Finite Group Databasebeta

← C3×C4⋊C4×Dic9 #13142548

Subgroups — C3×C4⋊C4×Dic9 #13142548

Order 1728.

674 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C9×C4⋊C4C211yesmaximal, characteristic
2C2×C3×C4⋊Dic9C211yesmaximal, characteristic
3C2×C3×C4×Dic9C212yesmaximal
4C2×C3×C4×Dic9C211yesmaximal, characteristic
5C3×C9⋊#95C212yesmaximal
6C3×Dic3×C4⋊C4—31nomaximal
7C4⋊C4×Dic9C311yesmaximal, characteristic, direct product factor
8C22×C3×C4×C9C2212yes—
9C22×C3×C4×C9C2211yescharacteristic
10C22×C3×Dic9C2211yescharacteristic
11C22×C3×Dic9C2212yes—
12C22×C3×Dic9C2211yescharacteristic
13C3×C9×C4⋊C4C414yescomplemented
14C3×C4⋊Dic9C414yescomplemented
15C3×C4×Dic9—24no—
16C3×C4×Dic9C414yescomplemented
17C2×C32×C4⋊C4D311yescharacteristic
18C2×C3×C4⋊Dic3—31no—
19C2×C3×C4×Dic3—31no—
20C2×C3×C4×Dic3—32no—
21C3×C3⋊#95—32no—
22C2×C9×C4⋊C4—21no—
23C2×C9×C4⋊C4C2×C311yescharacteristic
24C2×C4⋊Dic9C2×C311yescharacteristic
25C2×C4×Dic9C2×C312yes—
26C2×C4×Dic9C2×C311yescharacteristic
27C9⋊#95C2×C312yes—
28C23×C3×C9C2311yescharacteristic
29C2×C3×C4×C9—22no—
30C2×C3×C4×C9—22no—
31C2×C3×C4×C9C2×C414yes—
32C2×C3×C4×C9C2×C412yes—
33C2×C3×C4×C9C2×C412yes—
34C2×C3×C4×C9C2×C412yes—
35C2×C3×Dic9—22no—
36C2×C3×Dic9—21no—
37C2×C3×Dic9—21no—
38C2×C3×Dic9—22no—
39C2×C3×Dic9C2×C412yes—
40C2×C3×Dic9C2×C414yes—
41C2×C3×Dic9C2×C412yes—
42C2×C3×Dic9D412yes—
43C2×C3×Dic9Q812yes—
44C3×C4×C4⋊C4—91no—
45Dic3×C4⋊C4—31no—
46C22×C32×C4C2×D312yes—
47C22×C32×C4C2×D311yescharacteristic
48C22×C3×Dic3—31no—
49C22×C3×Dic3—32no—
50C22×C3×Dic3—31no—
51C32×C4⋊C4Dic314yes—
52C3×C4⋊Dic3—34no—
53C3×C4×Dic3—34no—
54C3×C4×Dic3—64no—
55C22×C4×C9—21no—
56C22×C4×C9—22no—
57C22×C4×C9C22×C312yes—
58C22×C4×C9C22×C311yescharacteristic
59C22×Dic9C22×C311yescharacteristic
60C22×Dic9C22×C312yes—
61C22×Dic9C22×C311yescharacteristic
62C9×C4⋊C4—24no—
63C9×C4⋊C4C3×C414yescomplemented
64C4⋊Dic9C3×C414yescomplemented
65C4×Dic9—24no—
66C4×Dic9C3×C414yescomplemented
67C22×C3×C9C22×C411yescharacteristic
68C22×C3×C9C22×C411yescharacteristic
69C22×C3×C9C22×C411yescharacteristic
70C22×C3×C9C2×D411yescharacteristic
71C22×C3×C9C2×Q811yescharacteristic
72C22×C3×C9#4111yescharacteristic
73C22×C3×C9#4111yescharacteristic
74C3×C4×C9—24no—
75C3×C4×C9C4214yescomplemented
76C3×Dic9—22no—
77C3×Dic9—24no—
78C3×Dic9C4⋊C414yesdirect product factor
79C2×C3×C4⋊C4—21no—
80C2×C3×C4⋊C4—91no—
81C2×C3×C4⋊C4D911yescharacteristic
82C2×C3×C4⋊C4C3×D311yescharacteristic
83C2×C3×C42—91no—
84C2×C3×C42—92no—
85C2×C4⋊Dic3—31no—
86C2×C4×Dic3—31no—
87C2×C4×Dic3—32no—
88C3×#95—92no—
89C3⋊#95—32no—
90C23×C32C22×D311yescharacteristic
91C2×C32×C4—22no—
92C2×C32×C4—22no—
93C2×C32×C4C4×D312yes—
94C2×C32×C4C4×D312yes—
95C2×C32×C4C2×Dic314yes—
96C2×C32×C4C2×Dic312yes—
97C2×C3×Dic3—32no—
98C2×C3×Dic3—32no—
99C2×C3×Dic3—32no—
100C2×C3×Dic3—32no—
101C2×C3×Dic3—34no—
102C2×C3×Dic3—62no—
103C2×C3×Dic3—61no—
104C2×C3×Dic3—61no—
105C2×C3×Dic3—62no—
106C23×C9—21no—
107C23×C9C23×C311yescharacteristic
108C2×C4×C9—22no—
109C2×C4×C9—22no—
110C2×C4×C9—22no—
111C2×C4×C9—22no—
112C2×C4×C9—22no—
113C2×C4×C9—24no—
114C2×C4×C9—42no—
115C2×C4×C9—42no—
116C2×C4×C9C2×C3×C412yes—
117C2×C4×C9C2×C3×C412yes—
118C2×C4×C9C2×C3×C414yes—
119C2×C4×C9C2×C3×C412yes—
120C2×Dic9—22no—
121C2×Dic9—21no—
122C2×Dic9—21no—
123C2×Dic9—22no—
124C2×Dic9C2×C3×C412yes—
125C2×Dic9C2×C3×C414yes—
126C2×Dic9C2×C3×C412yes—
127C2×Dic9C3×D412yes—
128C2×Dic9C3×Q812yes—
129C4×C4⋊C4—91noSylow
130C2×C3×C9C2×C4211yescharacteristic
131C2×C3×C9C2×C4⋊C411yescharacteristic
132C2×C3×C9#11711yescharacteristic
133C2×C3×C9C4×D411yescharacteristic
134C2×C3×C9C4×D411yescharacteristic
135C2×C3×C9C4×Q811yescharacteristic
136C2×C3×C9C4×Q811yescharacteristic
137C22×C3×C4—21no—
138C22×C3×C4—22no—
139C22×C3×C4—91no—
140C22×C3×C4—91no—
141C22×C3×C4—92no—
142C22×C3×C4C2×D912yes—
143C22×C3×C4C2×D911yescharacteristic
144C22×C3×C4C2×C3×D312yes—
145C22×C3×C4C2×C3×D311yescharacteristic
146C22×Dic3—31no—
147C22×Dic3—31no—
148C22×Dic3—32no—
149C3×C4⋊C4—24no—
150C3×C4⋊C4—94no—
151C3×C4⋊C4Dic914yesdirect product factor
152C3×C4⋊C4C3×Dic314yes—
153C3×C42—94no—
154C3×C42—184no—
155C4⋊Dic3—34no—
156C4×Dic3—34no—
157C4×Dic3—64no—
158C22×C32C2×C4×D311yescharacteristic
159C22×C32C2×C4×D311yescharacteristic
160C22×C32D3×D411yescharacteristic
161C22×C32#23711yescharacteristic
162C22×C32D3×Q811yescharacteristic
163C22×C32#23911yescharacteristic
164C22×C32C22×Dic311yescharacteristic
165C32×C4—24no—
166C32×C4C4×Dic314yes—
167C3×Dic3—34no—
168C3×Dic3—62no—
169C3×Dic3—64no—
170C22×C9—21no—
171C22×C9—21no—
172C22×C9—21no—
173C22×C9—21no—
174C22×C9—21no—
175C22×C9—21no—
176C22×C9—21no—
177C22×C9C22×C3×C411yescharacteristic
178C22×C9C22×C3×C411yescharacteristic
179C22×C9C22×C3×C411yescharacteristic
180C22×C9C2×C3×D411yescharacteristic
181C22×C9C2×C3×Q811yescharacteristic
182C22×C9C3×#4111yescharacteristic
183C22×C9C3×#4111yescharacteristic
184C4×C9—24no—
185C4×C9—24no—
186C4×C9—44no—
187C4×C9C3×C4214yescomplemented
188Dic9—22no—
189Dic9—24no—
190Dic9C3×C4⋊C414yesdirect product factor
191C2×C4⋊C4—91no—
192C2×C4⋊C4C3×D911yescharacteristic
193C2×C42—91no—
194C2×C42—92no—
195#95—92no—
196C3×C9C4×C4⋊C411yescharacteristic, complemented, Sylow
197C23×C3—21no—
198C23×C3C22×D911yescharacteristic
199C23×C3C22×C3×D311yescharacteristic
200C2×C3×C4—22no—
201C2×C3×C4—22no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—24no—
208C2×C3×C4—42no—
209C2×C3×C4—42no—
210C2×C3×C4—92no—
211C2×C3×C4—92no—
212C2×C3×C4—92no—
213C2×C3×C4—92no—
214C2×C3×C4—94no—
215C2×C3×C4—182no—
216C2×C3×C4—181no—
217C2×C3×C4—181no—
218C2×C3×C4—182no—
219C2×C3×C4C4×D912yes—
220C2×C3×C4C4×D912yes—
221C2×C3×C4C2×Dic914yes—
222C2×C3×C4C2×Dic912yes—
223C2×C3×C4C3×C4×D312yes—
224C2×C3×C4C3×C4×D312yes—
225C2×C3×C4C2×C3×Dic314yes—
226C2×C3×C4C2×C3×Dic312yes—
227C2×Dic3—32no—
228C2×Dic3—32no—
229C2×Dic3—32no—
230C2×Dic3—32no—
231C2×Dic3—34no—
232C2×Dic3—62no—
233C2×Dic3—61no—
234C2×Dic3—61no—
235C2×Dic3—62no—
236C2×C32#88711yescharacteristic
237C2×C32D3×C4⋊C411yescharacteristic
238C2×C32#89211yescharacteristic
239C2×C32#89311yescharacteristic
240C2×C32C2×C4×Dic311yescharacteristic
241C2×C32D4×Dic311yescharacteristic
242C2×C32Q8×Dic311yescharacteristic
243C2×C9—21no—
244C2×C9—21no—
245C2×C9—21no—
246C2×C9—21no—
247C2×C9—21no—
248C2×C9—21no—
249C2×C9—21no—
250C2×C9C2×C3×C4211yescharacteristic
251C2×C9C2×C3×C4⋊C411yescharacteristic
252C2×C9C3×#11711yescharacteristic
253C2×C9C3×C4×D411yescharacteristic
254C2×C9C3×C4×D411yescharacteristic
255C2×C9C3×C4×Q811yescharacteristic
256C2×C9C3×C4×Q811yescharacteristic
257C22×C4—91no—
258C22×C4—91no—
259C22×C4—92no—
260C22×C4C2×C3×D912yes—
261C22×C4C2×C3×D911yescharacteristic
262C4⋊C4—94no—
263C4⋊C4C3×Dic914yesdirect product factor
264C42—94no—
265C42—184no—
266C22×C3—21no—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3C2×C4×D911yescharacteristic
274C22×C3C2×C4×D911yescharacteristic
275C22×C3D4×D911yescharacteristic
276C22×C3#369911yescharacteristic
277C22×C3Q8×D911yescharacteristic
278C22×C3#370111yescharacteristic
279C22×C3C22×Dic911yescharacteristic
280C22×C3C2×C3×C4×D311yescharacteristic
281C22×C3C2×C3×C4×D311yescharacteristic
282C22×C3C3×D3×D411yescharacteristic
283C22×C3C3×#23711yescharacteristic
284C22×C3C3×D3×Q811yescharacteristic
285C22×C3C3×#23911yescharacteristic
286C22×C3C22×C3×Dic311yescharacteristic
287C3×C4—24no—
288C3×C4—24no—
289C3×C4—24no—
290C3×C4—44no—
291C3×C4—94no—
292C3×C4—182no—
293C3×C4—184no—
294C3×C4C4×Dic914yescomplemented
295C3×C4C3×C4×Dic314yes—
296Dic3—34no—
297Dic3—62no—
298Dic3—64no—
299C32Dic3×C4⋊C411yescharacteristic
300C9—21no—
301C9C3×C4×C4⋊C411yescharacteristic, complemented
302C23C22×C3×D911yescharacteristic
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—92no—
306C2×C4—92no—
307C2×C4—92no—
308C2×C4—92no—
309C2×C4—94no—
310C2×C4—182no—
311C2×C4—181no—
312C2×C4—181no—
313C2×C4—182no—
314C2×C4C3×C4×D912yes—
315C2×C4C3×C4×D912yes—
316C2×C4C2×C3×Dic914yes—
317C2×C4C2×C3×Dic912yes—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3#6344911yescharacteristic
326C2×C3C4⋊C4×D911yescharacteristic
327C2×C3#6345411yescharacteristic
328C2×C3#6345511yescharacteristic
329C2×C3C2×C4×Dic911yescharacteristic
330C2×C3D4×Dic911yescharacteristic
331C2×C3Q8×Dic911yescharacteristic
332C2×C3C3×#88711yescharacteristic
333C2×C3C3×D3×C4⋊C411yescharacteristic
334C2×C3C3×#89211yescharacteristic
335C2×C3C3×#89311yescharacteristic
336C2×C3C2×C3×C4×Dic311yescharacteristic
337C2×C3C3×D4×Dic311yescharacteristic
338C2×C3C3×Q8×Dic311yescharacteristic
339C22C2×C3×C4×D911yescharacteristic
340C22C2×C3×C4×D911yescharacteristic
341C22C3×D4×D911yescharacteristic
342C22C3×#369911yescharacteristic
343C22C3×Q8×D911yescharacteristic
344C22C3×#370111yescharacteristic
345C22C22×C3×Dic911yescharacteristic
346C4—24no—
347C4—94no—
348C4—182no—
349C4—184no—
350C4C3×C4×Dic914yescomplemented
351C3—21no—
352C3C4⋊C4×Dic911yescharacteristic, direct product factor
353C3C3×Dic3×C4⋊C411yescharacteristic
354C2C3×#6344911yescharacteristic
355C2C3×C4⋊C4×D911yescharacteristic
356C2C3×#6345411yescharacteristic
357C2C3×#6345511yescharacteristic
358C2C2×C3×C4×Dic911yescharacteristic
359C2C3×D4×Dic911yescharacteristic
360C2C3×Q8×Dic911yescharacteristic
subgroupG/H
centerC23×C3C22×D9
commutatorC2×C9C2×C3×C42
FrattiniC23×C3C22×C3×D3
FittingC2×C3×C9×C4⋊C4C2
socle, prime radicalC23×C32C22×D3
cosocleC23×C9C23×C3
hypercenterC2×C3×C4⋊C4D9
hypocenterC9C3×C4×C4⋊C4
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C23×C3 ◁ C2×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
7. C4⋊C4×Dic9C3direct (N × H)
13. C3×C9×C4⋊C4C4semidirect
14. C3×C4⋊Dic9C4semidirect
16. C3×C4×Dic9C4semidirect
63. C9×C4⋊C4C3×C4semidirect
64. C4⋊Dic9C3×C4semidirect
66. C4×Dic9C3×C4semidirect
75. C3×C4×C9C42semidirect
78. C3×Dic9C4⋊C4direct (N × H)
151. C3×C4⋊C4Dic9direct (N × H)
187. C4×C9C3×C42semidirect
190. Dic9C3×C4⋊C4direct (N × H)
196. C3×C9C4×C4⋊C4semidirect
263. C4⋊C4C3×Dic9direct (N × H)
294. C3×C4C4×Dic9semidirect
301. C9C3×C4×C4⋊C4semidirect
350. C4C3×C4×Dic9semidirect
352. C3C4⋊C4×Dic9direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C9×C4⋊C42
C2×C3×C4⋊Dic92
C2×C3×C4×Dic92
C3×C9⋊#952
C3×Dic3×C4⋊C43
C4⋊C4×Dic93