Finite Group Databasebeta

← #26221619

Subgroups — #26221619

Order 12032.

1678 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic
2C2×C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
3#20244372C212yesmaximal, complemented
4#20244223C212yesmaximal, complemented
5#20243839C214yesmaximal, complemented
6C4×#13093938C214yesmaximal, complemented
7C47×#2280C211yesmaximal, characteristic, complemented
8C22×#10625350C411yescharacteristic, complemented
9#15689634—21no—
10#15689634—21no—
11#15689634—21no—
12#15689634—21no—
13#15689634—21no—
14#15689634—21no—
15#15689634—21no—
16#15689634—21no—
17C2×#13094007C412yescomplemented
18C2×#13094003C411yescharacteristic, complemented
19C2×#13094003C2211yescharacteristic
20C2×#13093998C411yescharacteristic, complemented
21C2×#13093998C2211yescharacteristic
22C2×#13093993C2212yes—
23C2×C4×C22⋊D47C412yescomplemented
24C2×C4×C22⋊D47C2212yes—
25C2×#13093983C411yescharacteristic, complemented
26C22×C22⋊Dic47C2212yes—
27C22×C4×Dic47—21no—
28C2×#13093938C2218yes—
29C4×C22⋊Dic47—21no—
30C4×C22⋊Dic47—21no—
31C4×C22⋊Dic47C2212yes—
32C4×C22⋊Dic47C2212yes—
33C2×C47⋊#95—21no—
34#15688889C2218yes—
35C24×C4×C47C2211yescharacteristic
36C2×#117×C47—21no—
37C47×#381—21no—
38C47×#380—21no—
39C47×#380C2212yes—
40C47×#379C2212yes—
41C4×C22⋊C4×C47—21no—
42C4×C22⋊C4×C47C2212yes—
43C2×#10625350—21no—
44C2×#10625350—21no—
45C2×#10625350—21no—
46C2×#10625350—21no—
47C2×#10625350—44no—
48C22×Dic94C2×C411yescharacteristic, complemented
49C22×D188C2×C411yescharacteristic, complemented
50C22×C22⋊D47C2×C412yes—
51C22×C22⋊D47C2×C412yes—
52C22×C22⋊D47C2312yes—
53C23×Dic47—22no—
54C22×C4×D47C2×C412yescomplemented
55#13094007—22no—
56#13094007—22no—
57#13094007—22no—
58#13094007—22no—
59#13094003—21no—
60#13094003—21no—
61#13094003—21no—
62#13094003—21no—
63#13094003—21no—
64#13094003—21no—
65#13094003—21no—
66#13094003—21no—
67#13093998—21no—
68#13093998—21no—
69#13093998—21no—
70#13093998—21no—
71#13093998—21no—
72#13093998—21no—
73#13093998—21no—
74#13093998—21no—
75#13093993—22no—
76#13093993—22no—
77#13093993—22no—
78#13093993—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—
86C4×C22⋊D47—22no—
87#13093983—21no—
88#13093983—21no—
89#13093983—21no—
90#13093983—21no—
91C2×C4⋊Dic47C2×C411yescharacteristic, complemented
92C2×C4⋊Dic47C2×C411yescharacteristic, complemented
93C2×Dic47⋊C4C2×C412yescomplemented
94C2×Dic47⋊C4C2×C412yescomplemented
95C2×C22⋊Dic47—22no—
96C2×C22⋊Dic47—28no—
97C2×C22⋊Dic47C2×C412yes—
98C2×C22⋊Dic47C2×C412yes—
99C2×C22⋊Dic47C2312yes—
100C2×C22⋊Dic47C2314yes—
101C2×(C2×D47)⋊C4C2×C412yescomplemented
102C2×(C2×D47)⋊C4C2×C412yescomplemented
103C2×C4×Dic47—22no—
104C2×C4×Dic47—22no—
105C2×C4×Dic47—44no—
106C2×C4×Dic47C2×C412yescomplemented
107#13093938—216no—
108C47⋊#95—22no—
109C47⋊#95—22no—
110C25×C47C2311yescharacteristic
111C23×C4×C47—44no—
112C23×C4×C47C2×C411yescharacteristic
113C23×C4×C47C2×C411yescharacteristic
114C23×C4×C47C2×C411yescharacteristic
115C23×C4×C47C2×C411yescharacteristic
116C23×C4×C47D411yescharacteristic
117C23×C4×C47D411yescharacteristic
118C23×C4×C47D411yescharacteristic
119C23×C4×C47D411yescharacteristic
120C23×C4×C47D411yescharacteristic
121C23×C4×C47D411yescharacteristic
122C23×C4×C47D411yescharacteristic
123C23×C4×C47D411yescharacteristic
124C23×C4×C47C2311yescharacteristic
125C23×C4×C47C2311yescharacteristic
126#117×C47—44no—
127C2×C4⋊C4×C47—22no—
128C2×C22⋊C4×C47—22no—
129C2×C22⋊C4×C47—22no—
130C2×C22⋊C4×C47C2314yes—
131C2×C42×C47—22no—
132#95×C47—22no—
133#95×C47—22no—
134C24×C47—24no—
135C24×C47—42no—
136C24×C47—42no—
137C24×C47C22×C411yescharacteristic
138C24×C47C22×C411yescharacteristic
139C24×C47C2×D411yescharacteristic
140C24×C47C2×D411yescharacteristic
141C24×C47C2×D411yescharacteristic
142C24×C47C2×D411yescharacteristic
143C24×C47C2411yescharacteristic
144C23×D47C22×C412yes—
145C22×C4×C47—24no—
146C22×C4×C47—24no—
147C22×C4×C47—24no—
148C22×C4×C47—24no—
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×C47—42no—
159C22×C4×C47—42no—
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×C47C22×C411yescharacteristic
177C22×C4×C47C22×C411yescharacteristic
178C22×C4×C47C22×C411yescharacteristic
179C22×C4×C47C22×C411yescharacteristic
180C22×C4×C47C2×D411yescharacteristic
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C2×C22⋊D47—22no—
189C2×C22⋊D47—22no—
190C2×C22⋊D47—22no—
191C2×C22⋊D47—22no—
192C2×C22⋊D47—22no—
193C2×C22⋊D47—22no—
194C2×C22⋊D47—28no—
195C2×C22⋊D47—44no—
196C2×C22⋊D47—44no—
197C22×Dic47—28no—
198C22×Dic47—24no—
199C22×Dic47—44no—
200C22×Dic47—44no—
201C22×Dic47C22×C412yes—
202C22×Dic47C22×C412yes—
203C22×Dic47C22×C412yes—
204#10625350—44no—
205#10625350—44no—
206#10625350—44no—
207#10625350—44no—
208C2×D188—21no—
209C2×D188—21no—
210C2×D188—42no—
211C2×C4×D47—22no—
212C2×C4×D47—22no—
213C2×C4×D47—44no—
214C2×Dic94—21no—
215C2×Dic94—21no—
216C2×Dic94—42no—
217C4⋊C4×C47—44no—
218C22⋊C4×C47—28no—
219C22⋊C4×C47—44no—
220C22⋊C4×C47—44no—
221C42×C47—44no—
222C22⋊Dic47—28no—
223C22⋊Dic47—22no—
224C22⋊Dic47—22no—
225C22⋊Dic47—22no—
226C22⋊Dic47—22no—
227C22⋊Dic47—22no—
228C22⋊Dic47—22no—
229C22⋊Dic47—24no—
230C22⋊Dic47#4118yescomplemented
231(C2×D47)⋊C4—22no—
232(C2×D47)⋊C4—22no—
233(C2×D47)⋊C4—22no—
234(C2×D47)⋊C4—22no—
235C4⋊Dic47—21no—
236C4⋊Dic47—21no—
237C4⋊Dic47—21no—
238C4⋊Dic47—21no—
239Dic47⋊C4—22no—
240Dic47⋊C4—22no—
241Dic47⋊C4—22no—
242Dic47⋊C4—22no—
243C4×Dic47—22no—
244C4×Dic47—22no—
245C4×Dic47—44no—
246C4×Dic47—44no—
247C23×C47—22no—
248C23×C47—22no—
249C23×C47—22no—
250C23×C47—22no—
251C23×C47—22no—
252C23×C47—22no—
253C23×C47—22no—
254C23×C47—22no—
255C23×C47—22no—
256C23×C47—22no—
257C23×C47—22no—
258C23×C47—22no—
259C23×C47—41no—
260C23×C47—41no—
261C23×C47—41no—
262C23×C47—41no—
263C23×C47—41no—
264C23×C47—41no—
265C23×C47—41no—
266C23×C47—41no—
267C23×C47—416no—
268C23×C47C2×C22⋊C411yescharacteristic
269C23×C47C2×C22⋊C411yescharacteristic
270C23×C47C2×C22⋊C411yescharacteristic
271C23×C47C2×C22⋊C411yescharacteristic
272C23×C47C23×C411yescharacteristic
273C23×C47C22×D411yescharacteristic
274C23×C47C22×D411yescharacteristic
275C23×C47C2×#4114yes—
276C22×D47—22no—
277C22×D47—24no—
278C22×D47—42no—
279C22×D47—42no—
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—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—44no—
308C2×C4×C47—44no—
309C2×C4×C47—44no—
310C2×C4×C47#9914yescomplemented
311C2×C4×C47C2×C22⋊C411yescharacteristic
312C2×C4×C47C2×C22⋊C411yescharacteristic
313C2×C4×C47C2×C22⋊C411yescharacteristic
314C2×C4×C47C2×C22⋊C411yescharacteristic
315C2×C4×C47C2×C22⋊C411yescharacteristic
316C2×C4×C47C2×C22⋊C411yescharacteristic
317C2×C4×C47C2×C22⋊C411yescharacteristic
318C2×C4×C47C2×C22⋊C411yescharacteristic
319C22⋊D47—44no—
320C22⋊D47—44no—
321C22⋊D47—44no—
322C22⋊D47—44no—
323C22⋊D47—44no—
324C22⋊D47—44no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—24no—
329C2×Dic47—28no—
330C2×Dic47—44no—
331C2×Dic47—416no—
332C2×Dic47—44no—
333C2×Dic47—42no—
334C2×Dic47—42no—
335D188—42no—
336D188—42no—
337C4×D47—44no—
338C4×D47—44no—
339Dic94—42no—
340Dic94—42no—
341#21420—471nomaximal, Sylow
342C22×C47—28no—
343C22×C47—21no—
344C22×C47—21no—
345C22×C47—21no—
346C22×C47—21no—
347C22×C47—21no—
348C22×C47—21no—
349C22×C47—21no—
350C22×C47—21no—
351C22×C47—21no—
352C22×C47—21no—
353C22×C47—21no—
354C22×C47—21no—
355C22×C47—21no—
356C22×C47—21no—
357C22×C47—21no—
358C22×C47—21no—
359C22×C47—44no—
360C22×C47—44no—
361C22×C47—44no—
362C22×C47—44no—
363C22×C47—44no—
364C22×C47—44no—
365C22×C47C2×#9912yes—
366C22×C47#41012yes—
367C22×C47C22×C22⋊C411yescharacteristic
368C22×C47C4×#4112yes—
369C22×C47#52512yes—
370C22×C47#53212yes—
371C2×D47—42no—
372C2×D47—42no—
373C2×D47—42no—
374C2×D47—84no—
375C4×C47—21no—
376C4×C47—21no—
377C4×C47—21no—
378C4×C47—21no—
379C4×C47—21no—
380C4×C47—21no—
381C4×C47—84no—
382C4×C47C2×#9912yes—
383C4×C47C2×#9912yes—
384Dic47—48no—
385Dic47—42no—
386Dic47—42no—
387Dic47—42no—
388C2×#525—471no—
389#2280D4711yescharacteristic, complemented
390C2×C4×C22⋊C4—471no—
391#1996—472no—
392#1964—472no—
393#1898—474no—
394C4×#99—474no—
395C2×C47—22no—
396C2×C47—22no—
397C2×C47—22no—
398C2×C47—22no—
399C2×C47—22no—
400C2×C47—41no—
401C2×C47—41no—
402C2×C47#229711yescharacteristic
403C2×C47C22×#9911yescharacteristic
404C2×C47C2×#41011yescharacteristic
405D47—82no—
406C22×#41—471no—
407C24×C4C2×D4711yescharacteristic
408#525—941no—
409#525—941no—
410#525—941no—
411#525—941no—
412#525—941no—
413#525—941no—
414#525—941no—
415#525—941no—
416C2×#123—472no—
417C2×C22⋊Q8—471no—
418C2×C22⋊Q8—471no—
419C2×#121—471no—
420C2×#121—471no—
421C2×#120—472no—
422C2×C4×D4—472no—
423C2×C4×D4—472no—
424C2×#117—21no—
425C2×#117—471no—
426C22×C22⋊C4—472no—
427C22×C42—941no—
428C2×#99—478no—
429#381—21no—
430#380—21no—
431#380C2×D4712yes—
432#379C2×D4712yes—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—472no—
435C4×C22⋊C4—472no—
436C4×C22⋊C4—941no—
437C4×C22⋊C4—941no—
438C4×C22⋊C4C2×D4712yes—
439C2×#95—941no—
440#342—478no—
441C47#2142011yescharacteristic, complemented, Sylow
442C25C22×D4711yescharacteristic
443C2×#41—941no—
444C2×#41—941no—
445C2×#41—941no—
446C2×#41—941no—
447C2×#41—1884no—
448C22×Q8—471no—
449C22×D4—472no—
450C22×D4—472no—
451C22×D4—472no—
452C22×D4—471no—
453C23×C4—44no—
454C23×C4—472no—
455C23×C4—942no—
456C23×C4C4×D4711yescharacteristic
457C23×C4C4×D4711yescharacteristic
458C23×C4C4×D4711yescharacteristic
459C23×C4C4×D4711yescharacteristic
460C23×C4D18811yescharacteristic
461C23×C4D18811yescharacteristic
462C23×C4D18811yescharacteristic
463C23×C4D18811yescharacteristic
464C23×C4C22⋊D4711yescharacteristic
465C23×C4C22⋊D4711yescharacteristic
466C23×C4C22⋊D4711yescharacteristic
467C23×C4C22⋊D4711yescharacteristic
468C23×C4C22×D4711yescharacteristic
469C23×C4C22×D4711yescharacteristic
470#123—942no—
471#123—942no—
472#123—942no—
473#123—942no—
474C22⋊Q8—941no—
475C22⋊Q8—941no—
476C22⋊Q8—941no—
477C22⋊Q8—941no—
478C22⋊Q8—941no—
479C22⋊Q8—941no—
480C22⋊Q8—941no—
481C22⋊Q8—941no—
482#121—941no—
483#121—941no—
484#121—941no—
485#121—941no—
486#121—941no—
487#121—941no—
488#121—941no—
489#121—941no—
490#120—942no—
491#120—942no—
492#120—942no—
493#120—942no—
494C4×D4—942no—
495C4×D4—942no—
496C4×D4—942no—
497C4×D4—942no—
498C4×D4—942no—
499C4×D4—942no—
500C4×D4—942no—
501C4×D4—942no—
502#117—44no—
503#117—941no—
504#117—941no—
505#117—941no—
506#117—941no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—471no—
509C2×C4⋊C4—471no—
510C2×C4⋊C4—472no—
511C2×C4⋊C4—472no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—474no—
515C2×C22⋊C4—472no—
516C2×C22⋊C4—472no—
517C2×C22⋊C4—472no—
518C2×C22⋊C4—472no—
519C2×C22⋊C4—472no—
520C2×C22⋊C4—948no—
521C2×C22⋊C4—942no—
522C2×C22⋊C4C22×D4714yes—
523C2×C42—22no—
524C2×C42—472no—
525C2×C42—942no—
526C2×C42—942no—
527C2×C42—1884no—
528#99—9416no—
529#95—22no—
530#95—22no—
531#95—942no—
532#95—942no—
533C24—24no—
534C24—42no—
535C24—42no—
536C24—472no—
537C24C2×C4×D4711yescharacteristic
538C24C2×C4×D4711yescharacteristic
539C24C2×D18811yescharacteristic
540C24C2×D18811yescharacteristic
541C24C2×C22⋊D4711yescharacteristic
542C24C2×C22⋊D4711yescharacteristic
543C24C23×D4711yescharacteristic
544#41—1884no—
545#41—1884no—
546#41—1884no—
547#41—1884no—
548C2×Q8—941no—
549C2×Q8—941no—
550C2×Q8—1882no—
551C2×D4—942no—
552C2×D4—942no—
553C2×D4—942no—
554C2×D4—942no—
555C2×D4—942no—
556C2×D4—942no—
557C2×D4—948no—
558C2×D4—941no—
559C2×D4—941no—
560C2×D4—1882no—
561C2×D4—1884no—
562C2×D4—1884no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—472no—
579C22×C4—472no—
580C22×C4—472no—
581C22×C4—948no—
582C22×C4—944no—
583C22×C4—942no—
584C22×C4—942no—
585C22×C4—1884no—
586C22×C4—1884no—
587C22×C4—1884no—
588C22×C4(C2×D47)⋊C411yescharacteristic
589C22×C4(C2×D47)⋊C411yescharacteristic
590C22×C4(C2×D47)⋊C411yescharacteristic
591C22×C4(C2×D47)⋊C411yescharacteristic
592C22×C4(C2×D47)⋊C411yescharacteristic
593C22×C4(C2×D47)⋊C411yescharacteristic
594C22×C4(C2×D47)⋊C411yescharacteristic
595C22×C4(C2×D47)⋊C411yescharacteristic
596C22×C4(C2×D47)⋊C411yescharacteristic
597C22×C4(C2×D47)⋊C411yescharacteristic
598C22×C4(C2×D47)⋊C411yescharacteristic
599C22×C4(C2×D47)⋊C411yescharacteristic
600C22×C4(C2×D47)⋊C411yescharacteristic
601C22×C4(C2×D47)⋊C411yescharacteristic
602C22×C4(C2×D47)⋊C411yescharacteristic
603C22×C4(C2×D47)⋊C411yescharacteristic
604C22×C4C2×C4×D4711yescharacteristic
605C22×C4C2×C4×D4711yescharacteristic
606C22×C4C2×C4×D4711yescharacteristic
607C22×C4C2×C4×D4711yescharacteristic
608C22×C4C2×D18811yescharacteristic
609C22×C4C2×D18811yescharacteristic
610C22×C4C2×D18811yescharacteristic
611C22×C4C2×D18811yescharacteristic
612C22×C4C2×C22⋊D4711yescharacteristic
613C22×C4C2×C22⋊D4711yescharacteristic
614C22×C4C2×C22⋊D4711yescharacteristic
615C22×C4C2×C22⋊D4711yescharacteristic
616C4⋊C4—44no—
617C4⋊C4—942no—
618C4⋊C4—942no—
619C4⋊C4—942no—
620C4⋊C4—942no—
621C4⋊C4—941no—
622C4⋊C4—941no—
623C4⋊C4—941no—
624C4⋊C4—941no—
625C22⋊C4—28no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—478no—
629C22⋊C4—948no—
630C22⋊C4—942no—
631C22⋊C4—942no—
632C22⋊C4—942no—
633C22⋊C4—942no—
634C22⋊C4—942no—
635C22⋊C4—942no—
636C22⋊C4—944no—
637C22⋊C4—942no—
638C22⋊C4—942no—
639C22⋊C4—942no—
640C22⋊C4—942no—
641C42—44no—
642C42—942no—
643C42—942no—
644C42—1884no—
645C42—1884no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—416no—
667C23—944no—
668C23—942no—
669C23—1882no—
670C23—1882no—
671C23C2×(C2×D47)⋊C411yescharacteristic
672C23C2×(C2×D47)⋊C411yescharacteristic
673C23C2×(C2×D47)⋊C411yescharacteristic
674C23C2×(C2×D47)⋊C411yescharacteristic
675C23C22×C4×D4711yescharacteristic
676C23C22×C22⋊D4711yescharacteristic
677C23C22×D18811yescharacteristic
678C23#41×D4714yes—
679Q8—1882no—
680Q8—1882no—
681D4—1882no—
682D4—1884no—
683D4—1884no—
684D4—1884no—
685D4—1884no—
686D4—1884no—
687D4—1884no—
688D4—1882no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—944no—
723C2×C4—948no—
724C2×C4—1884no—
725C2×C4—1884no—
726C2×C4—18816no—
727C2×C4—1884no—
728C2×C4—1884no—
729C2×C4—1882no—
730C2×C4—1882no—
731C2×C4#1309393814yescomplemented
732C2×C4C2×(C2×D47)⋊C411yescharacteristic
733C2×C4C2×(C2×D47)⋊C411yescharacteristic
734C2×C4C2×(C2×D47)⋊C411yescharacteristic
735C2×C4C2×(C2×D47)⋊C411yescharacteristic
736C2×C4C2×(C2×D47)⋊C411yescharacteristic
737C2×C4C2×(C2×D47)⋊C411yescharacteristic
738C2×C4C2×(C2×D47)⋊C411yescharacteristic
739C2×C4C2×(C2×D47)⋊C411yescharacteristic
740C22—28no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—3764no—
764C22—1882no—
765C22—1882no—
766C22—1882no—
767C22C2×#1309393812yes—
768C22#1568909612yes—
769C22C22×(C2×D47)⋊C411yescharacteristic
770C22#1568959112yes—
771C22#1568963512yes—
772C22#1568966912yes—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—84no—
780C4—1888no—
781C4—1882no—
782C4—1882no—
783C4—1882no—
784C4C2×#1309393812yes—
785C4C2×#1309393812yes—
786C2—22no—
787C2—22no—
788C2—22no—
789C2—22no—
790C2—22no—
791C2—41no—
792C2—41no—
793C2—3762no—
794C2#2024587611yescharacteristic
795C2C22×#1309393811yescharacteristic
796C2C2×#1568909611yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D47)⋊C4
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC47×#2280C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#15689634C2
cosocleC24×C47C24
hypercenter#2280D47
hypocenterC47#21420
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊Dic47C2semidirect
3. #20244372C2semidirect
4. #20244223C2semidirect
5. #20243839C2semidirect
6. C4×#13093938C2semidirect
7. C47×#2280C2semidirect
8. C22×#10625350C4semidirect
17. C2×#13094007C4semidirect
18. C2×#13094003C4semidirect
20. C2×#13093998C4semidirect
23. C2×C4×C22⋊D47C4semidirect
25. C2×#13093983C4semidirect
48. C22×Dic94C2×C4semidirect
49. C22×D188C2×C4semidirect
54. C22×C4×D47C2×C4semidirect
91. C2×C4⋊Dic47C2×C4semidirect
92. C2×C4⋊Dic47C2×C4semidirect
93. C2×Dic47⋊C4C2×C4semidirect
94. C2×Dic47⋊C4C2×C4semidirect
101. C2×(C2×D47)⋊C4C2×C4semidirect
102. C2×(C2×D47)⋊C4C2×C4semidirect
106. C2×C4×Dic47C2×C4semidirect
230. C22⋊Dic47#41semidirect
310. C2×C4×C47#99semidirect
389. #2280D47semidirect
441. C47#21420semidirect
731. C2×C4#13093938semidirect

Maximal subgroups

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

subgroupindex
C2×#156896342
C2×C4×C22⋊Dic472
#202443722
#202442232
#202438392
C4×#130939382
C47×#22802
#2142047