Finite Group Databasebeta

← C3⋊D3×AGL(1,ℤ/16) #72222578

Subgroups — C3⋊D3×AGL(1,ℤ/16) #72222578

Order 2304.

2130 conjugacy classes of subgroups.

The subgroup lattice has 903 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#509C211yesmaximal, characteristic
2C3⋊D3×#444C211yesmaximal, characteristic, complemented
3C3⋊D3×#442C211yesmaximal, characteristic, complemented
4#11797962C211yesmaximal, characteristic, complemented
5#11797959C211yesmaximal, characteristic, complemented
6#11797956C211yesmaximal, characteristic, complemented
7#11797953C211yesmaximal, characteristic, complemented
8#11797950C211yesmaximal, characteristic, complemented
9#11797947C211yesmaximal, characteristic, complemented
10#11797944C211yesmaximal, characteristic, complemented
11C3⋊D3×#365C211yesmaximal, characteristic, complemented
12C3⋊D3×#361C211yesmaximal, characteristic, complemented
13C3⋊D3×#360C211yesmaximal, characteristic, complemented
14C3⋊D3×#347C211yesmaximal, characteristic, complemented
15C32×AGL(1,ℤ/16)C211yesmaximal, characteristic, complemented
16D3×AGL(1,ℤ/16)—34nomaximal
17C3⋊D3×#135C2211yescharacteristic
18C2×D8×C3⋊D3C2211yescharacteristic
19C3⋊D3×#131—21no—
20C4×D4×C3⋊D3—21no—
21C32×#509C2211yescharacteristic
22C32×#444C2211yescharacteristic, complemented
23C32×#442C2211yescharacteristic, complemented
24#10592896C2211yescharacteristic, complemented
25#10592892C2211yescharacteristic
26#10592851C2211yescharacteristic, complemented
27#10592846C2211yescharacteristic
28#10592844—21no—
29#10592713—21no—
30#10592613C412yescomplemented
31C3⋊D3×SD32C412yescomplemented
32#10592610C412yescomplemented
33C3⋊D3×D16C412yescomplemented
34#10592607C2211yescharacteristic
35C3⋊D3×M32C2211yescharacteristic
36C3⋊D3×M32C2211yescharacteristic
37#10592593C2211yescharacteristic, complemented
38C3⋊D3×#108C2211yescharacteristic
39#10592568C2211yescharacteristic, complemented
40C3⋊D3×#106C2211yescharacteristic
41#10592522—21no—
42C3⋊D3×#104—21no—
43#10592484—21no—
44C3⋊D3×#102—21no—
45#10592416C2211yescharacteristic, complemented
46#10592410C2211yescharacteristic, complemented
47C3⋊D3×#97C2211yescharacteristic
48C32×#365C2211yescharacteristic, complemented
49C32×#361C2211yescharacteristic, complemented
50C32×#360C2211yescharacteristic, complemented
51C32×#347C2211yescharacteristic, complemented
52#10589432C2211yescharacteristic, complemented
53#10589429C2211yescharacteristic, complemented
54#10589384C2211yescharacteristic, complemented
55#10589382C2211yescharacteristic, complemented
56#10589379C2211yescharacteristic, complemented
57#10589378C2211yescharacteristic, complemented
58#10589378C2211yescharacteristic, complemented
59#10589361C2211yescharacteristic, complemented
60#10589360C2211yescharacteristic, complemented
61#10589354C2211yescharacteristic, complemented
62#10589353C2211yescharacteristic, complemented
63#10589332C2211yescharacteristic, complemented
64D3×#509—34no—
65D3×#444—34no—
66D3×#442—34no—
67C3×AGL(1,ℤ/16)D314yescomplemented
68#71515—34no—
69#70929—34no—
70#70918—34no—
71D3×#365—34no—
72#69310—34no—
73D3×#361—34no—
74#69254—34no—
75D3×#360—34no—
76#69249—34no—
77#69091—34no—
78D3×#347—34no—
79#41×C3⋊D3—21no—
80C2×D4×C3⋊D3—21no—
81C22×C4×C3⋊D3—41no—
82C32×#135C2311yescharacteristic
83C2×C32×D8C2311yescharacteristic
84C32×#131—21no—
85C32×C4×D4—21no—
86#64159—21no—
87#64157—21no—
88D4×C3⋊Dic3—21no—
89C2×#3753—21no—
90C4×#638—41no—
91#64128C2×C411yescharacteristic, complemented
92Q16×C3⋊D3C2×C411yescharacteristic, complemented
93#64125—21no—
94SD16×C3⋊D3—21no—
95#64121C2×C411yescharacteristic, complemented
96D8×C3⋊D3—21no—
97D8×C3⋊D3—21no—
98D8×C3⋊D3C2×C412yes—
99D8×C3⋊D3C2×C412yes—
100D8×C3⋊D3C2×C411yescharacteristic, complemented
101#64116—21no—
102#64116—41no—
103M16×C3⋊D3—21no—
104M16×C3⋊D3—41no—
105#64113C2311yescharacteristic
106C2×#3745C2311yescharacteristic
107#64110—21no—
108#64110—41no—
109C2×C8×C3⋊D3—41no—
110C2×C8×C3⋊D3D411yescharacteristic
111C2×C8×C3⋊D3C2311yescharacteristic
112#64102—21no—
113C4⋊C4×C3⋊D3—21no—
114#64090—41no—
115C22⋊C4×C3⋊D3—41no—
116C4×C4⋊(C3⋊D3)—21no—
117C42×C3⋊D3D411yescharacteristic
118C32×SD32C2×C412yescomplemented
119C32×D16C2×C412yescomplemented
120C32×M32C2311yescharacteristic
121C32×M32C2311yescharacteristic
122C32×#108C2311yescharacteristic
123C32×#106C2311yescharacteristic
124C32×#104—21no—
125C32×#102—21no—
126C32×#97C2311yescharacteristic
127#63664—21no—
128#63659—21no—
129#63655C2×C412yescomplemented
130#63654C2×C412yescomplemented
131#63653C2×C412yescomplemented
132#63653C2×C412yescomplemented
133#63652—21no—
134#63649—21no—
135#63648—21no—
136#63646C2311yescharacteristic
137#63644C2311yescharacteristic
138#63642D411yescharacteristic
139#63642C2311yescharacteristic
140#63639C2311yescharacteristic
141#63639C2311yescharacteristic
142#63636—21no—
143#63635—21no—
144#63632—21no—
145#63630D411yescharacteristic
146#63627C2×C412yescomplemented
147#63626C2×C412yescomplemented
148#63625—21no—
149#63625C2×C412yescomplemented
150C16×C3⋊D3—21no—
151C16×C3⋊D3C2×C412yescomplemented
152C2×AGL(1,ℤ/16)—91noSylow
153D3×#135—34no—
154C2×D3×D8—34no—
155D3×#131—64no—
156C4×D3×D4—64no—
157C3×#509C2×D314yes—
158C3×#444C2×D314yescomplemented
159C3×#442C2×D314yescomplemented
160#5197—34no—
161#5193—34no—
162#5152—34no—
163#5147—34no—
164#5145—64no—
165#5014—64no—
166#4914—38no—
167D3×SD32—38no—
168#4911—38no—
169D3×D16—38no—
170#4908—34no—
171D3×M32—34no—
172D3×M32—34no—
173#4894—34no—
174D3×#108—34no—
175#4869—34no—
176D3×#106—34no—
177#4823—64no—
178D3×#104—64no—
179#4785—64no—
180D3×#102—64no—
181#4717—34no—
182#4711—34no—
183D3×#97—34no—
184C3×#365C2×D314yescomplemented
185C3×#361C2×D314yescomplemented
186C3×#360C2×D314yescomplemented
187C3×#347C2×D314yescomplemented
188#4566—34no—
189#4563—34no—
190#4518—34no—
191#4516—34no—
192#4513—34no—
193#4512—34no—
194#4512—34no—
195#4495—34no—
196#4494—34no—
197#4488—34no—
198#4487—34no—
199#4466—34no—
200C23×C3⋊D3—41no—
201C32×#41—21no—
202C2×C32×D4—21no—
203C22×C32×C4—41no—
204C2×#638—41no—
205C22×C3⋊Dic3—41no—
206#3832—21no—
207Q8×C3⋊D3—21no—
208#3830—21no—
209#3830—41no—
210D4×C3⋊D3—22no—
211D4×C3⋊D3—22no—
212D4×C3⋊D3—21no—
213D4×C3⋊D3—41no—
214D4×C3⋊D3—41no—
215D4×C3⋊D3—41no—
216#3828—21no—
217#3828—41no—
218C2×C4⋊(C3⋊D3)—21no—
219C2×C4×C3⋊D3—21no—
220C2×C4×C3⋊D3—41no—
221C2×C4×C3⋊D3—41no—
222C2×C4×C3⋊D3—41no—
223C2×C4×C3⋊D3—41no—
224C2×C4×C3⋊D3—84no—
225C2×C4×C3⋊D3C2×D411yescharacteristic
226C32×Q16C22×C411yescharacteristic, complemented
227C32×SD16—21no—
228C32×D8—21no—
229C32×D8C22×C412yes—
230C32×D8C22×C411yescharacteristic, complemented
231C32×M16—21no—
232C32×M16—41no—
233C2×C32×C8—41no—
234C2×C32×C8C2×D411yescharacteristic
235C2×C32×C8C2411yescharacteristic
236C32×C4⋊C4—21no—
237C32×C22⋊C4—41no—
238C32×C42C2×D411yescharacteristic
239#3757—41no—
240#3756—21no—
241#3755—21no—
242#3754—21no—
243#3753—22no—
244#3753—22no—
245#3753—21no—
246#3752—41no—
247#3752—41no—
248C4⋊(C3⋊Dic3)—21no—
249#3750—41no—
250C4×C3⋊Dic3—21no—
251C4×C3⋊Dic3C2×D411yescharacteristic
252#3748—21no—
253#3748—41no—
254C2×C3⋊(C3⋊C8)—41no—
255C2×C3⋊(C3⋊C8)C2×D411yescharacteristic
256C2×C3⋊(C3⋊C8)C2×D411yescharacteristic
257#3746C22×C411yescharacteristic, complemented
258#3745—21no—
259#3745C22×C412yes—
260#3745C22×C411yescharacteristic, complemented
261#3744—21no—
262#3743—41no—
263#3743—41no—
264#3743—41no—
265C8×C3⋊D3—21no—
266C8×C3⋊D3—21no—
267C8×C3⋊D3—41no—
268C8×C3⋊D3—41no—
269C8×C3⋊D3—41no—
270C8×C3⋊D3C22×C411yescharacteristic
271C8×C3⋊D3C22×C411yescharacteristic
272C8×C3⋊D3#4111yescharacteristic
273C8×C3⋊D3#4111yescharacteristic
274C32×C16—21no—
275C32×C16C22×C412yescomplemented
276C3⋊(C3⋊C16)—21no—
277C3⋊(C3⋊C16)C22×C412yescomplemented
278C2×#509—91no—
279C2×#444—91no—
280C2×#442—91no—
281AGL(1,ℤ/16)—91no—
282AGL(1,ℤ/16)—91no—
283AGL(1,ℤ/16)—91no—
284AGL(1,ℤ/16)—91no—
285AGL(1,ℤ/16)—91no—
286AGL(1,ℤ/16)—91no—
287AGL(1,ℤ/16)—91no—
288AGL(1,ℤ/16)C3⋊D311yescharacteristic, direct product factor
289C2×#365—91no—
290C2×#361—91no—
291C2×#360—91no—
292C2×#347—91no—
293D3×#41—64no—
294C2×D3×D4—64no—
295C22×C4×D3—124no—
296C3×#135C22×D314yes—
297C2×C3×D8C22×D314yes—
298C3×#131—24no—
299C3×C4×D4—24no—
300#950—64no—
301#948—64no—
302D4×Dic3—64no—
303C2×#213—64no—
304C4×#67—124no—
305#919—34no—
306D3×Q16—34no—
307#916—64no—
308D3×SD16—64no—
309#912—34no—
310D3×D8—38no—
311D3×D8—38no—
312D3×D8—34no—
313D3×D8—64no—
314D3×D8—64no—
315#907—64no—
316#907—124no—
317D3×M16—64no—
318D3×M16—124no—
319#904—34no—
320C2×D24—34no—
321#901—64no—
322#901—124no—
323C2×D3×C8—34no—
324C2×D3×C8—34no—
325C2×D3×C8—124no—
326#893—64no—
327D3×C4⋊C4—64no—
328#67⋊C4—124no—
329D3×C22⋊C4—124no—
330C4×D12—64no—
331C42×D3—34no—
332C3×SD32C4×D318yescomplemented
333C3×D16C4×D318yescomplemented
334C3×M32C22×D314yes—
335C3×M32C22×D314yes—
336C3×#108C22×D314yes—
337C3×#106C22×D314yes—
338C3×#104—24no—
339C3×#102—24no—
340C3×#97C22×D314yes—
341#837—64no—
342#832—64no—
343#828—38no—
344#827—38no—
345#826—38no—
346#826—38no—
347#825—64no—
348#822—64no—
349#821—64no—
350#819—34no—
351#817—34no—
352#815—34no—
353#815—34no—
354#812—34no—
355#812—34no—
356#809—64no—
357#808—64no—
358#805—64no—
359#803—34no—
360#800—38no—
361D48—38no—
362#798—38no—
363#798—64no—
364D3×C16—38no—
365D3×C16—64no—
366C23×C32—41no—
367C22×C3⋊D3—41no—
368C22×C3⋊D3—42no—
369C22×C3⋊D3—42no—
370C22×C3⋊D3—41no—
371C22×C3⋊D3—82no—
372C22×C3⋊D3—82no—
373C22×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
374C32×Q8—21no—
375C32×D4—22no—
376C32×D4—21no—
377C32×D4—41no—
378C32×D4—41no—
379C2×C32×C4—21no—
380C2×C32×C4—41no—
381C2×C32×C4—41no—
382C2×C32×C4—82no—
383C2×C32×C4C22×D411yescharacteristic
384#638—41no—
385#638—41no—
386#638—41no—
387#638—42no—
388#638—42no—
389C2×C3⋊Dic3—21no—
390C2×C3⋊Dic3—41no—
391C2×C3⋊Dic3—41no—
392C2×C3⋊Dic3—82no—
393C2×C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
394C4⋊(C3⋊D3)—21no—
395C4⋊(C3⋊D3)—22no—
396C4⋊(C3⋊D3)—41no—
397C4⋊(C3⋊D3)—41no—
398C4×C3⋊D3—42no—
399C4×C3⋊D3—41no—
400C4×C3⋊D3—41no—
401C4×C3⋊D3—41no—
402C4×C3⋊D3—82no—
403C4×C3⋊D3—82no—
404C4×C3⋊D3—82no—
405C4×C3⋊D3C4×D411yescharacteristic
406C4×C3⋊D3C4×D411yescharacteristic
407C4×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
408C4×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
409#634—21no—
410#634—41no—
411C32×C8—21no—
412C32×C8—41no—
413C32×C8C23×C411yescharacteristic
414C32×C8C2×#4111yescharacteristic
415C3⋊(C3⋊C8)—21no—
416C3⋊(C3⋊C8)—41no—
417C3⋊(C3⋊C8)C4×D411yescharacteristic
418C3⋊(C3⋊C8)C4×D411yescharacteristic
419C2×#135—91no—
420C22×D8—91no—
421C2×#131—181no—
422C2×C4×D4—181no—
423#509—91no—
424#509—91no—
425#509—92no—
426#509—92no—
427#509—91no—
428#509C2×C3⋊D311yescharacteristic
429C2×SD32—92no—
430C2×D16—92no—
431C2×M32—91no—
432C2×M32—91no—
433#444—91no—
434#444—91no—
435#444—91no—
436#444—181no—
437#444—181no—
438#444C2×C3⋊D311yescharacteristic, complemented
439#442—91no—
440#442—91no—
441#442—91no—
442#442—181no—
443#442—181no—
444#442C2×C3⋊D311yescharacteristic, complemented
445C2×#108—91no—
446C2×#106—91no—
447C2×#104—181no—
448C2×#102—181no—
449C2×#97—91no—
450#365—91no—
451#365—91no—
452#365—91no—
453#365C2×C3⋊D311yescharacteristic, complemented
454#361—91no—
455#361—91no—
456#361—91no—
457#361C2×C3⋊D311yescharacteristic, complemented
458#360—91no—
459#360—91no—
460#360—91no—
461#360C2×C3⋊D311yescharacteristic, complemented
462#347—91no—
463#347—91no—
464#347—91no—
465#347C2×C3⋊D311yescharacteristic, complemented
466C23×D3—124no—
467C3×#41—24no—
468C2×C3×D4—24no—
469C22×C3×C4—44no—
470C2×#67—124no—
471C22×Dic3—124no—
472#239—64no—
473D3×Q8—64no—
474#237—64no—
475#237—124no—
476D3×D4—68no—
477D3×D4—68no—
478D3×D4—64no—
479D3×D4—124no—
480D3×D4—124no—
481D3×D4—124no—
482#235—64no—
483#235—124no—
484C2×D12—64no—
485C2×C4×D3—34no—
486C2×C4×D3—64no—
487C2×C4×D3—124no—
488C2×C4×D3—124no—
489C2×C4×D3—124no—
490C2×C4×D3—124no—
491C2×C4×D3—2416no—
492C3×Q16C2×C4×D314yescomplemented
493C3×SD16—24no—
494C3×D8—24no—
495C3×D8C2×C4×D318yes—
496C3×D8C2×C4×D314yescomplemented
497C3×M16—24no—
498C3×M16—44no—
499C2×C3×C8—44no—
500C2×C3×C8D3×D414yes—
501C2×C3×C8C23×D314yes—
502C3×C4⋊C4—24no—
503C3×C22⋊C4—44no—
504C3×C42D3×D414yes—
505#217—124no—
506#216—64no—
507#215—64no—
508#214—64no—
509#213—68no—
510#213—68no—
511#213—64no—
512(C2×D3)⋊C4—124no—
513(C2×D3)⋊C4—124no—
514C4⋊Dic3—64no—
515Dic3⋊C4—124no—
516C4×Dic3—34no—
517C4×Dic3—64no—
518#208—64no—
519#208—124no—
520C2×C3⋊C8—34no—
521C2×C3⋊C8—34no—
522C2×C3⋊C8—124no—
523Dic12—34no—
524D24—34no—
525D24—38no—
526D24—64no—
527#204—64no—
528ΓL(1,𝔽25)—124no—
529ΓL(1,𝔽25)—124no—
530ΓL(1,𝔽25)—124no—
531D3×C8—34no—
532D3×C8—34no—
533D3×C8—34no—
534D3×C8—34no—
535D3×C8—64no—
536D3×C8—64no—
537D3×C8—124no—
538D3×C8—124no—
539D3×C8—124no—
540C3×C16—24no—
541C3×C16C2×C4×D318yescomplemented
542C3⋊C16—38no—
543C3⋊C16—64no—
544C22×C32—41no—
545C22×C32—42no—
546C22×C32—81no—
547C22×C32—81no—
548C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
549C2×C3⋊D3—22no—
550C2×C3⋊D3—41no—
551C2×C3⋊D3—42no—
552C2×C3⋊D3—84no—
553C2×C3⋊D3—81no—
554C2×C3⋊D3—81no—
555C2×C3⋊D3—82no—
556C2×C3⋊D3—84no—
557C2×C3⋊D3#44211yescharacteristic
558C2×C3⋊D3#44211yescharacteristic
559C32×C4—41no—
560C32×C4—41no—
561C32×C4—81no—
562C32×C4C2×C4×D411yescharacteristic
563C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
564C3⋊Dic3—41no—
565C3⋊Dic3—41no—
566C3⋊Dic3—81no—
567C3⋊Dic3#44211yescharacteristic
568C3⋊Dic3#44211yescharacteristic
569C2×#41—181no—
570C22×D4—181no—
571C23×C4—361no—
572#135—91no—
573#135—91no—
574#135—91no—
575#135—181no—
576#135—181no—
577#135C22×C3⋊D311yescharacteristic
578C2×Q16—91no—
579C2×SD16—181no—
580C2×D8—92no—
581C2×D8—92no—
582C2×D8—91no—
583C2×D8—91no—
584C2×D8—181no—
585C2×D8—181no—
586C2×D8—181no—
587C2×D8C22×C3⋊D311yescharacteristic
588#131—21no—
589#131—181no—
590#131—181no—
591#131—181no—
592#131—361no—
593#131—361no—
594C2×M16—181no—
595C2×M16—361no—
596C22×C8—91no—
597C22×C8—91no—
598C22×C8—361no—
599C4×D4—21no—
600C4×D4—181no—
601C4×D4—181no—
602C4×D4—181no—
603C4×D4—361no—
604C4×D4—361no—
605C2×C4⋊C4—181no—
606C2×C22⋊C4—361no—
607C2×C42—91no—
608SD32—92no—
609SD32—92no—
610SD32—92no—
611SD32C4×C3⋊D312yescomplemented
612D16—92no—
613D16—92no—
614D16—92no—
615D16C4×C3⋊D312yescomplemented
616M32—91no—
617M32—92no—
618M32—91no—
619M32—181no—
620M32C22×C3⋊D311yescharacteristic
621M32C22×C3⋊D311yescharacteristic
622C2×C16—92no—
623C2×C16—181no—
624#108—91no—
625#108—181no—
626#108C22×C3⋊D311yescharacteristic
627#106—91no—
628#106—181no—
629#106C22×C3⋊D311yescharacteristic
630#104—21no—
631#104—181no—
632#104—181no—
633#104—181no—
634#102—21no—
635#102—181no—
636#102—181no—
637#102—181no—
638#97—91no—
639#97—91no—
640#97—91no—
641#97C22×C3⋊D311yescharacteristic
642C23×C3—44no—
643C22×D3—34no—
644C22×D3—124no—
645C22×D3—128no—
646C22×D3—128no—
647C22×D3—124no—
648C22×D3—248no—
649C22×D3—248no—
650C3×Q8—24no—
651C3×D4—28no—
652C3×D4—24no—
653C3×D4—44no—
654C3×D4—44no—
655C2×C3×C4—24no—
656C2×C3×C4—44no—
657C2×C3×C4—44no—
658C2×C3×C4—88no—
659C2×C3×C4C2×D3×D414yes—
660#67—124no—
661#67—128no—
662#67—128no—
663#67—124no—
664#67—124no—
665C2×Dic3—34no—
666C2×Dic3—64no—
667C2×Dic3—124no—
668C2×Dic3—124no—
669C2×Dic3—248no—
670D12—64no—
671D12—68no—
672D12—124no—
673D12—124no—
674C4×D3—34no—
675C4×D3—34no—
676C4×D3—34no—
677C4×D3—34no—
678C4×D3—124no—
679C4×D3—124no—
680C4×D3—128no—
681C4×D3—124no—
682C4×D3—248no—
683C4×D3—248no—
684C4×D3—248no—
685Dic6—64no—
686Dic6—124no—
687C3×C8—24no—
688C3×C8—44no—
689C3×C8C22×C4×D314yes—
690C3×C8D3×#4114yes—
691C3⋊C8—34no—
692C3⋊C8—34no—
693C3⋊C8—64no—
694C3⋊C8—124no—
695C2×C32—21no—
696C2×C32—82no—
697C2×C32—81no—
698C2×C32C2×#44211yescharacteristic
699C3⋊D3—21no—
700C3⋊D3—81no—
701C3⋊D3—82no—
702C3⋊D3AGL(1,ℤ/16)12yesdirect product factor
703C24—361no—
704#41—21no—
705#41—181no—
706#41—181no—
707#41—181no—
708#41—361no—
709#41—361no—
710C2×Q8—181no—
711C2×D4—21no—
712C2×D4—182no—
713C2×D4—182no—
714C2×D4—181no—
715C2×D4—181no—
716C2×D4—361no—
717C2×D4—361no—
718C2×D4—361no—
719C2×D4—361no—
720C22×C4—41no—
721C22×C4—91no—
722C22×C4—181no—
723C22×C4—361no—
724C22×C4—361no—
725C22×C4—361no—
726C22×C4—361no—
727C22×C4—361no—
728C22×C4—724no—
729Q16—91no—
730Q16—181no—
731Q16C2×C4×C3⋊D311yescharacteristic, complemented
732SD16—21no—
733SD16—181no—
734SD16—181no—
735SD16—181no—
736D8—21no—
737D8—91no—
738D8—92no—
739D8—182no—
740D8—182no—
741D8—181no—
742D8—181no—
743D8C2×C4×C3⋊D312yes—
744D8C2×C4×C3⋊D311yescharacteristic, complemented
745M16—21no—
746M16—41no—
747M16—181no—
748M16—361no—
749M16—361no—
750M16—361no—
751M16—361no—
752C2×C8—41no—
753C2×C8—91no—
754C2×C8—91no—
755C2×C8—91no—
756C2×C8—91no—
757C2×C8—91no—
758C2×C8—91no—
759C2×C8—181no—
760C2×C8—181no—
761C2×C8—361no—
762C2×C8—361no—
763C2×C8—361no—
764C2×C8—361no—
765C2×C8D4×C3⋊D311yescharacteristic
766C2×C8C23×C3⋊D311yescharacteristic
767C4⋊C4—21no—
768C4⋊C4—181no—
769C4⋊C4—361no—
770C22⋊C4—41no—
771C22⋊C4—361no—
772C22⋊C4—361no—
773C22⋊C4—361no—
774C42—91no—
775C42—181no—
776C42D4×C3⋊D311yescharacteristic
777C16—21no—
778C16—92no—
779C16—181no—
780C16C2×C4×C3⋊D312yescomplemented
781C22×C3—44no—
782C22×C3—48no—
783C22×C3—84no—
784C22×C3—84no—
785C22×C3D3×AGL(1,ℤ/8)14yes—
786C2×D3—34no—
787C2×D3—34no—
788C2×D3—68no—
789C2×D3—124no—
790C2×D3—128no—
791C2×D3—2416no—
792C2×D3—248no—
793C2×D3—2416no—
794C2×D3—244no—
795C2×D3—244no—
796C3×C4—44no—
797C3×C4—44no—
798C3×C4—84no—
799C3×C4C4×D3×D414yes—
800C3×C4D3×AGL(1,ℤ/8)14yes—
801Dic3—34no—
802Dic3—34no—
803Dic3—124no—
804Dic3—124no—
805Dic3—244no—
806C32C2×AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
807C23—41no—
808C23—91no—
809C23—361no—
810C23—362no—
811C23—362no—
812C23—361no—
813C23—722no—
814C23—722no—
815Q8—21no—
816Q8—181no—
817Q8—361no—
818D4—22no—
819D4—21no—
820D4—41no—
821D4—41no—
822D4—182no—
823D4—181no—
824D4—361no—
825D4—362no—
826D4—362no—
827D4—361no—
828D4—361no—
829D4—361no—
830D4—361no—
831C2×C4—21no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—82no—
835C2×C4—91no—
836C2×C4—91no—
837C2×C4—91no—
838C2×C4—91no—
839C2×C4—91no—
840C2×C4—181no—
841C2×C4—361no—
842C2×C4—361no—
843C2×C4—362no—
844C2×C4—361no—
845C2×C4—361no—
846C2×C4—361no—
847C2×C4—722no—
848C2×C4—722no—
849C2×C4—722no—
850C2×C4—722no—
851C2×C4C2×D4×C3⋊D311yescharacteristic
852C8—21no—
853C8—41no—
854C8—91no—
855C8—91no—
856C8—181no—
857C8—361no—
858C8C22×C4×C3⋊D311yescharacteristic
859C8#41×C3⋊D311yescharacteristic
860C2×C3—24no—
861C2×C3—88no—
862C2×C3—84no—
863C2×C3D3×#44214yes—
864D3—38no—
865D3—64no—
866D3—248no—
867D3—244no—
868C22—41no—
869C22—42no—
870C22—81no—
871C22—81no—
872C22—91no—
873C22—91no—
874C22—182no—
875C22—361no—
876C22—362no—
877C22—721no—
878C22—721no—
879C22—724no—
880C22—722no—
881C22—724no—
882C22C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
883C4—41no—
884C4—41no—
885C4—81no—
886C4—91no—
887C4—91no—
888C4—361no—
889C4—361no—
890C4—721no—
891C4C4×D4×C3⋊D311yescharacteristic
892C4C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
893C3D3×AGL(1,ℤ/16)14yescomplemented
894C2—21no—
895C2—82no—
896C2—81no—
897C2—92no—
898C2—181no—
899C2—722no—
900C2—721no—
901C2C3⋊D3×#44211yescharacteristic
subgroupG/H
centerC2C3⋊D3×#442
commutatorC32×C8C23×C4
FrattiniC2×C8C23×C3⋊D3
FittingC32×AGL(1,ℤ/16)C2
socleC2×C32C2×#442
prime radicalC3⋊D3×#509C2
cosocleC2×C32×C8C24
hypercenterAGL(1,ℤ/16)C3⋊D3
hypocenterC32C2×AGL(1,ℤ/16)
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ AGL(1,ℤ/16)

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×#444C2semidirect
3. C3⋊D3×#442C2semidirect
4. #11797962C2semidirect
5. #11797959C2semidirect
6. #11797956C2semidirect
7. #11797953C2semidirect
8. #11797950C2semidirect
9. #11797947C2semidirect
10. #11797944C2semidirect
11. C3⋊D3×#365C2semidirect
12. C3⋊D3×#361C2semidirect
13. C3⋊D3×#360C2semidirect
14. C3⋊D3×#347C2semidirect
15. C32×AGL(1,ℤ/16)C2semidirect
22. C32×#444C22semidirect
23. C32×#442C22semidirect
24. #10592896C22semidirect
26. #10592851C22semidirect
30. #10592613C4semidirect
31. C3⋊D3×SD32C4semidirect
32. #10592610C4semidirect
33. C3⋊D3×D16C4semidirect
37. #10592593C22semidirect
39. #10592568C22semidirect
45. #10592416C22semidirect
46. #10592410C22semidirect
48. C32×#365C22semidirect
49. C32×#361C22semidirect
50. C32×#360C22semidirect
51. C32×#347C22semidirect
52. #10589432C22semidirect
53. #10589429C22semidirect
54. #10589384C22semidirect
55. #10589382C22semidirect
56. #10589379C22semidirect
57. #10589378C22semidirect
58. #10589378C22semidirect
59. #10589361C22semidirect
60. #10589360C22semidirect
61. #10589354C22semidirect
62. #10589353C22semidirect
63. #10589332C22semidirect
67. C3×AGL(1,ℤ/16)D3semidirect
91. #64128C2×C4semidirect
92. Q16×C3⋊D3C2×C4semidirect
95. #64121C2×C4semidirect
100. D8×C3⋊D3C2×C4semidirect
118. C32×SD32C2×C4semidirect
119. C32×D16C2×C4semidirect
129. #63655C2×C4semidirect
130. #63654C2×C4semidirect
131. #63653C2×C4semidirect
132. #63653C2×C4semidirect
146. #63627C2×C4semidirect
147. #63626C2×C4semidirect
149. #63625C2×C4semidirect
151. C16×C3⋊D3C2×C4semidirect
158. C3×#444C2×D3semidirect
159. C3×#442C2×D3semidirect
184. C3×#365C2×D3semidirect
185. C3×#361C2×D3semidirect
186. C3×#360C2×D3semidirect
187. C3×#347C2×D3semidirect
226. C32×Q16C22×C4semidirect
230. C32×D8C22×C4semidirect
257. #3746C22×C4semidirect
260. #3745C22×C4semidirect
275. C32×C16C22×C4semidirect
277. C3⋊(C3⋊C16)C22×C4semidirect
288. AGL(1,ℤ/16)C3⋊D3direct (N × H)
332. C3×SD32C4×D3semidirect
333. C3×D16C4×D3semidirect
438. #444C2×C3⋊D3semidirect
444. #442C2×C3⋊D3semidirect
453. #365C2×C3⋊D3semidirect
457. #361C2×C3⋊D3semidirect
461. #360C2×C3⋊D3semidirect
465. #347C2×C3⋊D3semidirect
492. C3×Q16C2×C4×D3semidirect
496. C3×D8C2×C4×D3semidirect
541. C3×C16C2×C4×D3semidirect
611. SD32C4×C3⋊D3semidirect
615. D16C4×C3⋊D3semidirect
702. C3⋊D3AGL(1,ℤ/16)direct (N × H)
731. Q16C2×C4×C3⋊D3semidirect
744. D8C2×C4×C3⋊D3semidirect
780. C16C2×C4×C3⋊D3semidirect
806. C32C2×AGL(1,ℤ/16)semidirect
893. C3D3×AGL(1,ℤ/16)semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#5092
C3⋊D3×#4442
C3⋊D3×#4422
#117979622
#117979592
#117979562
#117979532
#117979502
#117979472
#117979442
C3⋊D3×#3652
C3⋊D3×#3612
C3⋊D3×#3602
C3⋊D3×#3472
C32×AGL(1,ℤ/16)2
D3×AGL(1,ℤ/16)3