Finite Group Databasebeta

← C3×#73463 #11806038

Subgroups — C3×#73463 #11806038

Order 1152.

1249 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic
2C32×C4×C22⋊C4C211yesmaximal, characteristic, complemented
3C3×#5211C211yesmaximal, characteristic, complemented
4C3×#4957C212yesmaximal
5C3×#4945C212yesmaximal, complemented
6C3×#4940C212yesmaximal, complemented
7C3×C4×Dic3⋊C4C212yesmaximal, complemented
8C3×#4666C211yesmaximal, characteristic, complemented
9C3×#4664C211yesmaximal, characteristic, complemented
10C3×#4650C211yesmaximal, characteristic, complemented
11C3×#4649C211yesmaximal, characteristic, complemented
12C3×#2357—31nomaximal
13#73463C311yesmaximal, characteristic, direct product factor
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C2×C32×C22⋊C4C2212yes—
18C2×C32×C42C2212yes—
19C2×C3×#217C2212yes—
20C2×C3×#217C2211yescharacteristic
21C3×C4×#67C418yescomplemented
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×C4×Dic3C2212yes—
29C2×C3×C4×Dic3C2212yes—
30C2×C3×C4×Dic3C2211yescharacteristic
31C32×#95C2211yescharacteristic
32C32×#95C2211yescharacteristic
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C2×C3×C4×D4—31no—
39C2×C4×#67C2×C311yescharacteristic
40C3×#390—32no—
41C3×#388—32no—
42C3×#388—32no—
43C3×#382—31no—
44C3×#381—31no—
45C3×#381—31no—
46C3×C4×C4⋊C4—32no—
47C3×C4×C4⋊C4—31no—
48C3×C4×C22⋊C4—21no—
49C3×C4×C22⋊C4—31no—
50C3×C4×C22⋊C4D311yescharacteristic, complemented
51C3×C4×C22⋊C4C2×C311yescharacteristic, complemented
52#5211C2×C311yescharacteristic, complemented
53#4957C2×C312yes—
54#4945C2×C312yescomplemented
55#4940C2×C312yescomplemented
56C4×Dic3⋊C4C2×C312yescomplemented
57#4666C2×C311yescharacteristic, complemented
58#4664C2×C311yescharacteristic, complemented
59#4650C2×C311yescharacteristic, complemented
60#4649C2×C311yescharacteristic, complemented
61C24×C32C2311yescharacteristic
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4—42no—
64C22×C32×C4C2×C414yes—
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2312yes—
69C2×C3×#67—22no—
70C2×C3×#67—22no—
71C2×C3×#67C2×C414yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C2×C3×C4×D3—42no—
78C2×C3×C4×D3C2×C414yes—
79C32×C22⋊C4—24no—
80C32×C42—42no—
81C3×#217—42no—
82C3×#217C2×C414yes—
83C3×(C2×D3)⋊C4—24no—
84C3×(C2×D3)⋊C4—42no—
85C3×(C2×D3)⋊C4C2×C414yes—
86C3×Dic3⋊C4—24no—
87C3×Dic3⋊C4—24no—
88C3×Dic3⋊C4C2×C414yes—
89C3×C4×Dic3—24no—
90C3×C4×Dic3—42no—
91C3×C4×Dic3C2×C414yes—
92#2357—31noSylow
93C22×C3×D4—31no—
94C23×C3×C4—21no—
95C23×C3×C4—31no—
96C23×C3×C4C2×D311yescharacteristic
97C23×C3×C4C22×C311yescharacteristic
98C22×#67C22×C311yescharacteristic
99C22×C4×D3C22×C311yescharacteristic
100C3×C4×D4—38no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4—32no—
103C2×C3×C4⋊C4—32no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—31no—
106C2×C3×C22⋊C4—31no—
107C2×C3×C22⋊C4—32no—
108C2×C3×C22⋊C4—32no—
109C2×C3×C22⋊C4—32no—
110C2×C3×C22⋊C4C2×D312yes—
111C2×C3×C22⋊C4C22×C312yes—
112C2×C3×C42—22no—
113C2×C3×C42—31no—
114C2×C3×C42—32no—
115C2×C3×C42—32no—
116C2×C3×C42C2×D312yes—
117C2×C3×C42C22×C312yes—
118C2×#217C22×C312yes—
119C2×#217C22×C311yescharacteristic
120C4×#67C3×C418yescomplemented
121C2×(C2×D3)⋊C4C22×C312yes—
122C2×(C2×D3)⋊C4C22×C312yes—
123C2×(C2×D3)⋊C4C22×C311yescharacteristic
124C2×Dic3⋊C4C22×C312yes—
125C2×Dic3⋊C4C22×C312yes—
126C2×Dic3⋊C4C22×C311yescharacteristic
127C2×C4×Dic3C22×C312yes—
128C2×C4×Dic3C22×C312yes—
129C2×C4×Dic3C22×C311yescharacteristic
130C3×#95—21no—
131C3×#95—21no—
132C3×#95—31no—
133C3×#95—31no—
134C3×#95—32no—
135C3×#95—32no—
136C3×#95—32no—
137C3×#95C2×D311yescharacteristic
138C3×#95C2×D311yescharacteristic
139C3×#95C22×C311yescharacteristic
140C3×#95C22×C311yescharacteristic
141C3⋊#95C22×C311yescharacteristic
142C3⋊#95C22×C311yescharacteristic
143C3⋊#95C22×C312yes—
144C3⋊#95C22×C312yes—
145C3⋊#95C22×C312yes—
146C23×C32—22no—
147C23×C32—21no—
148C23×C32—21no—
149C23×C32—22no—
150C23×C32C22×C412yes—
151C23×C32C2411yescharacteristic
152C22×C3×D3—22no—
153C22×C3×D3—21no—
154C22×C3×D3—21no—
155C22×C3×D3—22no—
156C22×C3×D3C22×C412yes—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4—22no—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4—22no—
164C2×C32×C4—44no—
165C2×C32×C4C22×C412yes—
166C2×C32×C4C22×C412yes—
167C2×C32×C4#4114yes—
168C3×#67—28no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3C22×C412yes—
178C2×C3×Dic3C22×C412yes—
179C2×C3×Dic3C22×C412yes—
180C2×C3×Dic3#4112yes—
181C2×C3×Dic3#4112yes—
182C3×C4×D3—44no—
183C2×C4×D4—31no—
184#390—32no—
185#388—32no—
186#388—32no—
187#382—31no—
188#381—31no—
189#381—31no—
190C4×C4⋊C4—32no—
191C4×C4⋊C4—31no—
192C4×C22⋊C4—31no—
193C4×C22⋊C4C3×D311yescharacteristic, complemented
194C24×C3—21no—
195C24×C3—31no—
196C24×C3C22×D311yescharacteristic
197C24×C3C23×C311yescharacteristic
198C23×D3C23×C311yescharacteristic
199C2×C3×D4—34no—
200C2×C3×D4—62no—
201C2×C3×D4—62no—
202C22×C3×C4—24no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—31no—
208C22×C3×C4—31no—
209C22×C3×C4—31no—
210C22×C3×C4—34no—
211C22×C3×C4—32no—
212C22×C3×C4—32no—
213C22×C3×C4—42no—
214C22×C3×C4—42no—
215C22×C3×C4—44no—
216C22×C3×C4—122no—
217C22×C3×C4C4×D314yes—
218C22×C3×C4C2×C3×C414yes—
219C22×C3×C4C22×D312yes—
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D312yes—
223C22×C3×C4C23×C312yes—
224C22×C3×C4C23×C311yescharacteristic
225C22×C3×C4C23×C311yescharacteristic
226C22×C3×C4C23×C312yes—
227C2×#67—22no—
228C2×#67—22no—
229C2×#67C2×C3×C414yes—
230C22×Dic3C23×C312yes—
231C22×Dic3C23×C312yes—
232C22×Dic3C23×C311yescharacteristic
233C22×Dic3C23×C311yescharacteristic
234C22×Dic3C23×C311yescharacteristic
235C2×C4×D3—42no—
236C2×C4×D3C2×C3×C414yes—
237C3×C4⋊C4—34no—
238C3×C4⋊C4—64no—
239C3×C4⋊C4—64no—
240C3×C22⋊C4—28no—
241C3×C22⋊C4—24no—
242C3×C22⋊C4—24no—
243C3×C22⋊C4—34no—
244C3×C22⋊C4—34no—
245C3×C22⋊C4—64no—
246C3×C22⋊C4—122no—
247C3×C22⋊C4—122no—
248C3×C42—34no—
249C3×C42—42no—
250C3×C42—42no—
251C3×C42—44no—
252C3×C42—64no—
253C3×C42—122no—
254#217—42no—
255#217C2×C3×C414yes—
256(C2×D3)⋊C4—24no—
257(C2×D3)⋊C4—42no—
258(C2×D3)⋊C4C2×C3×C414yes—
259Dic3⋊C4—24no—
260Dic3⋊C4—24no—
261Dic3⋊C4C2×C3×C414yes—
262C4×Dic3—24no—
263C4×Dic3—42no—
264C4×Dic3C2×C3×C414yes—
265C22×C32—22no—
266C22×C32—22no—
267C22×C32—22no—
268C22×C32—42no—
269C22×C32—42no—
270C22×C32C23×C411yescharacteristic
271C22×C32C2×#4112yes—
272C22×C32C2×#4111yescharacteristic
273C22×C32C2×#4111yescharacteristic
274C22×C32H(5,𝔽2)12yes—
275C2×C3×D3—22no—
276C2×C3×D3—22no—
277C2×C3×D3—22no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C32×C4—22no—
281C32×C4—22no—
282C32×C4—24no—
283C32×C4—42no—
284C3×Dic3—22no—
285C3×Dic3—22no—
286C3×Dic3—42no—
287C3×Dic3—42no—
288C3×Dic3#11714yes—
289C22×D4—31no—
290C23×C4—31no—
291C23×C4C2×C3×D311yescharacteristic
292C4×D4—38no—
293C2×C4⋊C4—31no—
294C2×C4⋊C4—32no—
295C2×C4⋊C4—32no—
296C2×C22⋊C4—31no—
297C2×C22⋊C4—31no—
298C2×C22⋊C4—32no—
299C2×C22⋊C4—32no—
300C2×C22⋊C4—32no—
301C2×C22⋊C4C2×C3×D312yes—
302C2×C42—31no—
303C2×C42—32no—
304C2×C42—32no—
305C2×C42C2×C3×D312yes—
306#95—31no—
307#95—31no—
308#95—32no—
309#95—32no—
310#95—32no—
311#95C2×C3×D311yescharacteristic
312#95C2×C3×D311yescharacteristic
313C23×C3—24no—
314C23×C3—22no—
315C23×C3—22no—
316C23×C3—21no—
317C23×C3—21no—
318C23×C3—22no—
319C23×C3—21no—
320C23×C3—21no—
321C23×C3—22no—
322C23×C3—21no—
323C23×C3—22no—
324C23×C3—32no—
325C23×C3—42no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3—62no—
329C23×C3—62no—
330C23×C3—61no—
331C23×C3—61no—
332C23×C3C2×C4×D312yes—
333C23×C3C22×C3×C412yes—
334C23×C3C23×D311yescharacteristic
335C23×C3C24×C311yescharacteristic
336C22×D3—22no—
337C22×D3—21no—
338C22×D3—21no—
339C22×D3—22no—
340C22×D3C22×C3×C412yes—
341C3×D4—68no—
342C2×C3×C4—24no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—24no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—24no—
361C2×C3×C4—32no—
362C2×C3×C4—32no—
363C2×C3×C4—32no—
364C2×C3×C4—32no—
365C2×C3×C4—32no—
366C2×C3×C4—42no—
367C2×C3×C4—42no—
368C2×C3×C4—42no—
369C2×C3×C4—42no—
370C2×C3×C4—42no—
371C2×C3×C4—44no—
372C2×C3×C4—44no—
373C2×C3×C4—48no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—124no—
383C2×C3×C4C2×C4×D312yes—
384C2×C3×C4C2×C4×D312yes—
385C2×C3×C4#23514yes—
386C2×C3×C4C22×C3×C412yes—
387C2×C3×C4C22×C3×C412yes—
388C2×C3×C4C3×#4114yes—
389#67—28no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3C22×C3×C412yes—
399C2×Dic3C22×C3×C412yes—
400C2×Dic3C22×C3×C412yes—
401C2×Dic3C3×#4112yes—
402C2×Dic3C3×#4112yes—
403C4×D3—44no—
404C2×C32—42no—
405C2×C32C2×#11711yescharacteristic
406C2×C32C4×#4111yescharacteristic
407C2×C32#51811yescharacteristic
408C2×C32#55312yes—
409C2×C32#55912yes—
410C3×D3—42no—
411C24—31no—
412C24C22×C3×D311yescharacteristic
413C2×D4—34no—
414C2×D4—62no—
415C2×D4—62no—
416C22×C4—31no—
417C22×C4—31no—
418C22×C4—31no—
419C22×C4—34no—
420C22×C4—32no—
421C22×C4—32no—
422C22×C4—42no—
423C22×C4—122no—
424C22×C4C3×C4×D314yes—
425C22×C4C22×C3×D312yes—
426C22×C4C22×C3×D311yescharacteristic
427C22×C4C22×C3×D311yescharacteristic
428C22×C4C22×C3×D312yes—
429C4⋊C4—34no—
430C4⋊C4—64no—
431C4⋊C4—64no—
432C22⋊C4—24no—
433C22⋊C4—34no—
434C22⋊C4—34no—
435C22⋊C4—64no—
436C22⋊C4—122no—
437C22⋊C4—122no—
438C42—34no—
439C42—42no—
440C42—64no—
441C42—122no—
442C22×C3—24no—
443C22×C3—22no—
444C22×C3—22no—
445C22×C3—22no—
446C22×C3—22no—
447C22×C3—22no—
448C22×C3—22no—
449C22×C3—21no—
450C22×C3—22no—
451C22×C3—22no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—42no—
455C22×C3—42no—
456C22×C3—44no—
457C22×C3—44no—
458C22×C3—42no—
459C22×C3—42no—
460C22×C3—42no—
461C22×C3—42no—
462C22×C3—62no—
463C22×C3—62no—
464C22×C3—62no—
465C22×C3—122no—
466C22×C3—122no—
467C22×C3C22×C4×D311yescharacteristic
468C22×C3C2×#23512yes—
469C22×C3#100412yes—
470C22×C3D3×#4111yescharacteristic
471C22×C3D3×#4111yescharacteristic
472C22×C3C23×C3×C411yescharacteristic
473C22×C3C2×C3×#4112yes—
474C22×C3C2×C3×#4111yescharacteristic
475C22×C3C2×C3×#4111yescharacteristic
476C22×C3C3×H(5,𝔽2)12yes—
477C2×D3—22no—
478C2×D3—22no—
479C2×D3—22no—
480C2×D3—42no—
481C2×D3—42no—
482C3×C4—24no—
483C3×C4—22no—
484C3×C4—22no—
485C3×C4—24no—
486C3×C4—22no—
487C3×C4—22no—
488C3×C4—24no—
489C3×C4—34no—
490C3×C4—42no—
491C3×C4—44no—
492C3×C4—44no—
493C3×C4—42no—
494C3×C4—42no—
495C3×C4—62no—
496C3×C4—62no—
497C3×C4—122no—
498C3×C4—122no—
499Dic3—22no—
500Dic3—22no—
501Dic3—42no—
502Dic3—42no—
503Dic3C3×#11714yes—
504C32#235711yescharacteristic, complemented, Sylow
505C23—22no—
506C23—22no—
507C23—21no—
508C23—21no—
509C23—32no—
510C23—62no—
511C23—62no—
512C23—61no—
513C23—61no—
514C23C2×C3×C4×D312yes—
515C23C23×C3×D311yescharacteristic
516D4—68no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—32no—
525C2×C4—32no—
526C2×C4—32no—
527C2×C4—32no—
528C2×C4—32no—
529C2×C4—44no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—124no—
539C2×C4C2×C3×C4×D312yes—
540C2×C4C2×C3×C4×D312yes—
541C2×C4C3×#23514yes—
542C2×C3—21no—
543C2×C3—22no—
544C2×C3—22no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—44no—
548C2×C3—42no—
549C2×C3—42no—
550C2×C3—122no—
551C2×C3C4×#23511yescharacteristic
552C2×C3#548611yescharacteristic
553C2×C3D3×#11711yescharacteristic
554C2×C3#554012yes—
555C2×C3#555912yes—
556C2×C3C2×C3×#11711yescharacteristic
557C2×C3C3×C4×#4111yescharacteristic
558C2×C3C3×#51811yescharacteristic
559C2×C3C3×#55312yes—
560C2×C3C3×#55912yes—
561D3—42no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—42no—
566C22—42no—
567C22—62no—
568C22—62no—
569C22—62no—
570C22—122no—
571C22—122no—
572C22C22×C3×C4×D311yescharacteristic
573C22C2×C3×#23512yes—
574C22C3×#100412yes—
575C22C3×D3×#4111yescharacteristic
576C22C3×D3×#4111yescharacteristic
577C4—24no—
578C4—22no—
579C4—22no—
580C4—34no—
581C4—42no—
582C4—62no—
583C4—62no—
584C4—122no—
585C4—122no—
586C3—21no—
587C3#7346311yescharacteristic, direct product factor
588C3C3×#235711yescharacteristic, complemented
589C2—42no—
590C2—122no—
591C2C3×C4×#23511yescharacteristic
592C2C3×#548611yescharacteristic
593C2C3×D3×#11711yescharacteristic
594C2C3×#554012yes—
595C2C3×#555912yes—
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×C4×C22⋊C4C2
socleC23×C32C24
prime radicalC22×C3×#67C22
cosocleC23×C3C24×C3
hypercenterC3×C4×C22⋊C4D3
hypocenterC3C3×#2357
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C32×C4×C22⋊C4C2semidirect
3. C3×#5211C2semidirect
5. C3×#4945C2semidirect
6. C3×#4940C2semidirect
7. C3×C4×Dic3⋊C4C2semidirect
8. C3×#4666C2semidirect
9. C3×#4664C2semidirect
10. C3×#4650C2semidirect
11. C3×#4649C2semidirect
13. #73463C3direct (N × H)
21. C3×C4×#67C4semidirect
50. C3×C4×C22⋊C4D3semidirect
51. C3×C4×C22⋊C4C2×C3semidirect
52. #5211C2×C3semidirect
54. #4945C2×C3semidirect
55. #4940C2×C3semidirect
56. C4×Dic3⋊C4C2×C3semidirect
57. #4666C2×C3semidirect
58. #4664C2×C3semidirect
59. #4650C2×C3semidirect
60. #4649C2×C3semidirect
120. C4×#67C3×C4semidirect
193. C4×C22⋊C4C3×D3semidirect
504. C32#2357semidirect
587. C3#73463direct (N × H)
588. C3C3×#2357semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C32×C4×C22⋊C42
C3×#52112
C3×#49572
C3×#49452
C3×#49402
C3×C4×Dic3⋊C42
C3×#46662
C3×#46642
C3×#46502
C3×#46492
C3×#23573
#734633