Finite Group Databasebeta

← C3×#10591260 #13158214

Subgroups — C3×#10591260 #13158214

Order 1728.

1474 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×C3⋊D3C211yesmaximal, characteristic
2C2×C3×#3722C212yesmaximal
3C2×C3×Dic32C212yesmaximal, complemented
4C32×C3⋊#95C212yesmaximal, complemented
5C3×#4666—32nomaximal
6#10591260C311yesmaximal, characteristic, direct product factor
7C23×C3×C3⋊D3C2211yescharacteristic
8C22×C33×C4C2211yescharacteristic
9C22×C3×C3⋊Dic3C2211yescharacteristic
10C2×C3×C4×C3⋊D3—24no—
11C2×C3×C4×C3⋊D3C414yescomplemented
12C22×C32×Dic3C2214yes—
13C3×#3722C418yescomplemented
14C3×Dic32—24no—
15C22×C4×C3⋊D3C2×C311yescharacteristic
16C22×C3×C4×D3—32no—
17C22×C3×C4×D3—61no—
18C2×C3×(C2×D3)⋊C4—34no—
19C2×C3×C4×Dic3—34no—
20C2×#3722C2×C312yes—
21C2×Dic32C2×C312yescomplemented
22C32×#95—32no—
23C3×C3⋊#95—22no—
24C3×C3⋊#95D312yescomplemented
25C3×C3⋊#95C2×C312yescomplemented
26C23×C33C2311yescharacteristic
27C22×C3×C3⋊D3—22no—
28C22×C3×C3⋊D3—22no—
29C22×C3×C3⋊D3C2×C414yes—
30C22×C3×C3⋊D3C2×C412yes—
31C2×C33×C4—22no—
32C2×C33×C4C2×C412yes—
33C2×C3×C3⋊Dic3C2×C412yes—
34C2×C3×C3⋊Dic3D414yes—
35C3×C4×C3⋊D3—28no—
36C2×C32×Dic3—24no—
37C2×C32×Dic3—24no—
38C2×C32×Dic3C2×C418yescomplemented
39C3×C4×C22⋊C4—91no—
40#4666—32no—
41C23×C3⋊D3C22×C311yescharacteristic
42C23×C3×D3—32no—
43C23×C3×D3—61no—
44C22×C32×C4—21no—
45C22×C32×C4—22no—
46C22×C32×C4—34no—
47C22×C32×C4—41no—
48C22×C32×C4C2×D312yes—
49C22×C32×C4C22×C311yescharacteristic
50C22×C3⋊Dic3C22×C311yescharacteristic
51C2×C4×C3⋊D3—24no—
52C2×C4×C3⋊D3C3×C414yescomplemented
53C22×C3×Dic3—24no—
54C22×C3×Dic3—32no—
55C22×C3×Dic3—61no—
56C22×C3×Dic3C2×D314yes—
57C22×C3×Dic3C22×C314yes—
58C2×C3×C4×D3—38no—
59C2×C3×C4×D3—68no—
60C2×C3×C4×D3—64no—
61C2×C3×C4×D3—68no—
62C3×(C2×D3)⋊C4—316no—
63C3×C4×Dic3—68no—
64#3722C3×C418yescomplemented
65Dic32—24no—
66C22×C33C22×C411yescharacteristic
67C22×C33C22×C412yes—
68C22×C33C2×D412yes—
69C22×C33#4112yes—
70C2×C3×C3⋊D3—22no—
71C2×C3×C3⋊D3—22no—
72C2×C3×C3⋊D3—28no—
73C2×C3×C3⋊D3C4214yescomplemented
74C33×C4—22no—
75C3×C3⋊Dic3C22⋊C414yescomplemented
76C32×Dic3—28no—
77C23×C3×C4—91no—
78C22×C4×D3—32no—
79C22×C4×D3—61no—
80C2×C3×C22⋊C4—92no—
81C2×C3×C42—92no—
82C2×(C2×D3)⋊C4—34no—
83C2×C4×Dic3—34no—
84C3×#95—32no—
85C3×#95—32no—
86C3×#95—62no—
87C3⋊#95C3×D312yescomplemented
88C23×C32—21no—
89C23×C32—22no—
90C23×C32—41no—
91C23×C32C22×D312yes—
92C23×C32C23×C311yescharacteristic
93C22×C3⋊D3—22no—
94C22×C3⋊D3—22no—
95C22×C3⋊D3C2×C3×C414yes—
96C22×C3⋊D3C2×C3×C412yes—
97C22×C3×D3—38no—
98C22×C3×D3—34no—
99C22×C3×D3—64no—
100C22×C3×D3—62no—
101C22×C3×D3—64no—
102C22×C3×D3—64no—
103C22×C3×D3—64no—
104C22×C3×D3—62no—
105C22×C3×D3—62no—
106C2×C32×C4—22no—
107C2×C32×C4—24no—
108C2×C32×C4—24no—
109C2×C32×C4—22no—
110C2×C32×C4—24no—
111C2×C32×C4—38no—
112C2×C32×C4—42no—
113C2×C32×C4—44no—
114C2×C32×C4—44no—
115C2×C32×C4—64no—
116C2×C32×C4—64no—
117C2×C32×C4C4×D314yes—
118C2×C32×C4C2×C3×C412yes—
119C2×C3⋊Dic3C2×C3×C412yes—
120C2×C3⋊Dic3C3×D414yes—
121C4×C3⋊D3—28no—
122C2×C3×Dic3—24no—
123C2×C3×Dic3—24no—
124C2×C3×Dic3—24no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3—28no—
127C2×C3×Dic3—34no—
128C2×C3×Dic3—38no—
129C2×C3×Dic3—44no—
130C2×C3×Dic3—44no—
131C2×C3×Dic3—62no—
132C2×C3×Dic3—64no—
133C2×C3×Dic3C4×D318yescomplemented
134C2×C3×Dic3C2×C3×C418yescomplemented
135C3×C4×D3—616no—
136C3×C4×D3—616no—
137C4×C22⋊C4—91noSylow
138C2×C33C2×C4211yescharacteristic
139C2×C33C2×C22⋊C411yescharacteristic
140C2×C33#11711yescharacteristic
141C2×C33C4×D414yes—
142C3×C3⋊D3—24no—
143C24×C3—91no—
144C23×D3—32no—
145C23×D3—61no—
146C22×C3×C4—21no—
147C22×C3×C4—22no—
148C22×C3×C4—34no—
149C22×C3×C4—34no—
150C22×C3×C4—41no—
151C22×C3×C4—64no—
152C22×C3×C4—91no—
153C22×C3×C4—94no—
154C22×C3×C4—184no—
155C22×C3×C4D3211yescharacteristic
156C22×C3×C4C2×C3×D312yes—
157C22×Dic3—32no—
158C22×Dic3—61no—
159C22×Dic3C2×C3×D314yes—
160C2×C4×D3—38no—
161C2×C4×D3—64no—
162C2×C4×D3—68no—
163C2×C4×D3—68no—
164C3×C22⋊C4—98no—
165C3×C42—184no—
166(C2×D3)⋊C4—316no—
167C4×Dic3—68no—
168C22×C32—22no—
169C22×C32—22no—
170C22×C32—21no—
171C22×C32—22no—
172C22×C32—24no—
173C22×C32—22no—
174C22×C32—24no—
175C22×C32—22no—
176C22×C32—22no—
177C22×C32—41no—
178C22×C32—42no—
179C22×C32—42no—
180C22×C32—42no—
181C22×C32C2×C4×D314yes—
182C22×C32C2×C4×D312yes—
183C22×C32D3×D414yes—
184C22×C32#23712yes—
185C22×C32#23912yes—
186C22×C32C22×C3×C411yescharacteristic
187C22×C32C22×C3×C412yes—
188C22×C32C2×C3×D412yes—
189C22×C32C3×#4112yes—
190C2×C3⋊D3—22no—
191C2×C3⋊D3—22no—
192C2×C3⋊D3—28no—
193C2×C3⋊D3C3×C4214yescomplemented
194C2×C3×D3—38no—
195C2×C3×D3—64no—
196C2×C3×D3—64no—
197C2×C3×D3—64no—
198C2×C3×D3—616no—
199C2×C3×D3—64no—
200C2×C3×D3—68no—
201C2×C3×D3—64no—
202C2×C3×D3—68no—
203C32×C4—22no—
204C32×C4—24no—
205C32×C4—24no—
206C32×C4—44no—
207C32×C4—44no—
208C32×C4—68no—
209C3⋊Dic3C3×C22⋊C414yescomplemented
210C3×Dic3—28no—
211C3×Dic3—28no—
212C3×Dic3—38no—
213C3×Dic3—48no—
214C3×Dic3—64no—
215C23×C4—91no—
216C2×C22⋊C4—92no—
217C2×C42—92no—
218#95—32no—
219C33C4×C22⋊C411yescharacteristic, complemented, Sylow
220C23×C3—22no—
221C23×C3—21no—
222C23×C3—41no—
223C23×C3—94no—
224C23×C3—92no—
225C23×C3—182no—
226C23×C3—182no—
227C23×C3C2×D3211yescharacteristic
228C23×C3C22×C3×D312yes—
229C22×D3—38no—
230C22×D3—34no—
231C22×D3—62no—
232C22×D3—64no—
233C22×D3—64no—
234C22×D3—64no—
235C22×D3—64no—
236C22×D3—62no—
237C22×D3—62no—
238C2×C3×C4—24no—
239C2×C3×C4—22no—
240C2×C3×C4—24no—
241C2×C3×C4—22no—
242C2×C3×C4—24no—
243C2×C3×C4—38no—
244C2×C3×C4—38no—
245C2×C3×C4—44no—
246C2×C3×C4—44no—
247C2×C3×C4—42no—
248C2×C3×C4—68no—
249C2×C3×C4—64no—
250C2×C3×C4—64no—
251C2×C3×C4—64no—
252C2×C3×C4—64no—
253C2×C3×C4—92no—
254C2×C3×C4—94no—
255C2×C3×C4—124no—
256C2×C3×C4—124no—
257C2×C3×C4—188no—
258C2×C3×C4#62412yes—
259C2×C3×C4C3×C4×D314yes—
260C2×Dic3—24no—
261C2×Dic3—24no—
262C2×Dic3—34no—
263C2×Dic3—38no—
264C2×Dic3—62no—
265C2×Dic3—64no—
266C2×Dic3C3×C4×D318yescomplemented
267C4×D3—616no—
268C4×D3—616no—
269C2×C32—22no—
270C2×C32—24no—
271C2×C32—22no—
272C2×C32—24no—
273C2×C32—21no—
274C2×C32—24no—
275C2×C32—21no—
276C2×C32—21no—
277C2×C32—22no—
278C2×C32—41no—
279C2×C32—41no—
280C2×C32—41no—
281C2×C32—44no—
282C2×C32C42×D312yes—
283C2×C32D3×C22⋊C412yes—
284C2×C32#67⋊C414yes—
285C2×C32#89212yes—
286C2×C32#89314yes—
287C2×C32C2×C3×C4211yescharacteristic
288C2×C32C2×C3×C22⋊C411yescharacteristic
289C2×C32C3×#11711yescharacteristic
290C2×C32C3×C4×D414yes—
291C3⋊D3—24no—
292C3×D3—68no—
293C3×D3—68no—
294C24—91no—
295C22×C4—34no—
296C22×C4—91no—
297C22×C4—94no—
298C22×C4—184no—
299C22×C4C3×D3211yescharacteristic
300C22⋊C4—98no—
301C42—184no—
302C22×C3—22no—
303C22×C3—22no—
304C22×C3—22no—
305C22×C3—24no—
306C22×C3—22no—
307C22×C3—21no—
308C22×C3—22no—
309C22×C3—22no—
310C22×C3—24no—
311C22×C3—42no—
312C22×C3—42no—
313C22×C3—41no—
314C22×C3—42no—
315C22×C3—94no—
316C22×C3—182no—
317C22×C3—188no—
318C22×C3—182no—
319C22×C3#379612yes—
320C22×C3C4×D3212yes—
321C22×C3C2×#62411yescharacteristic
322C22×C3#381112yes—
323C22×C3C2×C3×C4×D314yes—
324C22×C3C2×C3×C4×D312yes—
325C22×C3C3×D3×D414yes—
326C22×C3C3×#23712yes—
327C22×C3C3×#23912yes—
328C2×D3—38no—
329C2×D3—64no—
330C2×D3—64no—
331C2×D3—64no—
332C2×D3—616no—
333C2×D3—64no—
334C2×D3—68no—
335C2×D3—64no—
336C2×D3—68no—
337C3×C4—24no—
338C3×C4—24no—
339C3×C4—22no—
340C3×C4—44no—
341C3×C4—44no—
342C3×C4—68no—
343C3×C4—68no—
344C3×C4—94no—
345C3×C4—128no—
346Dic3—28no—
347Dic3—38no—
348Dic3—64no—
349C32—22no—
350C32—21no—
351C32—41no—
352C32#466612yescomplemented
353C32C3×C4×C22⋊C411yescharacteristic, complemented
354C23—94no—
355C23—92no—
356C23—182no—
357C23—182no—
358C23C2×C3×D3211yescharacteristic
359C2×C4—22no—
360C2×C4—38no—
361C2×C4—64no—
362C2×C4—64no—
363C2×C4—92no—
364C2×C4—94no—
365C2×C4—188no—
366C2×C4C3×#62412yes—
367C2×C3—21no—
368C2×C3—22no—
369C2×C3—21no—
370C2×C3—22no—
371C2×C3—24no—
372C2×C3—24no—
373C2×C3—24no—
374C2×C3—21no—
375C2×C3—22no—
376C2×C3—41no—
377C2×C3—41no—
378C2×C3—44no—
379C2×C3—41no—
380C2×C3—184no—
381C2×C3#6384911yescharacteristic
382C2×C3#6388114yes—
383C2×C3C4×#62411yescharacteristic
384C2×C3#6397411yescharacteristic
385C2×C3C3×C42×D312yes—
386C2×C3C3×D3×C22⋊C412yes—
387C2×C3C3×#67⋊C414yes—
388C2×C3C3×#89212yes—
389C2×C3C3×#89314yes—
390D3—68no—
391D3—68no—
392C22—94no—
393C22—182no—
394C22—182no—
395C22—188no—
396C22C3×#379612yes—
397C22C3×C4×D3212yes—
398C22C2×C3×#62411yescharacteristic
399C22C3×#381112yes—
400C4—22no—
401C4—68no—
402C4—94no—
403C3—21no—
404C3—22no—
405C3—41no—
406C3#1059126011yescharacteristic, direct product factor
407C3C3×#466612yescomplemented
408C2—184no—
409C2C3×#6384911yescharacteristic
410C2C3×#6388114yes—
411C2C3×C4×#62411yescharacteristic
412C2C3×#6397411yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC2×C32C2×C3×C42
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C3×C3⋊D3C22
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×C4×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
3. C2×C3×Dic32C2semidirect
4. C32×C3⋊#95C2semidirect
6. #10591260C3direct (N × H)
11. C2×C3×C4×C3⋊D3C4semidirect
13. C3×#3722C4semidirect
21. C2×Dic32C2×C3semidirect
24. C3×C3⋊#95D3semidirect
25. C3×C3⋊#95C2×C3semidirect
38. C2×C32×Dic3C2×C4semidirect
52. C2×C4×C3⋊D3C3×C4semidirect
64. #3722C3×C4semidirect
73. C2×C3×C3⋊D3C42semidirect
75. C3×C3⋊Dic3C22⋊C4semidirect
87. C3⋊#95C3×D3semidirect
133. C2×C3×Dic3C4×D3semidirect
134. C2×C3×Dic3C2×C3×C4semidirect
193. C2×C3⋊D3C3×C42semidirect
209. C3⋊Dic3C3×C22⋊C4semidirect
219. C33C4×C22⋊C4semidirect
266. C2×Dic3C3×C4×D3semidirect
352. C32#4666semidirect
353. C32C3×C4×C22⋊C4semidirect
406. C3#10591260direct (N × H)
407. C3C3×#4666semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×C3⋊D32
C2×C3×#37222
C2×C3×Dic322
C32×C3⋊#952
C3×#46663
#105912603