Finite Group Databasebeta

← D3×#65381 #14438810

Subgroups — D3×#65381 #14438810

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×D3×C4⋊Q8C211yesmaximal, characteristic
2C2×D3×#689C214yesmaximal
3D3×#4015C211yesmaximal, characteristic
4#11751193C211yesmaximal, characteristic, complemented
5C3×#65381C211yesmaximal, characteristic, complemented
6#11749357C214yesmaximal, complemented
7#11747103C211yesmaximal, characteristic, complemented
8#11747096C211yesmaximal, characteristic, complemented
9C4×D3×#168C211yesmaximal, characteristic
10C2×#65381—31nomaximal, Hall
11C2×C5×D3×Q8C2212yes—
12C2×D3×Dic10C2212yes—
13C3×C5×C4⋊Q8C2211yescharacteristic
14C2×#6718C2214yes—
15#91758C2211yescharacteristic
16C5×#944C2212yes—
17C5×D3×C4⋊C4—22no—
18C5×#888—22no—
19C42×C5×D3C2211yescharacteristic
20C5×#869C2211yescharacteristic
21C2×C3×#689C2214yes—
22C3×#4015C2211yescharacteristic
23D3×#689—216no—
24#91469—22no—
25D3×C4⋊Dic5—22no—
26#91389C2212yes—
27C2×#6663C2214yes—
28C2×#6661C2214yes—
29C2×D3×#168C2212yes—
30C4×C3⋊#168C2211yescharacteristic
31C3×C4×#168C2211yescharacteristic
32Dic3×#168C2212yes—
33D3×#494—51nomaximal, Hall
34C2×C5×C4⋊Q8—31no—
35C22×#689—34no—
36C2×#4015—31no—
37#65381—34no—
38#65381—31no—
39#65381—31no—
40#65381—31no—
41#65381D311yescharacteristic, direct product factor
42C2×C4×#168—31no—
43C2×C3×C5×Q8C2312yes—
44C2×Dic30C2312yes—
45C5×D3×Q8—28no—
46C2×C4×C5×D3—22no—
47C2×C4×C5×D3D412yes—
48C2×C4×C5×D3C2311yescharacteristic
49C2×C5×Dic6—22no—
50C2×C5×Dic6C2312yes—
51C2×C3×Dic10C2312yes—
52C2×#1204—22no—
53C2×D3×Dic5—22no—
54D3×Dic10—28no—
55C3×C5×C4⋊C4—22no—
56C3×C42×C5C2311yescharacteristic
57#6718—28no—
58C4⋊Dic15—22no—
59C2×C3⋊#168C2312yes—
60C5×C4⋊Dic3—22no—
61C5×Dic3⋊C4—24no—
62C4×C5×Dic3D412yes—
63C4×C5×Dic3C2311yescharacteristic
64C3×#689—28no—
65C3×C4⋊Dic5—22no—
66C2×C3×#168C2312yes—
67Dic3⋊Dic5—24no—
68#6663—28no—
69#6661—28no—
70D3×#168D418yes—
71C2×D3×Q16—54no—
72D3×C4⋊Q8—51no—
73D3×C4⋊Q8D511yescharacteristic
74C3×#494—51no—
75#5183—54no—
76#5092—51no—
77#5092—51no—
78#4699—51no—
79C4×D3×C8—51no—
80C22×C5×Q8—32no—
81C22×Dic10—32no—
82C5×C4⋊Q8—32no—
83C5×C4⋊Q8—31no—
84C5×C4⋊Q8—62no—
85C5×C4⋊Q8C2×D311yescharacteristic
86C2×C5×C4⋊C4—62no—
87C2×C42×C5—31no—
88C2×#689—34no—
89C2×#689—34no—
90C2×#689—34no—
91C2×#689—616no—
92C2×#689C2×D314yes—
93C2×C4⋊Dic5—62no—
94C22×#168—32no—
95#4015—32no—
96#4015—31no—
97#4015—62no—
98#4015C2×D311yescharacteristic
99C4×#168—31no—
100C4×#168—32no—
101C4×#168C2×D311yescharacteristic
102C2×#494—151noSylow
103C22×C5×D3C2×D411yescharacteristic
104C3×C5×Q8—24no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5C2×D412yes—
107C2×C3×C4×C5C2411yescharacteristic
108C2×Dic15—22no—
109Dic30—24no—
110C2×C5×Dic3—22no—
111C2×C5×Dic3C2×D411yescharacteristic
112C2×C5×Dic3C2×D412yes—
113C4×C5×D3—44no—
114C4×C5×D3Q1618yescomplemented
115C4×C5×D3C2×D414yes—
116C5×Dic6—24no—
117C5×Dic6—44no—
118C2×C3×Dic5—22no—
119C3×Dic10—24no—
120#1204—44no—
121D3×Dic5—44no—
122C3⋊#168C2×D414yes—
123C3×#168C2×D414yes—
124C2×D3×Q8—52no—
125C2×D3×Q8C2×D512yes—
126C2×C3×Q16—54no—
127C3×C4⋊Q8—51no—
128C3×C4⋊Q8C2×D511yescharacteristic
129#944—52no—
130#944C2×D512yes—
131C2×#216—54no—
132C2×#216—54no—
133D3×Q16—1016no—
134C2×Dic12—54no—
135C2×D3×C8—52no—
136D3×C4⋊C4—22no—
137D3×C4⋊C4—102no—
138#888—22no—
139#888—102no—
140C42×D3C2×D511yescharacteristic
141#869—51no—
142#869C2×D511yescharacteristic
143C3×C4×C8—51no—
144C8×Dic3—52no—
145C4×C3⋊C8—51no—
146C2×C5×Q8—32no—
147C2×C5×Q8—62no—
148C2×C5×Q8—68no—
149C2×C5×Q8C22×D312yes—
150C22×C4×C5—32no—
151C22×C4×C5—31no—
152C22×C4×C5—62no—
153C22×Dic5—62no—
154C2×Dic10—32no—
155C2×Dic10—68no—
156C2×Dic10—62no—
157C2×Dic10C22×D312yes—
158C5×C4⋊C4—22no—
159C5×C4⋊C4—64no—
160C5×C4⋊C4—62no—
161C42×C5—32no—
162C42×C5—31no—
163C42×C5C22×D311yescharacteristic
164#689—28no—
165#689—68no—
166#689—68no—
167#689—68no—
168C4⋊Dic5—22no—
169C4⋊Dic5—64no—
170C4⋊Dic5—62no—
171C2×#168—32no—
172C2×#168—38no—
173C2×#168C22×D312yes—
174C22×Q16—154no—
175C2×C4⋊Q8—31no—
176C2×C4⋊Q8—151no—
177#494—51no—
178#494—151no—
179#494—151no—
180#494—154no—
181#494—151no—
182C2×C4×C8—151no—
183C22×C3×C5C22×D411yescharacteristic
184C2×C5×D3#12712yes—
185C2×C5×D3C2×Q1614yes—
186C3×C4×C5—42no—
187C3×C4×C5C2×Q1614yescomplemented
188C3×C4×C5C22×D412yes—
189Dic15—42no—
190C3×Dic5—42no—
191C5×Dic3—42no—
192C5×Dic3#12712yes—
193C5×Dic3C2×Q1614yescomplemented
194C2×C3×Q8—52no—
195C2×C3×Q8C22×D512yes—
196D3×Q8—28no—
197D3×Q8—108no—
198C2×C4×D3—22no—
199C2×C4×D3—102no—
200C2×C4×D3C22⋊D512yes—
201C2×C4×D3C22×D511yescharacteristic
202C2×Dic6—22no—
203C2×Dic6—52no—
204C2×Dic6—102no—
205C2×Dic6C22×D512yes—
206C3×Q16—108no—
207C2×C3×C8—52no—
208C3×C4⋊C4—22no—
209C3×C4⋊C4—102no—
210C3×C42C22×D511yescharacteristic
211#216—108no—
212#216—108no—
213C4⋊Dic3—22no—
214C4⋊Dic3—102no—
215Dic3⋊C4—24no—
216Dic3⋊C4—104no—
217C4×Dic3C22⋊D512yes—
218C4×Dic3C22×D511yescharacteristic
219C2×C3⋊C8—52no—
220Dic12—108no—
221D3×C8—58no—
222C23×C5—31no—
223C5×Q8—24no—
224C5×Q8—64no—
225C5×Q8—124no—
226C2×C4×C5—22no—
227C2×C4×C5—32no—
228C2×C4×C5—31no—
229C2×C4×C5—38no—
230C2×C4×C5—34no—
231C2×C4×C5—62no—
232C2×C4×C5—124no—
233C2×C4×C5D3×D412yes—
234C2×C4×C5C23×D311yescharacteristic
235C2×Dic5—22no—
236C2×Dic5—62no—
237C2×Dic5—124no—
238Dic10—24no—
239Dic10—64no—
240Dic10—124no—
241#168—34no—
242#168D3×D414yes—
243C22×Q8—32no—
244C22×Q8—152no—
245C2×Q16—54no—
246C2×Q16—154no—
247C2×Q16—154no—
248C2×Q16—154no—
249C2×Q16—3016no—
250C22×C8—152no—
251C4⋊Q8—32no—
252C4⋊Q8—31no—
253C4⋊Q8—51no—
254C4⋊Q8—62no—
255C4⋊Q8—152no—
256C4⋊Q8—151no—
257C4⋊Q8—302no—
258C4⋊Q8D3×D511yescharacteristic
259C2×C4⋊C4—62no—
260C2×C4⋊C4—302no—
261C2×C42—31no—
262C4×C8—51no—
263C4×C8—152no—
264C4×C8—151no—
265C2×C3×C5C2×#12711yescharacteristic
266C2×C3×C5C22×Q1612yes—
267C5×D3#49414yescomplemented
268C22×D3C2×C22⋊D511yescharacteristic
269C3×Q8—24no—
270C3×Q8—104no—
271C2×C3×C4—22no—
272C2×C3×C4—102no—
273C2×C3×C4C2×C22⋊D512yes—
274C2×C3×C4C23×D511yescharacteristic
275C2×Dic3—22no—
276C2×Dic3—102no—
277C2×Dic3C2×C22⋊D511yescharacteristic
278C2×Dic3C2×C22⋊D512yes—
279C4×D3—44no—
280C4×D3—204no—
281C4×D3#68918yescomplemented
282C4×D3D4×D514yes—
283Dic6—24no—
284Dic6—44no—
285Dic6—104no—
286Dic6—204no—
287C3×C8—54no—
288C3⋊C8—54no—
289C22×C5—32no—
290C22×C5—34no—
291C22×C5C2×D3×D411yescharacteristic
292C4×C5—32no—
293C4×C5—34no—
294C4×C5—42no—
295C4×C5—122no—
296C4×C5D3×Q1614yescomplemented
297C4×C5C2×D3×D412yes—
298Dic5—42no—
299Dic5—122no—
300C2×Q8—32no—
301C2×Q8—52no—
302C2×Q8—62no—
303C2×Q8—68no—
304C2×Q8—152no—
305C2×Q8—302no—
306C2×Q8—308no—
307C2×Q8C2×D3×D512yes—
308C22×C4—32no—
309C22×C4—31no—
310C22×C4—62no—
311C22×C4—302no—
312Q16—108no—
313Q16—308no—
314Q16—308no—
315Q16—308no—
316C2×C8—52no—
317C2×C8—158no—
318C2×C8—152no—
319C4⋊C4—22no—
320C4⋊C4—64no—
321C4⋊C4—62no—
322C4⋊C4—102no—
323C4⋊C4—304no—
324C4⋊C4—302no—
325C42—32no—
326C42—31no—
327C42C2×D3×D511yescharacteristic
328C3×C5C2×#49411yescharacteristic, complemented, Hall
329C22×C3C22×C22⋊D511yescharacteristic
330C2×D3#408612yes—
331C2×D3C2×#68914yes—
332C3×C4—42no—
333C3×C4—202no—
334C3×C4C2×#68914yescomplemented
335C3×C4C2×D4×D512yes—
336Dic3—42no—
337Dic3—202no—
338Dic3#408612yes—
339Dic3C2×#68914yescomplemented
340C2×C5—34no—
341C2×C5D3×#12711yescharacteristic
342C2×C5C2×D3×Q1612yes—
343C23—31no—
344Q8—24no—
345Q8—64no—
346Q8—104no—
347Q8—124no—
348Q8—304no—
349Q8—604no—
350C2×C4—22no—
351C2×C4—32no—
352C2×C4—31no—
353C2×C4—38no—
354C2×C4—34no—
355C2×C4—62no—
356C2×C4—102no—
357C2×C4—124no—
358C2×C4—302no—
359C2×C4—604no—
360C2×C4D3×C22⋊D512yes—
361C2×C4C22×D3×D511yescharacteristic
362C8—54no—
363C8—154no—
364C2×C3C2×#408611yescharacteristic
365C2×C3C22×#68912yes—
366D3#6538114yesdirect product factor
367C5D3×#49411yescharacteristic, complemented, Sylow
368C22—32no—
369C22—34no—
370C22C2×D3×C22⋊D511yescharacteristic
371C4—32no—
372C4—34no—
373C4—42no—
374C4—122no—
375C4—202no—
376C4—602no—
377C4D3×#68914yescomplemented
378C4D3×D4×D512yes—
379C3C2×#6538111yescharacteristic, complemented, Sylow
380C2—34no—
381C2D3×#408611yescharacteristic
382C2C2×D3×#68912yes—
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×#494
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
4. #11751193C2semidirect
5. C3×#65381C2semidirect
6. #11749357C2semidirect
7. #11747103C2semidirect
8. #11747096C2semidirect
41. #65381D3direct (N × H)
114. C4×C5×D3Q16semidirect
187. C3×C4×C5C2×Q16semidirect
193. C5×Dic3C2×Q16semidirect
267. C5×D3#494semidirect
281. C4×D3#689semidirect
296. C4×C5D3×Q16semidirect
328. C3×C5C2×#494semidirect
334. C3×C4C2×#689semidirect
339. Dic3C2×#689semidirect
366. D3#65381direct (N × H)
367. C5D3×#494semidirect
377. C4D3×#689semidirect
379. C3C2×#65381semidirect

Maximal subgroups

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

subgroupindex
C5×D3×C4⋊Q82
C2×D3×#6892
D3×#40152
#117511932
C3×#653812
#117493572
#117471032
#117470962
C4×D3×#1682
C2×#653813
D3×#4945