Finite Group Databasebeta

← C2×D3×#446 #11659540

Subgroups — C2×D3×#446 #11659540

Order 768.

2222 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×Q8C211yesmaximal, characteristic
2C2×C3×#446C211yesmaximal, characteristic, complemented
3C2×#5024C211yesmaximal, characteristic, complemented
4D3×#446C2116yesmaximal, direct product factor
5C2×D3×C4⋊C8C211yesmaximal, characteristic
6C2×D3×C4⋊C8C212yesmaximal
7C2×#4828C212yesmaximal, complemented
8C2×#4831C211yesmaximal, characteristic, complemented
9C2×D3×#97C212yesmaximal
10C2×#4701C212yesmaximal, complemented
11C2×C4×D3×C8C211yesmaximal, characteristic
12C2×#4679C211yesmaximal, characteristic, complemented
13C22×#446—31nomaximal, Sylow
14C22×D3×Q8C411yescharacteristic
15C2×C3×C4×Q8C2211yescharacteristic
16C2×Q8×Dic3C411yescharacteristic
17C22×D3×C8C2211yescharacteristic
18C22×D3×C8C2212yes—
19C22×D3×C8C2211yescharacteristic
20C4×D3×Q8C418yes—
21C4×D3×Q8C2218yes—
22C2×D3×C4⋊C4C412yes—
23C2×D3×C4⋊C4C411yescharacteristic
24C2×#887C411yescharacteristic
25C2×#887C412yes—
26C2×C42×D3C2211yescharacteristic
27C2×C42×D3C2212yes—
28C2×C4×Dic6C2211yescharacteristic
29C2×C4×Dic6C2212yes—
30C3×#446C2218yescomplemented
31C2×C3×C4⋊C8C2211yescharacteristic
32C2×C3×C4⋊C8C2212yes—
33C2×C3×#97C2212yes—
34C2×C3×C4×C8C2211yescharacteristic
35C2×#815C2212yes—
36C2×#815C2212yes—
37C2×Dic3⋊C8C2212yes—
38C2×Dic3⋊C8C2212yes—
39C2×Dic3⋊C8C2212yes—
40C2×C8×Dic3C2211yescharacteristic
41C2×C8×Dic3C2211yescharacteristic
42#5024C2218yescomplemented
43C2×C4⋊(C3⋊C8)C2211yescharacteristic
44C2×C4⋊(C3⋊C8)C2212yes—
45C2×#803C2212yes—
46C2×C4×C3⋊C8C2211yescharacteristic
47D3×C4⋊C8C2218yes—
48D3×C4⋊C8C22116yes—
49#4831C2218yescomplemented
50#4828C22116yescomplemented
51D3×#97C22116yes—
52#4701C22116yescomplemented
53C4×D3×C8C2218yes—
54#4679C2218yescomplemented
55C22×C4×Q8—31no—
56C2×#446—316no—
57C2×#446—31no—
58C2×#446—32no—
59C2×#446—32no—
60C2×#446—31no—
61C2×#446—31no—
62C2×#446D311yescharacteristic, direct product factor
63C22×C4⋊C8—32no—
64C22×C4⋊C8—31no—
65C22×#97—32no—
66C22×C4×C8—31no—
67C22×C3×Q8C2×C411yescharacteristic
68C2×D3×Q8—28no—
69C2×D3×Q8C2×C418yes—
70C22×C4×D3C2×C412yes—
71C22×C4×D3C2×C411yescharacteristic
72C22×C4×D3C2×C412yes—
73C22×C4×D3C2×C411yescharacteristic
74C22×C4×D3C2311yescharacteristic
75C22×Dic6C2×C411yescharacteristic
76C22×Dic6C2×C412yes—
77C22×C3×C8C2311yescharacteristic
78C22×C3×C8C2312yes—
79C22×C3×C8C2311yescharacteristic
80C3×C4×Q8C2×C414yes—
81C3×C4×Q8C2314yes—
82C2×C3×C4⋊C4C2×C412yes—
83C2×C3×C4⋊C4C2×C411yescharacteristic
84C2×C3×C42C2311yescharacteristic
85C2×C3×C42C2312yes—
86Q8×Dic3C2×C418yes—
87C2×C4⋊Dic3C2×C412yes—
88C2×C4⋊Dic3C2×C411yescharacteristic
89C2×Dic3⋊C4C2×C412yes—
90C2×Dic3⋊C4C2×C412yes—
91C2×Dic3⋊C4C2×C412yes—
92C2×C4×Dic3C2×C412yes—
93C2×C4×Dic3C2×C411yescharacteristic
94C2×C4×Dic3C2×C412yes—
95C2×C4×Dic3C2×C411yescharacteristic
96C2×C4×Dic3C2311yescharacteristic
97C2×C4×Dic3C2312yes—
98C22×C3⋊C8C2311yescharacteristic
99C22×C3⋊C8C2312yes—
100C22×C3⋊C8C2311yescharacteristic
101C2×D3×C8—24no—
102C2×D3×C8—28no—
103C2×D3×C8Q818yescomplemented
104C2×D3×C8C2314yes—
105C2×D3×C8C2318yes—
106C2×D3×C8C2314yes—
107D3×C4⋊C4C2×C4116yes—
108D3×C4⋊C4C2×C418yes—
109#887C2×C418yes—
110#887C2×C4116yes—
111C42×D3C2×C418yes—
112C42×D3C2×C414yes—
113C42×D3C2314yes—
114C42×D3C2318yes—
115C4×Dic6C2×C414yes—
116C4×Dic6C2×C418yes—
117C4×Dic6C2314yes—
118C4×Dic6C2318yes—
119C3×C4⋊C8C2318yes—
120C3×C4⋊C8C2314yes—
121C3×#97C2318yes—
122C3×C4×C8C2314yes—
123#815C2318yes—
124#815C2318yes—
125Dic3⋊C8C2318yes—
126Dic3⋊C8C2318yes—
127Dic3⋊C8C2318yes—
128C8×Dic3C2314yes—
129C8×Dic3C2314yes—
130C4⋊(C3⋊C8)C2314yes—
131C4⋊(C3⋊C8)C2318yes—
132#803C2318yes—
133C4×C3⋊C8C2314yes—
134C23×Q8—31no—
135C23×C8—31no—
136C23×C8—31no—
137C23×C8—32no—
138C2×C4×Q8—31no—
139C2×C4×Q8—38no—
140C2×C4×Q8—38no—
141C2×C4×Q8—32no—
142C2×C4×Q8—31no—
143C2×C4×Q8—32no—
144C2×C4×Q8—31no—
145C2×C4×Q8C2×D311yescharacteristic
146C22×C4⋊C4—31no—
147C22×C4⋊C4—32no—
148C22×C42—31no—
149C22×C42—32no—
150#446—38no—
151#446—316no—
152#446—38no—
153#446—316no—
154#446—38no—
155#446C2×D318yesdirect product factor
156C2×C4⋊C8—32no—
157C2×C4⋊C8—32no—
158C2×C4⋊C8—32no—
159C2×C4⋊C8—31no—
160C2×C4⋊C8—32no—
161C2×C4⋊C8—38no—
162C2×C4⋊C8—316no—
163C2×C4⋊C8C2×D311yescharacteristic
164C2×C4⋊C8C2×D312yes—
165C2×#97—32no—
166C2×#97—32no—
167C2×#97—32no—
168C2×#97—316no—
169C2×#97C2×D312yes—
170C2×C4×C8—31no—
171C2×C4×C8—31no—
172C2×C4×C8—31no—
173C2×C4×C8—38no—
174C2×C4×C8C2×D311yescharacteristic
175C23×D3C22×C411yescharacteristic
176C2×C3×Q8—24no—
177C2×C3×Q8C22×C414yes—
178C22×C3×C4C22×C411yescharacteristic
179C22×C3×C4C22×C412yes—
180C22×C3×C4C22×C412yes—
181C22×C3×C4C22×C411yescharacteristic
182C22×C3×C4C2411yescharacteristic
183C22×Dic3C22×C411yescharacteristic
184C22×Dic3C22×C412yes—
185C22×Dic3C22×C412yes—
186C22×Dic3C22×C411yescharacteristic
187C22×Dic3C22×C411yescharacteristic
188D3×Q8—232no—
189C2×C4×D3—28no—
190C2×C4×D3—24no—
191C2×C4×D3—28no—
192C2×C4×D3M1618yes—
193C2×C4×D3C22×C414yes—
194C2×C4×D3C22×C418yes—
195C2×C4×D3C22×C418yes—
196C2×C4×D3C22×C412yes—
197C2×C4×D3C22×C414yes—
198C2×C4×D3C2×Q814yes—
199C2×C4×D3#4114yes—
200C2×C4×D3C2412yes—
201C2×Dic6—24no—
202C2×Dic6—28no—
203C2×Dic6C22×C414yes—
204C2×Dic6C22×C418yes—
205C2×C3×C8—22no—
206C2×C3×C8—24no—
207C2×C3×C8C2×Q814yescomplemented
208C2×C3×C8C2412yes—
209C2×C3×C8C2414yes—
210C2×C3×C8C2412yes—
211C3×C4⋊C4C22×C418yes—
212C3×C4⋊C4C22×C414yes—
213C3×C42C22×C414yes—
214C3×C42C22×C412yes—
215C3×C42C2412yes—
216C3×C42C2414yes—
217C4⋊Dic3C22×C418yes—
218C4⋊Dic3C22×C414yes—
219Dic3⋊C4C22×C418yes—
220Dic3⋊C4C22×C418yes—
221Dic3⋊C4C22×C418yes—
222C4×Dic3C22×C414yes—
223C4×Dic3C22×C412yes—
224C4×Dic3C22×C418yes—
225C4×Dic3C22×C414yes—
226C4×Dic3C22×C418yes—
227C4×Dic3C22×C414yes—
228C4×Dic3C2412yes—
229C4×Dic3C2414yes—
230C2×C3⋊C8—22no—
231C2×C3⋊C8—24no—
232C2×C3⋊C8C2×Q814yescomplemented
233C2×C3⋊C8C2412yes—
234C2×C3⋊C8C2414yes—
235C2×C3⋊C8C2412yes—
236D3×C8—28no—
237D3×C8—216no—
238D3×C8C2×Q8116yescomplemented
239C22×Q8—38no—
240C22×Q8—32no—
241C22×Q8—31no—
242C22×Q8—68no—
243C22×Q8C4×D311yescharacteristic
244C23×C4—31no—
245C23×C4—31no—
246C23×C4—31no—
247C23×C4—32no—
248C23×C4—32no—
249C22×C8—31no—
250C22×C8—38no—
251C22×C8—34no—
252C22×C8—31no—
253C22×C8—32no—
254C22×C8—34no—
255C22×C8—38no—
256C22×C8—64no—
257C22×C8—68no—
258C22×C8C22×D311yescharacteristic
259C22×C8C22×D312yes—
260C22×C8C22×D311yescharacteristic
261C4×Q8—38no—
262C4×Q8—316no—
263C4×Q8—38no—
264C4×Q8—38no—
265C4×Q8—34no—
266C4×Q8—38no—
267C4×Q8—34no—
268C4×Q8C4×D314yes—
269C4×Q8C22×D314yes—
270C2×C4⋊C4—32no—
271C2×C4⋊C4—32no—
272C2×C4⋊C4—32no—
273C2×C4⋊C4—32no—
274C2×C4⋊C4—31no—
275C2×C4⋊C4—38no—
276C2×C4⋊C4—316no—
277C2×C4⋊C4C4×D312yes—
278C2×C4⋊C4C4×D311yescharacteristic
279C2×C42—31no—
280C2×C42—32no—
281C2×C42—31no—
282C2×C42—32no—
283C2×C42—31no—
284C2×C42—32no—
285C2×C42—34no—
286C2×C42—38no—
287C2×C42—34no—
288C2×C42—38no—
289C2×C42C22×D311yescharacteristic
290C2×C42C22×D312yes—
291C4⋊C8—38no—
292C4⋊C8—38no—
293C4⋊C8—38no—
294C4⋊C8—34no—
295C4⋊C8—38no—
296C4⋊C8C22×D314yes—
297C4⋊C8C22×D318yes—
298#97—38no—
299#97—38no—
300#97—38no—
301#97C22×D318yes—
302C4×C8—34no—
303C4×C8—34no—
304C4×C8—34no—
305C4×C8C22×D314yes—
306C23×C3C23×C411yescharacteristic
307C22×D3C4×Q814yes—
308C22×D3C2×M1614yes—
309C22×D3#13114yes—
310C22×D3C23×C412yes—
311C3×Q8—28no—
312C2×C3×C4—24no—
313C2×C3×C4—22no—
314C2×C3×C4—24no—
315C2×C3×C4C2×M1614yes—
316C2×C3×C4C23×C412yes—
317C2×C3×C4C23×C414yes—
318C2×C3×C4C23×C414yes—
319C2×C3×C4C23×C411yescharacteristic
320C2×C3×C4C23×C412yes—
321C2×C3×C4C22×Q812yes—
322C2×C3×C4C2×#4112yes—
323C2×C3×C4C2511yescharacteristic
324C2×Dic3—24no—
325C2×Dic3—22no—
326C2×Dic3—24no—
327C2×Dic3C4×Q814yes—
328C2×Dic3C2×M1614yes—
329C2×Dic3C23×C412yes—
330C2×Dic3C23×C414yes—
331C2×Dic3C23×C414yes—
332C2×Dic3C23×C412yes—
333C2×Dic3C23×C412yes—
334C4×D3—216no—
335C4×D3—28no—
336C4×D3—216no—
337C4×D3C4×Q818yes—
338C4×D3C2×M16116yes—
339C4×D3C22×Q814yes—
340C4×D3C2×#4114yes—
341Dic6—28no—
342Dic6—216no—
343C3×C8—22no—
344C3×C8—24no—
345C3×C8C22×Q814yescomplemented
346C3⋊C8—22no—
347C3⋊C8—24no—
348C3⋊C8C22×Q814yescomplemented
349C24—31no—
350C2×Q8—24no—
351C2×Q8—38no—
352C2×Q8—34no—
353C2×Q8—68no—
354C2×Q8—632no—
355C2×Q8—64no—
356C2×Q8C2×C4×D314yes—
357C22×C4—31no—
358C22×C4—31no—
359C22×C4—38no—
360C22×C4—32no—
361C22×C4—34no—
362C22×C4—34no—
363C22×C4—34no—
364C22×C4—32no—
365C22×C4—31no—
366C22×C4—32no—
367C22×C4—32no—
368C22×C4—34no—
369C22×C4—38no—
370C22×C4—38no—
371C22×C4—68no—
372C22×C4—64no—
373C22×C4—68no—
374C22×C4C2×C4×D311yescharacteristic
375C22×C4C2×C4×D312yes—
376C22×C4C2×C4×D312yes—
377C22×C4C2×C4×D311yescharacteristic
378C22×C4C23×D311yescharacteristic
379C2×C8—22no—
380C2×C8—24no—
381C2×C8—34no—
382C2×C8—32no—
383C2×C8—316no—
384C2×C8—32no—
385C2×C8—34no—
386C2×C8—68no—
387C2×C8—616no—
388C2×C8—62no—
389C2×C8—64no—
390C2×C8D3×Q814yescomplemented
391C2×C8C23×D312yes—
392C2×C8C23×D314yes—
393C2×C8C23×D312yes—
394C4⋊C4—38no—
395C4⋊C4—38no—
396C4⋊C4—38no—
397C4⋊C4—38no—
398C4⋊C4—34no—
399C4⋊C4C2×C4×D318yes—
400C4⋊C4C2×C4×D314yes—
401C42—34no—
402C42—38no—
403C42—34no—
404C42—38no—
405C42—32no—
406C42—34no—
407C42—32no—
408C42—34no—
409C42C2×C4×D314yes—
410C42C2×C4×D312yes—
411C42C23×D312yes—
412C42C23×D314yes—
413C22×C3C2×C4×Q812yes—
414C22×C3C22×M1612yes—
415C22×C3C2×#13112yes—
416C22×C3C24×C411yescharacteristic
417C2×D3#446116yesdirect product factor
418C2×D3C2×C4×Q814yes—
419C2×D3C22×M1614yes—
420C2×D3C2×#13114yes—
421C3×C4—24no—
422C3×C4—22no—
423C3×C4—24no—
424C3×C4C2×C4×Q812yes—
425C3×C4C22×M1614yes—
426C3×C4C23×Q811yescharacteristic
427C3×C4C22×#4111yescharacteristic
428Dic3—24no—
429Dic3—22no—
430Dic3—24no—
431Dic3C2×C4×Q814yes—
432Dic3C22×M1614yes—
433C23—32no—
434C23—34no—
435C23—34no—
436C23—34no—
437C23C22×C4×D311yescharacteristic
438Q8—28no—
439Q8—616no—
440Q8—68no—
441C2×C4—24no—
442C2×C4—22no—
443C2×C4—24no—
444C2×C4—32no—
445C2×C4—32no—
446C2×C4—34no—
447C2×C4—34no—
448C2×C4—34no—
449C2×C4—34no—
450C2×C4—316no—
451C2×C4—38no—
452C2×C4—32no—
453C2×C4—34no—
454C2×C4—34no—
455C2×C4—616no—
456C2×C4—68no—
457C2×C4—616no—
458C2×C4—64no—
459C2×C4—62no—
460C2×C4—64no—
461C2×C4D3×M1614yes—
462C2×C4C22×C4×D312yes—
463C2×C4C22×C4×D314yes—
464C2×C4C22×C4×D314yes—
465C2×C4C22×C4×D312yes—
466C2×C4C22×C4×D311yescharacteristic
467C2×C4C2×D3×Q812yes—
468C2×C4D3×#4112yes—
469C2×C4C24×D311yescharacteristic
470C8—22no—
471C8—24no—
472C8—34no—
473C8—62no—
474C8—64no—
475C8C2×D3×Q814yescomplemented
476C2×C3C2×#44614yescomplemented
477C2×C3C22×C4×Q811yescharacteristic
478C2×C3C23×M1611yescharacteristic
479C2×C3C22×#13111yescharacteristic
480D3C2×#44618yesdirect product factor
481C22—34no—
482C22—316no—
483C22—34no—
484C22—34no—
485C22C4×D3×Q812yes—
486C22C2×D3×M1612yes—
487C22D3×#13112yes—
488C22C23×C4×D311yescharacteristic
489C4—24no—
490C4—22no—
491C4—24no—
492C4—34no—
493C4—34no—
494C4—64no—
495C4—62no—
496C4—64no—
497C4C4×D3×Q812yes—
498C4C2×D3×M1614yes—
499C4C22×D3×Q811yescharacteristic
500C4C2×D3×#4111yescharacteristic
501C3C22×#44611yescharacteristic, complemented, Sylow
502C2—38no—
503C2D3×#44614yesdirect product factor
504C2C2×C4×D3×Q811yescharacteristic
505C2C22×D3×M1611yescharacteristic
506C2C2×D3×#13111yescharacteristic
subgroupG/H
centerC22×C4C23×D3
commutatorC22×C3C24×C4
FrattiniC2×C4C24×D3
FittingC2×C3×#446C2
socleC23×C3C23×C4
prime radicalC23×D3C22×C4
cosocleC2×C3×C4C25
hypercenterC2×#446D3
hypocenterC3C22×#446
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. C2×C3×#446C2semidirect
3. C2×#5024C2semidirect
4. D3×#446C2direct (N × H)
7. C2×#4828C2semidirect
8. C2×#4831C2semidirect
10. C2×#4701C2semidirect
12. C2×#4679C2semidirect
30. C3×#446C22semidirect
42. #5024C22semidirect
49. #4831C22semidirect
50. #4828C22semidirect
52. #4701C22semidirect
54. #4679C22semidirect
62. C2×#446D3direct (N × H)
103. C2×D3×C8Q8semidirect
155. #446C2×D3direct (N × H)
207. C2×C3×C8C2×Q8semidirect
232. C2×C3⋊C8C2×Q8semidirect
238. D3×C8C2×Q8semidirect
345. C3×C8C22×Q8semidirect
348. C3⋊C8C22×Q8semidirect
390. C2×C8D3×Q8semidirect
417. C2×D3#446direct (N × H)
475. C8C2×D3×Q8semidirect
476. C2×C3C2×#446semidirect
480. D3C2×#446direct (N × H)
501. C3C22×#446semidirect
503. C2D3×#446direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D3×Q82
C2×C3×#4462
C2×#50242
D3×#4462
C2×D3×C4⋊C82
C2×#48282
C2×#48312
C2×D3×#972
C2×#47012
C2×C4×D3×C82
C2×#46792
C22×#4463