Finite Group Databasebeta

← C3×#73367 #11803027

Subgroups — C3×#73367 #11803027

Order 1152.

1301 conjugacy classes of subgroups.

The subgroup lattice has 599 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic
2C2×C32×#95C211yesmaximal, characteristic, complemented
3C3×#5213C212yesmaximal
4C3×#5210C212yesmaximal, complemented
5C3×C4×#217C211yesmaximal, characteristic, complemented
6C3×#4669C212yesmaximal, complemented
7C3×#4667C211yesmaximal, characteristic, complemented
8C3×#4664C211yesmaximal, characteristic, complemented
9C3×#4652C212yesmaximal, complemented
10C3×#4651C211yesmaximal, characteristic, complemented
11C3×#4650C211yesmaximal, characteristic, complemented
12C3×#2318—31nomaximal
13#73367C311yesmaximal, characteristic, direct product factor
14C23×C32×C4C2212yes—
15C23×C32×C4C2211yescharacteristic
16C22×C3×#67C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C2×C3×#217C2212yes—
19C2×C3×#217C2211yescharacteristic
20C3×C4×#67C418yescomplemented
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×C4×Dic3C2212yes—
28C2×C3×C4×Dic3C2211yescharacteristic
29C32×#95C2211yescharacteristic
30C32×#95C2211yescharacteristic
31C32×#95C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C2×C3×C4×D4—31no—
39C2×C4×#67C2×C311yescharacteristic
40C3×#388—32no—
41C3×#387—32no—
42C3×#386—32no—
43C3×#385—32no—
44C3×#383—31no—
45C3×#382—31no—
46C3×#381—31no—
47C3×#380—31no—
48C3×C4×C22⋊C4—31no—
49C2×C3×#95—21no—
50C2×C3×#95D311yescharacteristic, complemented
51C2×C3×#95C2×C311yescharacteristic, complemented
52#5213C2×C312yes—
53#5210C2×C312yescomplemented
54C4×#217C2×C311yescharacteristic, complemented
55#4669C2×C312yescomplemented
56#4667C2×C311yescharacteristic, complemented
57#4664C2×C311yescharacteristic, complemented
58#4652C2×C312yescomplemented
59#4651C2×C311yescharacteristic, complemented
60#4650C2×C311yescharacteristic, complemented
61C24×C32C2311yescharacteristic
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4—24no—
64C22×C32×C4—42no—
65C22×C32×C4—42no—
66C22×C32×C4—42no—
67C22×C32×C4C2×C414yes—
68C22×C32×C4C2312yes—
69C22×C32×C4C2312yes—
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C2×C3×#67—24no—
73C2×C3×#67C2×C414yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2311yescharacteristic
79C2×C3×C4×D3—42no—
80C2×C3×C4×D3C2×C414yescomplemented
81C3×#217—24no—
82C3×#217C2×C414yes—
83C3×(C2×D3)⋊C4—42no—
84C3×(C2×D3)⋊C4—42no—
85C3×(C2×D3)⋊C4C2×C414yescomplemented
86C3×Dic3⋊C4—42no—
87C3×Dic3⋊C4—42no—
88C3×Dic3⋊C4C2×C414yescomplemented
89C3×C4×Dic3—42no—
90C3×C4×Dic3C2×C414yescomplemented
91#2318—31noSylow
92C22×C3×D4—31no—
93C23×C3×C4—22no—
94C23×C3×C4—21no—
95C23×C3×C4—31no—
96C23×C3×C4C2×D312yes—
97C23×C3×C4C2×D311yescharacteristic
98C23×C3×C4C22×C312yes—
99C23×C3×C4C22×C311yescharacteristic
100C22×#67C22×C311yescharacteristic
101C22×C4×D3C22×C311yescharacteristic
102C3×C4×D4—38no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C4⋊C4—32no—
105C2×C3×C4⋊C4—32no—
106C2×C3×C22⋊C4—31no—
107C2×C3×C22⋊C4—31no—
108C2×C3×C22⋊C4—32no—
109C2×C3×C22⋊C4—32no—
110C2×C3×C22⋊C4—32no—
111C2×C3×C42—31no—
112C2×C3×C42—32no—
113C2×#217C22×C312yes—
114C2×#217C22×C311yescharacteristic
115C4×#67C3×C418yescomplemented
116C2×(C2×D3)⋊C4C22×C312yes—
117C2×(C2×D3)⋊C4C22×C312yes—
118C2×(C2×D3)⋊C4C22×C311yescharacteristic
119C2×Dic3⋊C4C22×C312yes—
120C2×Dic3⋊C4C22×C312yes—
121C2×Dic3⋊C4C22×C311yescharacteristic
122C2×C4×Dic3C22×C312yes—
123C2×C4×Dic3C22×C311yescharacteristic
124C3×#95—21no—
125C3×#95—21no—
126C3×#95—22no—
127C3×#95—31no—
128C3×#95—31no—
129C3×#95—32no—
130C3×#95—32no—
131C3×#95—32no—
132C3×#95—32no—
133C3×#95C2×D311yescharacteristic
134C3×#95C2×D311yescharacteristic
135C3×#95C2×D312yes—
136C3×#95C22×C311yescharacteristic
137C3×#95C22×C311yescharacteristic
138C3×#95C22×C312yes—
139C3⋊#95C22×C312yes—
140C3⋊#95C22×C311yescharacteristic
141C3⋊#95C22×C312yes—
142C3⋊#95C22×C311yescharacteristic
143C3⋊#95C22×C312yes—
144C3⋊#95C22×C312yes—
145C23×C32—22no—
146C23×C32—21no—
147C23×C32—21no—
148C23×C32C22×C412yes—
149C23×C32#4114yes—
150C23×C32C2411yescharacteristic
151C22×C3×D3—22no—
152C22×C3×D3—21no—
153C22×C3×D3—22no—
154C22×C3×D3—21no—
155C22×C3×D3C22×C412yes—
156C2×C32×C4—22no—
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×C4—48no—
166C2×C32×C4C22×C412yes—
167C2×C32×C4C22×C412yes—
168C3×#67—28no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3C22×C412yes—
180C2×C3×Dic3C22×C412yes—
181C2×C3×Dic3C22×C412yes—
182C3×C4×D3—44no—
183C2×C4×D4—31no—
184#388—32no—
185#387—32no—
186#386—32no—
187#385—32no—
188#383—31no—
189#382—31no—
190#381—31no—
191#380—31no—
192C4×C22⋊C4—31no—
193C2×#95C3×D311yescharacteristic, complemented
194C24×C3—21no—
195C24×C3—31no—
196C24×C3C22×D311yescharacteristic
197C24×C3C23×C311yescharacteristic
198C23×D3C23×C311yescharacteristic
199C2×C3×D4—34no—
200C2×C3×D4—64no—
201C22×C3×C4—28no—
202C22×C3×C4—24no—
203C22×C3×C4—24no—
204C22×C3×C4—24no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—31no—
210C22×C3×C4—31no—
211C22×C3×C4—31no—
212C22×C3×C4—34no—
213C22×C3×C4—32no—
214C22×C3×C4—32no—
215C22×C3×C4—42no—
216C22×C3×C4—42no—
217C22×C3×C4—42no—
218C22×C3×C4—42no—
219C22×C3×C4—42no—
220C22×C3×C4—42no—
221C22×C3×C4—44no—
222C22×C3×C4—44no—
223C22×C3×C4—44no—
224C22×C3×C4—122no—
225C22×C3×C4C4×D314yes—
226C22×C3×C4C2×C3×C414yes—
227C22×C3×C4C22×D312yes—
228C22×C3×C4C22×D312yes—
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C23×C312yes—
232C22×C3×C4C23×C312yes—
233C22×C3×C4C23×C311yescharacteristic
234C22×C3×C4C23×C311yescharacteristic
235C2×#67—24no—
236C2×#67C2×C3×C414yes—
237C22×Dic3C23×C312yes—
238C22×Dic3C23×C312yes—
239C22×Dic3C23×C311yescharacteristic
240C22×Dic3C23×C311yescharacteristic
241C22×Dic3C23×C311yescharacteristic
242C2×C4×D3—42no—
243C2×C4×D3C2×C3×C414yescomplemented
244C3×C4⋊C4—34no—
245C3×C4⋊C4—122no—
246C3×C4⋊C4—122no—
247C3×C22⋊C4—34no—
248C3×C22⋊C4—34no—
249C3×C22⋊C4—64no—
250C3×C22⋊C4—122no—
251C3×C22⋊C4—122no—
252C3×C42—34no—
253C3×C42—122no—
254#217—24no—
255#217C2×C3×C414yes—
256(C2×D3)⋊C4—42no—
257(C2×D3)⋊C4—42no—
258(C2×D3)⋊C4C2×C3×C414yescomplemented
259Dic3⋊C4—42no—
260Dic3⋊C4—42no—
261Dic3⋊C4C2×C3×C414yescomplemented
262C4×Dic3—42no—
263C4×Dic3C2×C3×C414yescomplemented
264C22×C32—22no—
265C22×C32—22no—
266C22×C32—24no—
267C22×C32—24no—
268C22×C32#11714yes—
269C22×C32C23×C411yescharacteristic
270C22×C32C2×#4112yes—
271C22×C32H(5,𝔽2)12yes—
272C22×C32H(5,𝔽2)11yescharacteristic
273C22×C322−1+411yescharacteristic
274C2×C3×D3—22no—
275C2×C3×D3—22no—
276C2×C3×D3—22no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C32×C4—22no—
280C32×C4—22no—
281C32×C4—42no—
282C32×C4—42no—
283C3×Dic3—22no—
284C3×Dic3—22no—
285C3×Dic3—22no—
286C3×Dic3—42no—
287C3×Dic3—42no—
288C22×D4—31no—
289C23×C4—31no—
290C23×C4C2×C3×D312yes—
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×C42—31no—
302C2×C42—32no—
303#95—31no—
304#95—31no—
305#95—32no—
306#95—32no—
307#95—32no—
308#95—32no—
309#95C2×C3×D311yescharacteristic
310#95C2×C3×D311yescharacteristic
311#95C2×C3×D312yes—
312C23×C3—22no—
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—21no—
322C23×C3—22no—
323C23×C3—24no—
324C23×C3—32no—
325C23×C3—62no—
326C23×C3—61no—
327C23×C3—62no—
328C23×C3—61no—
329C23×C3C2×C4×D312yes—
330C23×C3#23514yes—
331C23×C3C22×C3×C412yes—
332C23×C3C3×#4114yes—
333C23×C3C23×D311yescharacteristic
334C23×C3C24×C311yescharacteristic
335C22×D3—22no—
336C22×D3—21no—
337C22×D3—22no—
338C22×D3—21no—
339C22×D3C22×C3×C412yes—
340C3×D4—68no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—24no—
346C2×C3×C4—24no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
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—22no—
361C2×C3×C4—32no—
362C2×C3×C4—32no—
363C2×C3×C4—32no—
364C2×C3×C4—42no—
365C2×C3×C4—42no—
366C2×C3×C4—42no—
367C2×C3×C4—42no—
368C2×C3×C4—42no—
369C2×C3×C4—42no—
370C2×C3×C4—44no—
371C2×C3×C4—44no—
372C2×C3×C4—48no—
373C2×C3×C4—416no—
374C2×C3×C4—48no—
375C2×C3×C4—48no—
376C2×C3×C4—62no—
377C2×C3×C4—61no—
378C2×C3×C4—62no—
379C2×C3×C4—61no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—124no—
387C2×C3×C4C2×C4×D312yes—
388C2×C3×C4C2×C4×D312yes—
389C2×C3×C4C22×C3×C412yes—
390C2×C3×C4C22×C3×C412yes—
391#67—28no—
392C2×Dic3—22no—
393C2×Dic3—21no—
394C2×Dic3—22no—
395C2×Dic3—21no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3C22×C3×C412yes—
403C2×Dic3C22×C3×C412yes—
404C2×Dic3C22×C3×C412yes—
405C4×D3—44no—
406C2×C32—24no—
407C2×C32C2×#11711yescharacteristic
408C2×C32#51811yescharacteristic
409C2×C32#52011yescharacteristic
410C2×C32#53812yes—
411C2×C32#53912yes—
412C3×D3—42no—
413C24—31no—
414C24C22×C3×D311yescharacteristic
415C2×D4—34no—
416C2×D4—64no—
417C22×C4—24no—
418C22×C4—31no—
419C22×C4—31no—
420C22×C4—31no—
421C22×C4—34no—
422C22×C4—32no—
423C22×C4—32no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—122no—
428C22×C4C3×C4×D314yes—
429C22×C4C22×C3×D312yes—
430C22×C4C22×C3×D312yes—
431C22×C4C22×C3×D311yescharacteristic
432C22×C4C22×C3×D311yescharacteristic
433C4⋊C4—34no—
434C4⋊C4—122no—
435C4⋊C4—122no—
436C22⋊C4—34no—
437C22⋊C4—34no—
438C22⋊C4—64no—
439C22⋊C4—122no—
440C22⋊C4—122no—
441C42—34no—
442C42—122no—
443C22×C3—28no—
444C22×C3—24no—
445C22×C3—24no—
446C22×C3—28no—
447C22×C3—22no—
448C22×C3—24no—
449C22×C3—22no—
450C22×C3—24no—
451C22×C3—22no—
452C22×C3—22no—
453C22×C3—24no—
454C22×C3—24no—
455C22×C3—21no—
456C22×C3—22no—
457C22×C3—21no—
458C22×C3—22no—
459C22×C3—21no—
460C22×C3—24no—
461C22×C3—62no—
462C22×C3—62no—
463C22×C3—62no—
464C22×C3—122no—
465C22×C3—122no—
466C22×C3#87214yes—
467C22×C3C3×#11714yes—
468C22×C3C22×C4×D311yescharacteristic
469C22×C3C2×#23512yes—
470C22×C3#100412yes—
471C22×C3#100411yescharacteristic
472C22×C3#100711yescharacteristic
473C22×C3C23×C3×C411yescharacteristic
474C22×C3C2×C3×#4112yes—
475C22×C3C3×H(5,𝔽2)12yes—
476C22×C3C3×H(5,𝔽2)11yescharacteristic
477C22×C3C3×2−1+411yescharacteristic
478C2×D3—22no—
479C2×D3—22no—
480C2×D3—22no—
481C2×D3—42no—
482C2×D3—42no—
483C3×C4—22no—
484C3×C4—22no—
485C3×C4—22no—
486C3×C4—22no—
487C3×C4—42no—
488C3×C4—42no—
489C3×C4—44no—
490C3×C4—44no—
491C3×C4—42no—
492C3×C4—42no—
493C3×C4—42no—
494C3×C4—42no—
495C3×C4—62no—
496C3×C4—62no—
497C3×C4—62no—
498C3×C4—122no—
499C3×C4—122no—
500Dic3—22no—
501Dic3—22no—
502Dic3—22no—
503Dic3—42no—
504Dic3—42no—
505C32#231811yescharacteristic, complemented, Sylow
506C23—21no—
507C23—22no—
508C23—21no—
509C23—32no—
510C23—62no—
511C23—61no—
512C23—62no—
513C23—61no—
514C23C2×C3×C4×D312yes—
515C23C3×#23514yes—
516C23C23×C3×D311yescharacteristic
517D4—68no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—32no—
527C2×C4—32no—
528C2×C4—32no—
529C2×C4—44no—
530C2×C4—48no—
531C2×C4—62no—
532C2×C4—61no—
533C2×C4—62no—
534C2×C4—61no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—62no—
541C2×C4—124no—
542C2×C4C2×C3×C4×D312yes—
543C2×C4C2×C3×C4×D312yes—
544C2×C3—28no—
545C2×C3—24no—
546C2×C3—24no—
547C2×C3—22no—
548C2×C3—21no—
549C2×C3—22no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—122no—
553C2×C3C2×#87211yescharacteristic
554C2×C3#548611yescharacteristic
555C2×C3#549412yes—
556C2×C3#550411yescharacteristic
557C2×C3#551512yes—
558C2×C3C2×C3×#11711yescharacteristic
559C2×C3C3×#51811yescharacteristic
560C2×C3C3×#52011yescharacteristic
561C2×C3C3×#53812yes—
562C2×C3C3×#53912yes—
563D3—42no—
564C22—24no—
565C22—22no—
566C22—24no—
567C22—22no—
568C22—62no—
569C22—62no—
570C22—62no—
571C22—122no—
572C22—122no—
573C22C3×#87214yes—
574C22C22×C3×C4×D311yescharacteristic
575C22C2×C3×#23512yes—
576C22C3×#100411yescharacteristic
577C22C3×#100412yes—
578C22C3×#100711yescharacteristic
579C4—22no—
580C4—22no—
581C4—42no—
582C4—42no—
583C4—62no—
584C4—62no—
585C4—62no—
586C4—122no—
587C4—122no—
588C3—21no—
589C3#7336711yescharacteristic, direct product factor
590C3C3×#231811yescharacteristic, complemented
591C2—24no—
592C2—122no—
593C2C2×C3×#87211yescharacteristic
594C2C3×#548611yescharacteristic
595C2C3×#549412yes—
596C2C3×#550411yescharacteristic
597C2C3×#551512yes—
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×#95C2
socleC23×C32C24
prime radicalC22×C3×#67C22
cosocleC23×C3C24×C3
hypercenterC2×C3×#95D3
hypocenterC3C3×#2318
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#95

Complements

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

NH ≅ G/Ntype
2. C2×C32×#95C2semidirect
4. C3×#5210C2semidirect
5. C3×C4×#217C2semidirect
6. C3×#4669C2semidirect
7. C3×#4667C2semidirect
8. C3×#4664C2semidirect
9. C3×#4652C2semidirect
10. C3×#4651C2semidirect
11. C3×#4650C2semidirect
13. #73367C3direct (N × H)
20. C3×C4×#67C4semidirect
50. C2×C3×#95D3semidirect
51. C2×C3×#95C2×C3semidirect
53. #5210C2×C3semidirect
54. C4×#217C2×C3semidirect
55. #4669C2×C3semidirect
56. #4667C2×C3semidirect
57. #4664C2×C3semidirect
58. #4652C2×C3semidirect
59. #4651C2×C3semidirect
60. #4650C2×C3semidirect
80. C2×C3×C4×D3C2×C4semidirect
85. C3×(C2×D3)⋊C4C2×C4semidirect
88. C3×Dic3⋊C4C2×C4semidirect
90. C3×C4×Dic3C2×C4semidirect
115. C4×#67C3×C4semidirect
193. C2×#95C3×D3semidirect
243. C2×C4×D3C2×C3×C4semidirect
258. (C2×D3)⋊C4C2×C3×C4semidirect
261. Dic3⋊C4C2×C3×C4semidirect
263. C4×Dic3C2×C3×C4semidirect
505. C32#2318semidirect
589. C3#73367direct (N × H)
590. C3C3×#2318semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C2×C32×#952
C3×#52132
C3×#52102
C3×C4×#2172
C3×#46692
C3×#46672
C3×#46642
C3×#46522
C3×#46512
C3×#46502
C3×#23183
#733673