Finite Group Databasebeta

← C3×C4×#940 #11802520

Subgroups — C3×C4×#940 #11802520

Order 1152.

2061 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic
3C2×C3×C4×#67C214yesmaximal, complemented
4C2×C3×C4×D12C211yesmaximal, characteristic, complemented
5C3×#5221C211yesmaximal, characteristic, complemented
6C3×#4988C211yesmaximal, characteristic, complemented
7C3×#4975C211yesmaximal, characteristic, complemented
8C3×#4957C214yesmaximal, complemented
9C3×C42×Dic3C211yesmaximal, characteristic, complemented
10C3×C4×#127—31nomaximal
11C4×#940C311yesmaximal, characteristic, direct product factor
12C22×C32×D4C2211yescharacteristic
13C23×C32×C4C2212yes—
14C22×C3×#67C2214yes—
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C32×C4×D4—24no—
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C22⋊C4C2212yes—
20C2×C32×C42C2211yescharacteristic
21C2×C3×#217C2214yes—
22C3×#940C418yesdirect product factor
23C3×C4×#67—216no—
24C2×C3×(C2×D3)⋊C4C2214yes—
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×Dic3⋊C4C2214yes—
28C2×C3×C4×Dic3C2212yes—
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2212yes—
32C3×C4×D12—24no—
33C2×C3×#127—31no—
34C2×C3×C4×D4—21no—
35C2×C3×C4×D4—34no—
36C2×C3×C4×D4—31no—
37C2×C3×C4×D4D311yescharacteristic, complemented
38C2×C3×C4×D4C2×C311yescharacteristic, complemented
39C2×#940C2×C311yescharacteristic
40C2×C4×#67C2×C314yescomplemented
41C2×C4×D12C2×C311yescharacteristic, complemented
42C3×#390—31no—
43C3×#390—31no—
44C3×#390—34no—
45C3×#384—31no—
46C3×C43—31no—
47#5221C2×C311yescharacteristic, complemented
48#4988C2×C311yescharacteristic, complemented
49#4975C2×C311yescharacteristic, complemented
50#4957C2×C314yescomplemented
51C42×Dic3C2×C311yescharacteristic, complemented
52C24×C32C2312yes—
53C23×C3×D3C2312yes—
54C2×C32×D4—22no—
55C2×C32×D4—22no—
56C2×C32×D4C2×C414yescomplemented
57C22×C32×C4—24no—
58C22×C32×C4—28no—
59C22×C32×C4C2312yes—
60C22×C32×C4C2311yescharacteristic
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C2×C3×#67—28no—
64C2×C3×#67—28no—
65C2×C3×#67C2×C4116yescomplemented
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C2×C3×D12—22no—
70C2×C3×D12—22no—
71C2×C3×D12C2×C414yescomplemented
72C2×C3×C4×D3—28no—
73C2×C3×C4×D3—24no—
74C32×C4⋊C4—22no—
75C32×C22⋊C4—24no—
76C32×C42D414yescomplemented
77C3×#217—28no—
78C3×(C2×D3)⋊C4—24no—
79C3×(C2×D3)⋊C4—28no—
80C3×C4⋊Dic3—22no—
81C3×Dic3⋊C4—28no—
82C3×C4×Dic3—22no—
83C3×C4×Dic3—24no—
84C3×C4×Dic3C2×C414yescomplemented
85C3×C4×Dic3D418yescomplemented
86C4×#127—31noSylow
87C22×C3×D4—21no—
88C22×C3×D4—34no—
89C22×C3×D4—31no—
90C22×C3×D4C2×D311yescharacteristic
91C22×C3×D4C22×C311yescharacteristic
92C23×C3×C4—22no—
93C23×C3×C4—32no—
94C23×C3×C4C2×D312yes—
95C23×C3×C4C22×C312yes—
96C22×#67C22×C314yes—
97C22×D12C22×C311yescharacteristic
98C22×C4×D3C22×C312yes—
99C3×#127—38no—
100C3×C4×D4—28no—
101C3×C4×D4—24no—
102C3×C4×D4—24no—
103C3×C4×D4—616no—
104C3×C4×D4—64no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4—34no—
107C2×C3×C4⋊C4—31no—
108C2×C3×C4⋊C4C2×D311yescharacteristic
109C2×C3×C4⋊C4C22×C311yescharacteristic
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—34no—
112C2×C3×C22⋊C4—34no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C22⋊C4C2×D312yes—
115C2×C3×C22⋊C4C22×C312yes—
116C2×C3×C42—21no—
117C2×C3×C42—31no—
118C2×C3×C42—32no—
119C2×C3×C42—32no—
120C2×C3×C42—31no—
121C2×C3×C42C2×D311yescharacteristic
122C2×C3×C42C22×C311yescharacteristic
123C2×#217C22×C314yes—
124#940C3×C418yesdirect product factor
125C4×#67—216no—
126C2×(C2×D3)⋊C4C22×C312yes—
127C2×(C2×D3)⋊C4C22×C314yes—
128C2×C4⋊Dic3C22×C311yescharacteristic
129C2×Dic3⋊C4C22×C314yes—
130C2×C4×Dic3C22×C312yes—
131C2×C4×Dic3C22×C311yescharacteristic
132C2×C4×Dic3C22×C311yescharacteristic
133C2×C4×Dic3C22×C312yes—
134C4×D12—24no—
135C23×C32—22no—
136C23×C32—22no—
137C23×C32—24no—
138C23×C32—24no—
139C23×C32C22×C414yes—
140C23×C32C2411yescharacteristic
141C22×C3×D3—22no—
142C22×C3×D3—24no—
143C22×C3×D3—22no—
144C22×C3×D3—24no—
145C22×C3×D3C22×C414yes—
146C32×D4—28no—
147C2×C32×C4—22no—
148C2×C32×C4—22no—
149C2×C32×C4—24no—
150C2×C32×C4—48no—
151C2×C32×C4C22×C412yes—
152C2×C32×C4C2×D414yes—
153C2×C32×C4C2×D412yes—
154C2×C32×C4C2×D412yes—
155C2×C32×C4C2×D412yes—
156C2×C32×C4#4112yes—
157C3×#67—232no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—24no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3C22×C414yes—
163C2×C3×Dic3C2×D414yes—
164C2×C3×Dic3C2×D414yes—
165C2×C3×Dic3#4114yes—
166C3×D12—28no—
167C3×C4×D3—48no—
168C2×#127—31no—
169C2×C4×D4—34no—
170C2×C4×D4—31no—
171C2×C4×D4C3×D311yescharacteristic, complemented
172#390—31no—
173#390—31no—
174#390—34no—
175#384—31no—
176C43—31no—
177C24×C3—22no—
178C24×C3—32no—
179C24×C3C22×D312yes—
180C24×C3C23×C312yes—
181C23×D3C23×C312yes—
182C2×C3×D4—24no—
183C2×C3×D4—24no—
184C2×C3×D4—22no—
185C2×C3×D4—22no—
186C2×C3×D4—22no—
187C2×C3×D4—22no—
188C2×C3×D4—24no—
189C2×C3×D4—316no—
190C2×C3×D4—34no—
191C2×C3×D4—68no—
192C2×C3×D4—68no—
193C2×C3×D4—62no—
194C2×C3×D4—62no—
195C2×C3×D4C4×D314yescomplemented
196C2×C3×D4C2×C3×C414yescomplemented
197C22×C3×C4—28no—
198C22×C3×C4—28no—
199C22×C3×C4—24no—
200C22×C3×C4—28no—
201C22×C3×C4—24no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—22no—
206C22×C3×C4—32no—
207C22×C3×C4—32no—
208C22×C3×C4—32no—
209C22×C3×C4—48no—
210C22×C3×C4—68no—
211C22×C3×C4—64no—
212C22×C3×C4C22×D312yes—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C23×C312yes—
217C22×C3×C4C23×C311yescharacteristic
218C22×C3×C4C23×C311yescharacteristic
219C22×C3×C4C23×C311yescharacteristic
220C2×#67—28no—
221C2×#67—28no—
222C2×#67C2×C3×C4116yescomplemented
223C22×Dic3C23×C312yes—
224C22×Dic3C23×C312yes—
225C22×Dic3C23×C312yes—
226C2×D12—22no—
227C2×D12—22no—
228C2×D12C2×C3×C414yescomplemented
229C2×C4×D3—24no—
230C2×C4×D3—28no—
231C3×C4⋊C4—24no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—68no—
235C3×C4⋊C4—62no—
236C3×C22⋊C4—28no—
237C3×C22⋊C4—24no—
238C3×C22⋊C4—24no—
239C3×C22⋊C4—68no—
240C3×C22⋊C4—68no—
241C3×C22⋊C4—64no—
242C3×C42—24no—
243C3×C42—34no—
244C3×C42—38no—
245C3×C42—64no—
246C3×C42—62no—
247C3×C42#6714yescomplemented
248C3×C42C3×D414yescomplemented
249#217—28no—
250(C2×D3)⋊C4—24no—
251(C2×D3)⋊C4—28no—
252C4⋊Dic3—22no—
253Dic3⋊C4—28no—
254C4×Dic3—22no—
255C4×Dic3—24no—
256C4×Dic3C2×C3×C414yescomplemented
257C4×Dic3C3×D418yescomplemented
258C22×C32—24no—
259C22×C32—28no—
260C22×C32—42no—
261C22×C32—44no—
262C22×C32—42no—
263C22×C32C23×C411yescharacteristic
264C22×C32C22×D412yes—
265C22×C32C22×D411yescharacteristic
266C22×C32C2×#4111yescharacteristic
267C22×C32C2×#4112yes—
268C2×C3×D3—24no—
269C2×C3×D3—28no—
270C2×C3×D3—42no—
271C2×C3×D3—44no—
272C2×C3×D3—42no—
273C32×C4—22no—
274C32×C4—42no—
275C32×C4C4×D414yescomplemented
276C32×C4#12714yescomplemented
277C3×Dic3—24no—
278C3×Dic3—42no—
279C3×Dic3C4×D418yescomplemented
280C22×D4—34no—
281C22×D4—31no—
282C22×D4C2×C3×D311yescharacteristic
283C23×C4—32no—
284C23×C4C2×C3×D312yes—
285#127—38no—
286C4×D4—24no—
287C4×D4—616no—
288C4×D4—64no—
289C2×C4⋊C4—34no—
290C2×C4⋊C4—31no—
291C2×C4⋊C4C2×C3×D311yescharacteristic
292C2×C22⋊C4—34no—
293C2×C22⋊C4—34no—
294C2×C22⋊C4—32no—
295C2×C22⋊C4C2×C3×D312yes—
296C2×C42—32no—
297C2×C42—31no—
298C2×C42—32no—
299C2×C42—31no—
300C2×C42C2×C3×D311yescharacteristic
301C23×C3—24no—
302C23×C3—24no—
303C23×C3—22no—
304C23×C3—24no—
305C23×C3—24no—
306C23×C3—22no—
307C23×C3—24no—
308C23×C3—22no—
309C23×C3—24no—
310C23×C3—22no—
311C23×C3—21no—
312C23×C3—24no—
313C23×C3—34no—
314C23×C3—44no—
315C23×C3—44no—
316C23×C3—62no—
317C23×C3—64no—
318C23×C3—64no—
319C23×C3—62no—
320C23×C3C2×C4×D314yes—
321C23×C3C22×C3×C414yes—
322C23×C3C23×D311yescharacteristic
323C23×C3C24×C311yescharacteristic
324C22×D3—22no—
325C22×D3—24no—
326C22×D3—22no—
327C22×D3—24no—
328C22×D3C22×C3×C414yes—
329C3×D4—216no—
330C3×D4—28no—
331C3×D4—28no—
332C3×D4—632no—
333C3×D4—68no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—24no—
337C2×C3×C4—24no—
338C2×C3×C4—22no—
339C2×C3×C4—24no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—24no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—34no—
348C2×C3×C4—34no—
349C2×C3×C4—34no—
350C2×C3×C4—34no—
351C2×C3×C4—42no—
352C2×C3×C4—44no—
353C2×C3×C4—416no—
354C2×C3×C4—48no—
355C2×C3×C4—48no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—64no—
359C2×C3×C4—62no—
360C2×C3×C4—128no—
361C2×C3×C4C2×C4×D312yes—
362C2×C3×C4#23512yes—
363C2×C3×C4D3×D414yes—
364C2×C3×C4C2×#6712yes—
365C2×C3×C4C2×#6712yes—
366C2×C3×C4C2×#6712yes—
367C2×C3×C4C22×C3×C412yes—
368C2×C3×C4C2×C3×D414yes—
369C2×C3×C4C2×C3×D412yes—
370C2×C3×C4C2×C3×D412yes—
371C2×C3×C4C2×C3×D412yes—
372C2×C3×C4C3×#4112yes—
373#67—232no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—24no—
377C2×Dic3—22no—
378C2×Dic3C22×C3×C414yes—
379C2×Dic3C2×C3×D414yes—
380C2×Dic3C2×C3×D414yes—
381C2×Dic3C3×#4114yes—
382D12—28no—
383C4×D3—48no—
384C2×C32—44no—
385C2×C32C2×C4×D411yescharacteristic
386C2×C32C2×C4×D412yes—
387C2×C32C2×#12711yescharacteristic
388C2×C32#53212yes—
389C2×C32#53211yescharacteristic
390C3×D3—44no—
391C24—32no—
392C24C22×C3×D312yes—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—316no—
396C2×D4—34no—
397C2×D4—68no—
398C2×D4—68no—
399C2×D4—62no—
400C2×D4—62no—
401C2×D4C3×C4×D314yescomplemented
402C22×C4—28no—
403C22×C4—24no—
404C22×C4—32no—
405C22×C4—32no—
406C22×C4—32no—
407C22×C4—68no—
408C22×C4—64no—
409C22×C4C22×C3×D312yes—
410C22×C4C22×C3×D311yescharacteristic
411C22×C4C22×C3×D311yescharacteristic
412C22×C4C22×C3×D311yescharacteristic
413C4⋊C4—22no—
414C4⋊C4—68no—
415C4⋊C4—62no—
416C22⋊C4—24no—
417C22⋊C4—68no—
418C22⋊C4—68no—
419C22⋊C4—64no—
420C42—34no—
421C42—38no—
422C42—64no—
423C42—62no—
424C42C3×#6714yescomplemented
425C22×C3—28no—
426C22×C3—24no—
427C22×C3—28no—
428C22×C3—28no—
429C22×C3—24no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—21no—
435C22×C3—48no—
436C22×C3—44no—
437C22×C3—48no—
438C22×C3—44no—
439C22×C3—42no—
440C22×C3—44no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—44no—
444C22×C3—42no—
445C22×C3—64no—
446C22×C3—68no—
447C22×C3—122no—
448C22×C3—124no—
449C22×C3—122no—
450C22×C3C22×C4×D311yescharacteristic
451C22×C3C2×#23511yescharacteristic
452C22×C3C2×D3×D412yes—
453C22×C3D3×#4112yes—
454C22×C3C22×#6711yescharacteristic
455C22×C3C23×C3×C411yescharacteristic
456C22×C3C22×C3×D412yes—
457C22×C3C22×C3×D411yescharacteristic
458C22×C3C2×C3×#4111yescharacteristic
459C22×C3C2×C3×#4112yes—
460C2×D3—24no—
461C2×D3—28no—
462C2×D3—42no—
463C2×D3—44no—
464C2×D3—42no—
465C3×C4—22no—
466C3×C4—22no—
467C3×C4—24no—
468C3×C4—24no—
469C3×C4—38no—
470C3×C4—42no—
471C3×C4—44no—
472C3×C4—42no—
473C3×C4—42no—
474C3×C4—64no—
475C3×C4—122no—
476C3×C4C4×#6714yescomplemented
477C3×C4#94014yesdirect product factor
478C3×C4C3×C4×D414yescomplemented
479C3×C4C3×#12714yescomplemented
480Dic3—24no—
481Dic3—42no—
482Dic3C3×C4×D418yescomplemented
483C32C4×#12711yescharacteristic, complemented, Sylow
484C23—22no—
485C23—24no—
486C23—24no—
487C23—22no—
488C23—34no—
489C23—62no—
490C23—64no—
491C23—64no—
492C23—62no—
493C23C2×C3×C4×D314yes—
494C23C23×C3×D311yescharacteristic
495D4—28no—
496D4—632no—
497D4—68no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—34no—
502C2×C4—34no—
503C2×C4—34no—
504C2×C4—34no—
505C2×C4—48no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—64no—
509C2×C4—62no—
510C2×C4—128no—
511C2×C4C2×C3×C4×D312yes—
512C2×C4C3×#23512yes—
513C2×C4C3×D3×D414yes—
514C2×C4C2×C3×#6712yes—
515C2×C4C2×C3×#6712yes—
516C2×C4C2×C3×#6712yes—
517C2×C3—21no—
518C2×C3—22no—
519C2×C3—21no—
520C2×C3—22no—
521C2×C3—21no—
522C2×C3—48no—
523C2×C3—44no—
524C2×C3—44no—
525C2×C3—124no—
526C2×C3C4×D3×D412yes—
527C2×C3#554812yes—
528C2×C3C2×C4×#6711yescharacteristic
529C2×C3C2×#94011yescharacteristic
530C2×C3#583211yescharacteristic
531C2×C3C2×C3×C4×D411yescharacteristic
532C2×C3C2×C3×C4×D412yes—
533C2×C3C2×C3×#12711yescharacteristic
534C2×C3C3×#53212yes—
535C2×C3C3×#53211yescharacteristic
536D3—44no—
537C22—24no—
538C22—28no—
539C22—42no—
540C22—44no—
541C22—42no—
542C22—64no—
543C22—68no—
544C22—122no—
545C22—124no—
546C22—122no—
547C22C22×C3×C4×D311yescharacteristic
548C22C2×C3×#23511yescharacteristic
549C22C2×C3×D3×D412yes—
550C22C3×D3×#4112yes—
551C22C22×C3×#6711yescharacteristic
552C4—22no—
553C4—38no—
554C4—42no—
555C4—64no—
556C4—122no—
557C4C3×C4×#6714yescomplemented
558C4C3×#94014yesdirect product factor
559C3—21no—
560C3C4×#94011yescharacteristic, direct product factor
561C3C3×C4×#12711yescharacteristic, complemented
562C2—44no—
563C2—124no—
564C2C3×C4×D3×D412yes—
565C2C3×#554812yes—
566C2C2×C3×C4×#6711yescharacteristic
567C2C2×C3×#94011yescharacteristic
568C2C3×#583211yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
prime radicalC2×C3×#940C2
cosocleC23×C3C24×C3
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×C4×#127
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
3. C2×C3×C4×#67C2semidirect
4. C2×C3×C4×D12C2semidirect
5. C3×#5221C2semidirect
6. C3×#4988C2semidirect
7. C3×#4975C2semidirect
8. C3×#4957C2semidirect
9. C3×C42×Dic3C2semidirect
11. C4×#940C3direct (N × H)
22. C3×#940C4direct (N × H)
37. C2×C3×C4×D4D3semidirect
38. C2×C3×C4×D4C2×C3semidirect
40. C2×C4×#67C2×C3semidirect
41. C2×C4×D12C2×C3semidirect
47. #5221C2×C3semidirect
48. #4988C2×C3semidirect
49. #4975C2×C3semidirect
50. #4957C2×C3semidirect
51. C42×Dic3C2×C3semidirect
56. C2×C32×D4C2×C4semidirect
65. C2×C3×#67C2×C4semidirect
71. C2×C3×D12C2×C4semidirect
76. C32×C42D4semidirect
84. C3×C4×Dic3C2×C4semidirect
85. C3×C4×Dic3D4semidirect
124. #940C3×C4direct (N × H)
171. C2×C4×D4C3×D3semidirect
195. C2×C3×D4C4×D3semidirect
196. C2×C3×D4C2×C3×C4semidirect
222. C2×#67C2×C3×C4semidirect
228. C2×D12C2×C3×C4semidirect
247. C3×C42#67semidirect
248. C3×C42C3×D4semidirect
256. C4×Dic3C2×C3×C4semidirect
257. C4×Dic3C3×D4semidirect
275. C32×C4C4×D4semidirect
276. C32×C4#127semidirect
279. C3×Dic3C4×D4semidirect
401. C2×D4C3×C4×D3semidirect
424. C42C3×#67semidirect
476. C3×C4C4×#67semidirect
477. C3×C4#940direct (N × H)
478. C3×C4C3×C4×D4semidirect
479. C3×C4C3×#127semidirect
482. Dic3C3×C4×D4semidirect
483. C32C4×#127semidirect
557. C4C3×C4×#67semidirect
558. C4C3×#940direct (N × H)
560. C3C4×#940direct (N × H)
561. C3C3×C4×#127semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×#9402
C2×C3×C4×#672
C2×C3×C4×D122
C3×#52212
C3×#49882
C3×#49752
C3×#49572
C3×C42×Dic32
C3×C4×#1273
C4×#9403