Finite Group Databasebeta

← C2×C3×#5202 #11864805

Subgroups — C2×C3×#5202 #11864805

Order 1152.

1649 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic
2C2×C32×#137C211yesmaximal, characteristic, complemented
3C2×C3×#947C211yesmaximal, characteristic, complemented
4C2×C3×#942C211yesmaximal, characteristic, complemented
5C2×C3×#837C211yesmaximal, characteristic, complemented
6C3×#5202C218yesmaximal, direct product factor
7C2×C3×#825C211yesmaximal, characteristic, complemented
8C2×C3×#823C211yesmaximal, characteristic, complemented
9C2×C3×#455—31nomaximal
10C2×#5202C311yesmaximal, characteristic, direct product factor
11C2×C32×#41C2211yescharacteristic
12C22×C32×Q8C2211yescharacteristic, complemented
13C3×#1009—22no—
14C3×#1009—22no—
15C3×#1009—22no—
16C3×#1009C2214yes—
17C2×C3×#239—21no—
18C2×C3×D3×D4—21no—
19C2×C3×D3×D4—22no—
20C2×C3×#235—21no—
21C2×C3×#235C2211yescharacteristic
22C22×C3×D12—21no—
23C22×C3×D12C2211yescharacteristic
24C32×#137—22no—
25C32×#137C2214yescomplemented
26C2×C32×Q16—21no—
27C2×C32×SD16—21no—
28C2×C32×M16C2211yescharacteristic, complemented
29C3×#947—22no—
30C3×#947C2214yescomplemented
31C2×C3×#216—21no—
32C3×#942—22no—
33C3×#942C2214yescomplemented
34C2×C3×#215—21no—
35C2×C3×(C2×D3)⋊C4—22no—
36C2×C3×C4×Dic3C2211yescharacteristic, complemented
37C2×C3×#208C2211yescharacteristic, complemented
38C3×#837C2214yescomplemented
39C3×#825C2214yescomplemented
40C3×#823C2214yescomplemented
41C2×C3×H(5,𝔽2)—31no—
42C2×#1009C2×C311yescharacteristic
43C2×C3×#137—21no—
44C2×C3×#137—31no—
45C2×C3×#137D311yescharacteristic, complemented
46C2×C3×#137C2×C311yescharacteristic, complemented
47C2×C3×#124—31no—
48C2×#947C2×C311yescharacteristic, complemented
49C2×#942C2×C311yescharacteristic, complemented
50C3×#455—38no—
51C2×C3×#104—31no—
52C2×C3×#104—31no—
53C2×C3×#100—31no—
54C2×#837C2×C311yescharacteristic, complemented
55#5202C2×C318yesdirect product factor
56C2×#825C2×C311yescharacteristic, complemented
57C2×#823C2×C311yescharacteristic, complemented
58C23×C3×D3—22no—
59C23×C3×D3D412yes—
60C32×#41—21no—
61C32×#41—21no—
62C32×#41D412yes—
63C32×#41C2312yes—
64C2×C32×Q8—21no—
65C2×C32×Q8—21no—
66C2×C32×Q8—21no—
67C2×C32×Q8—21no—
68C2×C32×Q8—21no—
69C2×C32×Q8D411yescharacteristic
70C2×C32×Q8C2312yescomplemented
71C2×C32×D4—21no—
72C2×C32×D4D411yescharacteristic
73C22×C32×C4—21no—
74C22×C32×C4—21no—
75C22×C32×C4C2311yescharacteristic
76C2×C3×#67—22no—
77C2×C3×#67—21no—
78C22×C3×Dic3—21no—
79C3×#239—24no—
80C3×#239—24no—
81C3×D3×D4—28no—
82C3×D3×D4—24no—
83C3×D3×D4—28no—
84C3×D3×D4—24no—
85C3×#235—24no—
86C3×#235—21no—
87C3×#235—21no—
88C3×#235—24no—
89C3×#235D412yes—
90C3×#235C2312yes—
91C2×C3×D12—22no—
92C2×C3×D12—24no—
93C2×C3×D12—21no—
94C2×C3×D12—21no—
95C2×C3×D12—21no—
96C2×C3×D12—21no—
97C2×C3×D12—24no—
98C2×C3×D12D412yes—
99C2×C3×D12D411yescharacteristic
100C2×C3×D12C2312yes—
101C2×C3×C4×D3—22no—
102C2×C3×C4×D3—21no—
103C2×C3×Dic6D411yescharacteristic
104C32×Q16—24no—
105C32×SD16—24no—
106C32×M16—21no—
107C32×M16C2312yescomplemented
108C2×C32×C8—21no—
109C3×#216—24no—
110C3×#215—24no—
111C3×(C2×D3)⋊C4—28no—
112C3×C4×Dic3—21no—
113C3×C4×Dic3C2312yescomplemented
114C3×#208—21no—
115C3×#208C2312yescomplemented
116C2×C3×C3⋊C8—21no—
117C2×#455—31noSylow
118C3×H(5,𝔽2)—34no—
119C3×H(5,𝔽2)—62no—
120C3×H(5,𝔽2)—62no—
121C3×H(5,𝔽2)—62no—
122C2×C3×#41—21no—
123C2×C3×#41—31no—
124C2×C3×#41—61no—
125C2×C3×#41—61no—
126C2×C3×#41C2×D311yescharacteristic
127C2×C3×#41C22×C311yescharacteristic
128C22×C3×Q8—21no—
129C22×C3×Q8C2×D311yescharacteristic, complemented
130C22×C3×Q8C22×C311yescharacteristic, complemented
131C22×C3×D4—31no—
132C22×C3×D4—61no—
133C22×C3×D4—62no—
134C22×C3×D4—61no—
135#1009—22no—
136#1009—22no—
137#1009—22no—
138#1009C22×C314yes—
139C2×#239—21no—
140C2×D3×D4—22no—
141C2×D3×D4—21no—
142C2×#235—21no—
143C2×#235C22×C311yescharacteristic
144C22×D12—21no—
145C22×D12C22×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, complemented
165C2×C3×M16C22×C311yescharacteristic, complemented
166C3×#124—34no—
167C3×#124—62no—
168C2×C3×C22⋊C4—62no—
169C2×C3×C42—31no—
170#947—22no—
171#947C22×C314yescomplemented
172C2×#216—21no—
173#942—22no—
174#942C22×C314yescomplemented
175C2×#215—21no—
176C2×(C2×D3)⋊C4—22no—
177C2×C4×Dic3C22×C311yescharacteristic, complemented
178C2×#208C22×C311yescharacteristic, complemented
179C3×#104—34no—
180C3×#104—34no—
181C3×#100—34no—
182#837C22×C314yescomplemented
183#825C22×C314yescomplemented
184#823C22×C314yescomplemented
185C23×C32—21no—
186C23×C32C2×D411yescharacteristic
187C22×C3×D3—21no—
188C22×C3×D3—22no—
189C22×C3×D3—28no—
190C22×C3×D3—22no—
191C22×C3×D3—44no—
192C22×C3×D3—84no—
193C22×C3×D3C2×D414yes—
194C32×Q8—22no—
195C32×Q8—21no—
196C32×Q8—22no—
197C32×Q8—41no—
198C32×Q8—41no—
199C32×Q8C2×D412yes—
200C32×D4—22no—
201C32×D4—22no—
202C32×D4—21no—
203C32×D4C2×D412yes—
204C2×C32×C4—21no—
205C2×C32×C4—22no—
206C2×C32×C4—22no—
207C2×C32×C4—22no—
208C2×C32×C4—41no—
209C2×C32×C4—41no—
210C2×C32×C4C2×D411yescharacteristic
211C2×C32×C4C2×D411yescharacteristic
212C2×C32×C4C2×D411yescharacteristic
213C2×C32×C4C2×D411yescharacteristic
214C2×C32×C4C2×D411yescharacteristic
215C2×C32×C4C2411yescharacteristic
216C3×#67—28no—
217C3×#67—22no—
218C3×#67—22no—
219C2×C3×Dic3—21no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3—42no—
222C3×D12—28no—
223C3×D12—22no—
224C3×D12—21no—
225C3×D12—22no—
226C3×D12—22no—
227C3×D12—22no—
228C3×D12C2×D412yes—
229C3×C4×D3—28no—
230C3×C4×D3—22no—
231C3×C4×D3—22no—
232C3×Dic6—21no—
233C3×Dic6C2×D412yes—
234C32×C8—22no—
235C3×C3⋊C8—22no—
236C2×H(5,𝔽2)—31no—
237C2×#137—31no—
238C2×#137C3×D311yescharacteristic, complemented
239C2×#124—31no—
240#455—38no—
241C2×#104—31no—
242C2×#104—31no—
243C2×#100—31no—
244C24×C3—32no—
245C24×C3—62no—
246C23×D3—22no—
247C23×D3C3×D412yes—
248C3×#41—21no—
249C3×#41—21no—
250C3×#41—21no—
251C3×#41—21no—
252C3×#41—22no—
253C3×#41—22no—
254C3×#41—32no—
255C3×#41—32no—
256C3×#41—41no—
257C3×#41—41no—
258C3×#41—64no—
259C3×#41—64no—
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—21no—
270C2×C3×Q8—22no—
271C2×C3×Q8—22no—
272C2×C3×Q8—21no—
273C2×C3×Q8—21no—
274C2×C3×Q8—21no—
275C2×C3×Q8—21no—
276C2×C3×Q8—21no—
277C2×C3×Q8—21no—
278C2×C3×Q8—21no—
279C2×C3×Q8—21no—
280C2×C3×Q8—21no—
281C2×C3×Q8—22no—
282C2×C3×Q8—31no—
283C2×C3×Q8—41no—
284C2×C3×Q8—41no—
285C2×C3×Q8—41no—
286C2×C3×Q8#6711yescharacteristic
287C2×C3×Q8C3×D411yescharacteristic
288C2×C3×Q8C22×D312yescomplemented
289C2×C3×Q8C23×C312yescomplemented
290C2×C3×D4—21no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4—31no—
294C2×C3×D4—32no—
295C2×C3×D4—32no—
296C2×C3×D4—41no—
297C2×C3×D4—64no—
298C2×C3×D4—62no—
299C2×C3×D4—64no—
300C2×C3×D4—68no—
301C2×C3×D4—68no—
302C2×C3×D4—64no—
303C2×C3×D4—62no—
304C2×C3×D4—61no—
305C2×C3×D4—64no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4#6711yescharacteristic
311C2×C3×D4C3×D411yescharacteristic
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—41no—
318C22×C3×C4—41no—
319C22×C3×C4—62no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C23×C311yescharacteristic
324C2×#67—22no—
325C2×#67—21no—
326C22×Dic3—21no—
327#239—24no—
328#239—24no—
329D3×D4—28no—
330D3×D4—24no—
331D3×D4—28no—
332D3×D4—24no—
333#235—24no—
334#235—21no—
335#235—21no—
336#235—24no—
337#235C3×D412yes—
338#235C23×C312yes—
339C2×D12—22no—
340C2×D12—24no—
341C2×D12—21no—
342C2×D12—21no—
343C2×D12—21no—
344C2×D12—21no—
345C2×D12—24no—
346C2×D12C3×D412yes—
347C2×D12C3×D411yescharacteristic
348C2×D12C23×C312yes—
349C2×C4×D3—22no—
350C2×C4×D3—21no—
351C2×Dic6C3×D411yescharacteristic
352C3×Q16—28no—
353C3×Q16—24no—
354C3×Q16—24no—
355C3×Q16—64no—
356C3×SD16—28no—
357C3×SD16—24no—
358C3×SD16—24no—
359C3×SD16—64no—
360C3×M16—22no—
361C3×M16—21no—
362C3×M16—21no—
363C3×M16—22no—
364C3×M16—32no—
365C3×M16—61no—
366C3×M16C22×D312yescomplemented
367C3×M16C23×C312yescomplemented
368C2×C3×C8—22no—
369C2×C3×C8—21no—
370C2×C3×C8—21no—
371C2×C3×C8—61no—
372C3×C22⋊C4—68no—
373C3×C42—32no—
374C3×C42—61no—
375#216—24no—
376#215—24no—
377(C2×D3)⋊C4—28no—
378C4×Dic3—21no—
379C4×Dic3C23×C312yescomplemented
380#208—21no—
381#208C23×C312yescomplemented
382C2×C3⋊C8—21no—
383C22×C32—22no—
384C22×C32—22no—
385C22×C32—42no—
386C22×C32#12011yescharacteristic
387C22×C32#12011yescharacteristic
388C22×C32C22×D411yescharacteristic
389C2×C3×D3—24no—
390C2×C3×D3—22no—
391C2×C3×D3—44no—
392C2×C3×D3—42no—
393C2×C3×D3—44no—
394C2×C3×D3—82no—
395C2×C3×D3—88no—
396C32×C4—22no—
397C32×C4—42no—
398C32×C4#12011yescharacteristic
399C32×C4#12011yescharacteristic
400C32×C4C22×D411yescharacteristic
401C32×C4C22×D411yescharacteristic
402C3×Dic3—22no—
403C3×Dic3—42no—
404H(5,𝔽2)—34no—
405H(5,𝔽2)—62no—
406H(5,𝔽2)—62no—
407H(5,𝔽2)—62no—
408C2×#41—31no—
409C2×#41—61no—
410C2×#41—61no—
411C2×#41C2×C3×D311yescharacteristic
412C22×Q8C2×C3×D311yescharacteristic, complemented
413C22×D4—31no—
414C22×D4—61no—
415C22×D4—62no—
416C22×D4—61no—
417#137—22no—
418#137—34no—
419#137—62no—
420#137C2×C3×D314yescomplemented
421C2×Q16—21no—
422C2×Q16—61no—
423C2×SD16—21no—
424C2×SD16—61no—
425C2×M16—31no—
426C2×M16C2×C3×D311yescharacteristic, complemented
427#124—34no—
428#124—62no—
429C2×C22⋊C4—62no—
430C2×C42—31no—
431#104—34no—
432#104—34no—
433#100—34no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—34no—
438C23×C3—41no—
439C23×C3—68no—
440C23×C3—61no—
441C23×C3—62no—
442C23×C3—62no—
443C23×C3—124no—
444C23×C3—244no—
445C23×C3D3×D411yescharacteristic
446C23×C3C2×C3×D411yescharacteristic
447C22×D3—22no—
448C22×D3—21no—
449C22×D3—28no—
450C22×D3—22no—
451C22×D3—44no—
452C22×D3—84no—
453C22×D3C2×C3×D414yes—
454C3×Q8—21no—
455C3×Q8—21no—
456C3×Q8—24no—
457C3×Q8—22no—
458C3×Q8—22no—
459C3×Q8—22no—
460C3×Q8—22no—
461C3×Q8—22no—
462C3×Q8—32no—
463C3×Q8—42no—
464C3×Q8—41no—
465C3×Q8—42no—
466C3×Q8—42no—
467C3×Q8—41no—
468C3×Q8—41no—
469C3×Q8—41no—
470C3×Q8—41no—
471C3×Q8—61no—
472C3×Q8C2×#6712yes—
473C3×Q8C2×C3×D412yes—
474C3×D4—22no—
475C3×D4—22no—
476C3×D4—22no—
477C3×D4—22no—
478C3×D4—21no—
479C3×D4—21no—
480C3×D4—22no—
481C3×D4—32no—
482C3×D4—41no—
483C3×D4—42no—
484C3×D4—42no—
485C3×D4—68no—
486C3×D4—68no—
487C3×D4—62no—
488C3×D4—62no—
489C3×D4—61no—
490C3×D4—62no—
491C3×D4—62no—
492C3×D4—62no—
493C3×D4—62no—
494C3×D4C2×#6712yes—
495C3×D4C2×C3×D412yes—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—42no—
511C2×C3×C4—42no—
512C2×C3×C4—41no—
513C2×C3×C4—42no—
514C2×C3×C4—42no—
515C2×C3×C4—42no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—68no—
521C2×C3×C4—61no—
522C2×C3×C4—62no—
523C2×C3×C4—62no—
524C2×C3×C4—62no—
525C2×C3×C4—122no—
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4C2×#6711yescharacteristic
530C2×C3×C4C2×#6711yescharacteristic
531C2×C3×C4C2×C3×D411yescharacteristic
532C2×C3×C4C2×C3×D411yescharacteristic
533C2×C3×C4C2×C3×D411yescharacteristic
534C2×C3×C4C2×C3×D411yescharacteristic
535C2×C3×C4C2×C3×D411yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537C2×C3×C4C24×C311yescharacteristic
538#67—28no—
539#67—22no—
540#67—22no—
541C2×Dic3—21no—
542C2×Dic3—22no—
543C2×Dic3—42no—
544D12—28no—
545D12—22no—
546D12—21no—
547D12—22no—
548D12—22no—
549D12—22no—
550D12C2×C3×D412yes—
551C4×D3—28no—
552C4×D3—22no—
553C4×D3—22no—
554Dic6—21no—
555Dic6C2×C3×D412yes—
556C3×C8—24no—
557C3×C8—22no—
558C3×C8—22no—
559C3×C8—62no—
560C3⋊C8—22no—
561C2×C32—21no—
562C2×C32—21no—
563C2×C32—42no—
564C2×C32#45512yescomplemented
565C2×C32C2×#12011yescharacteristic
566C3×D3—44no—
567C3×D3—42no—
568C24—32no—
569C24—62no—
570#41—21no—
571#41—21no—
572#41—32no—
573#41—32no—
574#41—64no—
575#41—64no—
576#41—64no—
577#41—64no—
578#41—61no—
579#41—61no—
580#41C3×#6712yes—
581#41C22×C3×D312yes—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—31no—
588C2×Q8C3×#6711yescharacteristic
589C2×Q8C22×C3×D312yescomplemented
590C2×D4—21no—
591C2×D4—32no—
592C2×D4—31no—
593C2×D4—32no—
594C2×D4—64no—
595C2×D4—62no—
596C2×D4—64no—
597C2×D4—68no—
598C2×D4—68no—
599C2×D4—64no—
600C2×D4—62no—
601C2×D4—61no—
602C2×D4—64no—
603C2×D4—61no—
604C2×D4—61no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4C3×#6711yescharacteristic
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—62no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4C22×C3×D311yescharacteristic
614Q16—24no—
615Q16—64no—
616SD16—24no—
617SD16—64no—
618M16—21no—
619M16—32no—
620M16—61no—
621M16C22×C3×D312yescomplemented
622C2×C8—21no—
623C2×C8—61no—
624C22⋊C4—68no—
625C42—32no—
626C42—61no—
627C22×C3—22no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—62no—
639C22×C3—64no—
640C22×C3—82no—
641C22×C3—124no—
642C22×C3—124no—
643C22×C3—122no—
644C22×C3—242no—
645C22×C3—248no—
646C22×C3#93711yescharacteristic
647C22×C3#93711yescharacteristic
648C22×C3C3×#12011yescharacteristic
649C22×C3C3×#12011yescharacteristic
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C22×C3×D411yescharacteristic
652C2×D3—24no—
653C2×D3—22no—
654C2×D3—44no—
655C2×D3—42no—
656C2×D3—44no—
657C2×D3—82no—
658C2×D3—88no—
659C3×C4—22no—
660C3×C4—22no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—42no—
666C3×C4—44no—
667C3×C4—42no—
668C3×C4—42no—
669C3×C4—62no—
670C3×C4—122no—
671C3×C4#93711yescharacteristic
672C3×C4#93711yescharacteristic
673C3×C4C3×#12011yescharacteristic
674C3×C4C3×#12011yescharacteristic
675C3×C4C2×D3×D411yescharacteristic
676C3×C4C22×#6711yescharacteristic
677C3×C4C22×C3×D411yescharacteristic
678C3×C4C22×C3×D411yescharacteristic
679Dic3—22no—
680Dic3—42no—
681C32C2×#45511yescharacteristic, complemented, Sylow
682C23—21no—
683C23—34no—
684C23—68no—
685C23—61no—
686C23—62no—
687C23—62no—
688C23—124no—
689C23—244no—
690C23C3×D3×D411yescharacteristic
691Q8—21no—
692Q8—22no—
693Q8—22no—
694Q8—32no—
695Q8—41no—
696Q8—41no—
697Q8—61no—
698Q8C2×C3×#6712yes—
699D4—22no—
700D4—22no—
701D4—21no—
702D4—32no—
703D4—68no—
704D4—68no—
705D4—62no—
706D4—62no—
707D4—61no—
708D4—62no—
709D4—62no—
710D4—62no—
711D4—62no—
712D4C2×C3×#6712yes—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—68no—
720C2×C4—61no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—122no—
725C2×C4C3×D3×D411yescharacteristic
726C2×C4C3×D3×D411yescharacteristic
727C2×C4C3×D3×D411yescharacteristic
728C2×C4C2×C3×#6711yescharacteristic
729C2×C4C2×C3×#6711yescharacteristic
730C2×C4C23×C3×D311yescharacteristic
731C8—22no—
732C8—62no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—22no—
738C2×C3—21no—
739C2×C3—41no—
740C2×C3—41no—
741C2×C3—42no—
742C2×C3—42no—
743C2×C3—82no—
744C2×C3—124no—
745C2×C3—122no—
746C2×C3#520212yesdirect product factor
747C2×C3C3×#45512yescomplemented
748C2×C3C2×#93711yescharacteristic
749C2×C3C2×C3×#12011yescharacteristic
750D3—44no—
751D3—42no—
752C22—22no—
753C22—22no—
754C22—42no—
755C22—62no—
756C22—64no—
757C22—124no—
758C22—124no—
759C22—122no—
760C22—242no—
761C22—248no—
762C22C3×#93711yescharacteristic
763C22C3×#93711yescharacteristic
764C22C2×C3×D3×D411yescharacteristic
765C4—22no—
766C4—42no—
767C4—62no—
768C4—122no—
769C4C3×#93711yescharacteristic
770C4C3×#93711yescharacteristic
771C4C2×C3×D3×D411yescharacteristic
772C4C22×C3×#6711yescharacteristic
773C3—21no—
774C3C2×#520211yescharacteristic, direct product factor
775C3C2×C3×#45511yescharacteristic, complemented
776C2—21no—
777C2—21no—
778C2—42no—
779C2—124no—
780C2—122no—
781C2C3×#520212yesdirect product factor
782C2C2×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×#1009C2
hypercenterC2×C3×#137D3
hypocenterC3C2×C3×#455
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×#947C2semidirect
4. C2×C3×#942C2semidirect
5. C2×C3×#837C2semidirect
6. C3×#5202C2direct (N × H)
7. C2×C3×#825C2semidirect
8. C2×C3×#823C2semidirect
10. C2×#5202C3direct (N × H)
12. C22×C32×Q8C22semidirect
25. C32×#137C22semidirect
28. C2×C32×M16C22semidirect
30. C3×#947C22semidirect
33. C3×#942C22semidirect
36. C2×C3×C4×Dic3C22semidirect
37. C2×C3×#208C22semidirect
38. C3×#837C22semidirect
39. C3×#825C22semidirect
40. C3×#823C22semidirect
45. C2×C3×#137D3semidirect
46. C2×C3×#137C2×C3semidirect
48. C2×#947C2×C3semidirect
49. C2×#942C2×C3semidirect
54. C2×#837C2×C3semidirect
55. #5202C2×C3direct (N × H)
56. C2×#825C2×C3semidirect
57. C2×#823C2×C3semidirect
70. C2×C32×Q8C23semidirect
107. C32×M16C23semidirect
113. C3×C4×Dic3C23semidirect
115. C3×#208C23semidirect
129. C22×C3×Q8C2×D3semidirect
130. C22×C3×Q8C22×C3semidirect
152. C3×#137C2×D3semidirect
153. C3×#137C22×C3semidirect
164. C2×C3×M16C2×D3semidirect
165. C2×C3×M16C22×C3semidirect
171. #947C22×C3semidirect
174. #942C22×C3semidirect
177. C2×C4×Dic3C22×C3semidirect
178. C2×#208C22×C3semidirect
182. #837C22×C3semidirect
183. #825C22×C3semidirect
184. #823C22×C3semidirect
238. C2×#137C3×D3semidirect
288. C2×C3×Q8C22×D3semidirect
289. C2×C3×Q8C23×C3semidirect
366. C3×M16C22×D3semidirect
367. C3×M16C23×C3semidirect
379. C4×Dic3C23×C3semidirect
381. #208C23×C3semidirect
412. C22×Q8C2×C3×D3semidirect
420. #137C2×C3×D3semidirect
426. C2×M16C2×C3×D3semidirect
564. C2×C32#455semidirect
589. C2×Q8C22×C3×D3semidirect
621. M16C22×C3×D3semidirect
681. C32C2×#455semidirect
746. C2×C3#5202direct (N × H)
747. C2×C3C3×#455semidirect
774. C3C2×#5202direct (N × H)
775. C3C2×C3×#455semidirect
781. C2C3×#5202direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#10092
C2×C32×#1372
C2×C3×#9472
C2×C3×#9422
C2×C3×#8372
C3×#52022
C2×C3×#8252
C2×C3×#8232
C2×C3×#4553
C2×#52023