Finite Group Databasebeta

← #26183637

Subgroups — #26183637

Order 12032.

1470 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic
2#20245771C211yesmaximal, characteristic, complemented
3#20241961C212yesmaximal, complemented
4#20241957C212yesmaximal, complemented
5#20241945C214yesmaximal, complemented
6#20241880C214yesmaximal, complemented
7C22×C22⋊C8×C47C211yesmaximal, characteristic, complemented
8C22×#10625350C411yescharacteristic, complemented
9#15689634—21no—
10#15689634—21no—
11#15689634—21no—
12#15689634—21no—
13#15689634C412yescomplemented
14#15689634C412yescomplemented
15#15689634C2212yes—
16#15689634C2212yes—
17C2×#13094007—21no—
18C2×#13094003C411yescharacteristic, complemented
19C2×#13094003C2211yescharacteristic
20C2×#13093998C411yescharacteristic, complemented
21C2×#13093998C2211yescharacteristic
22C2×#13093993—21no—
23C2×C4×C22⋊D47—21no—
24C2×C4×C22⋊D47—21no—
25C2×#13093983—21no—
26C2×#13093983C411yescharacteristic, complemented
27#15688986C2212yescomplemented
28#15688983—21no—
29#15688983C2212yes—
30#15688979—21no—
31C4×C22⋊Dic47—21no—
32C4×C22⋊Dic47C2212yescomplemented
33#15688861C2218yescomplemented
34#15688858C2218yescomplemented
35C24×C4×C47C2211yescharacteristic
36C23×C8×C47—21no—
37C2×C22⋊C8×C47—21no—
38C2×C22⋊C8×C47—21no—
39C2×C22⋊C8×C47—21no—
40C2×C22⋊C8×C47C2212yes—
41C2×C22⋊C8×C47C2212yescomplemented
42C2×C22⋊C8×C47C2212yescomplemented
43C2×#10625350—21no—
44C2×#10625350—21no—
45C2×#10625350—44no—
46C2×#10625350C2×C412yes—
47C2×#10625350C2×C412yes—
48C22×Dic94C2×C411yescharacteristic
49C22×D188C2×C411yescharacteristic
50C22×C22⋊D47—21no—
51C22×C22⋊D47—21no—
52C22×C22⋊D47—21no—
53C22×C4×D47—21no—
54#13094007—22no—
55#13094007—22no—
56#13094007—22no—
57#13094007—22no—
58#13094003—21no—
59#13094003—21no—
60#13094003—21no—
61#13094003—21no—
62#13094003C2×C412yes—
63#13094003C2×C412yes—
64#13094003C2×C412yes—
65#13094003C2312yes—
66#13093998—21no—
67#13093998—21no—
68#13093998—21no—
69#13093998—21no—
70#13093998C2×C412yes—
71#13093998C2×C412yes—
72#13093998C2×C412yes—
73#13093998C2312yes—
74#13093993—22no—
75#13093993—22no—
76#13093993—22no—
77#13093993—22no—
78C4×C22⋊D47—22no—
79C4×C22⋊D47—22no—
80C4×C22⋊D47—22no—
81C4×C22⋊D47—22no—
82C4×C22⋊D47—22no—
83C4×C22⋊D47—22no—
84C4×C22⋊D47—22no—
85C4×C22⋊D47—22no—
86#13093983—21no—
87#13093983—21no—
88#13093983—44no—
89#13093983C2×C412yes—
90#13093983C2×C412yes—
91C2×C4⋊Dic47—22no—
92C2×C4⋊Dic47C2×C411yescharacteristic
93C2×C4⋊Dic47C2×C411yescharacteristic
94C2×Dic47⋊C4—21no—
95C2×Dic47⋊C4—21no—
96C2×C22⋊Dic47—21no—
97C2×C22⋊Dic47—21no—
98C2×C22⋊Dic47—21no—
99C2×C22⋊Dic47—22no—
100C2×C22⋊Dic47—22no—
101C2×C22⋊Dic47—22no—
102C2×(C2×D47)⋊C4—21no—
103C2×(C2×D47)⋊C4—21no—
104C2×C4×Dic47—21no—
105C2×C4×Dic47—22no—
106C47⋊#95—22no—
107C47⋊#95C2314yes—
108C25×C47D411yescharacteristic
109C23×C4×C47—44no—
110C23×C4×C47C2×C411yescharacteristic
111C23×C4×C47C2×C411yescharacteristic
112C23×C4×C47C2×C411yescharacteristic
113C23×C4×C47C2×C411yescharacteristic
114C23×C4×C47D411yescharacteristic
115C23×C4×C47D411yescharacteristic
116C23×C4×C47D411yescharacteristic
117C23×C4×C47D411yescharacteristic
118C23×C4×C47D411yescharacteristic
119C23×C4×C47D411yescharacteristic
120C23×C4×C47D411yescharacteristic
121C23×C4×C47C2311yescharacteristic
122C23×C4×C47C2311yescharacteristic
123C23×C4×C47C2311yescharacteristic
124C22×C8×C47—22no—
125C22×C8×C47—22no—
126C22×C8×C47—22no—
127C22×C8×C47—44no—
128C22⋊C8×C47—22no—
129C22⋊C8×C47—22no—
130C22⋊C8×C47—22no—
131C22⋊C8×C47C2314yes—
132C24×C47—24no—
133C24×C47—42no—
134C24×C47—42no—
135C24×C47C22⋊C411yescharacteristic
136C24×C47C22⋊C411yescharacteristic
137C24×C47C22⋊C411yescharacteristic
138C24×C47C22⋊C411yescharacteristic
139C24×C47C2×D411yescharacteristic
140C24×C47C2×D411yescharacteristic
141C24×C47C2×D411yescharacteristic
142C23×D47—21no—
143C22×C4×C47—24no—
144C22×C4×C47—24no—
145C22×C4×C47—24no—
146C22×C4×C47—42no—
147C22×C4×C47—42no—
148C22×C4×C47—42no—
149C22×C4×C47—42no—
150C22×C4×C47—42no—
151C22×C4×C47—42no—
152C22×C4×C47—42no—
153C22×C4×C47—42no—
154C22×C4×C47—42no—
155C22×C4×C47—42no—
156C22×C4×C47—42no—
157C22×C4×C47C22⋊C411yescharacteristic
158C22×C4×C47C22⋊C411yescharacteristic
159C22×C4×C47C22⋊C411yescharacteristic
160C22×C4×C47C22⋊C411yescharacteristic
161C22×C4×C47C22⋊C411yescharacteristic
162C22×C4×C47C22⋊C411yescharacteristic
163C22×C4×C47C22⋊C411yescharacteristic
164C22×C4×C47C22⋊C411yescharacteristic
165C22×C4×C47C22⋊C411yescharacteristic
166C22×C4×C47C22⋊C411yescharacteristic
167C22×C4×C47C22⋊C411yescharacteristic
168C22×C4×C47C22⋊C411yescharacteristic
169C22×C4×C47C22×C411yescharacteristic
170C22×C4×C47C22×C411yescharacteristic
171C22×C4×C47C22×C411yescharacteristic
172C22×C4×C47C22×C411yescharacteristic
173C22×C4×C47C22×C411yescharacteristic
174C22×C4×C47C22×C411yescharacteristic
175C22×C4×C47C2×D411yescharacteristic
176C22×C4×C47C2×D411yescharacteristic
177C22×C4×C47C2×D411yescharacteristic
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2×D411yescharacteristic
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2411yescharacteristic
185C2×C22⋊D47—22no—
186C2×C22⋊D47—22no—
187C2×C22⋊D47—22no—
188C2×C22⋊D47—22no—
189C2×C22⋊D47—22no—
190C2×C22⋊D47—22no—
191C2×C22⋊D47—44no—
192C2×C22⋊D47—44no—
193C2×C22⋊D47—44no—
194C22×Dic47—21no—
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—24no—
198#10625350—44no—
199#10625350—44no—
200#10625350—44no—
201#10625350—44no—
202C2×D188—21no—
203C2×D188—42no—
204C2×D188C22×C412yes—
205C2×C4×D47—22no—
206C2×C4×D47—22no—
207C2×C4×D47—44no—
208C2×Dic94—21no—
209C2×Dic94—42no—
210C2×Dic94C22×C412yes—
211C2×C8×C47—24no—
212C2×C8×C47—44no—
213C2×C8×C47—44no—
214C2×C8×C47—44no—
215C22⋊Dic47—22no—
216C22⋊Dic47—22no—
217C22⋊Dic47—22no—
218C22⋊Dic47—22no—
219C22⋊Dic47—22no—
220C22⋊Dic47—22no—
221C22⋊Dic47—44no—
222C22⋊Dic47—44no—
223C22⋊Dic47—44no—
224(C2×D47)⋊C4—22no—
225(C2×D47)⋊C4—22no—
226(C2×D47)⋊C4—22no—
227(C2×D47)⋊C4—22no—
228C4⋊Dic47—21no—
229C4⋊Dic47—21no—
230C4⋊Dic47—44no—
231C4⋊Dic47C22×C412yes—
232C4⋊Dic47C22×C412yes—
233Dic47⋊C4—22no—
234Dic47⋊C4—22no—
235Dic47⋊C4—22no—
236Dic47⋊C4—22no—
237C4×Dic47—22no—
238C4×Dic47—22no—
239C4×Dic47—44no—
240C23×C47—22no—
241C23×C47—22no—
242C23×C47—22no—
243C23×C47—22no—
244C23×C47—22no—
245C23×C47—22no—
246C23×C47—22no—
247C23×C47—22no—
248C23×C47—22no—
249C23×C47—22no—
250C23×C47—22no—
251C23×C47—22no—
252C23×C47—41no—
253C23×C47—41no—
254C23×C47—41no—
255C23×C47—41no—
256C23×C47—41no—
257C23×C47—41no—
258C23×C47—41no—
259C23×C47—41no—
260C23×C47—416no—
261C23×C47C2×C22⋊C411yescharacteristic
262C23×C47C2×C22⋊C411yescharacteristic
263C23×C47C2×C22⋊C411yescharacteristic
264C23×C47C2×C22⋊C411yescharacteristic
265C23×C47C2×C22⋊C411yescharacteristic
266C23×C47C2×C22⋊C411yescharacteristic
267C23×C47#13514yes—
268C23×C47C22×D411yescharacteristic
269C22×D47—22no—
270C22×D47—42no—
271C22×D47—42no—
272C22×D47—42no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47#9914yes—
301C2×C4×C47C2×C22⋊C411yescharacteristic
302C2×C4×C47C2×C22⋊C411yescharacteristic
303C2×C4×C47C2×C22⋊C411yescharacteristic
304C2×C4×C47C2×C22⋊C411yescharacteristic
305C2×C4×C47C2×C22⋊C411yescharacteristic
306C2×C4×C47C2×C22⋊C411yescharacteristic
307C2×C4×C47C23×C411yescharacteristic
308C2×C4×C47C22×D411yescharacteristic
309C22⋊D47—44no—
310C22⋊D47—44no—
311C22⋊D47—44no—
312C22⋊D47—44no—
313C22⋊D47—44no—
314C22⋊D47—44no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—42no—
319C2×Dic47—42no—
320C2×Dic47—42no—
321C2×Dic47—44no—
322C2×Dic47—44no—
323C2×Dic47—44no—
324D188—42no—
325D188—42no—
326C4×D47—44no—
327C4×D47—44no—
328Dic94—42no—
329Dic94—42no—
330C8×C47—44no—
331#17572—471nomaximal, Sylow
332C22×C47—28no—
333C22×C47—21no—
334C22×C47—21no—
335C22×C47—21no—
336C22×C47—21no—
337C22×C47—21no—
338C22×C47—21no—
339C22×C47—21no—
340C22×C47—21no—
341C22×C47—21no—
342C22×C47—21no—
343C22×C47—21no—
344C22×C47—21no—
345C22×C47—21no—
346C22×C47—21no—
347C22×C47—21no—
348C22×C47—21no—
349C22×C47—44no—
350C22×C47—44no—
351C22×C47—44no—
352C22×C47—44no—
353C22×C47—44no—
354C22×C47—44no—
355C22×C47C2×#9912yes—
356C22×C47#41612yes—
357C22×C47#41612yes—
358C22×C47#42112yes—
359C22×C47C22×C22⋊C411yescharacteristic
360C22×C47C2×#13512yes—
361C2×D47—42no—
362C2×D47—42no—
363C2×D47—42no—
364C2×D47—84no—
365C4×C47—21no—
366C4×C47—21no—
367C4×C47—21no—
368C4×C47—21no—
369C4×C47—21no—
370C4×C47—21no—
371C4×C47C2×#9912yes—
372C4×C47C2×#9912yes—
373Dic47—42no—
374Dic47—42no—
375Dic47—42no—
376Dic47—84no—
377C2×#525—471no—
378C22×C22⋊C8D4711yescharacteristic, complemented
379#2280—471no—
380#1520—472no—
381#1519—472no—
382#1516—474no—
383#1501—474no—
384C2×C47—22no—
385C2×C47—22no—
386C2×C47—22no—
387C2×C47—22no—
388C2×C47—22no—
389C2×C47—41no—
390C2×C47—41no—
391C2×C47C22×#9911yescharacteristic
392C2×C47C2×#41611yescharacteristic
393C2×C47C2×#42111yescharacteristic
394D47—82no—
395C22×#41—471no—
396C24×C4C2×D4711yescharacteristic
397C23×C8—21no—
398#525—472no—
399#525—472no—
400#525—472no—
401#525—472no—
402#525—941no—
403#525—941no—
404#525—941no—
405#525—941no—
406C2×#123—941no—
407C2×C22⋊Q8—471no—
408C2×C22⋊Q8—471no—
409C2×#121—471no—
410C2×#121—471no—
411C2×#120—941no—
412C2×C4×D4—941no—
413C2×C4×D4—941no—
414C2×#117—471no—
415C2×#117—941no—
416C2×C22⋊C8—21no—
417C2×C22⋊C8—21no—
418C2×C22⋊C8—21no—
419C2×C22⋊C8C2×D4712yes—
420C2×C22⋊C8C2×D4712yescomplemented
421C2×C22⋊C8C2×D4712yescomplemented
422#381—472no—
423#380—472no—
424#380—941no—
425#379—941no—
426C4×C22⋊C4—472no—
427C4×C22⋊C4—941no—
428#328—478no—
429#327—478no—
430C47#1757211yescharacteristic, complemented, Sylow
431C25D18811yescharacteristic
432C2×#41—472no—
433C2×#41—472no—
434C2×#41—941no—
435C2×#41—941no—
436C2×#41—1884no—
437C22×Q8—471no—
438C22×D4—471no—
439C22×D4—941no—
440C22×D4—941no—
441C22×D4—941no—
442C23×C4—44no—
443C23×C4—941no—
444C23×C4C4×D4711yescharacteristic
445C23×C4C4×D4711yescharacteristic
446C23×C4C4×D4711yescharacteristic
447C23×C4C4×D4711yescharacteristic
448C23×C4D18811yescharacteristic
449C23×C4D18811yescharacteristic
450C23×C4D18811yescharacteristic
451C23×C4C22⋊D4711yescharacteristic
452C23×C4C22⋊D4711yescharacteristic
453C23×C4C22⋊D4711yescharacteristic
454C23×C4C22⋊D4711yescharacteristic
455C23×C4C22×D4711yescharacteristic
456C23×C4C22×D4711yescharacteristic
457C23×C4C22×D4711yescharacteristic
458C22×C8—22no—
459C22×C8—22no—
460C22×C8—22no—
461C22×C8—44no—
462#123—942no—
463#123—942no—
464#123—942no—
465#123—942no—
466C22⋊Q8—472no—
467C22⋊Q8—472no—
468C22⋊Q8—472no—
469C22⋊Q8—472no—
470C22⋊Q8—941no—
471C22⋊Q8—941no—
472C22⋊Q8—941no—
473C22⋊Q8—941no—
474#121—472no—
475#121—472no—
476#121—472no—
477#121—472no—
478#121—941no—
479#121—941no—
480#121—941no—
481#121—941no—
482#120—942no—
483#120—942no—
484#120—942no—
485#120—942no—
486C4×D4—942no—
487C4×D4—942no—
488C4×D4—942no—
489C4×D4—942no—
490C4×D4—942no—
491C4×D4—942no—
492C4×D4—942no—
493C4×D4—942no—
494#117—472no—
495#117—472no—
496#117—941no—
497#117—941no—
498#117—1884no—
499C2×C4⋊C4—471no—
500C2×C4⋊C4—471no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—942no—
504C2×C22⋊C4—941no—
505C2×C22⋊C4—941no—
506C2×C22⋊C4—941no—
507C2×C22⋊C4—941no—
508C2×C22⋊C4—941no—
509C2×C22⋊C4—942no—
510C2×C22⋊C4—942no—
511C2×C22⋊C4—942no—
512C2×C42—941no—
513C2×C42—942no—
514C22⋊C8—22no—
515C22⋊C8—22no—
516C22⋊C8—22no—
517C22⋊C8C22×D4714yes—
518#95—474no—
519#95—942no—
520C24—24no—
521C24—42no—
522C24—42no—
523C24—941no—
524C24(C2×D47)⋊C411yescharacteristic
525C24(C2×D47)⋊C411yescharacteristic
526C24(C2×D47)⋊C411yescharacteristic
527C24(C2×D47)⋊C411yescharacteristic
528C24C2×D18811yescharacteristic
529C24C2×D18811yescharacteristic
530C24C2×D18811yescharacteristic
531#41—1884no—
532#41—1884no—
533#41—1884no—
534#41—1884no—
535C2×Q8—472no—
536C2×Q8—941no—
537C2×Q8—1882no—
538C2×D4—472no—
539C2×D4—942no—
540C2×D4—942no—
541C2×D4—942no—
542C2×D4—942no—
543C2×D4—942no—
544C2×D4—942no—
545C2×D4—941no—
546C2×D4—1882no—
547C2×D4—1884no—
548C2×D4—1884no—
549C2×D4—1884no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—941no—
565C22×C4—941no—
566C22×C4—941no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4—944no—
570C22×C4—1884no—
571C22×C4(C2×D47)⋊C411yescharacteristic
572C22×C4(C2×D47)⋊C411yescharacteristic
573C22×C4(C2×D47)⋊C411yescharacteristic
574C22×C4(C2×D47)⋊C411yescharacteristic
575C22×C4(C2×D47)⋊C411yescharacteristic
576C22×C4(C2×D47)⋊C411yescharacteristic
577C22×C4(C2×D47)⋊C411yescharacteristic
578C22×C4(C2×D47)⋊C411yescharacteristic
579C22×C4(C2×D47)⋊C411yescharacteristic
580C22×C4(C2×D47)⋊C411yescharacteristic
581C22×C4(C2×D47)⋊C411yescharacteristic
582C22×C4(C2×D47)⋊C411yescharacteristic
583C22×C4C2×C4×D4711yescharacteristic
584C22×C4C2×C4×D4711yescharacteristic
585C22×C4C2×C4×D4711yescharacteristic
586C22×C4C2×C4×D4711yescharacteristic
587C22×C4C2×C4×D4711yescharacteristic
588C22×C4C2×C4×D4711yescharacteristic
589C22×C4C2×D18811yescharacteristic
590C22×C4C2×D18811yescharacteristic
591C22×C4C2×D18811yescharacteristic
592C22×C4C2×C22⋊D4711yescharacteristic
593C22×C4C2×C22⋊D4711yescharacteristic
594C22×C4C2×C22⋊D4711yescharacteristic
595C22×C4C2×C22⋊D4711yescharacteristic
596C22×C4C2×C22⋊D4711yescharacteristic
597C22×C4C2×C22⋊D4711yescharacteristic
598C22×C4C23×D4711yescharacteristic
599C2×C8—24no—
600C2×C8—44no—
601C2×C8—44no—
602C2×C8—44no—
603C4⋊C4—472no—
604C4⋊C4—472no—
605C4⋊C4—942no—
606C4⋊C4—942no—
607C4⋊C4—942no—
608C4⋊C4—941no—
609C4⋊C4—941no—
610C4⋊C4—942no—
611C4⋊C4—1884no—
612C22⋊C4—942no—
613C22⋊C4—942no—
614C22⋊C4—942no—
615C22⋊C4—942no—
616C22⋊C4—942no—
617C22⋊C4—942no—
618C22⋊C4—942no—
619C22⋊C4—942no—
620C22⋊C4—942no—
621C22⋊C4—942no—
622C22⋊C4—1884no—
623C22⋊C4—1884no—
624C22⋊C4—1884no—
625C42—942no—
626C42—942no—
627C42—1884no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—416no—
649C23—942no—
650C23—1882no—
651C23—1882no—
652C23—1882no—
653C23C2×(C2×D47)⋊C411yescharacteristic
654C23C2×(C2×D47)⋊C411yescharacteristic
655C23C2×(C2×D47)⋊C411yescharacteristic
656C23C2×(C2×D47)⋊C411yescharacteristic
657C23C2×(C2×D47)⋊C411yescharacteristic
658C23C2×(C2×D47)⋊C411yescharacteristic
659C23#1309404614yes—
660C23C22×D18811yescharacteristic
661Q8—1882no—
662Q8—1882no—
663D4—1882no—
664D4—1884no—
665D4—1884no—
666D4—1884no—
667D4—1884no—
668D4—1884no—
669D4—1884no—
670D4—1882no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
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—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—942no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—1884no—
702C2×C4—1884no—
703C2×C4—1884no—
704C2×C4—1884no—
705C2×C4—1882no—
706C2×C4—1882no—
707C2×C4—1882no—
708C2×C4—1884no—
709C2×C4#1309393814yes—
710C2×C4C2×(C2×D47)⋊C411yescharacteristic
711C2×C4C2×(C2×D47)⋊C411yescharacteristic
712C2×C4C2×(C2×D47)⋊C411yescharacteristic
713C2×C4C2×(C2×D47)⋊C411yescharacteristic
714C2×C4C2×(C2×D47)⋊C411yescharacteristic
715C2×C4C2×(C2×D47)⋊C411yescharacteristic
716C2×C4C22×C4×D4711yescharacteristic
717C2×C4C22×C22⋊D4711yescharacteristic
718C8—44no—
719C22—28no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—44no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—3764no—
743C22—1882no—
744C22—1882no—
745C22—1882no—
746C22C2×#1309393812yes—
747C22#1568912012yes—
748C22#1568912012yes—
749C22#1568913912yes—
750C22C22×(C2×D47)⋊C411yescharacteristic
751C22C2×#1309404612yes—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—3764no—
759C4—1882no—
760C4—1882no—
761C4—1882no—
762C4C2×#1309393812yes—
763C4C2×#1309393812yes—
764C2—22no—
765C2—22no—
766C2—22no—
767C2—22no—
768C2—22no—
769C2—41no—
770C2—41no—
771C2—3762no—
772C2C22×#1309393811yescharacteristic
773C2C2×#1568912011yescharacteristic
774C2C2×#1568913911yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×C22⋊C8×C47C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#15689634C2
cosocleC22×C4×C47C24
hypercenterC22×C22⋊C8D47
hypocenterC47#17572
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #20245771C2semidirect
3. #20241961C2semidirect
4. #20241957C2semidirect
5. #20241945C2semidirect
6. #20241880C2semidirect
7. C22×C22⋊C8×C47C2semidirect
8. C22×#10625350C4semidirect
13. #15689634C4semidirect
14. #15689634C4semidirect
18. C2×#13094003C4semidirect
20. C2×#13093998C4semidirect
26. C2×#13093983C4semidirect
27. #15688986C22semidirect
32. C4×C22⋊Dic47C22semidirect
33. #15688861C22semidirect
34. #15688858C22semidirect
41. C2×C22⋊C8×C47C22semidirect
42. C2×C22⋊C8×C47C22semidirect
378. C22×C22⋊C8D47semidirect
420. C2×C22⋊C8C2×D47semidirect
421. C2×C22⋊C8C2×D47semidirect
430. C47#17572semidirect

Maximal subgroups

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

subgroupindex
C2×#156896342
#202457712
#202419612
#202419572
#202419452
#202418802
C22×C22⋊C8×C472
#1757247