Finite Group Databasebeta

← D3×#5166 #11865690

Subgroups — D3×#5166 #11865690

Order 1152.

1056 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×SD16C211yesmaximal, characteristic
2D3×Q8×Dic3C211yesmaximal, characteristic, complemented
3C2×D3×#216C211yesmaximal, characteristic, complemented
4D3×#936C211yesmaximal, characteristic
5#10592865C211yesmaximal, characteristic, complemented
6C3×#5166C211yesmaximal, characteristic, complemented
7#10591612C211yesmaximal, characteristic, complemented
8#10591604C211yesmaximal, characteristic, complemented
9#10591443C211yesmaximal, characteristic, complemented
10#10591442C211yesmaximal, characteristic, complemented
11D3×#832C211yesmaximal, characteristic
12#10590859C211yesmaximal, characteristic, complemented
13#10590796C211yesmaximal, characteristic, complemented
14D3×#816C211yesmaximal, characteristic, complemented
15D3×Dic3⋊C8C211yesmaximal, characteristic, complemented
16C2×#5166—31nomaximal
17D3×#464—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic, complemented
23C2×#3756C2211yescharacteristic, complemented
24#64145C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#216C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C3×#936C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C3×D3×SD16—24no—
31C2×C3×#204C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic
33D3×#217—21no—
34D3×#217—21no—
35#63959—21no—
36#63959—21no—
37D3×#216—24no—
38D3×C4⋊Dic3—21no—
39D3×C4⋊Dic3C2211yescharacteristic
40C4×D3×Dic3—21no—
41C4×D3×Dic3C2211yescharacteristic
42#63863C2211yescharacteristic
43#63860C2211yescharacteristic
44#63843—21no—
45#63843C2211yescharacteristic, complemented
46Dic3×Dic6—21no—
47Dic3×Dic6C2211yescharacteristic, complemented
48C2×#3719C2211yescharacteristic, complemented
49C2×#3718C2211yescharacteristic, complemented
50C2×D3×C3⋊C8C2211yescharacteristic
51#63659C2211yescharacteristic
52#63643C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic
55C3×#816C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57#63572C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63563C2211yescharacteristic
62#63562C2211yescharacteristic
63C22×C3×SD16—31no—
64C2×Q8×Dic3—31no—
65C22×#216—31no—
66C2×#936—31no—
67C2×D3×Q16—31no—
68C2×D3×SD16D311yescharacteristic
69D3×#124—31no—
70C4×D3×Q8—31no—
71C3×#464—31no—
72C2×#832—31no—
73#5185—31no—
74#5166—31no—
75#5166—31no—
76#5166—31no—
77#5166—31no—
78#5166—31no—
79#5166—31no—
80#5166—31no—
81#5166—31no—
82#5166—61no—
83#5166D311yescharacteristic, direct product factor
84C2×#816—31no—
85C2×Dic3⋊C8—31no—
86#5054—31no—
87#5028—31no—
88#4845—31no—
89D3×C4⋊C8—31no—
90D3×#103—31no—
91#4798—31no—
92D3×#102—31no—
93#4767—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C3×D3×Q8—22no—
100C3×D3×Q8D414yes—
101C3×D3×D4—22no—
102C3×D3×D4—22no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3D411yescharacteristic
113C2×D3×Dic3D411yescharacteristic
114D3×Dic6—22no—
115D3×Dic6—22no—
116C32×SD16—22no—
117C2×C32×C8C2311yescharacteristic
118#3757—21no—
119#3757—21no—
120#3756—22no—
121C4⋊(C3⋊Dic3)—21no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123C4×C3⋊Dic3—21no—
124C4×C3⋊Dic3C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×#217—21no—
127C3×#217—21no—
128C3×#216—22no—
129C3×#215—22no—
130C3×#214—22no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×#204—22no—
138C3×D3×C8—22no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146Dic32—21no—
147Dic32—21no—
148Dic32D411yescharacteristic
149Dic32D411yescharacteristic
150#3719—22no—
151#3718—22no—
152D3×C3⋊C8—22no—
153C2×#464—91noSylow
154C22×C3×Q8—31no—
155C22×C3×D4—31no—
156C2×D3×Q8—31no—
157C2×D3×Q8C2×D311yescharacteristic
158C2×D3×D4C2×D311yescharacteristic
159C22×Dic6—31no—
160C2×C3×Q16—31no—
161C2×C3×SD16—21no—
162C2×C3×SD16—31no—
163C2×C3×SD16—31no—
164C2×C3×SD16—31no—
165C2×C3×SD16—64no—
166C2×C3×SD16C2×D311yescharacteristic
167C2×C3×SD16C2×D311yescharacteristic
168C22×C3×C8—31no—
169C3×#124—31no—
170C3×C4×Q8—31no—
171C2×#217—61no—
172C2×#217—61no—
173#947—31no—
174Q8×Dic3—31no—
175Q8×Dic3—31no—
176Q8×Dic3—31no—
177Q8×Dic3—31no—
178Q8×Dic3—61no—
179Q8×Dic3—61no—
180Q8×Dic3—61no—
181Q8×Dic3C2×D311yescharacteristic, complemented
182C2×#216—31no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#216—31no—
187C2×#216—61no—
188C2×#216—64no—
189C2×#216C2×D311yescharacteristic, complemented
190C2×#215C2×D311yescharacteristic
191#936—31no—
192#936—31no—
193#936—31no—
194#936—31no—
195#936—61no—
196#936—61no—
197#936—61no—
198#936C2×D311yescharacteristic
199C2×#214C2×D311yescharacteristic
200C2×C4⋊Dic3—31no—
201C2×C4⋊Dic3—61no—
202C2×C4×Dic3—31no—
203C2×C4×Dic3—61no—
204C22×C3⋊C8—31no—
205D3×Q16—64no—
206D3×SD16—24no—
207C2×Dic12—31no—
208C2×#204C2×D311yescharacteristic
209C2×D3×C8—31no—
210C2×D3×C8C2×D311yescharacteristic
211D3×C4⋊C4—31no—
212D3×C4⋊C4—61no—
213#887—31no—
214#887—61no—
215#885—61no—
216#885—61no—
217D3×C22⋊C4—61no—
218D3×C22⋊C4—61no—
219#875—31no—
220C42×D3—31no—
221C42×D3—61no—
222C4×Dic6—31no—
223C4×Dic6—61no—
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#102—31no—
227#835—31no—
228#832—31no—
229#832—31no—
230#832—31no—
231#832—31no—
232#832—61no—
233#832C2×D311yescharacteristic
234#821—31no—
235#816—31no—
236#816—31no—
237#816—31no—
238#816—31no—
239#816—61no—
240#816C2×D311yescharacteristic, complemented
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8—31no—
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—61no—
247Dic3⋊C8C2×D311yescharacteristic, complemented
248#810—31no—
249#809—31no—
250C4⋊(C3⋊C8)—31no—
251C23×C32—21no—
252C22×C3×D3—21no—
253C22×C3×D3—42no—
254C22×C3×D3—42no—
255C22×C3×D3—42no—
256C22×C3×D3C2×D411yescharacteristic
257C32×Q8—21no—
258C32×Q8C2×D412yes—
259C32×D4—21no—
260C32×D4—21no—
261C2×C32×C4—21no—
262C2×C32×C4C2411yescharacteristic
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3C2×D411yescharacteristic
266C2×C3⋊Dic3C2×D411yescharacteristic
267#634—21no—
268#634—21no—
269C3×#67—42no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C3×D12—21no—
277C3×D12—21no—
278C3×C4×D3—24no—
279C3×C4×D3C2×D412yes—
280C3×C4×D3#4112yes—
281C3×Dic6—21no—
282C3×Dic6—24no—
283C3×Dic6—21no—
284C3×Dic6—21no—
285C3×Dic6C2×D412yes—
286#627—42no—
287D3×Dic3—22no—
288D3×Dic3—22no—
289D3×Dic3—42no—
290D3×Dic3—42no—
291C32×C8—21no—
292C3⋊(C3⋊C8)—21no—
293C3×C3⋊C8—21no—
294C3×C3⋊C8—21no—
295C22×Q16—91no—
296C22×SD16—31no—
297C2×#124—91no—
298C2×C4×Q8—91no—
299#464—31no—
300#464—91no—
301#464—91no—
302#464—91no—
303#464—91no—
304#464—91no—
305#464—91no—
306#464—91no—
307C2×C4⋊C8—91no—
308C2×#103—91no—
309C2×#102—91no—
310C24×C3—61no—
311C23×D3—21no—
312C2×C3×Q8—21no—
313C2×C3×Q8—34no—
314C2×C3×Q8—31no—
315C2×C3×Q8—31no—
316C2×C3×Q8—61no—
317C2×C3×Q8—62no—
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×Q8C22×D311yescharacteristic
320C2×C3×D4—21no—
321C2×C3×D4—31no—
322C2×C3×D4—62no—
323C2×C3×D4—62no—
324C2×C3×D4—61no—
325C2×C3×D4C22×D311yescharacteristic
326C2×C3×D4C22×D311yescharacteristic
327C22×C3×C4—31no—
328C22×C3×C4—61no—
329C2×#67—21no—
330C22×Dic3—31no—
331C22×Dic3—31no—
332C22×Dic3—61no—
333C22×Dic3—61no—
334D3×Q8—22no—
335D3×Q8—62no—
336D3×Q8—62no—
337D3×Q8#6714yes—
338D3×D4—22no—
339D3×D4—22no—
340C2×D12C22×D311yescharacteristic
341C2×C4×D3—21no—
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3C22×D311yescharacteristic
347C2×Dic6—21no—
348C2×Dic6—31no—
349C2×Dic6—31no—
350C2×Dic6—61no—
351C2×Dic6—62no—
352C2×Dic6—62no—
353C2×Dic6—61no—
354C2×Dic6—61no—
355C2×Dic6C22×D311yescharacteristic
356C2×Dic6C22×D311yescharacteristic
357C3×Q16—62no—
358C3×SD16—22no—
359C3×SD16—22no—
360C3×SD16—42no—
361C3×SD16—62no—
362C3×SD16—62no—
363C3×SD16—62no—
364C2×C3×C8—21no—
365C2×C3×C8—31no—
366C2×C3×C8—31no—
367C2×C3×C8—62no—
368C2×C3×C8C22×D311yescharacteristic
369C2×C3×C8C22×D311yescharacteristic
370C3×C4⋊C4—31no—
371C3×C4⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C42—31no—
375C3×C42—61no—
376#217—21no—
377#217—21no—
378#217—61no—
379#217—61no—
380#217—61no—
381#217—61no—
382#217—61no—
383#217—61no—
384#217—61no—
385#217—61no—
386#217—121no—
387#217—121no—
388#216—22no—
389#216—62no—
390#216—62no—
391#216—62no—
392#216—62no—
393#216—62no—
394#216—122no—
395#215—22no—
396#214—22no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401C4⋊Dic3—21no—
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3—61no—
408C4⋊Dic3—61no—
409C4⋊Dic3—61no—
410C4⋊Dic3—121no—
411C4⋊Dic3C22×D311yescharacteristic
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415C4×Dic3—21no—
416C4×Dic3—31no—
417C4×Dic3—31no—
418C4×Dic3—31no—
419C4×Dic3—31no—
420C4×Dic3—31no—
421C4×Dic3—31no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C4×Dic3—61no—
425C4×Dic3—61no—
426C4×Dic3—61no—
427C4×Dic3—61no—
428C4×Dic3—61no—
429C4×Dic3—121no—
430C4×Dic3C22×D311yescharacteristic
431C2×C3⋊C8—31no—
432C2×C3⋊C8—31no—
433C2×C3⋊C8—61no—
434C2×C3⋊C8—62no—
435C2×C3⋊C8C22×D311yescharacteristic
436C2×C3⋊C8C22×D311yescharacteristic
437Dic12—62no—
438#204—22no—
439D3×C8—22no—
440D3×C8—62no—
441C22×C32—41no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32C22×D411yescharacteristic
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—84no—
449C2×C3×D3#12112yes—
450C2×C3×D3#13512yes—
451C2×C3×D3#13712yes—
452C32×C4—22no—
453C32×C4C22×D411yescharacteristic
454C32×C4C2×#4111yescharacteristic
455C3⋊Dic3—21no—
456C3⋊Dic3—21no—
457C3⋊Dic3—41no—
458C3⋊Dic3—41no—
459C3×Dic3—22no—
460C3×Dic3—21no—
461C3×Dic3—21no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3#12112yes—
465C22×Q8—31no—
466C22×Q8—91no—
467C22×D4—31no—
468C2×Q16—31no—
469C2×Q16—91no—
470C2×Q16—91no—
471C2×Q16—91no—
472C2×Q16—184no—
473C2×SD16—31no—
474C2×SD16—31no—
475C2×SD16—31no—
476C2×SD16—64no—
477C2×SD16D3211yescharacteristic
478C22×C8—31no—
479C22×C8—91no—
480#124—31no—
481#124—91no—
482#124—91no—
483#124—91no—
484#124—181no—
485#124—181no—
486C4×Q8—31no—
487C4×Q8—91no—
488C4×Q8—91no—
489C4×Q8—91no—
490C4×Q8—181no—
491C4×Q8—181no—
492C2×C4⋊C4—91no—
493C2×C4⋊C4—181no—
494C2×C22⋊C4—181no—
495C2×C22⋊C4—181no—
496C2×C42—91no—
497C2×C42—181no—
498C4⋊C8—31no—
499C4⋊C8—91no—
500C4⋊C8—91no—
501C4⋊C8—91no—
502#103—31no—
503#103—91no—
504#103—91no—
505#103—91no—
506#102—31no—
507#102—91no—
508#102—91no—
509#102—91no—
510C23×C3—21no—
511C23×C3—21no—
512C23×C3—31no—
513C23×C3—41no—
514C23×C3—61no—
515C23×C3—122no—
516C23×C3—122no—
517C23×C3—122no—
518C22×D3—21no—
519C22×D3—42no—
520C22×D3—42no—
521C22×D3—42no—
522C22×D3D3×D411yescharacteristic
523C3×Q8—21no—
524C3×Q8—21no—
525C3×Q8—22no—
526C3×Q8—32no—
527C3×Q8—41no—
528C3×Q8—64no—
529C3×Q8—61no—
530C3×Q8—61no—
531C3×Q8—61no—
532C3×Q8D3×D412yes—
533C3×Q8C2×#6712yes—
534C3×D4—21no—
535C3×D4—21no—
536C3×D4—21no—
537C3×D4—21no—
538C3×D4—41no—
539C3×D4—41no—
540C3×D4—61no—
541C3×D4—61no—
542C3×D4—122no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—31no—
547C2×C3×C4—32no—
548C2×C3×C4—32no—
549C2×C3×C4—31no—
550C2×C3×C4—31no—
551C2×C3×C4—41no—
552C2×C3×C4—64no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4C23×D311yescharacteristic
557C2×C3×C4C23×D311yescharacteristic
558#67—42no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—31no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—62no—
569C2×Dic3—62no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—121no—
575C2×Dic3—121no—
576C2×Dic3—122no—
577C2×Dic3—122no—
578C2×Dic3D3×D411yescharacteristic
579C2×Dic3D3×D411yescharacteristic
580C2×Dic3D3×D411yescharacteristic
581D12—21no—
582D12—21no—
583C4×D3—24no—
584C4×D3—62no—
585C4×D3—62no—
586C4×D3—122no—
587C4×D3—122no—
588C4×D3#23712yes—
589C4×D3C2×#6712yes—
590Dic6—21no—
591Dic6—24no—
592Dic6—21no—
593Dic6—21no—
594Dic6—61no—
595Dic6—61no—
596Dic6—61no—
597Dic6—61no—
598Dic6—121no—
599Dic6—121no—
600Dic6—122no—
601Dic6—122no—
602Dic6C2×#6712yes—
603C3×C8—21no—
604C3×C8—21no—
605C3×C8—41no—
606C3×C8—61no—
607C3×C8—61no—
608C3⋊C8—21no—
609C3⋊C8—21no—
610C3⋊C8—61no—
611C3⋊C8—61no—
612C3⋊C8—121no—
613C2×C32—81no—
614C2×C32C2×#12111yescharacteristic
615C2×C32C2×#13511yescharacteristic
616C2×C32C2×#13711yescharacteristic
617C3×D3—81no—
618C3×D3#46414yescomplemented
619C24—61no—
620C2×Q8—34no—
621C2×Q8—31no—
622C2×Q8—31no—
623C2×Q8—61no—
624C2×Q8—62no—
625C2×Q8—91no—
626C2×Q8—181no—
627C2×Q8—182no—
628C2×Q8—182no—
629C2×Q8C2×D3211yescharacteristic
630C2×D4—31no—
631C2×D4—62no—
632C2×D4—62no—
633C2×D4—61no—
634C2×D4C2×D3211yescharacteristic
635C22×C4—31no—
636C22×C4—61no—
637C22×C4—91no—
638C22×C4—91no—
639C22×C4—181no—
640C22×C4—181no—
641Q16—62no—
642Q16—182no—
643Q16—182no—
644Q16—182no—
645SD16—22no—
646SD16—62no—
647SD16—62no—
648SD16—62no—
649C2×C8—31no—
650C2×C8—31no—
651C2×C8—62no—
652C2×C8—91no—
653C2×C8—182no—
654C2×C8C2×D3211yescharacteristic
655C4⋊C4—31no—
656C4⋊C4—61no—
657C4⋊C4—91no—
658C4⋊C4—181no—
659C4⋊C4—181no—
660C4⋊C4—181no—
661C4⋊C4—181no—
662C22⋊C4—61no—
663C22⋊C4—61no—
664C22⋊C4—181no—
665C22⋊C4—181no—
666C22⋊C4—181no—
667C22⋊C4—181no—
668C22⋊C4—181no—
669C22⋊C4—181no—
670C42—31no—
671C42—61no—
672C42—91no—
673C42—91no—
674C42—91no—
675C42—181no—
676C42—181no—
677C42—181no—
678C22×C3—21no—
679C22×C3—32no—
680C22×C3—32no—
681C22×C3—32no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—81no—
689C22×C3—81no—
690C22×C3—81no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3—244no—
695C22×C3C2×D3×D411yescharacteristic
696C22×C3C2×D3×D411yescharacteristic
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—84no—
701C2×D3#91512yes—
702C2×D3#91612yes—
703C2×D3#93912yes—
704C3×C4—22no—
705C3×C4—22no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—32no—
709C3×C4—42no—
710C3×C4—61no—
711C3×C4—61no—
712C3×C4—62no—
713C3×C4—121no—
714C3×C4—121no—
715C3×C4C2×D3×D411yescharacteristic
716C3×C4C2×#23711yescharacteristic
717C3×C4D3×#4111yescharacteristic
718C3×C4C22×#6711yescharacteristic
719Dic3—21no—
720Dic3—21no—
721Dic3—22no—
722Dic3—41no—
723Dic3—41no—
724Dic3—61no—
725Dic3—61no—
726Dic3—61no—
727Dic3—61no—
728Dic3—121no—
729Dic3—121no—
730Dic3—121no—
731Dic3—121no—
732Dic3—121no—
733Dic3—121no—
734Dic3—241no—
735Dic3—241no—
736Dic3#93912yes—
737C32C2×#46411yescharacteristic, complemented, Sylow
738C23—21no—
739C23—31no—
740C23—61no—
741C23—122no—
742C23—122no—
743C23—122no—
744Q8—21no—
745Q8—32no—
746Q8—64no—
747Q8—61no—
748Q8—61no—
749Q8—61no—
750Q8—181no—
751Q8—181no—
752Q8—362no—
753Q8D3×#6712yes—
754D4—21no—
755D4—21no—
756D4—61no—
757D4—61no—
758D4—122no—
759C2×C4—21no—
760C2×C4—31no—
761C2×C4—32no—
762C2×C4—32no—
763C2×C4—31no—
764C2×C4—31no—
765C2×C4—64no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—91no—
770C2×C4—91no—
771C2×C4—182no—
772C2×C4—182no—
773C2×C4—181no—
774C2×C4—181no—
775C2×C4—362no—
776C2×C4—362no—
777C2×C4C22×D3211yescharacteristic
778C8—21no—
779C8—61no—
780C8—61no—
781C8—181no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—34no—
786C2×C3—81no—
787C2×C3—81no—
788C2×C3—161no—
789C2×C3—241no—
790C2×C3D3×#12111yescharacteristic
791C2×C3C2×#91511yescharacteristic
792C2×C3C2×#91611yescharacteristic
793C2×C3D3×#13511yescharacteristic
794C2×C3D3×#13711yescharacteristic
795C2×C3C2×#93911yescharacteristic
796D3—81no—
797D3#516614yesdirect product factor
798C22—32no—
799C22—32no—
800C22—32no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—121no—
805C22—121no—
806C22—121no—
807C22—244no—
808C22D32×D411yescharacteristic
809C4—22no—
810C4—32no—
811C4—61no—
812C4—61no—
813C4—62no—
814C4—121no—
815C4—121no—
816C4—181no—
817C4—181no—
818C4—361no—
819C4—361no—
820C4D3×#23711yescharacteristic
821C4C2×D3×#6711yescharacteristic
822C3—21no—
823C3D3×#46411yescharacteristic, complemented
824C3C2×#516611yescharacteristic, complemented
825C2—34no—
826C2—81no—
827C2—241no—
828C2D3×#91511yescharacteristic
829C2D3×#91611yescharacteristic
830C2D3×#93911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenterC2×SD16D32
hypocenterC32C2×#464
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. D3×Q8×Dic3C2semidirect
3. C2×D3×#216C2semidirect
5. #10592865C2semidirect
6. C3×#5166C2semidirect
7. #10591612C2semidirect
8. #10591604C2semidirect
9. #10591443C2semidirect
10. #10591442C2semidirect
12. #10590859C2semidirect
13. #10590796C2semidirect
14. D3×#816C2semidirect
15. D3×Dic3⋊C8C2semidirect
22. Q8×C3⋊Dic3C22semidirect
23. C2×#3756C22semidirect
25. C3×Q8×Dic3C22semidirect
26. C2×C3×#216C22semidirect
45. #63843C22semidirect
47. Dic3×Dic6C22semidirect
48. C2×#3719C22semidirect
49. C2×#3718C22semidirect
52. #63643C22semidirect
53. #63641C22semidirect
55. C3×#816C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. #63572C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63567C22semidirect
60. #63566C22semidirect
83. #5166D3direct (N × H)
181. Q8×Dic3C2×D3semidirect
189. C2×#216C2×D3semidirect
240. #816C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
618. C3×D3#464semidirect
737. C32C2×#464semidirect
797. D3#5166direct (N × H)
823. C3D3×#464semidirect
824. C3C2×#5166semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×SD162
D3×Q8×Dic32
C2×D3×#2162
D3×#9362
#105928652
C3×#51662
#105916122
#105916042
#105914432
#105914422
D3×#8322
#105908592
#105907962
D3×#8162
D3×Dic3⋊C82
C2×#51663
D3×#4643