Finite Group Databasebeta

← #26183555

Subgroups — #26183555

Order 12032.

1438 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
2C2×#15689087C211yesmaximal, characteristic, complemented
3#20241929C214yesmaximal, complemented
4#20241920C212yesmaximal, complemented
5#20241916C212yesmaximal, complemented
6#20241877C214yesmaximal, complemented
7C47×#2280C211yesmaximal, characteristic, complemented
8C22×#10625350C411yescharacteristic, complemented
9C22×#10625329—21no—
10#15689634—21no—
11#15689634—21no—
12#15689634—21no—
13#15689634—21no—
14#15689634C412yescomplemented
15#15689634C412yescomplemented
16#15689634C2212yes—
17#15689634C2212yes—
18C2×#13094007—21no—
19C2×#13094003C411yescharacteristic, complemented
20C2×#13094003C2211yescharacteristic
21C2×#13093998C411yescharacteristic, complemented
22C2×#13093998C2211yescharacteristic
23C2×#13093993—21no—
24C2×C4×C22⋊D47—21no—
25C2×C4×C22⋊D47—21no—
26C2×#13093983C411yescharacteristic, complemented
27#15689087—21no—
28#15689087—21no—
29#15689087C2212yes—
30#15689087C2212yescomplemented
31C2×C22⋊(C47⋊C8)—21no—
32C2×C22⋊(C47⋊C8)C2212yescomplemented
33#15688859C2218yescomplemented
34#15688856C2218yescomplemented
35C24×C4×C47C2211yescharacteristic
36C2×#117×C47—21no—
37C47×#381C2212yes—
38C47×#380—21no—
39C47×#380C2212yescomplemented
40C47×#379—21no—
41C4×C22⋊C4×C47—21no—
42C4×C22⋊C4×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—
54C2×#10625329—22no—
55C2×#10625329—22no—
56C2×#10625329—44no—
57C22×C47⋊C8—22no—
58#13094007—22no—
59#13094007—22no—
60#13094007—22no—
61#13094007—22no—
62#13094003—21no—
63#13094003—21no—
64#13094003—21no—
65#13094003—21no—
66#13094003C2×C412yes—
67#13094003C2×C412yes—
68#13094003C2×C412yes—
69#13094003C2312yes—
70#13093998—21no—
71#13093998—21no—
72#13093998—21no—
73#13093998—21no—
74#13093998C2×C412yes—
75#13093998C2×C412yes—
76#13093998C2×C412yes—
77#13093998C2312yes—
78#13093993—22no—
79#13093993—22no—
80#13093993—22no—
81#13093993—22no—
82C4×C22⋊D47—22no—
83C4×C22⋊D47—22no—
84C4×C22⋊D47—22no—
85C4×C22⋊D47—22no—
86C4×C22⋊D47—22no—
87C4×C22⋊D47—22no—
88C4×C22⋊D47—22no—
89C4×C22⋊D47—22no—
90#13093983—21no—
91#13093983—21no—
92#13093983C2×C412yes—
93#13093983C2×C412yes—
94C2×C4⋊Dic47C2×C411yescharacteristic
95C2×C4⋊Dic47C2×C411yescharacteristic
96C2×Dic47⋊C4—21no—
97C2×Dic47⋊C4—21no—
98C2×C22⋊Dic47—21no—
99C2×C22⋊Dic47—21no—
100C2×C22⋊Dic47—21no—
101C2×(C2×D47)⋊C4—21no—
102C2×(C2×D47)⋊C4—21no—
103C2×C4×Dic47—21no—
104C22⋊(C47⋊C8)—22no—
105C22⋊(C47⋊C8)—22no—
106C22⋊(C47⋊C8)—22no—
107C22⋊(C47⋊C8)C2314yes—
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
124#117×C47—44no—
125C2×C4⋊C4×C47—22no—
126C2×C22⋊C4×C47—22no—
127C2×C22⋊C4×C47—22no—
128C2×C22⋊C4×C47—22no—
129C2×C42×C47—22no—
130#95×C47—22no—
131#95×C47C2314yes—
132C24×C47—42no—
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—24no—
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×C47—42no—
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×C47C22×C411yescharacteristic
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×C47C2×D411yescharacteristic
185C22×C4×C47C2411yescharacteristic
186C2×C22⋊D47—22no—
187C2×C22⋊D47—22no—
188C2×C22⋊D47—22no—
189C2×C22⋊D47—22no—
190C2×C22⋊D47—22no—
191C2×C22⋊D47—22no—
192C2×C22⋊D47—44no—
193C2×C22⋊D47—44no—
194C2×C22⋊D47—44no—
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—21no—
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—
211C4⋊C4×C47—44no—
212C22⋊C4×C47—44no—
213C22⋊C4×C47—44no—
214C22⋊C4×C47—44no—
215C42×C47—44no—
216C22⋊Dic47—22no—
217C22⋊Dic47—22no—
218C22⋊Dic47—22no—
219C22⋊Dic47—22no—
220C22⋊Dic47—22no—
221C22⋊Dic47—22no—
222(C2×D47)⋊C4—22no—
223(C2×D47)⋊C4—22no—
224(C2×D47)⋊C4—22no—
225(C2×D47)⋊C4—22no—
226C4⋊Dic47—21no—
227C4⋊Dic47—21no—
228C4⋊Dic47C22×C412yes—
229C4⋊Dic47C22×C412yes—
230Dic47⋊C4—22no—
231Dic47⋊C4—22no—
232Dic47⋊C4—22no—
233Dic47⋊C4—22no—
234C4×Dic47—22no—
235C4×Dic47—22no—
236#10625329—44no—
237#10625329—44no—
238C2×C47⋊C8—24no—
239C2×C47⋊C8—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—41no—
250C23×C47—41no—
251C23×C47—41no—
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—41no—
261C23×C47—416no—
262C23×C47C2×C22⋊C411yescharacteristic
263C23×C47C2×C22⋊C411yescharacteristic
264C23×C47C2×C22⋊C411yescharacteristic
265C23×C47C2×C22⋊C411yescharacteristic
266C23×C47C2×C22⋊C411yescharacteristic
267C23×C47C2×C22⋊C411yescharacteristic
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—44no—
301C2×C4×C47—44no—
302C2×C4×C47—44no—
303C2×C4×C47#9914yes—
304C2×C4×C47C2×C22⋊C411yescharacteristic
305C2×C4×C47C2×C22⋊C411yescharacteristic
306C2×C4×C47C2×C22⋊C411yescharacteristic
307C2×C4×C47C2×C22⋊C411yescharacteristic
308C2×C4×C47C2×C22⋊C411yescharacteristic
309C2×C4×C47C2×C22⋊C411yescharacteristic
310C2×C4×C47C23×C411yescharacteristic
311C2×C4×C47C22×D411yescharacteristic
312C22⋊D47—44no—
313C22⋊D47—44no—
314C22⋊D47—44no—
315C22⋊D47—44no—
316C22⋊D47—44no—
317C22⋊D47—44no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—42no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324D188—42no—
325D188—42no—
326C4×D47—44no—
327C4×D47—44no—
328Dic94—42no—
329Dic94—42no—
330C47⋊C8—44no—
331#17559—471nomaximal, Sylow
332C22×C47—21no—
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—21no—
350C22×C47—44no—
351C22×C47—44no—
352C22×C47—44no—
353C22×C47—44no—
354C22×C47—44no—
355C22×C47—44no—
356C22×C47—44no—
357C22×C47C2×#9912yes—
358C22×C47#42112yes—
359C22×C47C22×C22⋊C411yescharacteristic
360C22×C47#57512yes—
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×C47—84no—
372C4×C47C2×#9912yes—
373C4×C47C2×#9912yes—
374Dic47—42no—
375Dic47—42no—
376Dic47—42no—
377C2×#525—471no—
378C2×#407—471no—
379#2280D4711yescharacteristic, complemented
380#1513—474no—
381#1511—472no—
382#1510—472no—
383#1501—474no—
384C2×C47—22no—
385C2×C47—22no—
386C2×C47—22no—
387C2×C47—41no—
388C2×C47—41no—
389C2×C47—41no—
390C2×C47—41no—
391C2×C47C22×#9911yescharacteristic
392C2×C47#289611yescharacteristic
393C2×C47C2×#42111yescharacteristic
394D47—82no—
395C22×#41—471no—
396C24×C4C2×D4711yescharacteristic
397C22×M16—941no—
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—21no—
415C2×#117—471no—
416#407—472no—
417#407—472no—
418#407—941no—
419#407—941no—
420C2×C22⋊C8—472no—
421C2×C22⋊C8—941no—
422#381C2×D4712yes—
423#380—21no—
424#380C2×D4712yescomplemented
425#379—21no—
426C4×C22⋊C4—21no—
427C4×C22⋊C4C2×D4712yescomplemented
428#328—478no—
429#327—478no—
430C47#1755911yescharacteristic, complemented, Sylow
431C25C22⋊D4711yescharacteristic
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×C4D18811yescharacteristic
452C23×C4C22⋊D4711yescharacteristic
453C23×C4C22⋊D4711yescharacteristic
454C23×C4C22⋊D4711yescharacteristic
455C23×C4C22×D4711yescharacteristic
456C23×C4C22×D4711yescharacteristic
457C23×C4C22×D4711yescharacteristic
458C2×M16—942no—
459C2×M16—942no—
460C2×M16—1884no—
461C22×C8—942no—
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—44no—
495#117—472no—
496#117—472no—
497#117—941no—
498#117—941no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—471no—
501C2×C4⋊C4—471no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—941no—
508C2×C22⋊C4—941no—
509C2×C22⋊C4—941no—
510C2×C22⋊C4—941no—
511C2×C22⋊C4—941no—
512C2×C42—22no—
513C2×C42—941no—
514C22⋊C8—474no—
515C22⋊C8—942no—
516C22⋊C8—942no—
517C22⋊C8—942no—
518#95—22no—
519#95C22×D4714yes—
520C24—42no—
521C24—42no—
522C24—42no—
523C24—941no—
524C24(C2×D47)⋊C411yescharacteristic
525C24(C2×D47)⋊C411yescharacteristic
526C24(C2×D47)⋊C411yescharacteristic
527C24(C2×D47)⋊C411yescharacteristic
528C24C2×C22⋊D4711yescharacteristic
529C24C2×C22⋊D4711yescharacteristic
530C24C2×C22⋊D4711yescharacteristic
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—24no—
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—42no—
565C22×C4—941no—
566C22×C4—941no—
567C22×C4—941no—
568C22×C4—942no—
569C22×C4—942no—
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×D18811yescharacteristic
593C22×C4C2×D18811yescharacteristic
594C22×C4C2×D18811yescharacteristic
595C22×C4C2×C22⋊D4711yescharacteristic
596C22×C4C2×C22⋊D4711yescharacteristic
597C22×C4C2×C22⋊D4711yescharacteristic
598C22×C4C23×D4711yescharacteristic
599M16—1884no—
600M16—1884no—
601C2×C8—944no—
602C2×C8—1884no—
603C4⋊C4—44no—
604C4⋊C4—472no—
605C4⋊C4—472no—
606C4⋊C4—942no—
607C4⋊C4—942no—
608C4⋊C4—942no—
609C4⋊C4—941no—
610C4⋊C4—941no—
611C4⋊C4—942no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—942no—
616C22⋊C4—942no—
617C22⋊C4—942no—
618C22⋊C4—942no—
619C22⋊C4—942no—
620C22⋊C4—942no—
621C22⋊C4—942no—
622C22⋊C4—942no—
623C22⋊C4—942no—
624C22⋊C4—942no—
625C42—44no—
626C42—942no—
627C42—942no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—416no—
650C23—942no—
651C23—1882no—
652C23—1882no—
653C23—1882no—
654C23C2×(C2×D47)⋊C411yescharacteristic
655C23C2×(C2×D47)⋊C411yescharacteristic
656C23C2×(C2×D47)⋊C411yescharacteristic
657C23C2×(C2×D47)⋊C411yescharacteristic
658C23C2×(C2×D47)⋊C411yescharacteristic
659C23C2×(C2×D47)⋊C411yescharacteristic
660C23C22×C22⋊D4711yescharacteristic
661Q8—1882no—
662Q8—1882no—
663D4—1882no—
664D4—1882no—
665D4—1884no—
666D4—1884no—
667D4—1884no—
668D4—1884no—
669D4—1884no—
670D4—1884no—
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—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—1882no—
705C2×C4—1882no—
706C2×C4—1882no—
707C2×C4—1884no—
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×D18811yescharacteristic
718C8—1884no—
719C22—21no—
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—21no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—3764no—
745C22—1882no—
746C22—1882no—
747C22—1882no—
748C22C2×#1309393812yes—
749C22#1568914112yes—
750C22C22×(C2×D47)⋊C411yescharacteristic
751C22#1568992112yes—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—84no—
759C4—1882no—
760C4—1882no—
761C4—1882no—
762C4C2×#1309393812yes—
763C4C2×#1309393812yes—
764C2—22no—
765C2—22no—
766C2—22no—
767C2—41no—
768C2—41no—
769C2—41no—
770C2—41no—
771C2—3762no—
772C2C22×#1309393811yescharacteristic
773C2#2025190511yescharacteristic
774C2C2×#1568914111yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2280C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#15689634C2
cosocleC22×C4×C47C24
hypercenter#2280D47
hypocenterC47#17559
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×#15689087C2semidirect
3. #20241929C2semidirect
4. #20241920C2semidirect
5. #20241916C2semidirect
6. #20241877C2semidirect
7. C47×#2280C2semidirect
8. C22×#10625350C4semidirect
14. #15689634C4semidirect
15. #15689634C4semidirect
19. C2×#13094003C4semidirect
21. C2×#13093998C4semidirect
26. C2×#13093983C4semidirect
30. #15689087C22semidirect
32. C2×C22⋊(C47⋊C8)C22semidirect
33. #15688859C22semidirect
34. #15688856C22semidirect
39. C47×#380C22semidirect
42. C4×C22⋊C4×C47C22semidirect
379. #2280D47semidirect
424. #380C2×D47semidirect
427. C4×C22⋊C4C2×D47semidirect
430. C47#17559semidirect

Maximal subgroups

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

subgroupindex
C2×#156896342
C2×#156890872
#202419292
#202419202
#202419162
#202418772
C47×#22802
#1755947