Finite Group Databasebeta

← #26234426

Subgroups — #26234426

Order 12032.

1042 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689195C211yesmaximal, characteristic
2C2×#15689163C211yesmaximal, characteristic, complemented
3C22×#13093955C211yesmaximal, characteristic, complemented
4#20246317C211yesmaximal, characteristic
5#20244156C211yesmaximal, characteristic, complemented
6#20244149C211yesmaximal, characteristic, complemented
7#20243585C211yesmaximal, characteristic, complemented
8#20243581C211yesmaximal, characteristic, complemented
9#20243580C211yesmaximal, characteristic, complemented
10#20243576C211yesmaximal, characteristic, complemented
11#20243554C211yesmaximal, characteristic, complemented
12#20243419C211yesmaximal, characteristic, complemented
13#20243415C211yesmaximal, characteristic, complemented
14#20243286C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C47C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C23×C47⋊C8C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20#15689195C418yescomplemented
21#15689163—24no—
22C2×#13093957C2211yescharacteristic
23C2×#13093957C2211yescharacteristic
24C2×#13093957C2211yescharacteristic
25C2×#13093957C2211yescharacteristic
26C2×#13093955—24no—
27C2×#13093955C2211yescharacteristic
28C2×#13093955C2211yescharacteristic
29C2×#13093955C2211yescharacteristic
30C2×#13093955C2211yescharacteristic
31C2×#13093955C2211yescharacteristic
32C2×#13093955C2211yescharacteristic
33C2×C4⋊(C47⋊C8)C2211yescharacteristic
34C2×C22⋊(C47⋊C8)C2211yescharacteristic
35C2×C22⋊(C47⋊C8)C2211yescharacteristic
36C2×#13093935C2211yescharacteristic
37#15689016—21no—
38#15689009—21no—
39#15689003—21no—
40#15688989C2211yescharacteristic
41#15688983C2211yescharacteristic
42#15688983C2211yescharacteristic
43C4×C4⋊Dic47C2211yescharacteristic
44C22⋊C4×Dic47—21no—
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51C2×C4×D4×C47—21no—
52C2×C4×D4×C47C2211yescharacteristic
53C22×C4⋊C4×C47C2211yescharacteristic
54C22×C4⋊C4×C47C2211yescharacteristic
55C47×#389—21no—
56C47×#385—21no—
57C47×#385—21no—
58C47×#384C2211yescharacteristic
59C47×#380C2211yescharacteristic
60C47×#380C2211yescharacteristic
61C4×C4⋊C4×C47C2211yescharacteristic
62C23×Dic47—21no—
63C2×#10625329—22no—
64C2×#10625329—22no—
65C2×#10625329C2×C414yescomplemented
66C22×C47⋊C8—22no—
67C22×C47⋊C8—22no—
68C22×C47⋊C8C2×C414yescomplemented
69C22×C47⋊C8C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73#13093983—22no—
74#13093983—41no—
75C2×C4⋊Dic47—22no—
76C2×C4⋊Dic47—21no—
77C2×C4⋊Dic47—41no—
78C2×C4⋊Dic47C2311yescharacteristic
79C2×C4⋊Dic47C2311yescharacteristic
80C2×C4⋊Dic47C2311yescharacteristic
81C2×C4⋊Dic47C2311yescharacteristic
82C2×C22⋊Dic47—21no—
83C2×C22⋊Dic47—21no—
84C2×C22⋊Dic47—21no—
85C2×C4×Dic47—21no—
86C2×C4×Dic47—21no—
87#13093957—22no—
88#13093957—22no—
89#13093957—22no—
90#13093957—41no—
91#13093955—22no—
92#13093955—22no—
93#13093955—22no—
94#13093955—22no—
95#13093955—41no—
96#13093955D414yescomplemented
97C4⋊(C47⋊C8)C2×C414yescomplemented
98C22⋊(C47⋊C8)C2×C414yescomplemented
99C22⋊(C47⋊C8)C2×C414yescomplemented
100#13093935C2×C414yescomplemented
101C47⋊#95—21no—
102C47⋊#95—21no—
103C47⋊#95—21no—
104C47⋊#95—21no—
105C47⋊#95—21no—
106C22×D4×C47D411yescharacteristic
107C23×C4×C47—21no—
108C23×C4×C47—21no—
109C23×C4×C47C2311yescharacteristic
110C23×C4×C47C2311yescharacteristic
111C4×D4×C47—44no—
112C4×D4×C47C2×C414yes—
113C4×D4×C47Q814yes—
114C2×C4⋊C4×C47—22no—
115C2×C4⋊C4×C47—22no—
116C2×C4⋊C4×C47—21no—
117C2×C4⋊C4×C47—21no—
118C2×C4⋊C4×C47—21no—
119C2×C4⋊C4×C47—21no—
120C2×C4⋊C4×C47—41no—
121C2×C4⋊C4×C47—41no—
122C2×C4⋊C4×C47D411yescharacteristic
123C2×C4⋊C4×C47C2311yescharacteristic
124C2×C4⋊C4×C47C2311yescharacteristic
125C2×C4⋊C4×C47C2311yescharacteristic
126C2×C4⋊C4×C47C2311yescharacteristic
127C2×C22⋊C4×C47—21no—
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47D411yescharacteristic
130C2×C22⋊C4×C47D411yescharacteristic
131C2×C42×C47—21no—
132C2×C42×C47C2311yescharacteristic
133#95×C47—21no—
134#95×C47—21no—
135#95×C47—21no—
136C24×C47C2×D411yescharacteristic
137C24×C47C2×D411yescharacteristic
138C2×D4×C47—22no—
139C2×D4×C47—22no—
140C2×D4×C47C4⋊C414yes—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—42no—
154C22×C4×C47—42no—
155C22×C4×C47—42no—
156C22×C4×C47—42no—
157C22×C4×C47—81no—
158C22×C4×C47—81no—
159C22×C4×C47C22×C412yes—
160C22×C4×C47C22×C412yes—
161C22×C4×C47C2×D411yescharacteristic
162C22×C4×C47C2×D411yescharacteristic
163C22×C4×C47C2×D411yescharacteristic
164C22×C4×C47C2×D411yescharacteristic
165C22×C4×C47C2×Q812yes—
166C22×C4×C47C2×Q812yes—
167C22×C4×C47C2411yescharacteristic
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—42no—
173C22×Dic47—42no—
174C22×Dic47—81no—
175C4⋊C4×C47—21no—
176C4⋊C4×C47—21no—
177C4⋊C4×C47—21no—
178C4⋊C4×C47—21no—
179C4⋊C4×C47—21no—
180C4⋊C4×C47—21no—
181C4⋊C4×C47—21no—
182C4⋊C4×C47—42no—
183C4⋊C4×C47—42no—
184C4⋊C4×C47—42no—
185C4⋊C4×C47—81no—
186C4⋊C4×C47C4⋊C414yes—
187C4⋊C4×C47C2×D412yes—
188C22⋊C4×C47—42no—
189C22⋊C4×C47—42no—
190C22⋊C4×C47C4⋊C414yes—
191C22⋊C4×C47C4⋊C414yes—
192C42×C47—42no—
193C42×C47C22×C412yes—
194C42×C47C2×Q812yes—
195C22⋊Dic47—42no—
196C22⋊Dic47—42no—
197C22⋊Dic47—81no—
198C4⋊Dic47—21no—
199C4⋊Dic47—21no—
200C4⋊Dic47—21no—
201C4⋊Dic47—21no—
202C4⋊Dic47—21no—
203C4⋊Dic47—21no—
204C4⋊Dic47—21no—
205C4⋊Dic47—42no—
206C4⋊Dic47C2×D412yes—
207C4×Dic47—42no—
208C4×Dic47—81no—
209#10625329—28no—
210C2×C47⋊C8—21no—
211C2×C47⋊C8—21no—
212C2×C47⋊C8—21no—
213C2×C47⋊C8—21no—
214C2×C47⋊C8—21no—
215C2×C47⋊C8—21no—
216C2×C47⋊C8—28no—
217C2×C47⋊C8C22×C412yes—
218C2×C47⋊C8C22×C412yes—
219C2×C47⋊C8C22×C412yes—
220C2×C47⋊C8C22×C412yes—
221C2×C47⋊C8C2×D412yes—
222C2×C47⋊C8#4112yes—
223C23×C47—21no—
224C23×C47—21no—
225C23×C47—21no—
226C23×C47—21no—
227C23×C47—21no—
228C23×C47—21no—
229C23×C47—21no—
230C23×C47—21no—
231C23×C47—21no—
232C23×C47—21no—
233C23×C47C2×C4⋊C412yes—
234C23×C47C2×C4⋊C412yes—
235C23×C47AGL(1,ℤ/8)12yes—
236C23×C47#13712yes—
237C23×C47C22×D411yescharacteristic
238D4×C47—28no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
244C2×C4×C47—21no—
245C2×C4×C47—21no—
246C2×C4×C47—21no—
247C2×C4×C47—22no—
248C2×C4×C47—22no—
249C2×C4×C47—22no—
250C2×C4×C47—22no—
251C2×C4×C47—22no—
252C2×C4×C47—22no—
253C2×C4×C47—22no—
254C2×C4×C47—22no—
255C2×C4×C47—22no—
256C2×C4×C47—41no—
257C2×C4×C47—41no—
258C2×C4×C47—41no—
259C2×C4×C47—41no—
260C2×C4×C47—41no—
261C2×C4×C47—41no—
262C2×C4×C47—41no—
263C2×C4×C47—41no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
266C2×C4×C47—41no—
267C2×C4×C47—84no—
268C2×C4×C47—84no—
269C2×C4×C47C2×C4⋊C412yes—
270C2×C4×C47C2×C4⋊C412yes—
271C2×C4×C47C2×C4⋊C412yes—
272C2×C4×C47C2×C4⋊C412yes—
273C2×C4×C47C23×C411yescharacteristic
274C2×C4×C47C22×D411yescharacteristic
275C2×C4×C47C22×Q811yescharacteristic
276C2×C4×C47C2×#4111yescharacteristic
277C2×C4×C47H(5,𝔽2)11yescharacteristic
278C2×C4×C472−1+411yescharacteristic
279C2×Dic47—22no—
280C2×Dic47—41no—
281C2×Dic47—41no—
282C2×Dic47—41no—
283C2×Dic47—41no—
284C2×Dic47—41no—
285C2×Dic47—41no—
286C2×Dic47—41no—
287C2×Dic47—41no—
288C2×Dic47—41no—
289C2×Dic47—41no—
290C2×Dic47—41no—
291C2×Dic47—84no—
292C47⋊C8—22no—
293C47⋊C8—22no—
294C47⋊C8—22no—
295C47⋊C8C4×D414yescomplemented
296#22659—471nomaximal, Sylow
297C22×C47—22no—
298C22×C47—22no—
299C22×C47—22no—
300C22×C47—22no—
301C22×C47—22no—
302C22×C47—22no—
303C22×C47—22no—
304C22×C47—22no—
305C22×C47—22no—
306C22×C47—41no—
307C22×C47—41no—
308C22×C47—41no—
309C22×C47—41no—
310C22×C47#42814yescomplemented
311C22×C47C22×C4⋊C411yescharacteristic
312C22×C47D4211yescharacteristic
313C22×C47#54711yescharacteristic
314C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
315C22×C47C2×#13711yescharacteristic
316C22×C47#57711yescharacteristic
317C22×C47#57711yescharacteristic
318C4×C47—22no—
319C4×C47—22no—
320C4×C47—22no—
321C4×C47—22no—
322C4×C47—42no—
323C4×C47—81no—
324C4×C47—81no—
325C4×C47—81no—
326C4×C47C2×C4×D411yescharacteristic
327C4×C47#52011yescharacteristic
328C4×C47D4×Q811yescharacteristic
329C4×C47#55411yescharacteristic
330Dic47—42no—
331Dic47—81no—
332Dic47—81no—
333Dic47—81no—
334C2×#435—471no—
335C2×#428—471no—
336C22×#106—471no—
337#2352—471no—
338D4×C4⋊C4D4711yescharacteristic
339#1949—471no—
340#1948—471no—
341#1854—471no—
342#1853—471no—
343#1853—471no—
344#1852—471no—
345#1847—471no—
346#1809—471no—
347#1808—471no—
348#1776—471no—
349C2×C47—24no—
350C2×C47—42no—
351C2×C47D4×C4⋊C411yescharacteristic
352C2×C47C2×#42811yescharacteristic
353C2×C47#291211yescharacteristic
354C2×C47#326511yescharacteristic
355C2×C47#326611yescharacteristic
356C2×C47#334411yescharacteristic
357C2×C47#334511yescharacteristic
358C22×M16—471no—
359C23×C8—471no—
360C2×C4×D4—21no—
361C2×C4×D4C2×D4711yescharacteristic
362C2×#117—471no—
363C22×C4⋊C4—471no—
364C22×C4⋊C4C2×D4711yescharacteristic
365C22×C4⋊C4C2×D4711yescharacteristic
366#435—478no—
367#428—944no—
368C2×#107—471no—
369C2×#107—471no—
370C2×#107—471no—
371C2×#107—471no—
372C2×#106—471no—
373C2×#106—471no—
374C2×#106—471no—
375C2×#106—471no—
376C2×#106—471no—
377C2×#106—471no—
378C2×#106—944no—
379C2×C4⋊C8—471no—
380C2×C22⋊C8—471no—
381C2×C22⋊C8—471no—
382C2×#97—471no—
383#389—21no—
384#388—941no—
385#387—941no—
386#386—941no—
387#385—21no—
388#385—21no—
389#384C2×D4711yescharacteristic
390#382—471no—
391#380—471no—
392#380—471no—
393#380C2×D4711yescharacteristic
394#380C2×D4711yescharacteristic
395C4×C4⋊C4—471no—
396C4×C4⋊C4C2×D4711yescharacteristic
397C4×C22⋊C4—941no—
398#340—471no—
399#340—471no—
400#340—471no—
401#340—471no—
402#340—471no—
403#340—471no—
404C47#2265911yescharacteristic, complemented, Sylow
405C22×D4C22⋊D4711yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—941no—
409C23×C4C22×D4711yescharacteristic
410C23×C4C22×D4711yescharacteristic
411C2×M16—474no—
412C2×M16—942no—
413C2×M16—942no—
414C22×C8—471no—
415C22×C8—474no—
416C22×C8—471no—
417C22×C8—471no—
418C22×C8—471no—
419C22×C8—942no—
420C22×C8—942no—
421C4×D4—44no—
422C4×D4Dic9414yes—
423C4×D4C4×D4714yes—
424#117—942no—
425#117—1881no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—41no—
433C2×C4⋊C4—41no—
434C2×C4⋊C4—471no—
435C2×C4⋊C4—471no—
436C2×C4⋊C4—471no—
437C2×C4⋊C4—471no—
438C2×C4⋊C4—942no—
439C2×C4⋊C4—941no—
440C2×C4⋊C4—1881no—
441C2×C4⋊C4C22⋊D4711yescharacteristic
442C2×C4⋊C4C22×D4711yescharacteristic
443C2×C4⋊C4C22×D4711yescharacteristic
444C2×C4⋊C4C22×D4711yescharacteristic
445C2×C4⋊C4C22×D4711yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—941no—
449C2×C22⋊C4—941no—
450C2×C22⋊C4—941no—
451C2×C22⋊C4C22⋊D4711yescharacteristic
452C2×C22⋊C4C22⋊D4711yescharacteristic
453C2×C42—21no—
454C2×C42—941no—
455C2×C42—941no—
456C2×C42C22×D4711yescharacteristic
457#107—942no—
458#107—942no—
459#107—942no—
460#107—1881no—
461#106—474no—
462#106—942no—
463#106—942no—
464#106—942no—
465#106—942no—
466#106—1881no—
467C4⋊C8—474no—
468C22⋊C8—474no—
469C22⋊C8—474no—
470#97—474no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—941no—
475#95—941no—
476#95—941no—
477#95—941no—
478#95—941no—
479C24C2×C22⋊D4711yescharacteristic
480C24C2×C22⋊D4711yescharacteristic
481C2×D4—22no—
482C2×D4—22no—
483C2×D4Dic47⋊C414yes—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4—941no—
503C22×C4—941no—
504C22×C4—941no—
505C22×C4—941no—
506C22×C4—3761no—
507C22×C4—1882no—
508C22×C4—1882no—
509C22×C4C2×Dic9412yes—
510C22×C4C2×Dic9412yes—
511C22×C4C2×C4×D4712yes—
512C22×C4C2×C4×D4712yes—
513C22×C4C2×C22⋊D4711yescharacteristic
514C22×C4C2×C22⋊D4711yescharacteristic
515C22×C4C2×C22⋊D4711yescharacteristic
516C22×C4C2×C22⋊D4711yescharacteristic
517C22×C4C23×D4711yescharacteristic
518M16—948no—
519C2×C8—472no—
520C2×C8—472no—
521C2×C8—472no—
522C2×C8—472no—
523C2×C8—472no—
524C2×C8—472no—
525C2×C8—948no—
526C2×C8—941no—
527C2×C8—941no—
528C2×C8—941no—
529C2×C8—941no—
530C2×C8—941no—
531C2×C8—941no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—81no—
543C4⋊C4—472no—
544C4⋊C4—941no—
545C4⋊C4—941no—
546C4⋊C4—941no—
547C4⋊C4—941no—
548C4⋊C4—941no—
549C4⋊C4—941no—
550C4⋊C4—941no—
551C4⋊C4—1882no—
552C4⋊C4Dic47⋊C414yes—
553C4⋊C4D4×D4712yes—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—3761no—
557C22⋊C4—1882no—
558C22⋊C4—1882no—
559C22⋊C4Dic47⋊C414yes—
560C22⋊C4Dic47⋊C414yes—
561C42—42no—
562C42—3761no—
563C42—1882no—
564C42C2×Dic9412yes—
565C42C2×C4×D4712yes—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23C2×Dic47⋊C412yes—
577C23C2×Dic47⋊C412yes—
578C23#1309405012yes—
579C23#1309405512yes—
580C23C22×C22⋊D4711yescharacteristic
581D4—28no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—84no—
611C2×C4—84no—
612C2×C4—942no—
613C2×C4—3764no—
614C2×C4—1881no—
615C2×C4—1881no—
616C2×C4—1881no—
617C2×C4—1881no—
618C2×C4—1881no—
619C2×C4—1881no—
620C2×C4—1881no—
621C2×C4—1881no—
622C2×C4—1881no—
623C2×C4—1881no—
624C2×C4—1881no—
625C2×C4C2×Dic47⋊C412yes—
626C2×C4C2×Dic47⋊C412yes—
627C2×C4C2×Dic47⋊C412yes—
628C2×C4C2×Dic47⋊C412yes—
629C2×C4C22×C4×D4711yescharacteristic
630C2×C4C2×D4×D4711yescharacteristic
631C2×C4C22×Dic9411yescharacteristic
632C2×C4#41×D4711yescharacteristic
633C2×C4#1309406911yescharacteristic
634C2×C4#1309407111yescharacteristic
635C8—474no—
636C8—942no—
637C8—942no—
638C8—942no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22#1568916314yescomplemented
653C22C22×Dic47⋊C411yescharacteristic
654C22D4×C22⋊D4711yescharacteristic
655C22#1568977211yescharacteristic
656C22C2×#1309405011yescharacteristic
657C22C2×#1309405511yescharacteristic
658C22#1568993111yescharacteristic
659C22#1568993411yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—42no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4—3761no—
669C4—3761no—
670C4—3761no—
671C4—1882no—
672C4C4×D4×D4711yescharacteristic
673C4#1568960211yescharacteristic
674C4D4×Dic9411yescharacteristic
675C4#1568983211yescharacteristic
676C2—24no—
677C2—42no—
678C2D4×Dic47⋊C411yescharacteristic
679C2C2×#1568916311yescharacteristic
680C2#2025198111yescharacteristic
681C2#2025487911yescharacteristic
682C2#2025489911yescharacteristic
683C2#2025583711yescharacteristic
684C2#2025585811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingD4×C4⋊C4×C47C2
socleC23×C47C22×D4
prime radicalC22×D4×C47D4
cosocleC22×C4×C47C24
hypercenterD4×C4⋊C4D47
hypocenterC47#22659
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#15689163C2semidirect
3. C22×#13093955C2semidirect
5. #20244156C2semidirect
6. #20244149C2semidirect
7. #20243585C2semidirect
8. #20243581C2semidirect
9. #20243580C2semidirect
10. #20243576C2semidirect
11. #20243554C2semidirect
12. #20243419C2semidirect
13. #20243415C2semidirect
14. #20243286C2semidirect
20. #15689195C4semidirect
65. C2×#10625329C2×C4semidirect
68. C22×C47⋊C8C2×C4semidirect
96. #13093955D4semidirect
97. C4⋊(C47⋊C8)C2×C4semidirect
98. C22⋊(C47⋊C8)C2×C4semidirect
99. C22⋊(C47⋊C8)C2×C4semidirect
100. #13093935C2×C4semidirect
295. C47⋊C8C4×D4semidirect
310. C22×C47#428semidirect
404. C47#22659semidirect
652. C22#15689163semidirect

Maximal subgroups

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

subgroupindex
C2×#156891952
C2×#156891632
C22×#130939552
#202463172
#202441562
#202441492
#202435852
#202435812
#202435802
#202435762
#202435542
#202434192
#202434152
#202432862
D4×C4⋊C4×C472
#2265947