Finite Group Databasebeta

← #385×Dic47 #26137448

Subgroups — #385×Dic47 #26137448

Order 12032.

2782 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×Dic47C211yesmaximal, characteristic
2C2×#15688998C211yesmaximal, characteristic
3C2×C4⋊C4×Dic47C212yesmaximal, complemented
4C2×C22⋊C4×Dic47C211yesmaximal, characteristic
5C2×C22⋊C4×Dic47C211yesmaximal, characteristic
6#20241622C212yesmaximal, complemented
7#20241620C212yesmaximal, complemented
8#20241611C211yesmaximal, characteristic
9#20241610C211yesmaximal, characteristic
10#95×Dic47C212yesmaximal, complemented
11C2×C47×#385C211yesmaximal, characteristic
12C24×Dic47C2211yescharacteristic
13C24×Dic47C2211yescharacteristic
14C22×C4⋊Dic47C2212yes—
15C22×C22⋊Dic47C2211yescharacteristic
16C22×C22⋊Dic47C2211yescharacteristic
17C22×C4×Dic47—24no—
18C22×C4×Dic47—28no—
19C22×C4×Dic47C2212yes—
20C22×C4×Dic47C2211yescharacteristic
21C22×C4×Dic47C2211yescharacteristic
22C22×C4×Dic47C2212yes—
23C22×C4×Dic47C2212yes—
24#15688998C418yescomplemented
25C4⋊C4×Dic47—28no—
26C22⋊C4×Dic47—24no—
27C22⋊C4×Dic47C418yescomplemented
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C24×C4×C47C2211yescharacteristic
37C22×C4⋊C4×C47C2212yes—
38C22×C22⋊C4×C47C2211yescharacteristic
39C22×C22⋊C4×C47C2211yescharacteristic
40C47×#385C418yescomplemented
41C2×#95×C47C2212yes—
42C23×Dic47—22no—
43C23×Dic47—22no—
44C23×Dic47—24no—
45C23×Dic47—24no—
46C23×Dic47—24no—
47C23×Dic47—24no—
48C23×Dic47C2×C414yes—
49C23×Dic47C2×C414yes—
50C23×Dic47D414yes—
51C23×Dic47Q814yes—
52C23×Dic47C2312yes—
53C23×Dic47C2311yescharacteristic
54C23×Dic47C2311yescharacteristic
55C23×Dic47C2311yescharacteristic
56C23×Dic47C2312yes—
57C23×Dic47C2311yescharacteristic
58C2×C4⋊Dic47—24no—
59C2×C4⋊Dic47—24no—
60C2×C4⋊Dic47C2×C418yescomplemented
61C2×C22⋊Dic47—22no—
62C2×C22⋊Dic47—22no—
63C2×C22⋊Dic47—22no—
64C2×C22⋊Dic47—22no—
65C2×C22⋊Dic47C2×C414yes—
66C2×C22⋊Dic47C2×C414yes—
67C2×C4×Dic47—232no—
68C2×C4×Dic47—24no—
69C2×C4×Dic47—24no—
70C2×C4×Dic47—24no—
71C2×C4×Dic47—24no—
72C2×C4×Dic47—24no—
73C2×C4×Dic47—24no—
74C2×C4×Dic47—24no—
75C2×C4×Dic47—22no—
76C2×C4×Dic47—22no—
77C2×C4×Dic47—24no—
78C2×C4×Dic47—24no—
79C2×C4×Dic47C2×C418yescomplemented
80C2×C4×Dic47D418yes—
81C47⋊#95—24no—
82C47⋊#95—24no—
83C47⋊#95—22no—
84C47⋊#95—22no—
85C47⋊#95—24no—
86C47⋊#95—24no—
87C47⋊#95C2×C418yescomplemented
88C47⋊#95C2×C418yescomplemented
89C25×C47C2311yescharacteristic
90C23×C4×C47—22no—
91C23×C4×C47—22no—
92C23×C4×C47—24no—
93C23×C4×C47—24no—
94C23×C4×C47C2×C414yes—
95C23×C4×C47C2311yescharacteristic
96C23×C4×C47C2311yescharacteristic
97C23×C4×C47C2312yes—
98C23×C4×C47C2312yes—
99C2×C4⋊C4×C47—24no—
100C2×C4⋊C4×C47—24no—
101C2×C4⋊C4×C47C2×C418yescomplemented
102C2×C22⋊C4×C47—22no—
103C2×C22⋊C4×C47—22no—
104C2×C22⋊C4×C47C2×C414yes—
105C2×C22⋊C4×C47C2×C414yes—
106C2×C22⋊C4×C47C2×C414yes—
107C2×C22⋊C4×C47C2×C414yes—
108#95×C47C2×C418yescomplemented
109C24×C47—22no—
110C24×C47—22no—
111C24×C47—22no—
112C24×C47—22no—
113C24×C47C22×C412yes—
114C24×C47C22×C412yes—
115C24×C47C22×C412yes—
116C24×C47C2×D412yes—
117C24×C47C2×Q812yes—
118C24×C47#4112yes—
119C24×C47#4112yes—
120C24×C47C2411yescharacteristic
121C22×C4×C47—216no—
122C22×C4×C47—28no—
123C22×C4×C47—28no—
124C22×C4×C47—28no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—216no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—22no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47C22×C412yes—
143C22×C4×C47C22×C412yes—
144C22×C4×C47C22×C414yes—
145C22×C4×C47C22×C414yes—
146C22×C4×C47C22×C414yes—
147C22×C4×C47C22×C414yes—
148C22×C4×C47C2×D414yes—
149C22×C4×C47#4114yes—
150C22×Dic47—28no—
151C22×Dic47—216no—
152C22×Dic47—28no—
153C22×Dic47—28no—
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—22no—
160C22×Dic47—216no—
161C22×Dic47—216no—
162C22×Dic47—28no—
163C22×Dic47—216no—
164C22×Dic47—28no—
165C22×Dic47—22no—
166C22×Dic47—21no—
167C22×Dic47—21no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47—21no—
177C22×Dic47—21no—
178C22×Dic47—22no—
179C22×Dic47C4⋊C4116yescomplemented
180C22×Dic47C22×C412yes—
181C22×Dic47C22×C414yes—
182C22×Dic47C22×C412yes—
183C22×Dic47C22×C412yes—
184C22×Dic47C22×C414yes—
185C22×Dic47C22×C412yes—
186C22×Dic47C2×D412yes—
187C22×Dic47C2×D414yes—
188C22×Dic47C2×D412yes—
189C22×Dic47C2×D414yes—
190C22×Dic47C2×Q812yes—
191C22×Dic47C2×Q812yes—
192C22×Dic47#4114yes—
193C22×Dic47#4114yes—
194C4⋊C4×C47—216no—
195C22⋊C4×C47—28no—
196C22⋊C4×C47C42116yescomplemented
197C22⋊Dic47—28no—
198C22⋊Dic47—28no—
199C4⋊Dic47—216no—
200C4×Dic47—216no—
201C4×Dic47—216no—
202C4×Dic47—216no—
203C4×Dic47—44no—
204C4×Dic47—44no—
205C23×C47—24no—
206C23×C47—24no—
207C23×C47—24no—
208C23×C47—24no—
209C23×C47—24no—
210C23×C47—24no—
211C23×C47—22no—
212C23×C47—24no—
213C23×C47—22no—
214C23×C47—22no—
215C23×C47—24no—
216C23×C47—22no—
217C23×C47—24no—
218C23×C47—24no—
219C23×C47—24no—
220C23×C47—24no—
221C23×C47C2×C4214yes—
222C23×C47C2×C4⋊C414yes—
223C23×C47#11714yes—
224C23×C47C4×D414yes—
225C23×C47C4×D414yes—
226C23×C47C4×Q814yes—
227C23×C47C4×Q814yes—
228C23×C47C23×C411yescharacteristic
229C23×C47C23×C411yescharacteristic
230C23×C47C23×C411yescharacteristic
231C23×C47C22×D411yescharacteristic
232C23×C47C22×D412yes—
233C23×C47C22×Q811yescharacteristic
234C23×C47C2×#4112yes—
235C23×C47C2×#4112yes—
236C23×C47C2×#4111yescharacteristic
237C23×C47C2×#4112yes—
238C23×C47C2×#4111yescharacteristic
239C2×C4×C47—232no—
240C2×C4×C47—24no—
241C2×C4×C47—24no—
242C2×C4×C47—24no—
243C2×C4×C47—24no—
244C2×C4×C47—24no—
245C2×C4×C47—24no—
246C2×C4×C47—24no—
247C2×C4×C47—24no—
248C2×C4×C47—24no—
249C2×C4×C47—24no—
250C2×C4×C47—24no—
251C2×C4×C47—24no—
252C2×C4×C47—22no—
253C2×C4×C47—22no—
254C2×C4×C47—24no—
255C2×C4×C47—24no—
256C2×C4×C47—41no—
257C2×C4×C47—41no—
258C2×C4×C47—42no—
259C2×C4×C47—41no—
260C2×C4×C47—41no—
261C2×C4×C47—42no—
262C2×C4×C47C2×C4218yescomplemented
263C2×C4×C47C4×D418yes—
264C2×Dic47—232no—
265C2×Dic47—24no—
266C2×Dic47—24no—
267C2×Dic47—24no—
268C2×Dic47—22no—
269C2×Dic47—24no—
270C2×Dic47—24no—
271C2×Dic47—22no—
272C2×Dic47—24no—
273C2×Dic47—24no—
274C2×Dic47—24no—
275C2×Dic47—232no—
276C2×Dic47—24no—
277C2×Dic47—24no—
278C2×Dic47—24no—
279C2×Dic47—22no—
280C2×Dic47—22no—
281C2×Dic47—24no—
282C2×Dic47—24no—
283C2×Dic47—41no—
284C2×Dic47—41no—
285C2×Dic47—42no—
286C2×Dic47—41no—
287C2×Dic47—41no—
288C2×Dic47—42no—
289C2×Dic47—42no—
290C2×Dic47—42no—
291C2×Dic47—42no—
292C2×Dic47—42no—
293C2×Dic47C2×C4⋊C414yes—
294C2×Dic47C2×C4⋊C414yes—
295C2×Dic47C4×D418yes—
296C2×Dic47C4×D418yes—
297C2×Dic47#12014yes—
298C2×Dic47C22⋊Q818yes—
299C2×Dic47#12314yes—
300C4×#385—471nomaximal, Sylow
301C22×C47—28no—
302C22×C47—24no—
303C22×C47—28no—
304C22×C47—24no—
305C22×C47—24no—
306C22×C47—24no—
307C22×C47—24no—
308C22×C47—24no—
309C22×C47—28no—
310C22×C47—28no—
311C22×C47C4×C4⋊C418yescomplemented
312C22×C47C22×C4211yescharacteristic
313C22×C47C22×C4⋊C411yescharacteristic
314C22×C47C2×#11711yescharacteristic
315C22×C47C2×C4×D412yes—
316C22×C47C2×C4×D412yes—
317C22×C47C2×C4×D411yescharacteristic
318C22×C47C2×C4×D411yescharacteristic
319C22×C47C2×C4×D412yes—
320C22×C47C2×C4×Q811yescharacteristic
321C22×C47C2×C4×Q811yescharacteristic
322C22×C47C4×#4112yes—
323C22×C47C4×#4112yes—
324C22×C47C4×#4112yes—
325C22×C47C2×#12011yescharacteristic
326C22×C47C2×C22⋊Q812yes—
327C22×C47C2×#12311yescharacteristic
328C22×C47#52512yes—
329C22×C47#52511yescharacteristic
330C22×C47#52511yescharacteristic
331C22×C47#52512yes—
332C22×C47#52912yes—
333C22×C47#52912yes—
334C22×C47#53312yes—
335C4×C47—28no—
336C4×C47—28no—
337C4×C47—42no—
338C4×C47—42no—
339Dic47—24no—
340Dic47—28no—
341Dic47—44no—
342Dic47—42no—
343Dic47—42no—
344Dic47#38518yesdirect product factor
345C23×C42—471no—
346C2×#385—471no—
347C2×#385D4711yescharacteristic
348C2×C4×C4⋊C4—472no—
349C2×C4×C22⋊C4—471no—
350C2×C4×C22⋊C4—471no—
351#1436—472no—
352#1436—472no—
353C22⋊#95—471no—
354C22⋊#95—471no—
355C4×#95—472no—
356C2×C47—28no—
357C2×C47C2×C4×C4⋊C411yescharacteristic
358C2×C47C42×D412yes—
359C2×C47C2×#38511yescharacteristic
360C2×C47#229012yes—
361C2×C47#229611yescharacteristic
362C2×C47C4×#12011yescharacteristic
363C2×C47C4×#12011yescharacteristic
364C2×C47C4×#12311yescharacteristic
365C2×C47C4×#12311yescharacteristic
366C2×C47C4×C22⋊Q812yes—
367C2×C47C4×C22⋊Q812yes—
368C24×C4—471no—
369C24×C4—471no—
370C24×C4C2×D4711yescharacteristic
371C22×C4⋊C4—472no—
372C22×C4⋊C4C2×D4712yes—
373C22×C22⋊C4—471no—
374C22×C22⋊C4—471no—
375C22×C22⋊C4C2×D4711yescharacteristic
376C22×C22⋊C4C2×D4711yescharacteristic
377C22×C42—472no—
378C22×C42—472no—
379C22×C42—472no—
380C22×C42—471no—
381C22×C42—471no—
382C22×C42—948no—
383C22×C42—944no—
384#385—478no—
385#385Dic4718yesdirect product factor
386C4×C4⋊C4—948no—
387C4×C22⋊C4—478no—
388C4×C22⋊C4—944no—
389C2×#95—472no—
390C2×#95—472no—
391C2×#95—472no—
392C2×#95—472no—
393C2×#95—472no—
394C2×#95—472no—
395C2×#95—471no—
396C2×#95—471no—
397C2×#95C2×D4712yes—
398C47C4×#38511yescharacteristic, complemented, Sylow
399C25C22×D4711yescharacteristic
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—471no—
405C23×C4—474no—
406C23×C4—474no—
407C23×C4—474no—
408C23×C4—472no—
409C23×C4—471no—
410C23×C4—474no—
411C23×C4—471no—
412C23×C4—471no—
413C23×C4—472no—
414C23×C4—944no—
415C23×C4—944no—
416C23×C4—944no—
417C23×C4—944no—
418C23×C4—942no—
419C23×C4—942no—
420C23×C4C2×Dic4714yes—
421C23×C4C22×D4711yescharacteristic
422C23×C4C22×D4711yescharacteristic
423C23×C4C22×D4712yes—
424C23×C4C22×D4712yes—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—478no—
428C2×C4⋊C4—944no—
429C2×C4⋊C4—944no—
430C2×C4⋊C4C2×Dic4718yescomplemented
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—474no—
434C2×C22⋊C4—474no—
435C2×C22⋊C4—942no—
436C2×C22⋊C4—942no—
437C2×C22⋊C4—942no—
438C2×C22⋊C4—942no—
439C2×C22⋊C4C4×D4714yes—
440C2×C22⋊C4C4×D4714yes—
441C2×C22⋊C4C2×Dic4714yes—
442C2×C22⋊C4C2×Dic4714yes—
443C2×C42—478no—
444C2×C42—478no—
445C2×C42—944no—
446C2×C42—944no—
447C2×C42—944no—
448C2×C42—944no—
449C2×C42—944no—
450C2×C42—944no—
451C2×C42—9432no—
452C2×C42—944no—
453C2×C42—942no—
454C2×C42—942no—
455C2×C42—944no—
456C2×C42—944no—
457#95—478no—
458#95—478no—
459#95—944no—
460#95—942no—
461#95—942no—
462#95—944no—
463#95—944no—
464#95—944no—
465#95C2×Dic4718yescomplemented
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24C2×C4×D4712yes—
471C24C2×C4×D4712yes—
472C24D4×D4712yes—
473C24#1062535212yes—
474C24Q8×D4712yes—
475C24#1062535412yes—
476C24C22×Dic4712yes—
477C24C23×D4711yescharacteristic
478C22×C4—28no—
479C22×C4—216no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—216no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—472no—
500C22×C4—474no—
501C22×C4—472no—
502C22×C4—472no—
503C22×C4—474no—
504C22×C4—4716no—
505C22×C4—472no—
506C22×C4—474no—
507C22×C4—472no—
508C22×C4—474no—
509C22×C4—472no—
510C22×C4—474no—
511C22×C4—472no—
512C22×C4—474no—
513C22×C4—472no—
514C22×C4—948no—
515C22×C4—9416no—
516C22×C4—9416no—
517C22×C4—948no—
518C22×C4—9416no—
519C22×C4—948no—
520C22×C4—948no—
521C22×C4—9416no—
522C22×C4—948no—
523C22×C4—942no—
524C22×C4—942no—
525C22×C4—942no—
526C22×C4—942no—
527C22×C4—942no—
528C22×C4—942no—
529C22×C4—942no—
530C22×C4—941no—
531C22×C4—941no—
532C22×C4—942no—
533C22×C4—942no—
534C22×C4—942no—
535C22×C4—942no—
536C22×C4—942no—
537C22×C4—942no—
538C22×C4—942no—
539C22×C4—942no—
540C22×C4—942no—
541C22×C4—941no—
542C22×C4—941no—
543C22×C4C2×C4×D4714yes—
544C22×C4C2×C4×D4714yes—
545C22×C4D4×D4714yes—
546C22×C4#1062535214yes—
547C22×C4C22×Dic4712yes—
548C22×C4C22×Dic4712yes—
549C22×C4C22×Dic4714yes—
550C22×C4C22×Dic4714yes—
551C4⋊C4—216no—
552C4⋊C4—9416no—
553C22⋊C4—28no—
554C22⋊C4—948no—
555C22⋊C4—948no—
556C22⋊C4C4×Dic47116yescomplemented
557C42—9416no—
558C42—9416no—
559C42—9416no—
560C42—1884no—
561C42—1884no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—22no—
569C23—24no—
570C23—22no—
571C23—22no—
572C23—24no—
573C23—22no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23C2×C4×Dic4714yes—
579C23C4⋊C4×D4714yes—
580C23#1309398214yes—
581C23#1309398614yes—
582C23D4×Dic4714yes—
583C23#1309398914yes—
584C23Q8×Dic4714yes—
585C23C22×C4×D4711yescharacteristic
586C23C22×C4×D4711yescharacteristic
587C23C23×Dic4711yescharacteristic
588C23C2×D4×D4711yescharacteristic
589C23C2×D4×D4712yes—
590C23C2×Q8×D4711yescharacteristic
591C23#41×D4712yes—
592C23#41×D4712yes—
593C23C2×#1062535211yescharacteristic
594C23C2×#1062535212yes—
595C23C2×#1062535411yescharacteristic
596C2×C4—232no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—474no—
620C2×C4—478no—
621C2×C4—474no—
622C2×C4—478no—
623C2×C4—474no—
624C2×C4—474no—
625C2×C4—478no—
626C2×C4—9432no—
627C2×C4—9432no—
628C2×C4—944no—
629C2×C4—944no—
630C2×C4—944no—
631C2×C4—942no—
632C2×C4—944no—
633C2×C4—944no—
634C2×C4—942no—
635C2×C4—944no—
636C2×C4—944no—
637C2×C4—944no—
638C2×C4—944no—
639C2×C4—944no—
640C2×C4—944no—
641C2×C4—942no—
642C2×C4—942no—
643C2×C4—944no—
644C2×C4—944no—
645C2×C4—1881no—
646C2×C4—1881no—
647C2×C4—1882no—
648C2×C4—1881no—
649C2×C4—1881no—
650C2×C4—1882no—
651C2×C4—1882no—
652C2×C4—1882no—
653C2×C4—1882no—
654C2×C4—1882no—
655C2×C4C2×C4×Dic4718yescomplemented
656C2×C4D4×Dic4718yes—
657C22—24no—
658C22—28no—
659C22—24no—
660C22—24no—
661C22—24no—
662C22—24no—
663C22—24no—
664C22—28no—
665C22—28no—
666C22—28no—
667C22C4⋊C4×Dic4718yescomplemented
668C22C22×C4×Dic4711yescharacteristic
669C22C2×C4⋊C4×D4711yescharacteristic
670C22C2×#1309398211yescharacteristic
671C22C4×D4×D4712yes—
672C22C4×D4×D4712yes—
673C22C2×#1309398611yescharacteristic
674C22C2×D4×Dic4711yescharacteristic
675C22C2×D4×Dic4712yes—
676C22C2×#1309398911yescharacteristic
677C22C2×Q8×Dic4711yescharacteristic
678C22C4×#1062535212yes—
679C22C4×#1062535212yes—
680C22#41×Dic4712yes—
681C22#120×D4711yescharacteristic
682C22C22⋊Q8×D4712yes—
683C22#123×D4711yescharacteristic
684C22#1568962912yes—
685C22#1568962911yescharacteristic
686C22#1568963111yescharacteristic
687C22#1568963612yes—
688C22#1568965012yes—
689C22#1568965912yes—
690C22#1568967512yes—
691C4—28no—
692C4—28no—
693C4—42no—
694C4—42no—
695C4—478no—
696C4—944no—
697C4—948no—
698C4—1884no—
699C4—1882no—
700C4—1882no—
701C2—28no—
702C2C2×C4⋊C4×Dic4711yescharacteristic
703C2C4×D4×Dic4712yes—
704C2#385×D4711yescharacteristic
705C2#2024582412yes—
706C2#2024586711yescharacteristic
707C2#2024588911yescharacteristic
708C2#120×Dic4711yescharacteristic
709C2#2024590711yescharacteristic
710C2#123×Dic4711yescharacteristic
711C2#2024592012yes—
712C2C22⋊Q8×Dic4712yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC2×C47×#385C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#385D47
hypocenterC47C4×#385
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic47C2semidirect
6. #20241622C2semidirect
7. #20241620C2semidirect
10. #95×Dic47C2semidirect
24. #15688998C4semidirect
27. C22⋊C4×Dic47C4semidirect
40. C47×#385C4semidirect
60. C2×C4⋊Dic47C2×C4semidirect
79. C2×C4×Dic47C2×C4semidirect
87. C47⋊#95C2×C4semidirect
88. C47⋊#95C2×C4semidirect
101. C2×C4⋊C4×C47C2×C4semidirect
108. #95×C47C2×C4semidirect
179. C22×Dic47C4⋊C4semidirect
196. C22⋊C4×C47C42semidirect
262. C2×C4×C47C2×C42semidirect
311. C22×C47C4×C4⋊C4semidirect
344. Dic47#385direct (N × H)
385. #385Dic47direct (N × H)
398. C47C4×#385semidirect
430. C2×C4⋊C4C2×Dic47semidirect
465. #95C2×Dic47semidirect
556. C22⋊C4C4×Dic47semidirect
655. C2×C4C2×C4×Dic47semidirect
667. C22C4⋊C4×Dic47semidirect

Maximal subgroups

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

subgroupindex
C23×C4×Dic472
C2×#156889982
C2×C4⋊C4×Dic472
C2×C22⋊C4×Dic472
#202416222
#202416202
#202416112
#202416102
#95×Dic472
C2×C47×#3852
C4×#38547