Finite Group Databasebeta

← D3×#5176 #11874343

Subgroups — D3×#5176 #11874343

Order 1152.

1408 conjugacy classes of subgroups.

The subgroup lattice has 875 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
3C2×D3×#215C211yesmaximal, characteristic, complemented
4D3×#940C211yesmaximal, characteristic, complemented
5C2×D3×#213C211yesmaximal, characteristic, complemented
6C2×D3×D24C211yesmaximal, characteristic, complemented
7#10592875C211yesmaximal, characteristic, complemented
8C3×#5176C211yesmaximal, characteristic, complemented
9#10591621C211yesmaximal, characteristic, complemented
10#10591619C211yesmaximal, characteristic, complemented
11#10591475C211yesmaximal, characteristic, complemented
12#10591472C211yesmaximal, characteristic, complemented
13#10590887C211yesmaximal, characteristic, complemented
14#10590881C211yesmaximal, characteristic, complemented
15D3×#815C211yesmaximal, characteristic, complemented
16C2×#5176—31nomaximal
17D3×#496—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×#67—22no—
21C2×D3×D12C2211yescharacteristic
22C2×D3×D12C2211yescharacteristic
23C2×C32×SD16C2211yescharacteristic, complemented
24#64156C2211yescharacteristic, complemented
25C2×#3755C2211yescharacteristic, complemented
26#64149C2211yescharacteristic, complemented
27C2×#3753C2211yescharacteristic, complemented
28C2×#3745C2211yescharacteristic, complemented
29C3×#947C2211yescharacteristic, complemented
30C2×C3×#215C2211yescharacteristic, complemented
31C2×C3×#215C2211yescharacteristic, complemented
32C3×#940C2211yescharacteristic, complemented
33C2×C3×#214C2211yescharacteristic, complemented
34C2×C3×#213C2211yescharacteristic, complemented
35C3×D3×SD16—24no—
36C2×C3×D24C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C2×C3×D3×C8C2211yescharacteristic
39#63979—22no—
40D3×#215—24no—
41D3×#213—24no—
42D3×(C2×D3)⋊C4—22no—
43#63914C2211yescharacteristic, complemented
44#63911C2211yescharacteristic, complemented
45#63907—22no—
46C4×D3×Dic3C2211yescharacteristic
47#63864C2211yescharacteristic, complemented
48#63863C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic, complemented
50C2×#3715C2211yescharacteristic, complemented
51C2×#3714C2211yescharacteristic, complemented
52C2×#3714C2211yescharacteristic, complemented
53C2×#3714C2211yescharacteristic, complemented
54C2×#3713C2211yescharacteristic, complemented
55C2×D3×C3⋊C8C2211yescharacteristic
56D3×D24—24no—
57#63642C2211yescharacteristic, complemented
58C3×#815C2211yescharacteristic, complemented
59#63555C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C22×C3×SD16—31no—
62C2×#947—31no—
63C22×#215—31no—
64C2×#940—31no—
65C22×#213—31no—
66C2×D3×SD16—31no—
67C2×D3×SD16D311yescharacteristic, complemented
68C2×D3×D8—31no—
69C2×D3×D8—31no—
70C22×D24—31no—
71D3×#127—31no—
72D3×#124—31no—
73C3×#496—31no—
74#5176—31no—
75#5176—31no—
76#5176—31no—
77#5176—31no—
78#5176—31no—
79#5176—31no—
80#5176—31no—
81#5176—31no—
82#5176—31no—
83#5176—61no—
84#5176D311yescharacteristic, direct product factor
85#5154—31no—
86#5154—31no—
87C2×#815—31no—
88#5074—31no—
89#5058—31no—
90#4712—31no—
91D3×#97—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#638—22no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C3×#67—22no—
101C2×C3×#67—21no—
102C3×D3×Q8—22no—
103C3×D3×Q8—22no—
104C3×D3×D4—22no—
105C3×D3×D4—22no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6—21no—
112C2×C3×Dic6C2311yescharacteristic
113D3×#67—48no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#626—22no—
117C2×#625—22no—
118C2×D3×Dic3D412yes—
119D3×D12—22no—
120D3×D12—22no—
121D3×D12—22no—
122D3×D12—22no—
123C32×SD16—22no—
124C2×C32×C8C2311yescharacteristic
125#3755—22no—
126#3753—22no—
127#3752—22no—
128C4×C3⋊Dic3C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130#3745—22no—
131C3×#215—22no—
132C3×#215—22no—
133C3×#214—22no—
134C3×#213—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×D24—22no—
140C3×#204—22no—
141C3×D3×C8D414yescomplemented
142#3722—22no—
143(C2×D3)⋊Dic3—22no—
144Dic32D412yes—
145#3717—22no—
146#3715—22no—
147#3714—22no—
148#3714—22no—
149#3714—22no—
150#3713—22no—
151D3×C3⋊C8D414yescomplemented
152C2×#496—91noSylow
153C22×C3×Q8—31no—
154C22×C3×D4—31no—
155C22×#67—62no—
156C2×D3×Q8C2×D311yescharacteristic
157C2×D3×D4—31no—
158C2×D3×D4—31no—
159C2×D3×D4—62no—
160C2×D3×D4C2×D311yescharacteristic
161C22×D12—31no—
162C22×D12—31no—
163C2×C3×SD16—21no—
164C2×C3×SD16—31no—
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—64no—
169C2×C3×SD16C2×D311yescharacteristic, complemented
170C2×C3×SD16C2×D311yescharacteristic, complemented
171C2×C3×D8—31no—
172C2×C3×D8—31no—
173C22×C3×C8—31no—
174C3×#127—31no—
175C3×#124—31no—
176#947—31no—
177#947—31no—
178#947—31no—
179#947—31no—
180#947—61no—
181#947—62no—
182#947C2×D311yescharacteristic, complemented
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—61no—
188C2×#215—64no—
189C2×#215C2×D311yescharacteristic, complemented
190C2×#215C2×D311yescharacteristic, complemented
191#940—31no—
192#940—31no—
193#940—31no—
194#940—31no—
195#940—31no—
196#940—61no—
197#940—62no—
198#940—62no—
199#940C2×D311yescharacteristic, complemented
200#936—31no—
201C2×#214—31no—
202C2×#214C2×D311yescharacteristic, complemented
203C2×#213—31no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—31no—
208C2×#213—31no—
209C2×#213—31no—
210C2×#213—61no—
211C2×#213—64no—
212C2×#213C2×D311yescharacteristic, complemented
213C2×(C2×D3)⋊C4—62no—
214C2×C4×Dic3—31no—
215C22×C3⋊C8—31no—
216D3×SD16—24no—
217D3×SD16—64no—
218D3×D8—64no—
219D3×D8—64no—
220C2×D24—31no—
221C2×D24—31no—
222C2×D24—31no—
223C2×D24—31no—
224C2×D24—31no—
225C2×D24—61no—
226C2×D24—64no—
227C2×D24C2×D311yescharacteristic, complemented
228C2×#204—31no—
229C2×#204C2×D311yescharacteristic, complemented
230C2×D3×C8—31no—
231C2×D3×C8C2×D311yescharacteristic
232#885—62no—
233D3×C22⋊C4—62no—
234#875—31no—
235#874—31no—
236C42×D3—31no—
237C3×#97—31no—
238#815—31no—
239#815—31no—
240#815—31no—
241#815—31no—
242#815—31no—
243#815—61no—
244#815C2×D311yescharacteristic, complemented
245#803—31no—
246C23×C32—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3—42no—
253C22×C3×D3—44no—
254C22×C3×D3C2×D411yescharacteristic
255C2×D32—42no—
256C2×D32—42no—
257C2×D32—44no—
258C2×D32—44no—
259C32×Q8—21no—
260C32×Q8—21no—
261C32×D4—21no—
262C32×D4—21no—
263C2×C32×C4—21no—
264C2×C32×C4C2411yescharacteristic
265#638—44no—
266C2×C3⋊Dic3C2×D412yes—
267C4⋊(C3⋊D3)—21no—
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C3×#67—44no—
272C3×#67—42no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3C2×D412yes—
275C2×C3×Dic3C2×D411yescharacteristic
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×C4×D3—42no—
283C3×C4×D3C2×D412yes—
284C3×C4×D3C2×D412yes—
285C3×Dic6—21no—
286C3×Dic6—21no—
287C3×Dic6—42no—
288#626—44no—
289#626—42no—
290#626—42no—
291#625—44no—
292D3×Dic3—24no—
293C32×C8C2×D412yescomplemented
294C3⋊(C3⋊C8)C2×D412yescomplemented
295C3×C3⋊C8C2×D412yescomplemented
296C3×C3⋊C8C2×D412yescomplemented
297C22×SD16—31no—
298C22×SD16—91no—
299C22×D8—91no—
300C22×D8—91no—
301C2×#127—91no—
302C2×#124—91no—
303#496—31no—
304#496—91no—
305#496—91no—
306#496—91no—
307#496—91no—
308#496—91no—
309#496—91no—
310#496—91no—
311C2×#97—91no—
312C24×C3—61no—
313C23×D3—21no—
314C23×D3—61no—
315C23×D3—61no—
316C23×D3—61no—
317C23×D3—61no—
318C2×C3×Q8—21no—
319C2×C3×Q8—31no—
320C2×C3×Q8—61no—
321C2×C3×Q8—62no—
322C2×C3×Q8—62no—
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×D4—21no—
326C2×C3×D4—31no—
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C2×C3×D4—62no—
330C2×C3×D4—62no—
331C2×C3×D4—61no—
332C2×C3×D4—62no—
333C2×C3×D4C22×D311yescharacteristic
334C2×C3×D4C22×D311yescharacteristic
335C22×C3×C4—31no—
336C22×C3×C4—61no—
337C2×#67—21no—
338C2×#67—22no—
339C2×#67—62no—
340C2×#67—62no—
341C2×#67—62no—
342C2×#67—62no—
343C2×#67—61no—
344C2×#67—62no—
345C2×#67—61no—
346C2×#67—122no—
347C2×#67—128no—
348C22×Dic3—32no—
349D3×Q8—22no—
350D3×Q8—22no—
351D3×D4—22no—
352D3×D4—22no—
353D3×D4—62no—
354D3×D4—62no—
355D3×D4—62no—
356D3×D4—62no—
357D3×D4—128no—
358C2×D12—31no—
359C2×D12—31no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—61no—
363C2×D12—61no—
364C2×D12—62no—
365C2×D12—62no—
366C2×D12—62no—
367C2×D12—62no—
368C2×D12—62no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12C22×D311yescharacteristic
372C2×D12C22×D311yescharacteristic
373C2×D12C22×D311yescharacteristic
374C2×C4×D3—21no—
375C2×C4×D3—32no—
376C2×C4×D3C22×D311yescharacteristic
377C2×Dic6—21no—
378C2×Dic6C22×D311yescharacteristic
379C3×SD16—22no—
380C3×SD16—22no—
381C3×SD16—42no—
382C3×SD16—62no—
383C3×SD16—62no—
384C3×SD16—62no—
385C3×SD16—62no—
386C3×D8—62no—
387C3×D8—62no—
388C2×C3×C8—21no—
389C2×C3×C8—31no—
390C2×C3×C8—31no—
391C2×C3×C8—34no—
392C2×C3×C8C22×D311yescharacteristic
393C2×C3×C8C22×D311yescharacteristic
394C3×C22⋊C4—62no—
395C3×C42—31no—
396#217—62no—
397#215—22no—
398#215—22no—
399#215—62no—
400#215—62no—
401#215—62no—
402#215—62no—
403#215—122no—
404#214—22no—
405#214—62no—
406#213—22no—
407#213—62no—
408#213—62no—
409#213—62no—
410#213—62no—
411#213—62no—
412#213—62no—
413#213—62no—
414#213—122no—
415(C2×D3)⋊C4—22no—
416(C2×D3)⋊C4—62no—
417(C2×D3)⋊C4—62no—
418(C2×D3)⋊C4—62no—
419(C2×D3)⋊C4—62no—
420(C2×D3)⋊C4—62no—
421(C2×D3)⋊C4—122no—
422C4×Dic3—31no—
423C4×Dic3—31no—
424C4×Dic3—32no—
425C4×Dic3—32no—
426C4×Dic3—61no—
427C4×Dic3C22×D311yescharacteristic
428C2×C3⋊C8—31no—
429C2×C3⋊C8—31no—
430C2×C3⋊C8—34no—
431C2×C3⋊C8—61no—
432C2×C3⋊C8C22×D311yescharacteristic
433C2×C3⋊C8C22×D311yescharacteristic
434D24—22no—
435D24—62no—
436D24—62no—
437D24—62no—
438D24—62no—
439D24—62no—
440D24—122no—
441#204—22no—
442#204—62no—
443D3×C8—34no—
444D3×C8#6714yescomplemented
445C22×C32—41no—
446C22×C32—42no—
447C22×C32C22×D411yescharacteristic
448C2×C3⋊D3—41no—
449C2×C3⋊D3—41no—
450C2×C3⋊D3—42no—
451C2×C3⋊D3—42no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3—42no—
456C2×C3×D3—42no—
457C2×C3×D3—42no—
458C2×C3×D3—84no—
459C2×C3×D3#12712yes—
460C2×C3×D3AGL(1,ℤ/8)14yes—
461D32—84no—
462D32—84no—
463C32×C4—41no—
464C32×C4C22×D411yescharacteristic
465C32×C4C22×D411yescharacteristic
466C3⋊Dic3—22no—
467C3×Dic3—22no—
468C3×Dic3—41no—
469C3×Dic3#12712yes—
470C22×Q8—31no—
471C22×D4—31no—
472C22×D4—91no—
473C22×D4—91no—
474C22×D4—182no—
475C2×SD16—31no—
476C2×SD16—31no—
477C2×SD16—31no—
478C2×SD16—31no—
479C2×SD16—64no—
480C2×SD16—91no—
481C2×SD16—91no—
482C2×SD16—91no—
483C2×SD16—184no—
484C2×SD16D3211yescharacteristic, complemented
485C2×D8—31no—
486C2×D8—31no—
487C2×D8—91no—
488C2×D8—91no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—91no—
492C2×D8—91no—
493C2×D8—184no—
494C2×D8—184no—
495C22×C8—31no—
496C22×C8—91no—
497#127—31no—
498#127—91no—
499#127—91no—
500#127—91no—
501#127—182no—
502#124—31no—
503#124—91no—
504#124—91no—
505#124—91no—
506#124—182no—
507C2×C22⋊C4—182no—
508C2×C42—91no—
509#97—31no—
510#97—91no—
511#97—91no—
512#97—91no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—31no—
516C23×C3—41no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3—61no—
520C23×C3—124no—
521C23×C3—122no—
522C22×D3—21no—
523C22×D3—21no—
524C22×D3—21no—
525C22×D3—44no—
526C22×D3—42no—
527C22×D3—61no—
528C22×D3—61no—
529C22×D3—61no—
530C22×D3—61no—
531C22×D3—121no—
532C22×D3—121no—
533C22×D3—122no—
534C22×D3—122no—
535C22×D3—124no—
536C22×D3—124no—
537C22×D3—124no—
538C22×D3—124no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3D3×D411yescharacteristic
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—21no—
545C3×Q8—21no—
546C3×Q8—41no—
547C3×Q8—41no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×Q8—122no—
551C3×D4—21no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—41no—
556C3×D4—41no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—122no—
564C3×D4—124no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—31no—
569C2×C3×C4—32no—
570C2×C3×C4—32no—
571C2×C3×C4—32no—
572C2×C3×C4—41no—
573C2×C3×C4—61no—
574C2×C3×C4—122no—
575C2×C3×C4C23×D311yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577#67—44no—
578#67—42no—
579#67—124no—
580#67—124no—
581#67—124no—
582#67—124no—
583#67—124no—
584#67—122no—
585#67—122no—
586#67—244no—
587C2×Dic3—21no—
588C2×Dic3—32no—
589C2×Dic3—32no—
590C2×Dic3—62no—
591C2×Dic3—64no—
592C2×Dic3D3×D412yes—
593C2×Dic3D3×D411yescharacteristic
594D12—21no—
595D12—21no—
596D12—21no—
597D12—21no—
598D12—21no—
599D12—21no—
600D12—61no—
601D12—61no—
602D12—61no—
603D12—61no—
604D12—61no—
605D12—61no—
606D12—61no—
607D12—61no—
608D12—121no—
609D12—121no—
610D12—121no—
611D12—121no—
612D12—122no—
613D12—122no—
614D12—124no—
615C4×D3—42no—
616C4×D3—64no—
617C4×D3D3×D412yes—
618C4×D3C2×#6712yes—
619Dic6—21no—
620Dic6—21no—
621Dic6—42no—
622C3×C8—22no—
623C3×C8—32no—
624C3×C8—32no—
625C3×C8D3×D412yescomplemented
626C3×C8C2×#6712yescomplemented
627C3⋊C8—32no—
628C3⋊C8—32no—
629C3⋊C8—62no—
630C3⋊C8D3×D412yescomplemented
631C3⋊C8C2×#6712yescomplemented
632C2×C32—81no—
633C2×C32C2×#12711yescharacteristic
634C2×C32C2×AGL(1,ℤ/8)12yes—
635C3⋊D3—81no—
636C3⋊D3—81no—
637C3×D3—81no—
638C3×D3—81no—
639C3×D3—81no—
640C3×D3#49614yescomplemented
641C24—61no—
642C24—181no—
643C24—181no—
644C2×Q8—31no—
645C2×Q8—61no—
646C2×Q8—62no—
647C2×Q8—62no—
648C2×Q8C2×D3211yescharacteristic
649C2×D4—31no—
650C2×D4—31no—
651C2×D4—31no—
652C2×D4—62no—
653C2×D4—62no—
654C2×D4—62no—
655C2×D4—61no—
656C2×D4—91no—
657C2×D4—91no—
658C2×D4—182no—
659C2×D4—182no—
660C2×D4—182no—
661C2×D4—182no—
662C2×D4—181no—
663C2×D4—182no—
664C2×D4—181no—
665C2×D4—182no—
666C2×D4—182no—
667C2×D4—368no—
668C2×D4C2×D3211yescharacteristic
669C22×C4—31no—
670C22×C4—61no—
671C22×C4—92no—
672SD16—22no—
673SD16—62no—
674SD16—62no—
675SD16—62no—
676SD16—62no—
677SD16—182no—
678SD16—182no—
679SD16—182no—
680D8—62no—
681D8—62no—
682D8—182no—
683D8—182no—
684D8—182no—
685D8—182no—
686D8—182no—
687D8—182no—
688C2×C8—31no—
689C2×C8—31no—
690C2×C8—34no—
691C2×C8—94no—
692C2×C8—91no—
693C2×C8C2×D3211yescharacteristic
694C22⋊C4—62no—
695C22⋊C4—182no—
696C22⋊C4—182no—
697C22⋊C4—182no—
698C42—31no—
699C42—92no—
700C42—91no—
701C22×C3—21no—
702C22×C3—32no—
703C22×C3—34no—
704C22×C3—41no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—41no—
708C22×C3—82no—
709C22×C3—81no—
710C22×C3—121no—
711C22×C3—122no—
712C22×C3—122no—
713C22×C3—122no—
714C22×C3—121no—
715C22×C3—121no—
716C22×C3—244no—
717C22×C3C2×D3×D411yescharacteristic
718C22×C3C2×D3×D411yescharacteristic
719C2×D3—41no—
720C2×D3—41no—
721C2×D3—42no—
722C2×D3—42no—
723C2×D3—42no—
724C2×D3—41no—
725C2×D3—84no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—122no—
729C2×D3—122no—
730C2×D3—122no—
731C2×D3—122no—
732C2×D3—121no—
733C2×D3—121no—
734C2×D3—241no—
735C2×D3—241no—
736C2×D3—242no—
737C2×D3—242no—
738C2×D3—244no—
739C2×D3—244no—
740C2×D3—244no—
741C2×D3—244no—
742C2×D3#91414yes—
743C2×D3#94012yes—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—32no—
747C3×C4—41no—
748C3×C4—41no—
749C3×C4—62no—
750C3×C4—81no—
751C3×C4—121no—
752C3×C4C2×D3×D411yescharacteristic
753C3×C4C2×D3×D411yescharacteristic
754C3×C4C2×D3×D411yescharacteristic
755C3×C4C22×#6711yescharacteristic
756Dic3—22no—
757Dic3—41no—
758Dic3—62no—
759Dic3—62no—
760Dic3—122no—
761Dic3#94012yes—
762C32C2×#49611yescharacteristic, complemented, Sylow
763C23—21no—
764C23—31no—
765C23—61no—
766C23—61no—
767C23—61no—
768C23—122no—
769C23—124no—
770C23—181no—
771C23—181no—
772C23—362no—
773C23—362no—
774C23—364no—
775C23—364no—
776Q8—21no—
777Q8—21no—
778Q8—61no—
779Q8—61no—
780Q8—122no—
781D4—21no—
782D4—21no—
783D4—61no—
784D4—61no—
785D4—61no—
786D4—61no—
787D4—61no—
788D4—61no—
789D4—122no—
790D4—124no—
791D4—181no—
792D4—181no—
793D4—181no—
794D4—181no—
795D4—362no—
796D4—362no—
797D4—364no—
798D4—364no—
799D4—364no—
800C2×C4—21no—
801C2×C4—31no—
802C2×C4—32no—
803C2×C4—32no—
804C2×C4—32no—
805C2×C4—61no—
806C2×C4—92no—
807C2×C4—122no—
808C2×C4—184no—
809C2×C4C22×D3211yescharacteristic
810C8—32no—
811C8—32no—
812C8—92no—
813C8D3×#6712yescomplemented
814C2×C3—22no—
815C2×C3—21no—
816C2×C3—34no—
817C2×C3—81no—
818C2×C3—81no—
819C2×C3—161no—
820C2×C3—241no—
821C2×C3—241no—
822C2×C3—241no—
823C2×C3D3×#12711yescharacteristic
824C2×C3C2×#91412yes—
825C2×C3D3×AGL(1,ℤ/8)12yes—
826C2×C3C2×#94011yescharacteristic
827D3—81no—
828D3—81no—
829D3—81no—
830D3—241no—
831D3—241no—
832D3—241no—
833D3—241no—
834D3—481no—
835D3—481no—
836D3#517614yesdirect product factor
837C22—34no—
838C22—32no—
839C22—42no—
840C22—41no—
841C22—122no—
842C22—122no—
843C22—122no—
844C22—121no—
845C22—121no—
846C22—121no—
847C22—244no—
848C22—362no—
849C22—362no—
850C22—361no—
851C22—361no—
852C22—724no—
853C22—724no—
854C22D32×D411yescharacteristic
855C4—32no—
856C4—41no—
857C4—62no—
858C4—121no—
859C4—182no—
860C4D32×D411yescharacteristic
861C4C2×D3×#6711yescharacteristic
862C3—21no—
863C3D3×#49611yescharacteristic, complemented
864C3C2×#517611yescharacteristic, complemented
865C2—34no—
866C2—81no—
867C2—241no—
868C2—241no—
869C2—241no—
870C2—721no—
871C2—721no—
872C2D3×#91412yes—
873C2D3×#94011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32C2×#496
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. C2×D3×#215C2semidirect
4. D3×#940C2semidirect
5. C2×D3×#213C2semidirect
6. C2×D3×D24C2semidirect
7. #10592875C2semidirect
8. C3×#5176C2semidirect
9. #10591621C2semidirect
10. #10591619C2semidirect
11. #10591475C2semidirect
12. #10591472C2semidirect
13. #10590887C2semidirect
14. #10590881C2semidirect
15. D3×#815C2semidirect
23. C2×C32×SD16C22semidirect
24. #64156C22semidirect
25. C2×#3755C22semidirect
26. #64149C22semidirect
27. C2×#3753C22semidirect
28. C2×#3745C22semidirect
29. C3×#947C22semidirect
30. C2×C3×#215C22semidirect
31. C2×C3×#215C22semidirect
32. C3×#940C22semidirect
33. C2×C3×#214C22semidirect
34. C2×C3×#213C22semidirect
36. C2×C3×D24C22semidirect
37. C2×C3×#204C22semidirect
43. #63914C22semidirect
44. #63911C22semidirect
47. #63864C22semidirect
48. #63863C22semidirect
49. C2×#3717C22semidirect
50. C2×#3715C22semidirect
51. C2×#3714C22semidirect
52. C2×#3714C22semidirect
53. C2×#3714C22semidirect
54. C2×#3713C22semidirect
57. #63642C22semidirect
58. C3×#815C22semidirect
59. #63555C22semidirect
60. #63554C22semidirect
67. C2×D3×SD16D3semidirect
84. #5176D3direct (N × H)
141. C3×D3×C8D4semidirect
151. D3×C3⋊C8D4semidirect
169. C2×C3×SD16C2×D3semidirect
170. C2×C3×SD16C2×D3semidirect
182. #947C2×D3semidirect
189. C2×#215C2×D3semidirect
190. C2×#215C2×D3semidirect
199. #940C2×D3semidirect
202. C2×#214C2×D3semidirect
212. C2×#213C2×D3semidirect
227. C2×D24C2×D3semidirect
229. C2×#204C2×D3semidirect
244. #815C2×D3semidirect
293. C32×C8C2×D4semidirect
294. C3⋊(C3⋊C8)C2×D4semidirect
295. C3×C3⋊C8C2×D4semidirect
296. C3×C3⋊C8C2×D4semidirect
444. D3×C8#67semidirect
484. C2×SD16D32semidirect
625. C3×C8D3×D4semidirect
626. C3×C8C2×#67semidirect
630. C3⋊C8D3×D4semidirect
631. C3⋊C8C2×#67semidirect
640. C3×D3#496semidirect
762. C32C2×#496semidirect
813. C8D3×#67semidirect
836. D3#5176direct (N × H)
863. C3D3×#496semidirect
864. C3C2×#5176semidirect

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
C2×D3×#2152
D3×#9402
C2×D3×#2132
C2×D3×D242
#105928752
C3×#51762
#105916212
#105916192
#105914752
#105914722
#105908872
#105908812
D3×#8152
C2×#51763
D3×#4963