Finite Group Databasebeta

← D3×#66146 #14479027

Subgroups — D3×#66146 #14479027

Order 1920.

2976 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×D3×Q8C211yesmaximal, characteristic
2#11756571C211yesmaximal, characteristic, complemented
3C3×#66146C211yesmaximal, characteristic, complemented
4D3×Q8×Dic5C218yesmaximal, complemented
5#11755144C218yesmaximal, complemented
6D3×#4072C216yesmaximal
7#11754211C216yesmaximal, complemented
8C2×#66146—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C2×C5×D3×Q8C4116yescomplemented
11C2×C5×D3×Q8C2214yes—
12C2×C5×D3×Q8C2214yes—
13C22×C4×C5×D3C2213yes—
14C22×C5×Dic6C2213yes—
15Q8×Dic15C2218yescomplemented
16#91815C2216yes—
17C3×Q8×Dic5C2218yescomplemented
18C3×#4072C2216yes—
19D3×C22⋊Dic5C2214yes—
20#91529C22112yes—
21D3×C4⋊Dic5C22112yes—
22C4×D3×Dic5C22112yes—
23#91371C22112yes—
24#91344C22124yescomplemented
25#91338C22112yes—
26Dic5×Dic6C22124yescomplemented
27D3×#519—51nomaximal, Hall
28C23×C5×Q8—31no—
29#66146—38no—
30#66146—36no—
31#66146—31no—
32#66146D311yescharacteristic, direct product factor
33C2×Q8×Dic5—38no—
34C2×#4072—36no—
35C23×C5×D3C2311yescharacteristic
36C2×C3×C5×Q8C2×C418yescomplemented
37C2×C3×C5×Q8C2314yes—
38C22×C3×C4×C5C2313yes—
39C22×C5×Dic3C2313yes—
40C5×D3×Q8C2×C4132yes—
41C5×D3×Q8C2×C4132yescomplemented
42C2×C4×C5×D3C2×C4124yes—
43C2×C4×C5×D3C2316yes—
44C2×C4×C5×D3C2316yes—
45C2×C5×Dic6C2×C4124yescomplemented
46C2×C5×Dic6C23112yes—
47C2×D3×Dic5C2318yes—
48#6719C2314yes—
49C4⋊Dic15C23112yes—
50C4×Dic15C23112yes—
51C3×C22⋊Dic5C2314yes—
52C3×C4⋊Dic5C23112yes—
53C3×C4×Dic5C23112yes—
54Dic3⋊Dic5C23124yes—
55(C2×D3)⋊Dic5C2318yes—
56Dic3×Dic5C23124yes—
57C22×D3×Q8D511yescharacteristic
58C3×#519—51no—
59#5812—51no—
60#5572—58no—
61C4×D3×Q8—58no—
62D3×#117—56no—
63#5516—56no—
64C22×C5×Q8—316no—
65C22×C5×Q8—34no—
66C22×C5×Q8—34no—
67C22×C5×Q8—33no—
68C22×C5×Q8C2×D311yescharacteristic
69C23×C4×C5—33no—
70C2×C22⋊Dic5—34no—
71Q8×Dic5—38no—
72Q8×Dic5—324no—
73Q8×Dic5—324no—
74Q8×Dic5C2×D318yescomplemented
75#4072—36no—
76#4072—312no—
77#4072—312no—
78#4072—312no—
79#4072C2×D316yes—
80C2×C4⋊Dic5—312no—
81C2×C4×Dic5—312no—
82C2×#519—151noSylow
83C23×C3×C5C2411yescharacteristic
84C22×C5×D3—24no—
85C22×C5×D3C22×C414yes—
86C22×C5×D3C2411yescharacteristic
87C22×C5×D3C2411yescharacteristic
88C3×C5×Q8C22×C4116yes—
89C2×C3×C4×C5C22×C4112yes—
90C2×C3×C4×C5C2416yes—
91C2×Dic15C2418yes—
92C2×C5×Dic3C22×C4112yes—
93C2×C5×Dic3C2416yes—
94C4×C5×D3C22×C4124yes—
95C4×C5×D3C22×C4124yes—
96C5×Dic6C22×C4148yes—
97C2×C3×Dic5C2418yes—
98D3×Dic5—216no—
99C22×C3×Q8C2×D511yescharacteristic
100C2×D3×Q8Dic5116yescomplemented
101C2×D3×Q8C2×D514yes—
102C2×D3×Q8C2×D514yes—
103C22×C4×D3C2×D513yes—
104C22×Dic6C2×D513yes—
105C3×C4×Q8—58no—
106C3×#117—56no—
107Q8×Dic3—58no—
108#926—56no—
109#892—512no—
110D3×C4⋊C4—512no—
111#887—524no—
112D3×C22⋊C4—54no—
113#877—512no—
114#872—512no—
115C42×D3—512no—
116C4×Dic6—524no—
117C24×C5—31no—
118C2×C5×Q8—332no—
119C2×C5×Q8—332no—
120C2×C5×Q8—324no—
121C2×C5×Q8—312no—
122C2×C5×Q8C4×D318yescomplemented
123C2×C5×Q8C22×D314yes—
124C22×C4×C5—33no—
125C22×C4×C5—324no—
126C22×C4×C5—36no—
127C22×C4×C5—36no—
128C22×C4×C5C22×D313yes—
129C22×Dic5—38no—
130C22⋊Dic5—34no—
131C22⋊Dic5—38no—
132C22⋊Dic5C22×D314yes—
133C4⋊Dic5—312no—
134C4⋊Dic5—324no—
135C4⋊Dic5C22×D3112yes—
136C4×Dic5—312no—
137C4×Dic5—324no—
138C4×Dic5C22×D3112yes—
139C23×Q8—31no—
140#519—51no—
141#519—156no—
142#519—158no—
143#519—151no—
144C2×C4×Q8—158no—
145C2×#117—156no—
146C22×C3×C5—22no—
147C22×C3×C5C23×C412yes—
148C22×C3×C5C2511yescharacteristic
149C2×C5×D3—22no—
150C2×C5×D3—28no—
151C2×C5×D3C23×C412yes—
152C2×C5×D3C23×C412yes—
153C2×C5×D32−1+414yes—
154C3×C4×C5C23×C4112yes—
155Dic15—28no—
156C3×Dic5—28no—
157C5×Dic3C23×C4112yes—
158C23×D3C22×D511yescharacteristic
159C2×C3×Q8C2×Dic518yescomplemented
160C2×C3×Q8C22×D514yes—
161C22×C3×C4C22×D513yes—
162C22×Dic3C22×D513yes—
163D3×Q8C2×Dic5132yes—
164D3×Q8C2×Dic5132yescomplemented
165C2×C4×D3—58no—
166C2×C4×D3C2×Dic5124yes—
167C2×C4×D3C22×D516yes—
168C2×C4×D3C22×D516yes—
169C2×Dic6C2×Dic5124yescomplemented
170C2×Dic6C22×D5112yes—
171C3×C4⋊C4—512no—
172C3×C22⋊C4—54no—
173C3×C42—512no—
174#217—54no—
175(C2×D3)⋊C4—58no—
176C4⋊Dic3—512no—
177Dic3⋊C4—524no—
178C4×Dic3—512no—
179C4×Dic3—524no—
180C23×C5—31no—
181C23×C5—34no—
182C23×C5—31no—
183C23×C5—64no—
184C23×C5C23×D311yescharacteristic
185C5×Q8—348no—
186C5×Q8C2×C4×D3116yes—
187C2×C4×C5—312no—
188C2×C4×C5—36no—
189C2×C4×C5—324no—
190C2×C4×C5—324no—
191C2×C4×C5C2×C4×D3112yes—
192C2×C4×C5C23×D316yes—
193C2×Dic5—38no—
194C2×Dic5—616no—
195C2×Dic5C23×D318yes—
196C22×Q8—316no—
197C22×Q8—34no—
198C22×Q8—34no—
199C22×Q8—33no—
200C22×Q8D3×D511yescharacteristic
201C23×C4—33no—
202C4×Q8—58no—
203C4×Q8—1524no—
204C4×Q8—1524no—
205C4×Q8—158no—
206#117—56no—
207#117—1512no—
208#117—1512no—
209#117—1512no—
210#117—156no—
211C2×C4⋊C4—1512no—
212C2×C22⋊C4—154no—
213C2×C42—1512no—
214C2×C3×C5—22no—
215C2×C3×C5C24×C411yescharacteristic
216C2×C3×C5C2×2−1+412yes—
217C5×D3—22no—
218C5×D3#51914yescomplemented
219C23×C3C23×D511yescharacteristic
220C22×D3—24no—
221C22×D3C22×Dic514yes—
222C22×D3C23×D511yescharacteristic
223C22×D3C23×D511yescharacteristic
224C3×Q8C22×Dic5116yes—
225C2×C3×C4—58no—
226C2×C3×C4C22×Dic5112yes—
227C2×C3×C4C23×D516yes—
228C2×Dic3—58no—
229C2×Dic3C22×Dic5112yes—
230C2×Dic3C23×D516yes—
231C4×D3—1016no—
232C4×D3C22×Dic5124yes—
233C4×D3C22×Dic5124yes—
234Dic6C22×Dic5148yes—
235C22×C5—22no—
236C22×C5—32no—
237C22×C5—34no—
238C22×C5—32no—
239C22×C5—68no—
240C22×C5—62no—
241C22×C5C22×C4×D312yes—
242C22×C5C24×D311yescharacteristic
243C4×C5—312no—
244C4×C5C22×C4×D3112yes—
245Dic5—28no—
246Dic5—68no—
247C24—31no—
248C2×Q8—332no—
249C2×Q8—332no—
250C2×Q8—324no—
251C2×Q8—312no—
252C2×Q8D3×Dic518yescomplemented
253C2×Q8C2×D3×D514yes—
254C22×C4—33no—
255C22×C4—324no—
256C22×C4—36no—
257C22×C4—36no—
258C22×C4—158no—
259C22×C4C2×D3×D513yes—
260C4⋊C4—512no—
261C4⋊C4—1524no—
262C4⋊C4—1512no—
263C22⋊C4—54no—
264C22⋊C4—158no—
265C22⋊C4—154no—
266C42—512no—
267C42—1524no—
268C42—1512no—
269C3×C5C2×#51911yescharacteristic, complemented, Hall
270C22×C3—22no—
271C22×C3C23×Dic512yes—
272C22×C3C24×D511yescharacteristic
273C2×D3—22no—
274C2×D3—28no—
275C2×D3#414714yes—
276C2×D3C23×Dic512yes—
277C2×D3C23×Dic512yes—
278C3×C4—108no—
279C3×C4C23×Dic5112yes—
280Dic3—108no—
281Dic3C23×Dic5112yes—
282C2×C5—22no—
283C2×C5—34no—
284C2×C5—62no—
285C2×C5C23×C4×D311yescharacteristic
286C2×C5D3×2−1+412yes—
287C23—31no—
288C23—34no—
289C23—31no—
290C23—64no—
291C23C22×D3×D511yescharacteristic
292Q8—348no—
293Q8C2×D3×Dic5116yes—
294C2×C4—312no—
295C2×C4—36no—
296C2×C4—324no—
297C2×C4—324no—
298C2×C4—58no—
299C2×C4—158no—
300C2×C4—3016no—
301C2×C4C2×D3×Dic5112yes—
302C2×C4C22×D3×D516yes—
303C2×C3—22no—
304C2×C3C2×#414712yes—
305C2×C3C24×Dic511yescharacteristic
306D3—22no—
307D3#6614614yesdirect product factor
308C5D3×#51911yescharacteristic, complemented, Sylow
309C22—22no—
310C22—32no—
311C22—34no—
312C22—32no—
313C22—68no—
314C22—62no—
315C22C22×D3×Dic512yes—
316C22C23×D3×D511yescharacteristic
317C4—312no—
318C4—108no—
319C4—308no—
320C4C22×D3×Dic5112yes—
321C3C2×#6614611yescharacteristic, complemented, Sylow
322C2—22no—
323C2—34no—
324C2—62no—
325C2D3×#414712yes—
326C2C23×D3×Dic511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutatorC2×C3×C5C24×C4
FittingC22×C3×C5×Q8C22
socle, cosocleC22×C3×C5C25
prime radicalC23×C5×D3C23
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#519
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. #11756571C2semidirect
3. C3×#66146C2semidirect
4. D3×Q8×Dic5C2semidirect
5. #11755144C2semidirect
7. #11754211C2semidirect
10. C2×C5×D3×Q8C4semidirect
15. Q8×Dic15C22semidirect
17. C3×Q8×Dic5C22semidirect
24. #91344C22semidirect
26. Dic5×Dic6C22semidirect
32. #66146D3direct (N × H)
36. C2×C3×C5×Q8C2×C4semidirect
41. C5×D3×Q8C2×C4semidirect
45. C2×C5×Dic6C2×C4semidirect
74. Q8×Dic5C2×D3semidirect
100. C2×D3×Q8Dic5semidirect
122. C2×C5×Q8C4×D3semidirect
159. C2×C3×Q8C2×Dic5semidirect
164. D3×Q8C2×Dic5semidirect
169. C2×Dic6C2×Dic5semidirect
218. C5×D3#519semidirect
252. C2×Q8D3×Dic5semidirect
269. C3×C5C2×#519semidirect
307. D3#66146direct (N × H)
308. C5D3×#519semidirect
321. C3C2×#66146semidirect

Maximal subgroups

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

subgroupindex
C22×C5×D3×Q82
#117565712
C3×#661462
D3×Q8×Dic52
#117551442
D3×#40722
#117542112
C2×#661463
D3×#5195