Finite Group Databasebeta

← C3×C3⋊D3×C22⋊C8 #13162763

Subgroups — C3×C3⋊D3×C22⋊C8 #13162763

Order 1728.

1412 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
1C22×C3×C4×C3⋊D3C211yesmaximal, characteristic
2C2×C3×C8×C3⋊D3C212yesmaximal, complemented
3C33×C22⋊C8C211yesmaximal, characteristic, complemented
4C3×#63657C211yesmaximal, characteristic, complemented
5C3×#63647C212yesmaximal, complemented
6C3⋊D3×C22⋊C8C311yesmaximal, characteristic, direct product factor
7C3×D3×C22⋊C8—34nomaximal
8C23×C3×C3⋊D3C411yescharacteristic
9C22×C33×C4C2211yescharacteristic
10C22×C3×C3⋊Dic3C411yescharacteristic
11C2×C3×C4×C3⋊D3—24no—
12C2×C3×C4×C3⋊D3C411yescharacteristic
13C2×C3×C4×C3⋊D3C411yescharacteristic
14C2×C3×C4×C3⋊D3C2211yescharacteristic
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C33×C8C2212yescomplemented
17C2×C3×C3⋊(C3⋊C8)C2212yescomplemented
18C3×C8×C3⋊D3—24no—
19C22×C4×C3⋊D3C2×C311yescharacteristic
20C22×C3×C4×D3—34no—
21C2×C8×C3⋊D3C2×C312yescomplemented
22C2×C3×D3×C8—38no—
23C32×C22⋊C8—24no—
24C32×C22⋊C8D314yescomplemented
25C32×C22⋊C8C2×C311yescharacteristic, complemented
26#63657C2×C311yescharacteristic, complemented
27#63647C2×C312yescomplemented
28C3×#830—34no—
29C3×(C2×D3)⋊C8—38no—
30C23×C33C2×C411yescharacteristic
31C22×C3×C3⋊D3—22no—
32C22×C3×C3⋊D3—22no—
33C22×C3×C3⋊D3C814yescomplemented
34C22×C3×C3⋊D3C2×C411yescharacteristic
35C22×C3×C3⋊D3C2×C411yescharacteristic
36C2×C33×C4—22no—
37C2×C33×C4C2×C411yescharacteristic
38C2×C33×C4C2311yescharacteristic
39C2×C3×C3⋊Dic3—22no—
40C2×C3×C3⋊Dic3C2×C411yescharacteristic
41C2×C3×C3⋊Dic3C2×C411yescharacteristic
42C3×C4×C3⋊D3—22no—
43C3×C4×C3⋊D3—22no—
44C3×C4×C3⋊D3—22no—
45C3×C4×C3⋊D3D414yes—
46C33×C8—22no—
47C3×C3⋊(C3⋊C8)—22no—
48C2×C3×C22⋊C8—91no—
49D3×C22⋊C8—34no—
50C23×C3⋊D3C3×C411yescharacteristic
51C23×C3×D3—34no—
52C22×C32×C4—24no—
53C22×C32×C4C2×D314yes—
54C22×C32×C4C22×C311yescharacteristic
55C22×C3⋊Dic3C3×C411yescharacteristic
56C2×C4×C3⋊D3—24no—
57C2×C4×C3⋊D3C3×C411yescharacteristic
58C2×C4×C3⋊D3C3×C411yescharacteristic
59C2×C4×C3⋊D3C22×C311yescharacteristic
60C2×C4×C3⋊D3C22×C311yescharacteristic
61C22×C3×Dic3—34no—
62C2×C3×C4×D3—34no—
63C2×C3×C4×D3—34no—
64C2×C3×C4×D3—34no—
65C2×C3×C4×D3—34no—
66C2×C3×C4×D3—616no—
67C2×C32×C8—28no—
68C2×C32×C8C2×D318yescomplemented
69C2×C32×C8C22×C312yescomplemented
70C2×C3⋊(C3⋊C8)C22×C312yescomplemented
71C8×C3⋊D3—24no—
72C2×C3×C3⋊C8—38no—
73C3×D3×C8—616no—
74C22×C33—21no—
75C22×C33—21no—
76C22×C33C2×C812yescomplemented
77C22×C33C22×C411yescharacteristic
78C2×C3×C3⋊D3—21no—
79C2×C3×C3⋊D3—21no—
80C2×C3×C3⋊D3—28no—
81C2×C3×C3⋊D3C22⋊C412yes—
82C2×C3×C3⋊D3C2×C812yes—
83C2×C3×C3⋊D3C2×C812yescomplemented
84C2×C3×C3⋊D3M1612yes—
85C33×C4—21no—
86C33×C4C2×D412yes—
87C3×C3⋊Dic3—21no—
88C3×C3⋊Dic3C22⋊C412yes—
89C23×C3×C4—91no—
90C22×C4×D3—34no—
91C22×C3×C8—92no—
92C2×D3×C8—38no—
93C3×C22⋊C8—24no—
94C3×C22⋊C8—91no—
95C3×C22⋊C8—92no—
96C3×C22⋊C8C3×D314yescomplemented
97C3×C22⋊C8C3⋊D311yescharacteristic, direct product factor
98#830—34no—
99(C2×D3)⋊C8—38no—
100C23×C32—24no—
101C23×C32C4×D314yes—
102C23×C32C2×C3×C411yescharacteristic
103C22×C3⋊D3—22no—
104C22×C3⋊D3—22no—
105C22×C3⋊D3C3×C814yescomplemented
106C22×C3⋊D3C2×C3×C411yescharacteristic
107C22×C3⋊D3C2×C3×C411yescharacteristic
108C22×C3×D3—34no—
109C22×C3×D3—316no—
110C22×C3×D3—34no—
111C22×C3×D3—68no—
112C22×C3×D3—68no—
113C2×C32×C4—22no—
114C2×C32×C4—24no—
115C2×C32×C4—24no—
116C2×C32×C4—28no—
117C2×C32×C4—48no—
118C2×C32×C4C4×D314yes—
119C2×C32×C4C2×C3×C411yescharacteristic
120C2×C32×C4C22×D314yes—
121C2×C32×C4C23×C311yescharacteristic
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3C2×C3×C411yescharacteristic
124C2×C3⋊Dic3C2×C3×C411yescharacteristic
125C4×C3⋊D3—22no—
126C4×C3⋊D3—22no—
127C4×C3⋊D3—22no—
128C4×C3⋊D3C3×D414yes—
129C2×C3×Dic3—34no—
130C2×C3×Dic3—34no—
131C2×C3×Dic3—68no—
132C3×C4×D3—316no—
133C3×C4×D3—68no—
134C3×C4×D3—68no—
135C3×C4×D3—68no—
136C32×C8—22no—
137C32×C8—28no—
138C32×C8—48no—
139C3⋊(C3⋊C8)—22no—
140C3×C3⋊C8—68no—
141C2×C22⋊C8—91noSylow
142C2×C33—22no—
143C2×C33C2×C22⋊C411yescharacteristic
144C2×C33C22×C811yescharacteristic
145C2×C33C2×M1611yescharacteristic
146C3×C3⋊D3—22no—
147C3×C3⋊D3C22⋊C814yesdirect product factor
148C24×C3—91no—
149C23×D3—34no—
150C22×C3×C4—24no—
151C22×C3×C4—91no—
152C22×C3×C4—91no—
153C22×C3×C4—91no—
154C22×C3×C4—91no—
155C22×C3×C4—91no—
156C22×C3×C4—184no—
157C22×C3×C4C2×C3×D314yes—
158C22×C3×C4C2×C3⋊D311yescharacteristic
159C22×Dic3—34no—
160C2×C4×D3—34no—
161C2×C4×D3—34no—
162C2×C4×D3—34no—
163C2×C4×D3—34no—
164C2×C4×D3—616no—
165C2×C3×C8—28no—
166C2×C3×C8—92no—
167C2×C3×C8—184no—
168C2×C3×C8C2×C3×D318yescomplemented
169C2×C3×C8C2×C3⋊D312yescomplemented
170C2×C3⋊C8—38no—
171D3×C8—616no—
172C22×C32—21no—
173C22×C32—21no—
174C22×C32—28no—
175C22×C32—24no—
176C22×C32—24no—
177C22×C32—24no—
178C22×C32—44no—
179C22×C32—44no—
180C22×C32D3×C818yescomplemented
181C22×C32C2×C3×C812yescomplemented
182C22×C32C2×C4×D314yes—
183C22×C32C22×C3×C411yescharacteristic
184C2×C3⋊D3—21no—
185C2×C3⋊D3—21no—
186C2×C3⋊D3—28no—
187C2×C3⋊D3C3×C22⋊C412yes—
188C2×C3⋊D3C2×C3×C812yes—
189C2×C3⋊D3C2×C3×C812yescomplemented
190C2×C3⋊D3C3×M1612yes—
191C2×C3×D3—38no—
192C2×C3×D3—38no—
193C2×C3×D3—38no—
194C2×C3×D3—38no—
195C2×C3×D3—632no—
196C2×C3×D3—64no—
197C2×C3×D3—64no—
198C32×C4—21no—
199C32×C4—28no—
200C32×C4—24no—
201C32×C4—44no—
202C32×C4D3×D418yes—
203C32×C4C2×C3×D412yes—
204C3⋊Dic3—21no—
205C3⋊Dic3C3×C22⋊C412yes—
206C3×Dic3—38no—
207C3×Dic3—64no—
208C23×C4—91no—
209C22×C8—92no—
210C22⋊C8—91no—
211C22⋊C8—92no—
212C22⋊C8C3×C3⋊D311yescharacteristic, direct product factor
213C33C2×C22⋊C811yescharacteristic, complemented, Sylow
214C23×C3—24no—
215C23×C3—91no—
216C23×C3—94no—
217C23×C3—91no—
218C23×C3—182no—
219C23×C3—182no—
220C23×C3C3×C4×D314yes—
221C23×C3C4×C3⋊D311yescharacteristic
222C22×D3—34no—
223C22×D3—316no—
224C22×D3—34no—
225C22×D3—68no—
226C22×D3—68no—
227C2×C3×C4—28no—
228C2×C3×C4—22no—
229C2×C3×C4—24no—
230C2×C3×C4—24no—
231C2×C3×C4—48no—
232C2×C3×C4—91no—
233C2×C3×C4—94no—
234C2×C3×C4—91no—
235C2×C3×C4—182no—
236C2×C3×C4—182no—
237C2×C3×C4—182no—
238C2×C3×C4—182no—
239C2×C3×C4C3×C4×D314yes—
240C2×C3×C4C4×C3⋊D311yescharacteristic
241C2×C3×C4C22×C3×D314yes—
242C2×C3×C4C22×C3⋊D311yescharacteristic
243C2×Dic3—34no—
244C2×Dic3—34no—
245C2×Dic3—68no—
246C4×D3—316no—
247C4×D3—68no—
248C4×D3—68no—
249C4×D3—68no—
250C3×C8—28no—
251C3×C8—22no—
252C3×C8—48no—
253C3×C8—182no—
254C3⋊C8—68no—
255C2×C32—22no—
256C2×C32—24no—
257C2×C32—24no—
258C2×C32—24no—
259C2×C32—28no—
260C2×C32—48no—
261C2×C32D3×C22⋊C414yes—
262C2×C32C2×D3×C814yes—
263C2×C32D3×M1614yes—
264C2×C32C2×C3×C22⋊C411yescharacteristic
265C2×C32C22×C3×C811yescharacteristic
266C2×C32C2×C3×M1611yescharacteristic
267C3⋊D3—22no—
268C3⋊D3C3×C22⋊C814yesdirect product factor
269C3×D3—316no—
270C3×D3—68no—
271C24—91no—
272C22×C4—91no—
273C22×C4—91no—
274C22×C4—91no—
275C22×C4—91no—
276C22×C4—91no—
277C22×C4—184no—
278C22×C4C2×C3×C3⋊D311yescharacteristic
279C2×C8—92no—
280C2×C8—184no—
281C2×C8C2×C3×C3⋊D312yescomplemented
282C22×C3—24no—
283C22×C3—24no—
284C22×C3—21no—
285C22×C3—21no—
286C22×C3—28no—
287C22×C3—24no—
288C22×C3—44no—
289C22×C3—44no—
290C22×C3—92no—
291C22×C3—92no—
292C22×C3—92no—
293C22×C3—92no—
294C22×C3—188no—
295C22×C3—181no—
296C22×C3—181no—
297C22×C3C3×D3×C818yescomplemented
298C22×C3C8×C3⋊D312yescomplemented
299C22×C3C2×C3×C4×D314yes—
300C22×C3C2×C4×C3⋊D311yescharacteristic
301C2×D3—38no—
302C2×D3—38no—
303C2×D3—38no—
304C2×D3—38no—
305C2×D3—632no—
306C2×D3—64no—
307C2×D3—64no—
308C3×C4—24no—
309C3×C4—21no—
310C3×C4—28no—
311C3×C4—44no—
312C3×C4—92no—
313C3×C4—181no—
314C3×C4C3×D3×D418yes—
315C3×C4D4×C3⋊D312yes—
316Dic3—38no—
317Dic3—64no—
318C32—24no—
319C32D3×C22⋊C814yescomplemented
320C32C2×C3×C22⋊C811yescharacteristic, complemented
321C23—91no—
322C23—94no—
323C23—91no—
324C23—182no—
325C23—182no—
326C23C3×C4×C3⋊D311yescharacteristic
327C2×C4—22no—
328C2×C4—91no—
329C2×C4—94no—
330C2×C4—91no—
331C2×C4—182no—
332C2×C4—182no—
333C2×C4—182no—
334C2×C4—182no—
335C2×C4C3×C4×C3⋊D311yescharacteristic
336C2×C4C22×C3×C3⋊D311yescharacteristic
337C8—22no—
338C8—182no—
339C2×C3—28no—
340C2×C3—22no—
341C2×C3—24no—
342C2×C3—24no—
343C2×C3—24no—
344C2×C3—48no—
345C2×C3—94no—
346C2×C3—182no—
347C2×C3C3×D3×C22⋊C414yes—
348C2×C3C2×C3×D3×C814yes—
349C2×C3C3×D3×M1614yes—
350C2×C3C22⋊C4×C3⋊D311yescharacteristic
351C2×C3C2×C8×C3⋊D311yescharacteristic
352C2×C3M16×C3⋊D311yescharacteristic
353D3—316no—
354D3—68no—
355C22—21no—
356C22—21no—
357C22—92no—
358C22—92no—
359C22—92no—
360C22—92no—
361C22—188no—
362C22—181no—
363C22—181no—
364C22C3×C8×C3⋊D312yescomplemented
365C22C2×C3×C4×C3⋊D311yescharacteristic
366C4—21no—
367C4—92no—
368C4—181no—
369C4C3×D4×C3⋊D312yes—
370C3—24no—
371C3C3×D3×C22⋊C814yescomplemented
372C3C3⋊D3×C22⋊C811yescharacteristic, direct product factor
373C2—22no—
374C2—94no—
375C2—182no—
376C2C3×C22⋊C4×C3⋊D311yescharacteristic
377C2C2×C3×C8×C3⋊D311yescharacteristic
378C2C3×M16×C3⋊D311yescharacteristic
subgroupG/H
centerC2×C3×C4C22×C3⋊D3
commutatorC2×C32C22×C3×C8
FrattiniC2×C4C22×C3×C3⋊D3
FittingC33×C22⋊C8C2
socleC22×C33C22×C4
prime radicalC23×C3×C3⋊D3C4
cosocleC2×C32×C4C23×C3
hypercenterC3×C22⋊C8C3⋊D3
hypocenterC32C2×C3×C22⋊C8
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3×C4 ◁ C3×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×C8×C3⋊D3C2semidirect
3. C33×C22⋊C8C2semidirect
4. C3×#63657C2semidirect
5. C3×#63647C2semidirect
6. C3⋊D3×C22⋊C8C3direct (N × H)
16. C2×C33×C8C22semidirect
17. C2×C3×C3⋊(C3⋊C8)C22semidirect
21. C2×C8×C3⋊D3C2×C3semidirect
24. C32×C22⋊C8D3semidirect
25. C32×C22⋊C8C2×C3semidirect
26. #63657C2×C3semidirect
27. #63647C2×C3semidirect
33. C22×C3×C3⋊D3C8semidirect
68. C2×C32×C8C2×D3semidirect
69. C2×C32×C8C22×C3semidirect
70. C2×C3⋊(C3⋊C8)C22×C3semidirect
76. C22×C33C2×C8semidirect
83. C2×C3×C3⋊D3C2×C8semidirect
96. C3×C22⋊C8C3×D3semidirect
97. C3×C22⋊C8C3⋊D3direct (N × H)
105. C22×C3⋊D3C3×C8semidirect
147. C3×C3⋊D3C22⋊C8direct (N × H)
168. C2×C3×C8C2×C3×D3semidirect
169. C2×C3×C8C2×C3⋊D3semidirect
180. C22×C32D3×C8semidirect
181. C22×C32C2×C3×C8semidirect
189. C2×C3⋊D3C2×C3×C8semidirect
212. C22⋊C8C3×C3⋊D3direct (N × H)
213. C33C2×C22⋊C8semidirect
268. C3⋊D3C3×C22⋊C8direct (N × H)
281. C2×C8C2×C3×C3⋊D3semidirect
297. C22×C3C3×D3×C8semidirect
298. C22×C3C8×C3⋊D3semidirect
319. C32D3×C22⋊C8semidirect
320. C32C2×C3×C22⋊C8semidirect
364. C22C3×C8×C3⋊D3semidirect
371. C3C3×D3×C22⋊C8semidirect
372. C3C3⋊D3×C22⋊C8direct (N × H)

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×C8×C3⋊D32
C33×C22⋊C82
C3×#636572
C3×#636472
C3⋊D3×C22⋊C83
C3×D3×C22⋊C83