Finite Group Databasebeta

← C2×C3×#4825 #11864814

Subgroups — C2×C3×#4825 #11864814

Order 1152.

1605 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic, complemented
3C2×C3×#909C211yesmaximal, characteristic, complemented
4C2×C3×#875C211yesmaximal, characteristic, complemented
5C2×C32×#104C211yesmaximal, characteristic, complemented
6C2×C3×#823C211yesmaximal, characteristic, complemented
7C2×C3×#805C211yesmaximal, characteristic, complemented
8C3×#4825C218yesmaximal, direct product factor
9C2×C3×#455—31nomaximal
10C2×#4825C311yesmaximal, characteristic, direct product factor
11C2×C32×#41C2211yescharacteristic
12C3×#1009—22no—
13C3×#1009—22no—
14C3×#1009—22no—
15C3×#1009C2214yes—
16C2×C3×#239—21no—
17C2×C3×D3×D4—21no—
18C2×C3×D3×D4—22no—
19C2×C3×#235—21no—
20C2×C3×#235C2211yescharacteristic
21C22×C3×D12—21no—
22C22×C3×D12C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic, complemented
24C2×C32×M16C2211yescharacteristic, complemented
25C2×C32×C42C2211yescharacteristic, complemented
26C3×#951—22no—
27C3×#951C2214yescomplemented
28C2×C3×#216—21no—
29C2×C3×#214—21no—
30C2×C3×(C2×D3)⋊C4—22no—
31C2×C3×#208C2211yescharacteristic, complemented
32C3×#909—22no—
33C3×#909C2214yescomplemented
34C2×C3×Dic12—21no—
35C2×C3×#204—21no—
36C3×#875—22no—
37C3×#875C2214yescomplemented
38C32×#104C2214yescomplemented
39C3×#823C2214yescomplemented
40C3×#805C2214yescomplemented
41C2×C3×H(5,𝔽2)—31no—
42C2×#1009C2×C311yescharacteristic
43C2×C3×#137—31no—
44C2×C3×#137—31no—
45C2×C3×#124—31no—
46C2×#951C2×C311yescharacteristic, complemented
47C2×#909C2×C311yescharacteristic, complemented
48C2×#875C2×C311yescharacteristic, complemented
49C3×#455—38no—
50C2×C3×#104—21no—
51C2×C3×#104—31no—
52C2×C3×#104D311yescharacteristic, complemented
53C2×C3×#104C2×C311yescharacteristic, complemented
54C2×C3×#100—31no—
55C2×#823C2×C311yescharacteristic, complemented
56C2×#805C2×C311yescharacteristic, complemented
57#4825C2×C318yesdirect product factor
58C23×C3×D3—22no—
59C23×C3×D3D412yes—
60C32×#41—21no—
61C32×#41—21no—
62C32×#41D412yes—
63C32×#41C2312yes—
64C2×C32×Q8D411yescharacteristic
65C2×C32×D4—21no—
66C2×C32×D4D411yescharacteristic
67C22×C32×C4—21no—
68C22×C32×C4—21no—
69C22×C32×C4C2311yescharacteristic
70C2×C3×#67—22no—
71C2×C3×#67—21no—
72C22×C3×Dic3—21no—
73C3×#239—24no—
74C3×#239—24no—
75C3×D3×D4—28no—
76C3×D3×D4—24no—
77C3×D3×D4—28no—
78C3×D3×D4—24no—
79C3×#235—24no—
80C3×#235—21no—
81C3×#235—21no—
82C3×#235—24no—
83C3×#235D412yes—
84C3×#235C2312yes—
85C2×C3×D12—22no—
86C2×C3×D12—24no—
87C2×C3×D12—21no—
88C2×C3×D12—21no—
89C2×C3×D12—21no—
90C2×C3×D12—21no—
91C2×C3×D12—24no—
92C2×C3×D12D412yes—
93C2×C3×D12D411yescharacteristic
94C2×C3×D12C2312yes—
95C2×C3×C4×D3—22no—
96C2×C3×C4×D3—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6—21no—
99C2×C3×Dic6—21no—
100C2×C3×Dic6—21no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6D411yescharacteristic
103C2×C3×Dic6C2312yescomplemented
104C32×M16—21no—
105C32×M16C2312yescomplemented
106C2×C32×C8—21no—
107C32×C42—21no—
108C32×C42C2312yescomplemented
109C3×#216—24no—
110C3×#214—24no—
111C3×(C2×D3)⋊C4—28no—
112C3×#208—21no—
113C3×#208C2312yescomplemented
114C2×C3×C3⋊C8—21no—
115C3×Dic12—24no—
116C3×#204—24no—
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—31no—
129C22×C3×D4—31no—
130C22×C3×D4—61no—
131C22×C3×D4—62no—
132C22×C3×D4—61no—
133#1009—22no—
134#1009—22no—
135#1009—22no—
136#1009C22×C314yes—
137C2×#239—21no—
138C2×D3×D4—22no—
139C2×D3×D4—21no—
140C2×#235—21no—
141C2×#235C22×C311yescharacteristic
142C22×D12—21no—
143C22×D12C22×C311yescharacteristic
144C22×Dic6C22×C311yescharacteristic, complemented
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, complemented
156C2×C3×M16C22×C311yescharacteristic, complemented
157C3×#124—34no—
158C3×#124—62no—
159C2×C3×C22⋊C4—62no—
160C2×C3×C42—21no—
161C2×C3×C42C2×D311yescharacteristic, complemented
162C2×C3×C42C22×C311yescharacteristic, complemented
163#951—22no—
164#951C22×C314yescomplemented
165C2×#216—21no—
166C2×#214—21no—
167C2×(C2×D3)⋊C4—22no—
168C2×#208C22×C311yescharacteristic, complemented
169#909—22no—
170#909C22×C314yescomplemented
171C2×Dic12—21no—
172C2×#204—21no—
173#875—22no—
174#875C22×C314yescomplemented
175C3×#104—24no—
176C3×#104—34no—
177C3×#104C2×D314yescomplemented
178C3×#104C22×C314yescomplemented
179C3×#100—34no—
180#823C22×C314yescomplemented
181#805C22×C314yescomplemented
182C23×C32—21no—
183C23×C32C2×D411yescharacteristic
184C22×C3×D3—21no—
185C22×C3×D3—22no—
186C22×C3×D3—28no—
187C22×C3×D3—22no—
188C22×C3×D3—44no—
189C22×C3×D3—84no—
190C22×C3×D3C2×D414yes—
191C32×Q8—21no—
192C32×Q8C2×D412yes—
193C32×D4—22no—
194C32×D4—22no—
195C32×D4—21no—
196C32×D4C2×D412yes—
197C2×C32×C4—21no—
198C2×C32×C4—22no—
199C2×C32×C4—22no—
200C2×C32×C4—22no—
201C2×C32×C4—42no—
202C2×C32×C4C2×D411yescharacteristic
203C2×C32×C4C2×D411yescharacteristic
204C2×C32×C4C2×D411yescharacteristic
205C2×C32×C4C2×D411yescharacteristic
206C2×C32×C4C2×D411yescharacteristic
207C2×C32×C4C2411yescharacteristic
208C3×#67—28no—
209C3×#67—22no—
210C3×#67—22no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—41no—
214C2×C3×Dic3—41no—
215C3×D12—28no—
216C3×D12—22no—
217C3×D12—21no—
218C3×D12—22no—
219C3×D12—22no—
220C3×D12—22no—
221C3×D12C2×D412yes—
222C3×C4×D3—28no—
223C3×C4×D3—22no—
224C3×C4×D3—22no—
225C3×Dic6—21no—
226C3×Dic6—22no—
227C3×Dic6—22no—
228C3×Dic6—41no—
229C3×Dic6—41no—
230C3×Dic6C2×D412yes—
231C32×C8—22no—
232C3×C3⋊C8—22no—
233C2×H(5,𝔽2)—31no—
234C2×#137—31no—
235C2×#137—31no—
236C2×#124—31no—
237#455—38no—
238C2×#104—31no—
239C2×#104C3×D311yescharacteristic, complemented
240C2×#100—31no—
241C24×C3—32no—
242C24×C3—62no—
243C23×D3—22no—
244C23×D3C3×D412yes—
245C3×#41—21no—
246C3×#41—21no—
247C3×#41—21no—
248C3×#41—21no—
249C3×#41—22no—
250C3×#41—22no—
251C3×#41—32no—
252C3×#41—32no—
253C3×#41—41no—
254C3×#41—41no—
255C3×#41—64no—
256C3×#41—64no—
257C3×#41—64no—
258C3×#41—64no—
259C3×#41—61no—
260C3×#41—61no—
261C3×#41D1212yes—
262C3×#41C3×D412yes—
263C3×#41C22×D312yes—
264C3×#41C23×C312yes—
265C2×C3×Q8—21no—
266C2×C3×Q8—31no—
267C2×C3×Q8—32no—
268C2×C3×Q8—61no—
269C2×C3×Q8—61no—
270C2×C3×Q8—61no—
271C2×C3×Q8—61no—
272C2×C3×Q8—61no—
273C2×C3×Q8D1211yescharacteristic
274C2×C3×Q8C3×D411yescharacteristic
275C2×C3×D4—21no—
276C2×C3×D4—21no—
277C2×C3×D4—21no—
278C2×C3×D4—31no—
279C2×C3×D4—32no—
280C2×C3×D4—32no—
281C2×C3×D4—41no—
282C2×C3×D4—64no—
283C2×C3×D4—62no—
284C2×C3×D4—64no—
285C2×C3×D4—68no—
286C2×C3×D4—68no—
287C2×C3×D4—64no—
288C2×C3×D4—62no—
289C2×C3×D4—61no—
290C2×C3×D4—64no—
291C2×C3×D4—61no—
292C2×C3×D4—61no—
293C2×C3×D4—61no—
294C2×C3×D4—61no—
295C2×C3×D4D1211yescharacteristic
296C2×C3×D4C3×D411yescharacteristic
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—41no—
303C22×C3×C4—41no—
304C22×C3×C4—62no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C23×C311yescharacteristic
309C2×#67—22no—
310C2×#67—21no—
311C22×Dic3—21no—
312#239—24no—
313#239—24no—
314D3×D4—28no—
315D3×D4—24no—
316D3×D4—28no—
317D3×D4—24no—
318#235—24no—
319#235—21no—
320#235—21no—
321#235—24no—
322#235C3×D412yes—
323#235C23×C312yes—
324C2×D12—22no—
325C2×D12—24no—
326C2×D12—21no—
327C2×D12—21no—
328C2×D12—21no—
329C2×D12—21no—
330C2×D12—24no—
331C2×D12C3×D412yes—
332C2×D12C3×D411yescharacteristic
333C2×D12C23×C312yes—
334C2×C4×D3—22no—
335C2×C4×D3—21no—
336C2×Dic6—21no—
337C2×Dic6—21no—
338C2×Dic6—21no—
339C2×Dic6—21no—
340C2×Dic6—21no—
341C2×Dic6C3×D411yescharacteristic
342C2×Dic6C23×C312yescomplemented
343C3×Q16—64no—
344C3×Q16—64no—
345C3×SD16—64no—
346C3×SD16—64no—
347C3×M16—21no—
348C3×M16—21no—
349C3×M16—22no—
350C3×M16—32no—
351C3×M16—41no—
352C3×M16—61no—
353C3×M16C22×D312yescomplemented
354C3×M16C23×C312yescomplemented
355C2×C3×C8—21no—
356C2×C3×C8—21no—
357C2×C3×C8—41no—
358C2×C3×C8—61no—
359C3×C22⋊C4—68no—
360C3×C42—21no—
361C3×C42—21no—
362C3×C42—22no—
363C3×C42—41no—
364C3×C42C22×D312yescomplemented
365C3×C42C23×C312yescomplemented
366#216—24no—
367#214—24no—
368(C2×D3)⋊C4—28no—
369#208—21no—
370#208C23×C312yescomplemented
371C2×C3⋊C8—21no—
372Dic12—24no—
373#204—24no—
374C22×C32—22no—
375C22×C32—22no—
376C22×C32—42no—
377C22×C32#12011yescharacteristic
378C22×C32#12011yescharacteristic
379C22×C32C22×D411yescharacteristic
380C2×C3×D3—24no—
381C2×C3×D3—22no—
382C2×C3×D3—44no—
383C2×C3×D3—42no—
384C2×C3×D3—44no—
385C2×C3×D3—82no—
386C2×C3×D3—88no—
387C32×C4—22no—
388C32×C4—42no—
389C32×C4#12011yescharacteristic
390C32×C4#12011yescharacteristic
391C32×C4C22×D411yescharacteristic
392C32×C4C22×D411yescharacteristic
393C3×Dic3—22no—
394C3×Dic3—42no—
395H(5,𝔽2)—34no—
396H(5,𝔽2)—62no—
397H(5,𝔽2)—62no—
398H(5,𝔽2)—62no—
399C2×#41—31no—
400C2×#41—61no—
401C2×#41—61no—
402C2×#41C2×C3×D311yescharacteristic
403C22×Q8—31no—
404C22×D4—31no—
405C22×D4—61no—
406C22×D4—62no—
407C22×D4—61no—
408#137—34no—
409#137—34no—
410#137—62no—
411#137—62no—
412C2×Q16—61no—
413C2×Q16—61no—
414C2×SD16—61no—
415C2×SD16—61no—
416C2×M16—31no—
417C2×M16C2×C3×D311yescharacteristic, complemented
418#124—34no—
419#124—62no—
420C2×C22⋊C4—62no—
421C2×C42C2×C3×D311yescharacteristic, complemented
422#104—34no—
423#104C2×C3×D314yescomplemented
424#100—34no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—34no—
429C23×C3—41no—
430C23×C3—68no—
431C23×C3—61no—
432C23×C3—62no—
433C23×C3—62no—
434C23×C3—124no—
435C23×C3—244no—
436C23×C3D3×D411yescharacteristic
437C23×C3C2×C3×D411yescharacteristic
438C22×D3—22no—
439C22×D3—21no—
440C22×D3—28no—
441C22×D3—22no—
442C22×D3—44no—
443C22×D3—84no—
444C22×D3C2×C3×D414yes—
445C3×Q8—21no—
446C3×Q8—21no—
447C3×Q8—22no—
448C3×Q8—32no—
449C3×Q8—41no—
450C3×Q8—61no—
451C3×Q8—62no—
452C3×Q8—62no—
453C3×Q8—121no—
454C3×Q8—121no—
455C3×Q8C2×D1212yes—
456C3×Q8C2×C3×D412yes—
457C3×D4—22no—
458C3×D4—22no—
459C3×D4—22no—
460C3×D4—22no—
461C3×D4—21no—
462C3×D4—21no—
463C3×D4—22no—
464C3×D4—32no—
465C3×D4—41no—
466C3×D4—42no—
467C3×D4—42no—
468C3×D4—68no—
469C3×D4—68no—
470C3×D4—62no—
471C3×D4—62no—
472C3×D4—61no—
473C3×D4—62no—
474C3×D4—62no—
475C3×D4—62no—
476C3×D4—62no—
477C3×D4C2×D1212yes—
478C3×D4C2×C3×D412yes—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—42no—
494C2×C3×C4—42no—
495C2×C3×C4—42no—
496C2×C3×C4—41no—
497C2×C3×C4—42no—
498C2×C3×C4—42no—
499C2×C3×C4—44no—
500C2×C3×C4—68no—
501C2×C3×C4—61no—
502C2×C3×C4—62no—
503C2×C3×C4—62no—
504C2×C3×C4—62no—
505C2×C3×C4—121no—
506C2×C3×C4—121no—
507C2×C3×C4C2×D1211yescharacteristic
508C2×C3×C4C2×D1211yescharacteristic
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4C2×C3×D411yescharacteristic
513C2×C3×C4C2×C3×D411yescharacteristic
514C2×C3×C4C2×C3×D411yescharacteristic
515C2×C3×C4C2×C3×D411yescharacteristic
516C2×C3×C4C2×C3×D411yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C24×C311yescharacteristic
519#67—28no—
520#67—22no—
521#67—22no—
522C2×Dic3—21no—
523C2×Dic3—22no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526D12—28no—
527D12—22no—
528D12—21no—
529D12—22no—
530D12—22no—
531D12—22no—
532D12C2×C3×D412yes—
533C4×D3—28no—
534C4×D3—22no—
535C4×D3—22no—
536Dic6—21no—
537Dic6—22no—
538Dic6—22no—
539Dic6—41no—
540Dic6—41no—
541Dic6C2×C3×D412yes—
542C3×C8—22no—
543C3×C8—22no—
544C3×C8—42no—
545C3×C8—62no—
546C3⋊C8—22no—
547C2×C32—21no—
548C2×C32—21no—
549C2×C32—42no—
550C2×C32#45512yescomplemented
551C2×C32C2×#12011yescharacteristic
552C3×D3—44no—
553C3×D3—42no—
554C24—32no—
555C24—62no—
556#41—21no—
557#41—21no—
558#41—32no—
559#41—32no—
560#41—64no—
561#41—64no—
562#41—64no—
563#41—64no—
564#41—61no—
565#41—61no—
566#41C3×D1212yes—
567#41C22×C3×D312yes—
568C2×Q8—32no—
569C2×Q8—31no—
570C2×Q8—61no—
571C2×Q8—61no—
572C2×Q8—61no—
573C2×Q8—61no—
574C2×Q8—61no—
575C2×Q8C3×D1211yescharacteristic
576C2×D4—21no—
577C2×D4—32no—
578C2×D4—31no—
579C2×D4—32no—
580C2×D4—64no—
581C2×D4—62no—
582C2×D4—64no—
583C2×D4—68no—
584C2×D4—68no—
585C2×D4—64no—
586C2×D4—62no—
587C2×D4—61no—
588C2×D4—64no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4—61no—
593C2×D4C3×D1211yescharacteristic
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—62no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4C22×C3×D311yescharacteristic
600Q16—64no—
601Q16—64no—
602SD16—64no—
603SD16—64no—
604M16—21no—
605M16—32no—
606M16—61no—
607M16C22×C3×D312yescomplemented
608C2×C8—21no—
609C2×C8—61no—
610C22⋊C4—68no—
611C42—21no—
612C42C22×C3×D312yescomplemented
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—42no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—62no—
625C22×C3—64no—
626C22×C3—82no—
627C22×C3—124no—
628C22×C3—124no—
629C22×C3—122no—
630C22×C3—242no—
631C22×C3—248no—
632C22×C3#88211yescharacteristic
633C22×C3#88211yescharacteristic
634C22×C3C3×#12011yescharacteristic
635C22×C3C3×#12011yescharacteristic
636C22×C3C2×D3×D411yescharacteristic
637C22×C3C22×C3×D411yescharacteristic
638C2×D3—24no—
639C2×D3—22no—
640C2×D3—44no—
641C2×D3—42no—
642C2×D3—44no—
643C2×D3—82no—
644C2×D3—88no—
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—42no—
652C3×C4—42no—
653C3×C4—42no—
654C3×C4—44no—
655C3×C4—62no—
656C3×C4—122no—
657C3×C4#88211yescharacteristic
658C3×C4#88211yescharacteristic
659C3×C4C3×#12011yescharacteristic
660C3×C4C3×#12011yescharacteristic
661C3×C4C22×D1211yescharacteristic
662C3×C4C2×D3×D411yescharacteristic
663C3×C4C22×C3×D411yescharacteristic
664C3×C4C22×C3×D411yescharacteristic
665Dic3—22no—
666Dic3—42no—
667C32C2×#45511yescharacteristic, complemented, Sylow
668C23—21no—
669C23—34no—
670C23—68no—
671C23—61no—
672C23—62no—
673C23—62no—
674C23—124no—
675C23—244no—
676C23C3×D3×D411yescharacteristic
677Q8—21no—
678Q8—32no—
679Q8—61no—
680Q8—62no—
681Q8—62no—
682Q8—121no—
683Q8—121no—
684Q8C2×C3×D1212yes—
685D4—22no—
686D4—22no—
687D4—21no—
688D4—32no—
689D4—68no—
690D4—68no—
691D4—62no—
692D4—62no—
693D4—61no—
694D4—62no—
695D4—62no—
696D4—62no—
697D4—62no—
698D4C2×C3×D1212yes—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—42no—
704C2×C4—68no—
705C2×C4—61no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4C2×C3×D1211yescharacteristic
712C2×C4C2×C3×D1211yescharacteristic
713C2×C4C3×D3×D411yescharacteristic
714C2×C4C3×D3×D411yescharacteristic
715C2×C4C3×D3×D411yescharacteristic
716C2×C4C23×C3×D311yescharacteristic
717C8—22no—
718C8—62no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—22no—
725C2×C3—41no—
726C2×C3—41no—
727C2×C3—42no—
728C2×C3—42no—
729C2×C3—82no—
730C2×C3—124no—
731C2×C3—122no—
732C2×C3#482512yesdirect product factor
733C2×C3C3×#45512yescomplemented
734C2×C3C2×#88211yescharacteristic
735C2×C3C2×C3×#12011yescharacteristic
736D3—44no—
737D3—42no—
738C22—22no—
739C22—22no—
740C22—42no—
741C22—62no—
742C22—64no—
743C22—124no—
744C22—124no—
745C22—122no—
746C22—242no—
747C22—248no—
748C22C3×#88211yescharacteristic
749C22C3×#88211yescharacteristic
750C22C2×C3×D3×D411yescharacteristic
751C4—22no—
752C4—42no—
753C4—62no—
754C4—122no—
755C4C3×#88211yescharacteristic
756C4C3×#88211yescharacteristic
757C4C22×C3×D1211yescharacteristic
758C4C2×C3×D3×D411yescharacteristic
759C3—21no—
760C3C2×#482511yescharacteristic, direct product factor
761C3C2×C3×#45511yescharacteristic, complemented
762C2—21no—
763C2—21no—
764C2—42no—
765C2—124no—
766C2—122no—
767C2C3×#482512yesdirect product factor
768C2C2×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×#1009C2
hypercenterC2×C3×#104D3
hypocenterC3C2×C3×#455
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×#875C2semidirect
5. C2×C32×#104C2semidirect
6. C2×C3×#823C2semidirect
7. C2×C3×#805C2semidirect
8. C3×#4825C2direct (N × H)
10. C2×#4825C3direct (N × H)
23. C22×C3×Dic6C22semidirect
24. C2×C32×M16C22semidirect
25. C2×C32×C42C22semidirect
27. C3×#951C22semidirect
31. C2×C3×#208C22semidirect
33. C3×#909C22semidirect
37. C3×#875C22semidirect
38. C32×#104C22semidirect
39. C3×#823C22semidirect
40. C3×#805C22semidirect
46. C2×#951C2×C3semidirect
47. C2×#909C2×C3semidirect
48. C2×#875C2×C3semidirect
52. C2×C3×#104D3semidirect
53. C2×C3×#104C2×C3semidirect
55. C2×#823C2×C3semidirect
56. C2×#805C2×C3semidirect
57. #4825C2×C3direct (N × H)
103. C2×C3×Dic6C23semidirect
105. C32×M16C23semidirect
108. C32×C42C23semidirect
113. C3×#208C23semidirect
144. C22×Dic6C22×C3semidirect
155. C2×C3×M16C2×D3semidirect
156. C2×C3×M16C22×C3semidirect
161. C2×C3×C42C2×D3semidirect
162. C2×C3×C42C22×C3semidirect
164. #951C22×C3semidirect
168. C2×#208C22×C3semidirect
170. #909C22×C3semidirect
174. #875C22×C3semidirect
177. C3×#104C2×D3semidirect
178. C3×#104C22×C3semidirect
180. #823C22×C3semidirect
181. #805C22×C3semidirect
239. C2×#104C3×D3semidirect
342. C2×Dic6C23×C3semidirect
353. C3×M16C22×D3semidirect
354. C3×M16C23×C3semidirect
364. C3×C42C22×D3semidirect
365. C3×C42C23×C3semidirect
370. #208C23×C3semidirect
417. C2×M16C2×C3×D3semidirect
421. C2×C42C2×C3×D3semidirect
423. #104C2×C3×D3semidirect
550. C2×C32#455semidirect
607. M16C22×C3×D3semidirect
612. C42C22×C3×D3semidirect
667. C32C2×#455semidirect
732. C2×C3#4825direct (N × H)
733. C2×C3C3×#455semidirect
760. C3C2×#4825direct (N × H)
761. C3C2×C3×#455semidirect
767. C2C3×#4825direct (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×C3×#9512
C2×C3×#9092
C2×C3×#8752
C2×C32×#1042
C2×C3×#8232
C2×C3×#8052
C3×#48252
C2×C3×#4553
C2×#48253