Finite Group Databasebeta

← D3×#5165 #11865540

Subgroups — D3×#5165 #11865540

Order 1152.

1190 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
2D3×#947C211yesmaximal, characteristic, complemented
3D3×D4×Dic3C211yesmaximal, characteristic, complemented
4C2×D3×#213C211yesmaximal, characteristic
5#10592864C211yesmaximal, characteristic, complemented
6C3×#5165C211yesmaximal, characteristic, complemented
7#10591570C211yesmaximal, characteristic, complemented
8#10591567C211yesmaximal, characteristic, complemented
9D3×#835C211yesmaximal, characteristic, complemented
10#10591476C211yesmaximal, characteristic, complemented
11#10591471C211yesmaximal, characteristic, complemented
12D3×#821C211yesmaximal, characteristic, complemented
13#10590754C211yesmaximal, characteristic, complemented
14#10590750C211yesmaximal, characteristic, complemented
15D3×Dic3⋊C8C211yesmaximal, characteristic, complemented
16C2×#5165—31nomaximal
17D3×#463—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×D3×Dic3—21no—
21C2×D3×D12C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23#64156C2211yescharacteristic, complemented
24D4×C3⋊Dic3C2211yescharacteristic, complemented
25C2×#3753C2211yescharacteristic
26C3×#947C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C3×D4×Dic3C2211yescharacteristic, complemented
29C2×C3×#214C2211yescharacteristic, complemented
30C2×C3×#213C2211yescharacteristic
31C3×D3×SD16—24no—
32C2×C3×#204C2211yescharacteristic, complemented
33C2×C3×D3×C8C2211yescharacteristic
34#67⋊Dic3—21no—
35Dic3×#67—21no—
36D3×#217—21no—
37D3×#213—24no—
38D3×(C2×D3)⋊C4—21no—
39D3×(C2×D3)⋊C4—21no—
40#63907—21no—
41#63907—21no—
42#63898C2211yescharacteristic, complemented
43Dic3×D12C2211yescharacteristic, complemented
44D3×C4⋊Dic3C2211yescharacteristic
45C4×D3×Dic3C2211yescharacteristic
46#63864C2211yescharacteristic, complemented
47#63863C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63662C2211yescharacteristic, complemented
52#63648C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57#63572C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C22×C3×SD16—31no—
64C2×#947—31no—
65C2×D4×Dic3—31no—
66C22×#213—31no—
67C2×D3×SD16D311yescharacteristic, complemented
68C2×D3×D8—31no—
69D3×#124—31no—
70C4×D3×D4—31no—
71C3×#463—31no—
72C2×#835—31no—
73#5165—31no—
74#5165—31no—
75#5165—31no—
76#5165—31no—
77#5165—31no—
78#5165—31no—
79#5165—31no—
80#5165—31no—
81#5165—61no—
82#5165D311yescharacteristic, direct product factor
83#5153—31no—
84C2×#821—31no—
85C2×Dic3⋊C8—31no—
86#5057—31no—
87#5016—31no—
88#4844—31no—
89D3×C4⋊C8—31no—
90#4819—31no—
91D3×#103—31no—
92#4787—31no—
93D3×#102—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C3⋊Dic3—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C3×D3×Q8—22no—
103C3×D3×Q8—22no—
104C3×D3×D4—22no—
105C3×D3×D4D414yes—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6—21no—
111C2×C3×Dic6C2311yescharacteristic
112C2×#626—21no—
113C2×D3×Dic3—21no—
114C2×D3×Dic3—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—44no—
117C2×D3×Dic3D411yescharacteristic
118C2×D3×Dic3D411yescharacteristic
119D3×D12—22no—
120D3×D12—22no—
121C32×SD16—22no—
122C2×C32×C8C2311yescharacteristic
123#3757—21no—
124#3753—22no—
125#3752—21no—
126#3752—21no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128C4×C3⋊Dic3C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#217—21no—
131C3×#215—22no—
132C3×#214—22no—
133C3×#213—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×#204—22no—
141C3×D3×C8—22no—
142Dic3⋊Dic3—21no—
143#3722—21no—
144#3722—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149Dic32D411yescharacteristic
150Dic32D411yescharacteristic
151#3714—22no—
152#3713—22no—
153D3×C3⋊C8—22no—
154C2×#463—91noSylow
155C22×C3×Q8—31no—
156C22×C3×D4—31no—
157C23×Dic3—61no—
158C2×D3×Q8C2×D311yescharacteristic
159C2×D3×D4—31no—
160C2×D3×D4C2×D311yescharacteristic
161C22×D12—31no—
162C22×C4×D3—61no—
163C2×C3×SD16—21no—
164C2×C3×SD16—31no—
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16—64no—
168C2×C3×SD16C2×D311yescharacteristic, complemented
169C2×C3×SD16C2×D311yescharacteristic, complemented
170C2×C3×D8—31no—
171C22×C3×C8—31no—
172C3×#124—31no—
173C3×C4×D4—31no—
174C2×#217—61no—
175#947—31no—
176#947—31no—
177#947—31no—
178#947—31no—
179#947—61no—
180#947—61no—
181#947—61no—
182#947C2×D311yescharacteristic, complemented
183C2×#215C2×D311yescharacteristic, complemented
184#936—31no—
185D4×Dic3—31no—
186D4×Dic3—31no—
187D4×Dic3—31no—
188D4×Dic3—31no—
189D4×Dic3—61no—
190D4×Dic3—61no—
191D4×Dic3—61no—
192D4×Dic3C2×D311yescharacteristic, complemented
193C2×#214C2×D311yescharacteristic, complemented
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—61no—
200C2×#213—64no—
201C2×#213C2×D311yescharacteristic
202C4×#67—61no—
203C2×(C2×D3)⋊C4—61no—
204C2×(C2×D3)⋊C4—61no—
205C2×C4⋊Dic3—31no—
206C2×C4×Dic3—31no—
207C22×C3⋊C8—31no—
208D3×SD16—24no—
209D3×D8—64no—
210C2×D24—31no—
211C2×#204C2×D311yescharacteristic, complemented
212C2×D3×C8—31no—
213C2×D3×C8C2×D311yescharacteristic
214#893—31no—
215D3×C4⋊C4—31no—
216#885—61no—
217#885—61no—
218#67⋊C4—61no—
219D3×C22⋊C4—61no—
220D3×C22⋊C4—61no—
221D3×C22⋊C4—61no—
222#875—31no—
223C4×D12—31no—
224C42×D3—31no—
225C3×C4⋊C8—31no—
226C3×#103—31no—
227C3×#102—31no—
228#835—31no—
229#835—31no—
230#835—31no—
231#835—31no—
232#835—61no—
233#835C2×D311yescharacteristic, complemented
234#832—31no—
235#821—31no—
236#821—31no—
237#821—31no—
238#821—31no—
239#821—61no—
240#821C2×D311yescharacteristic, complemented
241#816—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8—31no—
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—31no—
247Dic3⋊C8—61no—
248Dic3⋊C8C2×D311yescharacteristic, complemented
249#810—31no—
250#809—31no—
251C4⋊(C3⋊C8)—31no—
252C23×C32—21no—
253C22×C3⋊D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—24no—
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—42no—
263C32×Q8—21no—
264C32×Q8—21no—
265C32×D4—21no—
266C32×D4C2×D412yes—
267C2×C32×C4—21no—
268C2×C32×C4C2411yescharacteristic
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—42no—
271C2×C3⋊Dic3C2×D411yescharacteristic
272C2×C3⋊Dic3C2×D411yescharacteristic
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C3×#67—24no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—42no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12C2×D412yes—
286C3×C4×D3—42no—
287C3×C4×D3C2×D412yes—
288C3×C4×D3#4112yes—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—42no—
292#626—42no—
293D3×Dic3—22no—
294D3×Dic3—22no—
295D3×Dic3—42no—
296D3×Dic3—42no—
297D3×Dic3—42no—
298C32×C8—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C22×SD16—31no—
303C22×D8—91no—
304C2×#124—91no—
305C2×C4×D4—91no—
306#463—31no—
307#463—91no—
308#463—91no—
309#463—91no—
310#463—91no—
311#463—91no—
312#463—91no—
313#463—91no—
314C2×C4⋊C8—91no—
315C2×#103—91no—
316C2×#102—91no—
317C24×C3—61no—
318C23×D3—21no—
319C23×D3—61no—
320C23×D3—61no—
321C2×C3×Q8—21no—
322C2×C3×Q8—31no—
323C2×C3×Q8—61no—
324C2×C3×Q8—62no—
325C2×C3×Q8—62no—
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×D4—21no—
329C2×C3×D4—34no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—62no—
333C2×C3×D4—61no—
334C2×C3×D4C22×D311yescharacteristic
335C2×C3×D4C22×D311yescharacteristic
336C22×C3×C4—31no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C2×#67—21no—
340C2×#67—61no—
341C22×Dic3—21no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—61no—
345C22×Dic3—61no—
346C22×Dic3—61no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349C22×Dic3—121no—
350C22×Dic3—124no—
351D3×Q8—22no—
352D3×Q8—22no—
353D3×D4—22no—
354D3×D4—62no—
355D3×D4—62no—
356D3×D4#6714yes—
357C2×D12—31no—
358C2×D12—31no—
359C2×D12—61no—
360C2×D12—62no—
361C2×D12—62no—
362C2×D12—61no—
363C2×D12C22×D311yescharacteristic
364C2×D12C22×D311yescharacteristic
365C2×C4×D3—21no—
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—124no—
372C2×C4×D3C22×D311yescharacteristic
373C2×Dic6—21no—
374C2×Dic6C22×D311yescharacteristic
375C3×SD16—22no—
376C3×SD16—22no—
377C3×SD16—42no—
378C3×SD16—62no—
379C3×SD16—62no—
380C3×SD16—62no—
381C3×D8—62no—
382C2×C3×C8—21no—
383C2×C3×C8—31no—
384C2×C3×C8—31no—
385C2×C3×C8—62no—
386C2×C3×C8C22×D311yescharacteristic
387C2×C3×C8C22×D311yescharacteristic
388C3×C4⋊C4—31no—
389C3×C22⋊C4—61no—
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C42—31no—
393#217—21no—
394#217—61no—
395#217—61no—
396#217—61no—
397#217—61no—
398#217—61no—
399#217—61no—
400#217—121no—
401#215—22no—
402#214—22no—
403#213—22no—
404#213—62no—
405#213—62no—
406#213—62no—
407#213—62no—
408#213—62no—
409#213—122no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—121no—
425(C2×D3)⋊C4—121no—
426C4⋊Dic3—31no—
427C4⋊Dic3—31no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3C22×D311yescharacteristic
431Dic3⋊C4—61no—
432C4×Dic3—31no—
433C4×Dic3—31no—
434C4×Dic3—31no—
435C4×Dic3—31no—
436C4×Dic3—31no—
437C4×Dic3—31no—
438C4×Dic3—61no—
439C4×Dic3C22×D311yescharacteristic
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—61no—
443C2×C3⋊C8—62no—
444C2×C3⋊C8C22×D311yescharacteristic
445C2×C3⋊C8C22×D311yescharacteristic
446D24—62no—
447#204—22no—
448D3×C8—22no—
449D3×C8—62no—
450C22×C32—22no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32C22×D411yescharacteristic
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3×D3—22no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—48no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3#12112yes—
465C2×C3×D3#13512yes—
466C2×C3×D3AGL(1,ℤ/8)12yes—
467D32—84no—
468C32×C4—41no—
469C32×C4C22×D411yescharacteristic
470C32×C4C2×#4111yescharacteristic
471C3⋊Dic3—21no—
472C3⋊Dic3—21no—
473C3⋊Dic3—41no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3#12112yes—
479C22×Q8—31no—
480C22×D4—31no—
481C22×D4—91no—
482C23×C4—181no—
483C2×SD16—31no—
484C2×SD16—31no—
485C2×SD16—31no—
486C2×SD16—64no—
487C2×SD16D3211yescharacteristic, complemented
488C2×D8—31no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—91no—
492C2×D8—184no—
493C22×C8—31no—
494C22×C8—91no—
495#124—31no—
496#124—91no—
497#124—91no—
498#124—91no—
499#124—181no—
500#124—181no—
501C4×D4—31no—
502C4×D4—91no—
503C4×D4—91no—
504C4×D4—91no—
505C4×D4—181no—
506C4×D4—181no—
507C2×C4⋊C4—91no—
508C2×C22⋊C4—181no—
509C2×C22⋊C4—181no—
510C2×C22⋊C4—181no—
511C2×C42—91no—
512C4⋊C8—31no—
513C4⋊C8—91no—
514C4⋊C8—91no—
515C4⋊C8—91no—
516#103—31no—
517#103—91no—
518#103—91no—
519#103—91no—
520#102—31no—
521#102—91no—
522#102—91no—
523#102—91no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—31no—
527C23×C3—41no—
528C23×C3—64no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—122no—
532C23×C3—122no—
533C22×D3—21no—
534C22×D3—24no—
535C22×D3—21no—
536C22×D3—42no—
537C22×D3—42no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—121no—
541C22×D3—122no—
542C22×D3—122no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—122no—
547C22×D3D3×D411yescharacteristic
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—41no—
553C3×Q8—41no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×Q8—122no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—22no—
560C3×D4—32no—
561C3×D4—41no—
562C3×D4—64no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4D3×D412yes—
567C3×D4C2×#6712yes—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—31no—
572C2×C3×C4—32no—
573C2×C3×C4—32no—
574C2×C3×C4—31no—
575C2×C3×C4—31no—
576C2×C3×C4—41no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—122no—
580C2×C3×C4—122no—
581C2×C3×C4C23×D311yescharacteristic
582C2×C3×C4C23×D311yescharacteristic
583#67—24no—
584#67—122no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—42no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—62no—
595C2×Dic3—62no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—121no—
599C2×Dic3—122no—
600C2×Dic3—122no—
601C2×Dic3—122no—
602C2×Dic3—122no—
603C2×Dic3—122no—
604C2×Dic3—242no—
605C2×Dic3D3×D411yescharacteristic
606C2×Dic3D3×D411yescharacteristic
607C2×Dic3D3×D411yescharacteristic
608D12—21no—
609D12—21no—
610D12—21no—
611D12—61no—
612D12—61no—
613D12—61no—
614D12—61no—
615D12—121no—
616D12—121no—
617D12—122no—
618D12C2×#6712yes—
619C4×D3—42no—
620C4×D3—62no—
621C4×D3—62no—
622C4×D3—122no—
623C4×D3—122no—
624C4×D3—122no—
625C4×D3#23712yes—
626C4×D3C2×#6712yes—
627Dic6—21no—
628Dic6—21no—
629Dic6—42no—
630C3×C8—21no—
631C3×C8—21no—
632C3×C8—41no—
633C3×C8—61no—
634C3×C8—61no—
635C3⋊C8—21no—
636C3⋊C8—21no—
637C3⋊C8—61no—
638C3⋊C8—61no—
639C3⋊C8—121no—
640C2×C32—42no—
641C2×C32C2×#12111yescharacteristic
642C2×C32C2×#13511yescharacteristic
643C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
644C3⋊D3—81no—
645C3×D3—42no—
646C3×D3—81no—
647C3×D3#46314yescomplemented
648C24—61no—
649C24—181no—
650C2×Q8—31no—
651C2×Q8—61no—
652C2×Q8—62no—
653C2×Q8—62no—
654C2×Q8C2×D3211yescharacteristic
655C2×D4—34no—
656C2×D4—31no—
657C2×D4—31no—
658C2×D4—62no—
659C2×D4—61no—
660C2×D4—91no—
661C2×D4—182no—
662C2×D4—182no—
663C2×D4—181no—
664C2×D4C2×D3211yescharacteristic
665C22×C4—31no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—91no—
669C22×C4—91no—
670C22×C4—181no—
671C22×C4—181no—
672C22×C4—181no—
673C22×C4—181no—
674C22×C4—364no—
675SD16—22no—
676SD16—62no—
677SD16—62no—
678SD16—62no—
679D8—62no—
680D8—182no—
681D8—182no—
682D8—182no—
683C2×C8—31no—
684C2×C8—31no—
685C2×C8—62no—
686C2×C8—91no—
687C2×C8—182no—
688C2×C8C2×D3211yescharacteristic
689C4⋊C4—31no—
690C4⋊C4—91no—
691C4⋊C4—181no—
692C22⋊C4—61no—
693C22⋊C4—61no—
694C22⋊C4—61no—
695C22⋊C4—181no—
696C22⋊C4—181no—
697C22⋊C4—181no—
698C22⋊C4—181no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C42—31no—
705C42—91no—
706C42—91no—
707C42—91no—
708C22×C3—22no—
709C22×C3—22no—
710C22×C3—21no—
711C22×C3—32no—
712C22×C3—32no—
713C22×C3—32no—
714C22×C3—42no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—62no—
720C22×C3—81no—
721C22×C3—81no—
722C22×C3—128no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3C2×D3×D411yescharacteristic
729C22×C3C2×D3×D411yescharacteristic
730C2×D3—22no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—48no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—41no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—241no—
744C2×D3—241no—
745C2×D3—241no—
746C2×D3—244no—
747C2×D3—244no—
748C2×D3#91412yes—
749C2×D3#91612yes—
750C2×D3#93912yes—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—32no—
754C3×C4—41no—
755C3×C4—41no—
756C3×C4—61no—
757C3×C4—61no—
758C3×C4—81no—
759C3×C4—121no—
760C3×C4—121no—
761C3×C4C2×D3×D411yescharacteristic
762C3×C4C2×#23711yescharacteristic
763C3×C4D3×#4111yescharacteristic
764C3×C4C22×#6711yescharacteristic
765Dic3—21no—
766Dic3—21no—
767Dic3—41no—
768Dic3—41no—
769Dic3—61no—
770Dic3—61no—
771Dic3—61no—
772Dic3—61no—
773Dic3—121no—
774Dic3—121no—
775Dic3—121no—
776Dic3—121no—
777Dic3—241no—
778Dic3#93912yes—
779C32C2×#46311yescharacteristic, complemented, Sylow
780C23—21no—
781C23—31no—
782C23—64no—
783C23—61no—
784C23—61no—
785C23—122no—
786C23—122no—
787C23—181no—
788C23—362no—
789C23—362no—
790C23—362no—
791Q8—21no—
792Q8—21no—
793Q8—61no—
794Q8—61no—
795Q8—122no—
796D4—21no—
797D4—32no—
798D4—64no—
799D4—61no—
800D4—61no—
801D4—61no—
802D4—181no—
803D4—181no—
804D4—362no—
805D4D3×#6712yes—
806C2×C4—21no—
807C2×C4—31no—
808C2×C4—32no—
809C2×C4—32no—
810C2×C4—31no—
811C2×C4—31no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—91no—
815C2×C4—91no—
816C2×C4—122no—
817C2×C4—122no—
818C2×C4—182no—
819C2×C4—182no—
820C2×C4—181no—
821C2×C4—362no—
822C2×C4—362no—
823C2×C4—362no—
824C2×C4—362no—
825C2×C4C22×D3211yescharacteristic
826C8—21no—
827C8—61no—
828C8—61no—
829C8—181no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—34no—
834C2×C3—42no—
835C2×C3—42no—
836C2×C3—82no—
837C2×C3—122no—
838C2×C3—241no—
839C2×C3D3×#12111yescharacteristic
840C2×C3C2×#91411yescharacteristic
841C2×C3C2×#91611yescharacteristic
842C2×C3D3×#13511yescharacteristic
843C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
844C2×C3C2×#93911yescharacteristic
845D3—42no—
846D3—81no—
847D3—241no—
848D3—241no—
849D3—481no—
850D3#516514yesdirect product factor
851C22—22no—
852C22—32no—
853C22—32no—
854C22—32no—
855C22—41no—
856C22—41no—
857C22—62no—
858C22—128no—
859C22—121no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—121no—
864C22—361no—
865C22—361no—
866C22—361no—
867C22—724no—
868C22D32×D411yescharacteristic
869C4—32no—
870C4—41no—
871C4—61no—
872C4—61no—
873C4—121no—
874C4—121no—
875C4—181no—
876C4—181no—
877C4—361no—
878C4D3×#23711yescharacteristic
879C4C2×D3×#6711yescharacteristic
880C3—21no—
881C3D3×#46311yescharacteristic, complemented
882C3C2×#516511yescharacteristic, complemented
883C2—34no—
884C2—42no—
885C2—122no—
886C2—241no—
887C2—721no—
888C2D3×#91411yescharacteristic
889C2D3×#91611yescharacteristic
890C2D3×#93911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×D3×#213C2
hypercenterC2×SD16D32
hypocenterC32C2×#463
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
1. C2×C3×D3×SD16C2semidirect
2. D3×#947C2semidirect
3. D3×D4×Dic3C2semidirect
5. #10592864C2semidirect
6. C3×#5165C2semidirect
7. #10591570C2semidirect
8. #10591567C2semidirect
9. D3×#835C2semidirect
10. #10591476C2semidirect
11. #10591471C2semidirect
12. D3×#821C2semidirect
13. #10590754C2semidirect
14. #10590750C2semidirect
15. D3×Dic3⋊C8C2semidirect
22. C2×C32×SD16C22semidirect
23. #64156C22semidirect
24. D4×C3⋊Dic3C22semidirect
26. C3×#947C22semidirect
27. C2×C3×#215C22semidirect
28. C3×D4×Dic3C22semidirect
29. C2×C3×#214C22semidirect
32. C2×C3×#204C22semidirect
42. #63898C22semidirect
43. Dic3×D12C22semidirect
46. #63864C22semidirect
47. #63863C22semidirect
51. #63662C22semidirect
52. #63648C22semidirect
53. #63641C22semidirect
54. C3×#835C22semidirect
55. C3×#821C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. #63572C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
67. C2×D3×SD16D3semidirect
82. #5165D3direct (N × H)
168. C2×C3×SD16C2×D3semidirect
169. C2×C3×SD16C2×D3semidirect
182. #947C2×D3semidirect
183. C2×#215C2×D3semidirect
192. D4×Dic3C2×D3semidirect
193. C2×#214C2×D3semidirect
211. C2×#204C2×D3semidirect
233. #835C2×D3semidirect
240. #821C2×D3semidirect
248. Dic3⋊C8C2×D3semidirect
487. C2×SD16D32semidirect
647. C3×D3#463semidirect
779. C32C2×#463semidirect
850. D3#5165direct (N × H)
881. C3D3×#463semidirect
882. C3C2×#5165semidirect

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×#9472
D3×D4×Dic32
C2×D3×#2132
#105928642
C3×#51652
#105915702
#105915672
D3×#8352
#105914762
#105914712
D3×#8212
#105907542
#105907502
D3×Dic3⋊C82
C2×#51653
D3×#4633