Finite Group Databasebeta

← C2×C3×D3×#131 #11918451

Subgroups — C2×C3×D3×#131 #11918451

Order 1152.

3141 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic
2C2×C32×#131C211yesmaximal, characteristic, complemented
3C2×C3×#948C211yesmaximal, characteristic, complemented
4C3×D3×#131C2116yesmaximal, direct product factor
5C2×C3×#907C213yesmaximal, complemented
6C2×C3×D3×M16C213yesmaximal, complemented
7C2×C3×#901C213yesmaximal, complemented
8C22×C3×D3×C8C213yesmaximal, complemented
9C22×C3×#131—31nomaximal
10C2×D3×#131C311yesmaximal, characteristic, direct product factor
11C2×C32×#41C2211yescharacteristic
12C3×D3×#41C418yes—
13C3×D3×#41C2218yes—
14C2×C3×#239C411yescharacteristic
15C2×C3×D3×Q8C411yescharacteristic
16C2×C3×#237C413yes—
17C2×C3×D3×D4C413yes—
18C2×C3×#235C2213yes—
19C22×C3×C4×D3C2213yes—
20C32×#131C2218yescomplemented
21C2×C32×M16C2213yescomplemented
22C22×C32×C8C2213yescomplemented
23C3×#948C2218yescomplemented
24C2×C3×#208C2213yescomplemented
25C22×C3×C3⋊C8C2213yescomplemented
26C3×#907C22124yescomplemented
27C3×D3×M16C22124yescomplemented
28C3×#901C22124yescomplemented
29C2×C3×ΓL(1,𝔽25)C2216yescomplemented
30C2×C3×D3×C8C2213yes—
31C2×C3×D3×C8C2211yescharacteristic
32C2×C3×D3×C8C22124yescomplemented
33C2×C3×D3×C8C2213yescomplemented
34C2×C3×D3×C8C2213yescomplemented
35C22×C3×#41—31no—
36C2×D3×#41C2×C311yescharacteristic
37C2×C3×#131—21no—
38C2×C3×#131—31no—
39C2×C3×#131—316no—
40C2×C3×#131—33no—
41C2×C3×#131—33no—
42C2×C3×#131D311yescharacteristic, direct product factor
43C2×C3×#131C2×C311yescharacteristic, complemented
44C22×C3×M16—33no—
45C23×C3×C8—33no—
46C2×#948C2×C311yescharacteristic, complemented
47D3×#131C2×C3116yesdirect product factor
48C2×#907C2×C313yescomplemented
49C2×D3×M16C2×C313yescomplemented
50C2×#901C2×C313yescomplemented
51C22×D3×C8C2×C313yescomplemented
52C23×C3×D3C2×C413yes—
53C32×#41C2×C414yes—
54C32×#41C2314yes—
55C2×C32×Q8C2×C411yescharacteristic
56C2×C32×D4C2×C413yes—
57C22×C32×C4C2313yes—
58C2×C3×#67C2×C416yes—
59C22×C3×Dic3C2×C413yes—
60C3×#239C2×C418yes—
61C3×D3×Q8C2×C418yes—
62C3×#237C2×C4124yes—
63C3×D3×D4C2×C4124yes—
64C3×#235C2×C4112yes—
65C3×#235C23112yes—
66C2×C3×D12C2×C413yes—
67C2×C3×C4×D3C2×C413yes—
68C2×C3×C4×D3C2×C413yes—
69C2×C3×C4×D3C2×C4112yes—
70C2×C3×C4×D3C2311yescharacteristic
71C2×C3×C4×D3C2313yes—
72C2×C3×C4×D3C23112yes—
73C2×C3×Dic6C2×C413yes—
74C32×M16C23112yescomplemented
75C2×C32×C8C2313yes—
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C23112yescomplemented
78C3×#208C23112yescomplemented
79C2×C3×C3⋊C8C2311yescharacteristic
80C2×C3×C3⋊C8C2313yes—
81C2×C3×C3⋊C8C23112yescomplemented
82C3×ΓL(1,𝔽25)C23124yescomplemented
83C3×D3×C8C2314yes—
84C3×D3×C8C23112yes—
85C3×D3×C8C23112yescomplemented
86C3×D3×C8C23112yescomplemented
87C22×#131—31noSylow
88C2×C3×#41—21no—
89C2×C3×#41—38no—
90C2×C3×#41—38no—
91C2×C3×#41—31no—
92C2×C3×#41—33no—
93C2×C3×#41—33no—
94C2×C3×#41C2×D311yescharacteristic
95C2×C3×#41C22×C311yescharacteristic
96C22×C3×Q8—31no—
97C22×C3×D4—33no—
98C23×C3×C4—33no—
99D3×#41C3×C418yes—
100D3×#41C22×C318yes—
101C2×#239C3×C411yescharacteristic
102C2×D3×Q8C3×C411yescharacteristic
103C2×#237C3×C413yes—
104C2×D3×D4C3×C413yes—
105C2×#235C22×C313yes—
106C22×C4×D3C22×C313yes—
107C3×#131—28no—
108C3×#131—38no—
109C3×#131—324no—
110C3×#131—324no—
111C3×#131C2×D318yesdirect product factor
112C3×#131C22×C318yescomplemented
113C2×C3×M16—23no—
114C2×C3×M16—33no—
115C2×C3×M16—324no—
116C2×C3×M16—36no—
117C2×C3×M16C2×D313yescomplemented
118C2×C3×M16C22×C313yescomplemented
119C22×C3×C8—23no—
120C22×C3×C8—33no—
121C22×C3×C8—33no—
122C22×C3×C8—33no—
123C22×C3×C8—31no—
124C22×C3×C8—33no—
125C22×C3×C8—324no—
126C22×C3×C8C2×D313yescomplemented
127C22×C3×C8C22×C313yescomplemented
128#948C22×C318yescomplemented
129C2×#208C22×C313yescomplemented
130C22×C3⋊C8C22×C313yescomplemented
131#907C22×C3124yescomplemented
132D3×M16C22×C3124yescomplemented
133#901C22×C3124yescomplemented
134C2×ΓL(1,𝔽25)C22×C316yescomplemented
135C2×D3×C8C22×C311yescharacteristic
136C2×D3×C8C22×C313yes—
137C2×D3×C8C22×C3124yescomplemented
138C2×D3×C8C22×C313yescomplemented
139C2×D3×C8C22×C313yescomplemented
140C23×C32C22×C413yes—
141C22×C3×D3—212no—
142C22×C3×D3C22×C413yes—
143C22×C3×D3C22×C4112yes—
144C22×C3×D3C22×C411yescharacteristic
145C32×Q8C22×C414yes—
146C32×D4C22×C4112yes—
147C2×C32×C4C22×C413yes—
148C2×C32×C4C22×C416yes—
149C2×C32×C4C2411yescharacteristic
150C2×C32×C4C2416yes—
151C3×#67C22×C4124yes—
152C2×C3×Dic3C22×C413yes—
153C2×C3×Dic3C22×C411yescharacteristic
154C2×C3×Dic3C22×C4112yes—
155C3×D12C22×C4112yes—
156C3×C4×D3C22×C412yes—
157C3×C4×D3C22×C416yes—
158C3×C4×D3C22×C4112yes—
159C3×C4×D3C22×C4112yes—
160C3×C4×D3C2412yes—
161C3×C4×D3C2416yes—
162C3×Dic6C22×C4112yes—
163C32×C8C2412yes—
164C32×C8C2416yes—
165C3×C3⋊C8C2412yes—
166C3×C3⋊C8C2416yes—
167C22×#41—31no—
168C2×#131—31no—
169C2×#131—316no—
170C2×#131—33no—
171C2×#131—33no—
172C2×#131C3×D311yescharacteristic, direct product factor
173C22×M16—33no—
174C23×C8—33no—
175C24×C3—33no—
176C23×D3C2×C3×C413yes—
177C3×#41—24no—
178C3×#41—24no—
179C3×#41—38no—
180C3×#41—324no—
181C3×#41—312no—
182C3×#41—312no—
183C3×#41C4×D314yes—
184C3×#41C2×C3×C414yes—
185C3×#41C22×D314yes—
186C3×#41C23×C314yes—
187C2×C3×Q8—21no—
188C2×C3×Q8—38no—
189C2×C3×Q8—33no—
190C2×C3×Q8C4×D311yescharacteristic
191C2×C3×Q8C2×C3×C411yescharacteristic
192C2×C3×D4—23no—
193C2×C3×D4—36no—
194C2×C3×D4—324no—
195C2×C3×D4—33no—
196C2×C3×D4C4×D313yes—
197C2×C3×D4C2×C3×C413yes—
198C22×C3×C4—23no—
199C22×C3×C4—33no—
200C22×C3×C4—33no—
201C22×C3×C4—33no—
202C22×C3×C4—312no—
203C22×C3×C4—31no—
204C22×C3×C4—33no—
205C22×C3×C4—312no—
206C22×C3×C4C22×D313yes—
207C22×C3×C4C23×C313yes—
208C2×#67C2×C3×C416yes—
209C22×Dic3C2×C3×C413yes—
210#239C2×C3×C418yes—
211D3×Q8C2×C3×C418yes—
212#237C2×C3×C4124yes—
213D3×D4C2×C3×C4124yes—
214#235C2×C3×C4112yes—
215#235C23×C3112yes—
216C2×D12C2×C3×C413yes—
217C2×C4×D3C2×C3×C413yes—
218C2×C4×D3C2×C3×C413yes—
219C2×C4×D3C2×C3×C4112yes—
220C2×C4×D3C23×C311yescharacteristic
221C2×C4×D3C23×C313yes—
222C2×C4×D3C23×C3112yes—
223C2×Dic6C2×C3×C413yes—
224C3×M16—212no—
225C3×M16—312no—
226C3×M16—324no—
227C3×M16C22×D3112yescomplemented
228C3×M16C23×C3112yescomplemented
229C2×C3×C8—21no—
230C2×C3×C8—23no—
231C2×C3×C8—212no—
232C2×C3×C8—31no—
233C2×C3×C8—33no—
234C2×C3×C8—312no—
235C2×C3×C8—34no—
236C2×C3×C8—312no—
237C2×C3×C8—312no—
238C2×C3×C8—312no—
239C2×C3×C8C22×D313yes—
240C2×C3×C8C22×D311yescharacteristic
241C2×C3×C8C22×D3112yescomplemented
242C2×C3×C8C23×C311yescharacteristic
243C2×C3×C8C23×C313yes—
244C2×C3×C8C23×C3112yescomplemented
245#208C23×C3112yescomplemented
246C2×C3⋊C8C23×C311yescharacteristic
247C2×C3⋊C8C23×C313yes—
248C2×C3⋊C8C23×C3112yescomplemented
249ΓL(1,𝔽25)C23×C3124yescomplemented
250D3×C8C23×C314yes—
251D3×C8C23×C3112yes—
252D3×C8C23×C3112yescomplemented
253D3×C8C23×C3112yescomplemented
254C22×C32—26no—
255C22×C32C23×C416yes—
256C22×C32C23×C411yescharacteristic
257C2×C3×D3—26no—
258C2×C3×D3—224no—
259C2×C3×D3#13114yesdirect product factor
260C2×C3×D3C23×C416yes—
261C2×C3×D3C23×C412yes—
262C32×C4C23×C416yes—
263C32×C4C23×C411yescharacteristic
264C32×C4C2511yescharacteristic
265C3×Dic3C23×C416yes—
266C3×Dic3C23×C412yes—
267C2×#41—38no—
268C2×#41—38no—
269C2×#41—31no—
270C2×#41—33no—
271C2×#41—33no—
272C2×#41C2×C3×D311yescharacteristic
273C22×Q8—31no—
274C22×D4—33no—
275C23×C4—33no—
276#131—38no—
277#131—324no—
278#131—324no—
279#131C2×C3×D318yesdirect product factor
280C2×M16—33no—
281C2×M16—324no—
282C2×M16—36no—
283C2×M16C2×C3×D313yescomplemented
284C22×C8—33no—
285C22×C8—31no—
286C22×C8—33no—
287C22×C8—33no—
288C22×C8—33no—
289C22×C8—324no—
290C22×C8C2×C3×D313yescomplemented
291C23×C3—23no—
292C23×C3—31no—
293C23×C3—312no—
294C23×C3—33no—
295C23×C3—612no—
296C23×C3C2×C4×D313yes—
297C23×C3C22×C3×C413yes—
298C22×D3—212no—
299C22×D3C22×C3×C413yes—
300C22×D3C22×C3×C4112yes—
301C22×D3C22×C3×C411yescharacteristic
302C3×Q8—24no—
303C3×Q8—312no—
304C3×Q8C2×C4×D314yes—
305C3×Q8C22×C3×C414yes—
306C3×D4—212no—
307C3×D4—324no—
308C3×D4—312no—
309C3×D4C2×C4×D3112yes—
310C3×D4C22×C3×C4112yes—
311C2×C3×C4—21no—
312C2×C3×C4—26no—
313C2×C3×C4—23no—
314C2×C3×C4—26no—
315C2×C3×C4—31no—
316C2×C3×C4—33no—
317C2×C3×C4—312no—
318C2×C3×C4—32no—
319C2×C3×C4—312no—
320C2×C3×C4—312no—
321C2×C3×C4—36no—
322C2×C3×C4—32no—
323C2×C3×C4—36no—
324C2×C3×C4C2×C4×D313yes—
325C2×C3×C4C2×C4×D316yes—
326C2×C3×C4C22×C3×C413yes—
327C2×C3×C4C22×C3×C416yes—
328C2×C3×C4C23×D311yescharacteristic
329C2×C3×C4C23×D316yes—
330C2×C3×C4C24×C311yescharacteristic
331C2×C3×C4C24×C316yes—
332#67C22×C3×C4124yes—
333C2×Dic3C22×C3×C413yes—
334C2×Dic3C22×C3×C411yescharacteristic
335C2×Dic3C22×C3×C4112yes—
336D12C22×C3×C4112yes—
337C4×D3C22×C3×C412yes—
338C4×D3C22×C3×C416yes—
339C4×D3C22×C3×C4112yes—
340C4×D3C22×C3×C4112yes—
341C4×D3C24×C312yes—
342C4×D3C24×C316yes—
343Dic6C22×C3×C4112yes—
344C3×C8—22no—
345C3×C8—26no—
346C3×C8—32no—
347C3×C8—36no—
348C3×C8C23×D312yes—
349C3×C8C23×D316yes—
350C3×C8C24×C312yes—
351C3×C8C24×C316yes—
352C3⋊C8C24×C312yes—
353C3⋊C8C24×C316yes—
354C2×C32—26no—
355C2×C32C2×#13112yescomplemented
356C2×C32C24×C411yescharacteristic
357C3×D3—26no—
358C3×D3C2×#13114yesdirect product factor
359C24—33no—
360#41—38no—
361#41—324no—
362#41—312no—
363#41—312no—
364#41C3×C4×D314yes—
365#41C22×C3×D314yes—
366C2×Q8—38no—
367C2×Q8—33no—
368C2×Q8C3×C4×D311yescharacteristic
369C2×D4—36no—
370C2×D4—324no—
371C2×D4—33no—
372C2×D4C3×C4×D313yes—
373C22×C4—33no—
374C22×C4—31no—
375C22×C4—33no—
376C22×C4—312no—
377C22×C4—33no—
378C22×C4—33no—
379C22×C4—312no—
380C22×C4C22×C3×D313yes—
381M16—312no—
382M16—324no—
383M16C22×C3×D3112yescomplemented
384C2×C8—31no—
385C2×C8—33no—
386C2×C8—312no—
387C2×C8—34no—
388C2×C8—312no—
389C2×C8—312no—
390C2×C8—312no—
391C2×C8C22×C3×D311yescharacteristic
392C2×C8C22×C3×D313yes—
393C2×C8C22×C3×D3112yescomplemented
394C22×C3—26no—
395C22×C3—26no—
396C22×C3—21no—
397C22×C3—26no—
398C22×C3—32no—
399C22×C3—34no—
400C22×C3—36no—
401C22×C3—46no—
402C22×C3—624no—
403C22×C3—66no—
404C22×C3C22×C4×D316yes—
405C22×C3C22×C4×D311yescharacteristic
406C22×C3C23×C3×C416yes—
407C22×C3C23×C3×C411yescharacteristic
408C2×D3—26no—
409C2×D3—224no—
410C2×D3C3×#13114yesdirect product factor
411C2×D3C23×C3×C416yes—
412C2×D3C23×C3×C412yes—
413C3×C4—21no—
414C3×C4—26no—
415C3×C4—21no—
416C3×C4—32no—
417C3×C4—36no—
418C3×C4C22×C4×D311yescharacteristic
419C3×C4C22×C4×D316yes—
420C3×C4C23×C3×C416yes—
421C3×C4C23×C3×C411yescharacteristic
422C3×C4C24×D311yescharacteristic
423C3×C4C25×C311yescharacteristic
424Dic3C23×C3×C416yes—
425Dic3C23×C3×C412yes—
426C32C22×#13111yescharacteristic, complemented, Sylow
427C23—31no—
428C23—312no—
429C23—33no—
430C23—612no—
431C23C2×C3×C4×D313yes—
432Q8—312no—
433Q8C2×C3×C4×D314yes—
434D4—324no—
435D4—312no—
436D4C2×C3×C4×D3112yes—
437C2×C4—31no—
438C2×C4—33no—
439C2×C4—312no—
440C2×C4—32no—
441C2×C4—312no—
442C2×C4—312no—
443C2×C4—36no—
444C2×C4—32no—
445C2×C4—36no—
446C2×C4C2×C3×C4×D313yes—
447C2×C4C2×C3×C4×D316yes—
448C2×C4C23×C3×D311yescharacteristic
449C2×C4C23×C3×D316yes—
450C8—32no—
451C8—36no—
452C8C23×C3×D312yes—
453C8C23×C3×D316yes—
454C2×C3—26no—
455C2×C3—26no—
456C2×C3—22no—
457C2×C3—21no—
458C2×C3—34no—
459C2×C3—46no—
460C2×C3—66no—
461C2×C3D3×#13112yesdirect product factor
462C2×C3C2×C3×#13112yescomplemented
463C2×C3C23×C4×D311yescharacteristic
464C2×C3C24×C3×C411yescharacteristic
465D3—26no—
466D3C2×C3×#13114yesdirect product factor
467C22—26no—
468C22—34no—
469C22—32no—
470C22—36no—
471C22—624no—
472C22—66no—
473C22C22×C3×C4×D316yes—
474C22C22×C3×C4×D311yescharacteristic
475C4—32no—
476C4—36no—
477C4C22×C3×C4×D311yescharacteristic
478C4C22×C3×C4×D316yes—
479C4C24×C3×D311yescharacteristic
480C3—21no—
481C3C2×D3×#13111yescharacteristic, direct product factor
482C3C22×C3×#13111yescharacteristic, complemented
483C2—26no—
484C2—34no—
485C2—66no—
486C2C3×D3×#13112yesdirect product factor
487C2C23×C3×C4×D311yescharacteristic
subgroupG/H
centerC2×C3×C8C22×D3
commutatorC2×C3C24×C3×C4
FrattiniC4C24×C3×D3
FittingC2×C32×#131C2
socleC22×C32C23×C4
prime radicalC2×C3×D3×#41C2
cosocleC3×C4C25×C3
hypercenterC2×C3×#131D3
hypocenterC3C22×C3×#131
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C8 ◁ C2×C3×#131

Complements

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

NH ≅ G/Ntype
2. C2×C32×#131C2semidirect
3. C2×C3×#948C2semidirect
4. C3×D3×#131C2direct (N × H)
5. C2×C3×#907C2semidirect
6. C2×C3×D3×M16C2semidirect
7. C2×C3×#901C2semidirect
8. C22×C3×D3×C8C2semidirect
10. C2×D3×#131C3direct (N × H)
20. C32×#131C22semidirect
21. C2×C32×M16C22semidirect
22. C22×C32×C8C22semidirect
23. C3×#948C22semidirect
24. C2×C3×#208C22semidirect
25. C22×C3×C3⋊C8C22semidirect
26. C3×#907C22semidirect
27. C3×D3×M16C22semidirect
28. C3×#901C22semidirect
29. C2×C3×ΓL(1,𝔽25)C22semidirect
32. C2×C3×D3×C8C22semidirect
33. C2×C3×D3×C8C22semidirect
34. C2×C3×D3×C8C22semidirect
42. C2×C3×#131D3direct (N × H)
43. C2×C3×#131C2×C3semidirect
46. C2×#948C2×C3semidirect
47. D3×#131C2×C3direct (N × H)
48. C2×#907C2×C3semidirect
49. C2×D3×M16C2×C3semidirect
50. C2×#901C2×C3semidirect
51. C22×D3×C8C2×C3semidirect
74. C32×M16C23semidirect
77. C2×C32×C8C23semidirect
78. C3×#208C23semidirect
81. C2×C3×C3⋊C8C23semidirect
82. C3×ΓL(1,𝔽25)C23semidirect
85. C3×D3×C8C23semidirect
86. C3×D3×C8C23semidirect
111. C3×#131C2×D3direct (N × H)
112. C3×#131C22×C3semidirect
117. C2×C3×M16C2×D3semidirect
118. C2×C3×M16C22×C3semidirect
126. C22×C3×C8C2×D3semidirect
127. C22×C3×C8C22×C3semidirect
128. #948C22×C3semidirect
129. C2×#208C22×C3semidirect
130. C22×C3⋊C8C22×C3semidirect
131. #907C22×C3semidirect
132. D3×M16C22×C3semidirect
133. #901C22×C3semidirect
134. C2×ΓL(1,𝔽25)C22×C3semidirect
137. C2×D3×C8C22×C3semidirect
138. C2×D3×C8C22×C3semidirect
139. C2×D3×C8C22×C3semidirect
172. C2×#131C3×D3direct (N × H)
227. C3×M16C22×D3semidirect
228. C3×M16C23×C3semidirect
241. C2×C3×C8C22×D3semidirect
244. C2×C3×C8C23×C3semidirect
245. #208C23×C3semidirect
248. C2×C3⋊C8C23×C3semidirect
249. ΓL(1,𝔽25)C23×C3semidirect
252. D3×C8C23×C3semidirect
253. D3×C8C23×C3semidirect
259. C2×C3×D3#131direct (N × H)
279. #131C2×C3×D3direct (N × H)
283. C2×M16C2×C3×D3semidirect
290. C22×C8C2×C3×D3semidirect
355. C2×C32C2×#131semidirect
358. C3×D3C2×#131direct (N × H)
383. M16C22×C3×D3semidirect
393. C2×C8C22×C3×D3semidirect
410. C2×D3C3×#131direct (N × H)
426. C32C22×#131semidirect
461. C2×C3D3×#131direct (N × H)
462. C2×C3C2×C3×#131semidirect
466. D3C2×C3×#131direct (N × H)
481. C3C2×D3×#131direct (N × H)
482. C3C22×C3×#131semidirect
486. C2C3×D3×#131direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C2×C32×#1312
C2×C3×#9482
C3×D3×#1312
C2×C3×#9072
C2×C3×D3×M162
C2×C3×#9012
C22×C3×D3×C82
C22×C3×#1313
C2×D3×#1313