Finite Group Databasebeta

← Dic3×#4131 #14411508

Subgroups — Dic3×#4131 #14411508

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91990C211yesmaximal, characteristic
2C2×C3×#4131C211yesmaximal, characteristic
3Dic3×#711C211yesmaximal, characteristic
4#11751995C212yesmaximal, complemented
5Dic3×#704C212yesmaximal, complemented
6#11751988C212yesmaximal, complemented
7C2×Dic3×#170C212yesmaximal, complemented
8#11751782C211yesmaximal, characteristic, complemented
9Dic3×#700C211yesmaximal, characteristic, complemented
10#11751767C211yesmaximal, characteristic, complemented
11Dic3×D5⋊C8C211yesmaximal, characteristic, complemented
12C4×#4131—31nomaximal, Hall
13C2×C3×#711C2211yescharacteristic
14C2×#6762C2212yes—
15C22×C3⋊#170C2212yes—
16#91990C418yescomplemented
17C2×#6758C2211yescharacteristic
18C2×D5⋊(C3⋊C8)C2211yescharacteristic
19C2×C3×#704C2212yes—
20C22×C3×#170C2212yes—
21C3×#4131C418yescomplemented
22C2×C3×#700C2211yescharacteristic
23C2×C3×D5⋊C8C2211yescharacteristic
24D4×Dic15C411yescharacteristic
25C5×D4×Dic3C411yescharacteristic
26#91559C412yes—
27Dic3×C22⋊D5C412yes—
28#91528C2212yes—
29C2×Dic3×Dic5C2212yes—
30C4×D5×Dic3C2211yescharacteristic
31#91358C2211yescharacteristic
32#91331C411yescharacteristic
33Dic3×Dic10C411yescharacteristic
34#91169C2212yes—
35#91169C2212yes—
36#91169C2212yes—
37Dic3×#170C2211yescharacteristic
38Dic3×#170C2212yes—
39Dic3×#170C2212yes—
40Dic3×#170C2212yes—
41Dic3×#170C2211yescharacteristic
42Dic3×#170C2211yescharacteristic
43Dic3×#170C2211yescharacteristic
44Dic3×#131—51nomaximal, Hall
45C2×#4131—31no—
46C2×#4131D311yescharacteristic
47C4×#711—31no—
48C4×#704—32no—
49C2×C4×#170—32no—
50#65701—31no—
51#65701—31no—
52#65691—32no—
53#65691—32no—
54C4×#700—31no—
55C4×D5⋊C8—31no—
56C2×C3×C5×D4C2×C411yescharacteristic
57C22×Dic15C2×C412yes—
58C22×C5×Dic3C2×C412yes—
59C2×C3×C22⋊D5C2×C412yes—
60C22×C3×Dic5C2312yes—
61C3×#711C2×C414yes—
62C3×#711C2×C414yes—
63C2×C3×C4×D5C2311yescharacteristic
64C2×C3×Dic10C2×C411yescharacteristic
65C2×D5×Dic3C2×C411yescharacteristic
66C2×D5×Dic3C2×C411yescharacteristic
67#6762C2×C418yescomplemented
68C2×C3⋊#170C2×C418yescomplemented
69C2×C3⋊#170C2311yescharacteristic
70C2×C3⋊#170C2311yescharacteristic
71C2×C3⋊#170C2312yes—
72#6758C2×C414yescomplemented
73D5⋊(C3⋊C8)C2×C414yescomplemented
74C3×#704C2×C418yescomplemented
75C2×C3×#170C2×C418yescomplemented
76C2×C3×#170C2311yescharacteristic
77C2×C3×#170C2311yescharacteristic
78C2×C3×#170C2312yes—
79C3×#700C2×C414yescomplemented
80C3×D5⋊C8C2×C414yescomplemented
81#6719C2×C412yes—
82C4⋊Dic15C2×C411yescharacteristic
83C4×Dic15C2×C411yescharacteristic
84C5×#217C2×C412yes—
85C5×C4⋊Dic3C2×C411yescharacteristic
86C4×C5×Dic3C2×C411yescharacteristic
87#6668C2×C412yes—
88#6668C2×C412yes—
89#6665C2×C412yes—
90Dic3×Dic5C2×C412yes—
91Dic3×Dic5C2×C412yes—
92Dic3×Dic5C2311yescharacteristic
93Dic3×Dic5C2312yes—
94Dic3×Dic5C2311yescharacteristic
95C2×C3×#131—51no—
96Dic3×#41—51no—
97C2×#948—51no—
98#5122—52no—
99#5122—51no—
100Dic3×M16—52no—
101Dic3×M16—51no—
102#5101—52no—
103#5101—51no—
104C2×C8×Dic3—52no—
105C2×C8×Dic3—51no—
106C2×#711C2×D311yescharacteristic
107C2×#704—32no—
108C2×#704C2×D312yes—
109C22×#170—32no—
110C22×#170C2×D312yes—
111#4131—38no—
112#4131Dic318yesdirect product factor
113C2×#700—31no—
114C2×#700C2×D311yescharacteristic
115C2×D5⋊C8—31no—
116C2×D5⋊C8C2×D311yescharacteristic
117C4×C5×D4—31no—
118D4×Dic5—31no—
119C4×C22⋊D5—32no—
120C2×C4×Dic5—32no—
121#4038—31no—
122#4033—31no—
123#4027—32no—
124#4023—32no—
125C42×D5—31no—
126C4×Dic10—31no—
127#4002—32no—
128#4002—32no—
129#4002—32no—
130C4×#170—31no—
131C4×#170—31no—
132C4×#170—31no—
133C4×#170—31no—
134C4×#170—32no—
135C4×#170—32no—
136C4×#170—32no—
137C4×#131—151noSylow
138C23×C3×C5C22×C412yes—
139C22×C3×D5C22×C411yescharacteristic
140C3×C5×D4C4214yes—
141C2×C3×C4×C5C22×C411yescharacteristic
142C2×Dic15—24no—
143C2×Dic15C22×C412yes—
144C2×Dic15C22×C411yescharacteristic
145C2×Dic15C22×C411yescharacteristic
146C2×C5×Dic3—24no—
147C2×C5×Dic3C22×C412yes—
148C2×C5×Dic3C22×C411yescharacteristic
149C2×C5×Dic3C22×C411yescharacteristic
150C3×C22⋊D5C4218yes—
151C2×C3×Dic5C22×C412yes—
152C2×C3×Dic5C22×C414yes—
153C2×C3×Dic5C22×C414yes—
154C2×C3×Dic5C2411yescharacteristic
155C3×C4×D5C22×C412yes—
156C3×C4×D5C22×C412yes—
157C3×Dic10C4214yes—
158D5×Dic3—22no—
159D5×Dic3—22no—
160C3⋊#170C22×C412yes—
161C3⋊#170C22×C412yes—
162C3⋊#170C22×C414yes—
163C3×#170C22×C412yes—
164C3×#170C22×C412yes—
165C3×#170C22×C414yes—
166C2×C3×#41—51no—
167C3×#131—58no—
168C2×C3×M16—51no—
169C2×C3×M16—52no—
170C22×C3×C8—51no—
171C22×C3×C8—52no—
172#948—58no—
173Q8×Dic3—51no—
174Q8×Dic3—51no—
175D4×Dic3—51no—
176D4×Dic3—52no—
177D4×Dic3—52no—
178D4×Dic3AGL(1,𝔽5)11yescharacteristic
179#926—52no—
180#926—51no—
181C2×C4×Dic3—52no—
182C2×C4×Dic3—51no—
183C2×#208—51no—
184C2×#208—52no—
185C22×C3⋊C8—51no—
186C22×C3⋊C8—52no—
187#815—52no—
188#815—52no—
189#815—52no—
190C8×Dic3—51no—
191C8×Dic3—52no—
192C8×Dic3—51no—
193C8×Dic3—52no—
194C8×Dic3—51no—
195C8×Dic3—52no—
196C8×Dic3—51no—
197C2×C5×D4C4×D311yescharacteristic
198C22×C4×C5—32no—
199C2×C22⋊D5C4×D312yes—
200C22×Dic5—32no—
201C22×Dic5C22×D312yes—
202#711C4×D314yes—
203#711C2×Dic314yes—
204C2×C4×D5—31no—
205C2×C4×D5—31no—
206C2×C4×D5C22×D311yescharacteristic
207C2×Dic10C4×D311yescharacteristic
208#704—38no—
209#704C2×Dic318yescomplemented
210C2×#170—38no—
211C2×#170—31no—
212C2×#170—31no—
213C2×#170—32no—
214C2×#170C2×Dic318yescomplemented
215C2×#170C22×D311yescharacteristic
216C2×#170C22×D311yescharacteristic
217C2×#170C22×D312yes—
218#700—34no—
219#700C2×Dic314yescomplemented
220D5⋊C8—34no—
221D5⋊C8C2×Dic314yescomplemented
222C5×C4⋊C4—31no—
223C5×C22⋊C4—32no—
224C42×C5—31no—
225C22⋊Dic5—32no—
226#685—32no—
227C4⋊Dic5—31no—
228#683—32no—
229#683—32no—
230C4×Dic5—31no—
231C4×Dic5—32no—
232C4×Dic5—32no—
233C4×Dic5—31no—
234C4×Dic5—31no—
235C4×Dic5—32no—
236C2×#131—51no—
237C2×#131—151no—
238C4×#41—151no—
239#405—152no—
240#405—151no—
241#405—152no—
242#405—151no—
243C4×M16—151no—
244C4×M16—152no—
245C2×C4×C8—151no—
246C2×C4×C8—152no—
247C22×C3×C5—22no—
248C22×C3×C5—22no—
249C22×C3×C5C2×C4214yes—
250C22×C3×C5C23×C411yescharacteristic
251C2×C3×D5—21no—
252C2×C3×D5—21no—
253C2×C3×D5C2×C4212yes—
254C3×C4×C5C2×C4212yes—
255Dic15—21no—
256Dic15—22no—
257Dic15#13112yescomplemented
258C3×Dic5C2×C4214yes—
259C3×Dic5C23×C411yescharacteristic
260C3×Dic5C23×C411yescharacteristic
261C5×Dic3—21no—
262C5×Dic3—22no—
263C5×Dic3#13112yescomplemented
264C3×#41—54no—
265C3×#41—54no—
266C2×C3×Q8—51no—
267C2×C3×D4—52no—
268C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
269C22×C3×C4—52no—
270C22×C3×C4—51no—
271C22×Dic3—52no—
272C22×Dic3—51no—
273C22×Dic3—51no—
274C22×Dic3C2×AGL(1,𝔽5)12yes—
275C3×M16—54no—
276C3×M16—58no—
277C2×C3×C8—51no—
278C2×C3×C8—51no—
279C2×C3×C8—52no—
280C2×C3×C8—54no—
281C2×C3×C8—58no—
282#217—52no—
283#217—52no—
284#217C2×AGL(1,𝔽5)12yes—
285C4⋊Dic3—51no—
286C4⋊Dic3—52no—
287C4⋊Dic3—52no—
288C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
289C4×Dic3—51no—
290C4×Dic3—52no—
291C4×Dic3—52no—
292C4×Dic3—51no—
293C4×Dic3—52no—
294C4×Dic3—51no—
295C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
296#208—54no—
297#208—58no—
298C2×C3⋊C8—51no—
299C2×C3⋊C8—51no—
300C2×C3⋊C8—52no—
301C2×C3⋊C8—54no—
302C2×C3⋊C8—58no—
303C23×C5C2×C4×D312yes—
304C22×D5C2×C4×D311yescharacteristic
305C5×D4C4×Dic314yes—
306C2×C4×C5—31no—
307C2×C4×C5—32no—
308C2×C4×C5—31no—
309C2×C4×C5—64no—
310C2×C4×C5C2×C4×D311yescharacteristic
311C22⋊D5C4×Dic318yes—
312C2×Dic5—31no—
313C2×Dic5—31no—
314C2×Dic5—32no—
315C2×Dic5—64no—
316C2×Dic5C2×C4×D312yes—
317C2×Dic5C2×C4×D314yes—
318C2×Dic5C22×Dic314yes—
319C2×Dic5C23×D311yescharacteristic
320C4×D5—62no—
321C4×D5—62no—
322C4×D5C2×C4×D312yes—
323C4×D5C22×Dic312yes—
324Dic10C4×Dic314yes—
325#170—32no—
326#170—32no—
327#170—34no—
328#170C22×Dic312yes—
329#170C22×Dic312yes—
330#170C22×Dic314yes—
331C2×#41—51no—
332#131—58no—
333#131—158no—
334C2×M16—51no—
335C2×M16—52no—
336C2×M16—151no—
337C2×M16—152no—
338C22×C8—51no—
339C22×C8—52no—
340C22×C8—151no—
341C22×C8—152no—
342C4×Q8—151no—
343C4×Q8—151no—
344C4×D4—31no—
345C4×D4—152no—
346C4×D4—152no—
347C4×D4—151no—
348#117—152no—
349#117—151no—
350C2×C42—151no—
351C2×C42—152no—
352#97—152no—
353#97—152no—
354#97—152no—
355C4×C8—151no—
356C4×C8—151no—
357C4×C8—152no—
358C4×C8—151no—
359C4×C8—152no—
360C4×C8—151no—
361C4×C8—152no—
362C2×C3×C5—24no—
363C2×C3×C5C22×C4211yescharacteristic
364C2×C3×C5C2×#13111yescharacteristic
365C2×C3×C5C2×#13111yescharacteristic
366C3×D5—22no—
367C23×C3—51no—
368C23×C3C22×AGL(1,𝔽5)12yes—
369C3×Q8—54no—
370C3×D4—58no—
371C3×D4C4×AGL(1,𝔽5)14yes—
372C2×C3×C4—54no—
373C2×C3×C4—54no—
374C2×C3×C4—52no—
375C2×C3×C4—51no—
376C2×C3×C4—52no—
377C2×C3×C4—52no—
378C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
379C2×Dic3—24no—
380C2×Dic3—51no—
381C2×Dic3—51no—
382C2×Dic3—52no—
383C2×Dic3—102no—
384C2×Dic3—104no—
385C2×Dic3—102no—
386C2×Dic3C22×AGL(1,𝔽5)12yes—
387C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
388C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
389C3×C8—52no—
390C3×C8—52no—
391C3×C8—54no—
392C3⋊C8—52no—
393C3⋊C8—52no—
394C3⋊C8—54no—
395C22×C5—22no—
396C22×C5—22no—
397C22×C5C2×C4×Dic314yes—
398C22×C5C22×C4×D311yescharacteristic
399C2×D5—21no—
400C2×D5—21no—
401C2×D5C2×C4×Dic312yes—
402C4×C5—32no—
403C4×C5—61no—
404C4×C5—62no—
405C4×C5C2×C4×Dic312yes—
406Dic5—32no—
407Dic5—61no—
408Dic5—62no—
409Dic5C2×C4×Dic314yes—
410Dic5C22×C4×D311yescharacteristic
411Dic5C23×Dic311yescharacteristic
412#41—54no—
413#41—54no—
414C2×Q8—51no—
415C2×D4—52no—
416C2×D4D3×AGL(1,𝔽5)11yescharacteristic
417C22×C4—32no—
418C22×C4—52no—
419C22×C4—51no—
420C22×C4—151no—
421C22×C4—151no—
422C22×C4—152no—
423M16—54no—
424M16—58no—
425M16—154no—
426M16—158no—
427C2×C8—51no—
428C2×C8—51no—
429C2×C8—52no—
430C2×C8—54no—
431C2×C8—58no—
432C2×C8—151no—
433C2×C8—151no—
434C2×C8—152no—
435C2×C8—154no—
436C2×C8—158no—
437C4⋊C4—31no—
438C4⋊C4—152no—
439C4⋊C4—152no—
440C4⋊C4—151no—
441C22⋊C4—32no—
442C22⋊C4—152no—
443C22⋊C4—152no—
444C42—31no—
445C42—151no—
446C42—151no—
447C42—152no—
448C42—152no—
449C42—152no—
450C42—151no—
451C3×C5C4×#13111yescharacteristic, complemented, Hall
452C22×C3—22no—
453C22×C3—22no—
454C22×C3—52no—
455C22×C3—101no—
456C22×C3—101no—
457C22×C3C2×C4×AGL(1,𝔽5)14yes—
458C22×C3C23×AGL(1,𝔽5)11yescharacteristic
459C3×C4—54no—
460C3×C4—51no—
461C3×C4—51no—
462C3×C4C2×C4×AGL(1,𝔽5)12yes—
463Dic3—22no—
464Dic3—21no—
465Dic3—52no—
466Dic3—101no—
467Dic3—102no—
468Dic3#413112yesdirect product factor
469C2×C5—24no—
470C2×C5D3×#13111yescharacteristic
471C2×C5D3×#13111yescharacteristic
472C2×C5C22×C4×Dic311yescharacteristic
473D5—22no—
474C23—51no—
475C23C2×D3×AGL(1,𝔽5)12yes—
476Q8—54no—
477D4—58no—
478D4Dic3×AGL(1,𝔽5)14yes—
479C2×C4—31no—
480C2×C4—31no—
481C2×C4—32no—
482C2×C4—54no—
483C2×C4—54no—
484C2×C4—51no—
485C2×C4—52no—
486C2×C4—52no—
487C2×C4—52no—
488C2×C4—64no—
489C2×C4—151no—
490C2×C4—151no—
491C2×C4—152no—
492C2×C4—302no—
493C2×C4—302no—
494C2×C4—304no—
495C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
496C8—52no—
497C8—52no—
498C8—54no—
499C8—152no—
500C8—152no—
501C8—154no—
502C2×C3—24no—
503C2×C3—102no—
504C2×C3C22×C4×AGL(1,𝔽5)11yescharacteristic
505C2×C3C2×#413111yescharacteristic
506C2×C3D5⋊#13111yescharacteristic
507C5Dic3×#13111yescharacteristic, complemented, Sylow
508C22—22no—
509C22—22no—
510C22—52no—
511C22—101no—
512C22—101no—
513C22C2×Dic3×AGL(1,𝔽5)14yes—
514C22C22×D3×AGL(1,𝔽5)11yescharacteristic
515C4—32no—
516C4—51no—
517C4—51no—
518C4—54no—
519C4—62no—
520C4—61no—
521C4—152no—
522C4—301no—
523C4—302no—
524C4C2×Dic3×AGL(1,𝔽5)12yes—
525C3C4×#413111yescharacteristic, complemented, Sylow
526C2—24no—
527C2—102no—
528C2D3×#413111yescharacteristic
529C2#1175684011yescharacteristic
530C2C22×Dic3×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C42
FittingC2×C3×C5×D4C2×C4
socleC22×C3×C5C23×C4
prime radicalC2×C3×#711C22
cosocleC2×C3×Dic5C24
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5C4×#131
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
4. #11751995C2semidirect
5. Dic3×#704C2semidirect
6. #11751988C2semidirect
7. C2×Dic3×#170C2semidirect
8. #11751782C2semidirect
9. Dic3×#700C2semidirect
10. #11751767C2semidirect
11. Dic3×D5⋊C8C2semidirect
16. #91990C4semidirect
21. C3×#4131C4semidirect
67. #6762C2×C4semidirect
68. C2×C3⋊#170C2×C4semidirect
72. #6758C2×C4semidirect
73. D5⋊(C3⋊C8)C2×C4semidirect
74. C3×#704C2×C4semidirect
75. C2×C3×#170C2×C4semidirect
79. C3×#700C2×C4semidirect
80. C3×D5⋊C8C2×C4semidirect
112. #4131Dic3direct (N × H)
209. #704C2×Dic3semidirect
214. C2×#170C2×Dic3semidirect
219. #700C2×Dic3semidirect
221. D5⋊C8C2×Dic3semidirect
257. Dic15#131semidirect
263. C5×Dic3#131semidirect
451. C3×C5C4×#131semidirect
468. Dic3#4131direct (N × H)
507. C5Dic3×#131semidirect
525. C3C4×#4131semidirect

Maximal subgroups

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

subgroupindex
C2×#919902
C2×C3×#41312
Dic3×#7112
#117519952
Dic3×#7042
#117519882
C2×Dic3×#1702
#117517822
Dic3×#7002
#117517672
Dic3×D5⋊C82
C4×#41313
Dic3×#1315