Finite Group Databasebeta

← D47×#3299 #27092665

Subgroups — D47×#3299 #27092665

Order 12032.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#554×D47C211yesmaximal, characteristic
2D4×Q8×D47C211yesmaximal, characteristic
3#20255267C211yesmaximal, characteristic, complemented
4#20255266C211yesmaximal, characteristic, complemented
5#20255265C211yesmaximal, characteristic, complemented
6#20255264C211yesmaximal, characteristic, complemented
7#20255263C211yesmaximal, characteristic, complemented
8#20255262C212yesmaximal, complemented
9#20255261C211yesmaximal, characteristic, complemented
10#20255260C212yesmaximal, complemented
11#20255259C212yesmaximal, complemented
12#20255258C211yesmaximal, characteristic, complemented
13#20255257C212yesmaximal, complemented
14#487×D47C211yesmaximal, characteristic, complemented
15#484×D47C212yesmaximal, complemented
16#477×D47C211yesmaximal, characteristic, complemented
17#467×D47C212yesmaximal, complemented
18#462×D47C211yesmaximal, characteristic, complemented
19#451×D47C212yesmaximal, complemented
20C4×Q16×D47C211yesmaximal, characteristic, complemented
21C8×D4×D47C211yesmaximal, characteristic
22C2×#103×D47C212yesmaximal, complemented
23C47×#3299C211yesmaximal, characteristic, complemented
24C22×Q8×D47C2212yes—
25C2×Q16×D47C2211yescharacteristic
26C2×Q16×D47C2212yes—
27C22×C8×D47C2212yes—
28#15689834C2211yescharacteristic
29#15689833C2211yescharacteristic
30#15689832—21no—
31#15689831C2212yes—
32#15689830C2211yescharacteristic
33#15689829—21no—
34#15689828C2212yes—
35#15689827—22no—
36Q8×D188C2211yescharacteristic
37D4×Dic94—21no—
38D4×Dic94C2211yescharacteristic
39#15689788—21no—
40#15689788C2211yescharacteristic
41Q8×C22⋊D47C2212yes—
42#15689786—22no—
43#15689786C2212yes—
44C4⋊Q8×D47—21no—
45C4⋊Q8×D47C2211yescharacteristic
46C4⋊Q8×D47C2211yescharacteristic
47#125×D47—21no—
48C22⋊Q8×D47—22no—
49C22⋊Q8×D47—22no—
50C22⋊Q8×D47C2212yes—
51C22⋊Q8×D47C2212yes—
52C4×Q8×D47C2211yescharacteristic
53C4×Q8×D47C2211yescharacteristic
54C4×D4×D47—21no—
55C4×D4×D47—21no—
56C4×D4×D47C2211yescharacteristic
57C2×C4⋊C4×D47C2212yes—
58#15689475C2211yescharacteristic, complemented
59#15689474C2211yescharacteristic, complemented
60#15689473C2211yescharacteristic, complemented
61#15689472C2212yescomplemented
62#15689472C2212yescomplemented
63#15689460C2212yescomplemented
64#15689460C2212yescomplemented
65#15689459C2212yescomplemented
66#15689458C2212yescomplemented
67#15689457C2212yescomplemented
68#15689457C2212yescomplemented
69#15689456C2212yescomplemented
70#15689419C2211yescharacteristic, complemented
71#15689418C2211yescharacteristic, complemented
72#15689417C2212yescomplemented
73#15689416C2212yescomplemented
74#15689415C2211yescharacteristic, complemented
75#15689365C2212yescomplemented
76#15689364C2212yescomplemented
77#15689363C2212yescomplemented
78#15689363C2212yescomplemented
79#15689362C2212yescomplemented
80#15689362C2212yescomplemented
81#15689361C2212yescomplemented
82#15689334C2211yescharacteristic, complemented
83#15689333C2211yescharacteristic, complemented
84#15689332C2212yescomplemented
85#15689331C2212yescomplemented
86#15689330C2211yescharacteristic, complemented
87#15689281C2212yescomplemented
88#15689280C2212yescomplemented
89#15689280C2212yescomplemented
90#15689279C2212yescomplemented
91#15689278C2212yescomplemented
92#15689277C2212yescomplemented
93#15689277C2212yescomplemented
94C4×Dic188C2211yescharacteristic, complemented
95Q16×Dic47C2211yescharacteristic, complemented
96#15689217C2211yescharacteristic, complemented
97C4×#10625337C2211yescharacteristic, complemented
98C4×#10625337C2211yescharacteristic, complemented
99#15689215C2211yescharacteristic, complemented
100#15689215C2211yescharacteristic, complemented
101C8×D188C2211yescharacteristic
102D4×C47⋊C8C2211yescharacteristic
103#15689188C2211yescharacteristic
104C8×C22⋊D47C2212yes—
105(C22⋊D47)⋊C8C2212yes—
106#107×D47C2212yes—
107#107×D47C2211yescharacteristic
108C4⋊C8×D47C2211yescharacteristic
109C2×#13093949C2212yescomplemented
110C2×#13093948C2212yescomplemented
111C2×#13093947C2212yescomplemented
112#103×D47C2212yes—
113#103×D47C2212yes—
114#103×D47C2211yescharacteristic
115#103×D47C2212yes—
116#103×D47C2212yes—
117#103×D47C2211yescharacteristic
118#103×D47C2212yescomplemented
119#103×D47C2212yescomplemented
120#103×D47C2212yescomplemented
121#103×D47C2212yescomplemented
122C22⋊C8×D47C2212yes—
123C4×C8×D47C2211yescharacteristic
124C47×#554C2211yescharacteristic
125D4×Q8×C47C2211yescharacteristic
126C47×#487C2211yescharacteristic, complemented
127C47×#484C2212yescomplemented
128C47×#477C2211yescharacteristic, complemented
129C47×#467C2212yescomplemented
130C47×#462C2211yescharacteristic, complemented
131C47×#451C2212yescomplemented
132C4×Q16×C47C2211yescharacteristic, complemented
133C8×D4×C47C2211yescharacteristic
134C2×#103×C47C2212yescomplemented
135C22×Dic94—22no—
136C22×Dic94C2312yes—
137C2×Q8×D47—22no—
138C2×Q8×D47—22no—
139C2×Q8×D47—21no—
140C2×Q8×D47—28no—
141C2×Q8×D47—44no—
142C2×Q8×D47C2311yescharacteristic
143C2×Q8×D47C2312yes—
144C2×Q8×D47C2312yes—
145C2×Q8×D47C2312yes—
146C2×Q8×D47C2311yescharacteristic
147C2×D4×D47D411yescharacteristic
148C22×C4×D47—22no—
149C22×C4×D47—22no—
150C22×C4×D47C2312yes—
151C2×Dic188C2311yescharacteristic
152C2×Dic188C2312yes—
153C2×#10625337C2311yescharacteristic
154C2×#10625337C2311yescharacteristic
155C2×#10625337C2312yes—
156C2×#10625337C2312yes—
157Q16×D47—24no—
158Q16×D47—44no—
159C22×C47⋊C8C2312yes—
160C2×C8×D47—44no—
161C2×C8×D47C2311yescharacteristic
162C2×C8×D47C2311yescharacteristic
163C2×C8×D47C2312yes—
164C2×C8×D47C2312yes—
165C2×C8×D47C2312yes—
166#13094024—21no—
167#13094024C2311yescharacteristic
168#13094024C2311yescharacteristic
169#13094023—21no—
170#13094023—21no—
171#13094023—22no—
172#13094023—21no—
173#13094023—21no—
174#13094023—21no—
175#13094023C2312yes—
176#13094022—22no—
177#13094022—21no—
178#13094022C2312yes—
179#13094016—21no—
180#13094015—21no—
181#13094015—21no—
182#13094014—22no—
183#13094014—22no—
184#13094004—22no—
185#13094004—22no—
186#13094004C2312yes—
187#13094004C2312yes—
188#13094003—22no—
189#13094003—22no—
190#13094003C2312yes—
191#13094003C2312yes—
192#13094002—22no—
193#13094002—22no—
194#13094002—22no—
195#13094002—22no—
196#13094002—22no—
197#13094002—22no—
198#13094001—22no—
199#13094001—22no—
200#13094001—22no—
201#13094001—22no—
202#13094001—22no—
203#13094001—22no—
204#13094000—22no—
205#13094000—22no—
206#13094000C2312yes—
207#13094000C2312yes—
208Q8×Dic47C2311yescharacteristic
209Q8×Dic47C2311yescharacteristic
210C4×Dic94—21no—
211C4×Dic94—21no—
212C4×Dic94C2311yescharacteristic
213C4×Dic94C2311yescharacteristic
214#13093989—21no—
215#13093989—21no—
216#13093989C2311yescharacteristic
217#13093989C2311yescharacteristic
218C4×D188—21no—
219C4×D188—21no—
220C4×D188C2311yescharacteristic
221D4×Dic47—21no—
222D4×Dic47—21no—
223D4×Dic47D411yescharacteristic
224#13093986—21no—
225#13093986—21no—
226#13093986D411yescharacteristic
227C4×C22⋊D47—22no—
228C4×C22⋊D47—22no—
229C4×C22⋊D47C2312yes—
230(C22⋊D47)⋊C4—22no—
231(C22⋊D47)⋊C4—22no—
232(C22⋊D47)⋊C4D412yes—
233C2×C4⋊Dic47C2312yes—
234C2×Dic47⋊C4—22no—
235C4⋊C4×D47—22no—
236C4⋊C4×D47—22no—
237C4⋊C4×D47—21no—
238C4⋊C4×D47—21no—
239C4⋊C4×D47—21no—
240C4⋊C4×D47—21no—
241C4⋊C4×D47—21no—
242C4⋊C4×D47—22no—
243C4⋊C4×D47—22no—
244C4⋊C4×D47D411yescharacteristic
245C4⋊C4×D47C2311yescharacteristic
246C4⋊C4×D47C2312yes—
247C4⋊C4×D47C2312yes—
248C4⋊C4×D47C2312yes—
249C4⋊C4×D47C2311yescharacteristic
250C22⋊C4×D47—22no—
251C22⋊C4×D47—22no—
252C22⋊C4×D47D412yes—
253C42×D47—21no—
254C42×D47—21no—
255C42×D47C2311yescharacteristic
256#13093958C2311yescharacteristic
257#13093958C2312yes—
258#13093957C2311yescharacteristic
259#13093957C2311yescharacteristic
260#13093957C2312yes—
261#13093957C2312yes—
262C4⋊(C47⋊C8)C2311yescharacteristic
263Dic47⋊C8C2312yes—
264#13093949C2312yes—
265#13093949C2312yes—
266#13093949C2311yescharacteristic
267#13093949C2311yescharacteristic
268#13093949C2312yes—
269#13093949C2312yes—
270#13093948C2311yescharacteristic
271#13093948C2311yescharacteristic
272#13093948C2312yes—
273#13093948C2312yes—
274#13093948C2312yes—
275#13093948C2312yes—
276#13093947C2311yescharacteristic
277#13093947C2311yescharacteristic
278#13093947C2312yes—
279#13093947C2312yes—
280#13093947C2312yes—
281#13093947C2312yes—
282C22⋊(C47⋊C8)C2312yes—
283(C2×D47)⋊C8C2312yes—
284(C2×D47)⋊C8C2312yes—
285C4×C47⋊C8C2311yescharacteristic
286C8×Dic47C2311yescharacteristic
287C8×Dic47C2311yescharacteristic
288C22×Q8×C47C2312yes—
289C2×Q16×C47C2311yescharacteristic
290C2×Q16×C47C2312yes—
291C22×C8×C47C2312yes—
292C4⋊Q8×C47—21no—
293C4⋊Q8×C47C2311yescharacteristic
294C4⋊Q8×C47C2311yescharacteristic
295#125×C47—21no—
296C22⋊Q8×C47—22no—
297C22⋊Q8×C47—22no—
298C22⋊Q8×C47C2312yes—
299C22⋊Q8×C47C2312yes—
300C4×Q8×C47C2311yescharacteristic
301C4×Q8×C47C2311yescharacteristic
302C4×D4×C47—21no—
303C4×D4×C47—21no—
304C4×D4×C47C2311yescharacteristic
305C2×C4⋊C4×C47C2312yes—
306#107×C47C2311yescharacteristic
307#107×C47C2312yes—
308C4⋊C8×C47C2311yescharacteristic
309#103×C47C2312yes—
310#103×C47C2312yes—
311#103×C47C2312yes—
312#103×C47C2312yes—
313#103×C47C2311yescharacteristic
314#103×C47C2311yescharacteristic
315C22⋊C8×C47C2312yes—
316C4×C8×C47C2311yescharacteristic
317C23×D47C2×D412yes—
318C2×Q8×C47—22no—
319C2×Q8×C47—21no—
320C2×Q8×C47—24no—
321C2×Q8×C47—42no—
322C2×Q8×C47C2412yes—
323C2×Q8×C47C2411yescharacteristic
324C2×Q8×C47C2411yescharacteristic
325C2×D4×C47C2×D411yescharacteristic
326C22×C4×C47—22no—
327C22×C4×C47—22no—
328C22×C4×C47C2412yes—
329C2×C22⋊D47C2×D412yes—
330C22×Dic47—22no—
331C22×Dic47—22no—
332C22×Dic47C2×D412yes—
333Q8×D47—22no—
334Q8×D47—24no—
335Q8×D47—22no—
336Q8×D47—24no—
337Q8×D47—22no—
338Q8×D47—24no—
339Q8×D47—24no—
340Q8×D47—42no—
341Q8×D47—42no—
342Q8×D47—48no—
343Q8×D47—48no—
344Q8×D47—82no—
345Q8×D47#4114yes—
346D4×D47Q1618yescomplemented
347C2×D188C2×D411yescharacteristic
348C2×C4×D47—21no—
349C2×C4×D47—24no—
350C2×C4×D47—24no—
351C2×C4×D47—21no—
352C2×C4×D47—21no—
353C2×C4×D47—21no—
354C2×C4×D47—22no—
355C2×C4×D47—22no—
356C2×C4×D47—22no—
357C2×C4×D47—22no—
358C2×C4×D47—22no—
359C2×C4×D47—22no—
360C2×C4×D47—48no—
361C2×C4×D47—84no—
362C2×C4×D47C2×D411yescharacteristic
363C2×C4×D47C2×D412yes—
364C2×C4×D47C2×D412yes—
365C2×C4×D47C2×D411yescharacteristic
366C2×C4×D47C2412yes—
367C2×C4×D47C2411yescharacteristic
368C2×Dic94—21no—
369C2×Dic94—24no—
370C2×Dic94—22no—
371C2×Dic94—21no—
372C2×Dic94—22no—
373C2×Dic94—22no—
374C2×Dic94—22no—
375C2×Dic94—21no—
376C2×Dic94—22no—
377C2×Dic94—42no—
378C2×Dic94—48no—
379C2×Dic94C2412yes—
380C2×Dic94C2411yescharacteristic
381C2×Dic94C2411yescharacteristic
382Q16×C47—22no—
383Q16×C47—42no—
384C2×C8×C47—42no—
385C2×C8×C47C2411yescharacteristic
386C2×C8×C47C2412yes—
387C2×C8×C47C2411yescharacteristic
388C4⋊C4×C47—22no—
389C4⋊C4×C47—21no—
390C4⋊C4×C47—21no—
391C4⋊C4×C47—21no—
392C4⋊C4×C47—21no—
393C4⋊C4×C47—21no—
394C4⋊C4×C47—22no—
395C4⋊C4×C47—22no—
396C4⋊C4×C47C2×D411yescharacteristic
397C4⋊C4×C47C2411yescharacteristic
398C4⋊C4×C47C2412yes—
399C4⋊C4×C47C2411yescharacteristic
400C22⋊C4×C47—22no—
401C22⋊C4×C47—22no—
402C22⋊C4×C47C2×D412yes—
403C42×C47—21no—
404C42×C47—21no—
405C42×C47C2411yescharacteristic
406C22⋊Dic47—22no—
407C22⋊Dic47—22no—
408C22⋊Dic47C2×D412yes—
409#10625337—22no—
410#10625337—22no—
411#10625337—42no—
412#10625337—42no—
413(C2×D47)⋊C4—22no—
414(C2×D47)⋊C4—22no—
415(C2×D47)⋊C4—22no—
416(C2×D47)⋊C4—22no—
417(C2×D47)⋊C4C2×D412yes—
418(C2×D47)⋊C4C2×D412yes—
419C4⋊Dic47—22no—
420C4⋊Dic47—21no—
421C4⋊Dic47—21no—
422C4⋊Dic47—21no—
423C4⋊Dic47—21no—
424C4⋊Dic47—21no—
425C4⋊Dic47—22no—
426C4⋊Dic47—22no—
427C4⋊Dic47C2×D411yescharacteristic
428C4⋊Dic47C2411yescharacteristic
429C4⋊Dic47C2412yes—
430C4⋊Dic47C2411yescharacteristic
431Dic47⋊C4—21no—
432Dic47⋊C4—21no—
433Dic47⋊C4—22no—
434Dic47⋊C4—22no—
435Dic47⋊C4—21no—
436Dic47⋊C4—22no—
437Dic47⋊C4—22no—
438Dic47⋊C4—22no—
439Dic47⋊C4—22no—
440Dic47⋊C4—22no—
441Dic47⋊C4—21no—
442Dic47⋊C4—21no—
443Dic47⋊C4—22no—
444Dic47⋊C4—22no—
445Dic47⋊C4—22no—
446Dic47⋊C4—21no—
447Dic47⋊C4C2×D412yes—
448C4×Dic47—21no—
449C4×Dic47—21no—
450C4×Dic47—21no—
451C4×Dic47—21no—
452C4×Dic47—21no—
453C4×Dic47—21no—
454C4×Dic47C2×D411yescharacteristic
455C4×Dic47C2×D411yescharacteristic
456C4×Dic47C2411yescharacteristic
457C2×C47⋊C8—42no—
458C2×C47⋊C8C2411yescharacteristic
459C2×C47⋊C8C2411yescharacteristic
460C2×C47⋊C8C2412yes—
461Dic188—22no—
462Dic188—42no—
463C8×D47—22no—
464C8×D47—22no—
465C8×D47—24no—
466C8×D47—42no—
467C8×D47—42no—
468C23×C47C22×D412yes—
469C22×D47—24no—
470C22×D47—24no—
471C22×D47C2×Q1618yes—
472C22×D47C22×D412yes—
473C22×D47C22×D411yescharacteristic
474Q8×C47—21no—
475Q8×C47—21no—
476Q8×C47—22no—
477Q8×C47—21no—
478Q8×C47—22no—
479Q8×C47—44no—
480Q8×C47—81no—
481Q8×C47C2×#4112yes—
482D4×C47C2×Q1614yescomplemented
483C2×C4×C47—21no—
484C2×C4×C47—22no—
485C2×C4×C47—22no—
486C2×C4×C47—21no—
487C2×C4×C47—21no—
488C2×C4×C47—21no—
489C2×C4×C47—22no—
490C2×C4×C47—22no—
491C2×C4×C47—44no—
492C2×C4×C47—82no—
493C2×C4×C47C22×D411yescharacteristic
494C2×C4×C47C22×D412yes—
495C2×C4×C47C22×D411yescharacteristic
496C2×C4×C47C2511yescharacteristic
497C22⋊D47C2×Q1618yescomplemented
498C2×Dic47—21no—
499C2×Dic47—24no—
500C2×Dic47—21no—
501C2×Dic47—21no—
502C2×Dic47—21no—
503C2×Dic47—22no—
504C2×Dic47—22no—
505C2×Dic47—44no—
506C2×Dic47—82no—
507C2×Dic47C22×D411yescharacteristic
508C2×Dic47C22×D412yes—
509C2×Dic47C22×D411yescharacteristic
510C2×Dic47C22×D411yescharacteristic
511D188C2×Q1614yescomplemented
512C4×D47—24no—
513C4×D47—24no—
514C4×D47—22no—
515C4×D47—22no—
516C4×D47—22no—
517C4×D47—24no—
518C4×D47—44no—
519C4×D47—44no—
520C4×D47—44no—
521C4×D47—42no—
522C4×D47—42no—
523C4×D47—42no—
524C4×D47—44no—
525C4×D47—82no—
526C4×D47—82no—
527C4×D47C2×Q1614yes—
528C4×D47C2×#4112yes—
529C4×D47H(5,𝔽2)12yes—
530Dic94—21no—
531Dic94—24no—
532Dic94—21no—
533Dic94—22no—
534Dic94—21no—
535Dic94—22no—
536Dic94—44no—
537Dic94—44no—
538Dic94—44no—
539Dic94—44no—
540Dic94—42no—
541Dic94—82no—
542Dic94—81no—
543Dic94C2×#4112yes—
544C8×C47—21no—
545C8×C47—21no—
546C8×C47—22no—
547C47⋊C8—21no—
548C47⋊C8—21no—
549C47⋊C8—22no—
550C2×#3299—471nomaximal, Sylow
551C22×C47—22no—
552C22×C47—22no—
553C22×C47C22×Q1614yes—
554C22×C47C23×D411yescharacteristic
555C2×D47—22no—
556C2×D47—22no—
557C2×D47—216no—
558C2×D47#54612yes—
559C2×D47C22×Q1614yes—
560C2×D47C22×Q1612yes—
561C2×D47#57712yes—
562C4×C47—22no—
563C4×C47—22no—
564C4×C47—21no—
565C4×C47—42no—
566C4×C47—41no—
567C4×C47—42no—
568C4×C47—41no—
569C4×C47—41no—
570C4×C47C22×Q1612yes—
571C4×C47C22×#4111yescharacteristic
572C4×C47C2×H(5,𝔽2)11yescharacteristic
573Dic47—22no—
574Dic47—22no—
575Dic47—21no—
576Dic47—42no—
577Dic47—41no—
578Dic47—42no—
579Dic47—41no—
580Dic47—41no—
581Dic47#54612yes—
582Dic47C22×Q1612yes—
583C2×#554—471no—
584C2×D4×Q8—471no—
585#3299—471no—
586#3299—472no—
587#3299—471no—
588#3299—472no—
589#3299—471no—
590#3299—472no—
591#3299—471no—
592#3299—471no—
593#3299—472no—
594#3299—471no—
595#3299—471no—
596#3299D4711yescharacteristic, direct product factor
597C2×#487—471no—
598C2×#484—472no—
599C2×#477—471no—
600C2×#467—472no—
601C2×#462—471no—
602C2×#451—472no—
603C2×C4×Q16—471no—
604C2×C8×D4—471no—
605C22×#103—472no—
606C2×C47—24no—
607C2×C47C2×#54611yescharacteristic
608C2×C47C23×Q1611yescharacteristic
609C2×C47C2×#57711yescharacteristic
610D47—24no—
611D47#329914yesdirect product factor
612C23×Q8—472no—
613C22×Q16—471no—
614C22×Q16—472no—
615C23×C8—472no—
616#554—471no—
617#554—472no—
618#554—471no—
619#554—471no—
620#554—472no—
621#554—941no—
622#554—942no—
623#554—941no—
624#554C2×D4711yescharacteristic
625D4×Q8—472no—
626D4×Q8—471no—
627D4×Q8—472no—
628D4×Q8—471no—
629D4×Q8—471no—
630D4×Q8—941no—
631D4×Q8—942no—
632D4×Q8—941no—
633D4×Q8C2×D4711yescharacteristic
634C2×C4⋊Q8—471no—
635C2×C4⋊Q8—471no—
636C2×C4⋊Q8—941no—
637C2×#125—941no—
638C2×C22⋊Q8—472no—
639C2×C22⋊Q8—472no—
640C2×C22⋊Q8—942no—
641C2×C22⋊Q8—942no—
642C2×C4×Q8—471no—
643C2×C4×Q8—471no—
644C2×C4×D4—471no—
645C2×C4×D4—941no—
646C2×C4×D4—941no—
647C22×C4⋊C4—472no—
648#487—471no—
649#487—471no—
650#487—472no—
651#487—472no—
652#487—471no—
653#487C2×D4711yescharacteristic, complemented
654#484—472no—
655#484—472no—
656#484—472no—
657#484—472no—
658#484—472no—
659#484—472no—
660#484—472no—
661#484C2×D4712yescomplemented
662#477—471no—
663#477—471no—
664#477—472no—
665#477—471no—
666#477—472no—
667#477C2×D4711yescharacteristic, complemented
668#467—472no—
669#467—472no—
670#467—472no—
671#467—472no—
672#467—472no—
673#467—472no—
674#467—472no—
675#467C2×D4712yescomplemented
676#462—472no—
677#462—471no—
678#462—471no—
679#462—471no—
680#462—472no—
681#462C2×D4711yescharacteristic, complemented
682#451—472no—
683#451—472no—
684#451—472no—
685#451—472no—
686#451—472no—
687#451—472no—
688#451—472no—
689#451C2×D4712yescomplemented
690C4×Q16—471no—
691C4×Q16—471no—
692C4×Q16—471no—
693C4×Q16—471no—
694C4×Q16—471no—
695C4×Q16—471no—
696C4×Q16—471no—
697C4×Q16C2×D4711yescharacteristic, complemented
698C8×D4—472no—
699C8×D4—471no—
700C8×D4—471no—
701C8×D4—472no—
702C8×D4—471no—
703C8×D4C2×D4711yescharacteristic
704C2×#107—472no—
705C2×#107—471no—
706C2×C4⋊C8—471no—
707C2×#103—472no—
708C2×#103—472no—
709C2×#103—472no—
710C2×#103—472no—
711C2×#103—472no—
712C2×#103—472no—
713C2×#103—472no—
714C2×#103—471no—
715C2×#103—472no—
716C2×#103—472no—
717C2×#103—472no—
718C2×#103—472no—
719C2×#103—471no—
720C2×#103C2×D4712yescomplemented
721C2×C22⋊C8—472no—
722C2×C4×C8—471no—
723C47C2×#329911yescharacteristic, complemented, Sylow
724C22×Q8—471no—
725C22×Q8—471no—
726C22×Q8—472no—
727C22×Q8—472no—
728C22×Q8—472no—
729C22×Q8—472no—
730C22×Q8—942no—
731C22×Q8—941no—
732C22×Q8—942no—
733C22×Q8—942no—
734C22×Q8—948no—
735C22×Q8—1884no—
736C22×Q8C22×D4712yes—
737C22×D4—471no—
738C23×C4—472no—
739C23×C4—942no—
740C23×C4—942no—
741C2×Q16—471no—
742C2×Q16—471no—
743C2×Q16—472no—
744C2×Q16—472no—
745C2×Q16—471no—
746C2×Q16—472no—
747C2×Q16—944no—
748C2×Q16—1884no—
749C2×Q16C22×D4711yescharacteristic
750C2×Q16C22×D4712yes—
751C22×C8—472no—
752C22×C8—471no—
753C22×C8—472no—
754C22×C8—471no—
755C22×C8—472no—
756C22×C8—472no—
757C22×C8—1884no—
758C22×C8C22×D4712yes—
759C4⋊Q8—21no—
760C4⋊Q8—472no—
761C4⋊Q8—472no—
762C4⋊Q8—471no—
763C4⋊Q8—471no—
764C4⋊Q8—941no—
765C4⋊Q8—941no—
766C4⋊Q8—941no—
767C4⋊Q8—941no—
768C4⋊Q8—941no—
769C4⋊Q8—942no—
770C4⋊Q8—941no—
771C4⋊Q8—942no—
772C4⋊Q8—941no—
773C4⋊Q8C22×D4711yescharacteristic
774C4⋊Q8C22×D4711yescharacteristic
775#125—21no—
776#125—941no—
777#125—942no—
778#125—942no—
779#125—941no—
780#125—941no—
781C22⋊Q8—22no—
782C22⋊Q8—22no—
783C22⋊Q8—472no—
784C22⋊Q8—472no—
785C22⋊Q8—472no—
786C22⋊Q8—472no—
787C22⋊Q8—472no—
788C22⋊Q8—472no—
789C22⋊Q8—942no—
790C22⋊Q8—942no—
791C22⋊Q8—942no—
792C22⋊Q8—942no—
793C22⋊Q8—942no—
794C22⋊Q8—942no—
795C22⋊Q8—942no—
796C22⋊Q8—942no—
797C22⋊Q8—942no—
798C22⋊Q8—942no—
799C22⋊Q8—942no—
800C22⋊Q8—942no—
801C22⋊Q8—942no—
802C22⋊Q8—942no—
803C22⋊Q8—942no—
804C22⋊Q8—942no—
805C22⋊Q8—942no—
806C22⋊Q8—942no—
807C22⋊Q8C22×D4712yes—
808C22⋊Q8C22×D4712yes—
809C4×Q8—471no—
810C4×Q8—471no—
811C4×Q8—471no—
812C4×Q8—471no—
813C4×Q8—471no—
814C4×Q8—471no—
815C4×Q8—941no—
816C4×Q8—941no—
817C4×Q8—941no—
818C4×Q8—941no—
819C4×Q8C22×D4711yescharacteristic
820C4×Q8C22×D4711yescharacteristic
821C4×D4—21no—
822C4×D4—21no—
823C4×D4—471no—
824C4×D4—472no—
825C4×D4—471no—
826C4×D4—472no—
827C4×D4—471no—
828C4×D4—941no—
829C4×D4—941no—
830C4×D4—942no—
831C4×D4—942no—
832C4×D4—941no—
833C4×D4—941no—
834C4×D4—942no—
835C4×D4—942no—
836C4×D4—941no—
837C4×D4—941no—
838C4×D4C22×D4711yescharacteristic
839C2×C4⋊C4—471no—
840C2×C4⋊C4—472no—
841C2×C4⋊C4—471no—
842C2×C4⋊C4—472no—
843C2×C4⋊C4—472no—
844C2×C4⋊C4—472no—
845C2×C4⋊C4—471no—
846C2×C4⋊C4—942no—
847C2×C4⋊C4—942no—
848C2×C4⋊C4—941no—
849C2×C4⋊C4—941no—
850C2×C4⋊C4—941no—
851C2×C4⋊C4—941no—
852C2×C4⋊C4—942no—
853C2×C4⋊C4—942no—
854C2×C4⋊C4—941no—
855C2×C4⋊C4—942no—
856C2×C4⋊C4C22×D4712yes—
857C2×C22⋊C4—472no—
858C2×C22⋊C4—942no—
859C2×C22⋊C4—942no—
860C2×C42—471no—
861C2×C42—941no—
862C2×C42—941no—
863#107—471no—
864#107—472no—
865#107—471no—
866#107—471no—
867#107—472no—
868#107—472no—
869#107C22×D4711yescharacteristic
870#107C22×D4712yes—
871C4⋊C8—472no—
872C4⋊C8—471no—
873C4⋊C8C22×D4711yescharacteristic
874#103—471no—
875#103—472no—
876#103—472no—
877#103—472no—
878#103—471no—
879#103—472no—
880#103—471no—
881#103—472no—
882#103—472no—
883#103—472no—
884#103—471no—
885#103—472no—
886#103—471no—
887#103—472no—
888#103—472no—
889#103—472no—
890#103—471no—
891#103—472no—
892#103C22×D4711yescharacteristic
893#103C22×D4712yes—
894#103C22×D4712yes—
895#103C22×D4712yes—
896#103C22×D4711yescharacteristic
897#103C22×D4712yes—
898C22⋊C8—472no—
899C22⋊C8—472no—
900C22⋊C8—472no—
901C22⋊C8C22×D4712yes—
902C4×C8—471no—
903C4×C8—471no—
904C4×C8—471no—
905C4×C8C22×D4711yescharacteristic
906C24—472no—
907C2×Q8—22no—
908C2×Q8—21no—
909C2×Q8—24no—
910C2×Q8—42no—
911C2×Q8—474no—
912C2×Q8—471no—
913C2×Q8—472no—
914C2×Q8—471no—
915C2×Q8—941no—
916C2×Q8—942no—
917C2×Q8—941no—
918C2×Q8—942no—
919C2×Q8—942no—
920C2×Q8—942no—
921C2×Q8—944no—
922C2×Q8—942no—
923C2×Q8—942no—
924C2×Q8—942no—
925C2×Q8—944no—
926C2×Q8—944no—
927C2×Q8—941no—
928C2×Q8—942no—
929C2×Q8—944no—
930C2×Q8—944no—
931C2×Q8—3762no—
932C2×Q8—1882no—
933C2×Q8—1888no—
934C2×Q8—1888no—
935C2×Q8—1882no—
936C2×Q8—1882no—
937C2×Q8—1888no—
938C2×Q8C23×D4712yes—
939C2×Q8C23×D4711yescharacteristic
940C2×Q8C23×D4711yescharacteristic
941C2×D4—472no—
942C2×D4—478no—
943C2×D4—471no—
944C2×D4D4×D4711yescharacteristic
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—471no—
948C22×C4—471no—
949C22×C4—472no—
950C22×C4—471no—
951C22×C4—472no—
952C22×C4—472no—
953C22×C4—472no—
954C22×C4—944no—
955C22×C4—944no—
956C22×C4—941no—
957C22×C4—942no—
958C22×C4—942no—
959C22×C4—941no—
960C22×C4—941no—
961C22×C4—941no—
962C22×C4—942no—
963C22×C4—942no—
964C22×C4—942no—
965C22×C4—942no—
966C22×C4—942no—
967C22×C4—942no—
968C22×C4—3764no—
969C22×C4—1888no—
970C22×C4C23×D4712yes—
971Q16—22no—
972Q16—42no—
973Q16—942no—
974Q16—942no—
975Q16—942no—
976Q16—1882no—
977Q16—1882no—
978Q16—1882no—
979C2×C8—42no—
980C2×C8—471no—
981C2×C8—471no—
982C2×C8—472no—
983C2×C8—942no—
984C2×C8—944no—
985C2×C8—942no—
986C2×C8—1882no—
987C2×C8—1882no—
988C2×C8—1882no—
989C2×C8C23×D4711yescharacteristic
990C2×C8C23×D4711yescharacteristic
991C2×C8C23×D4712yes—
992C4⋊C4—22no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—22no—
999C4⋊C4—22no—
1000C4⋊C4—472no—
1001C4⋊C4—471no—
1002C4⋊C4—471no—
1003C4⋊C4—472no—
1004C4⋊C4—471no—
1005C4⋊C4—941no—
1006C4⋊C4—942no—
1007C4⋊C4—942no—
1008C4⋊C4—942no—
1009C4⋊C4—941no—
1010C4⋊C4—942no—
1011C4⋊C4—942no—
1012C4⋊C4—941no—
1013C4⋊C4—941no—
1014C4⋊C4—942no—
1015C4⋊C4—942no—
1016C4⋊C4—942no—
1017C4⋊C4—941no—
1018C4⋊C4—941no—
1019C4⋊C4—942no—
1020C4⋊C4—942no—
1021C4⋊C4—941no—
1022C4⋊C4—941no—
1023C4⋊C4—942no—
1024C4⋊C4—942no—
1025C4⋊C4—942no—
1026C4⋊C4—941no—
1027C4⋊C4—941no—
1028C4⋊C4—941no—
1029C4⋊C4D4×D4711yescharacteristic
1030C4⋊C4C23×D4711yescharacteristic
1031C4⋊C4C23×D4712yes—
1032C4⋊C4C23×D4711yescharacteristic
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—472no—
1036C22⋊C4—472no—
1037C22⋊C4—472no—
1038C22⋊C4—942no—
1039C22⋊C4—942no—
1040C22⋊C4—942no—
1041C22⋊C4—942no—
1042C22⋊C4—942no—
1043C22⋊C4—942no—
1044C22⋊C4D4×D4712yes—
1045C42—21no—
1046C42—21no—
1047C42—471no—
1048C42—471no—
1049C42—471no—
1050C42—941no—
1051C42—941no—
1052C42—941no—
1053C42—941no—
1054C42—941no—
1055C42—941no—
1056C42C23×D4711yescharacteristic
1057C23—471no—
1058C23—478no—
1059C23—472no—
1060C23—944no—
1061C23—944no—
1062C23C2×D4×D4712yes—
1063Q8—21no—
1064Q8—21no—
1065Q8—22no—
1066Q8—21no—
1067Q8—22no—
1068Q8—44no—
1069Q8—81no—
1070Q8—472no—
1071Q8—944no—
1072Q8—941no—
1073Q8—941no—
1074Q8—942no—
1075Q8—941no—
1076Q8—942no—
1077Q8—3761no—
1078Q8—3762no—
1079Q8—1884no—
1080Q8—1884no—
1081Q8—1882no—
1082Q8—1884no—
1083Q8—1884no—
1084Q8#41×D4712yes—
1085D4—478no—
1086D4—474no—
1087D4Q16×D4714yescomplemented
1088C2×C4—21no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—44no—
1097C2×C4—82no—
1098C2×C4—471no—
1099C2×C4—471no—
1100C2×C4—474no—
1101C2×C4—472no—
1102C2×C4—472no—
1103C2×C4—471no—
1104C2×C4—472no—
1105C2×C4—944no—
1106C2×C4—944no—
1107C2×C4—942no—
1108C2×C4—944no—
1109C2×C4—944no—
1110C2×C4—941no—
1111C2×C4—942no—
1112C2×C4—942no—
1113C2×C4—941no—
1114C2×C4—941no—
1115C2×C4—941no—
1116C2×C4—942no—
1117C2×C4—942no—
1118C2×C4—3762no—
1119C2×C4—3762no—
1120C2×C4—3762no—
1121C2×C4—1884no—
1122C2×C4—1884no—
1123C2×C4—1882no—
1124C2×C4—1882no—
1125C2×C4—1884no—
1126C2×C4—1884no—
1127C2×C4—1882no—
1128C2×C4—1884no—
1129C2×C4C2×D4×D4711yescharacteristic
1130C2×C4C2×D4×D4712yes—
1131C2×C4C2×D4×D4711yescharacteristic
1132C2×C4C24×D4711yescharacteristic
1133C8—21no—
1134C8—21no—
1135C8—22no—
1136C8—941no—
1137C8—941no—
1138C8—942no—
1139C22—22no—
1140C22—22no—
1141C22—472no—
1142C22—472no—
1143C22—472no—
1144C22—474no—
1145C22—9416no—
1146C22—942no—
1147C22—942no—
1148C22C2×Q16×D4714yes—
1149C22C22×D4×D4711yescharacteristic
1150C4—22no—
1151C4—22no—
1152C4—21no—
1153C4—42no—
1154C4—41no—
1155C4—41no—
1156C4—42no—
1157C4—41no—
1158C4—472no—
1159C4—472no—
1160C4—942no—
1161C4—942no—
1162C4—941no—
1163C4—1882no—
1164C4—1881no—
1165C4—1881no—
1166C4—1882no—
1167C4—1881no—
1168C4C2×Q16×D4712yes—
1169C4C2×#41×D4711yescharacteristic
1170C4H(5,𝔽2)×D4711yescharacteristic
1171C2—24no—
1172C2—474no—
1173C2—944no—
1174C2#546×D4711yescharacteristic
1175C2C22×Q16×D4711yescharacteristic
1176C2#577×D4711yescharacteristic
subgroupG/H
centerC22C22×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#3299C2
socleC22×C47C23×D4
prime radicalC2×D4×D47D4
hypercenter#3299D47
hypocenterC47C2×#3299
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3299

Complements

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

NH ≅ G/Ntype
3. #20255267C2semidirect
4. #20255266C2semidirect
5. #20255265C2semidirect
6. #20255264C2semidirect
7. #20255263C2semidirect
8. #20255262C2semidirect
9. #20255261C2semidirect
10. #20255260C2semidirect
11. #20255259C2semidirect
12. #20255258C2semidirect
13. #20255257C2semidirect
14. #487×D47C2semidirect
15. #484×D47C2semidirect
16. #477×D47C2semidirect
17. #467×D47C2semidirect
18. #462×D47C2semidirect
19. #451×D47C2semidirect
20. C4×Q16×D47C2semidirect
22. C2×#103×D47C2semidirect
23. C47×#3299C2semidirect
58. #15689475C22semidirect
59. #15689474C22semidirect
60. #15689473C22semidirect
61. #15689472C22semidirect
62. #15689472C22semidirect
63. #15689460C22semidirect
64. #15689460C22semidirect
65. #15689459C22semidirect
66. #15689458C22semidirect
67. #15689457C22semidirect
68. #15689457C22semidirect
69. #15689456C22semidirect
70. #15689419C22semidirect
71. #15689418C22semidirect
72. #15689417C22semidirect
73. #15689416C22semidirect
74. #15689415C22semidirect
75. #15689365C22semidirect
76. #15689364C22semidirect
77. #15689363C22semidirect
78. #15689363C22semidirect
79. #15689362C22semidirect
80. #15689362C22semidirect
81. #15689361C22semidirect
82. #15689334C22semidirect
83. #15689333C22semidirect
84. #15689332C22semidirect
85. #15689331C22semidirect
86. #15689330C22semidirect
87. #15689281C22semidirect
88. #15689280C22semidirect
89. #15689280C22semidirect
90. #15689279C22semidirect
91. #15689278C22semidirect
92. #15689277C22semidirect
93. #15689277C22semidirect
94. C4×Dic188C22semidirect
95. Q16×Dic47C22semidirect
96. #15689217C22semidirect
97. C4×#10625337C22semidirect
98. C4×#10625337C22semidirect
99. #15689215C22semidirect
100. #15689215C22semidirect
109. C2×#13093949C22semidirect
110. C2×#13093948C22semidirect
111. C2×#13093947C22semidirect
118. #103×D47C22semidirect
119. #103×D47C22semidirect
120. #103×D47C22semidirect
121. #103×D47C22semidirect
126. C47×#487C22semidirect
127. C47×#484C22semidirect
128. C47×#477C22semidirect
129. C47×#467C22semidirect
130. C47×#462C22semidirect
131. C47×#451C22semidirect
132. C4×Q16×C47C22semidirect
134. C2×#103×C47C22semidirect
346. D4×D47Q16semidirect
482. D4×C47C2×Q16semidirect
497. C22⋊D47C2×Q16semidirect
511. D188C2×Q16semidirect
596. #3299D47direct (N × H)
611. D47#3299direct (N × H)
653. #487C2×D47semidirect
661. #484C2×D47semidirect
667. #477C2×D47semidirect
675. #467C2×D47semidirect
681. #462C2×D47semidirect
689. #451C2×D47semidirect
697. C4×Q16C2×D47semidirect
720. C2×#103C2×D47semidirect
723. C47C2×#3299semidirect
1087. D4Q16×D47semidirect

Maximal subgroups

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

subgroupindex
#554×D472
D4×Q8×D472
#202552672
#202552662
#202552652
#202552642
#202552632
#202552622
#202552612
#202552602
#202552592
#202552582
#202552572
#487×D472
#484×D472
#477×D472
#467×D472
#462×D472
#451×D472
C4×Q16×D472
C8×D4×D472
C2×#103×D472
C47×#32992
C2×#329947