Finite Group Databasebeta

← D3×#65369 #14439908

Subgroups — D3×#65369 #14439908

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
1C5×D3×C4⋊Q8C211yesmaximal, characteristic
2D3×#4016C211yesmaximal, characteristic
3#11751182C211yesmaximal, characteristic, complemented
4C3×#65369C211yesmaximal, characteristic, complemented
5D3×#3940C212yesmaximal
6D3×#3939C212yesmaximal
7#11747162C212yesmaximal, complemented
8#11747160C212yesmaximal, complemented
9D3×#3935C211yesmaximal, characteristic
10#11746970C211yesmaximal, characteristic, complemented
11#11746957C211yesmaximal, characteristic, complemented
12C2×#65369—31nomaximal, Hall
13C2×C5×D3×Q8—21no—
14C3×C5×C4⋊Q8C2211yescharacteristic
15#91759C2211yescharacteristic
16C5×#944—21no—
17C5×D3×C4⋊C4—21no—
18C5×D3×C4⋊C4C2212yes—
19C5×#888—21no—
20C5×#888C2212yes—
21C42×C5×D3C2211yescharacteristic
22C5×#869C2211yescharacteristic
23C3×#4016C2211yescharacteristic
24D3×C4⋊Dic5C2211yescharacteristic
25D3×C4⋊Dic5C2211yescharacteristic
26D3×#683—21no—
27D3×#683—21no—
28#91381C2211yescharacteristic
29#91381C2211yescharacteristic
30#91379—21no—
31#91379—21no—
32C2×D3×#168C2212yes—
33#91092C2212yes—
34#91091C2212yes—
35#91087C2211yescharacteristic
36C3×#3940C2212yes—
37C3×#3939C2212yes—
38C3×#3935C2211yescharacteristic
39#90989C2212yes—
40#90988C2212yes—
41#90986C2212yes—
42#90985C2212yes—
43#90953C2212yes—
44D3×#501—51nomaximal, Hall
45C2×C5×C4⋊Q8—31no—
46C2×#4016—31no—
47#65369—31no—
48#65369—32no—
49#65369—32no—
50#65369—31no—
51#65369—31no—
52#65369D311yescharacteristic, direct product factor
53C2×#3940—32no—
54C2×#3939—32no—
55C2×#3935—31no—
56C2×C3×C5×Q8—21no—
57C5×D3×Q8—44no—
58C2×C4×C5×D3—22no—
59C2×C4×C5×D3D411yescharacteristic
60C2×C4×C5×D3D411yescharacteristic
61C2×C4×C5×D3C2311yescharacteristic
62C2×C5×Dic6—21no—
63C2×C5×Dic6—22no—
64C2×D3×Dic5—21no—
65C2×D3×Dic5—21no—
66C3×C5×C4⋊C4—21no—
67C3×C5×C4⋊C4C2312yes—
68C3×C42×C5C2311yescharacteristic
69C4⋊Dic15C2311yescharacteristic
70C4⋊Dic15C2311yescharacteristic
71#6712—21no—
72#6712—21no—
73C2×C3⋊#168C2312yes—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3C2312yes—
76C5×Dic3⋊C4—22no—
77C5×Dic3⋊C4—22no—
78C4×C5×Dic3D411yescharacteristic
79C4×C5×Dic3D411yescharacteristic
80C4×C5×Dic3C2311yescharacteristic
81C3×C4⋊Dic5C2311yescharacteristic
82C3×C4⋊Dic5C2311yescharacteristic
83C3×#683—21no—
84C3×#683—21no—
85C2×C3×#168C2312yes—
86Dic3⋊Dic5—21no—
87Dic3⋊Dic5—21no—
88#6669—21no—
89#6669—21no—
90#6668—21no—
91#6668—21no—
92D3×#168Q818yescomplemented
93D3×C4⋊Q8D511yescharacteristic
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×#97—51no—
103#4702—51no—
104C22×C5×Q8—61no—
105C5×C4⋊Q8—32no—
106C5×C4⋊Q8—31no—
107C5×C4⋊Q8—61no—
108C5×C4⋊Q8—61no—
109C5×C4⋊Q8C2×D311yescharacteristic
110C2×C5×C4⋊C4—32no—
111C2×C5×C4⋊C4—61no—
112C2×C42×C5—31no—
113C2×C4⋊Dic5—31no—
114C2×C4⋊Dic5—31no—
115C2×#683—61no—
116C2×#683—61no—
117C22×#168—32no—
118#4016—31no—
119#4016—31no—
120#4016—31no—
121#4016—61no—
122#4016—61no—
123#4016C2×D311yescharacteristic
124#3940—32no—
125#3940—32no—
126#3940—32no—
127#3940C2×D312yes—
128#3939—32no—
129#3939—32no—
130#3939—32no—
131#3939C2×D312yes—
132#3935—31no—
133#3935—32no—
134#3935C2×D311yescharacteristic
135C2×#501—151noSylow
136C22×C5×D3C2×D411yescharacteristic
137C3×C5×Q8—42no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—21no—
143C2×Dic15—21no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3C2×D411yescharacteristic
146C2×C5×Dic3C2×D411yescharacteristic
147C2×C5×Dic3C2×D411yescharacteristic
148C4×C5×D3—22no—
149C4×C5×D3—22no—
150C4×C5×D3—44no—
151C4×C5×D3C2×Q814yes—
152C5×Dic6—44no—
153C5×Dic6—42no—
154C2×C3×Dic5—21no—
155C2×C3×Dic5—21no—
156D3×Dic5—42no—
157D3×Dic5—42no—
158C3⋊#168C2×Q814yescomplemented
159C3×#168C2×Q814yescomplemented
160C2×D3×Q8—21no—
161C3×C4⋊Q8C2×D511yescharacteristic
162C3×#125—51no—
163#944—21no—
164C2×D3×C8—52no—
165D3×C4⋊C4—21no—
166D3×C4⋊C4—51no—
167D3×C4⋊C4—51no—
168D3×C4⋊C4—101no—
169D3×C4⋊C4—101no—
170D3×C4⋊C4C2×D512yes—
171#890—51no—
172#890—51no—
173#889—101no—
174#889—101no—
175#888—21no—
176#888C2×D512yes—
177C42×D3C2×D511yescharacteristic
178#870—51no—
179#869C2×D511yescharacteristic
180C3×#107—52no—
181C3×#106—52no—
182C3×#97—51no—
183#818—52no—
184#817—52no—
185#815—52no—
186#808—52no—
187#808—52no—
188#807—52no—
189#807—52no—
190#803—51no—
191C2×C5×Q8—21no—
192C2×C5×Q8—62no—
193C2×C5×Q8—61no—
194C2×C5×Q8—124no—
195C22×C4×C5—31no—
196C22×C4×C5—31no—
197C22×C4×C5—31no—
198C22×C4×C5—62no—
199C22×Dic5—61no—
200C22×Dic5—61no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4—32no—
203C5×C4⋊C4—62no—
204C5×C4⋊C4—62no—
205C5×C4⋊C4—61no—
206C5×C4⋊C4C22×D312yes—
207C42×C5—31no—
208C42×C5—31no—
209C42×C5—31no—
210C42×C5C22×D311yescharacteristic
211C4⋊Dic5—31no—
212C4⋊Dic5—31no—
213C4⋊Dic5—61no—
214C4⋊Dic5—61no—
215C4⋊Dic5C22×D311yescharacteristic
216C4⋊Dic5C22×D311yescharacteristic
217#683—21no—
218#683—21no—
219#683—61no—
220#683—61no—
221#683—61no—
222#683—61no—
223#683—61no—
224#683—61no—
225C2×#168—32no—
226C2×#168—38no—
227C2×#168C22×D312yes—
228C2×C4⋊Q8—31no—
229C2×#125—151no—
230#501—51no—
231#501—151no—
232#501—152no—
233#501—152no—
234#501—151no—
235#501—151no—
236C2×#107—152no—
237C2×#106—152no—
238C2×#97—151no—
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×C5—42no—
246C3×C4×C5C22×Q812yes—
247Dic15—41no—
248Dic15—41no—
249C3×Dic5—41no—
250C3×Dic5—41no—
251C5×Dic3—21no—
252C5×Dic3—21no—
253C5×Dic3—42no—
254C5×Dic3C4⋊Q812yes—
255C2×C3×Q8—21no—
256D3×Q8—44no—
257C2×C4×D3—22no—
258C2×C4×D3—101no—
259C2×C4×D3—101no—
260C2×C4×D3C22⋊D511yescharacteristic
261C2×C4×D3C22⋊D511yescharacteristic
262C2×C4×D3C22×D511yescharacteristic
263C2×Dic6—21no—
264C2×Dic6—22no—
265C2×C3×C8—52no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—51no—
268C3×C4⋊C4—51no—
269C3×C4⋊C4—101no—
270C3×C4⋊C4—101no—
271C3×C4⋊C4C22×D512yes—
272C3×C42C22×D511yescharacteristic
273C4⋊Dic3—21no—
274C4⋊Dic3—51no—
275C4⋊Dic3—51no—
276C4⋊Dic3—101no—
277C4⋊Dic3—101no—
278C4⋊Dic3C22×D512yes—
279Dic3⋊C4—22no—
280Dic3⋊C4—22no—
281Dic3⋊C4—101no—
282Dic3⋊C4—101no—
283Dic3⋊C4—101no—
284Dic3⋊C4—101no—
285Dic3⋊C4—101no—
286Dic3⋊C4—101no—
287C4×Dic3C22⋊D511yescharacteristic
288C4×Dic3C22⋊D511yescharacteristic
289C4×Dic3C22×D511yescharacteristic
290C2×C3⋊C8—52no—
291D3×C8—58no—
292C23×C5—31no—
293C5×Q8—42no—
294C5×Q8—122no—
295C5×Q8—124no—
296C2×C4×C5—22no—
297C2×C4×C5—31no—
298C2×C4×C5—34no—
299C2×C4×C5—31no—
300C2×C4×C5—31no—
301C2×C4×C5—62no—
302C2×C4×C5—62no—
303C2×C4×C5—62no—
304C2×C4×C5—124no—
305C2×C4×C5D3×D411yescharacteristic
306C2×C4×C5D3×D411yescharacteristic
307C2×C4×C5C23×D311yescharacteristic
308C2×Dic5—21no—
309C2×Dic5—21no—
310C2×Dic5—61no—
311C2×Dic5—61no—
312C2×Dic5—122no—
313C2×Dic5—122no—
314#168—34no—
315#168D3×Q814yescomplemented
316C22×Q8—61no—
317C22×C8—152no—
318C4⋊Q8—32no—
319C4⋊Q8—31no—
320C4⋊Q8—61no—
321C4⋊Q8—61no—
322C4⋊Q8D3×D511yescharacteristic
323#125—51no—
324#125—151no—
325#125—151no—
326#125—151no—
327#125—301no—
328#125—301no—
329C2×C4⋊C4—32no—
330C2×C4⋊C4—61no—
331C2×C4⋊C4—151no—
332C2×C4⋊C4—151no—
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—51no—
345#97—152no—
346#97—151no—
347C2×C3×C5C2×C4⋊Q811yescharacteristic
348C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
349C2×C3×C5C2×#13711yescharacteristic
350C5×D3#50114yescomplemented
351C22×D3C2×C22⋊D511yescharacteristic
352C3×Q8—42no—
353C2×C3×C4—22no—
354C2×C3×C4—101no—
355C2×C3×C4—101no—
356C2×C3×C4C2×C22⋊D511yescharacteristic
357C2×C3×C4C2×C22⋊D511yescharacteristic
358C2×C3×C4C23×D511yescharacteristic
359C2×Dic3—22no—
360C2×Dic3—101no—
361C2×Dic3—101no—
362C2×Dic3C2×C22⋊D511yescharacteristic
363C2×Dic3C2×C22⋊D511yescharacteristic
364C2×Dic3C2×C22⋊D511yescharacteristic
365C4×D3—22no—
366C4×D3—22no—
367C4×D3—44no—
368C4×D3—202no—
369C4×D3—202no—
370C4×D3Q8×D514yes—
371Dic6—44no—
372Dic6—42no—
373C3×C8—54no—
374C3⋊C8—54no—
375C22×C5—32no—
376C22×C5—32no—
377C22×C5—32no—
378C22×C5C2×D3×D411yescharacteristic
379C4×C5—21no—
380C4×C5—21no—
381C4×C5—32no—
382C4×C5—42no—
383C4×C5—61no—
384C4×C5—61no—
385C4×C5—122no—
386C4×C5C2×D3×Q812yes—
387Dic5—41no—
388Dic5—41no—
389Dic5—121no—
390Dic5—121no—
391C2×Q8—21no—
392C2×Q8—62no—
393C2×Q8—61no—
394C2×Q8—124no—
395C22×C4—31no—
396C22×C4—31no—
397C22×C4—31no—
398C22×C4—62no—
399C22×C4—301no—
400C22×C4—301no—
401C2×C8—52no—
402C2×C8—158no—
403C2×C8—152no—
404C4⋊C4—21no—
405C4⋊C4—32no—
406C4⋊C4—51no—
407C4⋊C4—51no—
408C4⋊C4—62no—
409C4⋊C4—62no—
410C4⋊C4—61no—
411C4⋊C4—101no—
412C4⋊C4—101no—
413C4⋊C4—151no—
414C4⋊C4—151no—
415C4⋊C4—301no—
416C4⋊C4—301no—
417C4⋊C4—301no—
418C4⋊C4—301no—
419C4⋊C4—301no—
420C4⋊C4—301no—
421C4⋊C4—301no—
422C4⋊C4—301no—
423C4⋊C4C2×D3×D512yes—
424C42—31no—
425C42—31no—
426C42—31no—
427C42C2×D3×D511yescharacteristic
428C3×C5C2×#50111yescharacteristic, complemented, Hall
429C22×C3C22×C22⋊D511yescharacteristic
430C2×D3#407812yes—
431C2×D3#408812yes—
432C2×D3#409012yes—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—42no—
436C3×C4—201no—
437C3×C4—201no—
438C3×C4C2×Q8×D512yes—
439Dic3—21no—
440Dic3—21no—
441Dic3—42no—
442Dic3—201no—
443Dic3—201no—
444Dic3#409012yes—
445C2×C5—34no—
446C2×C5D3×C4⋊Q811yescharacteristic
447C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
448C2×C5D3×#13711yescharacteristic
449C23—31no—
450Q8—42no—
451Q8—122no—
452Q8—124no—
453C2×C4—22no—
454C2×C4—31no—
455C2×C4—34no—
456C2×C4—31no—
457C2×C4—31no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—101no—
462C2×C4—101no—
463C2×C4—124no—
464C2×C4—301no—
465C2×C4—301no—
466C2×C4—602no—
467C2×C4—602no—
468C2×C4D3×C22⋊D511yescharacteristic
469C2×C4D3×C22⋊D511yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—54no—
472C8—154no—
473C2×C3C2×#407811yescharacteristic
474C2×C3C2×#408811yescharacteristic
475C2×C3C2×#409011yescharacteristic
476D3#6536914yesdirect product factor
477C5D3×#50111yescharacteristic, complemented, Sylow
478C22—32no—
479C22—32no—
480C22—32no—
481C22C2×D3×C22⋊D511yescharacteristic
482C4—21no—
483C4—21no—
484C4—32no—
485C4—42no—
486C4—61no—
487C4—61no—
488C4—122no—
489C4—201no—
490C4—201no—
491C4—601no—
492C4—601no—
493C4D3×Q8×D512yes—
494C3C2×#6536911yescharacteristic, complemented, Sylow
495C2—34no—
496C2D3×#407811yescharacteristic
497C2D3×#408811yescharacteristic
498C2D3×#409011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC22×C5×D3C2×D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5C2×#501
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #11751182C2semidirect
4. C3×#65369C2semidirect
7. #11747162C2semidirect
8. #11747160C2semidirect
10. #11746970C2semidirect
11. #11746957C2semidirect
52. #65369D3direct (N × H)
92. D3×#168Q8semidirect
158. C3⋊#168C2×Q8semidirect
159. C3×#168C2×Q8semidirect
315. #168D3×Q8semidirect
350. C5×D3#501semidirect
428. C3×C5C2×#501semidirect
476. D3#65369direct (N × H)
477. C5D3×#501semidirect
494. C3C2×#65369semidirect

Maximal subgroups

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

subgroupindex
C5×D3×C4⋊Q82
D3×#40162
#117511822
C3×#653692
D3×#39402
D3×#39392
#117471622
#117471602
D3×#39352
#117469702
#117469572
C2×#653693
D3×#5015