Finite Group Databasebeta

← C3×#78747 #11864580

Subgroups — C3×#78747 #11864580

Order 1152.

1629 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic, complemented
3C2×C3×#904C211yesmaximal, characteristic, complemented
4C3×#5510C211yesmaximal, characteristic, complemented
5C2×C32×#102C211yesmaximal, characteristic, complemented
6C3×#5110C211yesmaximal, characteristic, complemented
7C3×#4966C211yesmaximal, characteristic, complemented
8C3×#4783C212yesmaximal, complemented
9C3×#4781C212yesmaximal, complemented
10C3×#4776C212yesmaximal, complemented
11C3×#4773C212yesmaximal, complemented
12C3×#3012—31nomaximal
13#78747C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2211yescharacteristic
15C22×C3×#67—22no—
16C3×#1004—24no—
17C3×#1004—24no—
18C2×C3×#237—21no—
19C2×C3×#237C2212yes—
20C2×C3×D3×D4—21no—
21C2×C3×D3×D4C2212yes—
22C2×C3×#235C2211yescharacteristic
23C2×C3×#235C2211yescharacteristic
24C2×C3×#235C2211yescharacteristic, complemented
25C22×C32×C8C2211yescharacteristic, complemented
26C2×C32×C4⋊C4C2211yescharacteristic, complemented
27C2×C3×#214C2212yescomplemented
28C3×#932—24no—
29C2×C3×#213C2212yescomplemented
30C3×#930—22no—
31C2×C3×#208C2211yescharacteristic, complemented
32C2×C3×Dic12C2211yescharacteristic, complemented
33C3×#904—24no—
34C2×C3×D24C2211yescharacteristic, complemented
35C2×C3×#204C2211yescharacteristic, complemented
36C2×C3×#204C2211yescharacteristic, complemented
37C3×#897—21no—
38C3×#897C2212yescomplemented
39C3×#895—21no—
40C3×#895C2212yescomplemented
41C32×#102C2212yescomplemented
42C32×#102C2212yescomplemented
43C3×(C2×D3)⋊C8C2212yescomplemented
44C3×(C2×D3)⋊C8C2212yescomplemented
45C3×#810C2212yescomplemented
46C3×#809C2212yescomplemented
47C2×C3×H(5,𝔽2)—31no—
48C2×#1004C2×C311yescharacteristic, complemented
49C2×C3×AGL(1,ℤ/8)—31no—
50C2×C3×#135—31no—
51C3×#537—31no—
52C2×#932C2×C311yescharacteristic, complemented
53C2×#904C2×C311yescharacteristic, complemented
54#5510C2×C311yescharacteristic, complemented
55C3×#452—32no—
56C3×#450—32no—
57C3×#449—32no—
58C3×#447—32no—
59C3×#417—31no—
60C2×C3×#102—21no—
61C2×C3×#102D311yescharacteristic, complemented
62C2×C3×#102C2×C311yescharacteristic, complemented
63C3×#408—31no—
64#5110C2×C311yescharacteristic, complemented
65#4966C2×C311yescharacteristic, complemented
66#4783C2×C312yescomplemented
67#4781C2×C312yescomplemented
68#4776C2×C312yescomplemented
69#4773C2×C312yescomplemented
70C24×C32—21no—
71C23×C3×D3—22no—
72C2×C32×D4—21no—
73C2×C32×D4—22no—
74C2×C32×D4D414yescomplemented
75C2×C32×D4C2312yes—
76C22×C32×C4—21no—
77C22×C32×C4C2311yescharacteristic
78C2×C3×#67—216no—
79C2×C3×#67—21no—
80C2×C3×#67—22no—
81C2×C3×#67—21no—
82C2×C3×#67—22no—
83C2×C3×#67D412yes—
84C22×C3×Dic3—22no—
85C3×#237—28no—
86C3×#237—24no—
87C3×#237—24no—
88C3×D3×D4—28no—
89C3×D3×D4—24no—
90C3×D3×D4—24no—
91C3×#235—22no—
92C3×#235—22no—
93C3×#235—22no—
94C3×#235—22no—
95C3×#235—22no—
96C3×#235D414yescomplemented
97C2×C3×D12—22no—
98C2×C3×D12D411yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2312yes—
104C2×C3×Dic6D411yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C32×C8—22no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2312yes—
112C3×#214—24no—
113C3×#213—24no—
114C3×(C2×D3)⋊C4—22no—
115C3×(C2×D3)⋊C4—22no—
116C3×C4⋊Dic3—22no—
117C3×#208—22no—
118C2×C3×C3⋊C8C2312yes—
119C3×Dic12—22no—
120C3×D24—22no—
121C3×#204—22no—
122C3×#204—22no—
123#3012—31noSylow
124C3×H(5,𝔽2)—64no—
125C3×H(5,𝔽2)—64no—
126C2×C3×#41—31no—
127C2×C3×#41—32no—
128C2×C3×#41—31no—
129C2×C3×#41—31no—
130C2×C3×#41—61no—
131C22×C3×D4—21no—
132C22×C3×D4—32no—
133C22×C3×D4—61no—
134C22×C3×D4—62no—
135C22×C3×D4C2×D311yescharacteristic
136C22×C3×D4C22×C311yescharacteristic
137C22×#67—22no—
138#1004—24no—
139#1004—24no—
140C2×#237—21no—
141C2×#237C22×C312yes—
142C2×D3×D4—21no—
143C2×D3×D4C22×C312yes—
144C2×#235C22×C311yescharacteristic
145C2×#235C22×C311yescharacteristic
146C2×#235C22×C311yescharacteristic, complemented
147C3×AGL(1,ℤ/8)—64no—
148C3×#135—64no—
149C2×C3×Q16—31no—
150C2×C3×SD16—32no—
151C2×C3×SD16—31no—
152C2×C3×SD16—31no—
153C2×C3×D8—32no—
154C2×C3×D8—31no—
155C2×C3×M16—31no—
156C22×C3×C8—21no—
157C22×C3×C8C2×D311yescharacteristic, complemented
158C22×C3×C8C22×C311yescharacteristic, complemented
159C3×C22⋊Q8—32no—
160C3×C22⋊Q8—61no—
161C3×#121—32no—
162C3×#121—61no—
163C3×#121—62no—
164C2×C3×C4⋊C4—21no—
165C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
166C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
167C2×#214C22×C312yescomplemented
168#932—24no—
169C2×#213C22×C312yescomplemented
170#930—22no—
171C2×#208C22×C311yescharacteristic, complemented
172C2×Dic12C22×C311yescharacteristic, complemented
173#904—24no—
174C2×D24C22×C311yescharacteristic, complemented
175C2×#204C22×C311yescharacteristic, complemented
176C2×#204C22×C311yescharacteristic, complemented
177#897—21no—
178#897C22×C312yescomplemented
179#895—21no—
180#895C22×C312yescomplemented
181C3×#103—32no—
182C3×#102—22no—
183C3×#102—22no—
184C3×#102—32no—
185C3×#102C2×D312yescomplemented
186C3×#102C2×D312yescomplemented
187C3×#102C22×C312yescomplemented
188C3×#102C22×C312yescomplemented
189C3×C22⋊C8—32no—
190C3×C22⋊C8—32no—
191(C2×D3)⋊C8C22×C312yescomplemented
192(C2×D3)⋊C8C22×C312yescomplemented
193#810C22×C312yescomplemented
194#809C22×C312yescomplemented
195C23×C32—22no—
196C23×C32—24no—
197C23×C32—81no—
198C23×C32—81no—
199C23×C32C2×D411yescharacteristic
200C22×C3×D3—21no—
201C22×C3×D3—28no—
202C22×C3×D3—21no—
203C22×C3×D3—82no—
204C22×C3×D3—82no—
205C22×C3×D3C2×D412yes—
206C32×D4—24no—
207C32×D4—22no—
208C32×D4C2×D414yes—
209C2×C32×C4—22no—
210C2×C32×C4—81no—
211C2×C32×C4C2×D412yes—
212C2×C32×C4C2×D411yescharacteristic
213C2×C32×C4C2×D412yes—
214C2×C32×C4C2411yescharacteristic
215C3×#67—28no—
216C3×#67—28no—
217C3×#67—24no—
218C3×#67—24no—
219C3×#67—42no—
220C2×C3×Dic3—28no—
221C2×C3×Dic3—21no—
222C2×C3×Dic3—21no—
223C2×C3×Dic3C2×D412yes—
224C3×D12—22no—
225C3×D12—21no—
226C3×D12—21no—
227C3×D12—21no—
228C3×D12—82no—
229C3×D12C2×D412yes—
230C3×C4×D3—24no—
231C3×C4×D3—22no—
232C3×C4×D3—22no—
233C3×C4×D3—42no—
234C3×Dic6—22no—
235C3×Dic6—21no—
236C3×Dic6—21no—
237C3×Dic6—21no—
238C3×Dic6C2×D412yes—
239C32×C8—21no—
240C32×C8—21no—
241C3×C3⋊C8—22no—
242C2×H(5,𝔽2)—31no—
243C2×AGL(1,ℤ/8)—31no—
244C2×#135—31no—
245#537—31no—
246#452—32no—
247#450—32no—
248#449—32no—
249#447—32no—
250#417—31no—
251C2×#102C3×D311yescharacteristic, complemented
252#408—31no—
253C24×C3—21no—
254C24×C3—21no—
255C24×C3—41no—
256C24×C3—62no—
257C23×D3—22no—
258C3×#41—34no—
259C3×#41—64no—
260C3×#41—68no—
261C3×#41—64no—
262C3×#41—62no—
263C3×#41—62no—
264C3×#41—62no—
265C3×#41—62no—
266C3×#41—62no—
267C2×C3×Q8—31no—
268C2×C3×Q8—31no—
269C2×C3×Q8—31no—
270C2×C3×D4—21no—
271C2×C3×D4—22no—
272C2×C3×D4—21no—
273C2×C3×D4—22no—
274C2×C3×D4—24no—
275C2×C3×D4—22no—
276C2×C3×D4—32no—
277C2×C3×D4—31no—
278C2×C3×D4—31no—
279C2×C3×D4—31no—
280C2×C3×D4—41no—
281C2×C3×D4—42no—
282C2×C3×D4—62no—
283C2×C3×D4—62no—
284C2×C3×D4—64no—
285C2×C3×D4—68no—
286C2×C3×D4—62no—
287C2×C3×D4—616no—
288C2×C3×D4—61no—
289C2×C3×D4—64no—
290C2×C3×D4—61no—
291C2×C3×D4D1214yescomplemented
292C2×C3×D4C3×D414yescomplemented
293C2×C3×D4C22×D312yes—
294C2×C3×D4C23×C312yes—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—32no—
299C22×C3×C4—41no—
300C22×C3×C4—62no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C23×C311yescharacteristic
305C2×#67—216no—
306C2×#67—21no—
307C2×#67—22no—
308C2×#67—21no—
309C2×#67—22no—
310C2×#67C3×D412yes—
311C22×Dic3—22no—
312#237—28no—
313#237—24no—
314#237—24no—
315D3×D4—28no—
316D3×D4—24no—
317D3×D4—24no—
318#235—22no—
319#235—22no—
320#235—22no—
321#235—22no—
322#235—22no—
323#235C3×D414yescomplemented
324C2×D12—22no—
325C2×D12C3×D411yescharacteristic
326C2×D12C23×C311yescharacteristic
327C2×D12C23×C311yescharacteristic
328C2×C4×D3—21no—
329C2×C4×D3—21no—
330C2×C4×D3C23×C312yes—
331C2×Dic6C3×D411yescharacteristic
332C2×Dic6C23×C311yescharacteristic
333C2×Dic6C23×C311yescharacteristic
334C3×Q16—62no—
335C3×SD16—62no—
336C3×SD16—62no—
337C3×SD16—64no—
338C3×D8—62no—
339C3×D8—64no—
340C3×M16—62no—
341C2×C3×C8—22no—
342C2×C3×C8—22no—
343C2×C3×C8—21no—
344C2×C3×C8—21no—
345C2×C3×C8—32no—
346C2×C3×C8—42no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C23×C311yescharacteristic
350C2×C3×C8C23×C311yescharacteristic
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—22no—
354C3×C4⋊C4—41no—
355C3×C4⋊C4—62no—
356C3×C4⋊C4C22×D312yes—
357C3×C4⋊C4C23×C312yes—
358C3×C22⋊C4—62no—
359C3×C22⋊C4—62no—
360#214—24no—
361#213—24no—
362(C2×D3)⋊C4—22no—
363(C2×D3)⋊C4—22no—
364C4⋊Dic3—22no—
365#208—22no—
366C2×C3⋊C8C23×C312yes—
367Dic12—22no—
368D24—22no—
369#204—22no—
370#204—22no—
371C22×C32—21no—
372C22×C32—21no—
373C22×C32—24no—
374C22×C32—42no—
375C22×C32—42no—
376C22×C32—84no—
377C22×C32#12012yes—
378C22×C32C22×D411yescharacteristic
379C2×C3×D3—22no—
380C2×C3×D3—22no—
381C2×C3×D3—22no—
382C2×C3×D3—22no—
383C2×C3×D3—41no—
384C2×C3×D3—41no—
385C2×C3×D3—41no—
386C2×C3×D3—41no—
387C2×C3×D3—41no—
388C2×C3×D3—88no—
389C32×C4—42no—
390C32×C4#12012yes—
391C32×C4C22×D411yescharacteristic
392C32×C4C22×D411yescharacteristic
393C3×Dic3—22no—
394C3×Dic3—22no—
395C3×Dic3—41no—
396H(5,𝔽2)—64no—
397H(5,𝔽2)—64no—
398C2×#41—31no—
399C2×#41—32no—
400C2×#41—31no—
401C2×#41—31no—
402C2×#41—61no—
403C22×D4—32no—
404C22×D4—61no—
405C22×D4—62no—
406C22×D4C2×C3×D311yescharacteristic
407AGL(1,ℤ/8)—64no—
408#135—64no—
409C2×Q16—31no—
410C2×SD16—32no—
411C2×SD16—31no—
412C2×SD16—31no—
413C2×D8—32no—
414C2×D8—31no—
415C2×M16—31no—
416C22×C8C2×C3×D311yescharacteristic, complemented
417C22⋊Q8—32no—
418C22⋊Q8—61no—
419#121—32no—
420#121—61no—
421#121—62no—
422C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
423#103—32no—
424#102—32no—
425#102C2×C3×D312yescomplemented
426#102C2×C3×D312yescomplemented
427C22⋊C8—32no—
428C22⋊C8—32no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—24no—
432C23×C3—24no—
433C23×C3—21no—
434C23×C3—32no—
435C23×C3—42no—
436C23×C3—44no—
437C23×C3—68no—
438C23×C3—61no—
439C23×C3—61no—
440C23×C3—81no—
441C23×C3—81no—
442C23×C3—81no—
443C23×C3—81no—
444C23×C3—82no—
445C23×C3—82no—
446C23×C3—242no—
447C23×C3—242no—
448C23×C3D3×D411yescharacteristic
449C23×C3C2×C3×D411yescharacteristic
450C22×D3—21no—
451C22×D3—28no—
452C22×D3—21no—
453C22×D3—82no—
454C22×D3—82no—
455C22×D3C2×C3×D412yes—
456C3×Q8—32no—
457C3×Q8—62no—
458C3×Q8—61no—
459C3×Q8—61no—
460C3×Q8—61no—
461C3×D4—24no—
462C3×D4—24no—
463C3×D4—22no—
464C3×D4—22no—
465C3×D4—24no—
466C3×D4—32no—
467C3×D4—44no—
468C3×D4—42no—
469C3×D4—68no—
470C3×D4—68no—
471C3×D4—64no—
472C3×D4—64no—
473C3×D4—62no—
474C3×D4—61no—
475C3×D4—61no—
476C3×D4—61no—
477C3×D4—122no—
478C3×D4—242no—
479C3×D4C2×D1214yes—
480C3×D4C2×C3×D414yes—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—21no—
484C2×C3×C4—22no—
485C2×C3×C4—21no—
486C2×C3×C4—22no—
487C2×C3×C4—32no—
488C2×C3×C4—42no—
489C2×C3×C4—68no—
490C2×C3×C4—61no—
491C2×C3×C4—64no—
492C2×C3×C4—62no—
493C2×C3×C4—62no—
494C2×C3×C4—61no—
495C2×C3×C4—81no—
496C2×C3×C4—81no—
497C2×C3×C4—82no—
498C2×C3×C4—122no—
499C2×C3×C4C2×D1212yes—
500C2×C3×C4D3×D411yescharacteristic
501C2×C3×C4D3×D412yes—
502C2×C3×C4C2×C3×D412yes—
503C2×C3×C4C2×C3×D411yescharacteristic
504C2×C3×C4C2×C3×D412yes—
505C2×C3×C4C23×D311yescharacteristic
506C2×C3×C4C24×C311yescharacteristic
507#67—28no—
508#67—28no—
509#67—24no—
510#67—24no—
511#67—42no—
512C2×Dic3—28no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3C2×C3×D412yes—
516D12—22no—
517D12—21no—
518D12—21no—
519D12—21no—
520D12—82no—
521D12C2×C3×D412yes—
522C4×D3—24no—
523C4×D3—22no—
524C4×D3—22no—
525C4×D3—42no—
526Dic6—22no—
527Dic6—21no—
528Dic6—21no—
529Dic6—21no—
530Dic6C2×C3×D412yes—
531C3×C8—21no—
532C3×C8—21no—
533C3×C8—21no—
534C3×C8—21no—
535C3×C8—41no—
536C3×C8—41no—
537C3×C8—62no—
538C3⋊C8—22no—
539C2×C32—22no—
540C2×C32—44no—
541C2×C32C2×#12011yescharacteristic
542C2×C32#57611yescharacteristic
543C2×C32#57711yescharacteristic
544C3×D3—42no—
545C3×D3—42no—
546C3×D3—81no—
547C24—21no—
548C24—62no—
549#41—34no—
550#41—64no—
551#41—68no—
552#41—64no—
553#41—62no—
554#41—62no—
555#41—62no—
556#41—62no—
557#41—62no—
558C2×Q8—31no—
559C2×Q8—31no—
560C2×Q8—31no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—32no—
564C2×D4—31no—
565C2×D4—31no—
566C2×D4—31no—
567C2×D4—62no—
568C2×D4—62no—
569C2×D4—64no—
570C2×D4—68no—
571C2×D4—62no—
572C2×D4—616no—
573C2×D4—61no—
574C2×D4—64no—
575C2×D4—61no—
576C2×D4C3×D1214yescomplemented
577C2×D4C22×C3×D312yes—
578C22×C4—21no—
579C22×C4—32no—
580C22×C4—62no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4C22×C3×D311yescharacteristic
584Q16—62no—
585SD16—62no—
586SD16—62no—
587SD16—64no—
588D8—62no—
589D8—64no—
590M16—62no—
591C2×C8—22no—
592C2×C8—32no—
593C2×C8C22×C3×D311yescharacteristic
594C2×C8C22×C3×D311yescharacteristic
595C4⋊C4—21no—
596C4⋊C4—62no—
597C4⋊C4C22×C3×D312yes—
598C22⋊C4—62no—
599C22⋊C4—62no—
600C22×C3—22no—
601C22×C3—22no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—24no—
607C22×C3—24no—
608C22×C3—22no—
609C22×C3—21no—
610C22×C3—44no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—42no—
615C22×C3—62no—
616C22×C3—62no—
617C22×C3—62no—
618C22×C3—62no—
619C22×C3—82no—
620C22×C3—82no—
621C22×C3—84no—
622C22×C3—84no—
623C22×C3—88no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3—121no—
627C22×C3—121no—
628C22×C3—121no—
629C22×C3—248no—
630C22×C3#88212yes—
631C22×C3C3×#12012yes—
632C22×C3C2×D3×D411yescharacteristic
633C22×C3C22×C3×D411yescharacteristic
634C2×D3—22no—
635C2×D3—22no—
636C2×D3—22no—
637C2×D3—22no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—41no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—88no—
644C3×C4—22no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—42no—
648C3×C4—42no—
649C3×C4—62no—
650C3×C4—62no—
651C3×C4—82no—
652C3×C4—121no—
653C3×C4#88212yes—
654C3×C4C3×#12012yes—
655C3×C4C22×D1211yescharacteristic
656C3×C4C2×D3×D411yescharacteristic
657C3×C4C22×C3×D411yescharacteristic
658C3×C4C22×C3×D411yescharacteristic
659Dic3—22no—
660Dic3—22no—
661Dic3—41no—
662C32#301211yescharacteristic, complemented, Sylow
663C23—22no—
664C23—24no—
665C23—32no—
666C23—68no—
667C23—61no—
668C23—61no—
669C23—81no—
670C23—81no—
671C23—242no—
672C23—242no—
673C23C3×D3×D411yescharacteristic
674Q8—32no—
675Q8—62no—
676Q8—61no—
677Q8—61no—
678Q8—61no—
679D4—24no—
680D4—22no—
681D4—32no—
682D4—68no—
683D4—68no—
684D4—64no—
685D4—64no—
686D4—62no—
687D4—61no—
688D4—61no—
689D4—61no—
690D4—122no—
691D4—242no—
692D4C2×C3×D1214yes—
693C2×C4—22no—
694C2×C4—32no—
695C2×C4—68no—
696C2×C4—61no—
697C2×C4—64no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—61no—
701C2×C4—81no—
702C2×C4—122no—
703C2×C4C2×C3×D1212yes—
704C2×C4C3×D3×D411yescharacteristic
705C2×C4C3×D3×D412yes—
706C2×C4C23×C3×D311yescharacteristic
707C8—21no—
708C8—21no—
709C8—62no—
710C2×C3—24no—
711C2×C3—22no—
712C2×C3—22no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—44no—
717C2×C3—44no—
718C2×C3—84no—
719C2×C3—122no—
720C2×C3—122no—
721C2×C3—241no—
722C2×C3C2×#88211yescharacteristic
723C2×C3#575711yescharacteristic
724C2×C3#576211yescharacteristic
725C2×C3C2×C3×#12011yescharacteristic
726C2×C3C3×#57611yescharacteristic
727C2×C3C3×#57711yescharacteristic
728D3—42no—
729D3—42no—
730D3—81no—
731C22—21no—
732C22—21no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—62no—
737C22—62no—
738C22—62no—
739C22—62no—
740C22—84no—
741C22—121no—
742C22—121no—
743C22—121no—
744C22—121no—
745C22—121no—
746C22—248no—
747C22C3×#88212yes—
748C22C2×C3×D3×D411yescharacteristic
749C4—42no—
750C4—62no—
751C4—62no—
752C4—121no—
753C4C3×#88212yes—
754C4C22×C3×D1211yescharacteristic
755C4C2×C3×D3×D411yescharacteristic
756C3—21no—
757C3#7874711yescharacteristic, direct product factor
758C3C3×#301211yescharacteristic, complemented
759C2—22no—
760C2—44no—
761C2—122no—
762C2—122no—
763C2—241no—
764C2C2×C3×#88211yescharacteristic
765C2C3×#575711yescharacteristic
766C2C3×#576211yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#102C2
socleC22×C32C22×D4
hypercenterC2×C3×#102D3
hypocenterC3C3×#3012
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1004C2semidirect
2. C2×C3×#932C2semidirect
3. C2×C3×#904C2semidirect
4. C3×#5510C2semidirect
5. C2×C32×#102C2semidirect
6. C3×#5110C2semidirect
7. C3×#4966C2semidirect
8. C3×#4783C2semidirect
9. C3×#4781C2semidirect
10. C3×#4776C2semidirect
11. C3×#4773C2semidirect
13. #78747C3direct (N × H)
24. C2×C3×#235C22semidirect
25. C22×C32×C8C22semidirect
26. C2×C32×C4⋊C4C22semidirect
27. C2×C3×#214C22semidirect
29. C2×C3×#213C22semidirect
31. C2×C3×#208C22semidirect
32. C2×C3×Dic12C22semidirect
34. C2×C3×D24C22semidirect
35. C2×C3×#204C22semidirect
36. C2×C3×#204C22semidirect
38. C3×#897C22semidirect
40. C3×#895C22semidirect
41. C32×#102C22semidirect
42. C32×#102C22semidirect
43. C3×(C2×D3)⋊C8C22semidirect
44. C3×(C2×D3)⋊C8C22semidirect
45. C3×#810C22semidirect
46. C3×#809C22semidirect
48. C2×#1004C2×C3semidirect
52. C2×#932C2×C3semidirect
53. C2×#904C2×C3semidirect
54. #5510C2×C3semidirect
61. C2×C3×#102D3semidirect
62. C2×C3×#102C2×C3semidirect
64. #5110C2×C3semidirect
65. #4966C2×C3semidirect
66. #4783C2×C3semidirect
67. #4781C2×C3semidirect
68. #4776C2×C3semidirect
69. #4773C2×C3semidirect
74. C2×C32×D4D4semidirect
96. C3×#235D4semidirect
146. C2×#235C22×C3semidirect
157. C22×C3×C8C2×D3semidirect
158. C22×C3×C8C22×C3semidirect
165. C2×C3×C4⋊C4C2×D3semidirect
166. C2×C3×C4⋊C4C22×C3semidirect
167. C2×#214C22×C3semidirect
169. C2×#213C22×C3semidirect
171. C2×#208C22×C3semidirect
172. C2×Dic12C22×C3semidirect
174. C2×D24C22×C3semidirect
175. C2×#204C22×C3semidirect
176. C2×#204C22×C3semidirect
178. #897C22×C3semidirect
180. #895C22×C3semidirect
185. C3×#102C2×D3semidirect
186. C3×#102C2×D3semidirect
187. C3×#102C22×C3semidirect
188. C3×#102C22×C3semidirect
191. (C2×D3)⋊C8C22×C3semidirect
192. (C2×D3)⋊C8C22×C3semidirect
193. #810C22×C3semidirect
194. #809C22×C3semidirect
251. C2×#102C3×D3semidirect
291. C2×C3×D4D12semidirect
292. C2×C3×D4C3×D4semidirect
323. #235C3×D4semidirect
416. C22×C8C2×C3×D3semidirect
422. C2×C4⋊C4C2×C3×D3semidirect
425. #102C2×C3×D3semidirect
426. #102C2×C3×D3semidirect
576. C2×D4C3×D12semidirect
662. C32#3012semidirect
757. C3#78747direct (N × H)
758. C3C3×#3012semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C2×C3×#9322
C2×C3×#9042
C3×#55102
C2×C32×#1022
C3×#51102
C3×#49662
C3×#47832
C3×#47812
C3×#47762
C3×#47732
C3×#30123
#787473