Finite Group Databasebeta

← #26122125

Subgroups — #26122125

Order 12032.

998 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic47⋊C8C211yesmaximal, characteristic
2C2×#15688988C211yesmaximal, characteristic
3C2×C4⋊C4×Dic47C211yesmaximal, characteristic
4C2×#15688886C211yesmaximal, characteristic
5C2×#15688885C211yesmaximal, characteristic
6C2×#15688885C211yesmaximal, characteristic
7C2×C47×#340C211yesmaximal, characteristic
8C23×C47⋊C8C2211yescharacteristic
9C22×C4⋊Dic47C2211yescharacteristic
10C22×C4⋊Dic47C2211yescharacteristic
11C22×C4×Dic47—21no—
12C22×C4×Dic47C2211yescharacteristic
13C2×Dic47⋊C8—22no—
14C2×Dic47⋊C8—22no—
15C2×Dic47⋊C8C414yescomplemented
16#15688988—22no—
17#15688988C414yescomplemented
18C4⋊C4×Dic47—22no—
19C4⋊C4×Dic47C414yescomplemented
20C2×C47⋊#95—21no—
21C2×C47⋊#95—21no—
22C2×C47⋊#95—21no—
23#15688886—22no—
24#15688885—22no—
25#15688885—22no—
26C23×C8×C47C2211yescharacteristic
27C22×C4⋊C4×C47C2211yescharacteristic
28C22×C4⋊C4×C47C2211yescharacteristic
29C47×#340—22no—
30C23×Dic47—21no—
31C23×Dic47—21no—
32C23×Dic47D411yescharacteristic
33C23×Dic47D411yescharacteristic
34C22×C47⋊C8—21no—
35C22×C47⋊C8—21no—
36C22×C47⋊C8—21no—
37C22×C47⋊C8—21no—
38C22×C47⋊C8—21no—
39C22×C47⋊C8—21no—
40C22×C47⋊C8C2×C412yes—
41C2×C4⋊Dic47—21no—
42C2×C4⋊Dic47—21no—
43C2×C4⋊Dic47—21no—
44C2×C4⋊Dic47—21no—
45C2×C4⋊Dic47—21no—
46C2×C4⋊Dic47—21no—
47C2×C4⋊Dic47—21no—
48C2×C4⋊Dic47—21no—
49C2×C4⋊Dic47C2×C412yes—
50C2×C4⋊Dic47C2×C412yes—
51C2×C4⋊Dic47D412yes—
52C2×C4⋊Dic47Q812yes—
53C2×C4×Dic47—24no—
54C2×C4×Dic47—42no—
55C2×C4×Dic47—42no—
56C2×C4×Dic47C2×C412yes—
57C2×C4×Dic47C2×C412yes—
58C2×C4×Dic47C2×C412yes—
59C2×C4×Dic47D412yes—
60C2×C4×Dic47D412yes—
61C2×C4×Dic47Q812yes—
62Dic47⋊C8—28no—
63C47⋊#95—24no—
64C47⋊#95—24no—
65C47⋊#95—24no—
66C23×C4×C47—21no—
67C23×C4×C47—21no—
68C23×C4×C47C2311yescharacteristic
69C22×C8×C47—21no—
70C22×C8×C47—21no—
71C22×C8×C47—21no—
72C22×C8×C47—21no—
73C22×C8×C47—21no—
74C22×C8×C47—21no—
75C22×C8×C47C2×C412yes—
76C2×C4⋊C4×C47—21no—
77C2×C4⋊C4×C47—21no—
78C2×C4⋊C4×C47—21no—
79C2×C4⋊C4×C47—21no—
80C2×C4⋊C4×C47—21no—
81C2×C4⋊C4×C47—21no—
82C2×C4⋊C4×C47—21no—
83C2×C4⋊C4×C47—21no—
84C2×C4⋊C4×C47C2×C412yes—
85C2×C4⋊C4×C47C2×C412yes—
86C2×C4⋊C4×C47D412yes—
87C2×C4⋊C4×C47Q812yes—
88C24×C47C2×D411yescharacteristic
89C22×C4×C47—22no—
90C22×C4×C47—22no—
91C22×C4×C47—22no—
92C22×C4×C47—22no—
93C22×C4×C47—41no—
94C22×C4×C47—41no—
95C22×C4×C47—41no—
96C22×C4×C47—41no—
97C22×C4×C47—41no—
98C22×C4×C47—41no—
99C22×C4×C47—41no—
100C22×C4×C47—41no—
101C22×C4×C47—41no—
102C22×C4×C47—41no—
103C22×C4×C47C22×C411yescharacteristic
104C22×C4×C47C22×C411yescharacteristic
105C22×C4×C47C22×C411yescharacteristic
106C22×C4×C47C2×D411yescharacteristic
107C22×C4×C47C2×D411yescharacteristic
108C22×C4×C47C2×D411yescharacteristic
109C22×C4×C47C2×D411yescharacteristic
110C22×C4×C47C2×Q811yescharacteristic
111C22×C4×C47C2×Q811yescharacteristic
112C22×C4×C47C2×Q811yescharacteristic
113C22×C4×C47#4111yescharacteristic
114C22×C4×C47#4111yescharacteristic
115C22×C4×C47#4111yescharacteristic
116C22×C4×C47#4111yescharacteristic
117C22×Dic47—21no—
118C22×Dic47—21no—
119C22×Dic47—21no—
120C22×Dic47—21no—
121C22×Dic47—21no—
122C22×Dic47—21no—
123C22×Dic47—21no—
124C22×Dic47—21no—
125C22×Dic47—22no—
126C22×Dic47—22no—
127C22×Dic47—22no—
128C22×Dic47—22no—
129C22×Dic47—41no—
130C22×Dic47—41no—
131C22×Dic47—41no—
132C22×Dic47—41no—
133C22×Dic47—41no—
134C22×Dic47—41no—
135C22×Dic47—41no—
136C22×Dic47—41no—
137C22×Dic47—41no—
138C22×Dic47—41no—
139C22×Dic47C22⋊C412yes—
140C22×Dic47C22⋊C412yes—
141C22×Dic47C22⋊C412yes—
142C22×Dic47C22⋊C412yes—
143C22×Dic47C4⋊C412yes—
144C22×Dic47C4⋊C412yes—
145C2×C8×C47—22no—
146C2×C8×C47—22no—
147C2×C8×C47—22no—
148C2×C8×C47—41no—
149C2×C8×C47—41no—
150C2×C8×C47—41no—
151C2×C8×C47—41no—
152C4⋊C4×C47—22no—
153C4⋊C4×C47—22no—
154C4⋊C4×C47—22no—
155C4⋊C4×C47—22no—
156C4⋊C4×C47—22no—
157C4⋊C4×C47—41no—
158C4⋊C4×C47—41no—
159C4⋊C4×C47C4⋊C414yes—
160C4⋊Dic47—22no—
161C4⋊Dic47—22no—
162C4⋊Dic47—22no—
163C4⋊Dic47—22no—
164C4⋊Dic47—22no—
165C4⋊Dic47—41no—
166C4⋊Dic47—41no—
167C4⋊Dic47C4⋊C414yes—
168C4×Dic47—48no—
169C4×Dic47C4214yes—
170C4×Dic47C22⋊C414yes—
171C4×Dic47C4⋊C414yes—
172C4×Dic47C4⋊C414yes—
173C2×C47⋊C8—22no—
174C2×C47⋊C8—22no—
175C2×C47⋊C8—22no—
176C2×C47⋊C8—41no—
177C2×C47⋊C8—41no—
178C2×C47⋊C8—41no—
179C2×C47⋊C8—41no—
180C23×C47C2×C22⋊C411yescharacteristic
181C23×C47C2×C22⋊C411yescharacteristic
182C23×C47C2×C4⋊C411yescharacteristic
183C23×C47#12111yescharacteristic
184C23×C47#12111yescharacteristic
185C23×C47C22⋊Q811yescharacteristic
186C23×C47C22⋊Q811yescharacteristic
187C23×C47#13511yescharacteristic
188C23×C47#13511yescharacteristic
189C23×C47#13511yescharacteristic
190C23×C47#13511yescharacteristic
191C23×C47AGL(1,ℤ/8)11yescharacteristic
192C23×C47AGL(1,ℤ/8)11yescharacteristic
193C23×C47#13711yescharacteristic
194C23×C47#13711yescharacteristic
195C2×C4×C47—24no—
196C2×C4×C47—42no—
197C2×C4×C47—42no—
198C2×C4×C47—42no—
199C2×C4×C47—42no—
200C2×C4×C47—42no—
201C2×C4×C47—42no—
202C2×C4×C47—42no—
203C2×C4×C47—42no—
204C2×C4×C47—42no—
205C2×C4×C47—81no—
206C2×C4×C47—81no—
207C2×C4×C47—81no—
208C2×C4×C47—81no—
209C2×C4×C47C2×C4211yescharacteristic
210C2×C4×C47C2×C22⋊C411yescharacteristic
211C2×C4×C47C2×C4⋊C411yescharacteristic
212C2×C4×C47C2×C4⋊C411yescharacteristic
213C2×C4×C47C2×C4⋊C411yescharacteristic
214C2×C4×C47C2×C4⋊C411yescharacteristic
215C2×C4×C47#11711yescharacteristic
216C2×C4×C47#11711yescharacteristic
217C2×C4×C47C4×D411yescharacteristic
218C2×C4×C47C4×D411yescharacteristic
219C2×C4×C47C4×D411yescharacteristic
220C2×C4×C47C4×D411yescharacteristic
221C2×C4×C47C4×Q811yescharacteristic
222C2×C4×C47C4×Q811yescharacteristic
223C2×C4×C47C4×Q811yescharacteristic
224C2×C4×C47C4×Q811yescharacteristic
225C2×C4×C47#12111yescharacteristic
226C2×C4×C47#12111yescharacteristic
227C2×C4×C47C22⋊Q811yescharacteristic
228C2×C4×C47C22⋊Q811yescharacteristic
229C2×C4×C47#12411yescharacteristic
230C2×C4×C47#12411yescharacteristic
231C2×C4×C47#12511yescharacteristic
232C2×C4×C47#12511yescharacteristic
233C2×C4×C47#12711yescharacteristic
234C2×C4×C47C4⋊Q811yescharacteristic
235C2×C4×C47C4⋊Q811yescharacteristic
236C2×C4×C47C4⋊Q811yescharacteristic
237C2×Dic47—22no—
238C2×Dic47—22no—
239C2×Dic47—22no—
240C2×Dic47—22no—
241C2×Dic47—22no—
242C2×Dic47—22no—
243C2×Dic47—22no—
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—24no—
250C2×Dic47—42no—
251C2×Dic47—42no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254C2×Dic47—42no—
255C2×Dic47—42no—
256C2×Dic47—42no—
257C2×Dic47—42no—
258C2×Dic47—42no—
259C2×Dic47—81no—
260C2×Dic47—81no—
261C2×Dic47—81no—
262C2×Dic47—81no—
263C2×Dic47#9514yes—
264C2×Dic47#9514yes—
265C8×C47—42no—
266C47⋊C8—42no—
267#10850—471nomaximal, Sylow
268C22×C47C2×#9511yescharacteristic
269C22×C47#38011yescharacteristic
270C22×C47#38011yescharacteristic
271C22×C47#38911yescharacteristic
272C22×C47#38911yescharacteristic
273C22×C47#39011yescharacteristic
274C22×C47#39111yescharacteristic
275C22×C47#41611yescharacteristic
276C22×C47#41611yescharacteristic
277C22×C47#41611yescharacteristic
278C22×C47#41611yescharacteristic
279C22×C47#41711yescharacteristic
280C22×C47#41711yescharacteristic
281C22×C47#41811yescharacteristic
282C22×C47#41911yescharacteristic
283C22×C47#42711yescharacteristic
284C22×C47#42711yescharacteristic
285C22×C47#42811yescharacteristic
286C22×C47#42811yescharacteristic
287C22×C47#46311yescharacteristic
288C22×C47#46311yescharacteristic
289C22×C47#46311yescharacteristic
290C22×C47#46311yescharacteristic
291C22×C47#46411yescharacteristic
292C22×C47#46411yescharacteristic
293C22×C47#46411yescharacteristic
294C22×C47#46411yescharacteristic
295C22×C47#47811yescharacteristic
296C22×C47#47811yescharacteristic
297C22×C47#47811yescharacteristic
298C22×C47#47811yescharacteristic
299C22×C47#47911yescharacteristic
300C22×C47#47911yescharacteristic
301C22×C47#47911yescharacteristic
302C22×C47#47911yescharacteristic
303C4×C47—44no—
304C4×C47—82no—
305C4×C47C4×C4⋊C411yescharacteristic
306C4×C47C4×C4⋊C411yescharacteristic
307C4×C47#38211yescharacteristic
308C4×C47#38411yescharacteristic
309C4×C47#38911yescharacteristic
310C4×C47#38911yescharacteristic
311C4×C47#39011yescharacteristic
312C4×C47#39111yescharacteristic
313Dic47—24no—
314Dic47—24no—
315Dic47—44no—
316Dic47—82no—
317C22×C4⋊C8—471no—
318C2×#382—471no—
319C2×C4×C4⋊C4—471no—
320C2×#340—471no—
321C2×#340—471no—
322C2×#340—471no—
323C2×#340D4711yescharacteristic
324C2×C47C4⋊#9511yescharacteristic
325C2×C47#173511yescharacteristic
326C2×C47#173611yescharacteristic
327C2×C47#180411yescharacteristic
328C2×C47#180411yescharacteristic
329C2×C47#180511yescharacteristic
330C2×C47#180511yescharacteristic
331C2×C47#194911yescharacteristic
332C2×C47#194911yescharacteristic
333C2×C47#194911yescharacteristic
334C2×C47#194911yescharacteristic
335C2×C47#198311yescharacteristic
336C2×C47#198311yescharacteristic
337C2×C47#198911yescharacteristic
338C2×C47#198911yescharacteristic
339C23×C8—471no—
340C23×C8C2×D4711yescharacteristic
341C22×C4⋊C4—471no—
342C22×C4⋊C4—471no—
343C22×C4⋊C4C2×D4711yescharacteristic
344C22×C4⋊C4C2×D4711yescharacteristic
345C22×C42—471no—
346C22×C42—941no—
347C2×C4⋊C8—474no—
348C2×C4⋊C8—942no—
349C2×C4⋊C8—942no—
350#382—474no—
351#382—942no—
352C4×C4⋊C4—474no—
353C4×C4⋊C4—942no—
354C2×#95—941no—
355C2×#95—941no—
356C2×#95—941no—
357#340—22no—
358#340—942no—
359#340—942no—
360#340—942no—
361C47#1085011yescharacteristic, complemented, Sylow
362C23×C4—21no—
363C23×C4—21no—
364C23×C4—471no—
365C23×C4—471no—
366C23×C4—941no—
367C23×C4—941no—
368C23×C4C22×D4711yescharacteristic
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—472no—
376C22×C8—941no—
377C22×C8—941no—
378C22×C8—941no—
379C22×C8—941no—
380C22×C8—941no—
381C22×C8—941no—
382C22×C8C4×D4712yes—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—472no—
392C2×C4⋊C4—472no—
393C2×C4⋊C4—472no—
394C2×C4⋊C4—472no—
395C2×C4⋊C4—941no—
396C2×C4⋊C4—941no—
397C2×C4⋊C4—941no—
398C2×C4⋊C4—941no—
399C2×C4⋊C4—941no—
400C2×C4⋊C4—941no—
401C2×C4⋊C4—941no—
402C2×C4⋊C4—941no—
403C2×C4⋊C4Dic9412yes—
404C2×C4⋊C4C4×D4712yes—
405C2×C4⋊C4C4×D4712yes—
406C2×C4⋊C4C22⋊D4712yes—
407C2×C42—472no—
408C2×C42—472no—
409C2×C42—472no—
410C2×C42—472no—
411C2×C42—472no—
412C2×C42—472no—
413C2×C42—944no—
414C2×C42—1882no—
415C2×C42—1882no—
416C4⋊C8—948no—
417#95—944no—
418#95—944no—
419#95—944no—
420C24D4×D4711yescharacteristic
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—472no—
436C22×C4—472no—
437C22×C4—472no—
438C22×C4—472no—
439C22×C4—472no—
440C22×C4—472no—
441C22×C4—941no—
442C22×C4—941no—
443C22×C4—941no—
444C22×C4—941no—
445C22×C4—941no—
446C22×C4—941no—
447C22×C4—941no—
448C22×C4—941no—
449C22×C4—942no—
450C22×C4—942no—
451C22×C4—942no—
452C22×C4—942no—
453C22×C4—1881no—
454C22×C4—1881no—
455C22×C4—1881no—
456C22×C4—1881no—
457C22×C4—1881no—
458C22×C4—1881no—
459C22×C4—1881no—
460C22×C4—1881no—
461C22×C4—1881no—
462C22×C4—1881no—
463C22×C4C2×Dic9411yescharacteristic
464C22×C4C2×C4×D4711yescharacteristic
465C22×C4C2×C4×D4711yescharacteristic
466C22×C4C2×C4×D4711yescharacteristic
467C22×C4#1062535011yescharacteristic
468C22×C4#1062535011yescharacteristic
469C22×C4D4×D4711yescharacteristic
470C22×C4D4×D4711yescharacteristic
471C22×C4D4×D4711yescharacteristic
472C22×C4#1062535211yescharacteristic
473C22×C4#1062535211yescharacteristic
474C22×C4Q8×D4711yescharacteristic
475C22×C4Q8×D4711yescharacteristic
476C22×C4C2×C22⋊D4711yescharacteristic
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—942no—
485C2×C8—942no—
486C2×C8—942no—
487C2×C8—1881no—
488C2×C8—1881no—
489C2×C8—1881no—
490C2×C8—1881no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—474no—
499C4⋊C4—942no—
500C4⋊C4—942no—
501C4⋊C4—942no—
502C4⋊C4—942no—
503C4⋊C4—942no—
504C4⋊C4—1881no—
505C4⋊C4—1881no—
506C4⋊C4Dic47⋊C414yes—
507C42—474no—
508C42—474no—
509C42—474no—
510C42—474no—
511C42—1888no—
512C23C22⋊C4×D4711yescharacteristic
513C23C22⋊C4×D4711yescharacteristic
514C23C4⋊C4×D4711yescharacteristic
515C23#1309399611yescharacteristic
516C23#1309399711yescharacteristic
517C23#1309400111yescharacteristic
518C23#1309400211yescharacteristic
519C23#1309404311yescharacteristic
520C23#1309404511yescharacteristic
521C23#1309404511yescharacteristic
522C23#1309404711yescharacteristic
523C23#1309404811yescharacteristic
524C23#1309405111yescharacteristic
525C23#1309405311yescharacteristic
526C23#1309405611yescharacteristic
527C2×C4—24no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—81no—
538C2×C4—81no—
539C2×C4—81no—
540C2×C4—81no—
541C2×C4—474no—
542C2×C4—474no—
543C2×C4—942no—
544C2×C4—942no—
545C2×C4—942no—
546C2×C4—942no—
547C2×C4—942no—
548C2×C4—942no—
549C2×C4—942no—
550C2×C4—942no—
551C2×C4—942no—
552C2×C4—942no—
553C2×C4—942no—
554C2×C4—942no—
555C2×C4—944no—
556C2×C4—3761no—
557C2×C4—3761no—
558C2×C4—3761no—
559C2×C4—3761no—
560C2×C4—1882no—
561C2×C4—1882no—
562C2×C4—1882no—
563C2×C4—1882no—
564C2×C4—1882no—
565C2×C4—1882no—
566C2×C4—1882no—
567C2×C4—1882no—
568C2×C4—1882no—
569C2×C4C42×D4711yescharacteristic
570C2×C4C22⋊C4×D4711yescharacteristic
571C2×C4C4⋊C4×D4711yescharacteristic
572C2×C4C4⋊C4×D4711yescharacteristic
573C2×C4C4⋊C4×D4711yescharacteristic
574C2×C4C2×Dic47⋊C411yescharacteristic
575C2×C4#1309398011yescharacteristic
576C2×C4#1309398111yescharacteristic
577C2×C4(C22⋊D47)⋊C411yescharacteristic
578C2×C4(C22⋊D47)⋊C411yescharacteristic
579C2×C4C4×C22⋊D4711yescharacteristic
580C2×C4C4×C22⋊D4711yescharacteristic
581C2×C4#1309398911yescharacteristic
582C2×C4#1309398911yescharacteristic
583C2×C4C4×Dic9411yescharacteristic
584C2×C4C4×Dic9411yescharacteristic
585C2×C4#1309399611yescharacteristic
586C2×C4#1309399711yescharacteristic
587C2×C4#1309400111yescharacteristic
588C2×C4#1309400211yescharacteristic
589C2×C4#1309401011yescharacteristic
590C2×C4#1309401011yescharacteristic
591C2×C4#1309401411yescharacteristic
592C2×C4#1309401411yescharacteristic
593C2×C4#1309402011yescharacteristic
594C2×C4#1309402211yescharacteristic
595C2×C4#1309402311yescharacteristic
596C2×C4#1309402311yescharacteristic
597C8—42no—
598C8—1882no—
599C22#95×D4711yescharacteristic
600C22#1568898111yescharacteristic
601C22#1568898211yescharacteristic
602C22#1568901811yescharacteristic
603C22#1568902011yescharacteristic
604C22#1568902311yescharacteristic
605C22#1568902711yescharacteristic
606C22#1568911611yescharacteristic
607C22#1568911611yescharacteristic
608C22#1568911811yescharacteristic
609C22#1568911811yescharacteristic
610C22#1568912111yescharacteristic
611C22#1568912311yescharacteristic
612C22#1568912611yescharacteristic
613C22#1568913011yescharacteristic
614C22#1568915811yescharacteristic
615C22#1568916011yescharacteristic
616C22#1568916211yescharacteristic
617C22#1568916411yescharacteristic
618C22#1568933611yescharacteristic
619C22#1568933711yescharacteristic
620C22#1568934011yescharacteristic
621C22#1568934111yescharacteristic
622C22#1568934311yescharacteristic
623C22#1568934411yescharacteristic
624C22#1568934711yescharacteristic
625C22#1568934811yescharacteristic
626C22#1568942111yescharacteristic
627C22#1568942211yescharacteristic
628C22#1568942511yescharacteristic
629C22#1568942611yescharacteristic
630C22#1568942811yescharacteristic
631C22#1568942911yescharacteristic
632C22#1568943211yescharacteristic
633C22#1568943311yescharacteristic
634C4—44no—
635C4—82no—
636C4—944no—
637C4—944no—
638C4—3762no—
639C4—1884no—
640C4#1568897411yescharacteristic
641C4C4×Dic47⋊C411yescharacteristic
642C4#1568898711yescharacteristic
643C4#1568899211yescharacteristic
644C4#1568901811yescharacteristic
645C4#1568902011yescharacteristic
646C4#1568902311yescharacteristic
647C4#1568902711yescharacteristic
648C2Dic47⋊#9511yescharacteristic
649C2#2024310311yescharacteristic
650C2#2024310611yescharacteristic
651C2#2024339611yescharacteristic
652C2#2024339711yescharacteristic
653C2#2024340111yescharacteristic
654C2#2024340211yescharacteristic
655C2#2024415311yescharacteristic
656C2#2024415511yescharacteristic
657C2#2024415711yescharacteristic
658C2#2024415911yescharacteristic
659C2#2024431711yescharacteristic
660C2#2024431911yescharacteristic
661C2#2024434211yescharacteristic
662C2#2024434411yescharacteristic
subgroupG/H
centerC24D4×D47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C47×#340C2
socle, prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenterC2×#340D47
hypocenterC47#10850
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
15. C2×Dic47⋊C8C4semidirect
17. #15688988C4semidirect
19. C4⋊C4×Dic47C4semidirect
361. C47#10850semidirect

Maximal subgroups

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

subgroupindex
C22×Dic47⋊C82
C2×#156889882
C2×C4⋊C4×Dic472
C2×#156888862
C2×#156888852
C2×C47×#3402
#1085047