Finite Group Databasebeta

← D47×#3220 #27087601

Subgroups — D47×#3220 #27087601

Order 12032.

2342 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#540×D47C211yesmaximal, characteristic, complemented
2#535×D47C211yesmaximal, characteristic, complemented
3#20254441C211yesmaximal, characteristic, complemented
4#20254440C211yesmaximal, characteristic, complemented
5#20254439C211yesmaximal, characteristic, complemented
6#20254438C211yesmaximal, characteristic, complemented
7#20254437C212yesmaximal, complemented
8#20254436C212yesmaximal, complemented
9#20254435C212yesmaximal, complemented
10#20254434C212yesmaximal, complemented
11#20254433C211yesmaximal, characteristic, complemented
12#20254432C211yesmaximal, characteristic, complemented
13#20254431C211yesmaximal, characteristic, complemented
14#496×D47C211yesmaximal, characteristic, complemented
15#493×D47C211yesmaximal, characteristic, complemented
16#490×D47C211yesmaximal, characteristic, complemented
17#488×D47C211yesmaximal, characteristic, complemented
18#463×D47C212yesmaximal, complemented
19#459×D47C212yesmaximal, complemented
20#449×D47C212yesmaximal, complemented
21#447×D47C212yesmaximal, complemented
22#433×D47C211yesmaximal, characteristic, complemented
23C47×#3220C211yesmaximal, characteristic, complemented
24C2×#41×D47C2211yescharacteristic
25C22×D4×D47C2211yescharacteristic
26C2×SD16×D47C2212yescomplemented
27C2×D8×D47C2212yes—
28C2×D8×D47C2212yes—
29C2×D8×D47C2212yescomplemented
30#15689729C2211yescharacteristic, complemented
31#15689728C2211yescharacteristic, complemented
32#15689727C2211yescharacteristic, complemented
33#15689726C2212yescomplemented
34#15689725—22no—
35#15689724C2212yescomplemented
36#15689723—22no—
37#15689692C2211yescharacteristic, complemented
38#15689691C2211yescharacteristic, complemented
39#15689691C2211yescharacteristic, complemented
40#15689690C2211yescharacteristic, complemented
41#15689689—22no—
42#15689688—22no—
43#15689687C2211yescharacteristic, complemented
44#15689686C2211yescharacteristic, complemented
45#15689686C2211yescharacteristic, complemented
46#127×D47C2211yescharacteristic
47#127×D47C2211yescharacteristic
48#127×D47C2211yescharacteristic, complemented
49#125×D47C2211yescharacteristic, complemented
50#124×D47C2211yescharacteristic
51#124×D47C2211yescharacteristic
52#123×D47—22no—
53#121×D47—22no—
54#121×D47—22no—
55#121×D47C2212yes—
56#120×D47—22no—
57C4×D4×D47C2212yescomplemented
58#117×D47C2211yescharacteristic
59#15689513C2211yescharacteristic, complemented
60#15689512C2211yescharacteristic, complemented
61#15689511C2212yescomplemented
62#15689510C2211yescharacteristic, complemented
63#15689509C2212yescomplemented
64#15689500C2211yescharacteristic, complemented
65#15689499C2211yescharacteristic, complemented
66#15689499C2211yescharacteristic, complemented
67#15689498C2212yescomplemented
68#15689498C2212yescomplemented
69#15689489C2211yescharacteristic, complemented
70#15689488C2211yescharacteristic, complemented
71#15689487C2211yescharacteristic, complemented
72#15689486C2212yescomplemented
73#15689486C2212yescomplemented
74#15689480C2211yescharacteristic, complemented
75#15689479C2212yescomplemented
76#15689478C2211yescharacteristic, complemented
77#15689477C2211yescharacteristic, complemented
78#15689476C2212yescomplemented
79#15689341C2212yescomplemented
80#15689340C2212yescomplemented
81#15689339C2212yescomplemented
82#15689338C2212yescomplemented
83#15689337C2212yescomplemented
84#15689336C2212yescomplemented
85#15689335C2212yescomplemented
86#15689319C2212yescomplemented
87#15689318C2212yescomplemented
88#15689317C2212yescomplemented
89#15689317C2212yescomplemented
90#15689316C2212yescomplemented
91#15689316C2212yescomplemented
92#15689315C2212yescomplemented
93#15689271C2212yescomplemented
94#15689270C2212yescomplemented
95#15689269C2212yescomplemented
96#15689268C2212yescomplemented
97#15689267C2212yescomplemented
98#15689266C2212yescomplemented
99#15689265C2212yescomplemented
100#15689259C2212yescomplemented
101#15689258C2212yescomplemented
102#15689258C2212yescomplemented
103#15689257C2212yescomplemented
104#15689256C2212yescomplemented
105#15689255C2212yescomplemented
106#15689255C2212yescomplemented
107#15689185C2211yescharacteristic, complemented
108#15689184C2211yescharacteristic, complemented
109#15689183C2212yescomplemented
110#15689182C2211yescharacteristic, complemented
111#15689181C2212yescomplemented
112C4⋊C8×D47C2212yescomplemented
113#103×D47C2212yescomplemented
114#102×D47C2212yes—
115#102×D47C2212yes—
116#102×D47C2212yescomplemented
117C22⋊C8×D47C2212yes—
118#97×D47C2211yescharacteristic, complemented
119C4×C8×D47C2211yescharacteristic, complemented
120C47×#540C2211yescharacteristic, complemented
121C47×#535C2211yescharacteristic, complemented
122C47×#496C2211yescharacteristic, complemented
123C47×#493C2211yescharacteristic, complemented
124C47×#490C2211yescharacteristic, complemented
125C47×#488C2211yescharacteristic, complemented
126C47×#463C2212yescomplemented
127C47×#459C2212yescomplemented
128C47×#449C2212yescomplemented
129C47×#447C2212yescomplemented
130C47×#433C2211yescharacteristic, complemented
131C24×D47—21no—
132C2×#10625354C2311yescharacteristic
133C2×#10625350—21no—
134C2×#10625350C2311yescharacteristic
135C2×#10625352—21no—
136C2×#10625352C2311yescharacteristic
137#41×D47—44no—
138C2×Q8×D47C2311yescharacteristic
139C22×D188C2311yescharacteristic
140C22×C22⋊D47—21no—
141C2×D4×D47—21no—
142C2×D4×D47—22no—
143C2×D4×D47—21no—
144C2×D4×D47—21no—
145C2×D4×D47—22no—
146C2×D4×D47—22no—
147C2×D4×D47—22no—
148C2×D4×D47—44no—
149C2×D4×D47C2312yes—
150C2×D4×D47C2311yescharacteristic
151C2×D4×D47C2311yescharacteristic
152C2×D4×D47C2311yescharacteristic
153C2×D4×D47C2311yescharacteristic
154C2×D4×D47C2311yescharacteristic
155C22×C4×D47—21no—
156C22×C4×D47—22no—
157C22×C4×D47C2311yescharacteristic
158C2×#10625325C2312yescomplemented
159C2×#10625335C2312yescomplemented
160C2×#10625336C2312yescomplemented
161SD16×D47—44no—
162C2×D376C2312yes—
163C2×D376C2312yes—
164C2×D376C2312yescomplemented
165C2×#10625334C2312yes—
166C2×#10625334C2312yes—
167C2×#10625334C2312yes—
168C2×#10625334C2312yes—
169C2×#10625334C2312yescomplemented
170C2×#10625334C2312yescomplemented
171D8×D47—44no—
172D8×D47—44no—
173D8×D47—44no—
174C2×C8×D47C2312yes—
175C2×C8×D47C2312yes—
176#13094021C2311yescharacteristic
177#13094021C2311yescharacteristic
178#13094021C2311yescharacteristic, complemented
179#13094020—22no—
180#13094020—22no—
181#13094020—22no—
182#13094020C2311yescharacteristic
183#13094020C2311yescharacteristic
184#13094020C2311yescharacteristic
185#13094020C2311yescharacteristic
186#13094020C2312yescomplemented
187#13094016C2311yescharacteristic, complemented
188#13094015C2312yescomplemented
189#13094014—22no—
190#13094013C2311yescharacteristic
191#13094013C2311yescharacteristic
192#13094012C2311yescharacteristic
193#13094012C2311yescharacteristic
194#13094011C2311yescharacteristic
195#13094011C2311yescharacteristic
196#13094010—22no—
197#13094010—22no—
198#13094009—22no—
199#13094009—22no—
200#13094008—22no—
201#13094007—22no—
202#13094006—22no—
203#13094006—22no—
204#13094005—22no—
205#13093999—22no—
206#13093999—22no—
207#13093999C2312yes—
208#13093998—22no—
209#13093998—22no—
210#13093998C2312yes—
211#13093997—22no—
212#13093997—22no—
213#13093997—22no—
214#13093997—22no—
215#13093997—22no—
216#13093996—22no—
217#13093996—22no—
218#13093996—22no—
219#13093996—22no—
220#13093996—22no—
221#13093995—22no—
222#13093995—22no—
223#13093995C2312yes—
224#13093994—22no—
225#13093994—22no—
226#13093994—22no—
227#13093993—22no—
228#13093992—22no—
229#13093992—22no—
230#13093992—22no—
231C4×D188C2312yescomplemented
232D4×Dic47C2312yescomplemented
233#13093986C2312yescomplemented
234C4×C22⋊D47—22no—
235(C22⋊D47)⋊C4—22no—
236#13093983C2311yescharacteristic
237#13093982D412yes—
238#13093981C2311yescharacteristic
239#13093981C2311yescharacteristic
240#13093980D412yes—
241C4⋊C4×D47—22no—
242C4⋊C4×D47D412yes—
243C4⋊C4×D47C2312yes—
244C22⋊C4×D47—22no—
245C22⋊C4×D47—22no—
246C22⋊C4×D47—22no—
247C22⋊C4×D47—22no—
248C22⋊C4×D47D412yes—
249C42×D47C2311yescharacteristic
250C42×D47C2311yescharacteristic
251C4⋊(C47⋊C8)C2312yescomplemented
252Dic47⋊C8C2312yescomplemented
253Dic47⋊C8C2312yescomplemented
254#13093949C2312yescomplemented
255#13093948C2312yescomplemented
256#13093947C2312yescomplemented
257#13093946C2312yes—
258#13093946C2312yes—
259#13093946C2312yescomplemented
260#13093945C2312yes—
261#13093945C2312yes—
262#13093945C2312yescomplemented
263#13093944C2312yes—
264#13093944C2312yes—
265#13093944C2312yescomplemented
266C22⋊(C47⋊C8)C2312yes—
267(C2×D47)⋊C8C2312yes—
268(C2×D47)⋊C8C2312yes—
269#13093935C2311yescharacteristic, complemented
270#13093934C2312yescomplemented
271C4×C47⋊C8C2311yescharacteristic, complemented
272C8×Dic47C2312yescomplemented
273C2×#41×C47C2311yescharacteristic
274C22×D4×C47C2311yescharacteristic
275C2×SD16×C47C2312yescomplemented
276C2×D8×C47C2312yes—
277C2×D8×C47C2312yes—
278C2×D8×C47C2312yescomplemented
279#127×C47C2311yescharacteristic
280#127×C47C2311yescharacteristic
281#127×C47C2311yescharacteristic, complemented
282#125×C47C2311yescharacteristic, complemented
283#124×C47C2311yescharacteristic
284#124×C47C2311yescharacteristic
285#123×C47—22no—
286#121×C47—22no—
287#121×C47—22no—
288#121×C47C2312yes—
289#120×C47—22no—
290C4×D4×C47C2312yescomplemented
291#117×C47C2311yescharacteristic
292C4⋊C8×C47C2312yescomplemented
293#103×C47C2312yescomplemented
294#102×C47C2312yes—
295#102×C47C2312yes—
296#102×C47C2312yescomplemented
297C22⋊C8×C47C2312yes—
298#97×C47C2311yescharacteristic, complemented
299C4×C8×C47C2311yescharacteristic, complemented
300C24×C47—21no—
301C23×D47—21no—
302C23×D47—22no—
303C23×D47—21no—
304C23×D47—21no—
305C23×D47—21no—
306C23×D47—21no—
307C23×D47—21no—
308C23×D47—44no—
309C23×D47—84no—
310C23×D47C2×D411yescharacteristic
311#41×C47—42no—
312C2×Q8×C47C2411yescharacteristic
313C2×D4×C47—21no—
314C2×D4×C47—22no—
315C2×D4×C47—21no—
316C2×D4×C47—22no—
317C2×D4×C47—22no—
318C2×D4×C47—22no—
319C2×D4×C47—42no—
320C2×D4×C47C2412yes—
321C2×D4×C47C2411yescharacteristic
322C2×D4×C47C2411yescharacteristic
323C2×D4×C47C2411yescharacteristic
324C22×C4×C47—21no—
325C22×C4×C47—22no—
326C22×C4×C47C2411yescharacteristic
327C2×C22⋊D47—21no—
328C2×C22⋊D47—21no—
329C2×C22⋊D47—22no—
330C2×C22⋊D47—22no—
331C2×C22⋊D47—22no—
332C2×C22⋊D47—21no—
333C2×C22⋊D47—21no—
334C2×C22⋊D47—21no—
335C2×C22⋊D47—21no—
336C2×C22⋊D47—21no—
337C2×C22⋊D47—22no—
338C2×C22⋊D47—22no—
339C2×C22⋊D47—22no—
340C2×C22⋊D47—22no—
341C2×C22⋊D47—22no—
342C2×C22⋊D47—22no—
343C2×C22⋊D47—44no—
344C22×Dic47—21no—
345C22×Dic47—22no—
346C22×Dic47C2×D411yescharacteristic
347#10625354—42no—
348Q8×D47—24no—
349#10625352—42no—
350#10625352—44no—
351D4×D47—24no—
352D4×D47—24no—
353D4×D47—24no—
354D4×D47—24no—
355D4×D47—24no—
356D4×D47—42no—
357D4×D47—42no—
358D4×D47—44no—
359D4×D47—44no—
360D4×D47—44no—
361D4×D47—84no—
362D4×D47—84no—
363D4×D47—84no—
364D4×D47—84no—
365#10625350—42no—
366#10625350—44no—
367C2×D188—21no—
368C2×D188—21no—
369C2×D188—22no—
370C2×D188—22no—
371C2×D188—22no—
372C2×D188—22no—
373C2×D188—42no—
374C2×D188C2411yescharacteristic
375C2×D188C2411yescharacteristic
376C2×D188C2411yescharacteristic
377C2×D188C2412yes—
378C2×C4×D47—24no—
379C2×C4×D47—21no—
380C2×C4×D47—22no—
381C2×C4×D47—21no—
382C2×C4×D47—21no—
383C2×C4×D47—22no—
384C2×C4×D47—22no—
385C2×C4×D47—44no—
386C2×C4×D47—84no—
387C2×C4×D47C2×D412yes—
388C2×C4×D47C2×D412yes—
389C2×C4×D47C2×D411yescharacteristic
390C2×C4×D47C2×D411yescharacteristic
391C2×C4×D47C2411yescharacteristic
392C2×C4×D47C2411yescharacteristic
393C2×Dic94—21no—
394C2×Dic94C2411yescharacteristic
395SD16×C47—42no—
396D8×C47—42no—
397D8×C47—42no—
398D8×C47—42no—
399C2×C8×C47C2412yes—
400C2×C8×C47C2412yes—
401C4⋊C4×C47—22no—
402C4⋊C4×C47C2×D412yes—
403C4⋊C4×C47C2412yes—
404C22⋊C4×C47—22no—
405C22⋊C4×C47—22no—
406C22⋊C4×C47—22no—
407C22⋊C4×C47—22no—
408C22⋊C4×C47C2×D412yes—
409C42×C47C2411yescharacteristic
410C42×C47C2411yescharacteristic
411C22⋊Dic47—22no—
412C22⋊Dic47—22no—
413C22⋊Dic47—22no—
414C22⋊Dic47—22no—
415C22⋊Dic47C2×D412yes—
416#10625336—42no—
417#10625335—42no—
418#10625334—42no—
419#10625334—42no—
420#10625334—42no—
421#10625334—42no—
422#10625334—42no—
423#10625334—42no—
424(C2×D47)⋊C4—22no—
425(C2×D47)⋊C4—22no—
426(C2×D47)⋊C4—22no—
427(C2×D47)⋊C4—22no—
428(C2×D47)⋊C4—22no—
429(C2×D47)⋊C4—22no—
430(C2×D47)⋊C4—22no—
431(C2×D47)⋊C4—22no—
432(C2×D47)⋊C4C2×D412yes—
433(C2×D47)⋊C4C2×D412yes—
434C4⋊Dic47—22no—
435C4⋊Dic47C2×D412yes—
436C4⋊Dic47C2412yes—
437Dic47⋊C4—22no—
438Dic47⋊C4—22no—
439Dic47⋊C4—22no—
440Dic47⋊C4C2×D412yes—
441Dic47⋊C4C2×D412yes—
442C4×Dic47C2×D412yes—
443C4×Dic47C2×D412yes—
444C4×Dic47C2411yescharacteristic
445C4×Dic47C2411yescharacteristic
446C2×C47⋊C8C2412yes—
447C2×C47⋊C8C2412yes—
448D376—42no—
449D376—42no—
450D376—42no—
451#10625325—42no—
452C8×D47—24no—
453C8×D47—24no—
454C23×C47—22no—
455C23×C47—21no—
456C23×C47—21no—
457C23×C47—21no—
458C23×C47—42no—
459C23×C47—82no—
460C23×C47C22×D411yescharacteristic
461C22×D47—22no—
462C22×D47—24no—
463C22×D47—22no—
464C22×D47—21no—
465C22×D47—21no—
466C22×D47—21no—
467C22×D47—42no—
468C22×D47—42no—
469C22×D47—42no—
470C22×D47—42no—
471C22×D47—42no—
472C22×D47—42no—
473C22×D47—44no—
474C22×D47—44no—
475C22×D47—44no—
476C22×D47—44no—
477C22×D47—44no—
478C22×D47—44no—
479C22×D47—82no—
480C22×D47—82no—
481C22×D47—82no—
482C22×D47—816no—
483C22×D47C22×D411yescharacteristic
484C22×D47C22×D411yescharacteristic
485Q8×C47—22no—
486D4×C47—22no—
487D4×C47—22no—
488D4×C47—22no—
489D4×C47—22no—
490D4×C47—22no—
491D4×C47—42no—
492D4×C47—42no—
493D4×C47—82no—
494D4×C47—82no—
495D4×C47—82no—
496D4×C47—82no—
497C2×C4×C47—22no—
498C2×C4×C47—22no—
499C2×C4×C47—21no—
500C2×C4×C47—42no—
501C2×C4×C47—82no—
502C2×C4×C47C22×D412yes—
503C2×C4×C47C22×D412yes—
504C2×C4×C47C22×D411yescharacteristic
505C2×C4×C47C2511yescharacteristic
506C22⋊D47—42no—
507C22⋊D47—42no—
508C22⋊D47—42no—
509C22⋊D47—42no—
510C22⋊D47—42no—
511C22⋊D47—42no—
512C22⋊D47—42no—
513C22⋊D47—44no—
514C22⋊D47—82no—
515C22⋊D47—82no—
516C22⋊D47—82no—
517C22⋊D47—82no—
518C22⋊D47—82no—
519C22⋊D47—82no—
520C22⋊D47—82no—
521C22⋊D47—82no—
522C2×Dic47—22no—
523C2×Dic47—22no—
524C2×Dic47—21no—
525C2×Dic47—42no—
526C2×Dic47—82no—
527C2×Dic47C22×D412yes—
528C2×Dic47C22×D412yes—
529C2×Dic47C22×D411yescharacteristic
530C2×Dic47C22×D411yescharacteristic
531D188—22no—
532D188—22no—
533D188—22no—
534D188—22no—
535D188—22no—
536D188—42no—
537D188—42no—
538D188—82no—
539D188—82no—
540D188—82no—
541D188—82no—
542C4×D47—22no—
543C4×D47—24no—
544C4×D47—24no—
545C4×D47—22no—
546C4×D47—22no—
547C4×D47—42no—
548C4×D47—42no—
549C4×D47—42no—
550C4×D47—44no—
551C4×D47—82no—
552C4×D47—82no—
553C4×D47H(5,𝔽2)14yes—
554Dic94—22no—
555Dic94—42no—
556C8×C47—22no—
557C8×C47—22no—
558C47⋊C8—22no—
559C47⋊C8—22no—
560C2×#3220—471nomaximal, Sylow
561C22×C47—21no—
562C22×C47—22no—
563C22×C47—41no—
564C22×C47—41no—
565C22×C47—41no—
566C22×C47—42no—
567C22×C47—42no—
568C22×C47—42no—
569C22×C47—42no—
570C22×C47—42no—
571C22×C47—42no—
572C22×C47—84no—
573C22×C47C23×D411yescharacteristic
574C2×D47—21no—
575C2×D47—22no—
576C2×D47—44no—
577C2×D47—41no—
578C2×D47—41no—
579C2×D47—41no—
580C2×D47—42no—
581C2×D47—42no—
582C2×D47—42no—
583C2×D47—42no—
584C2×D47—42no—
585C2×D47—42no—
586C2×D47—84no—
587C2×D47—84no—
588C2×D47—84no—
589C2×D47—84no—
590C2×D47—88no—
591C2×D47—84no—
592C2×D47—84no—
593C2×D47#53512yes—
594C2×D47#57614yes—
595C4×C47—21no—
596C4×C47—22no—
597C4×C47—22no—
598C4×C47—41no—
599C4×C47—42no—
600C4×C47C2×H(5,𝔽2)12yes—
601Dic47—21no—
602Dic47—22no—
603Dic47—22no—
604Dic47—41no—
605Dic47—42no—
606Dic47#53512yes—
607C2×#540—471no—
608C2×#535—471no—
609#3220—471no—
610#3220—471no—
611#3220—471no—
612#3220—471no—
613#3220—472no—
614#3220—472no—
615#3220—472no—
616#3220—472no—
617#3220—471no—
618#3220—471no—
619#3220—471no—
620#3220D4711yescharacteristic, direct product factor
621C2×#496—471no—
622C2×#493—471no—
623C2×#490—471no—
624C2×#488—471no—
625C2×#463—472no—
626C2×#459—472no—
627C2×#449—472no—
628C2×#447—472no—
629C2×#433—471no—
630C2×C47—41no—
631C2×C47—81no—
632C2×C47—81no—
633C2×C47—81no—
634C2×C47—82no—
635C2×C47C2×#53511yescharacteristic
636C2×C47C2×#57612yes—
637D47—41no—
638D47—81no—
639D47—82no—
640D47—81no—
641D47—81no—
642D47#322014yesdirect product factor
643C22×#41—471no—
644C23×D4—471no—
645C22×SD16—472no—
646C22×D8—472no—
647C22×D8—472no—
648C22×D8—472no—
649#540—471no—
650#540—471no—
651#540—472no—
652#540—472no—
653#540—471no—
654#540—942no—
655#540—942no—
656#540C2×D4711yescharacteristic, complemented
657#535—471no—
658#535—471no—
659#535—471no—
660#535—471no—
661#535—471no—
662#535—471no—
663#535—471no—
664#535—942no—
665#535—942no—
666#535C2×D4711yescharacteristic, complemented
667C2×#127—471no—
668C2×#127—471no—
669C2×#127—471no—
670C2×#125—471no—
671C2×#124—471no—
672C2×#124—471no—
673C2×#123—942no—
674C2×#121—472no—
675C2×#121—942no—
676C2×#121—942no—
677C2×#120—942no—
678C2×C4×D4—472no—
679C2×#117—471no—
680#496—472no—
681#496—472no—
682#496—471no—
683#496—471no—
684#496—471no—
685#496C2×D4711yescharacteristic, complemented
686#493—472no—
687#493—472no—
688#493—471no—
689#493—471no—
690#493—471no—
691#493C2×D4711yescharacteristic, complemented
692#490—471no—
693#490—471no—
694#490—472no—
695#490—472no—
696#490—471no—
697#490C2×D4711yescharacteristic, complemented
698#488—471no—
699#488—471no—
700#488—472no—
701#488—472no—
702#488—471no—
703#488C2×D4711yescharacteristic, complemented
704#463—472no—
705#463—472no—
706#463—472no—
707#463—472no—
708#463—472no—
709#463—472no—
710#463—472no—
711#463C2×D4712yescomplemented
712#459—472no—
713#459—472no—
714#459—472no—
715#459—472no—
716#459—472no—
717#459—472no—
718#459—472no—
719#459C2×D4712yescomplemented
720#449—472no—
721#449—472no—
722#449—472no—
723#449—472no—
724#449—472no—
725#449—472no—
726#449—472no—
727#449C2×D4712yescomplemented
728#447—472no—
729#447—472no—
730#447—472no—
731#447—472no—
732#447—472no—
733#447—472no—
734#447—472no—
735#447C2×D4712yescomplemented
736#433—471no—
737#433—472no—
738#433—472no—
739#433—471no—
740#433—471no—
741#433C2×D4711yescharacteristic, complemented
742C2×C4⋊C8—472no—
743C2×#103—472no—
744C2×#102—472no—
745C2×#102—472no—
746C2×#102—472no—
747C2×C22⋊C8—472no—
748C2×#97—471no—
749C2×C4×C8—471no—
750C47C2×#322011yescharacteristic, complemented, Sylow
751C25—941no—
752C2×#41—471no—
753C2×#41—471no—
754C2×#41—471no—
755C2×#41—941no—
756C2×#41—941no—
757C2×#41—1884no—
758C2×#41C22×D4711yescharacteristic
759C22×Q8—471no—
760C22×D4—472no—
761C22×D4—471no—
762C22×D4—471no—
763C22×D4—471no—
764C22×D4—471no—
765C22×D4—471no—
766C22×D4—471no—
767C22×D4—942no—
768C22×D4—942no—
769C22×D4—942no—
770C22×D4—941no—
771C22×D4—941no—
772C22×D4—941no—
773C22×D4—942no—
774C22×D4—941no—
775C22×D4—1884no—
776C22×D4C22×D4711yescharacteristic
777C23×C4—471no—
778C23×C4—942no—
779C23×C4—941no—
780C2×SD16—472no—
781C2×SD16—472no—
782C2×SD16—472no—
783C2×SD16—1884no—
784C2×SD16C22×D4712yescomplemented
785C2×D8—472no—
786C2×D8—472no—
787C2×D8—472no—
788C2×D8—472no—
789C2×D8—472no—
790C2×D8—472no—
791C2×D8—472no—
792C2×D8—472no—
793C2×D8—472no—
794C2×D8—1884no—
795C2×D8—1884no—
796C2×D8—1884no—
797C2×D8C22×D4712yes—
798C2×D8C22×D4712yes—
799C2×D8C22×D4712yescomplemented
800C22×C8—472no—
801C22×C8—472no—
802#127—471no—
803#127—471no—
804#127—471no—
805#127—471no—
806#127—472no—
807#127—471no—
808#127—471no—
809#127—471no—
810#127—942no—
811#127—942no—
812#127—942no—
813#127C22×D4711yescharacteristic
814#127C22×D4711yescharacteristic
815#127C22×D4711yescharacteristic, complemented
816#125—472no—
817#125—471no—
818#125—942no—
819#125C22×D4711yescharacteristic, complemented
820#124—471no—
821#124—471no—
822#124—471no—
823#124—471no—
824#124—471no—
825#124—471no—
826#124—942no—
827#124—942no—
828#124C22×D4711yescharacteristic
829#124C22×D4711yescharacteristic
830#123—22no—
831#123—942no—
832#123—942no—
833#123—942no—
834#123—942no—
835#123—942no—
836#123—942no—
837#123—942no—
838#121—22no—
839#121—22no—
840#121—472no—
841#121—472no—
842#121—472no—
843#121—942no—
844#121—942no—
845#121—942no—
846#121—942no—
847#121—942no—
848#121—942no—
849#121—942no—
850#121—942no—
851#121—942no—
852#121—942no—
853#121—942no—
854#121—942no—
855#121—942no—
856#121—942no—
857#121—942no—
858#121—942no—
859#121C22×D4712yes—
860#120—22no—
861#120—942no—
862#120—942no—
863#120—942no—
864#120—942no—
865#120—942no—
866#120—942no—
867#120—942no—
868C4×D4—472no—
869C4×D4—472no—
870C4×D4—472no—
871C4×D4—942no—
872C4×D4—942no—
873C4×D4C22×D4712yescomplemented
874#117—471no—
875#117—472no—
876#117—472no—
877#117—471no—
878#117—471no—
879#117C22×D4711yescharacteristic
880C2×C4⋊C4—472no—
881C2×C4⋊C4—472no—
882C2×C4⋊C4—942no—
883C2×C22⋊C4—472no—
884C2×C22⋊C4—942no—
885C2×C22⋊C4—942no—
886C2×C22⋊C4—942no—
887C2×C22⋊C4—942no—
888C2×C42—471no—
889C2×C42—471no—
890C4⋊C8—472no—
891C4⋊C8—472no—
892C4⋊C8—472no—
893C4⋊C8C22×D4712yescomplemented
894#103—472no—
895#103—472no—
896#103—472no—
897#103C22×D4712yescomplemented
898#102—472no—
899#102—472no—
900#102—472no—
901#102—472no—
902#102—472no—
903#102—472no—
904#102—472no—
905#102—472no—
906#102—472no—
907#102C22×D4712yes—
908#102C22×D4712yes—
909#102C22×D4712yescomplemented
910C22⋊C8—472no—
911C22⋊C8—472no—
912C22⋊C8—472no—
913C22⋊C8C22×D4712yes—
914#97—472no—
915#97—471no—
916#97C22×D4711yescharacteristic, complemented
917C4×C8—472no—
918C4×C8—471no—
919C4×C8C22×D4711yescharacteristic, complemented
920C24—21no—
921C24—471no—
922C24—941no—
923C24—941no—
924C24—942no—
925C24—941no—
926C24—941no—
927C24—941no—
928C24—941no—
929C24—3764no—
930C24—1884no—
931#41—42no—
932#41—1882no—
933#41—1884no—
934#41—1882no—
935#41—1884no—
936#41—1882no—
937C2×Q8—471no—
938C2×Q8—941no—
939C2×Q8—944no—
940C2×Q8C23×D4711yescharacteristic
941C2×D4—21no—
942C2×D4—22no—
943C2×D4—21no—
944C2×D4—22no—
945C2×D4—22no—
946C2×D4—22no—
947C2×D4—42no—
948C2×D4—471no—
949C2×D4—471no—
950C2×D4—471no—
951C2×D4—472no—
952C2×D4—942no—
953C2×D4—941no—
954C2×D4—944no—
955C2×D4—944no—
956C2×D4—944no—
957C2×D4—944no—
958C2×D4—944no—
959C2×D4—942no—
960C2×D4—942no—
961C2×D4—942no—
962C2×D4—942no—
963C2×D4—942no—
964C2×D4—942no—
965C2×D4—942no—
966C2×D4—941no—
967C2×D4—941no—
968C2×D4—941no—
969C2×D4—941no—
970C2×D4—941no—
971C2×D4—942no—
972C2×D4—942no—
973C2×D4—941no—
974C2×D4—941no—
975C2×D4—942no—
976C2×D4—942no—
977C2×D4—942no—
978C2×D4—941no—
979C2×D4—3764no—
980C2×D4—3764no—
981C2×D4—3764no—
982C2×D4—3764no—
983C2×D4—1882no—
984C2×D4—1882no—
985C2×D4—1882no—
986C2×D4—1884no—
987C2×D4—1884no—
988C2×D4—1884no—
989C2×D4—1884no—
990C2×D4C23×D4711yescharacteristic
991C2×D4C23×D4711yescharacteristic
992C2×D4C23×D4711yescharacteristic
993C2×D4C23×D4712yes—
994C22×C4—21no—
995C22×C4—22no—
996C22×C4—471no—
997C22×C4—471no—
998C22×C4—472no—
999C22×C4—472no—
1000C22×C4—471no—
1001C22×C4—471no—
1002C22×C4—471no—
1003C22×C4—944no—
1004C22×C4—942no—
1005C22×C4—941no—
1006C22×C4—941no—
1007C22×C4—942no—
1008C22×C4—942no—
1009C22×C4—941no—
1010C22×C4—942no—
1011C22×C4—941no—
1012C22×C4—3764no—
1013C22×C4—1884no—
1014C22×C4C23×D4711yescharacteristic
1015SD16—42no—
1016SD16—1882no—
1017SD16—1882no—
1018SD16—1882no—
1019D8—42no—
1020D8—42no—
1021D8—42no—
1022D8—1882no—
1023D8—1882no—
1024D8—1882no—
1025D8—1882no—
1026D8—1882no—
1027D8—1882no—
1028D8—1882no—
1029D8—1882no—
1030D8—1882no—
1031C2×C8—472no—
1032C2×C8—472no—
1033C2×C8—944no—
1034C2×C8—944no—
1035C2×C8C23×D4712yes—
1036C2×C8C23×D4712yes—
1037C4⋊C4—22no—
1038C4⋊C4—472no—
1039C4⋊C4—472no—
1040C4⋊C4—472no—
1041C4⋊C4—472no—
1042C4⋊C4—942no—
1043C4⋊C4—942no—
1044C4⋊C4—942no—
1045C4⋊C4—942no—
1046C4⋊C4D4×D4712yes—
1047C4⋊C4C23×D4712yes—
1048C22⋊C4—22no—
1049C22⋊C4—22no—
1050C22⋊C4—22no—
1051C22⋊C4—22no—
1052C22⋊C4—472no—
1053C22⋊C4—472no—
1054C22⋊C4—472no—
1055C22⋊C4—942no—
1056C22⋊C4—942no—
1057C22⋊C4—942no—
1058C22⋊C4—942no—
1059C22⋊C4—942no—
1060C22⋊C4—942no—
1061C22⋊C4—942no—
1062C22⋊C4—942no—
1063C22⋊C4—942no—
1064C22⋊C4—942no—
1065C22⋊C4—942no—
1066C22⋊C4—942no—
1067C22⋊C4D4×D4712yes—
1068C42—472no—
1069C42—472no—
1070C42—471no—
1071C42—471no—
1072C42C23×D4711yescharacteristic
1073C42C23×D4711yescharacteristic
1074C23—22no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—42no—
1079C23—82no—
1080C23—471no—
1081C23—471no—
1082C23—942no—
1083C23—944no—
1084C23—942no—
1085C23—941no—
1086C23—941no—
1087C23—941no—
1088C23—3762no—
1089C23—3762no—
1090C23—3762no—
1091C23—37616no—
1092C23—1882no—
1093C23—1884no—
1094C23—1882no—
1095C23—1882no—
1096C23—1882no—
1097C23—1884no—
1098C23—1884no—
1099C23—1884no—
1100C23—1884no—
1101C23—1884no—
1102C23—1882no—
1103C23—1882no—
1104C23C2×D4×D4711yescharacteristic
1105Q8—22no—
1106Q8—942no—
1107Q8—1882no—
1108D4—22no—
1109D4—22no—
1110D4—22no—
1111D4—22no—
1112D4—22no—
1113D4—42no—
1114D4—42no—
1115D4—82no—
1116D4—82no—
1117D4—82no—
1118D4—82no—
1119D4—942no—
1120D4—942no—
1121D4—942no—
1122D4—942no—
1123D4—942no—
1124D4—3762no—
1125D4—3762no—
1126D4—3762no—
1127D4—3762no—
1128D4—3762no—
1129D4—3762no—
1130D4—3762no—
1131D4—3762no—
1132D4—3762no—
1133D4—3762no—
1134D4—3762no—
1135D4—3762no—
1136D4—1882no—
1137D4—1882no—
1138D4—1884no—
1139D4—1882no—
1140D4—1882no—
1141D4—1882no—
1142D4—1882no—
1143D4—1882no—
1144D4—1882no—
1145D4—1882no—
1146C2×C4—22no—
1147C2×C4—21no—
1148C2×C4—22no—
1149C2×C4—42no—
1150C2×C4—82no—
1151C2×C4—471no—
1152C2×C4—474no—
1153C2×C4—472no—
1154C2×C4—472no—
1155C2×C4—471no—
1156C2×C4—942no—
1157C2×C4—942no—
1158C2×C4—944no—
1159C2×C4—944no—
1160C2×C4—942no—
1161C2×C4—942no—
1162C2×C4—941no—
1163C2×C4—942no—
1164C2×C4—3762no—
1165C2×C4—3762no—
1166C2×C4—3762no—
1167C2×C4—1882no—
1168C2×C4—1882no—
1169C2×C4—1884no—
1170C2×C4—1882no—
1171C2×C4—1882no—
1172C2×C4C2×D4×D4712yes—
1173C2×C4C2×D4×D4712yes—
1174C2×C4C2×D4×D4711yescharacteristic
1175C2×C4C24×D4711yescharacteristic
1176C8—22no—
1177C8—22no—
1178C8—942no—
1179C8—942no—
1180C22—22no—
1181C22—21no—
1182C22—42no—
1183C22—42no—
1184C22—42no—
1185C22—42no—
1186C22—42no—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—42no—
1191C22—84no—
1192C22—474no—
1193C22—472no—
1194C22—942no—
1195C22—941no—
1196C22—3764no—
1197C22—3764no—
1198C22—3764no—
1199C22—3768no—
1200C22—3764no—
1201C22—3764no—
1202C22—3764no—
1203C22—1884no—
1204C22—1882no—
1205C22—1882no—
1206C22—1882no—
1207C22—1882no—
1208C22—1882no—
1209C22—1881no—
1210C22—1881no—
1211C22—1881no—
1212C22—1882no—
1213C22C22×D4×D4711yescharacteristic
1214C4—22no—
1215C4—22no—
1216C4—21no—
1217C4—42no—
1218C4—41no—
1219C4—472no—
1220C4—942no—
1221C4—942no—
1222C4—941no—
1223C4—1882no—
1224C4—1881no—
1225C4H(5,𝔽2)×D4712yes—
1226C2—41no—
1227C2—81no—
1228C2—81no—
1229C2—82no—
1230C2—81no—
1231C2—474no—
1232C2—3761no—
1233C2—3761no—
1234C2—3762no—
1235C2—3761no—
1236C2—1881no—
1237C2#535×D4711yescharacteristic
1238C2#576×D4712yes—
subgroupG/H
centerC22C22×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#3220C2
socleC22×C47C23×D4
hypercenter#3220D47
hypocenterC47C2×#3220
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #3220

Complements

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

NH ≅ G/Ntype
1. #540×D47C2semidirect
2. #535×D47C2semidirect
3. #20254441C2semidirect
4. #20254440C2semidirect
5. #20254439C2semidirect
6. #20254438C2semidirect
7. #20254437C2semidirect
8. #20254436C2semidirect
9. #20254435C2semidirect
10. #20254434C2semidirect
11. #20254433C2semidirect
12. #20254432C2semidirect
13. #20254431C2semidirect
14. #496×D47C2semidirect
15. #493×D47C2semidirect
16. #490×D47C2semidirect
17. #488×D47C2semidirect
18. #463×D47C2semidirect
19. #459×D47C2semidirect
20. #449×D47C2semidirect
21. #447×D47C2semidirect
22. #433×D47C2semidirect
23. C47×#3220C2semidirect
26. C2×SD16×D47C22semidirect
29. C2×D8×D47C22semidirect
30. #15689729C22semidirect
31. #15689728C22semidirect
32. #15689727C22semidirect
33. #15689726C22semidirect
35. #15689724C22semidirect
37. #15689692C22semidirect
38. #15689691C22semidirect
39. #15689691C22semidirect
40. #15689690C22semidirect
43. #15689687C22semidirect
44. #15689686C22semidirect
45. #15689686C22semidirect
48. #127×D47C22semidirect
49. #125×D47C22semidirect
57. C4×D4×D47C22semidirect
59. #15689513C22semidirect
60. #15689512C22semidirect
61. #15689511C22semidirect
62. #15689510C22semidirect
63. #15689509C22semidirect
64. #15689500C22semidirect
65. #15689499C22semidirect
66. #15689499C22semidirect
67. #15689498C22semidirect
68. #15689498C22semidirect
69. #15689489C22semidirect
70. #15689488C22semidirect
71. #15689487C22semidirect
72. #15689486C22semidirect
73. #15689486C22semidirect
74. #15689480C22semidirect
75. #15689479C22semidirect
76. #15689478C22semidirect
77. #15689477C22semidirect
78. #15689476C22semidirect
79. #15689341C22semidirect
80. #15689340C22semidirect
81. #15689339C22semidirect
82. #15689338C22semidirect
83. #15689337C22semidirect
84. #15689336C22semidirect
85. #15689335C22semidirect
86. #15689319C22semidirect
87. #15689318C22semidirect
88. #15689317C22semidirect
89. #15689317C22semidirect
90. #15689316C22semidirect
91. #15689316C22semidirect
92. #15689315C22semidirect
93. #15689271C22semidirect
94. #15689270C22semidirect
95. #15689269C22semidirect
96. #15689268C22semidirect
97. #15689267C22semidirect
98. #15689266C22semidirect
99. #15689265C22semidirect
100. #15689259C22semidirect
101. #15689258C22semidirect
102. #15689258C22semidirect
103. #15689257C22semidirect
104. #15689256C22semidirect
105. #15689255C22semidirect
106. #15689255C22semidirect
107. #15689185C22semidirect
108. #15689184C22semidirect
109. #15689183C22semidirect
110. #15689182C22semidirect
111. #15689181C22semidirect
112. C4⋊C8×D47C22semidirect
113. #103×D47C22semidirect
116. #102×D47C22semidirect
118. #97×D47C22semidirect
119. C4×C8×D47C22semidirect
120. C47×#540C22semidirect
121. C47×#535C22semidirect
122. C47×#496C22semidirect
123. C47×#493C22semidirect
124. C47×#490C22semidirect
125. C47×#488C22semidirect
126. C47×#463C22semidirect
127. C47×#459C22semidirect
128. C47×#449C22semidirect
129. C47×#447C22semidirect
130. C47×#433C22semidirect
158. C2×#10625325C23semidirect
159. C2×#10625335C23semidirect
160. C2×#10625336C23semidirect
164. C2×D376C23semidirect
169. C2×#10625334C23semidirect
170. C2×#10625334C23semidirect
178. #13094021C23semidirect
186. #13094020C23semidirect
187. #13094016C23semidirect
188. #13094015C23semidirect
231. C4×D188C23semidirect
232. D4×Dic47C23semidirect
233. #13093986C23semidirect
251. C4⋊(C47⋊C8)C23semidirect
252. Dic47⋊C8C23semidirect
253. Dic47⋊C8C23semidirect
254. #13093949C23semidirect
255. #13093948C23semidirect
256. #13093947C23semidirect
259. #13093946C23semidirect
262. #13093945C23semidirect
265. #13093944C23semidirect
269. #13093935C23semidirect
270. #13093934C23semidirect
271. C4×C47⋊C8C23semidirect
272. C8×Dic47C23semidirect
275. C2×SD16×C47C23semidirect
278. C2×D8×C47C23semidirect
281. #127×C47C23semidirect
282. #125×C47C23semidirect
290. C4×D4×C47C23semidirect
292. C4⋊C8×C47C23semidirect
293. #103×C47C23semidirect
296. #102×C47C23semidirect
298. #97×C47C23semidirect
299. C4×C8×C47C23semidirect
620. #3220D47direct (N × H)
642. D47#3220direct (N × H)
656. #540C2×D47semidirect
666. #535C2×D47semidirect
685. #496C2×D47semidirect
691. #493C2×D47semidirect
697. #490C2×D47semidirect
703. #488C2×D47semidirect
711. #463C2×D47semidirect
719. #459C2×D47semidirect
727. #449C2×D47semidirect
735. #447C2×D47semidirect
741. #433C2×D47semidirect
750. C47C2×#3220semidirect
784. C2×SD16C22×D47semidirect
799. C2×D8C22×D47semidirect
815. #127C22×D47semidirect
819. #125C22×D47semidirect
873. C4×D4C22×D47semidirect
893. C4⋊C8C22×D47semidirect
897. #103C22×D47semidirect
909. #102C22×D47semidirect
916. #97C22×D47semidirect
919. C4×C8C22×D47semidirect

Maximal subgroups

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

subgroupindex
#540×D472
#535×D472
#202544412
#202544402
#202544392
#202544382
#202544372
#202544362
#202544352
#202544342
#202544332
#202544322
#202544312
#496×D472
#493×D472
#490×D472
#488×D472
#463×D472
#459×D472
#449×D472
#447×D472
#433×D472
C47×#32202
C2×#322047