Finite Group Databasebeta

← C2×C3×#5205 #11864897

Subgroups — C2×C3×#5205 #11864897

Order 1152.

1545 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic
2C2×C32×#137C211yesmaximal, characteristic, complemented
3C2×C3×#944C211yesmaximal, characteristic, complemented
4C2×C3×#942C211yesmaximal, characteristic, complemented
5C2×C3×#837C211yesmaximal, characteristic, complemented
6C3×#5205C218yesmaximal, direct product factor
7C2×C3×#825C211yesmaximal, characteristic, complemented
8C2×C3×#824C211yesmaximal, characteristic, complemented
9C2×C3×#456—31nomaximal
10C2×#5205C311yesmaximal, characteristic, direct product factor
11C2×C32×#41C2211yescharacteristic
12C22×C32×Q8C2211yescharacteristic
13C3×#1010—22no—
14C3×#1010—22no—
15C3×#1010—22no—
16C3×#1010C2214yes—
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×#137—22no—
25C32×#137C2214yescomplemented
26C2×C32×Q16—21no—
27C2×C32×SD16—21no—
28C2×C32×M16C2211yescharacteristic
29C3×#944—22no—
30C3×#944C2214yescomplemented
31C2×C3×#216—21no—
32C3×#942—22no—
33C3×#942C2214yescomplemented
34C2×C3×#215—21no—
35C2×C3×Dic3⋊C4—22no—
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×C3×#208C2211yescharacteristic
38C3×#837C2214yescomplemented
39C3×#825C2214yescomplemented
40C3×#824C2214yescomplemented
41C2×C3×2−1+4—31no—
42C2×#1010C2×C311yescharacteristic
43C2×C3×#137—21no—
44C2×C3×#137—31no—
45C2×C3×#137D311yescharacteristic, complemented
46C2×C3×#137C2×C311yescharacteristic, complemented
47C2×C3×C4⋊Q8—31no—
48C2×#944C2×C311yescharacteristic, complemented
49C2×#942C2×C311yescharacteristic, complemented
50C3×#456—38no—
51C2×C3×#104—31no—
52C2×C3×#104—31no—
53C2×C3×#101—31no—
54C2×#837C2×C311yescharacteristic, complemented
55#5205C2×C318yesdirect product factor
56C2×#825C2×C311yescharacteristic, complemented
57C2×#824C2×C311yescharacteristic, complemented
58C32×#41—21no—
59C32×#41—21no—
60C32×#41D412yes—
61C32×#41C2312yes—
62C2×C32×Q8—21no—
63C2×C32×Q8—21no—
64C2×C32×Q8—21no—
65C2×C32×Q8—21no—
66C2×C32×Q8—21no—
67C2×C32×Q8D411yescharacteristic
68C2×C32×Q8C2312yes—
69C2×C32×D4—21no—
70C2×C32×D4D411yescharacteristic
71C22×C32×C4—21no—
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×Q16—24no—
105C32×SD16—24no—
106C32×M16—21no—
107C32×M16C2312yes—
108C2×C32×C8—21no—
109C3×#216—24no—
110C3×#215—24no—
111C3×Dic3⋊C4—28no—
112C3×C4×Dic3—21no—
113C3×C4×Dic3C2312yes—
114C3×#208—21no—
115C3×#208C2312yes—
116C2×C3×C3⋊C8—21no—
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—21no—
130C22×C3×Q8—31no—
131C22×C3×Q8—61no—
132C22×C3×Q8—61no—
133C22×C3×Q8C2×D311yescharacteristic
134C22×C3×Q8C22×C311yescharacteristic
135#1010—22no—
136#1010—22no—
137#1010—22no—
138#1010C22×C314yes—
139C2×D3×Q8—21no—
140C2×#237—21no—
141C2×#237—22no—
142C2×#235—21no—
143C2×#235C22×C311yescharacteristic
144C22×Dic6—21no—
145C22×Dic6C22×C311yescharacteristic
146C3×#137—24no—
147C3×#137—22no—
148C3×#137—22no—
149C3×#137—24no—
150C3×#137—34no—
151C3×#137—62no—
152C3×#137C2×D314yescomplemented
153C3×#137C22×C314yescomplemented
154C2×C3×Q16—22no—
155C2×C3×Q16—21no—
156C2×C3×Q16—21no—
157C2×C3×Q16—61no—
158C2×C3×SD16—22no—
159C2×C3×SD16—21no—
160C2×C3×SD16—21no—
161C2×C3×SD16—61no—
162C2×C3×M16—21no—
163C2×C3×M16—31no—
164C2×C3×M16C2×D311yescharacteristic
165C2×C3×M16C22×C311yescharacteristic
166C3×C4⋊Q8—34no—
167C3×C4⋊Q8—62no—
168C2×C3×C4⋊C4—62no—
169C2×C3×C42—31no—
170#944—22no—
171#944C22×C314yescomplemented
172C2×#216—21no—
173#942—22no—
174#942C22×C314yescomplemented
175C2×#215—21no—
176C2×Dic3⋊C4—22no—
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×C32C2×D411yescharacteristic
187C22×C3×D3—21no—
188C32×Q8—22no—
189C32×Q8—21no—
190C32×Q8—22no—
191C32×Q8—41no—
192C32×Q8—41no—
193C32×Q8C2×D412yes—
194C32×D4—22no—
195C32×D4—22no—
196C32×D4—21no—
197C32×D4C2×D412yes—
198C2×C32×C4—21no—
199C2×C32×C4—22no—
200C2×C32×C4—22no—
201C2×C32×C4—22no—
202C2×C32×C4—41no—
203C2×C32×C4—41no—
204C2×C32×C4C2×D411yescharacteristic
205C2×C32×C4C2×D411yescharacteristic
206C2×C32×C4C2×D411yescharacteristic
207C2×C32×C4C2×D411yescharacteristic
208C2×C32×C4C2×D411yescharacteristic
209C2×C32×C4C2411yescharacteristic
210C3×#67—28no—
211C3×#67—22no—
212C3×#67—22no—
213C2×C3×Dic3—28no—
214C2×C3×Dic3—24no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3—21no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3C2×D414yes—
220C3×D12—21no—
221C3×D12C2×D412yes—
222C3×C4×D3—28no—
223C3×C4×D3—22no—
224C3×C4×D3—22no—
225C3×Dic6—28no—
226C3×Dic6—22no—
227C3×Dic6—21no—
228C3×Dic6—22no—
229C3×Dic6—22no—
230C3×Dic6—22no—
231C3×Dic6C2×D412yes—
232C32×C8—22no—
233C3×C3⋊C8—22no—
234C2×2−1+4—31no—
235C2×#137—31no—
236C2×#137C3×D311yescharacteristic, complemented
237C2×C4⋊Q8—31no—
238#456—38no—
239C2×#104—31no—
240C2×#104—31no—
241C2×#101—31no—
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×#41#6712yes—
261C3×#41C3×D412yes—
262C3×#41C22×D312yes—
263C3×#41C23×C312yes—
264C2×C3×Q8—21no—
265C2×C3×Q8—21no—
266C2×C3×Q8—22no—
267C2×C3×Q8—22no—
268C2×C3×Q8—21no—
269C2×C3×Q8—21no—
270C2×C3×Q8—21no—
271C2×C3×Q8—21no—
272C2×C3×Q8—21no—
273C2×C3×Q8—21no—
274C2×C3×Q8—21no—
275C2×C3×Q8—21no—
276C2×C3×Q8—21no—
277C2×C3×Q8—22no—
278C2×C3×Q8—32no—
279C2×C3×Q8—32no—
280C2×C3×Q8—31no—
281C2×C3×Q8—41no—
282C2×C3×Q8—41no—
283C2×C3×Q8—41no—
284C2×C3×Q8—64no—
285C2×C3×Q8—62no—
286C2×C3×Q8—64no—
287C2×C3×Q8—64no—
288C2×C3×Q8—64no—
289C2×C3×Q8—61no—
290C2×C3×Q8—61no—
291C2×C3×Q8—61no—
292C2×C3×Q8—61no—
293C2×C3×Q8#6711yescharacteristic
294C2×C3×Q8C3×D411yescharacteristic
295C2×C3×Q8C22×D312yes—
296C2×C3×Q8C23×C312yes—
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—41no—
302C2×C3×D4—62no—
303C2×C3×D4—61no—
304C2×C3×D4#6711yescharacteristic
305C2×C3×D4C3×D411yescharacteristic
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—32no—
312C22×C3×C4—41no—
313C22×C3×C4—41no—
314C22×C3×C4—62no—
315C22×C3×C4—62no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C23×C311yescharacteristic
320C2×#67—22no—
321C2×#67—21no—
322C22×Dic3—22no—
323C22×Dic3—21no—
324C22×Dic3C3×D412yes—
325D3×Q8—24no—
326D3×Q8—24no—
327#237—28no—
328#237—24no—
329#237—24no—
330#237—28no—
331#235—24no—
332#235—21no—
333#235—21no—
334#235—24no—
335#235C3×D412yes—
336#235C23×C312yes—
337C2×D12C3×D411yescharacteristic
338C2×C4×D3—22no—
339C2×C4×D3—21no—
340C2×Dic6—22no—
341C2×Dic6—24no—
342C2×Dic6—21no—
343C2×Dic6—21no—
344C2×Dic6—21no—
345C2×Dic6—21no—
346C2×Dic6—24no—
347C2×Dic6C3×D412yes—
348C2×Dic6C3×D411yescharacteristic
349C2×Dic6C23×C312yes—
350C3×Q16—28no—
351C3×Q16—24no—
352C3×Q16—24no—
353C3×Q16—64no—
354C3×SD16—28no—
355C3×SD16—24no—
356C3×SD16—24no—
357C3×SD16—64no—
358C3×M16—22no—
359C3×M16—21no—
360C3×M16—21no—
361C3×M16—22no—
362C3×M16—32no—
363C3×M16—61no—
364C3×M16C22×D312yes—
365C3×M16C23×C312yes—
366C2×C3×C8—22no—
367C2×C3×C8—21no—
368C2×C3×C8—21no—
369C2×C3×C8—61no—
370C3×C4⋊C4—68no—
371C3×C42—32no—
372C3×C42—61no—
373#216—24no—
374#215—24no—
375Dic3⋊C4—28no—
376C4×Dic3—21no—
377C4×Dic3C23×C312yes—
378#208—21no—
379#208C23×C312yes—
380C2×C3⋊C8—21no—
381C22×C32—22no—
382C22×C32—22no—
383C22×C32—42no—
384C22×C32#12011yescharacteristic
385C22×C32#12011yescharacteristic
386C22×C32C22×D411yescharacteristic
387C2×C3×D3—22no—
388C2×C3×D3—42no—
389C32×C4—22no—
390C32×C4—42no—
391C32×C4#12011yescharacteristic
392C32×C4#12011yescharacteristic
393C32×C4C22×D411yescharacteristic
394C32×C4C22×D411yescharacteristic
395C3×Dic3—24no—
396C3×Dic3—24no—
397C3×Dic3—22no—
3982−1+4—34no—
3992−1+4—62no—
4002−1+4—62no—
4012−1+4—62no—
402C2×#41—31no—
403C2×#41—61no—
404C2×#41—62no—
405C2×#41—61no—
406C2×#41C2×C3×D311yescharacteristic
407C22×Q8—31no—
408C22×Q8—61no—
409C22×Q8—61no—
410C22×Q8C2×C3×D311yescharacteristic
411#137—22no—
412#137—34no—
413#137—62no—
414#137C2×C3×D314yescomplemented
415C2×Q16—21no—
416C2×Q16—61no—
417C2×SD16—21no—
418C2×SD16—61no—
419C2×M16—31no—
420C2×M16C2×C3×D311yescharacteristic
421C4⋊Q8—34no—
422C4⋊Q8—62no—
423C2×C4⋊C4—62no—
424C2×C42—31no—
425#104—34no—
426#104—34no—
427#101—34no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—41no—
432C23×C3—61no—
433C23×C3D3×D411yescharacteristic
434C23×C3C2×C3×D411yescharacteristic
435C22×D3—21no—
436C3×Q8—21no—
437C3×Q8—21no—
438C3×Q8—24no—
439C3×Q8—22no—
440C3×Q8—22no—
441C3×Q8—22no—
442C3×Q8—22no—
443C3×Q8—22no—
444C3×Q8—32no—
445C3×Q8—42no—
446C3×Q8—41no—
447C3×Q8—42no—
448C3×Q8—42no—
449C3×Q8—41no—
450C3×Q8—41no—
451C3×Q8—41no—
452C3×Q8—41no—
453C3×Q8—68no—
454C3×Q8—62no—
455C3×Q8—62no—
456C3×Q8—61no—
457C3×Q8—62no—
458C3×Q8—62no—
459C3×Q8C2×#6712yes—
460C3×Q8C2×C3×D412yes—
461C3×D4—22no—
462C3×D4—22no—
463C3×D4—22no—
464C3×D4—22no—
465C3×D4—21no—
466C3×D4—21no—
467C3×D4—22no—
468C3×D4—32no—
469C3×D4—41no—
470C3×D4—42no—
471C3×D4—42no—
472C3×D4—68no—
473C3×D4—62no—
474C3×D4—62no—
475C3×D4—61no—
476C3×D4C2×#6712yes—
477C3×D4C2×C3×D412yes—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—34no—
493C2×C3×C4—42no—
494C2×C3×C4—42no—
495C2×C3×C4—41no—
496C2×C3×C4—42no—
497C2×C3×C4—42no—
498C2×C3×C4—42no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—68no—
504C2×C3×C4—64no—
505C2×C3×C4—68no—
506C2×C3×C4—62no—
507C2×C3×C4—62no—
508C2×C3×C4—61no—
509C2×C3×C4—62no—
510C2×C3×C4—62no—
511C2×C3×C4—62no—
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4C2×#6711yescharacteristic
516C2×C3×C4C2×#6711yescharacteristic
517C2×C3×C4C2×C3×D411yescharacteristic
518C2×C3×C4C2×C3×D411yescharacteristic
519C2×C3×C4C2×C3×D411yescharacteristic
520C2×C3×C4C2×C3×D411yescharacteristic
521C2×C3×C4C2×C3×D411yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C24×C311yescharacteristic
524#67—28no—
525#67—22no—
526#67—22no—
527C2×Dic3—28no—
528C2×Dic3—24no—
529C2×Dic3—22no—
530C2×Dic3—21no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3C2×C3×D414yes—
534D12—21no—
535D12C2×C3×D412yes—
536C4×D3—28no—
537C4×D3—22no—
538C4×D3—22no—
539Dic6—28no—
540Dic6—22no—
541Dic6—21no—
542Dic6—22no—
543Dic6—22no—
544Dic6—22no—
545Dic6C2×C3×D412yes—
546C3×C8—24no—
547C3×C8—22no—
548C3×C8—22no—
549C3×C8—62no—
550C3⋊C8—22no—
551C2×C32—21no—
552C2×C32—21no—
553C2×C32—42no—
554C2×C32#45612yescomplemented
555C2×C32C2×#12011yescharacteristic
556C3×D3—42no—
557#41—21no—
558#41—21no—
559#41—32no—
560#41—32no—
561#41—64no—
562#41—64no—
563#41—68no—
564#41—68no—
565#41—64no—
566#41—64no—
567#41—61no—
568#41—61no—
569#41C3×#6712yes—
570#41C22×C3×D312yes—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—32no—
577C2×Q8—32no—
578C2×Q8—31no—
579C2×Q8—64no—
580C2×Q8—62no—
581C2×Q8—64no—
582C2×Q8—64no—
583C2×Q8—64no—
584C2×Q8—61no—
585C2×Q8—61no—
586C2×Q8—61no—
587C2×Q8—61no—
588C2×Q8C3×#6711yescharacteristic
589C2×Q8C22×C3×D312yes—
590C2×D4—21no—
591C2×D4—31no—
592C2×D4—62no—
593C2×D4—61no—
594C2×D4C3×#6711yescharacteristic
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—32no—
598C22×C4—62no—
599C22×C4—62no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4C22×C3×D311yescharacteristic
603Q16—24no—
604Q16—64no—
605SD16—24no—
606SD16—64no—
607M16—21no—
608M16—32no—
609M16—61no—
610M16C22×C3×D312yes—
611C2×C8—21no—
612C2×C8—61no—
613C4⋊C4—68no—
614C42—32no—
615C42—61no—
616C22×C3—22no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—42no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—42no—
627C22×C3—62no—
628C22×C3—82no—
629C22×C3—122no—
630C22×C3#93711yescharacteristic
631C22×C3#93711yescharacteristic
632C22×C3C3×#12011yescharacteristic
633C22×C3C3×#12011yescharacteristic
634C22×C3C2×D3×D411yescharacteristic
635C22×C3C22×C3×D411yescharacteristic
636C2×D3—22no—
637C2×D3—42no—
638C3×C4—22no—
639C3×C4—22no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—42no—
645C3×C4—44no—
646C3×C4—42no—
647C3×C4—42no—
648C3×C4—64no—
649C3×C4—64no—
650C3×C4—62no—
651C3×C4#93711yescharacteristic
652C3×C4#93711yescharacteristic
653C3×C4C3×#12011yescharacteristic
654C3×C4C3×#12011yescharacteristic
655C3×C4C2×D3×D411yescharacteristic
656C3×C4C22×#6711yescharacteristic
657C3×C4C22×C3×D411yescharacteristic
658C3×C4C22×C3×D411yescharacteristic
659Dic3—24no—
660Dic3—24no—
661Dic3—22no—
662C32C2×#45611yescharacteristic, complemented, Sylow
663C23—21no—
664C23—61no—
665C23C3×D3×D411yescharacteristic
666Q8—21no—
667Q8—22no—
668Q8—22no—
669Q8—32no—
670Q8—41no—
671Q8—41no—
672Q8—68no—
673Q8—62no—
674Q8—62no—
675Q8—61no—
676Q8—62no—
677Q8—62no—
678Q8C2×C3×#6712yes—
679D4—22no—
680D4—22no—
681D4—21no—
682D4—32no—
683D4—68no—
684D4—62no—
685D4—62no—
686D4—61no—
687D4C2×C3×#6712yes—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—34no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—68no—
696C2×C4—68no—
697C2×C4—64no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—61no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4C3×D3×D411yescharacteristic
705C2×C4C3×D3×D411yescharacteristic
706C2×C4C3×D3×D411yescharacteristic
707C2×C4C2×C3×#6711yescharacteristic
708C2×C4C2×C3×#6711yescharacteristic
709C2×C4C23×C3×D311yescharacteristic
710C8—22no—
711C8—62no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—22no—
717C2×C3—21no—
718C2×C3—41no—
719C2×C3—41no—
720C2×C3—42no—
721C2×C3—42no—
722C2×C3—82no—
723C2×C3—122no—
724C2×C3#520512yesdirect product factor
725C2×C3C3×#45612yescomplemented
726C2×C3C2×#93711yescharacteristic
727C2×C3C2×C3×#12011yescharacteristic
728D3—42no—
729C22—22no—
730C22—22no—
731C22—42no—
732C22—62no—
733C22—122no—
734C22C3×#93711yescharacteristic
735C22C3×#93711yescharacteristic
736C22C2×C3×D3×D411yescharacteristic
737C4—22no—
738C4—42no—
739C4—64no—
740C4—64no—
741C4—62no—
742C4C3×#93711yescharacteristic
743C4C3×#93711yescharacteristic
744C4C2×C3×D3×D411yescharacteristic
745C4C22×C3×#6711yescharacteristic
746C3—21no—
747C3C2×#520511yescharacteristic, direct product factor
748C3C2×C3×#45611yescharacteristic, complemented
749C2—21no—
750C2—21no—
751C2—42no—
752C2—122no—
753C2C3×#520512yesdirect product factor
754C2C2×C3×#93711yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#137C2
socleC22×C32#120
prime radicalC2×C3×#1010C2
hypercenterC2×C3×#137D3
hypocenterC3C2×C3×#456
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#137

Complements

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

NH ≅ G/Ntype
2. C2×C32×#137C2semidirect
3. C2×C3×#944C2semidirect
4. C2×C3×#942C2semidirect
5. C2×C3×#837C2semidirect
6. C3×#5205C2direct (N × H)
7. C2×C3×#825C2semidirect
8. C2×C3×#824C2semidirect
10. C2×#5205C3direct (N × H)
25. C32×#137C22semidirect
30. C3×#944C22semidirect
33. C3×#942C22semidirect
38. C3×#837C22semidirect
39. C3×#825C22semidirect
40. C3×#824C22semidirect
45. C2×C3×#137D3semidirect
46. C2×C3×#137C2×C3semidirect
48. C2×#944C2×C3semidirect
49. C2×#942C2×C3semidirect
54. C2×#837C2×C3semidirect
55. #5205C2×C3direct (N × H)
56. C2×#825C2×C3semidirect
57. C2×#824C2×C3semidirect
152. C3×#137C2×D3semidirect
153. C3×#137C22×C3semidirect
171. #944C22×C3semidirect
174. #942C22×C3semidirect
182. #837C22×C3semidirect
183. #825C22×C3semidirect
184. #824C22×C3semidirect
236. C2×#137C3×D3semidirect
414. #137C2×C3×D3semidirect
554. C2×C32#456semidirect
662. C32C2×#456semidirect
724. C2×C3#5205direct (N × H)
725. C2×C3C3×#456semidirect
747. C3C2×#5205direct (N × H)
748. C3C2×C3×#456semidirect
753. C2C3×#5205direct (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×#1372
C2×C3×#9442
C2×C3×#9422
C2×C3×#8372
C3×#52052
C2×C3×#8252
C2×C3×#8242
C2×C3×#4563
C2×#52053