Finite Group Databasebeta

← C3×#74146 #11856258

Subgroups — C3×#74146 #11856258

Order 1152.

2313 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D3C211yesmaximal, characteristic, complemented
2C2×C3×#929C211yesmaximal, characteristic, complemented
3C2×C3×#886C211yesmaximal, characteristic, complemented
4C2×C3×#882C211yesmaximal, characteristic
5C32×#381C211yesmaximal, characteristic, complemented
6C3×#4955C211yesmaximal, characteristic, complemented
7C3×#4943C211yesmaximal, characteristic, complemented
8C3×#4668C214yesmaximal, complemented
9C3×#4665C214yesmaximal, complemented
10C3×#2849—31nomaximal
11#74146C311yesmaximal, characteristic, direct product factor
12C24×C3×D3C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C22×C3×#67C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C22×C3×D12C2212yes—
17C22×C3×C4×D3—24no—
18C22×C3×C4×D3—24no—
19C22×C3×C4×D3—24no—
20C22×C3×C4×D3C2214yes—
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×C3×#217C2211yescharacteristic
24C3×#929—24no—
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×(C2×D3)⋊C4C2214yes—
27C2×C3×(C2×D3)⋊C4C2212yescomplemented
28C2×C3×(C2×D3)⋊C4C2212yescomplemented
29C2×C3×C4⋊Dic3C2212yescomplemented
30C2×C3×Dic3⋊C4C2212yescomplemented
31C3×#886—24no—
32C3×#882—24no—
33C32×#95C2214yescomplemented
34C3×C3⋊#95C2214yescomplemented
35C24×C3×C4—31no—
36C23×C4×D3C2×C311yescharacteristic, complemented
37C2×C3×#123—31no—
38C2×C3×#123—31no—
39C2×C3×#120—31no—
40C2×#929C2×C311yescharacteristic, complemented
41C2×#886C2×C311yescharacteristic, complemented
42C2×#882C2×C311yescharacteristic
43C3×#386—34no—
44C3×#385—34no—
45C3×#381—21no—
46C3×#381—31no—
47C3×#381D311yescharacteristic, complemented
48C3×#381C2×C311yescharacteristic, complemented
49C3×#379—31no—
50#4955C2×C311yescharacteristic, complemented
51#4943C2×C311yescharacteristic, complemented
52#4668C2×C314yescomplemented
53#4665C2×C314yescomplemented
54C24×C32C2311yescharacteristic
55C23×C3×D3—22no—
56C23×C3×D3—22no—
57C23×C3×D3—28no—
58C23×C3×D3D414yes—
59C23×C3×D3C2311yescharacteristic
60C23×C3×D3C2312yes—
61C22×C32×C4—22no—
62C22×C32×C4—22no—
63C22×C32×C4D414yescomplemented
64C22×C32×C4C2312yes—
65C22×C32×C4C2312yes—
66C22×C32×C4C2312yes—
67C2×C3×#67—22no—
68C2×C3×#67—22no—
69C2×C3×#67—22no—
70C22×C3×Dic3—22no—
71C22×C3×Dic3—22no—
72C22×C3×Dic3D414yescomplemented
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C2×C3×D12—24no—
77C2×C3×D12—28no—
78C2×C3×C4×D3—232no—
79C2×C3×C4×D3—28no—
80C2×C3×C4×D3—28no—
81C2×C3×C4×D3—28no—
82C32×C22⋊C4—22no—
83C32×C22⋊C4—22no—
84C3×#217—22no—
85C3×(C2×D3)⋊C4—24no—
86C3×(C2×D3)⋊C4—28no—
87C3×(C2×D3)⋊C4—24no—
88C3×(C2×D3)⋊C4—24no—
89C3×C4⋊Dic3—24no—
90C3×Dic3⋊C4—24no—
91#2849—31noSylow
92C25×C3—31no—
93C24×D3C22×C311yescharacteristic
94C22×C3×D4—31no—
95C22×C3×D4—32no—
96C23×C3×C4—21no—
97C23×C3×C4—31no—
98C23×C3×C4—34no—
99C23×C3×C4—64no—
100C23×C3×C4—64no—
101C23×C3×C4—64no—
102C23×C3×C4C2×D311yescharacteristic
103C23×C3×C4C22×C311yescharacteristic
104C22×#67C22×C311yescharacteristic
105C23×Dic3C22×C311yescharacteristic
106C22×D12C22×C312yes—
107C22×C4×D3—24no—
108C22×C4×D3—24no—
109C22×C4×D3—24no—
110C22×C4×D3C22×C314yes—
111C3×#123—64no—
112C3×#123—64no—
113C3×#120—64no—
114C2×C3×C4⋊C4—32no—
115C2×C3×C4⋊C4—32no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—31no—
119C2×C3×C22⋊C4—34no—
120C2×C3×C22⋊C4—32no—
121C2×C3×C22⋊C4—32no—
122C2×C3×C22⋊C4—32no—
123C2×C3×C22⋊C4C2×D311yescharacteristic
124C2×C3×C22⋊C4C2×D311yescharacteristic
125C2×C3×C22⋊C4C22×C311yescharacteristic
126C2×C3×C22⋊C4C22×C311yescharacteristic
127C2×#217C22×C311yescharacteristic
128#929—24no—
129C2×(C2×D3)⋊C4C22×C314yes—
130C2×(C2×D3)⋊C4C22×C312yes—
131C2×(C2×D3)⋊C4C22×C312yescomplemented
132C2×(C2×D3)⋊C4C22×C312yescomplemented
133C2×C4⋊Dic3C22×C312yescomplemented
134C2×Dic3⋊C4C22×C312yescomplemented
135#886—24no—
136#882—24no—
137C3×#95—24no—
138C3×#95—34no—
139C3×#95C2×D314yescomplemented
140C3×#95C22×C314yescomplemented
141C3⋊#95C22×C314yescomplemented
142C23×C32—24no—
143C23×C32C2×D412yes—
144C23×C32C2×D412yes—
145C23×C32C2×D412yes—
146C23×C32C2411yescharacteristic
147C22×C3×D3—216no—
148C22×C3×D3—216no—
149C22×C3×D3—28no—
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3—24no—
153C22×C3×D3—216no—
154C22×C3×D3—21no—
155C22×C3×D3—21no—
156C22×C3×D3—21no—
157C22×C3×D3—24no—
158C22×C3×D3C2×D414yes—
159C22×C3×D3#4118yes—
160C2×C32×C4—28no—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4—24no—
166C2×C32×C4—24no—
167C2×C32×C4C2×D414yes—
168C3×#67—44no—
169C2×C3×Dic3—28no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—24no—
177C2×C3×Dic3C2×D414yes—
178C3×D12—48no—
179C3×C4×D3—232no—
180C24×C4—31no—
181C2×#123—31no—
182C2×#123—31no—
183C2×#120—31no—
184#386—34no—
185#385—34no—
186#381—31no—
187#381C3×D311yescharacteristic, complemented
188#379—31no—
189C24×C3—21no—
190C24×C3—32no—
191C24×C3—34no—
192C24×C3—31no—
193C24×C3—68no—
194C24×C3—62no—
195C24×C3—62no—
196C24×C3C22×D311yescharacteristic
197C24×C3C23×C311yescharacteristic
198C23×D3—22no—
199C23×D3—22no—
200C23×D3—28no—
201C23×D3C3×D414yes—
202C23×D3C23×C311yescharacteristic
203C23×D3C23×C312yes—
204C2×C3×D4—64no—
205C2×C3×D4—68no—
206C2×C3×D4—62no—
207C2×C3×D4—62no—
208C2×C3×D4—62no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—24no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—34no—
218C22×C3×C4—32no—
219C22×C3×C4—32no—
220C22×C3×C4—31no—
221C22×C3×C4—42no—
222C22×C3×C4—42no—
223C22×C3×C4—68no—
224C22×C3×C4—68no—
225C22×C3×C4—632no—
226C22×C3×C4—62no—
227C22×C3×C4—62no—
228C22×C3×C4—68no—
229C22×C3×C4D1214yescomplemented
230C22×C3×C4C3×D414yescomplemented
231C22×C3×C4C22×D312yes—
232C22×C3×C4C22×D312yes—
233C22×C3×C4C22×D312yes—
234C22×C3×C4C23×C312yes—
235C22×C3×C4C23×C312yes—
236C22×C3×C4C23×C312yes—
237C2×#67—22no—
238C2×#67—22no—
239C2×#67—22no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3C3×D414yescomplemented
243C22×Dic3C23×C312yes—
244C22×Dic3C23×C311yescharacteristic
245C22×Dic3C23×C312yes—
246C2×D12—24no—
247C2×D12—28no—
248C2×C4×D3—232no—
249C2×C4×D3—28no—
250C2×C4×D3—28no—
251C2×C4×D3—28no—
252C3×C4⋊C4—64no—
253C3×C4⋊C4—64no—
254C3×C22⋊C4—22no—
255C3×C22⋊C4—22no—
256C3×C22⋊C4—22no—
257C3×C22⋊C4—22no—
258C3×C22⋊C4—42no—
259C3×C22⋊C4—42no—
260C3×C22⋊C4—64no—
261C3×C22⋊C4—68no—
262C3×C22⋊C4—64no—
263C3×C22⋊C4—62no—
264C3×C22⋊C4—64no—
265#217—22no—
266(C2×D3)⋊C4—24no—
267(C2×D3)⋊C4—28no—
268(C2×D3)⋊C4—24no—
269(C2×D3)⋊C4—24no—
270C4⋊Dic3—24no—
271Dic3⋊C4—24no—
272C22×C32—24no—
273C22×C32—24no—
274C22×C32—24no—
275C22×C32#12014yes—
276C22×C32C22×D411yescharacteristic
277C22×C32C22×D411yescharacteristic
278C22×C32C22×D411yescharacteristic
279C22×C32C2×#4114yes—
280C2×C3×D3—232no—
281C2×C3×D3—24no—
282C2×C3×D3—24no—
283C2×C3×D3—28no—
284C2×C3×D3—28no—
285C2×C3×D3—41no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C2×C3×D3#12318yescomplemented
290C32×C4—24no—
291C32×C4—42no—
292C32×C4—42no—
293C3×Dic3—24no—
294C3×Dic3—41no—
295C3×Dic3—42no—
296C25—31no—
297C22×D4—31no—
298C22×D4—32no—
299C23×C4—31no—
300C23×C4—34no—
301C23×C4—64no—
302C23×C4—64no—
303C23×C4—64no—
304C23×C4C2×C3×D311yescharacteristic
305#123—64no—
306#123—64no—
307#120—64no—
308C2×C4⋊C4—32no—
309C2×C4⋊C4—32no—
310C2×C22⋊C4—31no—
311C2×C22⋊C4—32no—
312C2×C22⋊C4—32no—
313C2×C22⋊C4—32no—
314C2×C22⋊C4—34no—
315C2×C22⋊C4C2×C3×D311yescharacteristic
316C2×C22⋊C4C2×C3×D311yescharacteristic
317#95—34no—
318#95C2×C3×D314yescomplemented
319C23×C3—24no—
320C23×C3—24no—
321C23×C3—21no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—34no—
326C23×C3—38no—
327C23×C3—44no—
328C23×C3—616no—
329C23×C3—616no—
330C23×C3—616no—
331C23×C3—68no—
332C23×C3—62no—
333C23×C3—62no—
334C23×C3—64no—
335C23×C3—61no—
336C23×C3—61no—
337C23×C3—61no—
338C23×C3—64no—
339C23×C3C2×D1212yes—
340C23×C3D3×D412yes—
341C23×C3D3×D412yes—
342C23×C3C2×C3×D412yes—
343C23×C3C2×C3×D412yes—
344C23×C3C2×C3×D412yes—
345C23×C3C23×D311yescharacteristic
346C23×C3C24×C311yescharacteristic
347C22×D3—216no—
348C22×D3—216no—
349C22×D3—28no—
350C22×D3—22no—
351C22×D3—22no—
352C22×D3—24no—
353C22×D3—216no—
354C22×D3—21no—
355C22×D3—21no—
356C22×D3—21no—
357C22×D3—24no—
358C22×D3C2×C3×D414yes—
359C22×D3C3×#4118yes—
360C3×D4—128no—
361C3×D4—124no—
362C2×C3×C4—28no—
363C2×C3×C4—28no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—24no—
375C2×C3×C4—24no—
376C2×C3×C4—24no—
377C2×C3×C4—34no—
378C2×C3×C4—48no—
379C2×C3×C4—42no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—42no—
383C2×C3×C4—44no—
384C2×C3×C4—44no—
385C2×C3×C4—632no—
386C2×C3×C4—68no—
387C2×C3×C4—62no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4—61no—
391C2×C3×C4—61no—
392C2×C3×C4—61no—
393C2×C3×C4—64no—
394C2×C3×C4C2×D1214yes—
395C2×C3×C4C2×C3×D414yes—
396#67—44no—
397C2×Dic3—28no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—21no—
401C2×Dic3—22no—
402C2×Dic3—21no—
403C2×Dic3—21no—
404C2×Dic3—24no—
405C2×Dic3C2×C3×D414yes—
406D12—48no—
407C4×D3—232no—
408C2×C32—24no—
409C2×C32C2×#12011yescharacteristic
410C2×C32C2×#12312yes—
411C2×C32#52512yes—
412C2×C32#52512yes—
413C3×D3—28no—
414C3×D3—81no—
415C24—32no—
416C24—34no—
417C24—31no—
418C24—68no—
419C24—62no—
420C24—62no—
421C24C22×C3×D311yescharacteristic
422C2×D4—64no—
423C2×D4—68no—
424C2×D4—62no—
425C2×D4—62no—
426C2×D4—62no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—32no—
430C22×C4—34no—
431C22×C4—32no—
432C22×C4—31no—
433C22×C4—68no—
434C22×C4—68no—
435C22×C4—632no—
436C22×C4—62no—
437C22×C4—62no—
438C22×C4—68no—
439C22×C4C3×D1214yescomplemented
440C22×C4C22×C3×D312yes—
441C22×C4C22×C3×D312yes—
442C22×C4C22×C3×D312yes—
443C4⋊C4—64no—
444C4⋊C4—64no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—64no—
448C22⋊C4—64no—
449C22⋊C4—68no—
450C22⋊C4—62no—
451C22⋊C4—64no—
452C22×C3—24no—
453C22×C3—24no—
454C22×C3—24no—
455C22×C3—24no—
456C22×C3—24no—
457C22×C3—24no—
458C22×C3—24no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—24no—
463C22×C3—38no—
464C22×C3—44no—
465C22×C3—44no—
466C22×C3—44no—
467C22×C3—632no—
468C22×C3—64no—
469C22×C3—68no—
470C22×C3—64no—
471C22×C3—68no—
472C22×C3—122no—
473C22×C3—122no—
474C22×C3—121no—
475C22×C3—122no—
476C22×C3#88214yes—
477C22×C3C3×#12014yes—
478C22×C3C22×D1211yescharacteristic
479C22×C3C2×D3×D411yescharacteristic
480C22×C3C2×D3×D411yescharacteristic
481C22×C3D3×#4114yes—
482C22×C3C22×C3×D411yescharacteristic
483C22×C3C22×C3×D411yescharacteristic
484C22×C3C22×C3×D411yescharacteristic
485C22×C3C2×C3×#4114yes—
486C2×D3—232no—
487C2×D3—24no—
488C2×D3—24no—
489C2×D3—28no—
490C2×D3—28no—
491C2×D3—41no—
492C2×D3—42no—
493C2×D3—42no—
494C2×D3—42no—
495C2×D3C3×#12318yescomplemented
496C3×C4—24no—
497C3×C4—24no—
498C3×C4—44no—
499C3×C4—42no—
500C3×C4—42no—
501C3×C4—42no—
502C3×C4—42no—
503C3×C4—64no—
504C3×C4—82no—
505C3×C4—82no—
506C3×C4—121no—
507C3×C4—122no—
508Dic3—24no—
509Dic3—41no—
510Dic3—42no—
511C32#284911yescharacteristic, complemented, Sylow
512C23—24no—
513C23—34no—
514C23—38no—
515C23—616no—
516C23—616no—
517C23—616no—
518C23—68no—
519C23—62no—
520C23—62no—
521C23—64no—
522C23—61no—
523C23—61no—
524C23—61no—
525C23—64no—
526C23C2×C3×D1212yes—
527C23C3×D3×D412yes—
528C23C3×D3×D412yes—
529C23C23×C3×D311yescharacteristic
530D4—128no—
531D4—124no—
532C2×C4—28no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—34no—
540C2×C4—632no—
541C2×C4—68no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—61no—
546C2×C4—61no—
547C2×C4—61no—
548C2×C4—64no—
549C2×C4C2×C3×D1214yes—
550C2×C3—24no—
551C2×C3—24no—
552C2×C3—21no—
553C2×C3—22no—
554C2×C3—22no—
555C2×C3—22no—
556C2×C3—44no—
557C2×C3—68no—
558C2×C3—241no—
559C2×C3C2×#88211yescharacteristic
560C2×C3#552412yes—
561C2×C3D3×#12312yes—
562C2×C3#565612yes—
563C2×C3C2×C3×#12011yescharacteristic
564C2×C3C2×C3×#12312yes—
565C2×C3C3×#52512yes—
566C2×C3C3×#52512yes—
567D3—28no—
568D3—81no—
569C22—24no—
570C22—24no—
571C22—24no—
572C22—38no—
573C22—632no—
574C22—64no—
575C22—68no—
576C22—64no—
577C22—68no—
578C22—121no—
579C22—122no—
580C22—122no—
581C22—122no—
582C22C3×#88214yes—
583C22C22×C3×D1211yescharacteristic
584C22C2×C3×D3×D411yescharacteristic
585C22C2×C3×D3×D411yescharacteristic
586C22C3×D3×#4114yes—
587C4—24no—
588C4—42no—
589C4—42no—
590C4—64no—
591C4—121no—
592C4—122no—
593C3—21no—
594C3#7414611yescharacteristic, direct product factor
595C3C3×#284911yescharacteristic, complemented
596C2—24no—
597C2—68no—
598C2—241no—
599C2C2×C3×#88211yescharacteristic
600C2C3×#552412yes—
601C2C3×D3×#12312yes—
602C2C3×#565612yes—
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#381C2
socleC23×C32C24
prime radicalC2×C3×#882C2
hypercenterC3×#381D3
hypocenterC3C3×#2849
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#381

Complements

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

NH ≅ G/Ntype
1. C23×C3×C4×D3C2semidirect
2. C2×C3×#929C2semidirect
3. C2×C3×#886C2semidirect
5. C32×#381C2semidirect
6. C3×#4955C2semidirect
7. C3×#4943C2semidirect
8. C3×#4668C2semidirect
9. C3×#4665C2semidirect
11. #74146C3direct (N × H)
27. C2×C3×(C2×D3)⋊C4C22semidirect
28. C2×C3×(C2×D3)⋊C4C22semidirect
29. C2×C3×C4⋊Dic3C22semidirect
30. C2×C3×Dic3⋊C4C22semidirect
33. C32×#95C22semidirect
34. C3×C3⋊#95C22semidirect
36. C23×C4×D3C2×C3semidirect
40. C2×#929C2×C3semidirect
41. C2×#886C2×C3semidirect
47. C3×#381D3semidirect
48. C3×#381C2×C3semidirect
50. #4955C2×C3semidirect
51. #4943C2×C3semidirect
52. #4668C2×C3semidirect
53. #4665C2×C3semidirect
63. C22×C32×C4D4semidirect
72. C22×C3×Dic3D4semidirect
131. C2×(C2×D3)⋊C4C22×C3semidirect
132. C2×(C2×D3)⋊C4C22×C3semidirect
133. C2×C4⋊Dic3C22×C3semidirect
134. C2×Dic3⋊C4C22×C3semidirect
139. C3×#95C2×D3semidirect
140. C3×#95C22×C3semidirect
141. C3⋊#95C22×C3semidirect
187. #381C3×D3semidirect
229. C22×C3×C4D12semidirect
230. C22×C3×C4C3×D4semidirect
242. C22×Dic3C3×D4semidirect
289. C2×C3×D3#123semidirect
318. #95C2×C3×D3semidirect
439. C22×C4C3×D12semidirect
495. C2×D3C3×#123semidirect
511. C32#2849semidirect
594. C3#74146direct (N × H)
595. C3C3×#2849semidirect

Maximal subgroups

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

subgroupindex
C23×C3×C4×D32
C2×C3×#9292
C2×C3×#8862
C2×C3×#8822
C32×#3812
C3×#49552
C3×#49432
C3×#46682
C3×#46652
C3×#28493
#741463