Finite Group Databasebeta

← #26139677

Subgroups — #26139677

Order 12032.

2474 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic47C211yesmaximal, characteristic
2C2×#15689026C211yesmaximal, characteristic
3C2×#15689022C211yesmaximal, characteristic, complemented
4C2×#15688998C212yesmaximal, complemented
5C2×C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
6#20241633C212yesmaximal, complemented
7#20241633C212yesmaximal, complemented
8#20241618C211yesmaximal, characteristic, complemented
9#20241617C211yesmaximal, characteristic, complemented
10#20241610C212yesmaximal, complemented
11C2×C47×#390C211yesmaximal, characteristic
12C24×Dic47C2212yes—
13C2×D4×Dic47—24no—
14C2×D4×Dic47—24no—
15C2×D4×Dic47—24no—
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×C4⋊Dic47C2212yes—
19C22×C4⋊Dic47C2211yescharacteristic
20C22×C4⋊Dic47C2211yescharacteristic
21C22×C22⋊Dic47C2212yes—
22C22×C22⋊Dic47C2212yes—
23C22×C22⋊Dic47C2212yes—
24C22×C4×Dic47C2211yescharacteristic
25C22×C4×Dic47C2211yescharacteristic
26#15689026—24no—
27#15689022—24no—
28#15688998—28no—
29C4×C4⋊Dic47—24no—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2211yescharacteristic
35C2×C47⋊#95C2212yes—
36C2×C47⋊#95C2212yes—
37C23×D4×C47C2211yescharacteristic
38C22×C4⋊C4×C47C2211yescharacteristic
39C22×C22⋊C4×C47C2212yes—
40C22×C22⋊C4×C47C2212yes—
41C22×C42×C47C2211yescharacteristic
42C47×#390C418yescomplemented
43C23×Dic47—24no—
44C23×Dic47—24no—
45C23×Dic47—24no—
46C23×Dic47—24no—
47C23×Dic47—24no—
48C23×Dic47—42no—
49C23×Dic47—42no—
50C23×Dic47C2312yes—
51C23×Dic47C2311yescharacteristic
52C23×Dic47C2312yes—
53C23×Dic47C2311yescharacteristic
54C23×Dic47C2311yescharacteristic
55C23×Dic47C2311yescharacteristic
56D4×Dic47—232no—
57C2×C4⋊Dic47—22no—
58C2×C4⋊Dic47—22no—
59C2×C4⋊Dic47—22no—
60C2×C4⋊Dic47—22no—
61C2×C4⋊Dic47—22no—
62C2×C4⋊Dic47—22no—
63C2×C4⋊Dic47—22no—
64C2×C4⋊Dic47—22no—
65C2×C4⋊Dic47—22no—
66C2×C4⋊Dic47—22no—
67C2×C4⋊Dic47—24no—
68C2×C4⋊Dic47—24no—
69C2×C4⋊Dic47—42no—
70C2×C4⋊Dic47D414yes—
71C2×C4⋊Dic47D414yescomplemented
72C2×C22⋊Dic47—24no—
73C2×C22⋊Dic47—24no—
74C2×C22⋊Dic47—24no—
75C2×C22⋊Dic47—24no—
76C2×C22⋊Dic47—24no—
77C2×C22⋊Dic47—24no—
78C2×C22⋊Dic47—24no—
79C2×C22⋊Dic47—42no—
80C2×C22⋊Dic47—42no—
81C2×C4×Dic47—22no—
82C2×C4×Dic47—22no—
83C2×C4×Dic47—22no—
84C2×C4×Dic47—22no—
85C2×C4×Dic47—22no—
86C2×C4×Dic47D414yes—
87C47⋊#95—24no—
88C47⋊#95—22no—
89C47⋊#95—22no—
90C47⋊#95—24no—
91C47⋊#95—24no—
92C47⋊#95—42no—
93C47⋊#95—42no—
94C25×C47C2312yes—
95C22×D4×C47—22no—
96C22×D4×C47—22no—
97C22×D4×C47—22no—
98C22×D4×C47—22no—
99C22×D4×C47C2×C414yes—
100C22×D4×C47D414yes—
101C22×D4×C47Q814yes—
102C23×C4×C47C2311yescharacteristic
103C23×C4×C47C2312yes—
104C23×C4×C47C2311yescharacteristic
105C23×C4×C47C2311yescharacteristic
106C2×C4⋊C4×C47—22no—
107C2×C4⋊C4×C47—22no—
108C2×C4⋊C4×C47C2×C414yescomplemented
109C2×C22⋊C4×C47—24no—
110C2×C22⋊C4×C47—24no—
111C2×C22⋊C4×C47—42no—
112C2×C22⋊C4×C47—42no—
113C2×C22⋊C4×C47C2×C418yescomplemented
114C2×C22⋊C4×C47C2×C418yescomplemented
115C2×C42×C47—22no—
116C2×C42×C47—22no—
117C2×C42×C47C2×C414yescomplemented
118C24×C47—22no—
119C24×C47—22no—
120C24×C47—22no—
121C24×C47—22no—
122C24×C47—22no—
123C24×C47—22no—
124C24×C47—22no—
125C24×C47—22no—
126C24×C47—22no—
127C24×C47—22no—
128C24×C47—22no—
129C24×C47—22no—
130C24×C47C22×C414yes—
131C24×C47C2×D414yes—
132C24×C47C2×Q814yes—
133C24×C47C2411yescharacteristic
134C2×D4×C47—28no—
135C2×D4×C47—28no—
136C2×D4×C47—28no—
137C2×D4×C47—28no—
138C2×D4×C47—28no—
139C2×D4×C47—28no—
140C2×D4×C47C4⋊C4116yescomplemented
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—21no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47C22×C412yes—
158C22×C4×C47C22×C414yes—
159C22×C4×C47C22×C412yes—
160C22×C4×C47C22×C412yes—
161C22×C4×C47C2×D412yes—
162C22×C4×C47C2×D412yes—
163C22×C4×C47C2×D412yes—
164C22×C4×C47C2×D412yes—
165C22×C4×C47C2×Q812yes—
166C22×C4×C47#4112yes—
167C22×C4×C47#4112yes—
168C22×C4×C47#4112yes—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47—216no—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—21no—
177C22×Dic47—22no—
178C22×Dic47—21no—
179C22×Dic47—21no—
180C22×Dic47—21no—
181C22×Dic47—21no—
182C22×Dic47—21no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—21no—
186C22×Dic47—21no—
187C22×Dic47—21no—
188C22×Dic47—21no—
189C22×Dic47—22no—
190C22×Dic47—21no—
191C22×Dic47—22no—
192C22×Dic47—21no—
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47—22no—
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47—22no—
201C22×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—48no—
206C22×Dic47—48no—
207C22×Dic47—48no—
208C22×Dic47—48no—
209C22×Dic47—48no—
210C22×Dic47—48no—
211C22×Dic47C2×D412yes—
212C22×Dic47C2×D414yes—
213C22×Dic47C2×D412yes—
214C22×Dic47C2×D412yes—
215C22×Dic47C2×D412yes—
216C22×Dic47#4112yes—
217C22×Dic47#4112yes—
218C4⋊C4×C47—28no—
219C22⋊C4×C47—216no—
220C22⋊C4×C47—48no—
221C42×C47—28no—
222C22⋊Dic47—216no—
223C22⋊Dic47—48no—
224C22⋊Dic47—48no—
225C4⋊Dic47—28no—
226C4⋊Dic47—28no—
227C4⋊Dic47—28no—
228C4⋊Dic47—48no—
229C4⋊Dic47—44no—
230C4×Dic47—28no—
231C4×Dic47—44no—
232C23×C47—24no—
233C23×C47—24no—
234C23×C47—24no—
235C23×C47—24no—
236C23×C47—24no—
237C23×C47—24no—
238C23×C47—24no—
239C23×C47—24no—
240C23×C47—24no—
241C23×C47—24no—
242C23×C47—24no—
243C23×C47—24no—
244C23×C47—24no—
245C23×C47—24no—
246C23×C47—24no—
247C23×C47—24no—
248C23×C47—24no—
249C23×C47—24no—
250C23×C47—42no—
251C23×C47—42no—
252C23×C47—42no—
253C23×C47—42no—
254C23×C47—42no—
255C23×C47—42no—
256C23×C47—42no—
257C23×C47—42no—
258C23×C47—42no—
259C23×C47—42no—
260C23×C47—42no—
261C23×C47—42no—
262C23×C47—42no—
263C23×C47—42no—
264C23×C47—42no—
265C23×C47—42no—
266C23×C47C2×C4⋊C418yes—
267C23×C47C23×C411yescharacteristic
268C23×C47C22×D411yescharacteristic
269C23×C47C22×D411yescharacteristic
270C23×C47C22×D411yescharacteristic
271C23×C47C22×D411yescharacteristic
272C23×C47C22×Q811yescharacteristic
273C23×C47C2×#4111yescharacteristic
274C23×C47C2×#4111yescharacteristic
275C23×C47C2×#4111yescharacteristic
276C23×C47C2×#4111yescharacteristic
277C23×C47C2×#4111yescharacteristic
278C23×C47H(5,𝔽2)11yescharacteristic
279C23×C47H(5,𝔽2)11yescharacteristic
280C23×C47H(5,𝔽2)11yescharacteristic
281C23×C472−1+411yescharacteristic
282D4×C47—232no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—24no—
291C2×C4×C47—24no—
292C2×C4×C47—22no—
293C2×C4×C47—24no—
294C2×C4×C47—22no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47—42no—
303C2×C4×C47C2×C4⋊C414yes—
304C2×C4×C47C4×D414yes—
305C2×C4×C47C4×D414yes—
306C2×C4×C47C4×D414yescomplemented
307C2×C4×C47#12014yes—
308C2×C4×C47C22⋊Q814yes—
309C2×C4×C47C22⋊Q814yes—
310C2×C4×C47#12314yes—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—24no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—24no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—24no—
328C2×Dic47—22no—
329C2×Dic47—432no—
330C2×Dic47—41no—
331C2×Dic47—41no—
332C2×Dic47—42no—
333C2×Dic47—41no—
334C2×Dic47—42no—
335C2×Dic47—41no—
336C2×Dic47—42no—
337C2×Dic47—41no—
338C2×Dic47—41no—
339C2×Dic47—41no—
340C2×Dic47—42no—
341C2×Dic47—41no—
342C2×Dic47—41no—
343C2×Dic47—41no—
344C2×Dic47—41no—
345C2×Dic47—41no—
346C2×Dic47—42no—
347C2×Dic47—42no—
348C2×Dic47—42no—
349C2×Dic47—42no—
350C2×Dic47—42no—
351C2×Dic47—42no—
352C2×Dic47—42no—
353C2×Dic47#12114yes—
354#14018—471nomaximal, Sylow
355C22×C47—28no—
356C22×C47—28no—
357C22×C47—28no—
358C22×C47—44no—
359C22×C47—44no—
360C22×C47—44no—
361C22×C47—44no—
362C22×C47—44no—
363C22×C47—44no—
364C22×C47—44no—
365C22×C47—44no—
366C22×C47—44no—
367C22×C47—44no—
368C22×C47—44no—
369C22×C47—44no—
370C22×C47C22×C4⋊C411yescharacteristic
371C22×C47C2×C4×D411yescharacteristic
372C22×C47C2×C4×D411yescharacteristic
373C22×C47C2×C4×D411yescharacteristic
374C22×C47C4×#4111yescharacteristic
375C22×C47#51811yescharacteristic
376C22×C47#52011yescharacteristic
377C22×C47C2×#12011yescharacteristic
378C22×C47C2×#12111yescharacteristic
379C22×C47C2×C22⋊Q811yescharacteristic
380C22×C47C2×C22⋊Q811yescharacteristic
381C22×C47C2×#12311yescharacteristic
382C22×C47#52511yescharacteristic
383C22×C47#52911yescharacteristic
384C22×C47#53211yescharacteristic
385C22×C47#53511yescharacteristic
386C22×C47#53711yescharacteristic
387C22×C47#54011yescharacteristic
388C22×C47#54211yescharacteristic
389C22×C47D4211yescharacteristic
390C22×C47D4211yescharacteristic
391C22×C47#54611yescharacteristic
392C22×C47#54611yescharacteristic
393C22×C47#54611yescharacteristic
394C22×C47#54711yescharacteristic
395C22×C47#54811yescharacteristic
396C22×C47D4×Q811yescharacteristic
397C22×C47#55011yescharacteristic
398C22×C47#55011yescharacteristic
399C22×C47#55411yescharacteristic
400C22×C47#55411yescharacteristic
401C22×C47#55411yescharacteristic
402C22×C47#55611yescharacteristic
403C22×C47#55911yescharacteristic
404C22×C47#55911yescharacteristic
405C4×C47—24no—
406C4×C47—42no—
407C4×C47—44no—
408C4×C47#38518yescomplemented
409Dic47—24no—
410Dic47—42no—
411Dic47—42no—
412Dic47—42no—
413Dic47—44no—
414Dic47—82no—
415C22×C4×D4—471no—
416C2×#390—471no—
417C2×#390D4711yescharacteristic
418C2×#389—471no—
419C2×#385—472no—
420C2×C4×C4⋊C4—471no—
421#1439—472no—
422#1439—472no—
423C4⋊#95—471no—
424C4⋊#95—471no—
425C22⋊#95—472no—
426C2×C47—48no—
427C2×C47C2×#38511yescharacteristic
428C2×C47C4×#12111yescharacteristic
429C2×C47#232411yescharacteristic
430C2×C47D4×C4⋊C411yescharacteristic
431C2×C47#234911yescharacteristic
432C2×C47#236611yescharacteristic
433C2×C47#236711yescharacteristic
434C2×C47#240711yescharacteristic
435C2×C47#240811yescharacteristic
436C2×C47#244511yescharacteristic
437C2×C47#244711yescharacteristic
438C2×C47#245211yescharacteristic
439C2×C47#245411yescharacteristic
440C2×C47#253811yescharacteristic
441C2×C47#258011yescharacteristic
442C23×D4C2×D4711yescharacteristic
443C24×C4—472no—
444C2×C4×D4—944no—
445C2×C4×D4—944no—
446C2×C4×D4—944no—
447C22×C4⋊C4—471no—
448C22×C4⋊C4—471no—
449C22×C4⋊C4—471no—
450C22×C4⋊C4—471no—
451C22×C4⋊C4—472no—
452C22×C4⋊C4C2×D4711yescharacteristic
453C22×C22⋊C4—472no—
454C22×C22⋊C4—472no—
455C22×C22⋊C4—472no—
456C22×C22⋊C4C2×D4712yes—
457C22×C22⋊C4C2×D4712yes—
458C22×C42—471no—
459C22×C42—471no—
460C22×C42C2×D4711yescharacteristic
461#390—944no—
462#390Dic4718yescomplemented
463#389—944no—
464#385—948no—
465C4×C4⋊C4—944no—
466C2×#95—471no—
467C2×#95—472no—
468C2×#95—472no—
469C2×#95—472no—
470C2×#95—471no—
471C2×#95—472no—
472C2×#95—472no—
473C47#1401811yescharacteristic, complemented, Sylow
474C25C22×D4712yes—
475C22×D4—22no—
476C22×D4—22no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4Dic9414yes—
480C22×D4D18814yes—
481C22×D4C2×Dic4714yes—
482C23×C4—471no—
483C23×C4—471no—
484C23×C4—471no—
485C23×C4—471no—
486C23×C4—472no—
487C23×C4—472no—
488C23×C4—944no—
489C23×C4—944no—
490C23×C4—944no—
491C23×C4—944no—
492C23×C4—944no—
493C23×C4—1882no—
494C23×C4—1882no—
495C23×C4C22×D4712yes—
496C23×C4C22×D4711yescharacteristic
497C23×C4C22×D4711yescharacteristic
498C23×C4C22×D4711yescharacteristic
499C4×D4—9432no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—474no—
503C2×C4⋊C4—474no—
504C2×C4⋊C4—942no—
505C2×C4⋊C4—942no—
506C2×C4⋊C4—942no—
507C2×C4⋊C4—942no—
508C2×C4⋊C4—942no—
509C2×C4⋊C4—942no—
510C2×C4⋊C4—942no—
511C2×C4⋊C4—944no—
512C2×C4⋊C4—944no—
513C2×C4⋊C4—942no—
514C2×C4⋊C4—942no—
515C2×C4⋊C4—942no—
516C2×C4⋊C4—1882no—
517C2×C4⋊C4C2×Dic4714yescomplemented
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—944no—
523C2×C22⋊C4—944no—
524C2×C22⋊C4—944no—
525C2×C22⋊C4—944no—
526C2×C22⋊C4—944no—
527C2×C22⋊C4—944no—
528C2×C22⋊C4—944no—
529C2×C22⋊C4—1882no—
530C2×C22⋊C4—1882no—
531C2×C22⋊C4C2×Dic4718yescomplemented
532C2×C22⋊C4C2×Dic4718yescomplemented
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—474no—
536C2×C42—942no—
537C2×C42—942no—
538C2×C42—942no—
539C2×C42—942no—
540C2×C42—942no—
541C2×C42C2×Dic4714yescomplemented
542#95—942no—
543#95—942no—
544#95—944no—
545#95—944no—
546#95—944no—
547#95—1882no—
548#95—1882no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24C2×Dic9414yes—
562C24C2×D18814yes—
563C24C22×Dic4714yes—
564C24C23×D4711yescharacteristic
565C2×D4—28no—
566C2×D4—28no—
567C2×D4—28no—
568C2×D4—28no—
569C2×D4—28no—
570C2×D4—28no—
571C2×D4C4⋊Dic47116yescomplemented
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—472no—
589C22×C4—472no—
590C22×C4—472no—
591C22×C4—472no—
592C22×C4—474no—
593C22×C4—472no—
594C22×C4—472no—
595C22×C4—941no—
596C22×C4—941no—
597C22×C4—941no—
598C22×C4—941no—
599C22×C4—9416no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—942no—
604C22×C4—941no—
605C22×C4—941no—
606C22×C4—942no—
607C22×C4—941no—
608C22×C4—941no—
609C22×C4—941no—
610C22×C4—942no—
611C22×C4—941no—
612C22×C4—941no—
613C22×C4—942no—
614C22×C4—941no—
615C22×C4—941no—
616C22×C4—941no—
617C22×C4—941no—
618C22×C4—941no—
619C22×C4—942no—
620C22×C4—942no—
621C22×C4—941no—
622C22×C4—941no—
623C22×C4—941no—
624C22×C4—942no—
625C22×C4—942no—
626C22×C4—942no—
627C22×C4—942no—
628C22×C4—942no—
629C22×C4—942no—
630C22×C4—942no—
631C22×C4—1888no—
632C22×C4—1888no—
633C22×C4—1888no—
634C22×C4—1888no—
635C22×C4—1888no—
636C22×C4—1888no—
637C22×C4C2×Dic9412yes—
638C22×C4C2×D18812yes—
639C22×C4D4×D4712yes—
640C22×C4D4×D4712yes—
641C22×C4D4×D4712yes—
642C22×C4#1062535212yes—
643C22×C4#1062535212yes—
644C22×C4#1062535212yes—
645C22×C4C22×Dic4712yes—
646C22×C4C22×Dic4714yes—
647C22×C4C22×Dic4712yes—
648C22×C4C22×Dic4712yes—
649C4⋊C4—28no—
650C4⋊C4—948no—
651C4⋊C4—948no—
652C4⋊C4—948no—
653C4⋊C4—1888no—
654C4⋊C4—1884no—
655C22⋊C4—216no—
656C22⋊C4—48no—
657C22⋊C4—9416no—
658C22⋊C4—1888no—
659C22⋊C4—1888no—
660C42—28no—
661C42—948no—
662C42—1884no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23C2×C4⋊Dic4718yes—
698C23C23×Dic4711yescharacteristic
699C23C2×D4×D4711yescharacteristic
700C23C2×D4×D4711yescharacteristic
701C23C2×D4×D4711yescharacteristic
702C23C22×D18811yescharacteristic
703C23C22×Dic9411yescharacteristic
704C23#41×D4711yescharacteristic
705C23#41×D4711yescharacteristic
706C23C2×#1062535211yescharacteristic
707C23C2×#1062535211yescharacteristic
708C23C2×#1062535211yescharacteristic
709C23#1309406911yescharacteristic
710C23#1309406911yescharacteristic
711C23#1309407011yescharacteristic
712C23#1309407111yescharacteristic
713D4—232no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—474no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—942no—
742C2×C4—944no—
743C2×C4—942no—
744C2×C4—944no—
745C2×C4—942no—
746C2×C4—942no—
747C2×C4—942no—
748C2×C4—944no—
749C2×C4—942no—
750C2×C4—942no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—18832no—
754C2×C4—1882no—
755C2×C4—1882no—
756C2×C4—1882no—
757C2×C4—1882no—
758C2×C4—1882no—
759C2×C4—1882no—
760C2×C4—1882no—
761C2×C4—1882no—
762C2×C4—1881no—
763C2×C4—1881no—
764C2×C4—1881no—
765C2×C4—1882no—
766C2×C4—1881no—
767C2×C4—1881no—
768C2×C4—1881no—
769C2×C4—1881no—
770C2×C4—1881no—
771C2×C4—1881no—
772C2×C4—1881no—
773C2×C4—1882no—
774C2×C4—1881no—
775C2×C4—1882no—
776C2×C4—1881no—
777C2×C4C2×C4⋊Dic4714yes—
778C2×C4D4×Dic4714yes—
779C2×C4D4×Dic4714yes—
780C2×C4D4×Dic4714yescomplemented
781C2×C4#1309399414yes—
782C2×C4#1309400114yes—
783C2×C4#1309400114yes—
784C2×C4#1309400814yes—
785C22—28no—
786C22—28no—
787C22—28no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22C22×C4⋊Dic4711yescharacteristic
801C22C2×D4×Dic4711yescharacteristic
802C22C2×D4×Dic4711yescharacteristic
803C22C2×D4×Dic4711yescharacteristic
804C22#41×Dic4711yescharacteristic
805C22#1568959811yescharacteristic
806C22#1568960611yescharacteristic
807C22C2×#1309399411yescharacteristic
808C22#121×D4711yescharacteristic
809C22C2×#1309400111yescharacteristic
810C22C2×#1309400111yescharacteristic
811C22C2×#1309400811yescharacteristic
812C22#1568963311yescharacteristic
813C22#1568965411yescharacteristic
814C22#1568966811yescharacteristic
815C22#1568968911yescharacteristic
816C22#1568970211yescharacteristic
817C22#1568972611yescharacteristic
818C22#1568974011yescharacteristic
819C22#1568975811yescharacteristic
820C22D4×D18811yescharacteristic
821C22#1568976611yescharacteristic
822C22#1568976811yescharacteristic
823C22#1568976811yescharacteristic
824C22#1568977711yescharacteristic
825C22#1568978111yescharacteristic
826C22D4×Dic9411yescharacteristic
827C22#1568979311yescharacteristic
828C22#1568979311yescharacteristic
829C22#1568983011yescharacteristic
830C22#1568983211yescharacteristic
831C22#1568983211yescharacteristic
832C22#1568984211yescharacteristic
833C22#1568985511yescharacteristic
834C22#1568985911yescharacteristic
835C4—24no—
836C4—42no—
837C4—44no—
838C4—944no—
839C4—3762no—
840C4—1882no—
841C4—1882no—
842C4—1884no—
843C4—1882no—
844C4#1568899818yescomplemented
845C2—48no—
846C2C2×#1568899811yescharacteristic
847C2#121×Dic4711yescharacteristic
848C2#2024608311yescharacteristic
849C2D4×C4⋊Dic4711yescharacteristic
850C2#2024629811yescharacteristic
851C2#2024645311yescharacteristic
852C2#2024646311yescharacteristic
853C2#2024673111yescharacteristic
854C2#2024674211yescharacteristic
855C2#2024715111yescharacteristic
856C2#2024717311yescharacteristic
857C2#2024724111yescharacteristic
858C2#2024726311yescharacteristic
859C2#2024830811yescharacteristic
860C2#2024874411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#390C2
socle, cosocleC24×C47C24
prime radicalC23×D4×C47C22
hypercenterC2×#390D47
hypocenterC47#14018
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
3. C2×#15689022C2semidirect
4. C2×#15688998C2semidirect
5. C2×C4×C4⋊Dic47C2semidirect
6. #20241633C2semidirect
7. #20241633C2semidirect
8. #20241618C2semidirect
9. #20241617C2semidirect
10. #20241610C2semidirect
42. C47×#390C4semidirect
71. C2×C4⋊Dic47D4semidirect
108. C2×C4⋊C4×C47C2×C4semidirect
113. C2×C22⋊C4×C47C2×C4semidirect
114. C2×C22⋊C4×C47C2×C4semidirect
117. C2×C42×C47C2×C4semidirect
140. C2×D4×C47C4⋊C4semidirect
306. C2×C4×C47C4×D4semidirect
408. C4×C47#385semidirect
462. #390Dic47semidirect
473. C47#14018semidirect
517. C2×C4⋊C4C2×Dic47semidirect
531. C2×C22⋊C4C2×Dic47semidirect
532. C2×C22⋊C4C2×Dic47semidirect
541. C2×C42C2×Dic47semidirect
571. C2×D4C4⋊Dic47semidirect
780. C2×C4D4×Dic47semidirect
844. C4#15688998semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic472
C2×#156890262
C2×#156890222
C2×#156889982
C2×C4×C4⋊Dic472
#202416332
#202416182
#202416172
#202416102
C2×C47×#3902
#1401847