Finite Group Databasebeta

← D3×#64991 #14439917

Subgroups — D3×#64991 #14439917

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#4016C211yesmaximal, characteristic
2D3×#4015C211yesmaximal, characteristic
3#11750803C211yesmaximal, characteristic, complemented
4C5×D3×#97C211yesmaximal, characteristic
5C3×#64991C211yesmaximal, characteristic, complemented
6#11748032C212yesmaximal, complemented
7#11748030C212yesmaximal, complemented
8D3×#3950C212yesmaximal
9D3×#3949C212yesmaximal
10#11746953C211yesmaximal, characteristic, complemented
11#11746952C211yesmaximal, characteristic, complemented
12C2×#64991—31nomaximal, Hall
13C2×D3×Dic10—21no—
14#91759C2211yescharacteristic
15#91758C2211yescharacteristic
16C2×C5×D3×C8C2212yes—
17C42×C5×D3C2211yescharacteristic
18C3×#4016C2211yescharacteristic
19C3×#4015C2211yescharacteristic
20#91469—21no—
21#91469C2212yes—
22D3×C4⋊Dic5—21no—
23D3×C4⋊Dic5C2211yescharacteristic
24D3×C4⋊Dic5C2212yes—
25D3×C4⋊Dic5C2211yescharacteristic
26D3×#683—21no—
27D3×#683—21no—
28#91389—21no—
29#91381C2211yescharacteristic
30#91381C2211yescharacteristic
31#91379—21no—
32#91379—21no—
33C3×C5×#97C2211yescharacteristic
34#91102C2212yes—
35#91101C2212yes—
36C5×#815C2212yes—
37C5×#803C2211yescharacteristic
38C3×#3950C2212yes—
39C3×#3949C2212yes—
40#90990C2212yes—
41#90990C2212yes—
42#90987C2212yes—
43#90987C2212yes—
44D3×#501—51nomaximal, Hall
45C2×#4016—31no—
46C2×#4015—31no—
47C2×C5×#97—31no—
48C2×#3950—32no—
49C2×#3949—32no—
50#64991—31no—
51#64991—31no—
52#64991—31no—
53#64991—32no—
54#64991—32no—
55#64991D311yescharacteristic, direct product factor
56C2×Dic30—21no—
57C2×C4×C5×D3D411yescharacteristic
58C2×C4×C5×D3D411yescharacteristic
59C2×C4×C5×D3C2311yescharacteristic
60C2×C3×Dic10—21no—
61C2×#1204—22no—
62C2×D3×Dic5—21no—
63C2×D3×Dic5—21no—
64C2×D3×Dic5—22no—
65D3×Dic10—44no—
66C2×C3×C5×C8C2312yes—
67C3×C42×C5C2311yescharacteristic
68C4⋊Dic15—21no—
69C4⋊Dic15C2312yes—
70C4⋊Dic15C2311yescharacteristic
71C4⋊Dic15C2311yescharacteristic
72#6712—21no—
73#6712—21no—
74C4×C5×Dic3D411yescharacteristic
75C4×C5×Dic3D411yescharacteristic
76C4×C5×Dic3C2311yescharacteristic
77C2×C5×C3⋊C8C2312yes—
78C5×D3×C8Q818yescomplemented
79C3×C4⋊Dic5—21no—
80C3×C4⋊Dic5C2312yes—
81C3×C4⋊Dic5C2311yescharacteristic
82C3×C4⋊Dic5C2311yescharacteristic
83C3×#683—21no—
84C3×#683—21no—
85Dic3⋊Dic5—22no—
86Dic3⋊Dic5—22no—
87Dic3⋊Dic5—21no—
88Dic3⋊Dic5—21no—
89#6669—21no—
90#6669—21no—
91#6668—21no—
92#6668—21no—
93D3×C4⋊Q8—51no—
94D3×#125—51no—
95C3×#501—51no—
96#5081—51no—
97#5064—51no—
98D3×#107—52no—
99#4876—52no—
100D3×#106—52no—
101#4856—52no—
102D3×#97D511yescharacteristic
103#4702—51no—
104C22×Dic10—61no—
105C22×C5×C8—32no—
106C2×C42×C5—31no—
107C2×C4⋊Dic5—32no—
108C2×C4⋊Dic5—31no—
109C2×C4⋊Dic5—31no—
110C2×C4⋊Dic5—61no—
111C2×#683—61no—
112C2×#683—61no—
113#4016—31no—
114#4016—31no—
115#4016—31no—
116#4016—61no—
117#4016—61no—
118#4016C2×D311yescharacteristic
119#4015—31no—
120#4015—32no—
121#4015—61no—
122#4015—61no—
123#4015C2×D311yescharacteristic
124C5×#97—32no—
125C5×#97—31no—
126C5×#97C2×D311yescharacteristic
127#3950—32no—
128#3950—32no—
129#3950—32no—
130#3950C2×D312yes—
131#3949—32no—
132#3949—32no—
133#3949—32no—
134#3949C2×D312yes—
135C2×#501—151noSylow
136C22×C5×D3C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2411yescharacteristic
140C2×Dic15—21no—
141C2×Dic15—21no—
142C2×Dic15—22no—
143Dic30—42no—
144C2×C5×Dic3C2×D411yescharacteristic
145C2×C5×Dic3C2×D411yescharacteristic
146C2×C5×Dic3C2×D411yescharacteristic
147C4×C5×D3—22no—
148C4×C5×D3—22no—
149C4×C5×D3C2×Q814yes—
150C2×C3×Dic5—21no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—22no—
153C3×Dic10—42no—
154#1204—44no—
155D3×Dic5—44no—
156D3×Dic5—42no—
157D3×Dic5—42no—
158C3×C5×C8C2×Q814yescomplemented
159C5×C3⋊C8C2×Q814yescomplemented
160C2×D3×Q8—101no—
161C3×C4⋊Q8—51no—
162C3×#125—51no—
163#944—101no—
164C2×D3×C8C2×D512yes—
165D3×C4⋊C4—51no—
166D3×C4⋊C4—52no—
167D3×C4⋊C4—51no—
168D3×C4⋊C4—101no—
169D3×C4⋊C4—101no—
170D3×C4⋊C4—101no—
171#890—51no—
172#890—51no—
173#889—101no—
174#889—101no—
175#888—52no—
176#888—101no—
177C42×D3C2×D511yescharacteristic
178#870—51no—
179#869—51no—
180C3×#107—52no—
181C3×#106—52no—
182C3×#97C2×D511yescharacteristic
183#818—52no—
184#817—52no—
185#815C2×D512yes—
186#808—52no—
187#808—52no—
188#807—52no—
189#807—52no—
190#803C2×D511yescharacteristic
191C22×C4×C5—31no—
192C22×C4×C5—31no—
193C22×C4×C5—31no—
194C22×Dic5—62no—
195C22×Dic5—61no—
196C22×Dic5—61no—
197C2×Dic10—21no—
198C2×Dic10—62no—
199C2×Dic10—61no—
200C2×Dic10—124no—
201C2×C5×C8—32no—
202C2×C5×C8—38no—
203C2×C5×C8C22×D312yes—
204C42×C5—31no—
205C42×C5—31no—
206C42×C5—31no—
207C42×C5C22×D311yescharacteristic
208C4⋊Dic5—21no—
209C4⋊Dic5—31no—
210C4⋊Dic5—32no—
211C4⋊Dic5—31no—
212C4⋊Dic5—62no—
213C4⋊Dic5—62no—
214C4⋊Dic5—61no—
215C4⋊Dic5—61no—
216C4⋊Dic5—61no—
217C4⋊Dic5C22×D311yescharacteristic
218C4⋊Dic5C22×D312yes—
219C4⋊Dic5C22×D311yescharacteristic
220#683—21no—
221#683—21no—
222#683—61no—
223#683—61no—
224#683—61no—
225#683—61no—
226#683—61no—
227#683—61no—
228C2×C4⋊Q8—151no—
229C2×#125—151no—
230#501—51no—
231#501—152no—
232#501—152no—
233#501—151no—
234#501—151no—
235#501—151no—
236C2×#107—152no—
237C2×#106—152no—
238C2×#97—31no—
239C22×C3×C5C22×D411yescharacteristic
240C2×C5×D3C4⋊Q812yes—
241C2×C5×D3AGL(1,ℤ/8)12yes—
242C2×C5×D3#13712yes—
243C3×C4×C5—21no—
244C3×C4×C5—21no—
245C3×C4×C5C22×Q812yes—
246Dic15—42no—
247Dic15—41no—
248Dic15—41no—
249C3×Dic5—42no—
250C3×Dic5—41no—
251C3×Dic5—41no—
252C5×Dic3—21no—
253C5×Dic3—21no—
254C5×Dic3C4⋊Q812yes—
255C2×C3×Q8—101no—
256D3×Q8—204no—
257C2×C4×D3—101no—
258C2×C4×D3—101no—
259C2×C4×D3—102no—
260C2×C4×D3D2011yescharacteristic
261C2×C4×D3D2011yescharacteristic
262C2×C4×D3C22×D511yescharacteristic
263C2×Dic6—101no—
264C2×Dic6—102no—
265C2×C3×C8C22×D512yes—
266C3×C4⋊C4—51no—
267C3×C4⋊C4—52no—
268C3×C4⋊C4—51no—
269C3×C4⋊C4—101no—
270C3×C4⋊C4—101no—
271C3×C4⋊C4—101no—
272C3×C42C22×D511yescharacteristic
273C4⋊Dic3—51no—
274C4⋊Dic3—52no—
275C4⋊Dic3—51no—
276C4⋊Dic3—101no—
277C4⋊Dic3—101no—
278C4⋊Dic3—101no—
279Dic3⋊C4—101no—
280Dic3⋊C4—101no—
281Dic3⋊C4—101no—
282Dic3⋊C4—101no—
283Dic3⋊C4—102no—
284Dic3⋊C4—102no—
285Dic3⋊C4—101no—
286Dic3⋊C4—101no—
287C4×Dic3D2011yescharacteristic
288C4×Dic3D2011yescharacteristic
289C4×Dic3C22×D511yescharacteristic
290C2×C3⋊C8C22×D512yes—
291D3×C8Dic1018yescomplemented
292C23×C5—31no—
293C2×C4×C5—31no—
294C2×C4×C5—34no—
295C2×C4×C5—31no—
296C2×C4×C5—31no—
297C2×C4×C5—62no—
298C2×C4×C5—62no—
299C2×C4×C5D3×D411yescharacteristic
300C2×C4×C5D3×D411yescharacteristic
301C2×C4×C5C23×D311yescharacteristic
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—22no—
305C2×Dic5—61no—
306C2×Dic5—61no—
307C2×Dic5—62no—
308C2×Dic5—124no—
309C2×Dic5—122no—
310C2×Dic5—122no—
311Dic10—42no—
312Dic10—124no—
313Dic10—122no—
314C5×C8—34no—
315C5×C8D3×Q814yescomplemented
316C22×Q8—301no—
317C22×C8—32no—
318C4⋊Q8—51no—
319C4⋊Q8—152no—
320C4⋊Q8—151no—
321C4⋊Q8—301no—
322C4⋊Q8—301no—
323#125—51no—
324#125—151no—
325#125—151no—
326#125—151no—
327#125—301no—
328#125—301no—
329C2×C4⋊C4—151no—
330C2×C4⋊C4—151no—
331C2×C4⋊C4—152no—
332C2×C4⋊C4—301no—
333C2×C4⋊C4—301no—
334C2×C4⋊C4—301no—
335C2×C42—31no—
336#107—52no—
337#107—152no—
338#107—152no—
339#107—152no—
340#106—52no—
341#106—152no—
342#106—152no—
343#106—152no—
344#97—32no—
345#97—31no—
346#97D3×D511yescharacteristic
347C2×C3×C5C2×C4⋊Q811yescharacteristic
348C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
349C2×C3×C5C2×#13711yescharacteristic
350C5×D3#50114yescomplemented
351C22×D3C2×D2011yescharacteristic
352C3×Q8—202no—
353C2×C3×C4—101no—
354C2×C3×C4—101no—
355C2×C3×C4—102no—
356C2×C3×C4C2×D2011yescharacteristic
357C2×C3×C4C2×D2011yescharacteristic
358C2×C3×C4C23×D511yescharacteristic
359C2×Dic3—101no—
360C2×Dic3—101no—
361C2×Dic3—102no—
362C2×Dic3C2×D2011yescharacteristic
363C2×Dic3C2×D2011yescharacteristic
364C2×Dic3C2×D2011yescharacteristic
365C4×D3—22no—
366C4×D3—22no—
367C4×D3—202no—
368C4×D3—204no—
369C4×D3—202no—
370C4×D3C2×Dic1014yes—
371Dic6—204no—
372Dic6—202no—
373C3×C8C2×Dic1014yescomplemented
374C3⋊C8C2×Dic1014yescomplemented
375C22×C5—32no—
376C22×C5—32no—
377C22×C5—32no—
378C22×C5C2×D3×D411yescharacteristic
379C4×C5—21no—
380C4×C5—21no—
381C4×C5—32no—
382C4×C5—61no—
383C4×C5—61no—
384C4×C5C2×D3×Q812yes—
385Dic5—42no—
386Dic5—41no—
387Dic5—41no—
388Dic5—122no—
389Dic5—121no—
390Dic5—121no—
391C2×Q8—101no—
392C2×Q8—302no—
393C2×Q8—301no—
394C2×Q8—604no—
395C22×C4—31no—
396C22×C4—31no—
397C22×C4—31no—
398C22×C4—301no—
399C22×C4—301no—
400C22×C4—302no—
401C2×C8—32no—
402C2×C8—38no—
403C2×C8C2×D3×D512yes—
404C4⋊C4—51no—
405C4⋊C4—52no—
406C4⋊C4—51no—
407C4⋊C4—101no—
408C4⋊C4—101no—
409C4⋊C4—101no—
410C4⋊C4—151no—
411C4⋊C4—152no—
412C4⋊C4—151no—
413C4⋊C4—301no—
414C4⋊C4—301no—
415C4⋊C4—302no—
416C4⋊C4—301no—
417C4⋊C4—301no—
418C4⋊C4—301no—
419C4⋊C4—301no—
420C4⋊C4—302no—
421C4⋊C4—301no—
422C4⋊C4—301no—
423C4⋊C4—301no—
424C42—31no—
425C42—31no—
426C42—31no—
427C42C2×D3×D511yescharacteristic
428C3×C5C2×#50111yescharacteristic, complemented, Hall
429C22×C3C22×D2011yescharacteristic
430C2×D3#401512yes—
431C2×D3#405412yes—
432C2×D3#405512yes—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—202no—
436C3×C4—201no—
437C3×C4—201no—
438C3×C4C22×Dic1012yes—
439Dic3—21no—
440Dic3—21no—
441Dic3—202no—
442Dic3—201no—
443Dic3—201no—
444Dic3#401512yes—
445C2×C5—34no—
446C2×C5D3×C4⋊Q811yescharacteristic
447C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
448C2×C5D3×#13711yescharacteristic
449C23—31no—
450Q8—202no—
451Q8—602no—
452Q8—604no—
453C2×C4—31no—
454C2×C4—34no—
455C2×C4—31no—
456C2×C4—31no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4—101no—
460C2×C4—101no—
461C2×C4—102no—
462C2×C4—301no—
463C2×C4—301no—
464C2×C4—302no—
465C2×C4—604no—
466C2×C4—602no—
467C2×C4—602no—
468C2×C4D3×D2011yescharacteristic
469C2×C4D3×D2011yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—34no—
472C8D3×Dic1014yescomplemented
473C2×C3C2×#401511yescharacteristic
474C2×C3C2×#405411yescharacteristic
475C2×C3C2×#405511yescharacteristic
476D3#6499114yesdirect product factor
477C5D3×#50111yescharacteristic, complemented, Sylow
478C22—32no—
479C22—32no—
480C22—32no—
481C22C2×D3×D2011yescharacteristic
482C4—21no—
483C4—21no—
484C4—32no—
485C4—61no—
486C4—61no—
487C4—202no—
488C4—201no—
489C4—201no—
490C4—602no—
491C4—601no—
492C4—601no—
493C4C2×D3×Dic1012yes—
494C3C2×#6499111yescharacteristic, complemented, Sylow
495C2—34no—
496C2D3×#401511yescharacteristic
497C2D3×#405411yescharacteristic
498C2D3×#405511yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#97C22
socleC22×C3×C5C22×D4
prime radicalC22×C5×D3C2×D4
hypercenter#97D3×D5
hypocenterC3×C5C2×#501
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
3. #11750803C2semidirect
5. C3×#64991C2semidirect
6. #11748032C2semidirect
7. #11748030C2semidirect
10. #11746953C2semidirect
11. #11746952C2semidirect
55. #64991D3direct (N × H)
78. C5×D3×C8Q8semidirect
158. C3×C5×C8C2×Q8semidirect
159. C5×C3⋊C8C2×Q8semidirect
291. D3×C8Dic10semidirect
315. C5×C8D3×Q8semidirect
350. C5×D3#501semidirect
373. C3×C8C2×Dic10semidirect
374. C3⋊C8C2×Dic10semidirect
428. C3×C5C2×#501semidirect
472. C8D3×Dic10semidirect
476. D3#64991direct (N × H)
477. C5D3×#501semidirect
494. C3C2×#64991semidirect

Maximal subgroups

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

subgroupindex
D3×#40162
D3×#40152
#117508032
C5×D3×#972
C3×#649912
#117480322
#117480302
D3×#39502
D3×#39492
#117469532
#117469522
C2×#649913
D3×#5015