Finite Group Databasebeta

← C2×C3×#5201 #11864851

Subgroups — C2×C3×#5201 #11864851

Order 1152.

1605 conjugacy classes of subgroups.

The subgroup lattice has 781 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C2×C32×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
3C2×C3×#936C211yesmaximal, characteristic, complemented
4C2×C3×#932C211yesmaximal, characteristic, complemented
5C2×C3×#837C211yesmaximal, characteristic, complemented
6C3×#5201C218yesmaximal, direct product factor
7C2×C3×#825C211yesmaximal, characteristic, complemented
8C2×C3×#824C211yesmaximal, characteristic, complemented
9C2×C3×#454—31nomaximal
10C2×#5201C311yesmaximal, characteristic, direct product factor
11C2×C32×#41C2211yescharacteristic
12C22×C32×D4C2211yescharacteristic
13C3×#1010—22no—
14C3×#1010—22no—
15C3×#1010—22no—
16C3×#1010C2214yescomplemented
17C2×C3×D3×Q8—21no—
18C2×C3×#237—21no—
19C2×C3×#237—22no—
20C2×C3×#235—21no—
21C2×C3×#235C2211yescharacteristic
22C22×C3×Dic6—21no—
23C22×C3×Dic6C2211yescharacteristic
24C32×AGL(1,ℤ/8)—22no—
25C32×AGL(1,ℤ/8)C2214yescomplemented
26C2×C32×SD16—21no—
27C2×C32×D8—21no—
28C2×C32×M16C2211yescharacteristic
29C2×C3×#217—22no—
30C3×#936—22no—
31C3×#936C2214yescomplemented
32C2×C3×#214—21no—
33C3×#932—22no—
34C3×#932C2214yescomplemented
35C2×C3×#213—21no—
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×C3×#208C2211yescharacteristic
38C3×#837C2214yescomplemented
39C3×#825C2214yescomplemented
40C3×#824C2214yescomplemented
41C2×C3×2−1+4—31no—
42C2×#1010C2×C311yescharacteristic, complemented
43C2×C3×AGL(1,ℤ/8)—21no—
44C2×C3×AGL(1,ℤ/8)—31no—
45C2×C3×AGL(1,ℤ/8)D311yescharacteristic, complemented
46C2×C3×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
47C2×C3×#124—31no—
48C2×#936C2×C311yescharacteristic, complemented
49C2×#932C2×C311yescharacteristic, complemented
50C3×#454—38no—
51C2×C3×#104—31no—
52C2×C3×#104—31no—
53C2×C3×#101—31no—
54C2×#837C2×C311yescharacteristic, complemented
55#5201C2×C318yesdirect product factor
56C2×#825C2×C311yescharacteristic, complemented
57C2×#824C2×C311yescharacteristic, complemented
58C24×C32—21no—
59C32×#41—21no—
60C32×#41—21no—
61C32×#41D412yes—
62C32×#41C2312yes—
63C2×C32×Q8D411yescharacteristic
64C2×C32×D4—21no—
65C2×C32×D4—21no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4—21no—
69C2×C32×D4—21no—
70C2×C32×D4D411yescharacteristic
71C2×C32×D4C2312yes—
72C22×C32×C4—21no—
73C22×C32×C4C2311yescharacteristic
74C2×C3×#67—22no—
75C2×C3×#67—21no—
76C22×C3×Dic3—22no—
77C22×C3×Dic3—21no—
78C22×C3×Dic3D412yes—
79C3×D3×Q8—24no—
80C3×D3×Q8—24no—
81C3×#237—28no—
82C3×#237—24no—
83C3×#237—24no—
84C3×#237—28no—
85C3×#235—24no—
86C3×#235—21no—
87C3×#235—21no—
88C3×#235—24no—
89C3×#235D412yes—
90C3×#235C2312yes—
91C2×C3×D12D411yescharacteristic
92C2×C3×C4×D3—22no—
93C2×C3×C4×D3—21no—
94C2×C3×Dic6—22no—
95C2×C3×Dic6—24no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6—21no—
99C2×C3×Dic6—21no—
100C2×C3×Dic6—24no—
101C2×C3×Dic6D412yes—
102C2×C3×Dic6D411yescharacteristic
103C2×C3×Dic6C2312yes—
104C32×SD16—24no—
105C32×D8—24no—
106C32×M16—21no—
107C32×M16C2312yes—
108C2×C32×C8—21no—
109C3×#217—28no—
110C3×#214—24no—
111C3×#213—24no—
112C3×C4×Dic3—21no—
113C3×C4×Dic3C2312yes—
114C3×#208—21no—
115C3×#208C2312yes—
116C2×C3×C3⋊C8—21no—
117C2×#454—31noSylow
118C3×2−1+4—34no—
119C3×2−1+4—62no—
120C3×2−1+4—62no—
121C3×2−1+4—62no—
122C2×C3×#41—21no—
123C2×C3×#41—31no—
124C2×C3×#41—61no—
125C2×C3×#41—62no—
126C2×C3×#41—61no—
127C2×C3×#41C2×D311yescharacteristic
128C2×C3×#41C22×C311yescharacteristic
129C22×C3×Q8—31no—
130C22×C3×Q8—61no—
131C22×C3×Q8—61no—
132C22×C3×D4—21no—
133C22×C3×D4C2×D311yescharacteristic
134C22×C3×D4C22×C311yescharacteristic
135#1010—22no—
136#1010—22no—
137#1010—22no—
138#1010C22×C314yescomplemented
139C2×D3×Q8—21no—
140C2×#237—21no—
141C2×#237—22no—
142C2×#235—21no—
143C2×#235C22×C311yescharacteristic
144C22×Dic6—21no—
145C22×Dic6C22×C311yescharacteristic
146C3×AGL(1,ℤ/8)—24no—
147C3×AGL(1,ℤ/8)—22no—
148C3×AGL(1,ℤ/8)—22no—
149C3×AGL(1,ℤ/8)—24no—
150C3×AGL(1,ℤ/8)—34no—
151C3×AGL(1,ℤ/8)—62no—
152C3×AGL(1,ℤ/8)C2×D314yescomplemented
153C3×AGL(1,ℤ/8)C22×C314yescomplemented
154C2×C3×SD16—22no—
155C2×C3×SD16—21no—
156C2×C3×SD16—21no—
157C2×C3×SD16—61no—
158C2×C3×D8—22no—
159C2×C3×D8—21no—
160C2×C3×D8—21no—
161C2×C3×D8—61no—
162C2×C3×M16—21no—
163C2×C3×M16—31no—
164C2×C3×M16C2×D311yescharacteristic
165C2×C3×M16C22×C311yescharacteristic
166C3×#124—34no—
167C3×#124—62no—
168C2×C3×C22⋊C4—62no—
169C2×C3×C42—31no—
170C2×#217—22no—
171#936—22no—
172#936C22×C314yescomplemented
173C2×#214—21no—
174#932—22no—
175#932C22×C314yescomplemented
176C2×#213—21no—
177C2×C4×Dic3C22×C311yescharacteristic
178C2×#208C22×C311yescharacteristic
179C3×#104—34no—
180C3×#104—34no—
181C3×#101—34no—
182#837C22×C314yescomplemented
183#825C22×C314yescomplemented
184#824C22×C314yescomplemented
185C23×C32—21no—
186C23×C32—22no—
187C23×C32—41no—
188C23×C32—41no—
189C23×C32—44no—
190C23×C32C2×D411yescharacteristic
191C22×C3×D3—21no—
192C32×Q8—21no—
193C32×Q8C2×D412yes—
194C32×D4—22no—
195C32×D4—22no—
196C32×D4—22no—
197C32×D4—21no—
198C32×D4—22no—
199C32×D4—41no—
200C32×D4—41no—
201C32×D4C2×D412yes—
202C2×C32×C4—21no—
203C2×C32×C4—22no—
204C2×C32×C4—22no—
205C2×C32×C4C2×D411yescharacteristic
206C2×C32×C4C2×D411yescharacteristic
207C2×C32×C4C2×D411yescharacteristic
208C2×C32×C4C2×D411yescharacteristic
209C2×C32×C4C2×D411yescharacteristic
210C2×C32×C4C2411yescharacteristic
211C3×#67—28no—
212C3×#67—22no—
213C3×#67—22no—
214C2×C3×Dic3—28no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3—21no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—42no—
220C2×C3×Dic3C2×D414yes—
221C3×D12—21no—
222C3×D12C2×D412yes—
223C3×C4×D3—28no—
224C3×C4×D3—22no—
225C3×C4×D3—22no—
226C3×Dic6—28no—
227C3×Dic6—22no—
228C3×Dic6—21no—
229C3×Dic6—22no—
230C3×Dic6—22no—
231C3×Dic6—22no—
232C3×Dic6C2×D412yes—
233C32×C8—22no—
234C3×C3⋊C8—22no—
235C2×2−1+4—31no—
236C2×AGL(1,ℤ/8)—31no—
237C2×AGL(1,ℤ/8)C3×D311yescharacteristic, complemented
238C2×#124—31no—
239#454—38no—
240C2×#104—31no—
241C2×#104—31no—
242C2×#101—31no—
243C24×C3—21no—
244C24×C3—21no—
245C24×C3—41no—
246C3×#41—21no—
247C3×#41—21no—
248C3×#41—21no—
249C3×#41—21no—
250C3×#41—22no—
251C3×#41—22no—
252C3×#41—32no—
253C3×#41—32no—
254C3×#41—41no—
255C3×#41—41no—
256C3×#41—64no—
257C3×#41—64no—
258C3×#41—68no—
259C3×#41—68no—
260C3×#41—64no—
261C3×#41—64no—
262C3×#41—61no—
263C3×#41—61no—
264C3×#41#6712yes—
265C3×#41C3×D412yes—
266C3×#41C22×D312yes—
267C3×#41C23×C312yes—
268C2×C3×Q8—21no—
269C2×C3×Q8—32no—
270C2×C3×Q8—32no—
271C2×C3×Q8—31no—
272C2×C3×Q8—64no—
273C2×C3×Q8—62no—
274C2×C3×Q8—64no—
275C2×C3×Q8—64no—
276C2×C3×Q8—64no—
277C2×C3×Q8—61no—
278C2×C3×Q8—61no—
279C2×C3×Q8—61no—
280C2×C3×Q8—61no—
281C2×C3×Q8#6711yescharacteristic
282C2×C3×Q8C3×D411yescharacteristic
283C2×C3×D4—21no—
284C2×C3×D4—21no—
285C2×C3×D4—22no—
286C2×C3×D4—22no—
287C2×C3×D4—21no—
288C2×C3×D4—21no—
289C2×C3×D4—21no—
290C2×C3×D4—21no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—22no—
299C2×C3×D4—31no—
300C2×C3×D4—41no—
301C2×C3×D4—41no—
302C2×C3×D4—41no—
303C2×C3×D4—41no—
304C2×C3×D4—62no—
305C2×C3×D4—61no—
306C2×C3×D4#6711yescharacteristic
307C2×C3×D4C3×D411yescharacteristic
308C2×C3×D4C22×D312yes—
309C2×C3×D4C23×C312yes—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—32no—
314C22×C3×C4—41no—
315C22×C3×C4—62no—
316C22×C3×C4—62no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C23×C311yescharacteristic
321C2×#67—22no—
322C2×#67—21no—
323C22×Dic3—22no—
324C22×Dic3—21no—
325C22×Dic3C3×D412yes—
326D3×Q8—24no—
327D3×Q8—24no—
328#237—28no—
329#237—24no—
330#237—24no—
331#237—28no—
332#235—24no—
333#235—21no—
334#235—21no—
335#235—24no—
336#235C3×D412yes—
337#235C23×C312yes—
338C2×D12C3×D411yescharacteristic
339C2×C4×D3—22no—
340C2×C4×D3—21no—
341C2×Dic6—22no—
342C2×Dic6—24no—
343C2×Dic6—21no—
344C2×Dic6—21no—
345C2×Dic6—21no—
346C2×Dic6—21no—
347C2×Dic6—24no—
348C2×Dic6C3×D412yes—
349C2×Dic6C3×D411yescharacteristic
350C2×Dic6C23×C312yes—
351C3×SD16—28no—
352C3×SD16—24no—
353C3×SD16—24no—
354C3×SD16—64no—
355C3×D8—28no—
356C3×D8—24no—
357C3×D8—24no—
358C3×D8—64no—
359C3×M16—22no—
360C3×M16—21no—
361C3×M16—21no—
362C3×M16—22no—
363C3×M16—32no—
364C3×M16—61no—
365C3×M16C22×D312yes—
366C3×M16C23×C312yes—
367C2×C3×C8—22no—
368C2×C3×C8—21no—
369C2×C3×C8—21no—
370C2×C3×C8—61no—
371C3×C22⋊C4—68no—
372C3×C42—32no—
373C3×C42—61no—
374#217—28no—
375#214—24no—
376#213—24no—
377C4×Dic3—21no—
378C4×Dic3C23×C312yes—
379#208—21no—
380#208C23×C312yes—
381C2×C3⋊C8—21no—
382C22×C32—22no—
383C22×C32—22no—
384C22×C32—42no—
385C22×C32—44no—
386C22×C32—42no—
387C22×C32—82no—
388C22×C32—82no—
389C22×C32#12011yescharacteristic
390C22×C32#12011yescharacteristic
391C22×C32C22×D411yescharacteristic
392C2×C3×D3—22no—
393C2×C3×D3—42no—
394C32×C4—22no—
395C32×C4#12011yescharacteristic
396C32×C4#12011yescharacteristic
397C32×C4C22×D411yescharacteristic
398C32×C4C22×D411yescharacteristic
399C3×Dic3—24no—
400C3×Dic3—22no—
401C3×Dic3—42no—
4022−1+4—34no—
4032−1+4—62no—
4042−1+4—62no—
4052−1+4—62no—
406C2×#41—31no—
407C2×#41—61no—
408C2×#41—62no—
409C2×#41—61no—
410C2×#41C2×C3×D311yescharacteristic
411C22×Q8—31no—
412C22×Q8—61no—
413C22×Q8—61no—
414C22×D4C2×C3×D311yescharacteristic
415AGL(1,ℤ/8)—22no—
416AGL(1,ℤ/8)—34no—
417AGL(1,ℤ/8)—62no—
418AGL(1,ℤ/8)C2×C3×D314yescomplemented
419C2×SD16—21no—
420C2×SD16—61no—
421C2×D8—21no—
422C2×D8—61no—
423C2×M16—31no—
424C2×M16C2×C3×D311yescharacteristic
425#124—34no—
426#124—62no—
427C2×C22⋊C4—62no—
428C2×C42—31no—
429#104—34no—
430#104—34no—
431#101—34no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—21no—
437C23×C3—41no—
438C23×C3—42no—
439C23×C3—42no—
440C23×C3—42no—
441C23×C3—44no—
442C23×C3—44no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—61no—
448C23×C3—84no—
449C23×C3D3×D411yescharacteristic
450C23×C3C2×C3×D411yescharacteristic
451C22×D3—21no—
452C3×Q8—21no—
453C3×Q8—21no—
454C3×Q8—22no—
455C3×Q8—32no—
456C3×Q8—41no—
457C3×Q8—68no—
458C3×Q8—62no—
459C3×Q8—62no—
460C3×Q8—61no—
461C3×Q8—62no—
462C3×Q8—62no—
463C3×Q8C2×#6712yes—
464C3×Q8C2×C3×D412yes—
465C3×D4—22no—
466C3×D4—22no—
467C3×D4—22no—
468C3×D4—22no—
469C3×D4—24no—
470C3×D4—21no—
471C3×D4—21no—
472C3×D4—22no—
473C3×D4—22no—
474C3×D4—22no—
475C3×D4—22no—
476C3×D4—22no—
477C3×D4—32no—
478C3×D4—42no—
479C3×D4—41no—
480C3×D4—42no—
481C3×D4—42no—
482C3×D4—42no—
483C3×D4—42no—
484C3×D4—41no—
485C3×D4—41no—
486C3×D4—41no—
487C3×D4—41no—
488C3×D4—68no—
489C3×D4—62no—
490C3×D4—62no—
491C3×D4—61no—
492C3×D4C2×#6712yes—
493C3×D4C2×C3×D412yes—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—34no—
507C2×C3×C4—42no—
508C2×C3×C4—42no—
509C2×C3×C4—41no—
510C2×C3×C4—68no—
511C2×C3×C4—68no—
512C2×C3×C4—62no—
513C2×C3×C4—62no—
514C2×C3×C4—61no—
515C2×C3×C4—62no—
516C2×C3×C4—62no—
517C2×C3×C4—62no—
518C2×C3×C4—122no—
519C2×C3×C4D3×D411yescharacteristic
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4C2×#6711yescharacteristic
523C2×C3×C4C2×#6711yescharacteristic
524C2×C3×C4C2×C3×D411yescharacteristic
525C2×C3×C4C2×C3×D411yescharacteristic
526C2×C3×C4C2×C3×D411yescharacteristic
527C2×C3×C4C2×C3×D411yescharacteristic
528C2×C3×C4C2×C3×D411yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C24×C311yescharacteristic
531#67—28no—
532#67—22no—
533#67—22no—
534C2×Dic3—28no—
535C2×Dic3—22no—
536C2×Dic3—21no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—42no—
540C2×Dic3C2×C3×D414yes—
541D12—21no—
542D12C2×C3×D412yes—
543C4×D3—28no—
544C4×D3—22no—
545C4×D3—22no—
546Dic6—28no—
547Dic6—22no—
548Dic6—21no—
549Dic6—22no—
550Dic6—22no—
551Dic6—22no—
552Dic6C2×C3×D412yes—
553C3×C8—24no—
554C3×C8—22no—
555C3×C8—22no—
556C3×C8—62no—
557C3⋊C8—22no—
558C2×C32—21no—
559C2×C32—21no—
560C2×C32—42no—
561C2×C32—82no—
562C2×C32#45412yescomplemented
563C2×C32C2×#12011yescharacteristic
564C3×D3—42no—
565C24—21no—
566#41—21no—
567#41—21no—
568#41—32no—
569#41—32no—
570#41—64no—
571#41—64no—
572#41—68no—
573#41—68no—
574#41—64no—
575#41—64no—
576#41—61no—
577#41—61no—
578#41C3×#6712yes—
579#41C22×C3×D312yes—
580C2×Q8—32no—
581C2×Q8—32no—
582C2×Q8—31no—
583C2×Q8—64no—
584C2×Q8—62no—
585C2×Q8—64no—
586C2×Q8—64no—
587C2×Q8—64no—
588C2×Q8—61no—
589C2×Q8—61no—
590C2×Q8—61no—
591C2×Q8—61no—
592C2×Q8C3×#6711yescharacteristic
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—31no—
600C2×D4—62no—
601C2×D4—61no—
602C2×D4C3×#6711yescharacteristic
603C2×D4C22×C3×D312yes—
604C22×C4—21no—
605C22×C4—32no—
606C22×C4—62no—
607C22×C4—62no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4C22×C3×D311yescharacteristic
611SD16—24no—
612SD16—64no—
613D8—24no—
614D8—64no—
615M16—21no—
616M16—32no—
617M16—61no—
618M16C22×C3×D312yes—
619C2×C8—21no—
620C2×C8—61no—
621C22⋊C4—68no—
622C42—32no—
623C42—61no—
624C22×C3—22no—
625C22×C3—22no—
626C22×C3—22no—
627C22×C3—22no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—42no—
632C22×C3—42no—
633C22×C3—44no—
634C22×C3—44no—
635C22×C3—44no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—62no—
641C22×C3—82no—
642C22×C3—84no—
643C22×C3—82no—
644C22×C3—82no—
645C22×C3—84no—
646C22×C3—84no—
647C22×C3—82no—
648C22×C3—82no—
649C22×C3—122no—
650C22×C3#93711yescharacteristic
651C22×C3#93711yescharacteristic
652C22×C3C3×#12011yescharacteristic
653C22×C3C3×#12011yescharacteristic
654C22×C3C2×D3×D411yescharacteristic
655C22×C3C22×C3×D411yescharacteristic
656C2×D3—22no—
657C2×D3—42no—
658C3×C4—22no—
659C3×C4—22no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—42no—
665C3×C4—64no—
666C3×C4—62no—
667C3×C4—122no—
668C3×C4#93711yescharacteristic
669C3×C4#93711yescharacteristic
670C3×C4C3×#12011yescharacteristic
671C3×C4C3×#12011yescharacteristic
672C3×C4C2×D3×D411yescharacteristic
673C3×C4C22×#6711yescharacteristic
674C3×C4C22×C3×D411yescharacteristic
675C3×C4C22×C3×D411yescharacteristic
676Dic3—24no—
677Dic3—22no—
678Dic3—42no—
679C32C2×#45411yescharacteristic, complemented, Sylow
680C23—21no—
681C23—22no—
682C23—44no—
683C23—41no—
684C23—41no—
685C23—61no—
686C23C3×D3×D411yescharacteristic
687Q8—21no—
688Q8—32no—
689Q8—68no—
690Q8—62no—
691Q8—62no—
692Q8—61no—
693Q8—62no—
694Q8—62no—
695Q8C2×C3×#6712yes—
696D4—22no—
697D4—22no—
698D4—21no—
699D4—22no—
700D4—22no—
701D4—32no—
702D4—41no—
703D4—41no—
704D4—68no—
705D4—62no—
706D4—62no—
707D4—61no—
708D4C2×C3×#6712yes—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—34no—
713C2×C4—68no—
714C2×C4—68no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—61no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—122no—
722C2×C4C3×D3×D411yescharacteristic
723C2×C4C3×D3×D411yescharacteristic
724C2×C4C3×D3×D411yescharacteristic
725C2×C4C2×C3×#6711yescharacteristic
726C2×C4C2×C3×#6711yescharacteristic
727C2×C4C23×C3×D311yescharacteristic
728C8—22no—
729C8—62no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—22no—
735C2×C3—21no—
736C2×C3—41no—
737C2×C3—41no—
738C2×C3—42no—
739C2×C3—42no—
740C2×C3—82no—
741C2×C3—84no—
742C2×C3—82no—
743C2×C3—82no—
744C2×C3—122no—
745C2×C3#520112yesdirect product factor
746C2×C3C3×#45412yescomplemented
747C2×C3C2×#93711yescharacteristic
748C2×C3C2×C3×#12011yescharacteristic
749D3—42no—
750C22—22no—
751C22—22no—
752C22—44no—
753C22—42no—
754C22—42no—
755C22—62no—
756C22—82no—
757C22—82no—
758C22—122no—
759C22C3×#93711yescharacteristic
760C22C3×#93711yescharacteristic
761C22C2×C3×D3×D411yescharacteristic
762C4—22no—
763C4—64no—
764C4—62no—
765C4—122no—
766C4C3×#93711yescharacteristic
767C4C3×#93711yescharacteristic
768C4C2×C3×D3×D411yescharacteristic
769C4C22×C3×#6711yescharacteristic
770C3—21no—
771C3C2×#520111yescharacteristic, direct product factor
772C3C2×C3×#45411yescharacteristic, complemented
773C2—21no—
774C2—21no—
775C2—42no—
776C2—82no—
777C2—122no—
778C2C3×#520112yesdirect product factor
779C2C2×C3×#93711yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×AGL(1,ℤ/8)C2
socleC22×C32#120
hypercenterC2×C3×AGL(1,ℤ/8)D3
hypocenterC3C2×C3×#454
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C2×C32×AGL(1,ℤ/8)C2semidirect
3. C2×C3×#936C2semidirect
4. C2×C3×#932C2semidirect
5. C2×C3×#837C2semidirect
6. C3×#5201C2direct (N × H)
7. C2×C3×#825C2semidirect
8. C2×C3×#824C2semidirect
10. C2×#5201C3direct (N × H)
16. C3×#1010C22semidirect
25. C32×AGL(1,ℤ/8)C22semidirect
31. C3×#936C22semidirect
34. C3×#932C22semidirect
38. C3×#837C22semidirect
39. C3×#825C22semidirect
40. C3×#824C22semidirect
42. C2×#1010C2×C3semidirect
45. C2×C3×AGL(1,ℤ/8)D3semidirect
46. C2×C3×AGL(1,ℤ/8)C2×C3semidirect
48. C2×#936C2×C3semidirect
49. C2×#932C2×C3semidirect
54. C2×#837C2×C3semidirect
55. #5201C2×C3direct (N × H)
56. C2×#825C2×C3semidirect
57. C2×#824C2×C3semidirect
138. #1010C22×C3semidirect
152. C3×AGL(1,ℤ/8)C2×D3semidirect
153. C3×AGL(1,ℤ/8)C22×C3semidirect
172. #936C22×C3semidirect
175. #932C22×C3semidirect
182. #837C22×C3semidirect
183. #825C22×C3semidirect
184. #824C22×C3semidirect
237. C2×AGL(1,ℤ/8)C3×D3semidirect
418. AGL(1,ℤ/8)C2×C3×D3semidirect
562. C2×C32#454semidirect
679. C32C2×#454semidirect
745. C2×C3#5201direct (N × H)
746. C2×C3C3×#454semidirect
771. C3C2×#5201direct (N × H)
772. C3C2×C3×#454semidirect
778. C2C3×#5201direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×C32×AGL(1,ℤ/8)2
C2×C3×#9362
C2×C3×#9322
C2×C3×#8372
C3×#52012
C2×C3×#8252
C2×C3×#8242
C2×C3×#4543
C2×#52013