Finite Group Databasebeta

← D3×#3004 #11661538

Subgroups — D3×#3004 #11661538

Order 768.

4970 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×Q8C211yesmaximal, characteristic, complemented
2C2×D3×#137C212yesmaximal, complemented
3D3×#525C211yesmaximal, characteristic
4C3×#3004C211yesmaximal, characteristic, complemented
5#84059C211yesmaximal, characteristic, complemented
6#83979C212yesmaximal, complemented
7#82933C211yesmaximal, characteristic, complemented
8#80183C214yesmaximal, complemented
9D3×#451C214yesmaximal, complemented
10#80039C214yesmaximal, complemented
11D3×#448C214yesmaximal, complemented
12#78958C212yesmaximal, complemented
13D3×#419C212yesmaximal, complemented
14#78645C211yesmaximal, characteristic, complemented
15D3×#407C211yesmaximal, characteristic, complemented
16C2×#3004—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic, complemented
18C2×D3×#41C2211yescharacteristic
19C22×D3×Q8—216no—
20C22×D3×Q8—21no—
21C22×D3×Q8—22no—
22C22×D3×Q8—21no—
23C22×D3×Q8—22no—
24C22×D3×Q8C2214yes—
25C22×D3×Q8C2212yes—
26C22×D3×Q8C2212yescomplemented
27C22×D3×Q8C2214yescomplemented
28C23×C4×D3—21no—
29C23×C4×D3C2211yescharacteristic
30C23×Dic6—21no—
31C23×Dic6C2211yescharacteristic, complemented
32C2×C3×#137C2212yescomplemented
33C3×#525C2211yescharacteristic
34#5828C2211yescharacteristic
35C2×#951C2212yescomplemented
36C2×#942C2212yescomplemented
37#5791C2211yescharacteristic
38D3×#137—216no—
39C2×#918C2214yescomplemented
40C2×D3×Q16C2214yescomplemented
41C2×#915C2214yescomplemented
42C2×D3×SD16C2214yescomplemented
43C2×#909C2212yescomplemented
44C2×D3×M16C2212yes—
45#5656—21no—
46D3×#123—21no—
47#5627C2212yes—
48D3×C22⋊Q8C2212yes—
49#5606C2212yes—
50D3×#121C2212yes—
51D3×#120—21no—
52#5586—21no—
53#5547—22no—
54C4×D3×D4—22no—
55#5524C2211yescharacteristic
56D3×#117C2211yescharacteristic
57C3×#451C2214yescomplemented
58C3×#448C2214yescomplemented
59C3×#419C2212yescomplemented
60C3×#407C2211yescharacteristic, complemented
61#5228C2214yescomplemented
62#5227C2214yescomplemented
63#5225C2212yescomplemented
64#5207C2211yescharacteristic, complemented
65#5186C2218yescomplemented
66#5170C2218yescomplemented
67#5126C2212yescomplemented
68#5120C2212yescomplemented
69#5050C2214yescomplemented
70#5040C2214yescomplemented
71#5004C2212yescomplemented
72#4809C2218yescomplemented
73#4806C2218yescomplemented
74#4802C2218yescomplemented
75D3×#103C2218yescomplemented
76#4739C2214yescomplemented
77#4738C2214yescomplemented
78#4726C2214yescomplemented
79D3×C22⋊C8C2214yes—
80C24×Q8—31no—
81C22×#137—32no—
82C2×#525—31no—
83#3004—34no—
84#3004—34no—
85#3004—32no—
86#3004—31no—
87#3004—31no—
88#3004—32no—
89#3004—31no—
90#3004D311yescharacteristic, direct product factor
91C2×#451—34no—
92C2×#448—34no—
93C2×#419—32no—
94C2×#407—31no—
95C24×D3D411yescharacteristic
96C2×C3×#41C2311yescharacteristic
97C22×C3×Q8—28no—
98C22×C3×Q8—22no—
99C22×C3×Q8—21no—
100C22×C3×Q8C2314yes—
101C22×C3×Q8C2312yes—
102C23×C3×C4—21no—
103C23×C3×C4C2311yescharacteristic
104C23×Dic3—21no—
105C23×Dic3D411yescharacteristic
106D3×#41—28no—
107C2×#239C2311yescharacteristic
108C2×D3×Q8—232no—
109C2×D3×Q8—232no—
110C2×D3×Q8—216no—
111C2×D3×Q8—216no—
112C2×D3×Q8—28no—
113C2×D3×Q8—232no—
114C2×D3×Q8—232no—
115C2×D3×Q8—28no—
116C2×D3×Q8—24no—
117C2×D3×Q8—24no—
118C2×D3×Q8—22no—
119C2×D3×Q8—22no—
120C2×D3×Q8—24no—
121C2×D3×Q8—24no—
122C2×D3×Q8—24no—
123C2×D3×Q8—28no—
124C2×D3×Q8D4116yescomplemented
125C2×D3×Q8C2318yes—
126C2×D3×Q8C2311yescharacteristic
127C2×D3×Q8C2314yes—
128C2×D3×Q8C2314yes—
129C2×#237—21no—
130C2×#237C2311yescharacteristic
131C2×D3×D4—21no—
132C2×D3×D4—22no—
133C2×D3×D4C2311yescharacteristic
134C2×#235—21no—
135C2×#235C2311yescharacteristic
136C22×C4×D3—216no—
137C22×C4×D3—24no—
138C22×C4×D3—22no—
139C22×C4×D3—22no—
140C22×C4×D3—24no—
141C22×C4×D3—28no—
142C22×C4×D3—21no—
143C22×C4×D3D411yescharacteristic
144C22×C4×D3D411yescharacteristic
145C22×C4×D3D412yes—
146C22×C4×D3D412yes—
147C22×C4×D3C2311yescharacteristic
148C22×C4×D3C2312yes—
149C22×C4×D3C2312yes—
150C22×C4×D3C2311yescharacteristic
151C22×Dic6—216no—
152C22×Dic6—22no—
153C22×Dic6—21no—
154C22×Dic6—24no—
155C22×Dic6—22no—
156C22×Dic6—24no—
157C22×Dic6—22no—
158C22×Dic6—28no—
159C22×Dic6C2314yes—
160C22×Dic6C2312yes—
161C3×#137—28no—
162C2×C3×Q16C2314yescomplemented
163C2×C3×SD16C2314yescomplemented
164C2×C3×M16C2312yes—
165C3×#123—21no—
166C3×C22⋊Q8C2312yes—
167C3×#121C2312yes—
168C3×#120—21no—
169C3×C4×D4—22no—
170C3×#117C2311yescharacteristic
171#953—21no—
172#951—28no—
173#946C2312yes—
174C2×#216C2314yescomplemented
175C2×#216C2314yescomplemented
176#942—28no—
177C2×#215C2314yescomplemented
178#939—22no—
179#938C2312yes—
180#937—21no—
181#937—22no—
182#935—21no—
183D4×Dic3—22no—
184C2×#214C2314yescomplemented
185#930C2312yes—
186#929—21no—
187C4×#67—22no—
188C4×#67—22no—
189#926C2311yescharacteristic
190#924C2312yes—
191C2×#208C2312yes—
192#918—216no—
193D3×Q16—216no—
194#915—216no—
195D3×SD16—216no—
196#909—28no—
197D3×M16—28no—
198C2×Dic12C2314yescomplemented
199C2×#204C2314yescomplemented
200C2×ΓL(1,𝔽25)C2314yes—
201C2×D3×C8C2314yes—
202#897C2312yes—
203#896—22no—
204#895C2312yes—
205#894—22no—
206#893—22no—
207#892C2312yes—
208D3×C4⋊C4—22no—
209D3×C4⋊C4C2312yes—
210#886—21no—
211#884—22no—
212#883—22no—
213#882—21no—
214#882—22no—
215#67⋊C4—22no—
216#67⋊C4—22no—
217D3×C22⋊C4—21no—
218D3×C22⋊C4—22no—
219D3×C22⋊C4—22no—
220#878—22no—
221#877—21no—
222C4×D12—22no—
223#872—21no—
224C42×D3—21no—
225C3×#103C2318yescomplemented
226C3×C22⋊C8C2314yes—
227#835C2318yescomplemented
228#830C2314yes—
229(C2×D3)⋊C8C2318yes—
230#816C2318yescomplemented
231#810C2318yescomplemented
232C22×#41—31no—
233C23×Q8—32no—
234C23×Q8—34no—
235C23×Q8—34no—
236C23×Q8—32no—
237C23×Q8—31no—
238C23×Q8—61no—
239C23×Q8—62no—
240C23×Q8—61no—
241C23×Q8—61no—
242C23×Q8—62no—
243C23×Q8—616no—
244C23×Q8C2×D311yescharacteristic, complemented
245C24×C4—31no—
246C24×C4—61no—
247C2×#137—32no—
248C2×#137—32no—
249C2×#137—34no—
250C2×#137—34no—
251C2×#137—32no—
252C2×#137—616no—
253C2×#137C2×D312yescomplemented
254C22×Q16—34no—
255C22×SD16—34no—
256C22×M16—32no—
257#525—31no—
258#525—31no—
259#525—32no—
260#525—32no—
261#525—31no—
262#525—62no—
263#525—61no—
264#525—61no—
265#525C2×D311yescharacteristic
266C2×#123—61no—
267C2×C22⋊Q8—32no—
268C2×#121—32no—
269C2×#120—61no—
270C2×C4×D4—62no—
271C2×#117—31no—
272#451—34no—
273#451—38no—
274#451—34no—
275#451—38no—
276#451—34no—
277#451C2×D314yescomplemented
278#448—34no—
279#448—38no—
280#448—34no—
281#448—38no—
282#448—34no—
283#448C2×D314yescomplemented
284#419—32no—
285#419—32no—
286#419—32no—
287#419—38no—
288#419C2×D312yescomplemented
289C2×#103—38no—
290#407—31no—
291#407—32no—
292#407—34no—
293#407C2×D311yescharacteristic, complemented
294C2×C22⋊C8—34no—
295C24×C3C2×D411yescharacteristic
296C23×D3—24no—
297C23×D3—28no—
298C23×D3—21no—
299C23×D3C2×D411yescharacteristic
300C23×D3C2×D412yes—
301C23×D3C2×D411yescharacteristic
302C23×D3C2×D412yes—
303C3×#41—24no—
304C2×C3×Q8—216no—
305C2×C3×Q8—28no—
306C2×C3×Q8—216no—
307C2×C3×Q8—24no—
308C2×C3×Q8—24no—
309C2×C3×Q8—22no—
310C2×C3×Q8C2×D418yescomplemented
311C2×C3×Q8C2411yescharacteristic
312C2×C3×Q8C2414yes—
313C2×C3×D4—22no—
314C2×C3×D4—21no—
315C2×C3×D4C2411yescharacteristic
316C22×C3×C4—28no—
317C22×C3×C4—24no—
318C22×C3×C4—22no—
319C22×C3×C4—24no—
320C22×C3×C4—21no—
321C22×C3×C4C2×D412yes—
322C22×C3×C4C2×D411yescharacteristic
323C22×C3×C4C2412yes—
324C22×C3×C4C2411yescharacteristic
325C2×#67—22no—
326C2×#67—21no—
327C2×#67—22no—
328C2×#67—21no—
329C2×#67—21no—
330C22×Dic3—28no—
331C22×Dic3—24no—
332C22×Dic3—22no—
333C22×Dic3—24no—
334C22×Dic3—21no—
335C22×Dic3C2×D412yes—
336C22×Dic3C2×D412yes—
337C22×Dic3C2×D411yescharacteristic
338C22×Dic3C2×D411yescharacteristic
339#239—24no—
340D3×Q8—232no—
341D3×Q8—232no—
342D3×Q8—232no—
343D3×Q8—232no—
344D3×Q8—232no—
345D3×Q8—216no—
346D3×Q8—216no—
347D3×Q8—216no—
348D3×Q8—28no—
349D3×Q8—28no—
350D3×Q8—216no—
351D3×Q8—24no—
352D3×Q8C2×D4116yes—
353D3×Q8C2×D4116yescomplemented
354#237—24no—
355#237—44no—
356D3×D4—24no—
357D3×D4—44no—
358D3×D4—48no—
359#235—24no—
360#235—44no—
361C2×D12—22no—
362C2×D12—21no—
363C2×D12C2411yescharacteristic
364C2×C4×D3—216no—
365C2×C4×D3—232no—
366C2×C4×D3—232no—
367C2×C4×D3—216no—
368C2×C4×D3—24no—
369C2×C4×D3—28no—
370C2×C4×D3—24no—
371C2×C4×D3—24no—
372C2×C4×D3—24no—
373C2×C4×D3—24no—
374C2×C4×D3—28no—
375C2×C4×D3—28no—
376C2×C4×D3—28no—
377C2×C4×D3—28no—
378C2×C4×D3—22no—
379C2×C4×D3—21no—
380C2×C4×D3—21no—
381C2×C4×D3—21no—
382C2×C4×D3—44no—
383C2×C4×D3C2×D412yes—
384C2×C4×D3C2×D412yes—
385C2×C4×D3C2×D412yes—
386C2×C4×D3C2×D412yes—
387C2×C4×D3C2×D412yes—
388C2×C4×D3C2×D411yescharacteristic
389C2×C4×D3C2×D411yescharacteristic
390C2×C4×D3C2×D418yes—
391C2×C4×D3C2412yes—
392C2×C4×D3C2411yescharacteristic
393C2×C4×D3C2411yescharacteristic
394C2×Dic6—216no—
395C2×Dic6—28no—
396C2×Dic6—216no—
397C2×Dic6—232no—
398C2×Dic6—232no—
399C2×Dic6—24no—
400C2×Dic6—22no—
401C2×Dic6—24no—
402C2×Dic6—216no—
403C2×Dic6—28no—
404C2×Dic6—24no—
405C2×Dic6—24no—
406C2×Dic6—216no—
407C2×Dic6—21no—
408C2×Dic6C2×D418yescomplemented
409C2×Dic6C2411yescharacteristic
410C2×Dic6C2414yes—
411C3×Q16—28no—
412C3×SD16—28no—
413C3×M16—24no—
414C2×C3×C8C2414yes—
415C3×C4⋊C4—22no—
416C3×C4⋊C4C2412yes—
417C3×C22⋊C4—21no—
418C3×C22⋊C4—22no—
419C3×C22⋊C4—22no—
420C3×C42—21no—
421#217—21no—
422#217—22no—
423#217—22no—
424#216—28no—
425#216—28no—
426#215—28no—
427#214—28no—
428(C2×D3)⋊C4—22no—
429(C2×D3)⋊C4—22no—
430(C2×D3)⋊C4—22no—
431(C2×D3)⋊C4—22no—
432(C2×D3)⋊C4—22no—
433C4⋊Dic3—22no—
434C4⋊Dic3C2412yes—
435Dic3⋊C4—22no—
436Dic3⋊C4—22no—
437Dic3⋊C4—22no—
438C4×Dic3—21no—
439C4×Dic3—22no—
440#208—24no—
441C2×C3⋊C8C2414yes—
442Dic12—28no—
443#204—28no—
444ΓL(1,𝔽25)—28no—
445D3×C8—28no—
446C25—31no—
447C2×#41—31no—
448C2×#41—31no—
449C2×#41—31no—
450C2×#41—61no—
451C2×#41—61no—
452C2×#41—68no—
453C2×#41C22×D311yescharacteristic
454C22×Q8—28no—
455C22×Q8—22no—
456C22×Q8—21no—
457C22×Q8—316no—
458C22×Q8—34no—
459C22×Q8—34no—
460C22×Q8—31no—
461C22×Q8—38no—
462C22×Q8—32no—
463C22×Q8—34no—
464C22×Q8—62no—
465C22×Q8—64no—
466C22×Q8—64no—
467C22×Q8—62no—
468C22×Q8—68no—
469C22×Q8—616no—
470C22×Q8—62no—
471C22×Q8—62no—
472C22×Q8—68no—
473C22×Q8—64no—
474C22×Q8—64no—
475C22×Q8—64no—
476C22×Q8—64no—
477C22×Q8—64no—
478C22×Q8—632no—
479C22×Q8—632no—
480C22×Q8—68no—
481C22×Q8—616no—
482C22×Q8—632no—
483C22×Q8—632no—
484C22×Q8—616no—
485C22×Q8—68no—
486C22×Q8—62no—
487C22×Q8—61no—
488C22×Q8C22×D314yes—
489C22×Q8C22×D312yes—
490C22×D4—31no—
491C22×D4—62no—
492C22×D4—61no—
493C23×C4—21no—
494C23×C4—31no—
495C23×C4—31no—
496C23×C4—32no—
497C23×C4—31no—
498C23×C4—31no—
499C23×C4—32no—
500C23×C4—32no—
501C23×C4—32no—
502C23×C4—31no—
503C23×C4—68no—
504C23×C4—61no—
505C23×C4—62no—
506C23×C4—64no—
507C23×C4—64no—
508C23×C4—62no—
509C23×C4—616no—
510C23×C4—61no—
511C23×C4C22×D311yescharacteristic
512#137—28no—
513#137—68no—
514#137—616no—
515#137—616no—
516#137—68no—
517#137—68no—
518C2×Q16—34no—
519C2×Q16—34no—
520C2×Q16—34no—
521C2×Q16—616no—
522C2×Q16C22×D314yescomplemented
523C2×SD16—34no—
524C2×SD16—34no—
525C2×SD16—34no—
526C2×SD16—616no—
527C2×SD16C22×D314yescomplemented
528C2×M16—32no—
529C2×M16—34no—
530C2×M16—68no—
531C2×M16C22×D312yes—
532C22×C8—34no—
533#123—21no—
534#123—62no—
535#123—61no—
536#123—62no—
537#123—61no—
538#123—61no—
539C22⋊Q8—32no—
540C22⋊Q8—32no—
541C22⋊Q8—32no—
542C22⋊Q8—62no—
543C22⋊Q8—62no—
544C22⋊Q8C22×D312yes—
545#121—32no—
546#121—32no—
547#121—32no—
548#121—62no—
549#121—62no—
550#121C22×D312yes—
551#120—21no—
552#120—61no—
553#120—62no—
554#120—62no—
555#120—61no—
556#120—61no—
557C4×D4—22no—
558C4×D4—62no—
559C4×D4—62no—
560C4×D4—62no—
561C4×D4—62no—
562C4×D4—62no—
563C4×D4—62no—
564C4×D4—62no—
565#117—31no—
566#117—32no—
567#117—61no—
568#117—61no—
569#117C22×D311yescharacteristic
570C2×C4⋊C4—32no—
571C2×C4⋊C4—62no—
572C2×C22⋊C4—62no—
573C2×C22⋊C4—61no—
574C2×C22⋊C4—62no—
575C2×C42—61no—
576#103—38no—
577#103—38no—
578#103—38no—
579#103C22×D318yescomplemented
580C22⋊C8—34no—
581C22⋊C8—38no—
582C22⋊C8C22×D314yes—
583C23×C3—22no—
584C23×C3—24no—
585C23×C3—21no—
586C23×C3C22×D411yescharacteristic
587C23×C3C22×D412yes—
588C22×D3—232no—
589C22×D3—22no—
590C22×D3—24no—
591C22×D3—24no—
592C22×D3—24no—
593C22×D3—24no—
594C22×D3—24no—
595C22×D3—24no—
596C22×D3—24no—
597C22×D3—21no—
598C22×D3—42no—
599C22×D3—44no—
600C22×D3#12014yes—
601C22×D3#13718yescomplemented
602C22×D3C22×D411yescharacteristic
603C22×D3C22×D412yes—
604C22×D3C22×D411yescharacteristic
605C3×Q8—216no—
606C3×Q8—28no—
607C3×Q8—24no—
608C3×Q8—22no—
609C3×Q8C22×D418yes—
610C3×D4—22no—
611C3×D4—42no—
612C3×D4—44no—
613C2×C3×C4—216no—
614C2×C3×C4—28no—
615C2×C3×C4—22no—
616C2×C3×C4—24no—
617C2×C3×C4—24no—
618C2×C3×C4—24no—
619C2×C3×C4—22no—
620C2×C3×C4—21no—
621C2×C3×C4—42no—
622C2×C3×C4C22×D412yes—
623C2×C3×C4C22×D411yescharacteristic
624C2×C3×C4C22×D414yes—
625C2×C3×C4C2511yescharacteristic
626#67—42no—
627#67—44no—
628#67—42no—
629#67—44no—
630#67—42no—
631C2×Dic3—216no—
632C2×Dic3—22no—
633C2×Dic3—28no—
634C2×Dic3—24no—
635C2×Dic3—24no—
636C2×Dic3—24no—
637C2×Dic3—22no—
638C2×Dic3—21no—
639C2×Dic3—42no—
640C2×Dic3#12014yes—
641C2×Dic3C22×D412yes—
642C2×Dic3C22×D411yescharacteristic
643C2×Dic3C22×D411yescharacteristic
644D12—22no—
645D12—42no—
646D12—44no—
647C4×D3—232no—
648C4×D3—216no—
649C4×D3—216no—
650C4×D3—24no—
651C4×D3—24no—
652C4×D3—24no—
653C4×D3—24no—
654C4×D3—24no—
655C4×D3—24no—
656C4×D3—42no—
657C4×D3—44no—
658C4×D3—42no—
659C4×D3—42no—
660C4×D3#12014yes—
661C4×D3#12014yes—
662C4×D3C22×D414yes—
663C4×D3C22×D414yes—
664Dic6—232no—
665Dic6—216no—
666Dic6—28no—
667Dic6—24no—
668Dic6—216no—
669Dic6—216no—
670Dic6—22no—
671Dic6—42no—
672Dic6C22×D418yes—
673C3×C8—24no—
674C3⋊C8—24no—
675C24—32no—
676C24—31no—
677C24—32no—
678C24—31no—
679C24—64no—
680C24—68no—
681C24—61no—
682C24D3×D411yescharacteristic
683#41—24no—
684#41—64no—
685#41—64no—
686#41—64no—
687#41—124no—
688#41—124no—
689C2×Q8—216no—
690C2×Q8—28no—
691C2×Q8—216no—
692C2×Q8—24no—
693C2×Q8—22no—
694C2×Q8—24no—
695C2×Q8—316no—
696C2×Q8—316no—
697C2×Q8—38no—
698C2×Q8—34no—
699C2×Q8—31no—
700C2×Q8—64no—
701C2×Q8—64no—
702C2×Q8—68no—
703C2×Q8—616no—
704C2×Q8—61no—
705C2×Q8—616no—
706C2×Q8—632no—
707C2×Q8—632no—
708C2×Q8—616no—
709C2×Q8—68no—
710C2×Q8—616no—
711C2×Q8—68no—
712C2×Q8—68no—
713C2×Q8—616no—
714C2×Q8—616no—
715C2×Q8—64no—
716C2×Q8—616no—
717C2×Q8—632no—
718C2×Q8—632no—
719C2×Q8—632no—
720C2×Q8—632no—
721C2×Q8—632no—
722C2×Q8—616no—
723C2×Q8—64no—
724C2×Q8—62no—
725C2×Q8—64no—
726C2×Q8D3×D418yescomplemented
727C2×Q8C23×D311yescharacteristic
728C2×Q8C23×D314yes—
729C2×D4—22no—
730C2×D4—21no—
731C2×D4—31no—
732C2×D4—62no—
733C2×D4—61no—
734C2×D4—64no—
735C2×D4—61no—
736C2×D4—62no—
737C2×D4—61no—
738C2×D4—62no—
739C2×D4—61no—
740C2×D4—124no—
741C2×D4—128no—
742C2×D4C23×D311yescharacteristic
743C22×C4—28no—
744C22×C4—24no—
745C22×C4—22no—
746C22×C4—24no—
747C22×C4—21no—
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—31no—
751C22×C4—38no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—32no—
755C22×C4—32no—
756C22×C4—31no—
757C22×C4—32no—
758C22×C4—32no—
759C22×C4—32no—
760C22×C4—32no—
761C22×C4—32no—
762C22×C4—32no—
763C22×C4—64no—
764C22×C4—68no—
765C22×C4—68no—
766C22×C4—68no—
767C22×C4—68no—
768C22×C4—61no—
769C22×C4—64no—
770C22×C4—64no—
771C22×C4—64no—
772C22×C4—68no—
773C22×C4—616no—
774C22×C4—632no—
775C22×C4—632no—
776C22×C4—616no—
777C22×C4—62no—
778C22×C4—61no—
779C22×C4—64no—
780C22×C4—61no—
781C22×C4—68no—
782C22×C4—64no—
783C22×C4—62no—
784C22×C4—64no—
785C22×C4—61no—
786C22×C4—124no—
787C22×C4D3×D412yes—
788C22×C4D3×D411yescharacteristic
789C22×C4C23×D312yes—
790C22×C4C23×D311yescharacteristic
791Q16—28no—
792Q16—68no—
793Q16—68no—
794Q16—68no—
795SD16—28no—
796SD16—68no—
797SD16—68no—
798SD16—68no—
799M16—24no—
800M16—68no—
801M16—64no—
802C2×C8—34no—
803C2×C8—68no—
804C2×C8C23×D314yes—
805C4⋊C4—22no—
806C4⋊C4—32no—
807C4⋊C4—62no—
808C4⋊C4—62no—
809C4⋊C4—62no—
810C4⋊C4—62no—
811C4⋊C4C23×D312yes—
812C22⋊C4—21no—
813C22⋊C4—22no—
814C22⋊C4—22no—
815C22⋊C4—62no—
816C22⋊C4—62no—
817C22⋊C4—62no—
818C22⋊C4—62no—
819C22⋊C4—62no—
820C22⋊C4—61no—
821C22⋊C4—62no—
822C22⋊C4—62no—
823C42—21no—
824C42—62no—
825C42—61no—
826C22×C3—28no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—41no—
831C22×C3—42no—
832C22×C3C2×#12012yes—
833C22×C3C2×#13714yescomplemented
834C22×C3C23×D411yescharacteristic
835C2×D3—216no—
836C2×D3—28no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—22no—
840C2×D3—28no—
841C2×D3—216no—
842C2×D3—41no—
843C2×D3—42no—
844C2×D3—84no—
845C2×D3C2×#12012yes—
846C2×D3C2×#12012yes—
847C2×D3C2×#13714yes—
848C2×D3C2×#13714yescomplemented
849C3×C4—28no—
850C3×C4—22no—
851C3×C4—41no—
852C3×C4—42no—
853C3×C4C2×#12012yes—
854C3×C4C23×D412yes—
855Dic3—22no—
856Dic3—28no—
857Dic3—41no—
858Dic3—42no—
859Dic3C2×#12012yes—
860Dic3C2×#12012yes—
861C23—24no—
862C23—22no—
863C23—21no—
864C23—31no—
865C23—32no—
866C23—31no—
867C23—38no—
868C23—34no—
869C23—64no—
870C23—64no—
871C23—64no—
872C23—64no—
873C23—64no—
874C23—64no—
875C23—632no—
876C23—64no—
877C23—62no—
878C23—61no—
879C23—122no—
880C23—124no—
881C23C2×D3×D412yes—
882C23C2×D3×D411yescharacteristic
883Q8—216no—
884Q8—24no—
885Q8—28no—
886Q8—22no—
887Q8—38no—
888Q8—616no—
889Q8—616no—
890Q8—632no—
891Q8—616no—
892Q8—64no—
893Q8—68no—
894Q8—62no—
895Q8—122no—
896Q8C2×D3×D418yes—
897D4—22no—
898D4—44no—
899D4—42no—
900D4—62no—
901D4—122no—
902D4—122no—
903D4—124no—
904D4—122no—
905D4—124no—
906D4—124no—
907D4—122no—
908C2×C4—216no—
909C2×C4—24no—
910C2×C4—28no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—31no—
917C2×C4—31no—
918C2×C4—34no—
919C2×C4—34no—
920C2×C4—34no—
921C2×C4—34no—
922C2×C4—34no—
923C2×C4—32no—
924C2×C4—42no—
925C2×C4—64no—
926C2×C4—64no—
927C2×C4—64no—
928C2×C4—64no—
929C2×C4—616no—
930C2×C4—616no—
931C2×C4—632no—
932C2×C4—64no—
933C2×C4—64no—
934C2×C4—616no—
935C2×C4—64no—
936C2×C4—62no—
937C2×C4—68no—
938C2×C4—64no—
939C2×C4—64no—
940C2×C4—62no—
941C2×C4—61no—
942C2×C4—122no—
943C2×C4—122no—
944C2×C4—122no—
945C2×C4—124no—
946C2×C4—122no—
947C2×C4C2×D3×D412yes—
948C2×C4C2×D3×D414yes—
949C2×C4C2×D3×D411yescharacteristic
950C2×C4C24×D311yescharacteristic
951C8—24no—
952C8—64no—
953C2×C3—22no—
954C2×C3—24no—
955C2×C3—81no—
956C2×C3C22×#12011yescharacteristic
957C2×C3C22×#13712yes—
958D3—22no—
959D3—24no—
960D3—81no—
961D3#300414yesdirect product factor
962C22—28no—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—34no—
967C22—32no—
968C22—34no—
969C22—32no—
970C22—42no—
971C22—41no—
972C22—616no—
973C22—68no—
974C22—616no—
975C22—68no—
976C22—62no—
977C22—62no—
978C22—62no—
979C22—122no—
980C22—121no—
981C22—244no—
982C22D3×#12012yes—
983C22D3×#13714yescomplemented
984C22C22×D3×D411yescharacteristic
985C4—28no—
986C4—22no—
987C4—32no—
988C4—32no—
989C4—42no—
990C4—41no—
991C4—62no—
992C4—68no—
993C4—122no—
994C4—121no—
995C4D3×#12012yes—
996C4C22×D3×D412yes—
997C3C2×#300411yescharacteristic, complemented, Sylow
998C2—24no—
999C2—22no—
1000C2—34no—
1001C2—64no—
1002C2—62no—
1003C2—81no—
1004C2—241no—
1005C2C2×D3×#12011yescharacteristic
1006C2C2×D3×#13712yes—
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3004C2
socleC22×C3C23×D4
prime radicalD3×#525C2
hypercenter#3004D3
hypocenterC3C2×#3004
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3004

Complements

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

NH ≅ G/Ntype
1. C23×D3×Q8C2semidirect
2. C2×D3×#137C2semidirect
4. C3×#3004C2semidirect
5. #84059C2semidirect
6. #83979C2semidirect
7. #82933C2semidirect
8. #80183C2semidirect
9. D3×#451C2semidirect
10. #80039C2semidirect
11. D3×#448C2semidirect
12. #78958C2semidirect
13. D3×#419C2semidirect
14. #78645C2semidirect
15. D3×#407C2semidirect
17. C23×C3×Q8C22semidirect
26. C22×D3×Q8C22semidirect
27. C22×D3×Q8C22semidirect
31. C23×Dic6C22semidirect
32. C2×C3×#137C22semidirect
35. C2×#951C22semidirect
36. C2×#942C22semidirect
39. C2×#918C22semidirect
40. C2×D3×Q16C22semidirect
41. C2×#915C22semidirect
42. C2×D3×SD16C22semidirect
43. C2×#909C22semidirect
57. C3×#451C22semidirect
58. C3×#448C22semidirect
59. C3×#419C22semidirect
60. C3×#407C22semidirect
61. #5228C22semidirect
62. #5227C22semidirect
63. #5225C22semidirect
64. #5207C22semidirect
65. #5186C22semidirect
66. #5170C22semidirect
67. #5126C22semidirect
68. #5120C22semidirect
69. #5050C22semidirect
70. #5040C22semidirect
71. #5004C22semidirect
72. #4809C22semidirect
73. #4806C22semidirect
74. #4802C22semidirect
75. D3×#103C22semidirect
76. #4739C22semidirect
77. #4738C22semidirect
78. #4726C22semidirect
90. #3004D3direct (N × H)
124. C2×D3×Q8D4semidirect
162. C2×C3×Q16C23semidirect
163. C2×C3×SD16C23semidirect
174. C2×#216C23semidirect
175. C2×#216C23semidirect
177. C2×#215C23semidirect
184. C2×#214C23semidirect
198. C2×Dic12C23semidirect
199. C2×#204C23semidirect
225. C3×#103C23semidirect
227. #835C23semidirect
230. #816C23semidirect
231. #810C23semidirect
244. C23×Q8C2×D3semidirect
253. C2×#137C2×D3semidirect
277. #451C2×D3semidirect
283. #448C2×D3semidirect
288. #419C2×D3semidirect
293. #407C2×D3semidirect
310. C2×C3×Q8C2×D4semidirect
353. D3×Q8C2×D4semidirect
408. C2×Dic6C2×D4semidirect
522. C2×Q16C22×D3semidirect
527. C2×SD16C22×D3semidirect
579. #103C22×D3semidirect
601. C22×D3#137semidirect
726. C2×Q8D3×D4semidirect
833. C22×C3C2×#137semidirect
848. C2×D3C2×#137semidirect
961. D3#3004direct (N × H)
983. C22D3×#137semidirect
997. C3C2×#3004semidirect

Maximal subgroups

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

subgroupindex
C23×D3×Q82
C2×D3×#1372
D3×#5252
C3×#30042
#840592
#839792
#829332
#801832
D3×#4512
#800392
D3×#4482
#789582
D3×#4192
#786452
D3×#4072
C2×#30043