Finite Group Databasebeta

← D3×#6714 #13087485

Subgroups — D3×#6714 #13087485

Order 1440.

562 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D15C211yesmaximal, characteristic
2C2×C3×C4×C5×D3C211yesmaximal, characteristic, complemented
3C2×D3×Dic15C211yesmaximal, characteristic, complemented
4#10623908C211yesmaximal, characteristic, complemented
5C3×#6714C211yesmaximal, characteristic, complemented
6#10623813C211yesmaximal, characteristic, complemented
7#10623811C211yesmaximal, characteristic, complemented
8C2×#6714—31nomaximal
9D3×#685—31nomaximal
10C22×C3⋊D15C2211yescharacteristic
11C22×C3×D15C2211yescharacteristic
12C22×C3×C5×D3C2211yescharacteristic
13C2×D3×D15—22no—
14C2×D3×D15—22no—
15C2×D3×D15C414yescomplemented
16C2×C32×C4×C5C2211yescharacteristic, complemented
17C2×C3⋊Dic15C2211yescharacteristic, complemented
18C2×C3×Dic15C2211yescharacteristic, complemented
19C2×C3×C5×Dic3C2211yescharacteristic, complemented
20C3×C4×C5×D3—22no—
21D3×Dic15—22no—
22D3×(C2×D3)⋊C4—51nomaximal, Hall
23C23×D15—31no—
24C22×D3×D5—31no—
25C22×C3×C4×C5—31no—
26C22×Dic15—31no—
27C2×C4×C5×D3D311yescharacteristic, complemented
28C2×D3×Dic5—31no—
29#6714—31no—
30#6714—31no—
31#6714—31no—
32#6714—31no—
33#6714—61no—
34#6714D311yescharacteristic, direct product factor
35C3×#685—31no—
36#6667—31no—
37#6665—31no—
38C22×C32×C5C2311yescharacteristic
39C2×C3⋊D15—21no—
40C2×C3⋊D15—21no—
41C2×C3⋊D15C2×C412yescomplemented
42C2×C3×D15—21no—
43C2×C3×D15—21no—
44C2×C3×D15C2×C412yescomplemented
45C2×C3×C5×D3C2×C412yes—
46C2×C3×C5×D3D412yes—
47C2×C3×C5×D3D412yes—
48D3×D15—28no—
49C32×C4×C5—21no—
50C3⋊Dic15—21no—
51C3×Dic15—21no—
52C3×C5×Dic3—21no—
53C2×#685—91noHall
54C22×D32—51no—
55C2×C3×C4×D3D511yescharacteristic, complemented
56C2×D3×Dic3—51no—
57#3752—51no—
58C3×(C2×D3)⋊C4—51no—
59#3722—51no—
60(C2×D3)⋊Dic3—51no—
61C23×C3×C5—31no—
62C22×D15—31no—
63C22×D15—31no—
64C22×D15—34no—
65C22×D15—62no—
66C22×D15—62no—
67C22×D15—61no—
68C22×D15C2×D311yescharacteristic
69C22×C5×D3C2×D311yescharacteristic
70C22×C3×D5—31no—
71C2×D3×D5—34no—
72C2×D3×D5—62no—
73C2×D3×D5—62no—
74C2×C3×C4×C5—21no—
75C2×C3×C4×C5—31no—
76C2×C3×C4×C5—62no—
77C2×C3×C4×C5C2×D311yescharacteristic, complemented
78C2×C3×C4×C5C2×D311yescharacteristic, complemented
79C2×Dic15—31no—
80C2×Dic15—31no—
81C2×Dic15—62no—
82C2×Dic15—61no—
83C2×Dic15C2×D311yescharacteristic, complemented
84C2×C5×Dic3C2×D311yescharacteristic, complemented
85C4×C5×D3—22no—
86C2×C3×Dic5—31no—
87D3×Dic5—62no—
88C2×(C2×D3)⋊C4—151no—
89D3×C22⋊C4—151no—
90C2×C32×C5C22×C411yescharacteristic
91C2×C32×C5C2×D411yescharacteristic
92C2×C32×C5C2×D411yescharacteristic
93C3⋊D15—22no—
94C3×D15—22no—
95C3×C5×D3C22⋊C414yescomplemented
96C23×D5—91no—
97C22×C4×C5—31no—
98C22×Dic5—91no—
99#685—31no—
100#685—91no—
101#685—91no—
102#685—91no—
103C22×C3⋊D3—51no—
104C22×C3×D3—51no—
105C22×C3×D3C2×D511yescharacteristic
106C2×D32—54no—
107C2×D32—102no—
108C2×D32—102no—
109C2×C32×C4C2×D511yescharacteristic, complemented
110C2×C3⋊Dic3—51no—
111C2×C3×Dic3—51no—
112C2×C3×Dic3C2×D511yescharacteristic, complemented
113C3×C4×D3—22no—
114D3×Dic3—102no—
115C22×C3×C5—21no—
116C22×C3×C5—32no—
117C22×C3×C5—32no—
118C22×C3×C5—32no—
119C22×C3×C5C22×D311yescharacteristic
120C22×C3×C5C22×D311yescharacteristic
121C2×D15—21no—
122C2×D15—21no—
123C2×D15—32no—
124C2×D15—32no—
125C2×D15—62no—
126C2×D15—68no—
127C2×D15—61no—
128C2×D15—61no—
129C2×D15—61no—
130C2×D15—61no—
131C2×D15—121no—
132C2×D15—121no—
133C2×D15C4×D312yescomplemented
134C2×C5×D3C4×D312yes—
135C2×C5×D3D1212yes—
136C2×C5×D3#6712yes—
137C2×C3×D5—32no—
138C2×C3×D5—61no—
139C2×C3×D5—61no—
140D3×D5—68no—
141C3×C4×C5—21no—
142C3×C4×C5—21no—
143C3×C4×C5—41no—
144C3×C4×C5—61no—
145Dic15—21no—
146Dic15—61no—
147Dic15—61no—
148Dic15—121no—
149C3×Dic5—61no—
150C5×Dic3—21no—
151C23×D3—151no—
152C23×D3—151no—
153C22×C3×C4—31no—
154C22×Dic3—151no—
155C2×C4×D3—151no—
156C2×C4×D3D1511yescharacteristic, complemented
157C3×C22⋊C4—151no—
158#217—151no—
159(C2×D3)⋊C4—51no—
160(C2×D3)⋊C4—151no—
161(C2×D3)⋊C4—151no—
162(C2×D3)⋊C4—151no—
163(C2×D3)⋊C4—151no—
164(C2×D3)⋊C4—151no—
165(C2×D3)⋊C4—301no—
166C32×C5C2×C22⋊C411yescharacteristic, complemented, Hall
167C23×C5—31no—
168C22×D5—31no—
169C22×D5—94no—
170C22×D5—91no—
171C22×D5—182no—
172C22×D5—182no—
173C2×C4×C5—31no—
174C2×C4×C5—62no—
175C2×C4×C5D3211yescharacteristic, complemented
176C2×Dic5—31no—
177C2×Dic5—91no—
178C2×Dic5—182no—
179C22×C32C22×D511yescharacteristic
180C2×C3⋊D3—52no—
181C2×C3⋊D3—101no—
182C2×C3⋊D3—101no—
183C2×C3×D3—52no—
184C2×C3×D3—101no—
185C2×C3×D3—101no—
186C2×C3×D3C4×D512yes—
187C2×C3×D3D2012yes—
188C2×C3×D3C22⋊D512yes—
189D32—108no—
190C32×C4—21no—
191C3⋊Dic3—101no—
192C3×Dic3—21no—
193C3×Dic3—101no—
194C2×C22⋊C4—451noSylow
195C2×C3×C5—21no—
196C2×C3×C5—21no—
197C2×C3×C5—21no—
198C2×C3×C5—34no—
199C2×C3×C5C2×C4×D311yescharacteristic
200C2×C3×C5C2×C4×D311yescharacteristic
201C2×C3×C5C2×D1211yescharacteristic
202C2×C3×C5D3×D411yescharacteristic
203C2×C3×C5D3×D411yescharacteristic
204C2×C3×C5C2×#6711yescharacteristic
205D15—22no—
206D15—62no—
207D15—62no—
208D15—122no—
209C3×D5—62no—
210C5×D3(C2×D3)⋊C414yescomplemented
211C23×C3—31no—
212C23×C3—151no—
213C22×D3—51no—
214C22×D3—154no—
215C22×D3—151no—
216C22×D3—151no—
217C22×D3—154no—
218C22×D3—301no—
219C22×D3—302no—
220C22×D3—302no—
221C22×D3—302no—
222C22×D3—302no—
223C22×D3C2×D1511yescharacteristic
224C2×C3×C4—21no—
225C2×C3×C4—31no—
226C2×C3×C4—62no—
227C2×C3×C4—151no—
228C2×C3×C4D3×D511yescharacteristic, complemented
229C2×C3×C4C2×D1511yescharacteristic, complemented
230C2×Dic3—51no—
231C2×Dic3—151no—
232C2×Dic3—151no—
233C2×Dic3—301no—
234C2×Dic3—302no—
235C2×Dic3C2×D1511yescharacteristic, complemented
236C4×D3—22no—
237C4×D3—302no—
238C22×C5—32no—
239C22×C5—32no—
240C22×C5—32no—
241C22×C5C2×D3211yescharacteristic
242C2×D5—32no—
243C2×D5—61no—
244C2×D5—61no—
245C2×D5—92no—
246C2×D5—188no—
247C2×D5—181no—
248C2×D5—181no—
249C4×C5—21no—
250C4×C5—61no—
251Dic5—61no—
252Dic5—181no—
253C2×C32C2×C4×D511yescharacteristic
254C2×C32C2×D2011yescharacteristic
255C2×C32C2×C22⋊D511yescharacteristic
256C3⋊D3—102no—
257C3×D3—102no—
258C3×D3#68514yescomplemented
259C24—451no—
260C22×C4—31no—
261C22×C4—451no—
262C22⋊C4—151no—
263C22⋊C4—451no—
264C22⋊C4—451no—
265C22⋊C4—451no—
266C3×C5—21no—
267C3×C5D3×C22⋊C411yescharacteristic, complemented
268C3×C5C2×(C2×D3)⋊C411yescharacteristic, complemented
269C22×C3—21no—
270C22×C3—32no—
271C22×C3—32no—
272C22×C3—32no—
273C22×C3—152no—
274C22×C3—301no—
275C22×C3—301no—
276C22×C3C2×D3×D511yescharacteristic
277C22×C3C22×D1511yescharacteristic
278C2×D3—52no—
279C2×D3—101no—
280C2×D3—101no—
281C2×D3—152no—
282C2×D3—152no—
283C2×D3—302no—
284C2×D3—308no—
285C2×D3—301no—
286C2×D3—301no—
287C2×D3—301no—
288C2×D3—301no—
289C2×D3—308no—
290C2×D3—601no—
291C2×D3—601no—
292C2×D3C4×D1512yes—
293C2×D3D6012yes—
294C2×D3#122012yes—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—41no—
298C3×C4—61no—
299C3×C4—301no—
300Dic3—21no—
301Dic3—101no—
302Dic3—301no—
303Dic3—301no—
304Dic3—601no—
305C2×C5—34no—
306C2×C5C4×D3211yescharacteristic
307C2×C5D3×D1211yescharacteristic
308C2×C5D3×#6711yescharacteristic
309D5—62no—
310D5—182no—
311C32C2×#68511yescharacteristic, complemented, Sylow
312C23—31no—
313C23—151no—
314C23—454no—
315C23—451no—
316C23—902no—
317C23—902no—
318C2×C4—31no—
319C2×C4—62no—
320C2×C4—151no—
321C2×C4—451no—
322C2×C4—902no—
323C2×C4D3×D1511yescharacteristic, complemented
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—34no—
328C2×C3—302no—
329C2×C3C4×D3×D511yescharacteristic
330C2×C3D3×D2011yescharacteristic
331C2×C3D3×C22⋊D511yescharacteristic
332C2×C3C2×C4×D1511yescharacteristic
333C2×C3C2×D6011yescharacteristic
334C2×C3C2×#122011yescharacteristic
335D3—102no—
336D3—302no—
337D3—302no—
338D3—602no—
339D3#671414yesdirect product factor
340C5D3×(C2×D3)⋊C411yescharacteristic, complemented, Sylow
341C22—32no—
342C22—32no—
343C22—32no—
344C22—152no—
345C22—301no—
346C22—301no—
347C22—452no—
348C22—908no—
349C22—901no—
350C22—901no—
351C22C2×D3×D1511yescharacteristic
352C4—21no—
353C4—61no—
354C4—301no—
355C4—901no—
356C3—21no—
357C3D3×#68511yescharacteristic, complemented
358C3C2×#671411yescharacteristic, complemented
359C2—34no—
360C2—302no—
361C2—902no—
362C2C4×D3×D1511yescharacteristic
363C2D3×D6011yescharacteristic
364C2D3×#122011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D15
commutatorC2×C32×C5C22×C4
FittingC2×C32×C4×C5C22
socle, cosocleC22×C32×C5C23
prime radicalC22×D3×D15C2
hypercenterC2×C4D3×D15
hypocenterC32×C5C2×C22⋊C4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×C5×D3C2semidirect
3. C2×D3×Dic15C2semidirect
4. #10623908C2semidirect
5. C3×#6714C2semidirect
6. #10623813C2semidirect
7. #10623811C2semidirect
15. C2×D3×D15C4semidirect
16. C2×C32×C4×C5C22semidirect
17. C2×C3⋊Dic15C22semidirect
18. C2×C3×Dic15C22semidirect
19. C2×C3×C5×Dic3C22semidirect
27. C2×C4×C5×D3D3semidirect
34. #6714D3direct (N × H)
41. C2×C3⋊D15C2×C4semidirect
44. C2×C3×D15C2×C4semidirect
55. C2×C3×C4×D3D5semidirect
77. C2×C3×C4×C5C2×D3semidirect
78. C2×C3×C4×C5C2×D3semidirect
83. C2×Dic15C2×D3semidirect
84. C2×C5×Dic3C2×D3semidirect
95. C3×C5×D3C22⋊C4semidirect
109. C2×C32×C4C2×D5semidirect
112. C2×C3×Dic3C2×D5semidirect
133. C2×D15C4×D3semidirect
156. C2×C4×D3D15semidirect
166. C32×C5C2×C22⋊C4semidirect
175. C2×C4×C5D32semidirect
210. C5×D3(C2×D3)⋊C4semidirect
228. C2×C3×C4D3×D5semidirect
229. C2×C3×C4C2×D15semidirect
235. C2×Dic3C2×D15semidirect
258. C3×D3#685semidirect
267. C3×C5D3×C22⋊C4semidirect
268. C3×C5C2×(C2×D3)⋊C4semidirect
311. C32C2×#685semidirect
323. C2×C4D3×D15semidirect
339. D3#6714direct (N × H)
340. C5D3×(C2×D3)⋊C4semidirect
357. C3D3×#685semidirect
358. C3C2×#6714semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D152
C2×C3×C4×C5×D32
C2×D3×Dic152
#106239082
C3×#67142
#106238132
#106238112
C2×#67143
D3×#6853
D3×(C2×D3)⋊C45