Finite Group Databasebeta

← D3×#63637 #13159425

Subgroups — D3×#63637 #13159425

Order 1728.

1140 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#634C211yesmaximal, characteristic
2C32×D3×C4⋊C4C211yesmaximal, characteristic
3C2×D3×C3⋊(C3⋊C8)C211yesmaximal, characteristic
4#11722180C211yesmaximal, characteristic, complemented
5C3×#63637C211yesmaximal, characteristic, complemented
6#11722041C211yesmaximal, characteristic, complemented
7#11722039C211yesmaximal, characteristic, complemented
8C2×#63637—31nomaximal
9D3×#810—34nomaximal
10C2×#6308C2211yescharacteristic
11C2×C3×#634C2211yescharacteristic
12C2×C32×C4×D3—21no—
13C2×C32×C4×D3C2211yescharacteristic
14C2×#6293—21no—
15C2×D3×C3⋊Dic3—21no—
16D3×#634—22no—
17D3×#634C414yescomplemented
18C33×C4⋊C4C2211yescharacteristic
19C2×C3⋊(C3⋊(C3⋊C8))C2211yescharacteristic
20C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
21C32×C4⋊Dic3C2211yescharacteristic
22C32×Dic3⋊C4—21no—
23D3×C3⋊(C3⋊C8)—22no—
24C22×#634—31no—
25C2×D3×Dic6—34no—
26C2×C32×C4⋊C4—31no—
27C22×C3⋊(C3⋊C8)—31no—
28C3×D3×C4⋊C4D314yes—
29C2×D3×C3⋊C8—34no—
30#63637—31no—
31#63637—31no—
32#63637—31no—
33#63637—34no—
34#63637—64no—
35#63637D311yescharacteristic, direct product factor
36C3×#810—34no—
37#63567—34no—
38#63565—34no—
39C22×C32×D3D411yescharacteristic
40C2×C33×C4—21no—
41C2×C33×C4C2311yescharacteristic
42C2×C3⋊(C3⋊Dic3)—21no—
43#6308—21no—
44#6308C2×C412yescomplemented
45C2×C3×C3⋊Dic3—21no—
46C3×#634—21no—
47C3×#634C2×C412yescomplemented
48C2×C32×Dic3—21no—
49C2×C32×Dic3D411yescharacteristic
50C32×C4×D3—42no—
51C32×C4×D3C2×C412yes—
52C32×C4×D3D412yes—
53#6293—24no—
54D3×C3⋊Dic3—24no—
55C3⋊(C3⋊(C3⋊C8))—21no—
56C3×C3⋊(C3⋊C8)—21no—
57C2×#810—94no—
58D3×#103—91no—
59C22×C32×C4—31no—
60C22×C32×C4—61no—
61C22×C3⋊Dic3—61no—
62C2×#634—31no—
63C2×#634—34no—
64C2×#634—34no—
65C2×#634—62no—
66C2×#634—61no—
67C2×#634—64no—
68C2×#634C2×D311yescharacteristic
69C2×C3×C4×D3—24no—
70C2×C3×C4×D3C2×D314yes—
71C2×C3×Dic6—34no—
72C2×#627—64no—
73C2×D3×Dic3—64no—
74D3×Dic6—316no—
75D3×Dic6—68no—
76C32×C4⋊C4—24no—
77C32×C4⋊C4—31no—
78C32×C4⋊C4—61no—
79C32×C4⋊C4C2×D314yes—
80C32×C4⋊C4C2×D311yescharacteristic
81C2×C3⋊(C3⋊C8)—31no—
82C2×C3⋊(C3⋊C8)—34no—
83C2×C3⋊(C3⋊C8)—62no—
84C2×C3⋊(C3⋊C8)—64no—
85C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
86C3×C4⋊Dic3C2×D314yes—
87C3×Dic3⋊C4—24no—
88C2×C3×C3⋊C8—34no—
89D3×C3⋊C8—68no—
90C22×C33C2×D411yescharacteristic
91C2×C32×D3C22⋊C412yes—
92C2×C32×D3SD1612yes—
93C2×C32×D3Q1612yes—
94C33×C4—41no—
95C33×C4C22×C411yescharacteristic
96C33×C4C2×D411yescharacteristic
97C3⋊(C3⋊Dic3)—22no—
98C3×C3⋊Dic3—22no—
99C32×Dic3—41no—
100C32×Dic3C22⋊C412yes—
101C2×D3×Q8—91no—
102C22×Dic6—94no—
103C2×C3×C4⋊C4—34no—
104C22×C3⋊C8—94no—
105C2×D3×C8—91no—
106D3×C4⋊C4C3⋊D311yescharacteristic
107C3×#103—91no—
108#835—91no—
109#816—91no—
110#810—34no—
111#810—94no—
112#810—94no—
113#810—94no—
114#810—91no—
115#810—184no—
116C23×C32—31no—
117C22×C3×D3#6714yes—
118C2×C32×C4—21no—
119C2×C32×C4—24no—
120C2×C32×C4—24no—
121C2×C32×C4—31no—
122C2×C32×C4—32no—
123C2×C32×C4—32no—
124C2×C32×C4—44no—
125C2×C32×C4—61no—
126C2×C32×C4—122no—
127C2×C32×C4C22×D314yes—
128C2×C32×C4C22×D311yescharacteristic
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—64no—
131C2×C3⋊Dic3—61no—
132C2×C3⋊Dic3—64no—
133C2×C3⋊Dic3—124no—
134#634—21no—
135#634—32no—
136#634—38no—
137#634—68no—
138#634—64no—
139#634—61no—
140#634—64no—
141#634—124no—
142#634C4×D312yescomplemented
143C2×C3×Dic3—24no—
144C2×C3×Dic3—64no—
145C2×C3×Dic3#6714yes—
146C3×C4×D3—48no—
147C3×C4×D3C4×D318yes—
148C3×C4×D3D1218yes—
149C3×Dic6—38no—
150C3×Dic6—64no—
151#627—616no—
152D3×Dic3—616no—
153C3⋊(C3⋊C8)—21no—
154C3⋊(C3⋊C8)—61no—
155C3⋊(C3⋊C8)—64no—
156C3⋊(C3⋊C8)—124no—
157C3×C3⋊C8—64no—
158C2×#103—271noSylow
159C2×C33C2×C22⋊C411yescharacteristic
160C2×C33C2×SD1611yescharacteristic
161C2×C33C2×Q1611yescharacteristic
162C32×D3#10314yescomplemented
163C2×C3×Q8—91no—
164C22×C3×C4—34no—
165C22×C3×C4—64no—
166C22×Dic3—184no—
167D3×Q8—94no—
168D3×Q8—182no—
169C2×C4×D3—21no—
170C2×C4×D3—181no—
171C2×C4×D3C2×C3⋊D311yescharacteristic
172C2×Dic6—34no—
173C2×Dic6—916no—
174C2×Dic6—94no—
175C2×Dic6—91no—
176C2×Dic6—184no—
177C2×Dic6—188no—
178C2×Dic6—184no—
179C2×Dic6—181no—
180C2×C3×C8—91no—
181C3×C4⋊C4—24no—
182C3×C4⋊C4—34no—
183C3×C4⋊C4—64no—
184C3×C4⋊C4D3214yes—
185C3×C4⋊C4C2×C3⋊D311yescharacteristic
186C4⋊Dic3C2×C3⋊D311yescharacteristic
187Dic3⋊C4—21no—
188C2×C3⋊C8—34no—
189C2×C3⋊C8—94no—
190C2×C3⋊C8—91no—
191C2×C3⋊C8—184no—
192C2×C3⋊C8—188no—
193D3×C8—182no—
194C22×C32—24no—
195C22×C32—32no—
196C22×C32—32no—
197C22×C32—32no—
198C22×C32D3×D411yescharacteristic
199C22×C32C2×#6714yes—
200C2×C3×D3(C2×D3)⋊C418yes—
201C2×C3×D3#21418yes—
202C2×C3×D3#21618yes—
203C32×C4—24no—
204C32×C4—24no—
205C32×C4—32no—
206C32×C4—41no—
207C32×C4—44no—
208C32×C4—84no—
209C32×C4—121no—
210C32×C4C2×C4×D314yes—
211C32×C4C2×C4×D311yescharacteristic
212C32×C4C2×D1214yes—
213C32×C4D3×D411yescharacteristic
214C3⋊Dic3—22no—
215C3⋊Dic3—62no—
216C3⋊Dic3—68no—
217C3⋊Dic3—128no—
218C3×Dic3—44no—
219C3×Dic3—68no—
220C3×Dic3(C2×D3)⋊C418yes—
221C22×Q8—271no—
222C22×C8—271no—
223C2×C4⋊C4—31no—
224#103—91no—
225#103—271no—
226#103—271no—
227#103—271no—
228C33C2×#10311yescharacteristic, complemented, Sylow
229C23×C3—34no—
230C22×D3#63811yescharacteristic
231C3×Q8—92no—
232C3×Q8—181no—
233C2×C3×C4—24no—
234C2×C3×C4—21no—
235C2×C3×C4—24no—
236C2×C3×C4—34no—
237C2×C3×C4—38no—
238C2×C3×C4—38no—
239C2×C3×C4—44no—
240C2×C3×C4—64no—
241C2×C3×C4—128no—
242C2×C3×C4—181no—
243C2×C3×C4C2×D3214yes—
244C2×C3×C4C22×C3⋊D311yescharacteristic
245C2×Dic3—21no—
246C2×Dic3—64no—
247C2×Dic3—1816no—
248C2×Dic3—184no—
249C2×Dic3—181no—
250C2×Dic3—364no—
251C2×Dic3#63811yescharacteristic
252C4×D3—42no—
253C4×D3—184no—
254C4×D3C4×C3⋊D312yes—
255C4×D3C4⋊(C3⋊D3)12yes—
256Dic6—38no—
257Dic6—64no—
258Dic6—98no—
259Dic6—92no—
260Dic6—188no—
261Dic6—1816no—
262Dic6—184no—
263Dic6—181no—
264Dic6—184no—
265Dic6—364no—
266C3×C8—181no—
267C3⋊C8—64no—
268C3⋊C8—184no—
269C3⋊C8—181no—
270C3⋊C8—364no—
271C2×C32—24no—
272C2×C32—24no—
273C2×C32—24no—
274C2×C32—34no—
275C2×C32D3×C22⋊C411yescharacteristic
276C2×C32D3×SD1611yescharacteristic
277C2×C32D3×Q1611yescharacteristic
278C2×C32C2×(C2×D3)⋊C414yes—
279C2×C32C2×#21414yes—
280C2×C32C2×#21614yes—
281C3×D3#810116yescomplemented
282C2×Q8—91no—
283C2×Q8—274no—
284C2×Q8—271no—
285C2×Q8—541no—
286C2×Q8—542no—
287C22×C4—31no—
288C22×C4—61no—
289C22×C4—541no—
290C2×C8—91no—
291C2×C8—271no—
292C2×C8—542no—
293C4⋊C4—31no—
294C4⋊C4—61no—
295C4⋊C4D3×C3⋊D311yescharacteristic
296C22×C3—24no—
297C22×C3—38no—
298C22×C3—38no—
299C22×C3—38no—
300C22×C3D3×#6714yes—
301C22×C3C2×#63811yescharacteristic
302C2×D3#375212yes—
303C2×D3#375412yes—
304C2×D3#375612yes—
305C3×C4—24no—
306C3×C4—24no—
307C3×C4—38no—
308C3×C4—41no—
309C3×C4—44no—
310C3×C4—84no—
311C3×C4—124no—
312C3×C4—182no—
313C3×C4C4×D3214yes—
314C3×C4D3×D1214yes—
315C3×C4C2×C4×C3⋊D311yescharacteristic
316C3×C4C2×C4⋊(C3⋊D3)11yescharacteristic
317Dic3—41no—
318Dic3—68no—
319Dic3—182no—
320Dic3—188no—
321Dic3—368no—
322Dic3#375212yes—
323C32—24no—
324C32D3×#10311yescharacteristic, complemented
325C32C2×#81014yescomplemented
326C23—31no—
327Q8—92no—
328Q8—181no—
329Q8—272no—
330Q8—544no—
331Q8—541no—
332C2×C4—21no—
333C2×C4—31no—
334C2×C4—32no—
335C2×C4—32no—
336C2×C4—61no—
337C2×C4—122no—
338C2×C4—181no—
339C2×C4—544no—
340C2×C4—541no—
341C2×C4C2×D3×C3⋊D311yescharacteristic
342C8—181no—
343C8—541no—
344C2×C3—24no—
345C2×C3—24no—
346C2×C3—24no—
347C2×C3—316no—
348C2×C3D3×(C2×D3)⋊C414yes—
349C2×C3D3×#21414yes—
350C2×C3D3×#21614yes—
351C2×C3C2×#375211yescharacteristic
352C2×C3C2×#375411yescharacteristic
353C2×C3C2×#375611yescharacteristic
354D3#6363714yesdirect product factor
355C22—32no—
356C22—32no—
357C22—32no—
358C22D3×#63811yescharacteristic
359C4—32no—
360C4—41no—
361C4—121no—
362C4—182no—
363C4—542no—
364C4C4×D3×C3⋊D311yescharacteristic
365C4D3×C4⋊(C3⋊D3)11yescharacteristic
366C3—24no—
367C3D3×#81014yescomplemented
368C3C2×#6363711yescharacteristic, complemented
369C2—34no—
370C2D3×#375211yescharacteristic
371C2D3×#375411yescharacteristic
372C2D3×#375611yescharacteristic
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×#103
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. #11722180C2semidirect
5. C3×#63637C2semidirect
6. #11722041C2semidirect
7. #11722039C2semidirect
17. D3×#634C4semidirect
35. #63637D3direct (N × H)
44. #6308C2×C4semidirect
47. C3×#634C2×C4semidirect
142. #634C4×D3semidirect
162. C32×D3#103semidirect
228. C33C2×#103semidirect
281. C3×D3#810semidirect
324. C32D3×#103semidirect
325. C32C2×#810semidirect
354. D3#63637direct (N × H)
367. C3D3×#810semidirect
368. C3C2×#63637semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6342
C32×D3×C4⋊C42
C2×D3×C3⋊(C3⋊C8)2
#117221802
C3×#636372
#117220412
#117220392
C2×#636373
D3×#8103