Finite Group Databasebeta

← C2×C3×#4827 #11864860

Subgroups — C2×C3×#4827 #11864860

Order 1152.

1541 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3C2×C3×#908C211yesmaximal, characteristic, complemented
4C2×C3×#875C211yesmaximal, characteristic, complemented
5C2×C32×#104C211yesmaximal, characteristic, complemented
6C2×C3×#824C211yesmaximal, characteristic, complemented
7C2×C3×#805C211yesmaximal, characteristic, complemented
8C3×#4827C218yesmaximal, direct product factor
9C2×C3×#454—31nomaximal
10C2×#4827C311yesmaximal, characteristic, direct product factor
11C2×C32×#41C2211yescharacteristic
12C3×#1010—22no—
13C3×#1010—22no—
14C3×#1010—22no—
15C3×#1010C2214yescomplemented
16C2×C3×D3×Q8—21no—
17C2×C3×#237—21no—
18C2×C3×#237—22no—
19C2×C3×#235—21no—
20C2×C3×#235C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×Dic6—21no—
23C22×C3×Dic6C2211yescharacteristic
24C2×C32×M16C2211yescharacteristic
25C2×C32×C42C2211yescharacteristic
26C3×#949—22no—
27C3×#949C2214yescomplemented
28C2×C3×#215—21no—
29C2×C3×#213—21no—
30C2×C3×(C2×D3)⋊C4—22no—
31C2×C3×#208C2211yescharacteristic
32C3×#908—22no—
33C3×#908C2214yescomplemented
34C2×C3×D24—21no—
35C2×C3×#204—21no—
36C3×#875—22no—
37C3×#875C2214yescomplemented
38C32×#104C2214yescomplemented
39C3×#824C2214yescomplemented
40C3×#805C2214yescomplemented
41C2×C3×2−1+4—31no—
42C2×#1010C2×C311yescharacteristic, complemented
43C2×C3×AGL(1,ℤ/8)—31no—
44C2×C3×AGL(1,ℤ/8)—31no—
45C2×C3×#124—31no—
46C2×#949C2×C311yescharacteristic, complemented
47C2×#908C2×C311yescharacteristic, complemented
48C2×#875C2×C311yescharacteristic, complemented
49C3×#454—38no—
50C2×C3×#104—21no—
51C2×C3×#104—31no—
52C2×C3×#104D311yescharacteristic, complemented
53C2×C3×#104C2×C311yescharacteristic, complemented
54C2×C3×#101—31no—
55C2×#824C2×C311yescharacteristic, complemented
56C2×#805C2×C311yescharacteristic, complemented
57#4827C2×C318yesdirect product factor
58C23×C3×D3—21no—
59C32×#41—21no—
60C32×#41—21no—
61C32×#41D412yes—
62C32×#41C2312yes—
63C2×C32×Q8D411yescharacteristic
64C2×C32×D4—21no—
65C2×C32×D4D411yescharacteristic
66C22×C32×C4—21no—
67C22×C32×C4—21no—
68C22×C32×C4C2311yescharacteristic
69C2×C3×#67—22no—
70C2×C3×#67—21no—
71C22×C3×Dic3—22no—
72C22×C3×Dic3D412yes—
73C3×D3×Q8—24no—
74C3×D3×Q8—24no—
75C3×#237—28no—
76C3×#237—24no—
77C3×#237—24no—
78C3×#237—28no—
79C3×#235—24no—
80C3×#235—21no—
81C3×#235—21no—
82C3×#235—24no—
83C3×#235D412yes—
84C3×#235C2312yes—
85C2×C3×D12—21no—
86C2×C3×D12—21no—
87C2×C3×D12—21no—
88C2×C3×D12—21no—
89C2×C3×D12—21no—
90C2×C3×D12D411yescharacteristic
91C2×C3×D12C2312yes—
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×M16—21no—
105C32×M16C2312yes—
106C2×C32×C8—21no—
107C32×C42—21no—
108C32×C42C2312yes—
109C3×#215—24no—
110C3×#213—24no—
111C3×(C2×D3)⋊C4—28no—
112C3×#208—21no—
113C3×#208C2312yes—
114C2×C3×C3⋊C8—21no—
115C3×D24—24no—
116C3×#204—24no—
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—31no—
133#1010—22no—
134#1010—22no—
135#1010—22no—
136#1010C22×C314yescomplemented
137C2×D3×Q8—21no—
138C2×#237—21no—
139C2×#237—22no—
140C2×#235—21no—
141C2×#235C22×C311yescharacteristic
142C22×D12C22×C311yescharacteristic
143C22×Dic6—21no—
144C22×Dic6C22×C311yescharacteristic
145C3×AGL(1,ℤ/8)—34no—
146C3×AGL(1,ℤ/8)—34no—
147C3×AGL(1,ℤ/8)—62no—
148C3×AGL(1,ℤ/8)—62no—
149C2×C3×SD16—61no—
150C2×C3×SD16—61no—
151C2×C3×D8—61no—
152C2×C3×D8—61no—
153C2×C3×M16—21no—
154C2×C3×M16—31no—
155C2×C3×M16C2×D311yescharacteristic
156C2×C3×M16C22×C311yescharacteristic
157C3×#124—34no—
158C3×#124—62no—
159C2×C3×C22⋊C4—62no—
160C2×C3×C42—21no—
161C2×C3×C42C2×D311yescharacteristic
162C2×C3×C42C22×C311yescharacteristic
163#949—22no—
164#949C22×C314yescomplemented
165C2×#215—21no—
166C2×#213—21no—
167C2×(C2×D3)⋊C4—22no—
168C2×#208C22×C311yescharacteristic
169#908—22no—
170#908C22×C314yescomplemented
171C2×D24—21no—
172C2×#204—21no—
173#875—22no—
174#875C22×C314yescomplemented
175C3×#104—24no—
176C3×#104—34no—
177C3×#104C2×D314yescomplemented
178C3×#104C22×C314yescomplemented
179C3×#101—34no—
180#824C22×C314yescomplemented
181#805C22×C314yescomplemented
182C23×C32—21no—
183C23×C32C2×D411yescharacteristic
184C22×C3×D3—21no—
185C22×C3×D3—22no—
186C22×C3×D3—44no—
187C22×C3×D3—41no—
188C22×C3×D3—41no—
189C32×Q8—21no—
190C32×Q8C2×D412yes—
191C32×D4—22no—
192C32×D4—22no—
193C32×D4—21no—
194C32×D4C2×D412yes—
195C2×C32×C4—21no—
196C2×C32×C4—22no—
197C2×C32×C4—22no—
198C2×C32×C4—22no—
199C2×C32×C4—42no—
200C2×C32×C4C2×D411yescharacteristic
201C2×C32×C4C2×D411yescharacteristic
202C2×C32×C4C2×D411yescharacteristic
203C2×C32×C4C2×D411yescharacteristic
204C2×C32×C4C2×D411yescharacteristic
205C2×C32×C4C2411yescharacteristic
206C3×#67—28no—
207C3×#67—22no—
208C3×#67—22no—
209C2×C3×Dic3—28no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3C2×D414yes—
214C3×D12—21no—
215C3×D12—22no—
216C3×D12—22no—
217C3×D12—41no—
218C3×D12—41no—
219C3×D12C2×D412yes—
220C3×C4×D3—28no—
221C3×C4×D3—22no—
222C3×C4×D3—22no—
223C3×Dic6—28no—
224C3×Dic6—22no—
225C3×Dic6—21no—
226C3×Dic6—22no—
227C3×Dic6—22no—
228C3×Dic6—22no—
229C3×Dic6C2×D412yes—
230C32×C8—22no—
231C3×C3⋊C8—22no—
232C2×2−1+4—31no—
233C2×AGL(1,ℤ/8)—31no—
234C2×AGL(1,ℤ/8)—31no—
235C2×#124—31no—
236#454—38no—
237C2×#104—31no—
238C2×#104C3×D311yescharacteristic, complemented
239C2×#101—31no—
240C24×C3—61no—
241C23×D3—21no—
242C3×#41—21no—
243C3×#41—21no—
244C3×#41—21no—
245C3×#41—21no—
246C3×#41—22no—
247C3×#41—22no—
248C3×#41—32no—
249C3×#41—32no—
250C3×#41—41no—
251C3×#41—41no—
252C3×#41—64no—
253C3×#41—64no—
254C3×#41—68no—
255C3×#41—68no—
256C3×#41—64no—
257C3×#41—64no—
258C3×#41—61no—
259C3×#41—61no—
260C3×#41D1212yes—
261C3×#41C3×D412yes—
262C3×#41C22×D312yes—
263C3×#41C23×C312yes—
264C2×C3×Q8—21no—
265C2×C3×Q8—32no—
266C2×C3×Q8—32no—
267C2×C3×Q8—31no—
268C2×C3×Q8—64no—
269C2×C3×Q8—62no—
270C2×C3×Q8—64no—
271C2×C3×Q8—64no—
272C2×C3×Q8—64no—
273C2×C3×Q8—61no—
274C2×C3×Q8—61no—
275C2×C3×Q8—61no—
276C2×C3×Q8—61no—
277C2×C3×Q8D1211yescharacteristic
278C2×C3×Q8C3×D411yescharacteristic
279C2×C3×D4—21no—
280C2×C3×D4—21no—
281C2×C3×D4—21no—
282C2×C3×D4—31no—
283C2×C3×D4—32no—
284C2×C3×D4—41no—
285C2×C3×D4—62no—
286C2×C3×D4—61no—
287C2×C3×D4—61no—
288C2×C3×D4—61no—
289C2×C3×D4—61no—
290C2×C3×D4—61no—
291C2×C3×D4—61no—
292C2×C3×D4D1211yescharacteristic
293C2×C3×D4C3×D411yescharacteristic
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—32no—
300C22×C3×C4—41no—
301C22×C3×C4—41no—
302C22×C3×C4—62no—
303C22×C3×C4—62no—
304C22×C3×C4—61no—
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C23×C311yescharacteristic
307C2×#67—22no—
308C2×#67—21no—
309C22×Dic3—22no—
310C22×Dic3C3×D412yes—
311D3×Q8—24no—
312D3×Q8—24no—
313#237—28no—
314#237—24no—
315#237—24no—
316#237—28no—
317#235—24no—
318#235—21no—
319#235—21no—
320#235—24no—
321#235C3×D412yes—
322#235C23×C312yes—
323C2×D12—21no—
324C2×D12—21no—
325C2×D12—21no—
326C2×D12—21no—
327C2×D12—21no—
328C2×D12C3×D411yescharacteristic
329C2×D12C23×C312yes—
330C2×C4×D3—22no—
331C2×C4×D3—21no—
332C2×Dic6—22no—
333C2×Dic6—24no—
334C2×Dic6—21no—
335C2×Dic6—21no—
336C2×Dic6—21no—
337C2×Dic6—21no—
338C2×Dic6—24no—
339C2×Dic6C3×D412yes—
340C2×Dic6C3×D411yescharacteristic
341C2×Dic6C23×C312yes—
342C3×SD16—64no—
343C3×SD16—64no—
344C3×D8—64no—
345C3×D8—64no—
346C3×M16—21no—
347C3×M16—21no—
348C3×M16—22no—
349C3×M16—32no—
350C3×M16—41no—
351C3×M16—61no—
352C3×M16C22×D312yes—
353C3×M16C23×C312yes—
354C2×C3×C8—21no—
355C2×C3×C8—21no—
356C2×C3×C8—41no—
357C2×C3×C8—61no—
358C3×C22⋊C4—68no—
359C3×C42—21no—
360C3×C42—21no—
361C3×C42—22no—
362C3×C42—41no—
363C3×C42C22×D312yes—
364C3×C42C23×C312yes—
365#215—24no—
366#213—24no—
367(C2×D3)⋊C4—28no—
368#208—21no—
369#208C23×C312yes—
370C2×C3⋊C8—21no—
371D24—24no—
372#204—24no—
373C22×C32—22no—
374C22×C32—22no—
375C22×C32—42no—
376C22×C32#12011yescharacteristic
377C22×C32#12011yescharacteristic
378C22×C32C22×D411yescharacteristic
379C2×C3×D3—22no—
380C2×C3×D3—42no—
381C2×C3×D3—44no—
382C2×C3×D3—42no—
383C2×C3×D3—82no—
384C2×C3×D3—82no—
385C32×C4—22no—
386C32×C4—42no—
387C32×C4#12011yescharacteristic
388C32×C4#12011yescharacteristic
389C32×C4C22×D411yescharacteristic
390C32×C4C22×D411yescharacteristic
391C3×Dic3—24no—
392C3×Dic3—22no—
3932−1+4—34no—
3942−1+4—62no—
3952−1+4—62no—
3962−1+4—62no—
397C2×#41—31no—
398C2×#41—61no—
399C2×#41—62no—
400C2×#41—61no—
401C2×#41C2×C3×D311yescharacteristic
402C22×Q8—31no—
403C22×Q8—61no—
404C22×Q8—61no—
405C22×D4—31no—
406AGL(1,ℤ/8)—34no—
407AGL(1,ℤ/8)—34no—
408AGL(1,ℤ/8)—62no—
409AGL(1,ℤ/8)—62no—
410C2×SD16—61no—
411C2×SD16—61no—
412C2×D8—61no—
413C2×D8—61no—
414C2×M16—31no—
415C2×M16C2×C3×D311yescharacteristic
416#124—34no—
417#124—62no—
418C2×C22⋊C4—62no—
419C2×C42C2×C3×D311yescharacteristic
420#104—34no—
421#104C2×C3×D314yescomplemented
422#101—34no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—41no—
427C23×C3—61no—
428C23×C3—62no—
429C23×C3—124no—
430C23×C3—121no—
431C23×C3—121no—
432C23×C3D3×D411yescharacteristic
433C23×C3C2×C3×D411yescharacteristic
434C22×D3—21no—
435C22×D3—22no—
436C22×D3—44no—
437C22×D3—41no—
438C22×D3—41no—
439C3×Q8—21no—
440C3×Q8—21no—
441C3×Q8—22no—
442C3×Q8—32no—
443C3×Q8—41no—
444C3×Q8—68no—
445C3×Q8—62no—
446C3×Q8—62no—
447C3×Q8—61no—
448C3×Q8—62no—
449C3×Q8—62no—
450C3×Q8C2×D1212yes—
451C3×Q8C2×C3×D412yes—
452C3×D4—22no—
453C3×D4—22no—
454C3×D4—22no—
455C3×D4—22no—
456C3×D4—21no—
457C3×D4—21no—
458C3×D4—22no—
459C3×D4—32no—
460C3×D4—41no—
461C3×D4—42no—
462C3×D4—42no—
463C3×D4—68no—
464C3×D4—62no—
465C3×D4—62no—
466C3×D4—61no—
467C3×D4—62no—
468C3×D4—62no—
469C3×D4—121no—
470C3×D4—121no—
471C3×D4C2×D1212yes—
472C3×D4C2×C3×D412yes—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—34no—
488C2×C3×C4—42no—
489C2×C3×C4—42no—
490C2×C3×C4—42no—
491C2×C3×C4—41no—
492C2×C3×C4—42no—
493C2×C3×C4—42no—
494C2×C3×C4—44no—
495C2×C3×C4—68no—
496C2×C3×C4—68no—
497C2×C3×C4—62no—
498C2×C3×C4—62no—
499C2×C3×C4—61no—
500C2×C3×C4—62no—
501C2×C3×C4—62no—
502C2×C3×C4C2×D1211yescharacteristic
503C2×C3×C4C2×D1211yescharacteristic
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4D3×D411yescharacteristic
506C2×C3×C4D3×D411yescharacteristic
507C2×C3×C4C2×C3×D411yescharacteristic
508C2×C3×C4C2×C3×D411yescharacteristic
509C2×C3×C4C2×C3×D411yescharacteristic
510C2×C3×C4C2×C3×D411yescharacteristic
511C2×C3×C4C2×C3×D411yescharacteristic
512C2×C3×C4C23×D311yescharacteristic
513C2×C3×C4C24×C311yescharacteristic
514#67—28no—
515#67—22no—
516#67—22no—
517C2×Dic3—28no—
518C2×Dic3—22no—
519C2×Dic3—21no—
520C2×Dic3—22no—
521C2×Dic3C2×C3×D414yes—
522D12—21no—
523D12—22no—
524D12—22no—
525D12—41no—
526D12—41no—
527D12C2×C3×D412yes—
528C4×D3—28no—
529C4×D3—22no—
530C4×D3—22no—
531Dic6—28no—
532Dic6—22no—
533Dic6—21no—
534Dic6—22no—
535Dic6—22no—
536Dic6—22no—
537Dic6C2×C3×D412yes—
538C3×C8—22no—
539C3×C8—22no—
540C3×C8—42no—
541C3×C8—62no—
542C3⋊C8—22no—
543C2×C32—21no—
544C2×C32—21no—
545C2×C32—42no—
546C2×C32#45412yescomplemented
547C2×C32C2×#12011yescharacteristic
548C3×D3—42no—
549C3×D3—82no—
550C24—61no—
551#41—21no—
552#41—21no—
553#41—32no—
554#41—32no—
555#41—64no—
556#41—64no—
557#41—68no—
558#41—68no—
559#41—64no—
560#41—64no—
561#41—61no—
562#41—61no—
563#41C3×D1212yes—
564#41C22×C3×D312yes—
565C2×Q8—32no—
566C2×Q8—32no—
567C2×Q8—31no—
568C2×Q8—64no—
569C2×Q8—62no—
570C2×Q8—64no—
571C2×Q8—64no—
572C2×Q8—64no—
573C2×Q8—61no—
574C2×Q8—61no—
575C2×Q8—61no—
576C2×Q8—61no—
577C2×Q8C3×D1211yescharacteristic
578C2×D4—21no—
579C2×D4—32no—
580C2×D4—31no—
581C2×D4—62no—
582C2×D4—61no—
583C2×D4—61no—
584C2×D4—61no—
585C2×D4—61no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4C3×D1211yescharacteristic
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—32no—
592C22×C4—62no—
593C22×C4—62no—
594C22×C4—61no—
595C22×C4C22×C3×D311yescharacteristic
596SD16—64no—
597SD16—64no—
598D8—64no—
599D8—64no—
600M16—21no—
601M16—32no—
602M16—61no—
603M16C22×C3×D312yes—
604C2×C8—21no—
605C2×C8—61no—
606C22⋊C4—68no—
607C42—21no—
608C42C22×C3×D312yes—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—62no—
621C22×C3—82no—
622C22×C3—124no—
623C22×C3—122no—
624C22×C3—122no—
625C22×C3—242no—
626C22×C3—242no—
627C22×C3#88211yescharacteristic
628C22×C3#88211yescharacteristic
629C22×C3C3×#12011yescharacteristic
630C22×C3C3×#12011yescharacteristic
631C22×C3C2×D3×D411yescharacteristic
632C22×C3C22×C3×D411yescharacteristic
633C2×D3—22no—
634C2×D3—42no—
635C2×D3—44no—
636C2×D3—42no—
637C2×D3—82no—
638C2×D3—82no—
639C3×C4—22no—
640C3×C4—22no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—42no—
646C3×C4—42no—
647C3×C4—42no—
648C3×C4—44no—
649C3×C4—64no—
650C3×C4—62no—
651C3×C4#88211yescharacteristic
652C3×C4#88211yescharacteristic
653C3×C4C3×#12011yescharacteristic
654C3×C4C3×#12011yescharacteristic
655C3×C4C22×D1211yescharacteristic
656C3×C4C2×D3×D411yescharacteristic
657C3×C4C22×C3×D411yescharacteristic
658C3×C4C22×C3×D411yescharacteristic
659Dic3—24no—
660Dic3—22no—
661C32C2×#45411yescharacteristic, complemented, Sylow
662C23—21no—
663C23—61no—
664C23—62no—
665C23—124no—
666C23—121no—
667C23—121no—
668C23C3×D3×D411yescharacteristic
669Q8—21no—
670Q8—32no—
671Q8—68no—
672Q8—62no—
673Q8—62no—
674Q8—61no—
675Q8—62no—
676Q8—62no—
677Q8C2×C3×D1212yes—
678D4—22no—
679D4—22no—
680D4—21no—
681D4—32no—
682D4—68no—
683D4—62no—
684D4—62no—
685D4—61no—
686D4—62no—
687D4—62no—
688D4—121no—
689D4—121no—
690D4C2×C3×D1212yes—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—34no—
696C2×C4—42no—
697C2×C4—68no—
698C2×C4—68no—
699C2×C4—62no—
700C2×C4—62no—
701C2×C4—61no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4C2×C3×D1211yescharacteristic
705C2×C4C2×C3×D1211yescharacteristic
706C2×C4C3×D3×D411yescharacteristic
707C2×C4C3×D3×D411yescharacteristic
708C2×C4C3×D3×D411yescharacteristic
709C2×C4C23×C3×D311yescharacteristic
710C8—22no—
711C8—62no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—22no—
718C2×C3—41no—
719C2×C3—41no—
720C2×C3—42no—
721C2×C3—42no—
722C2×C3—82no—
723C2×C3—122no—
724C2×C3—242no—
725C2×C3#482712yesdirect product factor
726C2×C3C3×#45412yescomplemented
727C2×C3C2×#88211yescharacteristic
728C2×C3C2×C3×#12011yescharacteristic
729D3—42no—
730D3—82no—
731C22—22no—
732C22—22no—
733C22—42no—
734C22—62no—
735C22—124no—
736C22—122no—
737C22—122no—
738C22—242no—
739C22—242no—
740C22C3×#88211yescharacteristic
741C22C3×#88211yescharacteristic
742C22C2×C3×D3×D411yescharacteristic
743C4—22no—
744C4—42no—
745C4—64no—
746C4—62no—
747C4C3×#88211yescharacteristic
748C4C3×#88211yescharacteristic
749C4C22×C3×D1211yescharacteristic
750C4C2×C3×D3×D411yescharacteristic
751C3—21no—
752C3C2×#482711yescharacteristic, direct product factor
753C3C2×C3×#45411yescharacteristic, complemented
754C2—21no—
755C2—21no—
756C2—42no—
757C2—122no—
758C2—242no—
759C2C3×#482712yesdirect product factor
760C2C2×C3×#88211yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#104C2
socleC22×C32#120
hypercenterC2×C3×#104D3
hypocenterC3C2×C3×#454
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#104

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C2×C3×#949C2semidirect
3. C2×C3×#908C2semidirect
4. C2×C3×#875C2semidirect
5. C2×C32×#104C2semidirect
6. C2×C3×#824C2semidirect
7. C2×C3×#805C2semidirect
8. C3×#4827C2direct (N × H)
10. C2×#4827C3direct (N × H)
15. C3×#1010C22semidirect
27. C3×#949C22semidirect
33. C3×#908C22semidirect
37. C3×#875C22semidirect
38. C32×#104C22semidirect
39. C3×#824C22semidirect
40. C3×#805C22semidirect
42. C2×#1010C2×C3semidirect
46. C2×#949C2×C3semidirect
47. C2×#908C2×C3semidirect
48. C2×#875C2×C3semidirect
52. C2×C3×#104D3semidirect
53. C2×C3×#104C2×C3semidirect
55. C2×#824C2×C3semidirect
56. C2×#805C2×C3semidirect
57. #4827C2×C3direct (N × H)
136. #1010C22×C3semidirect
164. #949C22×C3semidirect
170. #908C22×C3semidirect
174. #875C22×C3semidirect
177. C3×#104C2×D3semidirect
178. C3×#104C22×C3semidirect
180. #824C22×C3semidirect
181. #805C22×C3semidirect
238. C2×#104C3×D3semidirect
421. #104C2×C3×D3semidirect
546. C2×C32#454semidirect
661. C32C2×#454semidirect
725. C2×C3#4827direct (N × H)
726. C2×C3C3×#454semidirect
752. C3C2×#4827direct (N × H)
753. C3C2×C3×#454semidirect
759. C2C3×#4827direct (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×C3×#9492
C2×C3×#9082
C2×C3×#8752
C2×C32×#1042
C2×C3×#8242
C2×C3×#8052
C3×#48272
C2×C3×#4543
C2×#48273