Finite Group Databasebeta

← C3×#10592477 #13162815

Subgroups — C3×#10592477 #13162815

Order 1728.

944 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64147C211yesmaximal, characteristic
2C2×C3×#3754C211yesmaximal, characteristic, complemented
3C2×C3×C8×C3⋊D3C211yesmaximal, characteristic, complemented
4C3×#64106C211yesmaximal, characteristic, complemented
5C33×#102C211yesmaximal, characteristic, complemented
6C3×#63643C211yesmaximal, characteristic, complemented
7C3×#63635C211yesmaximal, characteristic, complemented
8#10592477C311yesmaximal, characteristic, direct product factor
9C3×#4778—34nomaximal
10C2×C33×D4C2211yescharacteristic
11C2×C3×#638—21no—
12C2×C3×C4×C3⋊D3C2211yescharacteristic
13C2×C3×#634C2211yescharacteristic
14C2×C33×C8C2211yescharacteristic
15C33×C4⋊C4C2211yescharacteristic
16C3×#3757—21no—
17C3×#3754—22no—
18C3×#3752—21no—
19C3×C4⋊(C3⋊Dic3)—21no—
20C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×C8×C3⋊D3—22no—
23#64147C2×C311yescharacteristic
24C2×#3754C2×C311yescharacteristic, complemented
25C2×C8×C3⋊D3C2×C311yescharacteristic, complemented
26#64106C2×C311yescharacteristic, complemented
27C3×#938—34no—
28C2×C3×#214—34no—
29C2×C3×D3×C8—34no—
30C3×#897—34no—
31C32×#102—24no—
32C32×#102D314yescomplemented
33C32×#102C2×C311yescharacteristic, complemented
34#63643C2×C311yescharacteristic, complemented
35#63635C2×C311yescharacteristic, complemented
36C3×#816—34no—
37C3×#808—34no—
38C23×C33—21no—
39C22×C3×C3⋊D3D411yescharacteristic
40C33×D4—21no—
41C33×D4—21no—
42C2×C33×C4—21no—
43C2×C33×C4C2311yescharacteristic
44C3×#638—42no—
45C2×C3×C3⋊Dic3—21no—
46C2×C3×C3⋊Dic3—21no—
47C2×C3×C3⋊Dic3D411yescharacteristic
48C3×C4×C3⋊D3—21no—
49C3×C4×C3⋊D3—21no—
50C3×#634—21no—
51C3×#634—21no—
52C33×C8—21no—
53C3×C3⋊(C3⋊C8)D412yescomplemented
54C3×#465—91no—
55#4778—34no—
56C2×C32×D4—24no—
57C2×C32×D4C2×D314yes—
58C2×C32×D4C22×C311yescharacteristic
59C2×#638—21no—
60C2×C4×C3⋊D3C22×C311yescharacteristic
61C2×#634C22×C311yescharacteristic
62C2×C3×#67—64no—
63C2×C3×C4×D3—34no—
64C2×C3×Dic6—34no—
65C2×C32×C8—24no—
66C2×C32×C8C2×D314yes—
67C2×C32×C8C22×C311yescharacteristic
68C32×C4⋊C4—24no—
69C32×C4⋊C4C2×D314yes—
70C32×C4⋊C4C22×C311yescharacteristic
71#3757—21no—
72#3754—22no—
73#3752—21no—
74C4⋊(C3⋊Dic3)—21no—
75C4⋊(C3⋊Dic3)C22×C311yescharacteristic
76C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
77C8×C3⋊D3—22no—
78C3×#217—64no—
79C3×#214—68no—
80C3×(C2×D3)⋊C4—64no—
81C3×C4⋊Dic3—34no—
82C3×C4⋊Dic3—64no—
83C2×C3×C3⋊C8—34no—
84C3×D3×C8—68no—
85C22×C33—41no—
86C22×C33—41no—
87C22×C33—41no—
88C22×C33C2×D411yescharacteristic
89C2×C3×C3⋊D3—21no—
90C2×C3×C3⋊D3—21no—
91C2×C3×C3⋊D3SD1612yescomplemented
92C33×C4—41no—
93C33×C4C2×D411yescharacteristic
94C33×C4#4111yescharacteristic
95C3×C3⋊Dic3—21no—
96C3×C3⋊Dic3—41no—
97C3×C3⋊Dic3—41no—
98C2×C3×SD16—91no—
99C22×C3×C8—91no—
100C3×C22⋊Q8—91no—
101C3×#121—91no—
102#938—34no—
103C2×#214—34no—
104C2×D3×C8—34no—
105#897—34no—
106C3×#106—91no—
107C3×#103—91no—
108C3×#102—24no—
109C3×#102C3×D314yescomplemented
110C3×#102C3⋊D311yescharacteristic, complemented
111#816—34no—
112#808—34no—
113C23×C32—21no—
114C23×C32—24no—
115C23×C32—44no—
116C22×C3⋊D3C3×D411yescharacteristic
117C22×C3×D3—34no—
118C32×D4—28no—
119C32×D4—24no—
120C32×D4—21no—
121C32×D4—21no—
122C32×D4—24no—
123C32×D4—44no—
124C2×C32×C4—21no—
125C2×C32×C4—24no—
126C2×C32×C4—24no—
127C2×C32×C4—44no—
128C2×C32×C4C22×D314yes—
129C2×C32×C4C23×C311yescharacteristic
130#638—42no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3C3×D411yescharacteristic
134C4×C3⋊D3—21no—
135C4×C3⋊D3—21no—
136#634—21no—
137#634—21no—
138C3×#67—128no—
139C2×C3×Dic3—34no—
140C2×C3×Dic3—64no—
141C2×C3×Dic3—64no—
142C3×C4×D3—64no—
143C3×C4×D3—64no—
144C3×Dic6—64no—
145C3×Dic6—64no—
146C32×C8—21no—
147C32×C8—24no—
148C32×C8—44no—
149C3⋊(C3⋊C8)C3×D412yescomplemented
150C3×C3⋊C8—38no—
151#465—91noSylow
152C2×C33—81no—
153C2×C33#12111yescharacteristic
154C2×C33C2×SD1611yescharacteristic
155C2×C33#13511yescharacteristic
156C3×C3⋊D3—22no—
157C2×C3×Q8—91no—
158C2×C3×D4—24no—
159C2×C3×D4—181no—
160C2×C3×D4C2×C3×D314yes—
161C2×C3×D4C2×C3⋊D311yescharacteristic
162C22×C3×C4—91no—
163C2×#67—64no—
164C2×C4×D3—34no—
165C2×Dic6—34no—
166C3×SD16—182no—
167C2×C3×C8—24no—
168C2×C3×C8—91no—
169C2×C3×C8—182no—
170C2×C3×C8C2×C3×D314yes—
171C2×C3×C8C2×C3⋊D311yescharacteristic
172C3×C4⋊C4—24no—
173C3×C4⋊C4—91no—
174C3×C4⋊C4—181no—
175C3×C4⋊C4C2×C3×D314yes—
176C3×C4⋊C4C2×C3⋊D311yescharacteristic
177C3×C22⋊C4—181no—
178C3×C22⋊C4—181no—
179#217—64no—
180#214—68no—
181(C2×D3)⋊C4—64no—
182C4⋊Dic3—34no—
183C4⋊Dic3—64no—
184C2×C3⋊C8—34no—
185D3×C8—68no—
186C22×C32—24no—
187C22×C32—48no—
188C22×C32—44no—
189C22×C32—41no—
190C22×C32—41no—
191C22×C32—41no—
192C22×C32—44no—
193C22×C32—44no—
194C22×C32—84no—
195C22×C32—84no—
196C22×C32D3×D414yes—
197C22×C32C2×C3×D411yescharacteristic
198C2×C3⋊D3—21no—
199C2×C3⋊D3—21no—
200C2×C3⋊D3C3×SD1612yescomplemented
201C2×C3×D3—38no—
202C2×C3×D3—64no—
203C2×C3×D3—64no—
204C32×C4—24no—
205C32×C4—24no—
206C32×C4—41no—
207C32×C4—44no—
208C32×C4—84no—
209C32×C4#23514yes—
210C32×C4D3×D414yes—
211C32×C4C2×C3×D411yescharacteristic
212C32×C4C3×#4111yescharacteristic
213C3⋊Dic3—21no—
214C3⋊Dic3—41no—
215C3⋊Dic3—41no—
216C3×Dic3—64no—
217C3×Dic3—124no—
218C3×Dic3—124no—
219C2×SD16—91no—
220C22×C8—91no—
221C22⋊Q8—91no—
222#121—91no—
223#106—91no—
224#103—91no—
225#102C3×C3⋊D311yescharacteristic, complemented
226C33#46511yescharacteristic, complemented, Sylow
227C23×C3—24no—
228C23×C3—21no—
229C23×C3—44no—
230C23×C3—91no—
231C22×D3—34no—
232C3×Q8—181no—
233C3×Q8—181no—
234C3×D4—28no—
235C3×D4—24no—
236C3×D4—24no—
237C3×D4—21no—
238C3×D4—21no—
239C3×D4—44no—
240C3×D4—362no—
241C2×C3×C4—24no—
242C2×C3×C4—21no—
243C2×C3×C4—24no—
244C2×C3×C4—44no—
245C2×C3×C4—91no—
246C2×C3×C4—181no—
247C2×C3×C4—181no—
248C2×C3×C4—181no—
249C2×C3×C4—181no—
250C2×C3×C4C22×C3×D314yes—
251C2×C3×C4C22×C3⋊D311yescharacteristic
252#67—128no—
253C2×Dic3—34no—
254C2×Dic3—64no—
255C2×Dic3—64no—
256C4×D3—64no—
257C4×D3—64no—
258Dic6—64no—
259Dic6—64no—
260C3×C8—24no—
261C3×C8—21no—
262C3×C8—44no—
263C3×C8—92no—
264C3⋊C8—38no—
265C2×C32—24no—
266C2×C32—24no—
267C2×C32—24no—
268C2×C32—88no—
269C2×C32—84no—
270C2×C32—81no—
271C2×C32#88414yes—
272C2×C32#91214yes—
273C2×C32D3×SD1614yes—
274C2×C32C3×#12111yescharacteristic
275C2×C32C2×C3×SD1611yescharacteristic
276C2×C32C3×#13511yescharacteristic
277C3⋊D3—22no—
278C3×D3—68no—
279C2×Q8—91no—
280C2×D4—181no—
281C2×D4C2×C3×C3⋊D311yescharacteristic
282C22×C4—91no—
283SD16—182no—
284C2×C8—91no—
285C2×C8—182no—
286C2×C8C2×C3×C3⋊D311yescharacteristic
287C4⋊C4—91no—
288C4⋊C4—181no—
289C4⋊C4C2×C3×C3⋊D311yescharacteristic
290C22⋊C4—181no—
291C22⋊C4—181no—
292C22×C3—24no—
293C22×C3—48no—
294C22×C3—44no—
295C22×C3—44no—
296C22×C3—44no—
297C22×C3—41no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3—84no—
301C22×C3—84no—
302C22×C3—92no—
303C22×C3—181no—
304C22×C3—181no—
305C22×C3C3×D3×D414yes—
306C22×C3D4×C3⋊D311yescharacteristic
307C2×D3—38no—
308C2×D3—64no—
309C2×D3—64no—
310C3×C4—24no—
311C3×C4—24no—
312C3×C4—44no—
313C3×C4—41no—
314C3×C4—84no—
315C3×C4—181no—
316C3×C4—361no—
317C3×C4—361no—
318C3×C4C3×#23514yes—
319C3×C4C3×D3×D414yes—
320C3×C4#382811yescharacteristic
321C3×C4D4×C3⋊D311yescharacteristic
322Dic3—64no—
323Dic3—124no—
324Dic3—124no—
325C32—24no—
326C32#477814yescomplemented
327C32C3×#46511yescharacteristic, complemented
328C23—21no—
329C23—91no—
330Q8—181no—
331Q8—181no—
332D4—21no—
333D4—21no—
334D4—362no—
335C2×C4—21no—
336C2×C4—91no—
337C2×C4—181no—
338C2×C4—181no—
339C2×C4—181no—
340C2×C4—181no—
341C2×C4C22×C3×C3⋊D311yescharacteristic
342C8—21no—
343C8—92no—
344C2×C3—24no—
345C2×C3—24no—
346C2×C3—24no—
347C2×C3—88no—
348C2×C3—84no—
349C2×C3—81no—
350C2×C3—182no—
351C2×C3C3×#88414yes—
352C2×C3C3×#91214yes—
353C2×C3C3×D3×SD1614yes—
354C2×C3#6409311yescharacteristic
355C2×C3#6412111yescharacteristic
356C2×C3SD16×C3⋊D311yescharacteristic
357D3—68no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—92no—
362C22—181no—
363C22—181no—
364C22C3×D4×C3⋊D311yescharacteristic
365C4—41no—
366C4—181no—
367C4—361no—
368C4—361no—
369C4C3×#382811yescharacteristic
370C4C3×D4×C3⋊D311yescharacteristic
371C3—24no—
372C3C3×#477814yescomplemented
373C3#1059247711yescharacteristic, direct product factor
374C2—81no—
375C2—182no—
376C2C3×#6409311yescharacteristic
377C2C3×#6412111yescharacteristic
378C2C3×SD16×C3⋊D311yescharacteristic
subgroupG/H
centerC22×C3D4×C3⋊D3
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C22×C3×C3⋊D3
FittingC33×#102C2
socleC22×C33C2×D4
prime radicalC3×#64147C2
hypercenterC3×#102C3⋊D3
hypocenterC32C3×#465
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#102

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3754C2semidirect
3. C2×C3×C8×C3⋊D3C2semidirect
4. C3×#64106C2semidirect
5. C33×#102C2semidirect
6. C3×#63643C2semidirect
7. C3×#63635C2semidirect
8. #10592477C3direct (N × H)
24. C2×#3754C2×C3semidirect
25. C2×C8×C3⋊D3C2×C3semidirect
26. #64106C2×C3semidirect
32. C32×#102D3semidirect
33. C32×#102C2×C3semidirect
34. #63643C2×C3semidirect
35. #63635C2×C3semidirect
53. C3×C3⋊(C3⋊C8)D4semidirect
91. C2×C3×C3⋊D3SD16semidirect
109. C3×#102C3×D3semidirect
110. C3×#102C3⋊D3semidirect
149. C3⋊(C3⋊C8)C3×D4semidirect
200. C2×C3⋊D3C3×SD16semidirect
225. #102C3×C3⋊D3semidirect
226. C33#465semidirect
326. C32#4778semidirect
327. C32C3×#465semidirect
372. C3C3×#4778semidirect
373. C3#10592477direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#641472
C2×C3×#37542
C2×C3×C8×C3⋊D32
C3×#641062
C33×#1022
C3×#636432
C3×#636352
#105924773
C3×#47783