Finite Group Databasebeta

← D3×#4683 #11874919

Subgroups — D3×#4683 #11874919

Order 1152.

763 conjugacy classes of subgroups.

The subgroup lattice has 331 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#870C212yesmaximal
2#10592382C211yesmaximal, characteristic, complemented
3C3×C4×D3×C8C211yesmaximal, characteristic
4C3×#4683C211yesmaximal, characteristic, complemented
5#10590873C212yesmaximal, complemented
6#10590871C212yesmaximal, complemented
7D3×#818C212yesmaximal
8D3×#817C212yesmaximal
9#10590304C212yesmaximal, complemented
10D3×#499—31nomaximal
11C2×#4683—31nomaximal
12#64079C2212yes—
13C2×C3×D3×C8C2211yescharacteristic
14C2×C3×D3×C8C2211yescharacteristic
15C3×C42×D3C2211yescharacteristic
16C3×#870C2212yes—
17D3×C4⋊Dic3C2214yes—
18D3×Dic3⋊C4—24no—
19#63869C2214yes—
20#63867—24no—
21C32×C4×C8C2211yescharacteristic
22#63645C2212yes—
23#63644C2212yes—
24C3×#818C2212yes—
25C3×#817C2212yes—
26C3×C8×Dic3C2211yescharacteristic
27C3×C8×Dic3C2211yescharacteristic
28C3×C4×C3⋊C8C2211yescharacteristic
29#63575C2214yes—
30#63573C2214yes—
31D3×#125—32no—
32C2×#870—32no—
33C3×#499—31no—
34C2×C3×C4×C8—31no—
35C2×#818—32no—
36C2×#817—32no—
37#5065—32no—
38D3×#107—32no—
39#4878—32no—
40D3×#106—32no—
41#4858—32no—
42C4×D3×C8D311yescharacteristic
43#4683—32no—
44#4683—31no—
45#4683—31no—
46#4683—32no—
47#4683—32no—
48#4683—61no—
49#4683D311yescharacteristic, direct product factor
50C2×C3×C4×D3D412yes—
51C2×C3×C4×D3C2311yescharacteristic
52C2×D3×Dic3—24no—
53C2×C32×C8C2311yescharacteristic
54C2×C32×C8C2311yescharacteristic
55C32×C42C2311yescharacteristic
56C4⋊(C3⋊Dic3)C2314yes—
57#3750—24no—
58C3×C4⋊Dic3C2314yes—
59C3×Dic3⋊C4—24no—
60C3×C4×Dic3D412yes—
61C3×C4×Dic3C2311yescharacteristic
62C2×C3×C3⋊C8C2311yescharacteristic
63C2×C3×C3⋊C8C2311yescharacteristic
64C3×D3×C8Q814yes—
65C3×D3×C8Q814yes—
66#3724—24no—
67Dic3⋊Dic3—24no—
68Dic3⋊Dic3—24no—
69C2×#499—91noSylow
70C22×C3×C8—31no—
71C22×C3×C8—31no—
72C3×#125—32no—
73C2×C3×C42—31no—
74C2×C4⋊Dic3—34no—
75C2×Dic3⋊C4—64no—
76C2×D3×C8C2×D311yescharacteristic
77C2×D3×C8C2×D311yescharacteristic
78D3×C4⋊C4—34no—
79D3×C4⋊C4—64no—
80#890—34no—
81#889—64no—
82C42×D3C2×D311yescharacteristic
83#870—32no—
84#870—32no—
85#870—34no—
86#870—62no—
87#870—64no—
88#870C2×D312yes—
89C3×#107—32no—
90C3×#106—32no—
91C3×C4×C8—21no—
92C3×C4×C8—31no—
93C3×C4×C8—31no—
94C3×C4×C8—31no—
95C3×C4×C8C2×D311yescharacteristic
96C3×C4×C8C2×D311yescharacteristic
97#818—32no—
98#818—32no—
99#818—34no—
100#818—62no—
101#818C2×D312yes—
102#817—32no—
103#817—32no—
104#817—34no—
105#817—62no—
106#817C2×D312yes—
107C8×Dic3C2×D311yescharacteristic
108C8×Dic3C2×D311yescharacteristic
109#808—34no—
110#807—34no—
111C4×C3⋊C8C2×D311yescharacteristic
112C22×C3×D3C2×D411yescharacteristic
113C2×C32×C4C2×D412yes—
114C2×C32×C4C2411yescharacteristic
115C2×C3⋊Dic3—24no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3C2×D412yes—
118C2×C3×Dic3C2×D411yescharacteristic
119C3×C4×D3—24no—
120C3×C4×D3C2×Q812yes—
121C3×C4×D3C2×Q812yes—
122D3×Dic3—48no—
123C32×C8C2×Q812yes—
124C32×C8C2×Q812yes—
125C3×C3⋊C8C2×Q812yes—
126C3×C3⋊C8C2×Q812yes—
127C2×#125—92no—
128#499—31no—
129#499—92no—
130#499—92no—
131#499—92no—
132#499—91no—
133C2×#107—92no—
134C2×#106—92no—
135C2×C4×C8—31no—
136C22×C3×C4—31no—
137C22×C3×C4—32no—
138C22×Dic3—64no—
139C2×C4×D3—64no—
140C2×C4×D3D1212yes—
141C2×C4×D3C22×D311yescharacteristic
142C2×C3×C8—21no—
143C2×C3×C8—21no—
144C2×C3×C8—31no—
145C2×C3×C8—31no—
146C2×C3×C8—34no—
147C2×C3×C8—34no—
148C2×C3×C8C22×D311yescharacteristic
149C2×C3×C8C22×D311yescharacteristic
150C2×C3×C8C22×D311yescharacteristic
151C2×C3×C8C22×D311yescharacteristic
152C3×C4⋊C4—34no—
153C3×C4⋊C4—64no—
154C3×C42—21no—
155C3×C42—32no—
156C3×C42—31no—
157C3×C42C22×D311yescharacteristic
158C3×C42C22×D311yescharacteristic
159C4⋊Dic3—34no—
160C4⋊Dic3—34no—
161C4⋊Dic3—64no—
162C4⋊Dic3—64no—
163C4⋊Dic3—64no—
164C4⋊Dic3C22×D314yes—
165Dic3⋊C4—24no—
166Dic3⋊C4—64no—
167Dic3⋊C4—64no—
168Dic3⋊C4—64no—
169Dic3⋊C4—64no—
170Dic3⋊C4—64no—
171Dic3⋊C4—64no—
172Dic3⋊C4—124no—
173C4×Dic3D1212yes—
174C4×Dic3C22×D311yescharacteristic
175C2×C3⋊C8C22×D311yescharacteristic
176C2×C3⋊C8C22×D311yescharacteristic
177D3×C8Dic614yes—
178D3×C8Dic614yes—
179C22×C32C22×D411yescharacteristic
180C2×C3×D3C4⋊Q812yes—
181C2×C3×D3#13514yes—
182C32×C4—22no—
183C32×C4C22×Q811yescharacteristic
184C32×C4C22×Q811yescharacteristic
185C3⋊Dic3—44no—
186C3×Dic3—22no—
187C3×Dic3—44no—
188C3×Dic3C4⋊Q812yes—
189C22×C8—31no—
190C22×C8—31no—
191#125—32no—
192#125—94no—
193#125—92no—
194#125—184no—
195C2×C4⋊C4—94no—
196C2×C4⋊C4—184no—
197C2×C42—31no—
198#107—32no—
199#107—94no—
200#107—92no—
201#106—32no—
202#106—94no—
203#106—92no—
204C4×C8—31no—
205C4×C8—31no—
206C4×C8—31no—
207C4×C8D3211yescharacteristic
208C23×C3—31no—
209C22×D3C2×D1211yescharacteristic
210C2×C3×C4—21no—
211C2×C3×C4—22no—
212C2×C3×C4—31no—
213C2×C3×C4—32no—
214C2×C3×C4—32no—
215C2×C3×C4—32no—
216C2×C3×C4—64no—
217C2×C3×C4—64no—
218C2×C3×C4C2×D1212yes—
219C2×C3×C4D3×D412yes—
220C2×C3×C4C23×D311yescharacteristic
221C2×C3×C4C23×D311yescharacteristic
222C2×Dic3—24no—
223C2×Dic3—64no—
224C2×Dic3—64no—
225C2×Dic3—124no—
226C2×Dic3—128no—
227C2×Dic3C2×D1212yes—
228C2×Dic3C2×D1211yescharacteristic
229C4×D3—24no—
230C4×D3—128no—
231C4×D3C2×Dic612yes—
232C4×D3C2×Dic612yes—
233C3×C8—22no—
234C3×C8—22no—
235C3×C8—32no—
236C3×C8—32no—
237C3×C8C2×Dic612yes—
238C3×C8C2×Dic612yes—
239C3×C8D3×Q812yes—
240C3×C8D3×Q812yes—
241C3⋊C8C2×Dic612yes—
242C3⋊C8C2×Dic612yes—
243C2×C32C2×C4⋊Q811yescharacteristic
244C2×C32C2×#13512yes—
245C3×D3#49914yescomplemented
246C22×C4—31no—
247C22×C4—32no—
248C22×C4—184no—
249C2×C8—31no—
250C2×C8—31no—
251C2×C8—34no—
252C2×C8—34no—
253C2×C8C2×D3211yescharacteristic
254C2×C8C2×D3211yescharacteristic
255C4⋊C4—34no—
256C4⋊C4—64no—
257C4⋊C4—94no—
258C4⋊C4—184no—
259C4⋊C4—184no—
260C4⋊C4—184no—
261C4⋊C4—184no—
262C42—31no—
263C42—32no—
264C42C2×D3211yescharacteristic
265C22×C3—21no—
266C22×C3—32no—
267C22×C3—34no—
268C22×C3C22×D1211yescharacteristic
269C22×C3C2×D3×D411yescharacteristic
270C2×D3#86912yes—
271C2×D3#90414yes—
272C3×C4—22no—
273C3×C4—22no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—32no—
277C3×C4—42no—
278C3×C4—62no—
279C3×C4—124no—
280C3×C4C22×Dic611yescharacteristic
281C3×C4C22×Dic611yescharacteristic
282C3×C4C2×D3×Q811yescharacteristic
283C3×C4C2×D3×Q811yescharacteristic
284Dic3—22no—
285Dic3—44no—
286Dic3—124no—
287Dic3—124no—
288Dic3—244no—
289Dic3#86912yes—
290C32C2×#49911yescharacteristic, complemented, Sylow
291C23—31no—
292C2×C4—31no—
293C2×C4—32no—
294C2×C4—32no—
295C2×C4—32no—
296C2×C4—64no—
297C2×C4—64no—
298C2×C4—184no—
299C2×C4—368no—
300C2×C4D3×D1212yes—
301C2×C4C22×D3211yescharacteristic
302C8—32no—
303C8—32no—
304C8D3×Dic612yes—
305C8D3×Dic612yes—
306C2×C3—21no—
307C2×C3—22no—
308C2×C3—34no—
309C2×C3C2×#86911yescharacteristic
310C2×C3D3×C4⋊Q811yescharacteristic
311C2×C3C2×#90412yes—
312C2×C3D3×#13512yes—
313D3#468314yesdirect product factor
314C22—32no—
315C22—34no—
316C22C2×D3×D1211yescharacteristic
317C4—22no—
318C4—32no—
319C4—62no—
320C4—124no—
321C4—364no—
322C4C2×D3×Dic611yescharacteristic
323C4C2×D3×Dic611yescharacteristic
324C3—21no—
325C3C2×#468311yescharacteristic, complemented
326C3D3×#49911yescharacteristic, complemented
327C2—34no—
328C2D3×#86911yescharacteristic
329C2D3×#90412yes—
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4×C8D32
hypocenterC32C2×#499
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10592382C2semidirect
4. C3×#4683C2semidirect
5. #10590873C2semidirect
6. #10590871C2semidirect
9. #10590304C2semidirect
49. #4683D3direct (N × H)
245. C3×D3#499semidirect
290. C32C2×#499semidirect
313. D3#4683direct (N × H)
325. C3C2×#4683semidirect
326. C3D3×#499semidirect

Maximal subgroups

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

subgroupindex
D3×#8702
#105923822
C3×C4×D3×C82
C3×#46832
#105908732
#105908712
D3×#8182
D3×#8172
#105903042
D3×#4993
C2×#46833