Finite Group Databasebeta

← D3×#464 #80596

Subgroups — D3×#464 #80596

Order 384.

500 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Q16C211yesmaximal, characteristic, complemented
2C2×D3×SD16C211yesmaximal, characteristic
3D3×#124C211yesmaximal, characteristic
4C4×D3×Q8C211yesmaximal, characteristic, complemented
5C3×#464C211yesmaximal, characteristic, complemented
6#5185C211yesmaximal, characteristic, complemented
7#5166C211yesmaximal, characteristic, complemented
8#5054C211yesmaximal, characteristic, complemented
9#5028C211yesmaximal, characteristic, complemented
10#4845C211yesmaximal, characteristic, complemented
11D3×C4⋊C8C211yesmaximal, characteristic, complemented
12D3×#103C211yesmaximal, characteristic, complemented
13#4798C211yesmaximal, characteristic, complemented
14D3×#102C211yesmaximal, characteristic
15#4767C211yesmaximal, characteristic, complemented
16C2×#464—31nomaximal, Sylow
17C2×D3×Q8C2211yescharacteristic
18C2×D3×Q8C2211yescharacteristic
19C2×D3×D4C2211yescharacteristic
20C2×C3×Q16C2211yescharacteristic, complemented
21C2×C3×SD16C2211yescharacteristic
22C3×#124C2211yescharacteristic
23C3×C4×Q8C2211yescharacteristic, complemented
24#947C2211yescharacteristic
25Q8×Dic3C2211yescharacteristic, complemented
26C2×#216C2211yescharacteristic, complemented
27C2×#216C2211yescharacteristic, complemented
28C2×#215C2211yescharacteristic
29#936C2211yescharacteristic
30C2×#214C2211yescharacteristic
31D3×Q16—24no—
32D3×SD16—24no—
33C2×Dic12C2211yescharacteristic, complemented
34C2×#204C2211yescharacteristic
35C2×D3×C8C2211yescharacteristic
36C2×D3×C8C2211yescharacteristic
37D3×C4⋊C4—21no—
38D3×C4⋊C4C2211yescharacteristic
39#887—21no—
40#887C2211yescharacteristic, complemented
41#885—21no—
42#885—21no—
43D3×C22⋊C4—21no—
44D3×C22⋊C4—21no—
45#875C2211yescharacteristic
46C42×D3—21no—
47C42×D3C2211yescharacteristic
48C4×Dic6—21no—
49C4×Dic6C2211yescharacteristic, complemented
50C3×C4⋊C8C2211yescharacteristic, complemented
51C3×#103C2211yescharacteristic, complemented
52C3×#102C2211yescharacteristic
53#835C2211yescharacteristic, complemented
54#832C2211yescharacteristic
55#821C2211yescharacteristic
56#816C2211yescharacteristic, complemented
57Dic3⋊C8C2211yescharacteristic, complemented
58Dic3⋊C8C2211yescharacteristic, complemented
59#810C2211yescharacteristic, complemented
60#809C2211yescharacteristic
61C4⋊(C3⋊C8)C2211yescharacteristic, complemented
62C22×Q16—31no—
63C22×SD16—31no—
64C2×#124—31no—
65C2×C4×Q8—31no—
66#464—31no—
67#464—31no—
68#464—31no—
69#464—31no—
70#464—31no—
71#464—31no—
72#464—31no—
73#464D311yescharacteristic, direct product factor
74C2×C4⋊C8—31no—
75C2×#103—31no—
76C2×#102—31no—
77C23×D3—21no—
78C2×C3×Q8C2311yescharacteristic
79C2×C3×Q8C2311yescharacteristic
80C2×C3×D4C2311yescharacteristic
81C2×#67—21no—
82D3×Q8—22no—
83D3×Q8—22no—
84D3×Q8—22no—
85D3×Q8D414yes—
86D3×D4—22no—
87D3×D4—22no—
88C2×D12C2311yescharacteristic
89C2×C4×D3—21no—
90C2×C4×D3—21no—
91C2×C4×D3—21no—
92C2×C4×D3D411yescharacteristic
93C2×C4×D3D411yescharacteristic
94C2×C4×D3C2311yescharacteristic
95C2×Dic6—21no—
96C2×Dic6—21no—
97C2×Dic6C2311yescharacteristic
98C2×Dic6C2311yescharacteristic
99C3×Q16—22no—
100C3×SD16—22no—
101C2×C3×C8C2311yescharacteristic
102C2×C3×C8C2311yescharacteristic
103C3×C4⋊C4—21no—
104C3×C4⋊C4C2311yescharacteristic
105C3×C22⋊C4—21no—
106C3×C22⋊C4—21no—
107C3×C42—21no—
108C3×C42C2311yescharacteristic
109#217—21no—
110#217—21no—
111#216—22no—
112#216—22no—
113#215—22no—
114#214—22no—
115(C2×D3)⋊C4—21no—
116(C2×D3)⋊C4—21no—
117(C2×D3)⋊C4—21no—
118(C2×D3)⋊C4—21no—
119C4⋊Dic3—21no—
120C4⋊Dic3C2311yescharacteristic
121Dic3⋊C4—21no—
122Dic3⋊C4—21no—
123Dic3⋊C4—21no—
124C4×Dic3—21no—
125C4×Dic3—21no—
126C4×Dic3—21no—
127C4×Dic3D411yescharacteristic
128C4×Dic3D411yescharacteristic
129C4×Dic3C2311yescharacteristic
130C2×C3⋊C8C2311yescharacteristic
131C2×C3⋊C8C2311yescharacteristic
132Dic12—22no—
133#204—22no—
134D3×C8—22no—
135D3×C8—22no—
136C22×Q8—31no—
137C22×Q8—31no—
138C22×D4—31no—
139C2×Q16—31no—
140C2×Q16—31no—
141C2×Q16—31no—
142C2×Q16—64no—
143C2×Q16C2×D311yescharacteristic, complemented
144C2×SD16—31no—
145C2×SD16—31no—
146C2×SD16—31no—
147C2×SD16—64no—
148C2×SD16C2×D311yescharacteristic
149C22×C8—31no—
150C22×C8—31no—
151#124—31no—
152#124—31no—
153#124—31no—
154#124—61no—
155#124—61no—
156#124C2×D311yescharacteristic
157C4×Q8—31no—
158C4×Q8—31no—
159C4×Q8—31no—
160C4×Q8—61no—
161C4×Q8—61no—
162C4×Q8C2×D311yescharacteristic, complemented
163C2×C4⋊C4—31no—
164C2×C4⋊C4—61no—
165C2×C22⋊C4—61no—
166C2×C22⋊C4—61no—
167C2×C42—31no—
168C2×C42—61no—
169C4⋊C8—31no—
170C4⋊C8—31no—
171C4⋊C8—31no—
172C4⋊C8C2×D311yescharacteristic, complemented
173#103—31no—
174#103—31no—
175#103—31no—
176#103C2×D311yescharacteristic, complemented
177#102—31no—
178#102—31no—
179#102—31no—
180#102C2×D311yescharacteristic
181C23×C3—21no—
182C22×D3—21no—
183C22×D3—42no—
184C22×D3—42no—
185C22×D3—42no—
186C22×D3C2×D411yescharacteristic
187C3×Q8—21no—
188C3×Q8—21no—
189C3×Q8—21no—
190C3×Q8C2×D412yes—
191C3×D4—21no—
192C3×D4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4C2×D411yescharacteristic
197C2×C3×C4C2×D411yescharacteristic
198C2×C3×C4C2411yescharacteristic
199#67—42no—
200C2×Dic3—21no—
201C2×Dic3—21no—
202C2×Dic3—21no—
203C2×Dic3C2×D411yescharacteristic
204C2×Dic3C2×D411yescharacteristic
205C2×Dic3C2×D411yescharacteristic
206D12—21no—
207D12—21no—
208C4×D3—24no—
209C4×D3—22no—
210C4×D3—22no—
211C4×D3—42no—
212C4×D3—42no—
213C4×D3C2×D412yes—
214C4×D3#4112yes—
215Dic6—21no—
216Dic6—24no—
217Dic6—21no—
218Dic6—21no—
219Dic6—42no—
220Dic6C2×D412yes—
221C3×C8—21no—
222C3×C8—21no—
223C3⋊C8—21no—
224C3⋊C8—21no—
225C24—61no—
226C2×Q8—34no—
227C2×Q8—31no—
228C2×Q8—31no—
229C2×Q8—61no—
230C2×Q8—61no—
231C2×Q8—62no—
232C2×Q8—62no—
233C2×Q8—62no—
234C2×Q8C22×D311yescharacteristic
235C2×Q8C22×D311yescharacteristic
236C2×D4—31no—
237C2×D4—62no—
238C2×D4—62no—
239C2×D4—61no—
240C2×D4C22×D311yescharacteristic
241C22×C4—31no—
242C22×C4—31no—
243C22×C4—31no—
244C22×C4—61no—
245C22×C4—61no—
246C22×C4—61no—
247Q16—22no—
248Q16—62no—
249Q16—62no—
250Q16—62no—
251SD16—22no—
252SD16—62no—
253SD16—62no—
254SD16—62no—
255C2×C8—31no—
256C2×C8—31no—
257C2×C8—62no—
258C2×C8—62no—
259C2×C8C22×D311yescharacteristic
260C2×C8C22×D311yescharacteristic
261C4⋊C4—21no—
262C4⋊C4—31no—
263C4⋊C4—61no—
264C4⋊C4—61no—
265C4⋊C4—61no—
266C4⋊C4—61no—
267C4⋊C4C22×D311yescharacteristic
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—61no—
271C22⋊C4—61no—
272C22⋊C4—61no—
273C22⋊C4—61no—
274C22⋊C4—61no—
275C22⋊C4—61no—
276C42—21no—
277C42—31no—
278C42—31no—
279C42—31no—
280C42—61no—
281C42—61no—
282C42—61no—
283C42C22×D311yescharacteristic
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3C22×D411yescharacteristic
288C2×D3—41no—
289C2×D3—41no—
290C2×D3—41no—
291C2×D3—84no—
292C2×D3#12112yes—
293C2×D3#13512yes—
294C2×D3#13712yes—
295C3×C4—22no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—41no—
299C3×C4—41no—
300C3×C4C22×D411yescharacteristic
301C3×C4C2×#4111yescharacteristic
302Dic3—22no—
303Dic3—21no—
304Dic3—21no—
305Dic3—41no—
306Dic3—41no—
307Dic3#12112yes—
308C23—21no—
309C23—31no—
310C23—61no—
311C23—122no—
312C23—122no—
313C23—122no—
314Q8—21no—
315Q8—21no—
316Q8—21no—
317Q8—32no—
318Q8—64no—
319Q8—61no—
320Q8—61no—
321Q8—61no—
322Q8—122no—
323Q8D3×D412yes—
324D4—21no—
325D4—21no—
326D4—61no—
327D4—61no—
328D4—122no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—31no—
333C2×C4—32no—
334C2×C4—32no—
335C2×C4—31no—
336C2×C4—31no—
337C2×C4—62no—
338C2×C4—62no—
339C2×C4—64no—
340C2×C4—61no—
341C2×C4—61no—
342C2×C4—61no—
343C2×C4—122no—
344C2×C4—122no—
345C2×C4D3×D411yescharacteristic
346C2×C4D3×D411yescharacteristic
347C2×C4C23×D311yescharacteristic
348C8—21no—
349C8—21no—
350C8—61no—
351C8—61no—
352C2×C3—81no—
353C2×C3C2×#12111yescharacteristic
354C2×C3C2×#13511yescharacteristic
355C2×C3C2×#13711yescharacteristic
356D3—81no—
357D3#46414yesdirect product factor
358C22—32no—
359C22—32no—
360C22—32no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—121no—
365C22—121no—
366C22—121no—
367C22—244no—
368C22C2×D3×D411yescharacteristic
369C4—21no—
370C4—21no—
371C4—22no—
372C4—32no—
373C4—41no—
374C4—41no—
375C4—61no—
376C4—61no—
377C4—62no—
378C4—121no—
379C4—121no—
380C4C2×D3×D411yescharacteristic
381C4D3×#4111yescharacteristic
382C3C2×#46411yescharacteristic, complemented, Sylow
383C2—34no—
384C2—81no—
385C2—241no—
386C2D3×#12111yescharacteristic
387C2D3×#13511yescharacteristic
388C2D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#464C2
socleC22×C3C22×D4
prime radicalC2×D3×D4C22
hypercenter#464D3
hypocenterC3C2×#464
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×D3×Q16C2semidirect
4. C4×D3×Q8C2semidirect
5. C3×#464C2semidirect
6. #5185C2semidirect
7. #5166C2semidirect
8. #5054C2semidirect
9. #5028C2semidirect
10. #4845C2semidirect
11. D3×C4⋊C8C2semidirect
12. D3×#103C2semidirect
13. #4798C2semidirect
15. #4767C2semidirect
20. C2×C3×Q16C22semidirect
23. C3×C4×Q8C22semidirect
25. Q8×Dic3C22semidirect
26. C2×#216C22semidirect
27. C2×#216C22semidirect
33. C2×Dic12C22semidirect
40. #887C22semidirect
49. C4×Dic6C22semidirect
50. C3×C4⋊C8C22semidirect
51. C3×#103C22semidirect
53. #835C22semidirect
56. #816C22semidirect
57. Dic3⋊C8C22semidirect
58. Dic3⋊C8C22semidirect
59. #810C22semidirect
61. C4⋊(C3⋊C8)C22semidirect
73. #464D3direct (N × H)
143. C2×Q16C2×D3semidirect
162. C4×Q8C2×D3semidirect
172. C4⋊C8C2×D3semidirect
176. #103C2×D3semidirect
357. D3#464direct (N × H)
382. C3C2×#464semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Q162
C2×D3×SD162
D3×#1242
C4×D3×Q82
C3×#4642
#51852
#51662
#50542
#50282
#48452
D3×C4⋊C82
D3×#1032
#47982
D3×#1022
#47672
C2×#4643