Finite Group Databasebeta

← #26138232

Subgroups — #26138232

Order 12032.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689013C212yesmaximal
2C2×#15688980C211yesmaximal, characteristic
3C2×#15688980C211yesmaximal, characteristic
4C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
6#20241647C212yesmaximal, complemented
7#20241630C212yesmaximal
8#20241620C212yesmaximal, complemented
9#20241618C211yesmaximal, characteristic, complemented
10#20241617C211yesmaximal, characteristic, complemented
11C2×C47×#384C211yesmaximal, characteristic, complemented
12C23×C4×D47C2211yescharacteristic
13C22×C4⋊Dic47C2211yescharacteristic
14C22×C4⋊Dic47C2211yescharacteristic
15C22×(C2×D47)⋊C4C2212yes—
16C22×(C2×D47)⋊C4C2212yes—
17C22×(C2×D47)⋊C4C2211yescharacteristic
18C22×(C2×D47)⋊C4C2211yescharacteristic
19C22×C4×Dic47C2212yes—
20C22×C4×Dic47C2211yescharacteristic
21#15689013—28no—
22#15688980—24no—
23#15688980—24no—
24C4⋊C4×Dic47—24no—
25C4×(C2×D47)⋊C4C418yescomplemented
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2211yescharacteristic
35C22×C4⋊C4×C47C2211yescharacteristic
36C22×C4⋊C4×C47C2212yes—
37C22×C4⋊C4×C47C2212yes—
38C22×C4⋊C4×C47C2211yescharacteristic
39C22×C42×C47C2211yescharacteristic
40C47×#384—24no—
41C24×D47C2311yescharacteristic
42C23×Dic47C2312yes—
43C23×Dic47C2311yescharacteristic
44C23×Dic47C2311yescharacteristic
45C23×Dic47C2312yes—
46C23×Dic47C2311yescharacteristic
47C22×C4×D47—22no—
48C22×C4×D47—22no—
49C22×C4×D47—22no—
50C22×C4×D47—22no—
51C22×C4×D47—22no—
52C22×C4×D47—22no—
53C22×C4×D47C2×C414yes—
54C2×C4⋊Dic47—22no—
55C2×C4⋊Dic47—22no—
56C2×C4⋊Dic47—22no—
57C2×C4⋊Dic47—22no—
58C2×C4⋊Dic47—22no—
59C2×C4⋊Dic47D414yes—
60C2×(C2×D47)⋊C4—22no—
61C2×(C2×D47)⋊C4—22no—
62C2×(C2×D47)⋊C4—24no—
63C2×(C2×D47)⋊C4—24no—
64C2×(C2×D47)⋊C4—24no—
65C2×(C2×D47)⋊C4—24no—
66C2×(C2×D47)⋊C4—42no—
67C2×(C2×D47)⋊C4—42no—
68C2×(C2×D47)⋊C4C2×C414yes—
69C2×(C2×D47)⋊C4C2×C414yes—
70C2×(C2×D47)⋊C4D414yes—
71C2×(C2×D47)⋊C4Q814yes—
72C2×C4×Dic47—22no—
73C2×C4×Dic47—22no—
74C2×C4×Dic47—24no—
75C2×C4×Dic47—24no—
76C2×C4×Dic47—42no—
77C2×C4×Dic47C2×C414yes—
78C47⋊#95—24no—
79C47⋊#95—24no—
80C47⋊#95—24no—
81C47⋊#95—24no—
82C47⋊#95—24no—
83C47⋊#95—24no—
84C47⋊#95—42no—
85C47⋊#95C2×C414yes—
86C47⋊#95C2×C414yes—
87C23×C4×C47C2312yes—
88C23×C4×C47C2312yes—
89C23×C4×C47C2311yescharacteristic
90C23×C4×C47C2311yescharacteristic
91C23×C4×C47C2311yescharacteristic
92C2×C4⋊C4×C47—22no—
93C2×C4⋊C4×C47—22no—
94C2×C4⋊C4×C47—22no—
95C2×C4⋊C4×C47—24no—
96C2×C4⋊C4×C47—24no—
97C2×C4⋊C4×C47—24no—
98C2×C4⋊C4×C47—22no—
99C2×C4⋊C4×C47—24no—
100C2×C4⋊C4×C47—22no—
101C2×C4⋊C4×C47—42no—
102C2×C4⋊C4×C47—42no—
103C2×C4⋊C4×C47D414yes—
104C2×C42×C47—22no—
105C2×C42×C47—22no—
106C2×C42×C47C2×C414yes—
107C24×C47C2411yescharacteristic
108C23×D47—21no—
109C23×D47—21no—
110C23×D47—21no—
111C23×D47—21no—
112C23×D47—21no—
113C23×D47—21no—
114C23×D47—21no—
115C23×D47—21no—
116C23×D47—21no—
117C23×D47—21no—
118C23×D47—21no—
119C23×D47—21no—
120C23×D47C22×C412yes—
121C23×D47C2×D412yes—
122C23×D47C2×Q812yes—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
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—22no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47C22×C412yes—
145C22×C4×C47C22×C412yes—
146C22×C4×C47C22×C412yes—
147C22×C4×C47C2×D414yes—
148C22×C4×C47C2×D412yes—
149C22×C4×C47C2×D412yes—
150C22×C4×C47C2×D412yes—
151C22×C4×C47C2×Q812yes—
152C22×C4×C47#4112yes—
153C22×C4×C47#4112yes—
154C22×C4×C47#4112yes—
155C22×C4×C47#4112yes—
156C22×C4×C47#4112yes—
157C22×C4×C47#4112yes—
158C22×Dic47—21no—
159C22×Dic47—21no—
160C22×Dic47—21no—
161C22×Dic47—21no—
162C22×Dic47—21no—
163C22×Dic47—21no—
164C22×Dic47—21no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—21no—
173C22×Dic47—21no—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—21no—
177C22×Dic47—22no—
178C22×Dic47—21no—
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×Dic47C22×C412yes—
188C22×Dic47C22×C412yes—
189C22×Dic47C22×C412yes—
190C22×Dic47C2×D414yes—
191C22×Dic47C2×D412yes—
192C22×Dic47C2×Q812yes—
193C2×C4×D47—28no—
194C2×C4×D47—28no—
195C2×C4×D47—28no—
196C2×C4×D47—44no—
197C2×C4×D47—44no—
198C2×C4×D47—44no—
199C2×C4×D47—44no—
200C4⋊C4×C47—28no—
201C4⋊C4×C47—48no—
202C4⋊C4×C47—48no—
203C4⋊C4×C47—44no—
204C42×C47—28no—
205(C2×D47)⋊C4—28no—
206(C2×D47)⋊C4—48no—
207(C2×D47)⋊C4—48no—
208(C2×D47)⋊C4C4⋊C4116yescomplemented
209C4⋊Dic47—28no—
210C4⋊Dic47—44no—
211C4×Dic47—28no—
212C4×Dic47—48no—
213C23×C47C23×C411yescharacteristic
214C23×C47C22×D411yescharacteristic
215C23×C47C22×D411yescharacteristic
216C23×C47C22×D411yescharacteristic
217C23×C47C22×Q811yescharacteristic
218C23×C47C2×#4111yescharacteristic
219C23×C47C2×#4111yescharacteristic
220C23×C47C2×#4111yescharacteristic
221C23×C47C2×#4111yescharacteristic
222C23×C47C2×#4111yescharacteristic
223C23×C47C2×#4111yescharacteristic
224C23×C47H(5,𝔽2)11yescharacteristic
225C23×C47H(5,𝔽2)11yescharacteristic
226C23×C472−1+411yescharacteristic
227C23×C472−1+411yescharacteristic
228C22×D47—22no—
229C22×D47—22no—
230C22×D47—22no—
231C22×D47—22no—
232C22×D47—22no—
233C22×D47—22no—
234C22×D47—22no—
235C22×D47—22no—
236C22×D47—22no—
237C22×D47—22no—
238C22×D47—22no—
239C22×D47—22no—
240C22×D47—22no—
241C22×D47—22no—
242C22×D47—22no—
243C22×D47—22no—
244C22×D47—22no—
245C22×D47—22no—
246C22×D47—41no—
247C22×D47—41no—
248C22×D47—41no—
249C22×D47—41no—
250C22×D47—41no—
251C22×D47—41no—
252C22×D47—41no—
253C22×D47—41no—
254C22×D47—41no—
255C22×D47—41no—
256C22×D47—41no—
257C22×D47—41no—
258C22×D47—41no—
259C22×D47—41no—
260C22×D47—41no—
261C22×D47—41no—
262C22×D47C2×C4⋊C414yes—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—24no—
276C2×C4×C47—24no—
277C2×C4×C47—24no—
278C2×C4×C47—42no—
279C2×C4×C47—42no—
280C2×C4×C47—42no—
281C2×C4×C47—42no—
282C2×C4×C47—42no—
283C2×C4×C47—42no—
284C2×C4×C47—42no—
285C2×C4×C47—42no—
286C2×C4×C47—42no—
287C2×C4×C47—42no—
288C2×C4×C47—42no—
289C2×C4×C47C2×C4⋊C414yes—
290C2×C4×C47#11714yes—
291C2×C4×C47#11714yes—
292C2×C4×C47C4×D414yes—
293C2×C4×C47C4×D414yes—
294C2×C4×C47#12114yes—
295C2×C4×C47#12314yes—
296C2×C4×C47#12414yes—
297C2×C4×C47#12614yes—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—24no—
311C2×Dic47—24no—
312C2×Dic47—24no—
313C2×Dic47—41no—
314C2×Dic47—41no—
315C2×Dic47—41no—
316C2×Dic47—41no—
317C2×Dic47—42no—
318C2×Dic47—42no—
319C2×Dic47—42no—
320C2×Dic47—41no—
321C2×Dic47—41no—
322C2×Dic47—42no—
323C2×Dic47—41no—
324C2×Dic47—41no—
325C2×Dic47—42no—
326C2×Dic47—42no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329C2×Dic47—42no—
330C2×Dic47—42no—
331C2×Dic47—42no—
332C2×Dic47C2×C4⋊C414yes—
333C4×D47—416no—
334#13876—471nomaximal, Sylow
335C22×C47C22×C4⋊C411yescharacteristic
336C22×C47C2×#11711yescharacteristic
337C22×C47C2×#11711yescharacteristic
338C22×C47C2×C4×D411yescharacteristic
339C22×C47C2×C4×D411yescharacteristic
340C22×C47#52011yescharacteristic
341C22×C47#52011yescharacteristic
342C22×C47C2×#12111yescharacteristic
343C22×C47C2×#12311yescharacteristic
344C22×C47C2×#12411yescharacteristic
345C22×C47C2×#12611yescharacteristic
346C22×C47#53211yescharacteristic
347C22×C47#53211yescharacteristic
348C22×C47#53311yescharacteristic
349C22×C47#53311yescharacteristic
350C22×C47#54011yescharacteristic
351C22×C47#54111yescharacteristic
352C22×C47#54211yescharacteristic
353C22×C47#54211yescharacteristic
354C22×C47D4211yescharacteristic
355C22×C47D4211yescharacteristic
356C22×C47#54611yescharacteristic
357C22×C47#54711yescharacteristic
358C22×C47#54711yescharacteristic
359C22×C47#54711yescharacteristic
360C22×C47#54811yescharacteristic
361C22×C47D4×Q811yescharacteristic
362C22×C47D4×Q811yescharacteristic
363C22×C47#55011yescharacteristic
364C22×C47#55211yescharacteristic
365C22×C47#55311yescharacteristic
366C22×C47#55411yescharacteristic
367C22×C47#55411yescharacteristic
368C22×C47#55511yescharacteristic
369C22×C47#55611yescharacteristic
370C2×D47—24no—
371C2×D47—24no—
372C2×D47—24no—
373C2×D47—42no—
374C2×D47—42no—
375C2×D47—42no—
376C2×D47—42no—
377C2×D47—42no—
378C2×D47—42no—
379C2×D47—42no—
380C2×D47—42no—
381C2×D47—42no—
382C2×D47—42no—
383C2×D47—42no—
384C2×D47—42no—
385C4×C47—24no—
386C4×C47—24no—
387C4×C47—44no—
388C4×C47—82no—
389C4×C47#38818yescomplemented
390Dic47—24no—
391Dic47—42no—
392Dic47—44no—
393Dic47—42no—
394Dic47—82no—
395C2×#388—472no—
396C2×#384D4711yescharacteristic, complemented
397C2×#380—471no—
398C2×#380—471no—
399C2×C4×C4⋊C4—471no—
400C2×C4×C22⋊C4—471no—
401#1442—472no—
402#1439—472no—
403#1436—472no—
404C4⋊#95—471no—
405C4⋊#95—471no—
406C2×C47#228511yescharacteristic
407C2×C47C2×#38811yescharacteristic
408C2×C47#231411yescharacteristic
409C2×C47D4×C4⋊C411yescharacteristic
410C2×C47D4×C4⋊C411yescharacteristic
411C2×C47#235211yescharacteristic
412C2×C47#235411yescharacteristic
413C2×C47#242211yescharacteristic
414C2×C47#242311yescharacteristic
415C2×C47#242811yescharacteristic
416C2×C47#242911yescharacteristic
417C2×C47#249111yescharacteristic
418C2×C47#249211yescharacteristic
419C2×C47#249611yescharacteristic
420C2×C47#249711yescharacteristic
421D47—44no—
422C24×C4—471no—
423C22×C4⋊C4—471no—
424C22×C4⋊C4—471no—
425C22×C4⋊C4C2×D4711yescharacteristic
426C22×C4⋊C4C2×D4712yes—
427C22×C4⋊C4C2×D4712yes—
428C22×C4⋊C4C2×D4711yescharacteristic
429C22×C22⋊C4—471no—
430C22×C22⋊C4—471no—
431C22×C22⋊C4—472no—
432C22×C22⋊C4—472no—
433C22×C42—471no—
434C22×C42—472no—
435C22×C42C2×D4711yescharacteristic
436#388—948no—
437#384—24no—
438#380—944no—
439#380—944no—
440C4×C4⋊C4—944no—
441C4×C22⋊C4—478no—
442C2×#95—471no—
443C2×#95—471no—
444C2×#95—472no—
445C2×#95—472no—
446C2×#95—472no—
447C2×#95—472no—
448C2×#95—472no—
449C2×#95—472no—
450C2×#95—472no—
451C47#1387611yescharacteristic, complemented, Sylow
452C25—471no—
453C23×C4—471no—
454C23×C4—472no—
455C23×C4—471no—
456C23×C4—471no—
457C23×C4—474no—
458C23×C4—472no—
459C23×C4—942no—
460C23×C4—942no—
461C23×C4—942no—
462C23×C4—942no—
463C23×C4—942no—
464C23×C4—942no—
465C23×C4C22×D4712yes—
466C23×C4C22×D4712yes—
467C23×C4C22×D4711yescharacteristic
468C23×C4C22×D4711yescharacteristic
469C23×C4C22×D4711yescharacteristic
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—474no—
482C2×C4⋊C4—942no—
483C2×C4⋊C4—942no—
484C2×C4⋊C4—942no—
485C2×C4⋊C4—942no—
486C2×C4⋊C4—942no—
487C2×C4⋊C4C22⋊D4714yes—
488C2×C22⋊C4—474no—
489C2×C22⋊C4—474no—
490C2×C22⋊C4—474no—
491C2×C22⋊C4—474no—
492C2×C22⋊C4—942no—
493C2×C22⋊C4—942no—
494C2×C22⋊C4—944no—
495C2×C22⋊C4—944no—
496C2×C22⋊C4—944no—
497C2×C22⋊C4—944no—
498C2×C22⋊C4—1882no—
499C2×C22⋊C4—1882no—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—474no—
503C2×C42—942no—
504C2×C42—942no—
505C2×C42—944no—
506C2×C42—944no—
507C2×C42—1882no—
508C2×C42C4×D4714yes—
509#95—474no—
510#95—474no—
511#95—944no—
512#95—944no—
513#95—944no—
514#95—944no—
515#95—944no—
516#95—944no—
517#95—1882no—
518C24—472no—
519C24—472no—
520C24—472no—
521C24—941no—
522C24—941no—
523C24—941no—
524C24—941no—
525C24—941no—
526C24—941no—
527C24—941no—
528C24—941no—
529C24—941no—
530C24—941no—
531C24—941no—
532C24—941no—
533C24C23×D4711yescharacteristic
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—472no—
556C22×C4—472no—
557C22×C4—472no—
558C22×C4—472no—
559C22×C4—472no—
560C22×C4—474no—
561C22×C4—941no—
562C22×C4—941no—
563C22×C4—941no—
564C22×C4—941no—
565C22×C4—941no—
566C22×C4—941no—
567C22×C4—942no—
568C22×C4—941no—
569C22×C4—941no—
570C22×C4—941no—
571C22×C4—942no—
572C22×C4—941no—
573C22×C4—942no—
574C22×C4—941no—
575C22×C4—941no—
576C22×C4—942no—
577C22×C4—941no—
578C22×C4—941no—
579C22×C4—941no—
580C22×C4—942no—
581C22×C4—942no—
582C22×C4—941no—
583C22×C4—948no—
584C22×C4—948no—
585C22×C4—948no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—942no—
590C22×C4—942no—
591C22×C4—942no—
592C22×C4—942no—
593C22×C4—1884no—
594C22×C4—1884no—
595C22×C4—1884no—
596C22×C4—1884no—
597C22×C4C2×C4×D4712yes—
598C22×C4C2×C4×D4712yes—
599C22×C4C2×C4×D4712yes—
600C22×C4#1062535012yes—
601C22×C4D4×D4712yes—
602C22×C4D4×D4712yes—
603C22×C4#1062535212yes—
604C22×C4#1062535212yes—
605C22×C4Q8×D4712yes—
606C22×C4#1062535412yes—
607C22×C4#1062535412yes—
608C22×C4#1062535412yes—
609C22×C4C2×C22⋊D4714yes—
610C22×C4C2×C22⋊D4712yes—
611C4⋊C4—28no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4—44no—
615C4⋊C4—948no—
616C4⋊C4—1884no—
617C22⋊C4—4716no—
618C22⋊C4—948no—
619C22⋊C4—1888no—
620C22⋊C4—1888no—
621C42—28no—
622C42—948no—
623C42—1888no—
624C23—474no—
625C23—942no—
626C23—942no—
627C23—942no—
628C23—942no—
629C23—942no—
630C23—942no—
631C23—942no—
632C23—942no—
633C23—942no—
634C23—942no—
635C23—942no—
636C23—942no—
637C23—942no—
638C23—942no—
639C23—942no—
640C23—942no—
641C23—942no—
642C23—942no—
643C23—1881no—
644C23—1881no—
645C23—1881no—
646C23—1881no—
647C23—1881no—
648C23—1881no—
649C23—1881no—
650C23—1881no—
651C23—1881no—
652C23—1881no—
653C23—1881no—
654C23—1881no—
655C23—1881no—
656C23—1881no—
657C23—1881no—
658C23—1881no—
659C23C22×C4×D4711yescharacteristic
660C23C2×D4×D4711yescharacteristic
661C23C2×D4×D4711yescharacteristic
662C23C22×C22⋊D4711yescharacteristic
663C23C2×Q8×D4711yescharacteristic
664C23C2×#1062535211yescharacteristic
665C23C2×#1062535211yescharacteristic
666C23C2×#1062535011yescharacteristic
667C23C2×#1062535411yescharacteristic
668C23C2×#1062535411yescharacteristic
669C23C2×#1062535411yescharacteristic
670C23#1309406911yescharacteristic
671C23#1309406911yescharacteristic
672C23#1309407211yescharacteristic
673C23#1309407211yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—474no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—942no—
705C2×C4—942no—
706C2×C4—942no—
707C2×C4—944no—
708C2×C4—944no—
709C2×C4—942no—
710C2×C4—942no—
711C2×C4—942no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—944no—
716C2×C4—1882no—
717C2×C4—1882no—
718C2×C4—1882no—
719C2×C4—1882no—
720C2×C4—1882no—
721C2×C4—1882no—
722C2×C4—1882no—
723C2×C4—1882no—
724C2×C4—1882no—
725C2×C4—1881no—
726C2×C4—1881no—
727C2×C4—1882no—
728C2×C4—1881no—
729C2×C4—1881no—
730C2×C4—1881no—
731C2×C4—1881no—
732C2×C4—1881no—
733C2×C4—1881no—
734C2×C4—1882no—
735C2×C4—18816no—
736C2×C4C4⋊C4×D4714yes—
737C2×C4#1309398214yes—
738C2×C4#1309398214yes—
739C2×C4C4×C22⋊D4714yes—
740C2×C4#1309398614yes—
741C2×C4#1309399614yes—
742C2×C4#1309400914yes—
743C2×C4#1309401314yes—
744C2×C4#1309401914yes—
745C22—944no—
746C22—944no—
747C22—944no—
748C22—1882no—
749C22—1882no—
750C22—1882no—
751C22—1882no—
752C22—1882no—
753C22—1882no—
754C22—1882no—
755C22—1882no—
756C22—1882no—
757C22—1882no—
758C22—1882no—
759C22—1882no—
760C22C2×C4⋊C4×D4711yescharacteristic
761C22C2×#1309398211yescharacteristic
762C22C2×#1309398211yescharacteristic
763C22C2×C4×C22⋊D4711yescharacteristic
764C22C2×#1309398611yescharacteristic
765C22#1568960411yescharacteristic
766C22#1568960411yescharacteristic
767C22C2×#1309399611yescharacteristic
768C22C2×#1309400911yescharacteristic
769C22C2×#1309401311yescharacteristic
770C22C2×#1309401911yescharacteristic
771C22#1568967111yescharacteristic
772C22#1568967411yescharacteristic
773C22#1568967811yescharacteristic
774C22#1568967811yescharacteristic
775C22#1568972711yescharacteristic
776C22#1568973411yescharacteristic
777C22#1568974711yescharacteristic
778C22#1568974711yescharacteristic
779C22D4×C22⋊D4711yescharacteristic
780C22#1568975811yescharacteristic
781C22#1568976711yescharacteristic
782C22#1568977411yescharacteristic
783C22#1568977611yescharacteristic
784C22#1568977611yescharacteristic
785C22#1568978411yescharacteristic
786C22Q8×C22⋊D4711yescharacteristic
787C22#1568978811yescharacteristic
788C22#1568979311yescharacteristic
789C22#1568980811yescharacteristic
790C22#1568982111yescharacteristic
791C22#1568982811yescharacteristic
792C22#1568983411yescharacteristic
793C22#1568983911yescharacteristic
794C22#1568984711yescharacteristic
795C4—24no—
796C4—24no—
797C4—44no—
798C4—82no—
799C4—944no—
800C4—3762no—
801C4—1882no—
802C4—1882no—
803C4—1884no—
804C4#1568901318yescomplemented
805C2—1884no—
806C2#2024579311yescharacteristic
807C2C2×#1568901311yescharacteristic
808C2#2024599611yescharacteristic
809C2C4⋊C4×C22⋊D4711yescharacteristic
810C2#2024628811yescharacteristic
811C2#2024631311yescharacteristic
812C2#2024633911yescharacteristic
813C2#2024690511yescharacteristic
814C2#2024691611yescharacteristic
815C2#2024697911yescharacteristic
816C2#2024699011yescharacteristic
817C2#2024775411yescharacteristic
818C2#2024776511yescharacteristic
819C2#2024781311yescharacteristic
820C2#2024782411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#384C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenterC2×#384D47
hypocenterC47#13876
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊C4×Dic47C2semidirect
6. #20241647C2semidirect
8. #20241620C2semidirect
9. #20241618C2semidirect
10. #20241617C2semidirect
11. C2×C47×#384C2semidirect
25. C4×(C2×D47)⋊C4C4semidirect
208. (C2×D47)⋊C4C4⋊C4semidirect
389. C4×C47#388semidirect
396. C2×#384D47semidirect
451. C47#13876semidirect
804. C4#15689013semidirect

Maximal subgroups

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

subgroupindex
C2×#156890132
C2×#156889802
C2×C4⋊C4×Dic472
C2×C4×(C2×D47)⋊C42
#202416472
#202416302
#202416202
#202416182
#202416172
C2×C47×#3842
#1387647