—
216C2×C4×D47—48no—
217C2×C4×D47—44no—
218C2×C4×D47—48no—
219C2×C4×D47—44no—
220C2×C4×D47C22⋊C4116yescomplemented
221C4⋊C4×C47—28no—
222C4⋊C4×C47—28no—
223(C2×D47)⋊C4—28no—
224(C2×D47)⋊C4—28no—
225(C2×D47)⋊C4—48no—
226(C2×D47)⋊C4—48no—
227(C2×D47)⋊C4—48no—
228C4⋊Dic47—28no—
229Dic47⋊C4—216no—
230Dic47⋊C4—48no—
231C4×Dic47—28no—
232C23×C47C23×C411yescharacteristic
233C23×C47C22×D411yescharacteristic
234C23×C47C22×D411yescharacteristic
235C23×C47C22×D411yescharacteristic
236C23×C47C22×D412yes—
237C23×C47C22×Q811yescharacteristic
238C23×C47C2×#4111yescharacteristic
239C23×C47C2×#4111yescharacteristic
240C23×C47C2×#4112yes—
241C23×C47H(5,𝔽2)12yes—
242C23×C472−1+412yes—
243C22×D47—24no—
244C22×D47—24no—
245C22×D47—22no—
246C22×D47—24no—
247C22×D47—22no—
248C22×D47—22no—
249C22×D47—22no—
250C22×D47—24no—
251C22×D47—24no—
252C22×D47—24no—
253C22×D47—24no—
254C22×D47—24no—
255C22×D47—24no—
256C22×D47—24no—
257C22×D47—24no—
258C22×D47—24no—
259C22×D47—22no—
260C22×D47—22no—
261C22×D47—24no—
262C22×D47—24no—
263C22×D47—22no—
264C22×D47—22no—
265C22×D47—22no—
266C22×D47—22no—
267C22×D47—24no—
268C22×D47—24no—
269C22×D47—24no—
270C22×D47—24no—
271C22×D47—41no—
272C22×D47—42no—
273C22×D47—41no—
274C22×D47—41no—
275C22×D47—41no—
276C22×D47—42no—
277C22×D47—42no—
278C22×D47—42no—
279C22×D47—42no—
280C22×D47—42no—
281C22×D47C2×C22⋊C414yes—
282C22×D47C2×C4⋊C414yes—
283C22×D47C2×C4⋊C414yescomplemented
284C22×D47#11714yes—
285C22×D47#12114yes—
286C22×D47#12114yes—
287C22×D47C22⋊Q814yes—
288C22×D47C22⋊Q814yes—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—24no—
292C2×C4×C47—22no—
293C2×C4×C47—24no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—24no—
301C2×C4×C47—24no—
302C2×C4×C47—24no—
303C2×C4×C47—24no—
304C2×C4×C47—41no—
305C2×C4×C47—42no—
306C2×C4×C47—42no—
307C2×C4×C47—41no—
308C2×C4×C47—42no—
309C2×C4×C47—42no—
310C2×C4×C47—42no—
311C2×C4×C47—42no—
312C2×C4×C47—42no—
313C2×C4×C47—42no—
314C2×C4×C47—42no—
315C2×C4×C47—42no—
316C2×C4×C47—42no—
317C2×C4×C47—42no—
318C2×C4×C47C2×C22⋊C414yes—
319C2×C4×C47C2×C4⋊C414yescomplemented
320C2×Dic47—22no—
321C2×Dic47—24no—
322C2×Dic47—24no—
323C2×Dic47—24no—
324C2×Dic47—24no—
325C2×Dic47—42no—
326C2×Dic47—42no—
327C2×Dic47—41no—
328C2×Dic47—41no—
329C2×Dic47—42no—
330C2×Dic47—42no—
331C2×Dic47—42no—
332C2×Dic47—42no—
333C2×Dic47—42no—
334C2×Dic47—42no—
335C2×Dic47—42no—
336C2×Dic47—42no—
337C2×Dic47—42no—
338C2×Dic47—42no—
339C2×Dic47C2×C22⋊C414yes—
340C2×Dic47C4×D418yes—
341C2×Dic47#12014yes—
342C2×Dic47#12118yes—
343C2×Dic47#12314yes—
344D188—232no—
345C4×D47—232no—
346C4×D47—432no—
347C4×D47—416no—
348#13872—471nomaximal, Sylow
349C22×C47C22×C22⋊C411yescharacteristic
350C22×C47C22×C4⋊C411yescharacteristic
351C22×C47C2×#11711yescharacteristic
352C22×C47C2×C4×D412yes—
353C22×C47#52012yes—
354C22×C47C2×#12011yescharacteristic
355C22×C47C2×#12111yescharacteristic
356C22×C47C2×#12111yescharacteristic
357C22×C47C2×#12112yes—
358C22×C47C2×C22⋊Q811yescharacteristic
359C22×C47C2×C22⋊Q811yescharacteristic
360C22×C47C2×#12311yescharacteristic
361C22×C47#53511yescharacteristic
362C22×C47#53611yescharacteristic
363C22×C47#53712yes—
364C22×C47D4212yes—
365C22×C47#54612yes—
366C22×C47#54712yes—
367C22×C47#54812yes—
368C22×C47D4×Q812yes—
369C22×C47#55212yes—
370C22×C47#55312yes—
371C22×C47#55412yes—
372C2×D47—24no—
373C2×D47—28no—
374C2×D47—28no—
375C2×D47—24no—
376C2×D47—24no—
377C2×D47—28no—
378C2×D47—28no—
379C2×D47—24no—
380C2×D47—24no—
381C2×D47—24no—
382C2×D47—28no—
383C2×D47—24no—
384C2×D47—42no—
385C2×D47—44no—
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—44no—
389C2×D47—44no—
390C2×D47—42no—
391C2×D47—42no—
392C2×D47—42no—
393C2×D47#38018yescomplemented
394C4×C47—24no—
395C4×C47—24no—
396C4×C47—44no—
397C4×C47—42no—
398C4×C47—82no—
399Dic47—42no—
400Dic47—44no—
401Dic47—82no—
402Dic47#38618yescomplemented
403C22×C4×D4—471no—
404C23×C4⋊C4—471no—
405C2×#386—472no—
406C2×#380—471no—
407C2×#380—472no—
408#1441—471no—
409#1441D4711yescharacteristic, complemented
410#1439—471no—
411#1439—471no—
412C4⋊#95—472no—
413C22⋊#95—472no—
414C2×C47C2×#38011yescharacteristic
415C2×C47C2×#38611yescharacteristic
416C2×C47#231111yescharacteristic
417C2×C47D4×C4⋊C412yes—
418C2×C47#235212yes—
419C2×C47#240811yescharacteristic
420C2×C47#240911yescharacteristic
421C2×C47#241612yes—
422C2×C47#241712yes—
423C2×C47#248611yescharacteristic
424C2×C47#248711yescharacteristic
425D47—28no—
426D47—44no—
427C23×D4—471no—
428C24×C4—471no—
429C24×C4—471no—
430C24×C4—472no—
431C2×C4×D4—478no—
432C2×C4×D4—944no—
433C2×C4×D4—944no—
434C22×C4⋊C4—472no—
435C22×C4⋊C4—471no—
436C22×C4⋊C4—472no—
437C22×C4⋊C4—948no—
438C22×C4⋊C4—944no—
439C22×C4⋊C4C2×D4711yescharacteristic
440C22×C4⋊C4C2×D4711yescharacteristic
441C22×C22⋊C4—471no—
442C22×C22⋊C4—471no—
443C22×C22⋊C4—472no—
444C22×C22⋊C4—472no—
445C22×C22⋊C4—472no—
446C22×C42—471no—
447#386—948no—
448#380—948no—
449#380—944no—
450C2×#95—472no—
451C2×#95—472no—
452C2×#95—471no—
453C2×#95—472no—
454C2×#95—472no—
455C2×#95C2×D4712yes—
456C2×#95C2×D4712yes—
457C2×#95C2×D4711yescharacteristic
458C47#1387211yescharacteristic, complemented, Sylow
459C25—471no—
460C25—471no—
461C22×D4—474no—
462C22×D4—474no—
463C22×D4—474no—
464C22×D4—942no—
465C22×D4—942no—
466C22×D4—942no—
467C22×D4—942no—
468C23×C4—471no—
469C23×C4—474no—
470C23×C4—474no—
471C23×C4—474no—
472C23×C4—471no—
473C23×C4—472no—
474C23×C4—474no—
475C23×C4—472no—
476C23×C4—944no—
477C23×C4—944no—
478C23×C4—944no—
479C23×C4—942no—
480C23×C4—942no—
481C23×C4—944no—
482C23×C4—944no—
483C23×C4—944no—
484C23×C4—944no—
485C23×C4—944no—
486C23×C4—944no—
487C23×C4—1882no—
488C23×C4—1882no—
489C23×C4C22×D4712yes—
490C23×C4C22×D4711yescharacteristic
491C23×C4C22×D4712yes—
492C23×C4C22×D4711yescharacteristic
493C23×C4C22×D4711yescharacteristic
494C4×D4—9432no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—478no—
500C2×C4⋊C4—9432no—
501C2×C4⋊C4—944no—
502C2×C4⋊C4—944no—
503C2×C4⋊C4—944no—
504C2×C4⋊C4—942no—
505C2×C4⋊C4—944no—
506C2×C4⋊C4—944no—
507C2×C4⋊C4—944no—
508C2×C4⋊C4C4×D4714yescomplemented
509C2×C22⋊C4—474no—
510C2×C22⋊C4—474no—
511C2×C22⋊C4—942no—
512C2×C22⋊C4—942no—
513C2×C22⋊C4—942no—
514C2×C22⋊C4—942no—
515C2×C22⋊C4—944no—
516C2×C22⋊C4—944no—
517C2×C22⋊C4—944no—
518C2×C22⋊C4—944no—
519C2×C22⋊C4—944no—
520C2×C22⋊C4—944no—
521C2×C22⋊C4—944no—
522C2×C22⋊C4—1882no—
523C2×C22⋊C4—1882no—
524C2×C42—474no—
525C2×C42—942no—
526C2×C42—942no—
527#95—24no—
528#95—22no—
529#95—24no—
530#95—944no—
531#95—942no—
532#95—944no—
533#95—1882no—
534#95—1882no—
535C24—472no—
536C24—472no—
537C24—472no—
538C24—472no—
539C24—472no—
540C24—472no—
541C24—472no—
542C24—472no—
543C24—472no—
544C24—472no—
545C24—942no—
546C24—942no—
547C24—942no—
548C24—942no—
549C24—942no—
550C24—941no—
551C24—941no—
552C24—942no—
553C24—941no—
554C24—941no—
555C24—942no—
556C24—942no—
557C24C23×D4711yescharacteristic
558C2×D4—4716no—
559C2×D4—948no—
560C2×D4—948no—
561C2×D4—948no—
562C2×D4—948no—
563C2×D4—948no—
564C2×D4—948no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—472no—
589C22×C4—472no—
590C22×C4—472no—
591C22×C4—474no—
592C22×C4—474no—
593C22×C4—4716no—
594C22×C4—472no—
595C22×C4—474no—
596C22×C4—948no—
597C22×C4—9416no—
598C22×C4—9416no—
599C22×C4—948no—
600C22×C4—948no—
601C22×C4—9416no—
602C22×C4—9416no—
603C22×C4—942no—
604C22×C4—941no—
605C22×C4—941no—
606C22×C4—942no—
607C22×C4—942no—
608C22×C4—942no—
609C22×C4—942no—
610C22×C4—942no—
611C22×C4—942no—
612C22×C4—942no—
613C22×C4—942no—
614C22×C4—942no—
615C22×C4—942no—
616C22×C4—942no—
617C22×C4—942no—
618C22×C4—942no—
619C22×C4—942no—
620C22×C4—1888no—
621C22×C4—1888no—
622C22×C4—1884no—
623C22×C4—1888no—
624C22×C4—1884no—
625C22×C4—1888no—
626C22×C4—1888no—
627C22×C4—1888no—
628C22×C4—1888no—
629C22×C4C2×C4×D4712yes—
630C22×C4C2×C4×D4712yes—
631C22×C4C2×C4×D4712yes—
632C22×C4D4×D4714yes—
633C22×C4D4×D4712yes—
634C22×C4D4×D4712yes—
635C22×C4D4×D4712yes—
636C22×C4Q8×D4712yes—
637C4⋊C4—28no—
638C4⋊C4—28no—
639C4⋊C4—9416no—
640C4⋊C4—948no—
641C4⋊C4—1888no—
642C22⋊C4—948no—
643C22⋊C4—948no—
644C22⋊C4—1888no—
645C22⋊C4—1888no—
646C22⋊C4—1888no—
647C42—948no—
648C23—474no—
649C23—474no—
650C23—474no—
651C23—474no—
652C23—474no—
653C23—474no—
654C23—474no—
655C23—474no—
656C23—944no—
657C23—944no—
658C23—944no—
659C23—944no—
660C23—944no—
661C23—944no—
662C23—944no—
663C23—944no—
664C23—944no—
665C23—944no—
666C23—942no—
667C23—944no—
668C23—942no—
669C23—942no—
670C23—942no—
671C23—944no—
672C23—944no—
673C23—944no—
674C23—944no—
675C23—942no—
676C23—944no—
677C23—942no—
678C23—944no—
679C23—944no—
680C23—942no—
681C23—942no—
682C23—942no—
683C23—942no—
684C23—1882no—
685C23—1882no—
686C23—1882no—
687C23—1882no—
688C23—1881no—
689C23—1882no—
690C23—1881no—
691C23—1881no—
692C23—1881no—
693C23—1882no—
694C23C22×C4×D4711yescharacteristic
695C23C2×D4×D4711yescharacteristic
696C23C2×D4×D4712yes—
697C23C2×D4×D4711yescharacteristic
698C23C2×D4×D4711yescharacteristic
699C23C2×Q8×D4711yescharacteristic
700C23#41×D4711yescharacteristic
701C23#41×D4712yes—
702C23#41×D4711yescharacteristic
703C23#1309407012yes—
704C23#1309407212yes—
705D4—9432no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—474no—
736C2×C4—478no—
737C2×C4—474no—
738C2×C4—478no—
739C2×C4—474no—
740C2×C4—9432no—
741C2×C4—944no—
742C2×C4—944no—
743C2×C4—942no—
744C2×C4—944no—
745C2×C4—944no—
746C2×C4—18816no—
747C2×C4—18832no—
748C2×C4—1882no—
749C2×C4—1882no—
750C2×C4—1882no—
751C2×C4—1882no—
752C2×C4—1882no—
753C2×C4—1882no—
754C2×C4—1882no—
755C2×C4—1882no—
756C2×C4—1882no—
757C2×C4—1882no—
758C2×C4—1881no—
759C2×C4—1882no—
760C2×C4—1881no—
761C2×C4—1882no—
762C2×C4C22⋊C4×D4714yes—
763C2×C4C4⋊C4×D4714yescomplemented
764C22—478no—
765C22—948no—
766C22—948no—
767C22—948no—
768C22—944no—
769C22—948no—
770C22—944no—
771C22—944no—
772C22—944no—
773C22—944no—
774C22—944no—
775C22—948no—
776C22—944no—
777C22—1884no—
778C22—1884no—
779C22—1882no—
780C22—1884no—
781C22—1882no—
782C22—1882no—
783C22—1882no—
784C22—1882no—
785C22—1882no—
786C22C2×C22⋊C4×D4711yescharacteristic
787C22C2×C4⋊C4×D4711yescharacteristic
788C22#117×D4711yescharacteristic
789C22C4×D4×D4712yes—
790C22#1568960512yes—
791C22#120×D4711yescharacteristic
792C22#121×D4711yescharacteristic
793C22#121×D4712yes—
794C22#121×D4711yescharacteristic
795C22C22⋊Q8×D4711yescharacteristic
796C22C22⋊Q8×D4711yescharacteristic
797C22#123×D4711yescharacteristic
798C22#1568969111yescharacteristic
799C22#1568969811yescharacteristic
800C22#1568970312yes—
801C22#1568975712yes—
802C22#1568976512yes—
803C22#1568977512yes—
804C22#1568978312yes—
805C22#1568978812yes—
806C22#1568980512yes—
807C22#1568982412yes—
808C22#1568982912yes—
809C4—24no—
810C4—24no—
811C4—42no—
812C4—44no—
813C4—82no—
814C4—478no—
815C4—3762no—
816C4—1884no—
817C4—1882no—
818C2—948no—
819C2—1884no—
820C2#380×D4711yescharacteristic
821C2#386×D4711yescharacteristic
822C2#2024597911yescharacteristic
823C2#2024628912yes—
824C2#2024631212yes—
825C2#2024673911yescharacteristic
826C2#2024674811yescharacteristic
827C2#2024682312yes—
828C2#2024683412yes—
829C2#2024769111yescharacteristic
830C2#2024770011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1441C2
socle, cosocleC24×C47C24
prime radicalC23×D188C22
hypercenter#1441D47
hypocenterC47#13872
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D47C2semidirect
4. C2×#15688982C2semidirect
5. C2×#15688982C2semidirect
6. #20241641C2semidirect
7. #20241634C2semidirect
8. #20241630C2semidirect
9. Dic47⋊#95C2semidirect
10. (C2×D47)⋊#95C2semidirect
11. C47×#1441C2semidirect
18. C2×#13093986C4semidirect
70. C22×C4×D47C2×C4semidirect
81. C2×Dic47⋊C4D4semidirect
97. C2×(C2×D47)⋊C4C2×C4semidirect
100. C2×C4×Dic47C2×C4semidirect
115. C2×C4⋊C4×C47C2×C4semidirect
203. C2×D188C4⋊C4semidirect
220. C2×C4×D47C22⋊C4semidirect
283. C22×D47C2×C4⋊C4semidirect
319. C2×C4×C47C2×C4⋊C4semidirect
393. C2×D47#380semidirect
402. Dic47#386semidirect
409. #1441D47semidirect
458. C47#13872semidirect
508. C2×C4⋊C4C4×D47semidirect
763. C2×C4C4⋊C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×#130939862
C22×C4⋊C4×D472
C2×#156890012
C2×#156889822
#202416412
#202416342
#202416302
Dic47⋊#952
(C2×D47)⋊#952
C47×#14412
#1387247