Finite Group Databasebeta

← C2×C3×#4826 #11864906

Subgroups — C2×C3×#4826 #11864906

Order 1152.

1501 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic, complemented
3C2×C3×#909C211yesmaximal, characteristic, complemented
4C2×C3×#869C211yesmaximal, characteristic, complemented
5C2×C32×#104C211yesmaximal, characteristic, complemented
6C2×C3×#824C211yesmaximal, characteristic, complemented
7C2×C3×#805C211yesmaximal, characteristic, complemented
8C3×#4826C218yesmaximal, direct product factor
9C2×C3×#456—31nomaximal
10C2×#4826C311yesmaximal, characteristic, direct product factor
11C2×C32×#41C2211yescharacteristic
12C3×#1010—22no—
13C3×#1010—22no—
14C3×#1010—22no—
15C3×#1010C2214yes—
16C2×C3×D3×Q8—21no—
17C2×C3×#237—21no—
18C2×C3×#237—22no—
19C2×C3×#235—21no—
20C2×C3×#235C2211yescharacteristic
21C22×C3×Dic6—21no—
22C22×C3×Dic6C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic
24C2×C32×M16C2211yescharacteristic
25C2×C32×C42C2211yescharacteristic
26C3×#951—22no—
27C3×#951C2214yescomplemented
28C2×C3×#216—21no—
29C2×C3×#214—21no—
30C2×C3×C4⋊Dic3—22no—
31C2×C3×#208C2211yescharacteristic
32C3×#909—22no—
33C3×#909C2214yescomplemented
34C2×C3×Dic12—21no—
35C2×C3×#204—21no—
36C3×#869—22no—
37C3×#869C2214yescomplemented
38C32×#104C2214yescomplemented
39C3×#824C2214yescomplemented
40C3×#805C2214yescomplemented
41C2×C3×2−1+4—31no—
42C2×#1010C2×C311yescharacteristic
43C2×C3×#137—31no—
44C2×C3×#137—31no—
45C2×C3×C4⋊Q8—31no—
46C2×#951C2×C311yescharacteristic, complemented
47C2×#909C2×C311yescharacteristic, complemented
48C2×#869C2×C311yescharacteristic, complemented
49C3×#456—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#4826C2×C318yesdirect product factor
58C32×#41—21no—
59C32×#41—21no—
60C32×#41D412yes—
61C32×#41C2312yes—
62C2×C32×Q8D411yescharacteristic
63C2×C32×D4—21no—
64C2×C32×D4D411yescharacteristic
65C22×C32×C4—21no—
66C22×C32×C4—21no—
67C22×C32×C4C2311yescharacteristic
68C2×C3×#67—22no—
69C2×C3×#67—21no—
70C22×C3×Dic3—22no—
71C22×C3×Dic3—21no—
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×D12D411yescharacteristic
86C2×C3×C4×D3—22no—
87C2×C3×C4×D3—21no—
88C2×C3×Dic6—22no—
89C2×C3×Dic6—24no—
90C2×C3×Dic6—21no—
91C2×C3×Dic6—21no—
92C2×C3×Dic6—21no—
93C2×C3×Dic6—21no—
94C2×C3×Dic6—24no—
95C2×C3×Dic6—21no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6—21no—
99C2×C3×Dic6—21no—
100C2×C3×Dic6D412yes—
101C2×C3×Dic6D411yescharacteristic
102C2×C3×Dic6C2312yes—
103C2×C3×Dic6C2312yes—
104C32×M16—21no—
105C32×M16C2312yes—
106C2×C32×C8—21no—
107C32×C42—21no—
108C32×C42C2312yes—
109C3×#216—24no—
110C3×#214—24no—
111C3×C4⋊Dic3—28no—
112C3×#208—21no—
113C3×#208C2312yes—
114C2×C3×C3⋊C8—21no—
115C3×Dic12—24no—
116C3×#204—24no—
117C2×#456—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—31no—
131C22×C3×Q8—61no—
132C22×C3×Q8—61no—
133#1010—22no—
134#1010—22no—
135#1010—22no—
136#1010C22×C314yes—
137C2×D3×Q8—21no—
138C2×#237—21no—
139C2×#237—22no—
140C2×#235—21no—
141C2×#235C22×C311yescharacteristic
142C22×Dic6—21no—
143C22×Dic6C22×C311yescharacteristic
144C22×Dic6C22×C311yescharacteristic
145C3×#137—34no—
146C3×#137—34no—
147C3×#137—62no—
148C3×#137—62no—
149C2×C3×Q16—61no—
150C2×C3×Q16—61no—
151C2×C3×SD16—61no—
152C2×C3×SD16—61no—
153C2×C3×M16—21no—
154C2×C3×M16—31no—
155C2×C3×M16C2×D311yescharacteristic
156C2×C3×M16C22×C311yescharacteristic
157C3×C4⋊Q8—34no—
158C3×C4⋊Q8—62no—
159C2×C3×C4⋊C4—62no—
160C2×C3×C42—21no—
161C2×C3×C42C2×D311yescharacteristic
162C2×C3×C42C22×C311yescharacteristic
163#951—22no—
164#951C22×C314yescomplemented
165C2×#216—21no—
166C2×#214—21no—
167C2×C4⋊Dic3—22no—
168C2×#208C22×C311yescharacteristic
169#909—22no—
170#909C22×C314yescomplemented
171C2×Dic12—21no—
172C2×#204—21no—
173#869—22no—
174#869C22×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—
185C32×Q8—21no—
186C32×Q8C2×D412yes—
187C32×D4—22no—
188C32×D4—22no—
189C32×D4—21no—
190C32×D4C2×D412yes—
191C2×C32×C4—24no—
192C2×C32×C4—21no—
193C2×C32×C4—22no—
194C2×C32×C4—22no—
195C2×C32×C4—22no—
196C2×C32×C4C2×D411yescharacteristic
197C2×C32×C4C2×D411yescharacteristic
198C2×C32×C4C2×D411yescharacteristic
199C2×C32×C4C2×D411yescharacteristic
200C2×C32×C4C2×D411yescharacteristic
201C2×C32×C4C2411yescharacteristic
202C3×#67—28no—
203C3×#67—22no—
204C3×#67—22no—
205C2×C3×Dic3—28no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—21no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—41no—
211C2×C3×Dic3—41no—
212C2×C3×Dic3C2×D414yes—
213C3×D12—21no—
214C3×D12C2×D412yes—
215C3×C4×D3—28no—
216C3×C4×D3—22no—
217C3×C4×D3—22no—
218C3×Dic6—28no—
219C3×Dic6—22no—
220C3×Dic6—21no—
221C3×Dic6—22no—
222C3×Dic6—22no—
223C3×Dic6—22no—
224C3×Dic6—22no—
225C3×Dic6—22no—
226C3×Dic6—41no—
227C3×Dic6—41no—
228C3×Dic6C2×D412yes—
229C32×C8—22no—
230C3×C3⋊C8—22no—
231C2×2−1+4—31no—
232C2×#137—31no—
233C2×#137—31no—
234C2×C4⋊Q8—31no—
235#456—38no—
236C2×#104—31no—
237C2×#104C3×D311yescharacteristic, complemented
238C2×#101—31no—
239C3×#41—21no—
240C3×#41—21no—
241C3×#41—21no—
242C3×#41—21no—
243C3×#41—22no—
244C3×#41—22no—
245C3×#41—32no—
246C3×#41—32no—
247C3×#41—41no—
248C3×#41—41no—
249C3×#41—64no—
250C3×#41—64no—
251C3×#41—68no—
252C3×#41—68no—
253C3×#41—64no—
254C3×#41—64no—
255C3×#41—61no—
256C3×#41—61no—
257C3×#41D1212yes—
258C3×#41C3×D412yes—
259C3×#41C22×D312yes—
260C3×#41C23×C312yes—
261C2×C3×Q8—21no—
262C2×C3×Q8—32no—
263C2×C3×Q8—32no—
264C2×C3×Q8—31no—
265C2×C3×Q8—32no—
266C2×C3×Q8—64no—
267C2×C3×Q8—62no—
268C2×C3×Q8—64no—
269C2×C3×Q8—64no—
270C2×C3×Q8—64no—
271C2×C3×Q8—61no—
272C2×C3×Q8—61no—
273C2×C3×Q8—61no—
274C2×C3×Q8—61no—
275C2×C3×Q8—61no—
276C2×C3×Q8—61no—
277C2×C3×Q8—61no—
278C2×C3×Q8—61no—
279C2×C3×Q8—61no—
280C2×C3×Q8D1211yescharacteristic
281C2×C3×Q8C3×D411yescharacteristic
282C2×C3×D4—21no—
283C2×C3×D4—21no—
284C2×C3×D4—21no—
285C2×C3×D4—31no—
286C2×C3×D4—41no—
287C2×C3×D4—62no—
288C2×C3×D4—61no—
289C2×C3×D4D1211yescharacteristic
290C2×C3×D4C3×D411yescharacteristic
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—32no—
297C22×C3×C4—41no—
298C22×C3×C4—41no—
299C22×C3×C4—62no—
300C22×C3×C4—62no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C23×C311yescharacteristic
305C2×#67—22no—
306C2×#67—21no—
307C22×Dic3—22no—
308C22×Dic3—21no—
309C22×Dic3C3×D412yes—
310D3×Q8—24no—
311D3×Q8—24no—
312#237—28no—
313#237—24no—
314#237—24no—
315#237—28no—
316#235—24no—
317#235—21no—
318#235—21no—
319#235—24no—
320#235C3×D412yes—
321#235C23×C312yes—
322C2×D12C3×D411yescharacteristic
323C2×C4×D3—22no—
324C2×C4×D3—21no—
325C2×Dic6—22no—
326C2×Dic6—24no—
327C2×Dic6—21no—
328C2×Dic6—21no—
329C2×Dic6—21no—
330C2×Dic6—21no—
331C2×Dic6—24no—
332C2×Dic6—21no—
333C2×Dic6—21no—
334C2×Dic6—21no—
335C2×Dic6—21no—
336C2×Dic6—21no—
337C2×Dic6C3×D412yes—
338C2×Dic6C3×D411yescharacteristic
339C2×Dic6C23×C312yes—
340C2×Dic6C23×C312yes—
341C3×Q16—64no—
342C3×Q16—64no—
343C3×SD16—64no—
344C3×SD16—64no—
345C3×M16—21no—
346C3×M16—21no—
347C3×M16—22no—
348C3×M16—32no—
349C3×M16—41no—
350C3×M16—61no—
351C3×M16C22×D312yes—
352C3×M16C23×C312yes—
353C2×C3×C8—21no—
354C2×C3×C8—21no—
355C2×C3×C8—41no—
356C2×C3×C8—61no—
357C3×C4⋊C4—68no—
358C3×C42—21no—
359C3×C42—21no—
360C3×C42—22no—
361C3×C42—41no—
362C3×C42C22×D312yes—
363C3×C42C23×C312yes—
364#216—24no—
365#214—24no—
366C4⋊Dic3—28no—
367#208—21no—
368#208C23×C312yes—
369C2×C3⋊C8—21no—
370Dic12—24no—
371#204—24no—
372C22×C32—22no—
373C22×C32—22no—
374C22×C32—42no—
375C22×C32#12011yescharacteristic
376C22×C32#12011yescharacteristic
377C22×C32C22×D411yescharacteristic
378C2×C3×D3—22no—
379C2×C3×D3—42no—
380C32×C4—24no—
381C32×C4—22no—
382C32×C4#12011yescharacteristic
383C32×C4#12011yescharacteristic
384C32×C4C22×D411yescharacteristic
385C32×C4C22×D411yescharacteristic
386C3×Dic3—24no—
387C3×Dic3—22no—
388C3×Dic3—42no—
3892−1+4—34no—
3902−1+4—62no—
3912−1+4—62no—
3922−1+4—62no—
393C2×#41—31no—
394C2×#41—61no—
395C2×#41—62no—
396C2×#41—61no—
397C2×#41C2×C3×D311yescharacteristic
398C22×Q8—31no—
399C22×Q8—31no—
400C22×Q8—61no—
401C22×Q8—61no—
402#137—34no—
403#137—34no—
404#137—62no—
405#137—62no—
406C2×Q16—61no—
407C2×Q16—61no—
408C2×SD16—61no—
409C2×SD16—61no—
410C2×M16—31no—
411C2×M16C2×C3×D311yescharacteristic
412C4⋊Q8—34no—
413C4⋊Q8—62no—
414C2×C4⋊C4—62no—
415C2×C42C2×C3×D311yescharacteristic
416#104—34no—
417#104C2×C3×D314yescomplemented
418#101—34no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—41no—
423C23×C3—61no—
424C23×C3D3×D411yescharacteristic
425C23×C3C2×C3×D411yescharacteristic
426C22×D3—21no—
427C3×Q8—21no—
428C3×Q8—21no—
429C3×Q8—22no—
430C3×Q8—32no—
431C3×Q8—41no—
432C3×Q8—68no—
433C3×Q8—62no—
434C3×Q8—62no—
435C3×Q8—61no—
436C3×Q8—62no—
437C3×Q8—62no—
438C3×Q8—62no—
439C3×Q8—62no—
440C3×Q8—121no—
441C3×Q8—121no—
442C3×Q8C2×D1212yes—
443C3×Q8C2×C3×D412yes—
444C3×D4—22no—
445C3×D4—22no—
446C3×D4—22no—
447C3×D4—22no—
448C3×D4—21no—
449C3×D4—21no—
450C3×D4—22no—
451C3×D4—32no—
452C3×D4—41no—
453C3×D4—42no—
454C3×D4—42no—
455C3×D4—68no—
456C3×D4—62no—
457C3×D4—62no—
458C3×D4—61no—
459C3×D4C2×D1212yes—
460C3×D4C2×C3×D412yes—
461C2×C3×C4—24no—
462C2×C3×C4—24no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—34no—
478C2×C3×C4—42no—
479C2×C3×C4—42no—
480C2×C3×C4—42no—
481C2×C3×C4—41no—
482C2×C3×C4—44no—
483C2×C3×C4—68no—
484C2×C3×C4—68no—
485C2×C3×C4—62no—
486C2×C3×C4—62no—
487C2×C3×C4—61no—
488C2×C3×C4—62no—
489C2×C3×C4—62no—
490C2×C3×C4—62no—
491C2×C3×C4—121no—
492C2×C3×C4—121no—
493C2×C3×C4C2×D1211yescharacteristic
494C2×C3×C4C2×D1211yescharacteristic
495C2×C3×C4D3×D411yescharacteristic
496C2×C3×C4D3×D411yescharacteristic
497C2×C3×C4D3×D411yescharacteristic
498C2×C3×C4C2×C3×D411yescharacteristic
499C2×C3×C4C2×C3×D411yescharacteristic
500C2×C3×C4C2×C3×D411yescharacteristic
501C2×C3×C4C2×C3×D411yescharacteristic
502C2×C3×C4C2×C3×D411yescharacteristic
503C2×C3×C4C23×D311yescharacteristic
504C2×C3×C4C24×C311yescharacteristic
505#67—28no—
506#67—22no—
507#67—22no—
508C2×Dic3—28no—
509C2×Dic3—22no—
510C2×Dic3—21no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3C2×C3×D414yes—
516D12—21no—
517D12C2×C3×D412yes—
518C4×D3—28no—
519C4×D3—22no—
520C4×D3—22no—
521Dic6—28no—
522Dic6—22no—
523Dic6—21no—
524Dic6—22no—
525Dic6—22no—
526Dic6—22no—
527Dic6—22no—
528Dic6—22no—
529Dic6—41no—
530Dic6—41no—
531Dic6C2×C3×D412yes—
532C3×C8—22no—
533C3×C8—22no—
534C3×C8—42no—
535C3×C8—62no—
536C3⋊C8—22no—
537C2×C32—21no—
538C2×C32—21no—
539C2×C32—42no—
540C2×C32#45612yescomplemented
541C2×C32C2×#12011yescharacteristic
542C3×D3—42no—
543#41—21no—
544#41—21no—
545#41—32no—
546#41—32no—
547#41—64no—
548#41—64no—
549#41—68no—
550#41—68no—
551#41—64no—
552#41—64no—
553#41—61no—
554#41—61no—
555#41C3×D1212yes—
556#41C22×C3×D312yes—
557C2×Q8—32no—
558C2×Q8—32no—
559C2×Q8—32no—
560C2×Q8—31no—
561C2×Q8—64no—
562C2×Q8—62no—
563C2×Q8—64no—
564C2×Q8—64no—
565C2×Q8—64no—
566C2×Q8—61no—
567C2×Q8—61no—
568C2×Q8—61no—
569C2×Q8—61no—
570C2×Q8—61no—
571C2×Q8—61no—
572C2×Q8—61no—
573C2×Q8—61no—
574C2×Q8—61no—
575C2×Q8C3×D1211yescharacteristic
576C2×D4—21no—
577C2×D4—31no—
578C2×D4—62no—
579C2×D4—61no—
580C2×D4C3×D1211yescharacteristic
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—32no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4C22×C3×D311yescharacteristic
589Q16—64no—
590Q16—64no—
591SD16—64no—
592SD16—64no—
593M16—21no—
594M16—32no—
595M16—61no—
596M16C22×C3×D312yes—
597C2×C8—21no—
598C2×C8—61no—
599C4⋊C4—68no—
600C42—21no—
601C42C22×C3×D312yes—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—42no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—62no—
614C22×C3—82no—
615C22×C3—122no—
616C22×C3#88211yescharacteristic
617C22×C3#88211yescharacteristic
618C22×C3C3×#12011yescharacteristic
619C22×C3C3×#12011yescharacteristic
620C22×C3C2×D3×D411yescharacteristic
621C22×C3C22×C3×D411yescharacteristic
622C2×D3—22no—
623C2×D3—42no—
624C3×C4—24no—
625C3×C4—24no—
626C3×C4—22no—
627C3×C4—22no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—42no—
633C3×C4—44no—
634C3×C4—64no—
635C3×C4—62no—
636C3×C4—122no—
637C3×C4#88211yescharacteristic
638C3×C4#88211yescharacteristic
639C3×C4C3×#12011yescharacteristic
640C3×C4C3×#12011yescharacteristic
641C3×C4C22×D1211yescharacteristic
642C3×C4C2×D3×D411yescharacteristic
643C3×C4C22×C3×D411yescharacteristic
644C3×C4C22×C3×D411yescharacteristic
645Dic3—24no—
646Dic3—22no—
647Dic3—42no—
648C32C2×#45611yescharacteristic, complemented, Sylow
649C23—21no—
650C23—61no—
651C23C3×D3×D411yescharacteristic
652Q8—21no—
653Q8—32no—
654Q8—68no—
655Q8—62no—
656Q8—62no—
657Q8—61no—
658Q8—62no—
659Q8—62no—
660Q8—62no—
661Q8—62no—
662Q8—121no—
663Q8—121no—
664Q8C2×C3×D1212yes—
665D4—22no—
666D4—22no—
667D4—21no—
668D4—32no—
669D4—68no—
670D4—62no—
671D4—62no—
672D4—61no—
673D4C2×C3×D1212yes—
674C2×C4—24no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—34no—
680C2×C4—68no—
681C2×C4—68no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—61no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—62no—
688C2×C4—121no—
689C2×C4—121no—
690C2×C4C2×C3×D1211yescharacteristic
691C2×C4C2×C3×D1211yescharacteristic
692C2×C4C3×D3×D411yescharacteristic
693C2×C4C3×D3×D411yescharacteristic
694C2×C4C3×D3×D411yescharacteristic
695C2×C4C23×C3×D311yescharacteristic
696C8—22no—
697C8—62no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—22no—
704C2×C3—41no—
705C2×C3—41no—
706C2×C3—42no—
707C2×C3—42no—
708C2×C3—82no—
709C2×C3—122no—
710C2×C3#482612yesdirect product factor
711C2×C3C3×#45612yescomplemented
712C2×C3C2×#88211yescharacteristic
713C2×C3C2×C3×#12011yescharacteristic
714D3—42no—
715C22—22no—
716C22—22no—
717C22—42no—
718C22—62no—
719C22—122no—
720C22C3×#88211yescharacteristic
721C22C3×#88211yescharacteristic
722C22C2×C3×D3×D411yescharacteristic
723C4—24no—
724C4—22no—
725C4—64no—
726C4—62no—
727C4—122no—
728C4C3×#88211yescharacteristic
729C4C3×#88211yescharacteristic
730C4C22×C3×D1211yescharacteristic
731C4C2×C3×D3×D411yescharacteristic
732C3—21no—
733C3C2×#482611yescharacteristic, direct product factor
734C3C2×C3×#45611yescharacteristic, complemented
735C2—21no—
736C2—21no—
737C2—42no—
738C2—122no—
739C2C3×#482612yesdirect product factor
740C2C2×C3×#88211yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#104C2
socleC22×C32#120
prime radicalC2×C3×#1010C2
hypercenterC2×C3×#104D3
hypocenterC3C2×C3×#456
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
2. C2×C3×#951C2semidirect
3. C2×C3×#909C2semidirect
4. C2×C3×#869C2semidirect
5. C2×C32×#104C2semidirect
6. C2×C3×#824C2semidirect
7. C2×C3×#805C2semidirect
8. C3×#4826C2direct (N × H)
10. C2×#4826C3direct (N × H)
27. C3×#951C22semidirect
33. C3×#909C22semidirect
37. C3×#869C22semidirect
38. C32×#104C22semidirect
39. C3×#824C22semidirect
40. C3×#805C22semidirect
46. C2×#951C2×C3semidirect
47. C2×#909C2×C3semidirect
48. C2×#869C2×C3semidirect
52. C2×C3×#104D3semidirect
53. C2×C3×#104C2×C3semidirect
55. C2×#824C2×C3semidirect
56. C2×#805C2×C3semidirect
57. #4826C2×C3direct (N × H)
164. #951C22×C3semidirect
170. #909C22×C3semidirect
174. #869C22×C3semidirect
177. C3×#104C2×D3semidirect
178. C3×#104C22×C3semidirect
180. #824C22×C3semidirect
181. #805C22×C3semidirect
237. C2×#104C3×D3semidirect
417. #104C2×C3×D3semidirect
540. C2×C32#456semidirect
648. C32C2×#456semidirect
710. C2×C3#4826direct (N × H)
711. C2×C3C3×#456semidirect
733. C3C2×#4826direct (N × H)
734. C3C2×C3×#456semidirect
739. C2C3×#4826direct (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×#9512
C2×C3×#9092
C2×C3×#8692
C2×C32×#1042
C2×C3×#8242
C2×C3×#8052
C3×#48262
C2×C3×#4563
C2×#48263