Finite Group Databasebeta

← C3×D3×#557 #11903665

Subgroups — C3×D3×#557 #11903665

Order 1152.

2196 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#557C211yesmaximal, characteristic, complemented
2C3×D3×C4⋊Q8C213yesmaximal
3C3×#5721C213yesmaximal, complemented
4C3×D3×#125C216yesmaximal
5C3×#5685C216yesmaximal, complemented
6C3×C4×D3×Q8C213yesmaximal
7C3×C4×D3×Q8C211yesmaximal, characteristic
8C3×C4×D3×Q8C212yesmaximal
9C3×#5570C211yesmaximal, characteristic, complemented
10C3×#5569C212yesmaximal, complemented
11C3×#5567C213yesmaximal, complemented
12C2×C3×#557—31nomaximal
13D3×#557C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8C2213yes—
15C2×C3×D3×Q8C2211yescharacteristic
16C32×C4⋊Q8C2213yes—
17C32×#125C2216yes—
18C32×C4×Q8C2213yes—
19C32×C4×Q8C2212yes—
20C32×C4×Q8C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C3×Q8×Dic3C2212yes—
23C3×Q8×Dic3C2213yes—
24C3×#944C2216yes—
25C3×D3×C4⋊C4C2211yescharacteristic
26C3×D3×C4⋊C4C2213yes—
27C3×D3×C4⋊C4C2216yes—
28C3×D3×C4⋊C4C2216yes—
29C3×D3×C4⋊C4C2216yes—
30C3×#890C2216yes—
31C3×#890C2216yes—
32C3×#889C22112yes—
33C3×#889C22112yes—
34C3×#888C2216yes—
35C3×#888C2216yes—
36C3×#887C2213yes—
37C3×#887C2213yes—
38C3×#887C2216yes—
39C3×#887C2216yes—
40C3×C42×D3C2216yes—
41C3×C42×D3C2213yes—
42C3×#870C2216yes—
43C3×#869C2213yes—
44C3×C4×Dic6C2216yes—
45C3×C4×Dic6C2213yes—
46C3×C4×Dic6C2216yes—
47C3×C4×Dic6C2213yes—
48C3×#557—21no—
49C3×#557—33no—
50C3×#557—36no—
51C3×#557—33no—
52C3×#557—32no—
53C3×#557—31no—
54C3×#557D311yescharacteristic, direct product factor
55C3×#557C2×C311yescharacteristic, complemented
56C2×C3×C4⋊Q8—33no—
57C2×C3×#125—36no—
58C2×C3×C4×Q8—32no—
59C2×C3×C4×Q8—33no—
60C2×C3×C4×Q8—31no—
61D3×C4⋊Q8C2×C313yes—
62#5721C2×C313yescomplemented
63D3×#125C2×C316yes—
64#5685C2×C316yescomplemented
65C4×D3×Q8C2×C312yes—
66C4×D3×Q8C2×C313yes—
67C4×D3×Q8C2×C311yescharacteristic
68#5570C2×C311yescharacteristic, complemented
69#5569C2×C312yescomplemented
70#5567C2×C313yescomplemented
71C2×C32×Q8C2313yes—
72C2×C32×Q8C2311yescharacteristic
73C3×D3×Q8—212no—
74C3×D3×Q8Q818yescomplemented
75C2×C3×C4×D3C2313yes—
76C2×C3×C4×D3C2316yes—
77C2×C3×C4×D3C2312yes—
78C2×C3×C4×D3C2313yes—
79C2×C3×C4×D3C2311yescharacteristic
80C2×C3×Dic6C2316yes—
81C2×C3×Dic6C2313yes—
82C2×C3×Dic6C2313yes—
83C32×C4⋊C4C2311yescharacteristic
84C32×C4⋊C4C2316yes—
85C32×C4⋊C4C2316yes—
86C32×C4⋊C4C2313yes—
87C32×C4⋊C4C2316yes—
88C32×C42C2316yes—
89C32×C42C2313yes—
90C3×C4⋊Dic3C2316yes—
91C3×C4⋊Dic3C2316yes—
92C3×C4⋊Dic3C2316yes—
93C3×C4⋊Dic3C2313yes—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×Dic3⋊C4C2312yes—
96C3×Dic3⋊C4C23112yes—
97C3×Dic3⋊C4C2316yes—
98C3×Dic3⋊C4C2316yes—
99C3×Dic3⋊C4C2316yes—
100C3×Dic3⋊C4C23112yes—
101C3×C4×Dic3C2313yes—
102C3×C4×Dic3C2316yes—
103C3×C4×Dic3C2316yes—
104C3×C4×Dic3C2313yes—
105C3×C4×Dic3C2316yes—
106C3×C4×Dic3C2313yes—
107C2×#557—31noSylow
108C22×C3×Q8—31no—
109C22×C3×Q8—33no—
110C2×D3×Q8C22×C313yes—
111C2×D3×Q8C22×C311yescharacteristic
112C3×C4⋊Q8—23no—
113C3×C4⋊Q8—36no—
114C3×C4⋊Q8—36no—
115C3×C4⋊Q8—36no—
116C3×C4⋊Q8—33no—
117C3×C4⋊Q8C2×D313yes—
118C3×C4⋊Q8C22×C313yes—
119C3×#125—26no—
120C3×#125—312no—
121C3×#125—312no—
122C3×#125—36no—
123C3×#125—36no—
124C3×#125—36no—
125C3×#125C2×D316yes—
126C3×#125C22×C316yes—
127C3×C4×Q8—22no—
128C3×C4×Q8—23no—
129C3×C4×Q8—21no—
130C3×C4×Q8—32no—
131C3×C4×Q8—33no—
132C3×C4×Q8—31no—
133C3×C4×Q8—36no—
134C3×C4×Q8—36no—
135C3×C4×Q8—33no—
136C3×C4×Q8—33no—
137C3×C4×Q8—36no—
138C3×C4×Q8—33no—
139C3×C4×Q8—36no—
140C3×C4×Q8—33no—
141C3×C4×Q8C2×D312yes—
142C3×C4×Q8C2×D313yes—
143C3×C4×Q8C2×D311yescharacteristic
144C3×C4×Q8C22×C313yes—
145C3×C4×Q8C22×C312yes—
146C3×C4×Q8C22×C311yescharacteristic
147C2×C3×C4⋊C4—31no—
148C2×C3×C4⋊C4—33no—
149C2×C3×C4⋊C4—36no—
150C2×C3×C4⋊C4—36no—
151C2×C3×C4⋊C4—36no—
152C2×C3×C42—36no—
153C2×C3×C42—33no—
154Q8×Dic3C22×C313yes—
155Q8×Dic3C22×C311yescharacteristic
156Q8×Dic3C22×C312yes—
157#944C22×C316yes—
158D3×C4⋊C4C22×C316yes—
159D3×C4⋊C4C22×C316yes—
160D3×C4⋊C4C22×C313yes—
161D3×C4⋊C4C22×C316yes—
162D3×C4⋊C4C22×C311yescharacteristic
163#890C22×C316yes—
164#890C22×C316yes—
165#889C22×C3112yes—
166#889C22×C3112yes—
167#888C22×C316yes—
168#888C22×C316yes—
169#887C22×C316yes—
170#887C22×C313yes—
171#887C22×C316yes—
172#887C22×C313yes—
173C42×D3C22×C316yes—
174C42×D3C22×C313yes—
175#870C22×C316yes—
176#869C22×C313yes—
177C4×Dic6C22×C316yes—
178C4×Dic6C22×C316yes—
179C4×Dic6C22×C313yes—
180C4×Dic6C22×C313yes—
181C22×C3×D3C2411yescharacteristic
182C32×Q8—26no—
183C32×Q8C2×Q814yescomplemented
184C2×C32×C4C2412yes—
185C2×C32×C4C2413yes—
186C2×C32×C4C2416yes—
187C2×C32×C4C2413yes—
188C2×C32×C4C2411yescharacteristic
189C2×C3×Dic3C2412yes—
190C2×C3×Dic3C2413yes—
191C2×C3×Dic3C2416yes—
192C2×C3×Dic3C2413yes—
193C2×C3×Dic3C2411yescharacteristic
194C3×C4×D3—212no—
195C3×C4×D3—26no—
196C3×C4×D3—24no—
197C3×C4×D3C2×Q8112yes—
198C3×C4×D3#4114yes—
199C3×Dic6—26no—
200C3×Dic6—212no—
201C3×Dic6C2×Q8112yescomplemented
202#557—33no—
203#557—36no—
204#557—33no—
205#557—32no—
206#557—31no—
207#557C3×D311yescharacteristic, direct product factor
208C2×C4⋊Q8—33no—
209C2×#125—36no—
210C2×C4×Q8—32no—
211C2×C4×Q8—33no—
212C2×C4×Q8—31no—
213C2×C3×Q8—21no—
214C2×C3×Q8—23no—
215C2×C3×Q8—38no—
216C2×C3×Q8—33no—
217C2×C3×Q8—36no—
218C2×C3×Q8—33no—
219C2×C3×Q8—612no—
220C2×C3×Q8C22×D313yes—
221C2×C3×Q8C22×D311yescharacteristic
222C2×C3×Q8C23×C313yes—
223C2×C3×Q8C23×C311yescharacteristic
224C22×C3×C4—33no—
225C22×C3×C4—31no—
226C22×C3×C4—32no—
227C22×C3×C4—33no—
228C22×C3×C4—36no—
229D3×Q8—212no—
230D3×Q8C3×Q818yescomplemented
231C2×C4×D3C23×C312yes—
232C2×C4×D3C23×C313yes—
233C2×C4×D3C23×C316yes—
234C2×C4×D3C23×C313yes—
235C2×C4×D3C23×C311yescharacteristic
236C2×Dic6C23×C313yes—
237C2×Dic6C23×C316yes—
238C2×Dic6C23×C313yes—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—23no—
241C3×C4⋊C4—26no—
242C3×C4⋊C4—26no—
243C3×C4⋊C4—26no—
244C3×C4⋊C4—32no—
245C3×C4⋊C4—36no—
246C3×C4⋊C4—36no—
247C3×C4⋊C4—36no—
248C3×C4⋊C4—312no—
249C3×C4⋊C4—312no—
250C3×C4⋊C4—31no—
251C3×C4⋊C4—36no—
252C3×C4⋊C4—33no—
253C3×C4⋊C4—36no—
254C3×C4⋊C4—36no—
255C3×C4⋊C4C22×D311yescharacteristic
256C3×C4⋊C4C22×D316yes—
257C3×C4⋊C4C22×D313yes—
258C3×C4⋊C4C22×D316yes—
259C3×C4⋊C4C22×D316yes—
260C3×C4⋊C4C23×C311yescharacteristic
261C3×C4⋊C4C23×C316yes—
262C3×C4⋊C4C23×C316yes—
263C3×C4⋊C4C23×C313yes—
264C3×C4⋊C4C23×C316yes—
265C3×C42—26no—
266C3×C42—23no—
267C3×C42—36no—
268C3×C42—36no—
269C3×C42—36no—
270C3×C42—33no—
271C3×C42—33no—
272C3×C42—33no—
273C3×C42C22×D316yes—
274C3×C42C22×D313yes—
275C3×C42C23×C313yes—
276C3×C42C23×C316yes—
277C4⋊Dic3C23×C311yescharacteristic
278C4⋊Dic3C23×C316yes—
279C4⋊Dic3C23×C313yes—
280C4⋊Dic3C23×C316yes—
281C4⋊Dic3C23×C316yes—
282Dic3⋊C4C23×C312yes—
283Dic3⋊C4C23×C316yes—
284Dic3⋊C4C23×C3112yes—
285Dic3⋊C4C23×C316yes—
286Dic3⋊C4C23×C316yes—
287Dic3⋊C4C23×C3112yes—
288C4×Dic3C23×C316yes—
289C4×Dic3C23×C313yes—
290C4×Dic3C23×C316yes—
291C4×Dic3C23×C313yes—
292C4×Dic3C23×C313yes—
293C4×Dic3C23×C316yes—
294C22×C32C2511yescharacteristic
295C2×C3×D3C22×Q812yes—
296C2×C3×D3C2×#4112yes—
297C2×C3×D32−1+412yes—
298C32×C4—26no—
299C32×C4—22no—
300C32×C4—23no—
301C32×C4C22×Q816yes—
302C32×C4C2×#4112yes—
303C3×Dic3—26no—
304C3×Dic3—22no—
305C3×Dic3—23no—
306C3×Dic3C22×Q816yes—
307C3×Dic3C2×#4112yes—
308C22×Q8—31no—
309C22×Q8—33no—
310C4⋊Q8—36no—
311C4⋊Q8—36no—
312C4⋊Q8—36no—
313C4⋊Q8—33no—
314C4⋊Q8C2×C3×D313yes—
315#125—312no—
316#125—312no—
317#125—36no—
318#125—36no—
319#125—36no—
320#125C2×C3×D316yes—
321C4×Q8—32no—
322C4×Q8—33no—
323C4×Q8—31no—
324C4×Q8—36no—
325C4×Q8—36no—
326C4×Q8—33no—
327C4×Q8—33no—
328C4×Q8—36no—
329C4×Q8—33no—
330C4×Q8—36no—
331C4×Q8—33no—
332C4×Q8C2×C3×D312yes—
333C4×Q8C2×C3×D313yes—
334C4×Q8C2×C3×D311yescharacteristic
335C2×C4⋊C4—31no—
336C2×C4⋊C4—33no—
337C2×C4⋊C4—36no—
338C2×C4⋊C4—36no—
339C2×C4⋊C4—36no—
340C2×C42—36no—
341C2×C42—33no—
342C23×C3—31no—
343C22×D3C24×C311yescharacteristic
344C3×Q8—26no—
345C3×Q8—26no—
346C3×Q8—24no—
347C3×Q8—312no—
348C3×Q8—46no—
349C3×Q8—612no—
350C3×Q8—66no—
351C3×Q8D3×Q814yescomplemented
352C3×Q8C2×C3×Q814yescomplemented
353C2×C3×C4—23no—
354C2×C3×C4—21no—
355C2×C3×C4—22no—
356C2×C3×C4—23no—
357C2×C3×C4—26no—
358C2×C3×C4—33no—
359C2×C3×C4—31no—
360C2×C3×C4—312no—
361C2×C3×C4—34no—
362C2×C3×C4—32no—
363C2×C3×C4—33no—
364C2×C3×C4—36no—
365C2×C3×C4—64no—
366C2×C3×C4—66no—
367C2×C3×C4—612no—
368C2×C3×C4C23×D312yes—
369C2×C3×C4C23×D313yes—
370C2×C3×C4C23×D316yes—
371C2×C3×C4C23×D313yes—
372C2×C3×C4C23×D311yescharacteristic
373C2×C3×C4C24×C312yes—
374C2×C3×C4C24×C313yes—
375C2×C3×C4C24×C316yes—
376C2×C3×C4C24×C313yes—
377C2×C3×C4C24×C311yescharacteristic
378C2×Dic3C24×C312yes—
379C2×Dic3C24×C313yes—
380C2×Dic3C24×C316yes—
381C2×Dic3C24×C313yes—
382C2×Dic3C24×C311yescharacteristic
383C4×D3—212no—
384C4×D3—24no—
385C4×D3—26no—
386C4×D3C2×C3×Q8112yes—
387C4×D3C3×#4114yes—
388Dic6—26no—
389Dic6—212no—
390Dic6C2×C3×Q8112yescomplemented
391C2×C32C23×Q811yescharacteristic
392C2×C32C22×#4111yescharacteristic
393C2×C32C2×2−1+411yescharacteristic
394C3×D3#55714yesdirect product factor
395C2×Q8—38no—
396C2×Q8—33no—
397C2×Q8—36no—
398C2×Q8—33no—
399C2×Q8—612no—
400C2×Q8C22×C3×D313yes—
401C2×Q8C22×C3×D311yescharacteristic
402C22×C4—33no—
403C22×C4—31no—
404C22×C4—32no—
405C22×C4—33no—
406C22×C4—36no—
407C4⋊C4—32no—
408C4⋊C4—31no—
409C4⋊C4—36no—
410C4⋊C4—36no—
411C4⋊C4—36no—
412C4⋊C4—36no—
413C4⋊C4—33no—
414C4⋊C4—312no—
415C4⋊C4—36no—
416C4⋊C4—312no—
417C4⋊C4—36no—
418C4⋊C4C22×C3×D311yescharacteristic
419C4⋊C4C22×C3×D316yes—
420C4⋊C4C22×C3×D313yes—
421C4⋊C4C22×C3×D316yes—
422C4⋊C4C22×C3×D316yes—
423C42—36no—
424C42—36no—
425C42—36no—
426C42—33no—
427C42—33no—
428C42—33no—
429C42C22×C3×D316yes—
430C42C22×C3×D313yes—
431C22×C3—21no—
432C22×C3—32no—
433C22×C3—32no—
434C22×C3—32no—
435C22×C3C24×D311yescharacteristic
436C22×C3C25×C311yescharacteristic
437C2×D3C22×C3×Q812yes—
438C2×D3C2×C3×#4112yes—
439C2×D3C3×2−1+412yes—
440C3×C4—26no—
441C3×C4—22no—
442C3×C4—23no—
443C3×C4—26no—
444C3×C4—22no—
445C3×C4—23no—
446C3×C4—26no—
447C3×C4—22no—
448C3×C4—36no—
449C3×C4—32no—
450C3×C4—46no—
451C3×C4—42no—
452C3×C4—43no—
453C3×C4—66no—
454C3×C4—62no—
455C3×C4—63no—
456C3×C4C2×D3×Q816yes—
457C3×C4D3×#4112yes—
458C3×C4C22×C3×Q816yes—
459C3×C4C2×C3×#4112yes—
460Dic3—26no—
461Dic3—22no—
462Dic3—23no—
463Dic3C22×C3×Q816yes—
464Dic3C2×C3×#4112yes—
465C32C2×#55711yescharacteristic, complemented, Sylow
466C23—31no—
467Q8—26no—
468Q8—312no—
469Q8—612no—
470Q8—66no—
471Q8C3×D3×Q814yescomplemented
472C2×C4—33no—
473C2×C4—31no—
474C2×C4—312no—
475C2×C4—34no—
476C2×C4—32no—
477C2×C4—33no—
478C2×C4—36no—
479C2×C4—612no—
480C2×C4—64no—
481C2×C4—66no—
482C2×C4C23×C3×D312yes—
483C2×C4C23×C3×D313yes—
484C2×C4C23×C3×D316yes—
485C2×C4C23×C3×D313yes—
486C2×C4C23×C3×D311yescharacteristic
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—34no—
491C2×C3C22×D3×Q811yescharacteristic
492C2×C3C2×D3×#4111yescharacteristic
493C2×C3D3×2−1+411yescharacteristic
494C2×C3C23×C3×Q811yescharacteristic
495C2×C3C22×C3×#4111yescharacteristic
496C2×C3C2×C3×2−1+411yescharacteristic
497D3C3×#55714yesdirect product factor
498C22—32no—
499C22—32no—
500C22—32no—
501C22C24×C3×D311yescharacteristic
502C4—26no—
503C4—22no—
504C4—23no—
505C4—36no—
506C4—32no—
507C4—66no—
508C4—62no—
509C4—63no—
510C4C2×C3×D3×Q816yes—
511C4C3×D3×#4112yes—
512C3—21no—
513C3D3×#55711yescharacteristic, direct product factor
514C3C2×C3×#55711yescharacteristic, complemented
515C2—34no—
516C2C22×C3×D3×Q811yescharacteristic
517C2C2×C3×D3×#4111yescharacteristic
518C2C3×D3×2−1+411yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#557C2
socleC22×C32C25
prime radicalC22×C3×D3C24
hypercenterC3×#557D3
hypocenterC3C2×C3×#557
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#557

Complements

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

NH ≅ G/Ntype
1. C32×#557C2semidirect
3. C3×#5721C2semidirect
5. C3×#5685C2semidirect
9. C3×#5570C2semidirect
10. C3×#5569C2semidirect
11. C3×#5567C2semidirect
13. D3×#557C3direct (N × H)
54. C3×#557D3direct (N × H)
55. C3×#557C2×C3semidirect
62. #5721C2×C3semidirect
64. #5685C2×C3semidirect
68. #5570C2×C3semidirect
69. #5569C2×C3semidirect
70. #5567C2×C3semidirect
74. C3×D3×Q8Q8semidirect
183. C32×Q8C2×Q8semidirect
201. C3×Dic6C2×Q8semidirect
207. #557C3×D3direct (N × H)
230. D3×Q8C3×Q8semidirect
351. C3×Q8D3×Q8semidirect
352. C3×Q8C2×C3×Q8semidirect
390. Dic6C2×C3×Q8semidirect
394. C3×D3#557direct (N × H)
465. C32C2×#557semidirect
471. Q8C3×D3×Q8semidirect
497. D3C3×#557direct (N × H)
513. C3D3×#557direct (N × H)
514. C3C2×C3×#557semidirect

Maximal subgroups

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

subgroupindex
C32×#5572
C3×D3×C4⋊Q82
C3×#57212
C3×D3×#1252
C3×#56852
C3×C4×D3×Q82
C3×#55702
C3×#55692
C3×#55672
C2×C3×#5573
D3×#5573