Finite Group Databasebeta

← C3×D3×#339 #11783166

Subgroups — C3×D3×#339 #11783166

Order 1152.

1031 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×M16C211yesmaximal, characteristic
2C3×D3×#117C211yesmaximal, characteristic
3C2×C3×C42×D3C211yesmaximal, characteristic
4C32×#339C211yesmaximal, characteristic, complemented
5C3×#4555C211yesmaximal, characteristic, complemented
6C3×#4532C211yesmaximal, characteristic, complemented
7C3×#4523C211yesmaximal, characteristic, complemented
8C2×C3×#339—31nomaximal
9D3×#339C311yesmaximal, characteristic, direct product factor
10C22×C3×C4×D3—21no—
11C22×C3×C4×D3C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C32×#117C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×C4×Dic3—21no—
17C2×C3×C4×Dic3C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C3×D3×M16—22no—
20C3×D3×M16C414yescomplemented
21C2×C3×ΓL(1,𝔽25)—21no—
22C2×C3×D3×C8—21no—
23C3×#892C412yescomplemented
24C3×D3×C4⋊C4C412yescomplemented
25C3×D3×C22⋊C4—21no—
26C3×#877—21no—
27C3×#872—21no—
28C3×C42×D3—21no—
29C3×C42×D3—22no—
30C3×C42×D3C414yescomplemented
31C22×C3×M16—31no—
32C2×C3×#117—31no—
33C22×C3×C42—31no—
34C2×D3×M16C2×C311yescharacteristic
35D3×#117C2×C311yescharacteristic
36C2×C42×D3C2×C311yescharacteristic
37C3×#339—21no—
38C3×#339—31no—
39C3×#339—31no—
40C3×#339—31no—
41C3×#339D311yescharacteristic, direct product factor
42C3×#339C2×C311yescharacteristic, complemented
43#4555C2×C311yescharacteristic, complemented
44#4532C2×C311yescharacteristic, complemented
45#4523C2×C311yescharacteristic, complemented
46C23×C3×D3D411yescharacteristic
47C22×C32×C4—21no—
48C22×C32×C4C2311yescharacteristic
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C2×C3×C4×D3—28no—
52C2×C3×C4×D3—24no—
53C2×C3×C4×D3—22no—
54C2×C3×C4×D3C2×C412yes—
55C2×C3×C4×D3C2×C411yescharacteristic
56C2×C3×C4×D3C2×C411yescharacteristic
57C2×C3×C4×D3C2×C412yes—
58C2×C3×C4×D3D411yescharacteristic
59C2×C3×C4×D3D411yescharacteristic
60C2×C3×C4×D3D412yes—
61C2×C3×C4×D3Q812yes—
62C32×M16—21no—
63C32×M16C2×C412yescomplemented
64C2×C32×C8—21no—
65C32×C4⋊C4C2×C412yescomplemented
66C32×C22⋊C4—21no—
67C32×C42—21no—
68C32×C42—21no—
69C32×C42C2×C412yescomplemented
70C3×#217—21no—
71C3×(C2×D3)⋊C4—22no—
72C3×C4⋊Dic3C2×C412yescomplemented
73C3×Dic3⋊C4—22no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3—22no—
77C3×C4×Dic3—24no—
78C3×C4×Dic3C2×C412yescomplemented
79C3×#208—21no—
80C3×#208C2×C412yescomplemented
81C2×C3×C3⋊C8—21no—
82C3×ΓL(1,𝔽25)—24no—
83C3×D3×C8—24no—
84C2×#339—31noSylow
85C23×C3×C4—31no—
86C23×C3×C4—61no—
87C22×C4×D3—21no—
88C22×C4×D3C22×C311yescharacteristic
89C2×C3×M16—21no—
90C2×C3×M16—31no—
91C2×C3×M16—34no—
92C2×C3×M16—61no—
93C2×C3×M16—62no—
94C2×C3×M16C2×D311yescharacteristic
95C2×C3×M16C22×C311yescharacteristic
96C22×C3×C8—61no—
97C3×#117—21no—
98C3×#117—31no—
99C3×#117—32no—
100C3×#117—61no—
101C3×#117—61no—
102C3×#117C2×D311yescharacteristic
103C3×#117C22×C311yescharacteristic
104C2×C3×C4⋊C4—32no—
105C2×C3×C22⋊C4—61no—
106C2×C3×C42—21no—
107C2×C3×C42—31no—
108C2×C3×C42—34no—
109C2×C3×C42—62no—
110C2×C3×C42—61no—
111C2×C3×C42—61no—
112C2×C3×C42C2×D311yescharacteristic
113C2×C3×C42C22×C311yescharacteristic
114#926C22×C311yescharacteristic
115C2×C4×Dic3—21no—
116C2×C4×Dic3C22×C311yescharacteristic
117C2×#208C22×C311yescharacteristic
118D3×M16—22no—
119D3×M16C3×C414yescomplemented
120C2×ΓL(1,𝔽25)—21no—
121C2×D3×C8—21no—
122#892C3×C412yescomplemented
123D3×C4⋊C4C3×C412yescomplemented
124D3×C22⋊C4—21no—
125#877—21no—
126#872—21no—
127C42×D3—22no—
128C42×D3—21no—
129C42×D3C3×C414yescomplemented
130C23×C32C2×D411yescharacteristic
131C22×C3×D3—24no—
132C22×C3×D3C22⋊C411yescharacteristic
133C22×C3×D3C22⋊C412yes—
134C22×C3×D3C22⋊C411yescharacteristic
135C22×C3×D3C4⋊C412yes—
136C2×C32×C4—24no—
137C2×C32×C4—22no—
138C2×C32×C4—22no—
139C2×C32×C4C22×C411yescharacteristic
140C2×C32×C4C22×C411yescharacteristic
141C2×C32×C4C22×C411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×Q811yescharacteristic
145C2×C3×Dic3—24no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3C22⋊C412yes—
149C2×C3×Dic3C22⋊C411yescharacteristic
150C2×C3×Dic3C22⋊C411yescharacteristic
151C2×C3×Dic3C4⋊C412yes—
152C3×C4×D3—216no—
153C3×C4×D3—44no—
154C3×C4×D3C4212yes—
155C3×C4×D3C4212yes—
156C3×C4×D3C22⋊C412yes—
157C3×C4×D3C22⋊C412yes—
158C3×C4×D3C4⋊C412yes—
159C3×C4×D3C4⋊C412yes—
160C3×C4×D3C4⋊C412yes—
161C3×C4×D3C4⋊C412yes—
162C32×C8—22no—
163C3×C3⋊C8—22no—
164C22×M16—31no—
165C2×#117—31no—
166C22×C42—31no—
167#339—31no—
168#339—31no—
169#339—31no—
170#339C3×D311yescharacteristic, direct product factor
171C24×C3—31no—
172C23×D3C3×D411yescharacteristic
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—31no—
177C22×C3×C4—32no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C22×C3×C4—32no—
181C22×C3×C4—32no—
182C22×C3×C4—31no—
183C22×C3×C4—31no—
184C22×C3×C4—32no—
185C22×C3×C4—41no—
186C22×C3×C4—64no—
187C22×C3×C4—68no—
188C22×C3×C4—62no—
189C22×C3×C4—61no—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C23×C311yescharacteristic
192C22×Dic3—21no—
193C22×Dic3C3×D411yescharacteristic
194C2×C4×D3—28no—
195C2×C4×D3—24no—
196C2×C4×D3—22no—
197C2×C4×D3C2×C3×C412yes—
198C2×C4×D3C2×C3×C412yes—
199C2×C4×D3C2×C3×C411yescharacteristic
200C2×C4×D3C2×C3×C411yescharacteristic
201C2×C4×D3C3×D411yescharacteristic
202C2×C4×D3C3×D412yes—
203C2×C4×D3C3×D411yescharacteristic
204C2×C4×D3C3×Q812yes—
205C3×M16—21no—
206C3×M16—21no—
207C3×M16—22no—
208C3×M16—32no—
209C3×M16—41no—
210C3×M16—64no—
211C3×M16—61no—
212C3×M16C4×D312yescomplemented
213C3×M16C2×C3×C412yescomplemented
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—41no—
217C2×C3×C8—64no—
218C2×C3×C8—61no—
219C3×C4⋊C4—22no—
220C3×C4⋊C4—32no—
221C3×C4⋊C4—62no—
222C3×C4⋊C4C4×D312yescomplemented
223C3×C4⋊C4C2×C3×C412yescomplemented
224C3×C22⋊C4—21no—
225C3×C22⋊C4—21no—
226C3×C22⋊C4—41no—
227C3×C22⋊C4—62no—
228C3×C22⋊C4—61no—
229C3×C42—21no—
230C3×C42—21no—
231C3×C42—21no—
232C3×C42—21no—
233C3×C42—22no—
234C3×C42—32no—
235C3×C42—41no—
236C3×C42—41no—
237C3×C42—64no—
238C3×C42—62no—
239C3×C42—61no—
240C3×C42—61no—
241C3×C42C4×D312yescomplemented
242C3×C42C2×C3×C412yescomplemented
243#217—21no—
244(C2×D3)⋊C4—22no—
245C4⋊Dic3C2×C3×C412yescomplemented
246Dic3⋊C4—22no—
247C4×Dic3—21no—
248C4×Dic3—21no—
249C4×Dic3—24no—
250C4×Dic3—22no—
251C4×Dic3C2×C3×C412yescomplemented
252#208—21no—
253#208C2×C3×C412yescomplemented
254C2×C3⋊C8—21no—
255ΓL(1,𝔽25)—24no—
256D3×C8—24no—
257C22×C32—22no—
258C22×C32C2×C22⋊C411yescharacteristic
259C22×C32C2×C22⋊C411yescharacteristic
260C22×C32C2×C4⋊C411yescharacteristic
261C2×C3×D3—22no—
262C2×C3×D3—24no—
263C2×C3×D3—24no—
264C2×C3×D3#9512yes—
265C2×C3×D3#9512yes—
266C2×C3×D3#10414yes—
267C32×C4—24no—
268C32×C4—42no—
269C32×C4C2×C4211yescharacteristic
270C32×C4C2×C22⋊C411yescharacteristic
271C32×C4C2×C4⋊C411yescharacteristic
272C32×C4C2×C4⋊C411yescharacteristic
273C3×Dic3—24no—
274C3×Dic3—42no—
275C3×Dic3#9512yes—
276C3×Dic3#9512yes—
277C23×C4—31no—
278C23×C4—61no—
279C2×M16—31no—
280C2×M16—34no—
281C2×M16—61no—
282C2×M16—62no—
283C2×M16C2×C3×D311yescharacteristic
284C22×C8—61no—
285#117—31no—
286#117—32no—
287#117—61no—
288#117—61no—
289#117C2×C3×D311yescharacteristic
290C2×C4⋊C4—32no—
291C2×C22⋊C4—61no—
292C2×C42—31no—
293C2×C42—34no—
294C2×C42—61no—
295C2×C42—62no—
296C2×C42—61no—
297C2×C42C2×C3×D311yescharacteristic
298C23×C3—21no—
299C23×C3—31no—
300C23×C3—31no—
301C23×C3—32no—
302C23×C3—32no—
303C23×C3—64no—
304C23×C3D3×D411yescharacteristic
305C23×C3C2×C3×D411yescharacteristic
306C22×D3—24no—
307C22×D3C3×C22⋊C411yescharacteristic
308C22×D3C3×C22⋊C412yes—
309C22×D3C3×C22⋊C411yescharacteristic
310C22×D3C3×C4⋊C412yes—
311C2×C3×C4—24no—
312C2×C3×C4—24no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—32no—
324C2×C3×C4—31no—
325C2×C3×C4—31no—
326C2×C3×C4—32no—
327C2×C3×C4—32no—
328C2×C3×C4—32no—
329C2×C3×C4—32no—
330C2×C3×C4—32no—
331C2×C3×C4—32no—
332C2×C3×C4—32no—
333C2×C3×C4—32no—
334C2×C3×C4—32no—
335C2×C3×C4—42no—
336C2×C3×C4—44no—
337C2×C3×C4—42no—
338C2×C3×C4—616no—
339C2×C3×C4—64no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—124no—
343C2×C3×C4C2×C4×D311yescharacteristic
344C2×C3×C4C2×C4×D311yescharacteristic
345C2×C3×C4C2×C4×D311yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×Q811yescharacteristic
349C2×C3×C4C22×C3×C411yescharacteristic
350C2×C3×C4C22×C3×C411yescharacteristic
351C2×C3×C4C22×C3×C411yescharacteristic
352C2×C3×C4C2×C3×D411yescharacteristic
353C2×C3×C4C2×C3×D411yescharacteristic
354C2×C3×C4C2×C3×Q811yescharacteristic
355C2×Dic3—24no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3C3×C22⋊C412yes—
359C2×Dic3C3×C22⋊C411yescharacteristic
360C2×Dic3C3×C22⋊C411yescharacteristic
361C2×Dic3C3×C4⋊C412yes—
362C4×D3—216no—
363C4×D3—44no—
364C4×D3C3×C4212yes—
365C4×D3C3×C4212yes—
366C4×D3C3×C22⋊C412yes—
367C4×D3C3×C22⋊C412yes—
368C4×D3C3×C4⋊C412yes—
369C4×D3C3×C4⋊C412yes—
370C4×D3C3×C4⋊C412yes—
371C4×D3C3×C4⋊C412yes—
372C3×C8—22no—
373C3×C8—22no—
374C3×C8—42no—
375C3×C8—62no—
376C3⋊C8—22no—
377C2×C32—21no—
378C2×C32—21no—
379C2×C32C2×#9511yescharacteristic
380C2×C32C2×#10412yes—
381C3×D3—22no—
382C3×D3#33914yesdirect product factor
383C24—31no—
384C22×C4—21no—
385C22×C4—31no—
386C22×C4—32no—
387C22×C4—31no—
388C22×C4—31no—
389C22×C4—32no—
390C22×C4—31no—
391C22×C4—32no—
392C22×C4—31no—
393C22×C4—32no—
394C22×C4—64no—
395C22×C4—68no—
396C22×C4—62no—
397C22×C4—61no—
398C22×C4C22×C3×D311yescharacteristic
399M16—21no—
400M16—32no—
401M16—64no—
402M16—61no—
403M16C3×C4×D312yescomplemented
404C2×C8—21no—
405C2×C8—64no—
406C2×C8—61no—
407C4⋊C4—32no—
408C4⋊C4—62no—
409C4⋊C4C3×C4×D312yescomplemented
410C22⋊C4—21no—
411C22⋊C4—62no—
412C22⋊C4—61no—
413C42—21no—
414C42—21no—
415C42—32no—
416C42—64no—
417C42—62no—
418C42—61no—
419C42—61no—
420C42C3×C4×D312yescomplemented
421C22×C3—22no—
422C22×C3—22no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—32no—
427C22×C3—34no—
428C22×C3—32no—
429C22×C3—42no—
430C22×C3—64no—
431C22×C3—64no—
432C22×C3—62no—
433C22×C3D3×C22⋊C411yescharacteristic
434C22×C3D3×C22⋊C411yescharacteristic
435C22×C3D3×C4⋊C411yescharacteristic
436C22×C3C2×C3×C22⋊C411yescharacteristic
437C22×C3C2×C3×C22⋊C411yescharacteristic
438C22×C3C2×C3×C4⋊C411yescharacteristic
439C2×D3—22no—
440C2×D3—24no—
441C2×D3—24no—
442C2×D3C3×#9512yes—
443C2×D3C3×#9512yes—
444C2×D3C3×#10414yes—
445C3×C4—24no—
446C3×C4—24no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—32no—
452C3×C4—32no—
453C3×C4—44no—
454C3×C4—42no—
455C3×C4—42no—
456C3×C4—64no—
457C3×C4—82no—
458C3×C4—122no—
459C3×C4C42×D311yescharacteristic
460C3×C4D3×C22⋊C411yescharacteristic
461C3×C4D3×C4⋊C411yescharacteristic
462C3×C4D3×C4⋊C411yescharacteristic
463C3×C4C2×C3×C4211yescharacteristic
464C3×C4C2×C3×C22⋊C411yescharacteristic
465C3×C4C2×C3×C4⋊C411yescharacteristic
466C3×C4C2×C3×C4⋊C411yescharacteristic
467Dic3—24no—
468Dic3—42no—
469Dic3C3×#9512yes—
470Dic3C3×#9512yes—
471C32C2×#33911yescharacteristic, complemented, Sylow
472C23—31no—
473C23—31no—
474C23—32no—
475C23—32no—
476C23—64no—
477C23C3×D3×D411yescharacteristic
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—32no—
482C2×C4—31no—
483C2×C4—31no—
484C2×C4—32no—
485C2×C4—32no—
486C2×C4—32no—
487C2×C4—32no—
488C2×C4—32no—
489C2×C4—32no—
490C2×C4—32no—
491C2×C4—32no—
492C2×C4—32no—
493C2×C4—616no—
494C2×C4—64no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—124no—
498C2×C4C2×C3×C4×D311yescharacteristic
499C2×C4C2×C3×C4×D311yescharacteristic
500C2×C4C2×C3×C4×D311yescharacteristic
501C2×C4C3×D3×D411yescharacteristic
502C2×C4C3×D3×D411yescharacteristic
503C2×C4C3×D3×Q811yescharacteristic
504C8—22no—
505C8—62no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—22no—
512C2×C3—34no—
513C2×C3—41no—
514C2×C3—41no—
515C2×C3—62no—
516C2×C3D3×#9511yescharacteristic
517C2×C3D3×#10412yes—
518C2×C3C2×C3×#9511yescharacteristic
519C2×C3C2×C3×#10412yes—
520D3—22no—
521D3C3×#33914yesdirect product factor
522C22—22no—
523C22—32no—
524C22—34no—
525C22—32no—
526C22—64no—
527C22—64no—
528C22—62no—
529C22C3×D3×C22⋊C411yescharacteristic
530C22C3×D3×C22⋊C411yescharacteristic
531C22C3×D3×C4⋊C411yescharacteristic
532C4—24no—
533C4—32no—
534C4—32no—
535C4—42no—
536C4—64no—
537C4—122no—
538C4C3×C42×D311yescharacteristic
539C4C3×D3×C22⋊C411yescharacteristic
540C4C3×D3×C4⋊C411yescharacteristic
541C4C3×D3×C4⋊C411yescharacteristic
542C3—21no—
543C3D3×#33911yescharacteristic, direct product factor
544C3C2×C3×#33911yescharacteristic, complemented
545C2—21no—
546C2—21no—
547C2—34no—
548C2—62no—
549C2C3×D3×#9511yescharacteristic
550C2C3×D3×#10412yes—
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC3×C4C2×C3×C42
FrattiniC22×C4C22×C3×D3
FittingC32×#339C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3D4
cosocleC22×C3×C4C23×C3
hypercenterC3×#339D3
hypocenterC3C2×C3×#339
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C3×#339

Complements

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

NH ≅ G/Ntype
4. C32×#339C2semidirect
5. C3×#4555C2semidirect
6. C3×#4532C2semidirect
7. C3×#4523C2semidirect
9. D3×#339C3direct (N × H)
20. C3×D3×M16C4semidirect
23. C3×#892C4semidirect
24. C3×D3×C4⋊C4C4semidirect
30. C3×C42×D3C4semidirect
41. C3×#339D3direct (N × H)
42. C3×#339C2×C3semidirect
43. #4555C2×C3semidirect
44. #4532C2×C3semidirect
45. #4523C2×C3semidirect
63. C32×M16C2×C4semidirect
65. C32×C4⋊C4C2×C4semidirect
69. C32×C42C2×C4semidirect
72. C3×C4⋊Dic3C2×C4semidirect
78. C3×C4×Dic3C2×C4semidirect
80. C3×#208C2×C4semidirect
119. D3×M16C3×C4semidirect
122. #892C3×C4semidirect
123. D3×C4⋊C4C3×C4semidirect
129. C42×D3C3×C4semidirect
170. #339C3×D3direct (N × H)
212. C3×M16C4×D3semidirect
213. C3×M16C2×C3×C4semidirect
222. C3×C4⋊C4C4×D3semidirect
223. C3×C4⋊C4C2×C3×C4semidirect
241. C3×C42C4×D3semidirect
242. C3×C42C2×C3×C4semidirect
245. C4⋊Dic3C2×C3×C4semidirect
251. C4×Dic3C2×C3×C4semidirect
253. #208C2×C3×C4semidirect
382. C3×D3#339direct (N × H)
403. M16C3×C4×D3semidirect
409. C4⋊C4C3×C4×D3semidirect
420. C42C3×C4×D3semidirect
471. C32C2×#339semidirect
521. D3C3×#339direct (N × H)
543. C3D3×#339direct (N × H)
544. C3C2×C3×#339semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×M162
C3×D3×#1172
C2×C3×C42×D32
C32×#3392
C3×#45552
C3×#45322
C3×#45232
C2×C3×#3393
D3×#3393