Finite Group Databasebeta

← D3×#63635 #13159321

Subgroups — D3×#63635 #13159321

Order 1728.

924 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
1C32×D3×C4⋊C4C211yesmaximal, characteristic
2D3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
3C2×D3×C3⋊(C3⋊C8)C211yesmaximal, characteristic
4#11722178C211yesmaximal, characteristic, complemented
5C3×#63635C211yesmaximal, characteristic, complemented
6#11722054C211yesmaximal, characteristic, complemented
7#11722053C211yesmaximal, characteristic, complemented
8C2×#63635—31nomaximal
9D3×#808—34nomaximal
10C2×C32×C4×D3—21no—
11C2×C32×C4×D3C2211yescharacteristic
12C2×D3×C3⋊Dic3—21no—
13C33×C4⋊C4C2211yescharacteristic
14C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
15C2×C3⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
18C32×C4⋊Dic3C2211yescharacteristic
19C32×Dic3⋊C4—21no—
20Dic3⋊(C3⋊Dic3)—21no—
21D3×C3⋊(C3⋊C8)C414yescomplemented
22C2×C32×C4⋊C4—31no—
23C2×C4⋊(C3⋊Dic3)—31no—
24C22×C3⋊(C3⋊C8)—31no—
25C3×D3×C4⋊C4D314yes—
26D3×C4⋊Dic3—34no—
27C2×D3×C3⋊C8—34no—
28#63635—31no—
29#63635—31no—
30#63635—31no—
31#63635—34no—
32#63635—64no—
33#63635D311yescharacteristic, direct product factor
34C3×#808—34no—
35#63574—34no—
36#63573—34no—
37C22×C32×D3D411yescharacteristic
38C2×C33×C4—21no—
39C2×C33×C4C2311yescharacteristic
40C2×C3⋊(C3⋊Dic3)—21no—
41C2×C3×C3⋊Dic3—21no—
42C2×C32×Dic3—21no—
43C2×C32×Dic3D411yescharacteristic
44C32×C4×D3—42no—
45C32×C4×D3C2×C412yes—
46C32×C4×D3Q812yes—
47D3×C3⋊Dic3—42no—
48C3⋊(C3⋊(C3⋊C8))C2×C412yescomplemented
49C3×C3⋊(C3⋊C8)C2×C412yescomplemented
50C2×#808—94no—
51D3×#106—91no—
52C22×C32×C4—31no—
53C22×C32×C4—61no—
54C22×C3⋊Dic3—61no—
55C2×C3×C4×D3—24no—
56C2×C3×C4×D3C2×D314yes—
57C2×D3×Dic3—64no—
58C32×C4⋊C4—24no—
59C32×C4⋊C4—31no—
60C32×C4⋊C4—61no—
61C32×C4⋊C4C2×D314yes—
62C32×C4⋊C4C2×D311yescharacteristic
63C4⋊(C3⋊Dic3)—31no—
64C4⋊(C3⋊Dic3)—34no—
65C4⋊(C3⋊Dic3)—61no—
66C4⋊(C3⋊Dic3)—64no—
67C4⋊(C3⋊Dic3)C2×D311yescharacteristic
68C2×C3⋊(C3⋊C8)—31no—
69C2×C3⋊(C3⋊C8)—34no—
70C2×C3⋊(C3⋊C8)—34no—
71C2×C3⋊(C3⋊C8)—64no—
72C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
73C3×C4⋊Dic3—34no—
74C3×C4⋊Dic3C2×D314yes—
75C3×Dic3⋊C4—24no—
76C2×C3×C3⋊C8—34no—
77Dic3⋊Dic3—64no—
78D3×C3⋊C8—316no—
79C22×C33C2×D411yescharacteristic
80C2×C32×D3C4⋊C412yes—
81C2×C32×D3SD1612yes—
82C2×C32×D3SD1612yes—
83C33×C4—41no—
84C33×C4C22×C411yescharacteristic
85C33×C4C2×Q811yescharacteristic
86C3⋊(C3⋊Dic3)—41no—
87C3×C3⋊Dic3—41no—
88C32×Dic3—41no—
89C32×Dic3C4⋊C412yes—
90C2×C3×C4⋊C4—34no—
91C2×C4⋊Dic3—94no—
92C22×C3⋊C8—94no—
93C2×D3×C8—91no—
94D3×C4⋊C4—91no—
95D3×C4⋊C4C3⋊D311yescharacteristic
96C3×#106—91no—
97#817—91no—
98#808—34no—
99#808—94no—
100#808—94no—
101#808—94no—
102#808—91no—
103#808—91no—
104#808—184no—
105C23×C32—31no—
106C22×C3×D3#6714yes—
107C2×C32×C4—21no—
108C2×C32×C4—24no—
109C2×C32×C4—24no—
110C2×C32×C4—31no—
111C2×C32×C4—32no—
112C2×C32×C4—32no—
113C2×C32×C4—44no—
114C2×C32×C4—61no—
115C2×C32×C4—122no—
116C2×C32×C4C22×D314yes—
117C2×C32×C4C22×D311yescharacteristic
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—61no—
120C2×C3⋊Dic3—64no—
121C2×C3⋊Dic3—124no—
122C2×C3⋊Dic3—122no—
123C2×C3×Dic3—24no—
124C2×C3×Dic3—64no—
125C2×C3×Dic3#6714yes—
126C3×C4×D3—48no—
127C3×C4×D3Dic618yes—
128C3×C4×D3C4×D318yes—
129D3×Dic3—128no—
130C3⋊(C3⋊C8)—32no—
131C3⋊(C3⋊C8)—38no—
132C3⋊(C3⋊C8)—68no—
133C3⋊(C3⋊C8)C4×D312yescomplemented
134C3×C3⋊C8—38no—
135C2×#106—271noSylow
136C2×C33C2×C4⋊C411yescharacteristic
137C2×C33C2×SD1611yescharacteristic
138C2×C33C2×SD1611yescharacteristic
139C32×D3#10614yescomplemented
140C22×C3×C4—34no—
141C22×C3×C4—64no—
142C22×Dic3—184no—
143C2×C4×D3—21no—
144C2×C4×D3—181no—
145C2×C4×D3C2×C3⋊D311yescharacteristic
146C2×C3×C8—91no—
147C3×C4⋊C4—24no—
148C3×C4⋊C4—34no—
149C3×C4⋊C4—64no—
150C3×C4⋊C4—91no—
151C3×C4⋊C4D3214yes—
152C3×C4⋊C4C2×C3⋊D311yescharacteristic
153C4⋊Dic3—34no—
154C4⋊Dic3—94no—
155C4⋊Dic3—91no—
156C4⋊Dic3—184no—
157C4⋊Dic3—184no—
158C4⋊Dic3C2×C3⋊D311yescharacteristic
159Dic3⋊C4—21no—
160Dic3⋊C4—181no—
161C2×C3⋊C8—34no—
162C2×C3⋊C8—916no—
163C2×C3⋊C8—94no—
164C2×C3⋊C8—91no—
165C2×C3⋊C8—184no—
166D3×C8—94no—
167C22×C32—24no—
168C22×C32—32no—
169C22×C32—32no—
170C22×C32—32no—
171C22×C32D3×D411yescharacteristic
172C22×C32C2×#6714yes—
173C2×C3×D3Dic3⋊C418yes—
174C2×C3×D3#21418yes—
175C2×C3×D3#21518yes—
176C32×C4—24no—
177C32×C4—24no—
178C32×C4—32no—
179C32×C4—41no—
180C32×C4—44no—
181C32×C4—84no—
182C32×C4—121no—
183C32×C4C2×Dic614yes—
184C32×C4C2×C4×D314yes—
185C32×C4C2×C4×D311yescharacteristic
186C32×C4D3×Q811yescharacteristic
187C3⋊Dic3—41no—
188C3⋊Dic3—121no—
189C3⋊Dic3—124no—
190C3⋊Dic3—244no—
191C3×Dic3—44no—
192C3×Dic3—124no—
193C3×Dic3Dic3⋊C418yes—
194C22×C8—271no—
195C2×C4⋊C4—31no—
196C2×C4⋊C4—271no—
197#106—91no—
198#106—271no—
199#106—271no—
200#106—271no—
201C33C2×#10611yescharacteristic, complemented, Sylow
202C23×C3—34no—
203C22×D3#63811yescharacteristic
204C2×C3×C4—24no—
205C2×C3×C4—21no—
206C2×C3×C4—24no—
207C2×C3×C4—34no—
208C2×C3×C4—38no—
209C2×C3×C4—38no—
210C2×C3×C4—44no—
211C2×C3×C4—64no—
212C2×C3×C4—128no—
213C2×C3×C4—181no—
214C2×C3×C4C2×D3214yes—
215C2×C3×C4C22×C3⋊D311yescharacteristic
216C2×Dic3—21no—
217C2×Dic3—64no—
218C2×Dic3—184no—
219C2×Dic3—181no—
220C2×Dic3—364no—
221C2×Dic3—368no—
222C2×Dic3#63811yescharacteristic
223C4×D3—42no—
224C4×D3—362no—
225C4×D3#63412yes—
226C4×D3C4×C3⋊D312yes—
227C3×C8—92no—
228C3⋊C8—38no—
229C3⋊C8—98no—
230C3⋊C8—92no—
231C3⋊C8—188no—
232C2×C32—24no—
233C2×C32—24no—
234C2×C32—24no—
235C2×C32—34no—
236C2×C32D3×C4⋊C411yescharacteristic
237C2×C32D3×SD1611yescharacteristic
238C2×C32D3×SD1611yescharacteristic
239C2×C32C2×Dic3⋊C414yes—
240C2×C32C2×#21414yes—
241C2×C32C2×#21514yes—
242C3×D3#808116yescomplemented
243C22×C4—31no—
244C22×C4—61no—
245C22×C4—541no—
246C2×C8—91no—
247C2×C8—274no—
248C2×C8—271no—
249C4⋊C4—31no—
250C4⋊C4—61no—
251C4⋊C4—91no—
252C4⋊C4—271no—
253C4⋊C4—541no—
254C4⋊C4D3×C3⋊D311yescharacteristic
255C22×C3—24no—
256C22×C3—38no—
257C22×C3—38no—
258C22×C3—38no—
259C22×C3D3×#6714yes—
260C22×C3C2×#63811yescharacteristic
261C2×D3#375012yes—
262C2×D3#375412yes—
263C2×D3#375512yes—
264C3×C4—24no—
265C3×C4—24no—
266C3×C4—38no—
267C3×C4—41no—
268C3×C4—44no—
269C3×C4—84no—
270C3×C4—124no—
271C3×C4—361no—
272C3×C4D3×Dic614yes—
273C3×C4C4×D3214yes—
274C3×C4C2×#63411yescharacteristic
275C3×C4C2×C4×C3⋊D311yescharacteristic
276Dic3—41no—
277Dic3—124no—
278Dic3—361no—
279Dic3—364no—
280Dic3—724no—
281Dic3#375012yes—
282C32—24no—
283C32D3×#10611yescharacteristic, complemented
284C32C2×#80814yescomplemented
285C23—31no—
286C2×C4—21no—
287C2×C4—31no—
288C2×C4—32no—
289C2×C4—32no—
290C2×C4—61no—
291C2×C4—122no—
292C2×C4—181no—
293C2×C4—541no—
294C2×C4—1082no—
295C2×C4C2×D3×C3⋊D311yescharacteristic
296C8—92no—
297C8—272no—
298C2×C3—24no—
299C2×C3—24no—
300C2×C3—24no—
301C2×C3—316no—
302C2×C3D3×Dic3⋊C414yes—
303C2×C3D3×#21414yes—
304C2×C3D3×#21514yes—
305C2×C3C2×#375011yescharacteristic
306C2×C3C2×#375411yescharacteristic
307C2×C3C2×#375511yescharacteristic
308D3#6363514yesdirect product factor
309C22—32no—
310C22—32no—
311C22—32no—
312C22D3×#63811yescharacteristic
313C4—32no—
314C4—41no—
315C4—121no—
316C4—361no—
317C4—1081no—
318C4D3×#63411yescharacteristic
319C4C4×D3×C3⋊D311yescharacteristic
320C3—24no—
321C3D3×#80814yescomplemented
322C3C2×#6363511yescharacteristic, complemented
323C2—34no—
324C2D3×#375011yescharacteristic
325C2D3×#375411yescharacteristic
326C2D3×#375511yescharacteristic
subgroupG/H
centerC22D3×#638
commutatorC33×C4C22×C4
FrattiniC2×C4C2×D3×C3⋊D3
FittingC33×C4⋊C4C22
socleC22×C33C2×D4
prime radicalC22×C32×D3D4
cosocleC2×C33×C4C23
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33C2×#106
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11722178C2semidirect
5. C3×#63635C2semidirect
6. #11722054C2semidirect
7. #11722053C2semidirect
21. D3×C3⋊(C3⋊C8)C4semidirect
33. #63635D3direct (N × H)
48. C3⋊(C3⋊(C3⋊C8))C2×C4semidirect
49. C3×C3⋊(C3⋊C8)C2×C4semidirect
133. C3⋊(C3⋊C8)C4×D3semidirect
139. C32×D3#106semidirect
201. C33C2×#106semidirect
242. C3×D3#808semidirect
283. C32D3×#106semidirect
284. C32C2×#808semidirect
308. D3#63635direct (N × H)
321. C3D3×#808semidirect
322. C3C2×#63635semidirect

Maximal subgroups

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

subgroupindex
C32×D3×C4⋊C42
D3×C4⋊(C3⋊Dic3)2
C2×D3×C3⋊(C3⋊C8)2
#117221782
C3×#636352
#117220542
#117220532
C2×#636353
D3×#8083