Finite Group Databasebeta

← #27084665

Subgroups — #27084665

Order 12032.

2570 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256684C211yesmaximal, characteristic, complemented
2#20253526C214yesmaximal, complemented
3#20253487C212yesmaximal, complemented
4#20253479C212yesmaximal, complemented
5#20253435C214yesmaximal, complemented
6#20253396C212yesmaximal, complemented
7#20253388C212yesmaximal, complemented
8#20253311C212yesmaximal, complemented
9#20253185C212yesmaximal, complemented
10#20252852C212yesmaximal, complemented
11#20252615C212yesmaximal, complemented
12C4×#13094050C214yesmaximal, complemented
13#20252021C211yesmaximal, characteristic, complemented
14C22×C4×D4×C47C211yesmaximal, characteristic, complemented
15C2×#13094050C2214yes—
16#15689680C2211yescharacteristic, complemented
17#15689680C2211yescharacteristic, complemented
18#15689680C2211yescharacteristic, complemented
19#15689673C2211yescharacteristic, complemented
20#15689673C2211yescharacteristic, complemented
21#15689673C2211yescharacteristic, complemented
22#15689657—21no—
23#15689657—21no—
24#15689657—21no—
25#15689657—21no—
26#15689657C2212yescomplemented
27#15689657C2212yescomplemented
28#15689634—21no—
29#15689634—21no—
30#15689634C2212yes—
31C4×#10625350—21no—
32C4×#10625350—21no—
33C4×#10625350C2212yescomplemented
34#15689458C2214yescomplemented
35#15689453C2214yescomplemented
36#15689441C2214yescomplemented
37#15689436C2214yescomplemented
38#15689423C2218yescomplemented
39#15689413C2214yescomplemented
40#15689403C2214yescomplemented
41#15689338C2218yescomplemented
42#15689328C2214yescomplemented
43#15689318C2214yescomplemented
44#15689274C2214yes—
45#15689274C2214yes—
46#15689257C2214yes—
47#15689257C2214yes—
48#15689233C2218yescomplemented
49#15689223C2218yescomplemented
50C4×#10625335C2218yescomplemented
51C4×#10625334C2218yescomplemented
52#15689180C2212yescomplemented
53#15689180C2212yescomplemented
54#15689176C2212yescomplemented
55#15689176C2212yescomplemented
56#15689163C2214yescomplemented
57#15689147C2212yescomplemented
58#15689128C2214yes—
59#15689122C2214yescomplemented
60#15689087C2212yes—
61C4×#10625329C2212yescomplemented
62C23×D4×C47C2211yescharacteristic
63C24×C4×C47—21no—
64C2×C4×D4×C47—21no—
65C2×C4×D4×C47—21no—
66C2×C4×D4×C47—21no—
67C2×C4×D4×C47—21no—
68C2×C4×D4×C47—21no—
69C2×C4×D4×C47—21no—
70C2×C4×D4×C47C2212yes—
71C2×C4×D4×C47C2212yes—
72C2×C4×D4×C47C2212yes—
73C2×C4×D4×C47C2212yes—
74C2×C4×D4×C47C2212yes—
75C2×C4×D4×C47C2212yes—
76C22×C4⋊C4×C47C2211yescharacteristic
77C22×C22⋊C4×C47—21no—
78C22×C42×C47C2211yescharacteristic
79C2×#10625350—21no—
80C2×#10625350—21no—
81C2×#10625350C2312yes—
82#13094050—216no—
83C2×#10625335C2318yes—
84C2×#10625334C2318yes—
85C2×#10625329C2314yes—
86#13094024C2311yescharacteristic, complemented
87#13094024C2311yescharacteristic, complemented
88#13094024C2311yescharacteristic, complemented
89#13094021C2311yescharacteristic, complemented
90#13094018—22no—
91#13094018—22no—
92#13094016—21no—
93#13094016—21no—
94#13094016C2312yescomplemented
95#13094012—21no—
96#13094012—21no—
97#13094012C2312yescomplemented
98#13094007—22no—
99#13094007—22no—
100#13094007—22no—
101#13094003—21no—
102#13094003—21no—
103#13094003—21no—
104#13094003—21no—
105#13094003C2312yes—
106#13094003C2312yes—
107#13093998—21no—
108#13093998—21no—
109#13093998—21no—
110#13093998—21no—
111#13093998C2312yes—
112#13093998C2312yes—
113#13093993—22no—
114C4×Dic94—21no—
115C4×Dic94—21no—
116C4×Dic94—21no—
117C4×Dic94—21no—
118C4×Dic94C2312yescomplemented
119C4×Dic94C2312yescomplemented
120C4×D188—21no—
121C4×D188—21no—
122C4×D188—21no—
123C4×D188—21no—
124C4×D188C2312yescomplemented
125C4×D188C2312yescomplemented
126C4×C22⋊D47—22no—
127C4×C22⋊D47—22no—
128C4×C22⋊D47—22no—
129C4×C22⋊D47—22no—
130C4×C22⋊D47—22no—
131C4×C22⋊D47—22no—
132#13093983—21no—
133#13093983—21no—
134#13093983C2312yes—
135#13093981—22no—
136#13093981—22no—
137#13093981—22no—
138C42×D47—22no—
139#13093957C2318yescomplemented
140#13093955C2318yescomplemented
141C4⋊(C47⋊C8)C2314yescomplemented
142C4⋊(C47⋊C8)C2314yescomplemented
143#13093947C2318yescomplemented
144#13093945C2318yes—
145#13093945C2318yes—
146#13093944C2318yescomplemented
147C22⋊(C47⋊C8)C2314yes—
148C22⋊(C47⋊C8)C2314yes—
149#13093935C2314yescomplemented
150C4×C47⋊C8C2314yescomplemented
151C25×C47—21no—
152C22×D4×C47—28no—
153C22×D4×C47—21no—
154C22×D4×C47—21no—
155C22×D4×C47—21no—
156C22×D4×C47C2312yes—
157C22×D4×C47C2312yes—
158C22×D4×C47C2312yes—
159C23×C4×C47—21no—
160C23×C4×C47—22no—
161C23×C4×C47—22no—
162C23×C4×C47—22no—
163C23×C4×C47—22no—
164C23×C4×C47—22no—
165C23×C4×C47—22no—
166C23×C4×C47—48no—
167C23×C4×C47D411yescharacteristic
168C23×C4×C47D411yescharacteristic
169C23×C4×C47C2311yescharacteristic
170C4×D4×C47—22no—
171C4×D4×C47—22no—
172C4×D4×C47—22no—
173C4×D4×C47—22no—
174C4×D4×C47—22no—
175C4×D4×C47—22no—
176C4×D4×C47—22no—
177C4×D4×C47—22no—
178C4×D4×C47—22no—
179C4×D4×C47—22no—
180C4×D4×C47—22no—
181C4×D4×C47—22no—
182C4×D4×C47C2314yes—
183C4×D4×C47C2314yes—
184C4×D4×C47C2314yes—
185C4×D4×C47C2314yes—
186C2×C4⋊C4×C47—21no—
187C2×C4⋊C4×C47—21no—
188C2×C4⋊C4×C47—21no—
189C2×C4⋊C4×C47C2312yes—
190C2×C4⋊C4×C47C2312yes—
191C2×C4⋊C4×C47C2312yes—
192C2×C22⋊C4×C47—22no—
193C2×C22⋊C4×C47—22no—
194C2×C22⋊C4×C47—22no—
195C2×C22⋊C4×C47—22no—
196C2×C22⋊C4×C47—22no—
197C2×C22⋊C4×C47—22no—
198C2×C42×C47D411yescharacteristic
199C2×C42×C47D411yescharacteristic
200C2×C42×C47D411yescharacteristic
201C2×C42×C47D411yescharacteristic
202C2×C42×C47D411yescharacteristic
203C2×C42×C47D411yescharacteristic
204C2×C42×C47C2311yescharacteristic
205C2×C42×C47C2311yescharacteristic
206C2×C42×C47C2311yescharacteristic
207C2×C42×C47C2311yescharacteristic
208C2×C42×C47C2311yescharacteristic
209C2×C42×C47C2311yescharacteristic
210C24×C47—28no—
211C24×C47—22no—
212C24×C47—22no—
213C24×C47—22no—
214C24×C47—44no—
215C24×C47—44no—
216C24×C47C2×D411yescharacteristic
217C2×D4×C47—28no—
218C2×D4×C47—28no—
219C2×D4×C47—28no—
220C2×D4×C47—28no—
221C2×D4×C47—28no—
222C2×D4×C47—22no—
223C2×D4×C47—22no—
224C2×D4×C47—22no—
225C2×D4×C47—24no—
226C2×D4×C47#4118yescomplemented
227C2×D4×C47C2414yes—
228C22×C4×C47—24no—
229C22×C4×C47—24no—
230C22×C4×C47—22no—
231C22×C4×C47—22no—
232C22×C4×C47—22no—
233C22×C4×C47—24no—
234C22×C4×C47—24no—
235C22×C4×C47—24no—
236C22×C4×C47—24no—
237C22×C4×C47—42no—
238C22×C4×C47—48no—
239C22×C4×C47—48no—
240C22×C4×C47—48no—
241C22×C4×C47—48no—
242C22×C4×C47—48no—
243C22×C4×C47—44no—
244C22×C4×C47—48no—
245C22×C4×C47C2×D411yescharacteristic
246C22×C4×C47C2×D411yescharacteristic
247C22×C4×C47C2×D411yescharacteristic
248C22×C4×C47C2×D411yescharacteristic
249C22×C4×C47C2×D411yescharacteristic
250C22×C4×C47C2×D411yescharacteristic
251C22×C4×C47C2×D411yescharacteristic
252C22×C4×C47C2×D411yescharacteristic
253C22×C4×C47C2×D411yescharacteristic
254C22×C4×C47C2×D411yescharacteristic
255C22×C4×C47C2×D411yescharacteristic
256C22×C4×C47C2×D411yescharacteristic
257C22×C4×C47C2×D411yescharacteristic
258C22×C4×C47C2×D411yescharacteristic
259C22×C4×C47C2×D411yescharacteristic
260C22×C4×C47C2411yescharacteristic
261C22×C4×C47C2411yescharacteristic
262C22×C4×C47C2411yescharacteristic
263C2×C22⋊D47—22no—
264C2×C22⋊D47—22no—
265C2×C22⋊D47—22no—
266#10625350—28no—
267#10625350—44no—
268#10625350—44no—
269C2×D188—21no—
270C2×D188—21no—
271C2×D188C2412yes—
272C2×C4×D47—22no—
273C2×C4×D47—22no—
274C2×C4×D47—22no—
275C2×Dic94—21no—
276C2×Dic94—21no—
277C2×Dic94C2412yes—
278C4⋊C4×C47—22no—
279C4⋊C4×C47—22no—
280C4⋊C4×C47—22no—
281C4⋊C4×C47C2414yes—
282C22⋊C4×C47—24no—
283C22⋊C4×C47—24no—
284C22⋊C4×C47—24no—
285C22⋊C4×C47—24no—
286C42×C47C2×D411yescharacteristic
287C42×C47C2×D411yescharacteristic
288C42×C47C2×D411yescharacteristic
289C42×C47C2×D411yescharacteristic
290C42×C47C2×D411yescharacteristic
291C42×C47C2×D411yescharacteristic
292C42×C47C2×D411yescharacteristic
293C42×C47C2×D411yescharacteristic
294C42×C47C2×D411yescharacteristic
295C42×C47C2×D411yescharacteristic
296C42×C47C2×D411yescharacteristic
297C42×C47C2×D411yescharacteristic
298C42×C47C2411yescharacteristic
299C42×C47C2411yescharacteristic
300C42×C47C2411yescharacteristic
301C42×C47C2411yescharacteristic
302C22⋊Dic47—22no—
303C22⋊Dic47—22no—
304C22⋊Dic47—22no—
305#10625335—216no—
306#10625334—216no—
307(C2×D47)⋊C4—22no—
308(C2×D47)⋊C4—22no—
309(C2×D47)⋊C4—22no—
310(C2×D47)⋊C4—22no—
311(C2×D47)⋊C4—22no—
312(C2×D47)⋊C4—22no—
313C4⋊Dic47—21no—
314C4⋊Dic47—21no—
315C4⋊Dic47—21no—
316C4⋊Dic47—21no—
317C4⋊Dic47C2412yes—
318C4⋊Dic47C2412yes—
319Dic47⋊C4—22no—
320Dic47⋊C4—22no—
321Dic47⋊C4—22no—
322Dic47⋊C4—22no—
323Dic47⋊C4—22no—
324Dic47⋊C4—22no—
325C4×Dic47—22no—
326C4×Dic47—22no—
327C4×Dic47—22no—
328#10625329—28no—
329C2×C47⋊C8C2418yes—
330C23×C47—22no—
331C23×C47—22no—
332C23×C47—22no—
333C23×C47—28no—
334C23×C47—28no—
335C23×C47—28no—
336C23×C47—24no—
337C23×C47—44no—
338C23×C47—44no—
339C23×C47—432no—
340C23×C47—44no—
341C23×C47—44no—
342C23×C47—44no—
343C23×C47—44no—
344C23×C47C22×D411yescharacteristic
345C23×C47C22×D411yescharacteristic
346C23×C47C22×D411yescharacteristic
347C22×D47—22no—
348D4×C47—28no—
349D4×C47—28no—
350D4×C47—28no—
351D4×C47—24no—
352D4×C47C2×#4118yes—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—22no—
365C2×C4×C47—24no—
366C2×C4×C47—41no—
367C2×C4×C47—41no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
370C2×C4×C47—48no—
371C2×C4×C47—48no—
372C2×C4×C47—44no—
373C2×C4×C47—44no—
374C2×C4×C47—44no—
375C2×C4×C47—48no—
376C2×C4×C47—48no—
377C2×C4×C47AGL(1,ℤ/8)14yescomplemented
378C2×C4×C47C22×D411yescharacteristic
379C2×C4×C47C22×D411yescharacteristic
380C2×C4×C47C22×D411yescharacteristic
381C2×C4×C47C22×D411yescharacteristic
382C2×C4×C47C22×D411yescharacteristic
383C2×C4×C47C22×D411yescharacteristic
384C2×C4×C47C22×D411yescharacteristic
385C2×C4×C47C22×D411yescharacteristic
386C2×C4×C47C22×D411yescharacteristic
387C2×C4×C47C22×D411yescharacteristic
388C2×C4×C47C22×D411yescharacteristic
389C2×C4×C47C2×#4114yes—
390C2×C4×C47C2511yescharacteristic
391C22⋊D47—44no—
392C22⋊D47—44no—
393C22⋊D47—44no—
394C2×Dic47—22no—
395C2×Dic47—22no—
396C2×Dic47—22no—
397D188—24no—
398D188—42no—
399D188—42no—
400C4×D47—44no—
401C4×D47—44no—
402C4×D47—44no—
403Dic94—24no—
404Dic94—42no—
405Dic94—42no—
406C47⋊C8—28no—
407#60558—471nomaximal, Sylow
408C22×C47—28no—
409C22×C47—21no—
410C22×C47—21no—
411C22×C47—21no—
412C22×C47—21no—
413C22×C47—21no—
414C22×C47—21no—
415C22×C47—28no—
416C22×C47—416no—
417C22×C47—416no—
418C22×C47—416no—
419C22×C47—44no—
420C22×C47—44no—
421C22×C47#52512yes—
422C22×C47C2×AGL(1,ℤ/8)12yes—
423C22×C47#57512yes—
424C22×C47C23×D411yescharacteristic
425C2×D47—42no—
426C2×D47—42no—
427C2×D47—42no—
428C4×C47—21no—
429C4×C47—21no—
430C4×C47—21no—
431C4×C47—21no—
432C4×C47—21no—
433C4×C47—21no—
434C4×C47—21no—
435C4×C47—21no—
436C4×C47—44no—
437C4×C47#52512yes—
438C4×C47C2×AGL(1,ℤ/8)12yes—
439C4×C47C2×AGL(1,ℤ/8)12yes—
440C4×C47C22×#4112yes—
441Dic47—42no—
442Dic47—42no—
443Dic47—42no—
444#3444—471no—
445C22×C4×D4D4711yescharacteristic, complemented
446#3114—474no—
447#3110—472no—
448#3109—472no—
449#3105—474no—
450#3101—472no—
451#3100—472no—
452#3092—472no—
453#3077—472no—
454#3036—472no—
455#3003—472no—
456C4×AGL(1,ℤ/8)—474no—
457#2920—471no—
458C2×C47—22no—
459C2×C47—22no—
460C2×C47—22no—
461C2×C47—48no—
462C2×C47C2×#52511yescharacteristic
463C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
464C2×C47C2×#57511yescharacteristic
465D47—82no—
466C23×D4C2×D4711yescharacteristic
467C24×C4—21no—
468C2×AGL(1,ℤ/8)—474no—
469#533—471no—
470#533—471no—
471#533—471no—
472#532—471no—
473#532—471no—
474#532—471no—
475#529—472no—
476#529—472no—
477#529—941no—
478#529—941no—
479#529—941no—
480#529—941no—
481#525—472no—
482#525—941no—
483#525—941no—
484C4×#41—472no—
485C4×#41—941no—
486C4×#41—941no—
487C2×C4×D4—21no—
488C2×C4×D4—21no—
489C2×C4×D4—21no—
490C2×C4×D4—21no—
491C2×C4×D4—21no—
492C2×C4×D4—21no—
493C2×C4×D4C2×D4712yes—
494C2×C4×D4C2×D4712yes—
495C2×C4×D4C2×D4712yes—
496C2×C4×D4C2×D4712yes—
497C2×C4×D4C2×D4712yes—
498C2×C4×D4C2×D4712yes—
499C22×C4⋊C4C2×D4711yescharacteristic
500C22×C22⋊C4—21no—
501C22×C42C2×D4711yescharacteristic
502#484—474no—
503#483—474no—
504#481—474no—
505#480—474no—
506#478—478no—
507#476—474no—
508#474—474no—
509#463—478no—
510#461—474no—
511#459—474no—
512#450—474no—
513#450—474no—
514#447—474no—
515#447—474no—
516#442—478no—
517#440—478no—
518C4×SD16—478no—
519C4×D8—478no—
520#432—472no—
521#432—472no—
522#431—472no—
523#431—472no—
524#428—474no—
525#423—472no—
526#418—474no—
527#417—474no—
528#407—472no—
529C4×M16—472no—
530C47#6055811yescharacteristic, complemented, Sylow
531C25—21no—
532C2×#41—472no—
533C2×#41—941no—
534C2×#41—941no—
535C22×D4—28no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4C22×D4712yes—
540C22×D4C22×D4712yes—
541C22×D4C22×D4712yes—
542C23×C4—21no—
543C23×C4—22no—
544C23×C4—22no—
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—22no—
549C23×C4—48no—
550C23×C4C22⋊D4711yescharacteristic
551C23×C4C22⋊D4711yescharacteristic
552C23×C4C22×D4711yescharacteristic
553AGL(1,ℤ/8)—9416no—
554C2×SD16—478no—
555C2×D8—478no—
556C2×M16—474no—
557C4⋊Q8—471no—
558C4⋊Q8—471no—
559C4⋊Q8—471no—
560#127—471no—
561#126—942no—
562#126—942no—
563#125—472no—
564#125—941no—
565#125—941no—
566#124—472no—
567#124—941no—
568#124—941no—
569#123—942no—
570#123—942no—
571#123—942no—
572C22⋊Q8—472no—
573C22⋊Q8—472no—
574C22⋊Q8—941no—
575C22⋊Q8—941no—
576C22⋊Q8—941no—
577C22⋊Q8—941no—
578#121—472no—
579#121—472no—
580#121—941no—
581#121—941no—
582#121—941no—
583#121—941no—
584#120—942no—
585C4×Q8—472no—
586C4×Q8—472no—
587C4×Q8—941no—
588C4×Q8—941no—
589C4×Q8—941no—
590C4×Q8—941no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—472no—
604C4×D4—472no—
605C4×D4—942no—
606C4×D4—942no—
607C4×D4—942no—
608C4×D4—942no—
609C4×D4—942no—
610C4×D4—942no—
611C4×D4—941no—
612C4×D4—941no—
613C4×D4—941no—
614C4×D4—941no—
615C4×D4C22×D4714yes—
616C4×D4C22×D4714yes—
617C4×D4C22×D4714yes—
618C4×D4C22×D4714yes—
619#117—472no—
620#117—941no—
621#117—941no—
622#117—942no—
623#117—942no—
624#117—942no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4C22×D4712yes—
629C2×C4⋊C4C22×D4712yes—
630C2×C4⋊C4C22×D4712yes—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C42—942no—
638C2×C42C22⋊D4711yescharacteristic
639C2×C42C22⋊D4711yescharacteristic
640C2×C42C22⋊D4711yescharacteristic
641C2×C42C22⋊D4711yescharacteristic
642C2×C42C22⋊D4711yescharacteristic
643C2×C42C22⋊D4711yescharacteristic
644C2×C42C22×D4711yescharacteristic
645C2×C42C22×D4711yescharacteristic
646C2×C42C22×D4711yescharacteristic
647C2×C42C22×D4711yescharacteristic
648C2×C42C22×D4711yescharacteristic
649C2×C42C22×D4711yescharacteristic
650#107—478no—
651#106—478no—
652C4⋊C8—474no—
653C4⋊C8—474no—
654#103—478no—
655#102—478no—
656#102—478no—
657#102—478no—
658C22⋊C8—474no—
659C22⋊C8—474no—
660#97—474no—
661C4×C8—474no—
662C24—28no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—44no—
667C24—44no—
668C24C2×C22⋊D4711yescharacteristic
669#41—948no—
670#41—1884no—
671#41—1884no—
672C2×Q8—472no—
673C2×Q8—941no—
674C2×Q8—941no—
675C2×D4—28no—
676C2×D4—28no—
677C2×D4—28no—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—22no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—24no—
684C2×D4—472no—
685C2×D4—942no—
686C2×D4—942no—
687C2×D4—942no—
688C2×D4—941no—
689C2×D4—941no—
690C2×D4#1062535018yescomplemented
691C2×D4C23×D4714yes—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—24no—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—42no—
702C22×C4—48no—
703C22×C4—48no—
704C22×C4—48no—
705C22×C4—48no—
706C22×C4—48no—
707C22×C4—44no—
708C22×C4—48no—
709C22×C4—942no—
710C22×C4—942no—
711C22×C4—942no—
712C22×C4C2×C22⋊D4711yescharacteristic
713C22×C4C2×C22⋊D4711yescharacteristic
714C22×C4C2×C22⋊D4711yescharacteristic
715C22×C4C2×C22⋊D4711yescharacteristic
716C22×C4C2×C22⋊D4711yescharacteristic
717C22×C4C2×C22⋊D4711yescharacteristic
718C22×C4C2×C22⋊D4711yescharacteristic
719C22×C4C2×C22⋊D4711yescharacteristic
720C22×C4C2×C22⋊D4711yescharacteristic
721C22×C4C2×C22⋊D4711yescharacteristic
722C22×C4C2×C22⋊D4711yescharacteristic
723C22×C4C2×C22⋊D4711yescharacteristic
724C22×C4C2×C22⋊D4711yescharacteristic
725C22×C4C2×C22⋊D4711yescharacteristic
726C22×C4C2×C22⋊D4711yescharacteristic
727C22×C4C23×D4711yescharacteristic
728C22×C4C23×D4711yescharacteristic
729C22×C4C23×D4711yescharacteristic
730SD16—9416no—
731D8—9416no—
732M16—948no—
733C2×C8—478no—
734C4⋊C4—22no—
735C4⋊C4—22no—
736C4⋊C4—22no—
737C4⋊C4—472no—
738C4⋊C4—472no—
739C4⋊C4—942no—
740C4⋊C4—942no—
741C4⋊C4—942no—
742C4⋊C4—942no—
743C4⋊C4—942no—
744C4⋊C4—942no—
745C4⋊C4—941no—
746C4⋊C4—941no—
747C4⋊C4—941no—
748C4⋊C4—941no—
749C4⋊C4C23×D4714yes—
750C22⋊C4—24no—
751C22⋊C4—24no—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—942no—
755C22⋊C4—942no—
756C22⋊C4—942no—
757C22⋊C4—942no—
758C22⋊C4—942no—
759C22⋊C4—942no—
760C22⋊C4—942no—
761C22⋊C4—942no—
762C22⋊C4—942no—
763C42—942no—
764C42—942no—
765C42—942no—
766C42C2×C22⋊D4711yescharacteristic
767C42C2×C22⋊D4711yescharacteristic
768C42C2×C22⋊D4711yescharacteristic
769C42C2×C22⋊D4711yescharacteristic
770C42C2×C22⋊D4711yescharacteristic
771C42C2×C22⋊D4711yescharacteristic
772C42C2×C22⋊D4711yescharacteristic
773C42C2×C22⋊D4711yescharacteristic
774C42C2×C22⋊D4711yescharacteristic
775C42C2×C22⋊D4711yescharacteristic
776C42C2×C22⋊D4711yescharacteristic
777C42C2×C22⋊D4711yescharacteristic
778C42C23×D4711yescharacteristic
779C42C23×D4711yescharacteristic
780C42C23×D4711yescharacteristic
781C42C23×D4711yescharacteristic
782C23—22no—
783C23—22no—
784C23—22no—
785C23—28no—
786C23—28no—
787C23—28no—
788C23—24no—
789C23—44no—
790C23—44no—
791C23—432no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—942no—
797C23C22×C22⋊D4711yescharacteristic
798C23C22×C22⋊D4711yescharacteristic
799C23C22×C22⋊D4711yescharacteristic
800Q8—944no—
801Q8—1882no—
802Q8—1882no—
803D4—28no—
804D4—28no—
805D4—28no—
806D4—24no—
807D4—944no—
808D4—1882no—
809D4—1884no—
810D4—1884no—
811D4—1884no—
812D4—1882no—
813D4C2×#1062535018yes—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—48no—
832C2×C4—48no—
833C2×C4—44no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—48no—
837C2×C4—48no—
838C2×C4—942no—
839C2×C4—942no—
840C2×C4—942no—
841C2×C4—1884no—
842C2×C4—1884no—
843C2×C4—1884no—
844C2×C4#1309405014yescomplemented
845C2×C4C22×C22⋊D4711yescharacteristic
846C2×C4C22×C22⋊D4711yescharacteristic
847C2×C4C22×C22⋊D4711yescharacteristic
848C2×C4C22×C22⋊D4711yescharacteristic
849C2×C4C22×C22⋊D4711yescharacteristic
850C2×C4C22×C22⋊D4711yescharacteristic
851C2×C4C22×C22⋊D4711yescharacteristic
852C2×C4C22×C22⋊D4711yescharacteristic
853C2×C4C22×C22⋊D4711yescharacteristic
854C2×C4C22×C22⋊D4711yescharacteristic
855C2×C4C22×C22⋊D4711yescharacteristic
856C2×C4C2×#1062535014yes—
857C2×C4C24×D4711yescharacteristic
858C8—948no—
859C22—28no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—28no—
867C22—416no—
868C22—416no—
869C22—416no—
870C22—44no—
871C22—44no—
872C22—1882no—
873C22—1882no—
874C22—1882no—
875C22#1568963412yes—
876C22C2×#1309405012yes—
877C22#1568992112yes—
878C22C23×C22⋊D4711yescharacteristic
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—44no—
888C4—1882no—
889C4—1882no—
890C4—1882no—
891C4#1568963412yes—
892C4C2×#1309405012yes—
893C4C2×#1309405012yes—
894C4C22×#1062535012yes—
895C2—22no—
896C2—22no—
897C2—22no—
898C2—48no—
899C2—3762no—
900C2C2×#1568963411yescharacteristic
901C2C22×#1309405011yescharacteristic
902C2C2×#1568992111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC22×C4×D4×C47C2
socleC22×C47C23×D4
hypercenterC22×C4×D4D47
hypocenterC47#60558
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. #20256684C2semidirect
2. #20253526C2semidirect
3. #20253487C2semidirect
4. #20253479C2semidirect
5. #20253435C2semidirect
6. #20253396C2semidirect
7. #20253388C2semidirect
8. #20253311C2semidirect
9. #20253185C2semidirect
10. #20252852C2semidirect
11. #20252615C2semidirect
12. C4×#13094050C2semidirect
13. #20252021C2semidirect
14. C22×C4×D4×C47C2semidirect
16. #15689680C22semidirect
17. #15689680C22semidirect
18. #15689680C22semidirect
19. #15689673C22semidirect
20. #15689673C22semidirect
21. #15689673C22semidirect
26. #15689657C22semidirect
27. #15689657C22semidirect
33. C4×#10625350C22semidirect
34. #15689458C22semidirect
35. #15689453C22semidirect
36. #15689441C22semidirect
37. #15689436C22semidirect
38. #15689423C22semidirect
39. #15689413C22semidirect
40. #15689403C22semidirect
41. #15689338C22semidirect
42. #15689328C22semidirect
43. #15689318C22semidirect
48. #15689233C22semidirect
49. #15689223C22semidirect
50. C4×#10625335C22semidirect
51. C4×#10625334C22semidirect
52. #15689180C22semidirect
53. #15689180C22semidirect
54. #15689176C22semidirect
55. #15689176C22semidirect
56. #15689163C22semidirect
57. #15689147C22semidirect
59. #15689122C22semidirect
61. C4×#10625329C22semidirect
86. #13094024C23semidirect
87. #13094024C23semidirect
88. #13094024C23semidirect
89. #13094021C23semidirect
94. #13094016C23semidirect
97. #13094012C23semidirect
118. C4×Dic94C23semidirect
119. C4×Dic94C23semidirect
124. C4×D188C23semidirect
125. C4×D188C23semidirect
139. #13093957C23semidirect
140. #13093955C23semidirect
141. C4⋊(C47⋊C8)C23semidirect
142. C4⋊(C47⋊C8)C23semidirect
143. #13093947C23semidirect
146. #13093944C23semidirect
149. #13093935C23semidirect
150. C4×C47⋊C8C23semidirect
226. C2×D4×C47#41semidirect
377. C2×C4×C47AGL(1,ℤ/8)semidirect
445. C22×C4×D4D47semidirect
530. C47#60558semidirect
690. C2×D4#10625350semidirect
844. C2×C4#13094050semidirect

Maximal subgroups

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

subgroupindex
#202566842
#202535262
#202534872
#202534792
#202534352
#202533962
#202533882
#202533112
#202531852
#202528522
#202526152
C4×#130940502
#202520212
C22×C4×D4×C472
#6055847