Finite Group Databasebeta

← #27084667

Subgroups — #27084667

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
2C22×C4×D188C211yesmaximal, characteristic, complemented
3#20253528C214yesmaximal, complemented
4#20253488C212yesmaximal, complemented
5#20253480C212yesmaximal, complemented
6#20253437C214yesmaximal, complemented
7#20253397C212yesmaximal, complemented
8#20253389C212yesmaximal, complemented
9#20253313C212yesmaximal, complemented
10#20253187C212yesmaximal, complemented
11#20252854C212yesmaximal, complemented
12#20252618C212yesmaximal, complemented
13C4×#13094052C214yesmaximal, complemented
14C47×#2920C211yesmaximal, characteristic, complemented
15C23×D188C2211yescharacteristic
16C23×C4×D47—21no—
17C2×#13094052C2214yes—
18#15689680C2211yescharacteristic, complemented
19#15689680C2211yescharacteristic, complemented
20#15689680C2211yescharacteristic, complemented
21#15689673C2211yescharacteristic, complemented
22#15689673C2211yescharacteristic, complemented
23#15689673C2211yescharacteristic, complemented
24#15689657—21no—
25#15689657—21no—
26#15689657—21no—
27#15689657—21no—
28#15689657C2212yescomplemented
29#15689657C2212yescomplemented
30#15689634—21no—
31#15689634—21no—
32#15689634C2212yes—
33C4×#10625350—21no—
34C4×#10625350—21no—
35C4×#10625350C2212yescomplemented
36C2×C4×D188—21no—
37C2×C4×D188—21no—
38C2×C4×D188—21no—
39C2×C4×D188—21no—
40C2×C4×D188—21no—
41C2×C4×D188—21no—
42C2×C4×D188C2212yes—
43C2×C4×D188C2212yes—
44C2×C4×D188C2212yes—
45C2×C4×D188C2212yes—
46C2×C4×D188C2212yes—
47C2×C4×D188C2212yes—
48C22×C4⋊Dic47C2211yescharacteristic
49C22×(C2×D47)⋊C4—21no—
50#15689459C2214yescomplemented
51#15689454C2214yescomplemented
52#15689442C2214yescomplemented
53#15689437C2214yescomplemented
54#15689424C2218yescomplemented
55#15689414C2214yescomplemented
56#15689404C2214yescomplemented
57#15689339C2218yescomplemented
58#15689329C2214yescomplemented
59#15689319C2214yescomplemented
60#15689276C2214yes—
61#15689276C2214yes—
62#15689259C2214yes—
63#15689259C2214yes—
64#15689236C2218yescomplemented
65#15689225C2218yescomplemented
66C4×#10625325C2218yescomplemented
67C4×D376C2218yescomplemented
68#15689165C2214yescomplemented
69#15689129C2214yes—
70#15689125C2214yescomplemented
71C22×C42×C47C2211yescharacteristic
72C47×#432C2212yescomplemented
73C47×#432C2212yescomplemented
74C47×#431C2212yescomplemented
75C47×#431C2212yescomplemented
76C47×#423C2212yescomplemented
77C47×#407C2212yes—
78C4×M16×C47C2212yescomplemented
79C24×D47—21no—
80C2×#10625350—21no—
81C2×#10625350—21no—
82C2×#10625350C2312yes—
83C22×D188—21no—
84C22×D188—21no—
85C22×D188—21no—
86C22×D188—28no—
87C22×D188C2312yes—
88C22×D188C2312yes—
89C22×D188C2312yes—
90C23×Dic47—21no—
91C22×C4×D47—22no—
92C22×C4×D47—22no—
93C22×C4×D47—22no—
94C22×C4×D47—22no—
95C22×C4×D47—22no—
96C22×C4×D47—22no—
97C22×C4×D47—48no—
98#13094052—216no—
99C2×#10625325C2318yes—
100C2×D376C2318yes—
101#13094024C2311yescharacteristic, complemented
102#13094024C2311yescharacteristic, complemented
103#13094024C2311yescharacteristic, complemented
104#13094021C2311yescharacteristic, complemented
105#13094018—22no—
106#13094018—22no—
107#13094016—21no—
108#13094016—21no—
109#13094016C2312yescomplemented
110#13094012—21no—
111#13094012—21no—
112#13094012C2312yescomplemented
113#13094007—22no—
114#13094007—22no—
115#13094007—22no—
116#13094003—21no—
117#13094003—21no—
118#13094003—21no—
119#13094003—21no—
120#13094003C2312yes—
121#13094003C2312yes—
122#13093998—21no—
123#13093998—21no—
124#13093998—21no—
125#13093998—21no—
126#13093998C2312yes—
127#13093998C2312yes—
128#13093993—22no—
129C4×Dic94—21no—
130C4×Dic94—21no—
131C4×Dic94—21no—
132C4×Dic94—21no—
133C4×Dic94C2312yescomplemented
134C4×Dic94C2312yescomplemented
135C4×D188—22no—
136C4×D188—22no—
137C4×D188—22no—
138C4×D188—22no—
139C4×D188—22no—
140C4×D188—22no—
141C4×D188—22no—
142C4×D188—22no—
143C4×D188—22no—
144C4×D188—22no—
145C4×D188—22no—
146C4×D188—22no—
147C4×D188—21no—
148C4×D188—21no—
149C4×D188—21no—
150C4×D188—21no—
151C4×D188C2314yes—
152C4×D188C2314yes—
153C4×D188C2314yes—
154C4×D188C2314yes—
155C4×D188C2312yescomplemented
156C4×D188C2312yescomplemented
157C4×C22⋊D47—22no—
158C4×C22⋊D47—22no—
159C4×C22⋊D47—22no—
160C4×C22⋊D47—22no—
161C4×C22⋊D47—22no—
162C4×C22⋊D47—22no—
163#13093983—21no—
164#13093983—21no—
165#13093983C2312yes—
166#13093981—22no—
167#13093981—22no—
168#13093981—22no—
169C2×C4⋊Dic47—21no—
170C2×C4⋊Dic47—21no—
171C2×C4⋊Dic47—21no—
172C2×C4⋊Dic47C2312yes—
173C2×C4⋊Dic47C2312yes—
174C2×C4⋊Dic47C2312yes—
175C2×(C2×D47)⋊C4—22no—
176C2×(C2×D47)⋊C4—22no—
177C2×(C2×D47)⋊C4—22no—
178C2×(C2×D47)⋊C4—22no—
179C2×(C2×D47)⋊C4—22no—
180C2×(C2×D47)⋊C4—22no—
181C42×D47—22no—
182#13093958C2318yescomplemented
183#13093956C2318yescomplemented
184#13093949C2318yescomplemented
185#13093946C2318yes—
186#13093946C2318yes—
187#13093946C2318yescomplemented
188C23×C4×C47D411yescharacteristic
189C23×C4×C47D411yescharacteristic
190C23×C4×C47C2311yescharacteristic
191C2×M16×C47C2314yes—
192C2×C42×C47D411yescharacteristic
193C2×C42×C47D411yescharacteristic
194C2×C42×C47D411yescharacteristic
195C2×C42×C47D411yescharacteristic
196C2×C42×C47D411yescharacteristic
197C2×C42×C47D411yescharacteristic
198C2×C42×C47C2311yescharacteristic
199C2×C42×C47C2311yescharacteristic
200C2×C42×C47C2311yescharacteristic
201C2×C42×C47C2311yescharacteristic
202C2×C42×C47C2311yescharacteristic
203C2×C42×C47C2311yescharacteristic
204C4⋊C8×C47C2314yescomplemented
205C4⋊C8×C47C2314yescomplemented
206C22⋊C8×C47C2314yes—
207C22⋊C8×C47C2314yes—
208#97×C47C2314yescomplemented
209C4×C8×C47C2314yescomplemented
210C24×C47C2×D411yescharacteristic
211C23×D47—28no—
212C23×D47—22no—
213C23×D47—22no—
214C23×D47—22no—
215C23×D47—44no—
216C23×D47—44no—
217C22×C4×C47—24no—
218C22×C4×C47—24no—
219C22×C4×C47—42no—
220C22×C4×C47C2×D411yescharacteristic
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2×D411yescharacteristic
225C22×C4×C47C2×D411yescharacteristic
226C22×C4×C47C2×D411yescharacteristic
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2×D411yescharacteristic
230C22×C4×C47C2×D411yescharacteristic
231C22×C4×C47C2×D411yescharacteristic
232C22×C4×C47C2×D411yescharacteristic
233C22×C4×C47C2×D411yescharacteristic
234C22×C4×C47C2×D411yescharacteristic
235C22×C4×C47C2411yescharacteristic
236C22×C4×C47C2411yescharacteristic
237C22×C4×C47C2411yescharacteristic
238C2×C22⋊D47—22no—
239C2×C22⋊D47—22no—
240C2×C22⋊D47—22no—
241C22×Dic47—22no—
242C22×Dic47—22no—
243C22×Dic47—22no—
244C22×Dic47—44no—
245#10625350—28no—
246#10625350—44no—
247#10625350—44no—
248C2×D188—28no—
249C2×D188—28no—
250C2×D188—28no—
251C2×D188—22no—
252C2×D188—22no—
253C2×D188—22no—
254C2×D188—24no—
255C2×D188—28no—
256C2×D188—28no—
257C2×D188—21no—
258C2×D188—21no—
259C2×D188#4118yescomplemented
260C2×D188C2412yes—
261C2×D188C2414yes—
262C2×C4×D47—22no—
263C2×C4×D47—22no—
264C2×C4×D47—22no—
265C2×C4×D47—24no—
266C2×C4×D47—24no—
267C2×C4×D47—24no—
268C2×C4×D47—24no—
269C2×C4×D47—48no—
270C2×C4×D47—48no—
271C2×C4×D47—48no—
272C2×C4×D47—48no—
273C2×C4×D47—48no—
274C2×C4×D47—48no—
275C2×Dic94—21no—
276C2×Dic94—21no—
277C2×Dic94C2412yes—
278M16×C47—28no—
279C2×C8×C47C2418yes—
280C42×C47C2×D411yescharacteristic
281C42×C47C2×D411yescharacteristic
282C42×C47C2×D411yescharacteristic
283C42×C47C2×D411yescharacteristic
284C42×C47C2×D411yescharacteristic
285C42×C47C2×D411yescharacteristic
286C42×C47C2×D411yescharacteristic
287C42×C47C2×D411yescharacteristic
288C42×C47C2×D411yescharacteristic
289C42×C47C2×D411yescharacteristic
290C42×C47C2×D411yescharacteristic
291C42×C47C2×D411yescharacteristic
292C42×C47C2411yescharacteristic
293C42×C47C2411yescharacteristic
294C42×C47C2411yescharacteristic
295C42×C47C2411yescharacteristic
296C22⋊Dic47—22no—
297C22⋊Dic47—22no—
298C22⋊Dic47—22no—
299(C2×D47)⋊C4—24no—
300(C2×D47)⋊C4—24no—
301(C2×D47)⋊C4—24no—
302(C2×D47)⋊C4—24no—
303(C2×D47)⋊C4—22no—
304(C2×D47)⋊C4—22no—
305(C2×D47)⋊C4—22no—
306(C2×D47)⋊C4—22no—
307(C2×D47)⋊C4—22no—
308(C2×D47)⋊C4—22no—
309C4⋊Dic47—22no—
310C4⋊Dic47—22no—
311C4⋊Dic47—22no—
312C4⋊Dic47—21no—
313C4⋊Dic47—21no—
314C4⋊Dic47—21no—
315C4⋊Dic47—21no—
316C4⋊Dic47C2412yes—
317C4⋊Dic47C2412yes—
318C4⋊Dic47C2414yes—
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—
328D376—216no—
329#10625325—216no—
330C23×C47—22no—
331C23×C47—22no—
332C23×C47—22no—
333C23×C47C22×D411yescharacteristic
334C23×C47C22×D411yescharacteristic
335C23×C47C22×D411yescharacteristic
336C22×D47—28no—
337C22×D47—28no—
338C22×D47—28no—
339C22×D47—24no—
340C22×D47—22no—
341C22×D47—44no—
342C22×D47—44no—
343C22×D47—432no—
344C22×D47—44no—
345C22×D47—44no—
346C22×D47—44no—
347C22×D47—44no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
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—41no—
361C2×C4×C47—41no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
364C2×C4×C47AGL(1,ℤ/8)14yescomplemented
365C2×C4×C47C22×D411yescharacteristic
366C2×C4×C47C22×D411yescharacteristic
367C2×C4×C47C22×D411yescharacteristic
368C2×C4×C47C22×D411yescharacteristic
369C2×C4×C47C22×D411yescharacteristic
370C2×C4×C47C22×D411yescharacteristic
371C2×C4×C47C22×D411yescharacteristic
372C2×C4×C47C22×D411yescharacteristic
373C2×C4×C47C22×D411yescharacteristic
374C2×C4×C47C22×D411yescharacteristic
375C2×C4×C47C22×D411yescharacteristic
376C2×C4×C47C2×#4114yes—
377C2×C4×C47C2511yescharacteristic
378C22⋊D47—44no—
379C22⋊D47—44no—
380C22⋊D47—44no—
381C2×Dic47—22no—
382C2×Dic47—22no—
383C2×Dic47—22no—
384C2×Dic47—24no—
385C2×Dic47—44no—
386C2×Dic47—44no—
387C2×Dic47—44no—
388D188—28no—
389D188—28no—
390D188—28no—
391D188—24no—
392D188—24no—
393D188—42no—
394D188—42no—
395D188C2×#4118yes—
396C4×D47—48no—
397C4×D47—48no—
398C4×D47—44no—
399C4×D47—44no—
400C4×D47—48no—
401C4×D47—48no—
402C4×D47—44no—
403Dic94—24no—
404Dic94—42no—
405Dic94—42no—
406C8×C47—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#52512yes—
416C22×C47C2×AGL(1,ℤ/8)12yes—
417C22×C47#57512yes—
418C22×C47C23×D411yescharacteristic
419C2×D47—28no—
420C2×D47—416no—
421C2×D47—416no—
422C2×D47—416no—
423C2×D47—44no—
424C2×D47—44no—
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#52512yes—
437C4×C47C2×AGL(1,ℤ/8)12yes—
438C4×C47C2×AGL(1,ℤ/8)12yes—
439C4×C47C22×#4112yes—
440Dic47—42no—
441Dic47—42no—
442Dic47—44no—
443Dic47—42no—
444#3444—471no—
445C22×C4×D4—471no—
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#2920D4711yescharacteristic, complemented
458C2×C47—22no—
459C2×C47—22no—
460C2×C47—22no—
461C2×C47C2×#52511yescharacteristic
462C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
463C2×C47C2×#57511yescharacteristic
464D47—48no—
465D47—82no—
466C23×D4—471no—
467C24×C4—941no—
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—472no—
488C2×C4×D4—472no—
489C2×C4×D4—472no—
490C2×C4×D4—472no—
491C2×C4×D4—472no—
492C2×C4×D4—472no—
493C2×C4×D4—941no—
494C2×C4×D4—941no—
495C2×C4×D4—941no—
496C2×C4×D4—941no—
497C2×C4×D4—941no—
498C2×C4×D4—941no—
499C22×C4⋊C4—471no—
500C22×C22⋊C4—941no—
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#432C2×D4712yescomplemented
521#432C2×D4712yescomplemented
522#431C2×D4712yescomplemented
523#431C2×D4712yescomplemented
524#428—474no—
525#423C2×D4712yescomplemented
526#418—474no—
527#417—474no—
528#407C2×D4712yes—
529C4×M16C2×D4712yescomplemented
530C47#6055811yescharacteristic, complemented, Sylow
531C25—941no—
532C2×#41—472no—
533C2×#41—941no—
534C2×#41—941no—
535C22×D4—472no—
536C22×D4—472no—
537C22×D4—472no—
538C22×D4—948no—
539C22×D4—941no—
540C22×D4—941no—
541C22×D4—941no—
542C23×C4—941no—
543C23×C4—942no—
544C23×C4—942no—
545C23×C4—942no—
546C23×C4—942no—
547C23×C4—942no—
548C23×C4—942no—
549C23×C4—1888no—
550C23×C4D18811yescharacteristic
551C23×C4D18811yescharacteristic
552C23×C4C22×D4711yescharacteristic
553AGL(1,ℤ/8)—9416no—
554C2×SD16—478no—
555C2×D8—478no—
556C2×M16C22×D4714yes—
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—474no—
592C4×D4—474no—
593C4×D4—474no—
594C4×D4—474no—
595C4×D4—472no—
596C4×D4—472no—
597C4×D4—942no—
598C4×D4—942no—
599C4×D4—942no—
600C4×D4—942no—
601C4×D4—942no—
602C4×D4—942no—
603C4×D4—942no—
604C4×D4—942no—
605C4×D4—942no—
606C4×D4—942no—
607C4×D4—942no—
608C4×D4—942no—
609C4×D4—942no—
610C4×D4—942no—
611C4×D4—942no—
612C4×D4—942no—
613C4×D4—942no—
614C4×D4—942no—
615C4×D4—941no—
616C4×D4—941no—
617C4×D4—941no—
618C4×D4—941no—
619#117—472no—
620#117—941no—
621#117—941no—
622#117—942no—
623#117—942no—
624#117—942no—
625C2×C4⋊C4—472no—
626C2×C4⋊C4—472no—
627C2×C4⋊C4—472no—
628C2×C4⋊C4—941no—
629C2×C4⋊C4—941no—
630C2×C4⋊C4—941no—
631C2×C22⋊C4—942no—
632C2×C22⋊C4—942no—
633C2×C22⋊C4—942no—
634C2×C22⋊C4—942no—
635C2×C22⋊C4—942no—
636C2×C22⋊C4—942no—
637C2×C42—942no—
638C2×C42D18811yescharacteristic
639C2×C42D18811yescharacteristic
640C2×C42D18811yescharacteristic
641C2×C42D18811yescharacteristic
642C2×C42D18811yescharacteristic
643C2×C42D18811yescharacteristic
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⋊C8C22×D4714yescomplemented
653C4⋊C8C22×D4714yescomplemented
654#103—478no—
655#102—478no—
656#102—478no—
657#102—478no—
658C22⋊C8C22×D4714yes—
659C22⋊C8C22×D4714yes—
660#97C22×D4714yescomplemented
661C4×C8C22×D4714yescomplemented
662C24—948no—
663C24—942no—
664C24—942no—
665C24—942no—
666C24—1884no—
667C24—1884no—
668C24C2×D18811yescharacteristic
669#41—948no—
670#41—1884no—
671#41—1884no—
672C2×Q8—472no—
673C2×Q8—941no—
674C2×Q8—941no—
675C2×D4—478no—
676C2×D4—474no—
677C2×D4—472no—
678C2×D4—948no—
679C2×D4—948no—
680C2×D4—948no—
681C2×D4—948no—
682C2×D4—948no—
683C2×D4—942no—
684C2×D4—942no—
685C2×D4—942no—
686C2×D4—942no—
687C2×D4—942no—
688C2×D4—942no—
689C2×D4—941no—
690C2×D4—941no—
691C2×D4—944no—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—42no—
695C22×C4—942no—
696C22×C4—942no—
697C22×C4—942no—
698C22×C4—942no—
699C22×C4—942no—
700C22×C4—944no—
701C22×C4—944no—
702C22×C4—944no—
703C22×C4—942no—
704C22×C4—944no—
705C22×C4—1888no—
706C22×C4—1888no—
707C22×C4—1888no—
708C22×C4—1888no—
709C22×C4—1888no—
710C22×C4—1884no—
711C22×C4—1888no—
712C22×C4C2×D18811yescharacteristic
713C22×C4C2×D18811yescharacteristic
714C22×C4C2×D18811yescharacteristic
715C22×C4C2×D18811yescharacteristic
716C22×C4C2×D18811yescharacteristic
717C22×C4C2×D18811yescharacteristic
718C22×C4C2×D18811yescharacteristic
719C22×C4C2×D18811yescharacteristic
720C22×C4C2×D18811yescharacteristic
721C22×C4C2×D18811yescharacteristic
722C22×C4C2×D18811yescharacteristic
723C22×C4C2×D18811yescharacteristic
724C22×C4C2×D18811yescharacteristic
725C22×C4C2×D18811yescharacteristic
726C22×C4C2×D18811yescharacteristic
727C22×C4C23×D4711yescharacteristic
728C22×C4C23×D4711yescharacteristic
729C22×C4C23×D4711yescharacteristic
730SD16—9416no—
731D8—9416no—
732M16—28no—
733C2×C8C23×D4718yes—
734C4⋊C4—472no—
735C4⋊C4—472no—
736C4⋊C4—474no—
737C4⋊C4—942no—
738C4⋊C4—942no—
739C4⋊C4—942no—
740C4⋊C4—942no—
741C4⋊C4—942no—
742C4⋊C4—942no—
743C4⋊C4—942no—
744C4⋊C4—942no—
745C4⋊C4—942no—
746C4⋊C4—941no—
747C4⋊C4—941no—
748C4⋊C4—941no—
749C4⋊C4—941no—
750C22⋊C4—942no—
751C22⋊C4—942no—
752C22⋊C4—942no—
753C22⋊C4—944no—
754C22⋊C4—944no—
755C22⋊C4—944no—
756C22⋊C4—944no—
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×D18811yescharacteristic
767C42C2×D18811yescharacteristic
768C42C2×D18811yescharacteristic
769C42C2×D18811yescharacteristic
770C42C2×D18811yescharacteristic
771C42C2×D18811yescharacteristic
772C42C2×D18811yescharacteristic
773C42C2×D18811yescharacteristic
774C42C2×D18811yescharacteristic
775C42C2×D18811yescharacteristic
776C42C2×D18811yescharacteristic
777C42C2×D18811yescharacteristic
778C42C23×D4711yescharacteristic
779C42C23×D4711yescharacteristic
780C42C23×D4711yescharacteristic
781C42C23×D4711yescharacteristic
782C23—22no—
783C23—22no—
784C23—22no—
785C23—948no—
786C23—948no—
787C23—948no—
788C23—944no—
789C23—942no—
790C23—1884no—
791C23—1884no—
792C23—18832no—
793C23—1884no—
794C23—1884no—
795C23—1884no—
796C23—1884no—
797C23C22×D18811yescharacteristic
798C23C22×D18811yescharacteristic
799C23C22×D18811yescharacteristic
800Q8—944no—
801Q8—1882no—
802Q8—1882no—
803D4—478no—
804D4—948no—
805D4—948no—
806D4—948no—
807D4—944no—
808D4—944no—
809D4—1882no—
810D4—1884no—
811D4—1884no—
812D4—1884no—
813D4—1882no—
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—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—942no—
831C2×C4—942no—
832C2×C4—942no—
833C2×C4—944no—
834C2×C4—1888no—
835C2×C4—1888no—
836C2×C4—1884no—
837C2×C4—1884no—
838C2×C4—1884no—
839C2×C4—1884no—
840C2×C4—1884no—
841C2×C4—1888no—
842C2×C4—1888no—
843C2×C4—1884no—
844C2×C4#1309405214yescomplemented
845C2×C4C22×D18811yescharacteristic
846C2×C4C22×D18811yescharacteristic
847C2×C4C22×D18811yescharacteristic
848C2×C4C22×D18811yescharacteristic
849C2×C4C22×D18811yescharacteristic
850C2×C4C22×D18811yescharacteristic
851C2×C4C22×D18811yescharacteristic
852C2×C4C22×D18811yescharacteristic
853C2×C4C22×D18811yescharacteristic
854C2×C4C22×D18811yescharacteristic
855C2×C4C22×D18811yescharacteristic
856C2×C4#41×D4714yes—
857C2×C4C24×D4711yescharacteristic
858C8—28no—
859C22—28no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—948no—
867C22—18816no—
868C22—18816no—
869C22—18816no—
870C22—1882no—
871C22—1882no—
872C22—1882no—
873C22—1884no—
874C22—1884no—
875C22#1568963512yes—
876C22C2×#1309405212yes—
877C22#1568992312yes—
878C22C23×D18811yescharacteristic
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—1884no—
888C4—1882no—
889C4—1882no—
890C4—1882no—
891C4#1568963512yes—
892C4C2×#1309405212yes—
893C4C2×#1309405212yes—
894C4C2×#41×D4712yes—
895C2—22no—
896C2—22no—
897C2—22no—
898C2—3762no—
899C2—1888no—
900C2C2×#1568963511yescharacteristic
901C2C22×#1309405211yescharacteristic
902C2C2×#1568992311yescharacteristic
subgroupG/H
centerC2×C4C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#2920C2
socleC22×C47C23×D4
hypercenter#2920D47
hypocenterC47#60558
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
1. #20256684C2semidirect
2. C22×C4×D188C2semidirect
3. #20253528C2semidirect
4. #20253488C2semidirect
5. #20253480C2semidirect
6. #20253437C2semidirect
7. #20253397C2semidirect
8. #20253389C2semidirect
9. #20253313C2semidirect
10. #20253187C2semidirect
11. #20252854C2semidirect
12. #20252618C2semidirect
13. C4×#13094052C2semidirect
14. C47×#2920C2semidirect
18. #15689680C22semidirect
19. #15689680C22semidirect
20. #15689680C22semidirect
21. #15689673C22semidirect
22. #15689673C22semidirect
23. #15689673C22semidirect
28. #15689657C22semidirect
29. #15689657C22semidirect
35. C4×#10625350C22semidirect
50. #15689459C22semidirect
51. #15689454C22semidirect
52. #15689442C22semidirect
53. #15689437C22semidirect
54. #15689424C22semidirect
55. #15689414C22semidirect
56. #15689404C22semidirect
57. #15689339C22semidirect
58. #15689329C22semidirect
59. #15689319C22semidirect
64. #15689236C22semidirect
65. #15689225C22semidirect
66. C4×#10625325C22semidirect
67. C4×D376C22semidirect
68. #15689165C22semidirect
70. #15689125C22semidirect
72. C47×#432C22semidirect
73. C47×#432C22semidirect
74. C47×#431C22semidirect
75. C47×#431C22semidirect
76. C47×#423C22semidirect
78. C4×M16×C47C22semidirect
101. #13094024C23semidirect
102. #13094024C23semidirect
103. #13094024C23semidirect
104. #13094021C23semidirect
109. #13094016C23semidirect
112. #13094012C23semidirect
133. C4×Dic94C23semidirect
134. C4×Dic94C23semidirect
155. C4×D188C23semidirect
156. C4×D188C23semidirect
182. #13093958C23semidirect
183. #13093956C23semidirect
184. #13093949C23semidirect
187. #13093946C23semidirect
204. C4⋊C8×C47C23semidirect
205. C4⋊C8×C47C23semidirect
208. #97×C47C23semidirect
209. C4×C8×C47C23semidirect
259. C2×D188#41semidirect
364. C2×C4×C47AGL(1,ℤ/8)semidirect
457. #2920D47semidirect
520. #432C2×D47semidirect
521. #432C2×D47semidirect
522. #431C2×D47semidirect
523. #431C2×D47semidirect
525. #423C2×D47semidirect
529. C4×M16C2×D47semidirect
530. C47#60558semidirect
652. C4⋊C8C22×D47semidirect
653. C4⋊C8C22×D47semidirect
660. #97C22×D47semidirect
661. C4×C8C22×D47semidirect
844. C2×C4#13094052semidirect

Maximal subgroups

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

subgroupindex
#202566842
C22×C4×D1882
#202535282
#202534882
#202534802
#202534372
#202533972
#202533892
#202533132
#202531872
#202528542
#202526182
C4×#130940522
C47×#29202
#6055847