Finite Group Databasebeta

← C3⋊D3×D27⋊C3 #72243551

Subgroups — C3⋊D3×D27⋊C3 #72243551

Order 2916.

484 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊(C3⋊(D27⋊C3))C211yesmaximal, characteristic, complemented
2C32×D27⋊C3C211yesmaximal, characteristic, complemented
3C3⋊D3×C27⋊C3C211yesmaximal, characteristic, complemented
4C3×D9×C3⋊D3—31nomaximal
5C3⋊D3×D27C311yesmaximal, characteristic, complemented
6D3×D27⋊C3—31nomaximal
7D3×D27⋊C3—31nomaximal
8D3×D27⋊C3—32nomaximal
9C32×C27⋊C3C2211yescharacteristic, complemented, Sylow
10C3×C3⋊(C3⋊D9)—31no—
11C3×C9×C3⋊D3D311yescharacteristic
12C33×D9—31no—
13C3⋊(C3⋊D27)C2×C311yescharacteristic, complemented
14C3⋊(D27⋊C3)—31no—
15C3⋊(D27⋊C3)—31no—
16C3⋊(D27⋊C3)—32no—
17C3⋊(D27⋊C3)—61no—
18C3⋊(D27⋊C3)—61no—
19C3⋊(D27⋊C3)—62no—
20C3⋊D3×C27—21no—
21C3⋊D3×C27C2×C311yescharacteristic, complemented
22D3×C27⋊C3—31no—
23D3×C27⋊C3—31no—
24D3×C27⋊C3—32no—
25C3×D27⋊C3—21no—
26C3×D27⋊C3—21no—
27C3×D27⋊C3—22no—
28C3×D27⋊C3D311yescharacteristic, complemented
29C3×D27⋊C3D311yescharacteristic, complemented
30C3×D27⋊C3D312yescomplemented
31C32×D27C2×C311yescharacteristic, complemented
32C3×D3×C3⋊D3—91no—
33D9×C3⋊D3—31no—
34C3×D3×D9—91no—
35C3×D3×D9—91no—
36C3×D3×D9—92no—
37C2×D27⋊C3—91no—
38D3×D27—31no—
39D3×D27—31no—
40D3×D27—32no—
41C33×C9C2×D311yescharacteristic
42C3×C27⋊C3—21no—
43C3×C27⋊C3—21no—
44C3×C27⋊C3—22no—
45C3×C27⋊C3—21no—
46C3×C27⋊C3—22no—
47C3×C27⋊C3—21no—
48C3×C27⋊C3—41no—
49C3×C27⋊C3—42no—
50C3×C27⋊C3—41no—
51C3×C27⋊C3C2×D311yescharacteristic, complemented
52C3×C27⋊C3C2×D311yescharacteristic, complemented
53C3×C27⋊C3C2×D312yescomplemented
54C32×C27—21no—
55C32×C27C22×C311yescharacteristic, complemented
56C3×C3⋊(C3⋊D3)—91no—
57C32×C3⋊D3D911yescharacteristic
58C33×D3—91no—
59C3⋊(C3⋊D9)—31no—
60C9×C3⋊D3—21no—
61C9×C3⋊D3C3×D311yescharacteristic
62C3×C3⋊D9—91no—
63C3×C3⋊D9—91no—
64C3×C3⋊D9—92no—
65C3×C3⋊D9—181no—
66C3×C3⋊D9—181no—
67C3×C3⋊D9—182no—
68C3×D3×C9—31no—
69C3×D3×C9—31no—
70C3×D3×C9—32no—
71C32×D9—31no—
72C32×D9—31no—
73C32×D9—31no—
74C32×D9—32no—
75C32×D9—61no—
76C32×D9—61no—
77C32×D9—62no—
78C2×C27⋊C3—91no—
79C3⋊D27—31no—
80C3⋊D27—31no—
81C3⋊D27—32no—
82C3⋊D27—61no—
83C3⋊D27—61no—
84C3⋊D27—62no—
85D27⋊C3—21no—
86D27⋊C3—22no—
87D27⋊C3—21no—
88D27⋊C3—91no—
89D27⋊C3—182no—
90D27⋊C3—181no—
91D27⋊C3—181no—
92D27⋊C3C3⋊D311yescharacteristic, direct product factor
93D3×C27—31no—
94D3×C27—31no—
95D3×C27—32no—
96D3×C27—61no—
97D3×C27—61no—
98D3×C27—62no—
99C3×D27C3×D311yescharacteristic, complemented
100C3×D27C3×D311yescharacteristic, complemented
101C3×D27C3×D312yescomplemented
102C2×C3×C3⋊D3—271no—
103D3×C3⋊D3—91no—
104C3×D32—271no—
105C3×D32—271no—
106C3×D32—272no—
107C2×C3×D9—271no—
108D3×D9—91no—
109D3×D9—91no—
110D3×D9—92no—
111C2×D27—91no—
112C34C2×D911yescharacteristic
113C32×C9—21no—
114C32×C9—21no—
115C32×C9—22no—
116C32×C9—21no—
117C32×C9—21no—
118C32×C9—22no—
119C32×C9—21no—
120C32×C9—41no—
121C32×C9—42no—
122C32×C9—41no—
123C32×C9D3211yescharacteristic
124C32×C9D3211yescharacteristic
125C32×C9D3212yes—
126C32×C9C2×C3×D311yescharacteristic
127C27⋊C3—22no—
128C27⋊C3—21no—
129C27⋊C3—21no—
130C27⋊C3—21no—
131C27⋊C3—22no—
132C27⋊C3—21no—
133C27⋊C3—41no—
134C27⋊C3—42no—
135C27⋊C3—41no—
136C27⋊C3—41no—
137C27⋊C3—42no—
138C27⋊C3—42no—
139C27⋊C3—42no—
140C27⋊C3—42no—
141C27⋊C3—42no—
142C27⋊C3—41no—
143C27⋊C3C2×C3⋊D311yescharacteristic, complemented
144C3×C27—21no—
145C3×C27—21no—
146C3×C27—22no—
147C3×C27—21no—
148C3×C27—21no—
149C3×C27—22no—
150C3×C27—41no—
151C3×C27—41no—
152C3×C27—42no—
153C3×C27C2×C3×D311yescharacteristic, complemented
154C3×C27C2×C3×D311yescharacteristic, complemented
155C3×C27C2×C3×D312yescomplemented
156C2×C33—271no—
157C3⋊(C3⋊D3)—91no—
158C3×C3⋊D3—61no—
159C3×C3⋊D3—271no—
160C3×C3⋊D3—271no—
161C3×C3⋊D3—271no—
162C3×C3⋊D3—272no—
163C3×C3⋊D3—541no—
164C3×C3⋊D3—541no—
165C3×C3⋊D3—542no—
166C3×C3⋊D3C3×D911yescharacteristic
167C32×D3—31no—
168C32×D3—31no—
169C32×D3—32no—
170C32×D3—91no—
171C32×D3—91no—
172C32×D3—91no—
173C32×D3—92no—
174C32×D3—181no—
175C32×D3—181no—
176C32×D3—182no—
177C2×C3×C9—91no—
178C3⋊D9—91no—
179C3⋊D9—91no—
180C3⋊D9—92no—
181C3⋊D9—181no—
182C3⋊D9—181no—
183C3⋊D9—182no—
184D3×C9—31no—
185D3×C9—31no—
186D3×C9—32no—
187D3×C9—61no—
188D3×C9—61no—
189D3×C9—62no—
190C3×D9—31no—
191C3×D9—31no—
192C3×D9—32no—
193C3×D9—31no—
194C3×D9—61no—
195C3×D9—62no—
196C3×D9—61no—
197C3×D9—271no—
198C3×D9—542no—
199C3×D9—541no—
200C3×D9—541no—
201C2×C27—91no—
202C2×C27—181no—
203D27—91no—
204D27—182no—
205D27—181no—
206D27—181no—
207D27C3×C3⋊D311yescharacteristic, complemented
208C2×C3⋊D3—271no—
209C2×C3×D3—811no—
210C2×C3×D3—811no—
211C2×C3×D3—811no—
212C2×C3×D3—812no—
213D32—271no—
214D32—271no—
215D32—272no—
216C2×D9—271no—
217C33—21no—
218C33—22no—
219C33—21no—
220C33—61no—
221C33—61no—
222C33—61no—
223C33—122no—
224C33D3×D911yescharacteristic
225C33D3×D911yescharacteristic
226C33D3×D912yes—
227C33C2×C3×D911yescharacteristic
228C3×C9—21no—
229C3×C9—21no—
230C3×C9—22no—
231C3×C9—21no—
232C3×C9—21no—
233C3×C9—22no—
234C3×C9—22no—
235C3×C9—21no—
236C3×C9—21no—
237C3×C9—21no—
238C3×C9—22no—
239C3×C9—21no—
240C3×C9—41no—
241C3×C9—42no—
242C3×C9—41no—
243C3×C9—41no—
244C3×C9—42no—
245C3×C9—42no—
246C3×C9—42no—
247C3×C9—42no—
248C3×C9—42no—
249C3×C9—41no—
250C3×C9—41no—
251C3×C9—41no—
252C3×C9—42no—
253C3×C9C3×D3211yescharacteristic
254C3×C9C3×D3211yescharacteristic
255C3×C9C3×D3212yes—
256C3×C9D3×C3⋊D311yescharacteristic
257C27—22no—
258C27—21no—
259C27—21no—
260C27—21no—
261C27—41no—
262C27—41no—
263C27—42no—
264C27C2×C3×C3⋊D311yescharacteristic, complemented
265C2×C32—91no—
266C2×C32—271no—
267C2×C32—271no—
268C2×C32—271no—
269C2×C32—272no—
270C2×C32—541no—
271C2×C32—541no—
272C2×C32—542no—
273C3⋊D3—271no—
274C3⋊D3—271no—
275C3⋊D3—271no—
276C3⋊D3—272no—
277C3⋊D3—541no—
278C3⋊D3—541no—
279C3⋊D3—542no—
280C3⋊D3D27⋊C311yescharacteristic, direct product factor
281C3×D3—31no—
282C3×D3—31no—
283C3×D3—32no—
284C3×D3—91no—
285C3×D3—91no—
286C3×D3—91no—
287C3×D3—92no—
288C3×D3—91no—
289C3×D3—181no—
290C3×D3—182no—
291C3×D3—181no—
292C3×D3—182no—
293C3×D3—181no—
294C3×D3—811no—
295C3×D3—811no—
296C3×D3—812no—
297C3×D3—811no—
298C3×D3—1621no—
299C3×D3—1621no—
300C3×D3—1622no—
301C2×C9—91no—
302C2×C9—181no—
303D9—31no—
304D9—271no—
305D9—542no—
306D9—541no—
307D9—541no—
308C22×C3—2431no—
309C2×D3—811no—
310C2×D3—811no—
311C2×D3—812no—
312C2×D3—811no—
313C32—21no—
314C32—21no—
315C32—22no—
316C32—21no—
317C32—22no—
318C32—21no—
319C32—31no—
320C32—61no—
321C32—61no—
322C32—61no—
323C32—62no—
324C32—61no—
325C32—122no—
326C32—122no—
327C32—121no—
328C32—121no—
329C32—121no—
330C32—122no—
331C32C2×D27⋊C311yescharacteristic, complemented
332C32C3×D3×D911yescharacteristic
333C32C3×D3×D911yescharacteristic
334C32C3×D3×D912yes—
335C32D9×C3⋊D311yescharacteristic
336C9—22no—
337C9—21no—
338C9—21no—
339C9—21no—
340C9—41no—
341C9—41no—
342C9—42no—
343C9C3×D3×C3⋊D311yescharacteristic
344C2×C3—91no—
345C2×C3—271no—
346C2×C3—271no—
347C2×C3—271no—
348C2×C3—272no—
349C2×C3—541no—
350C2×C3—541no—
351C2×C3—542no—
352C2×C3—541no—
353C2×C3—2431no—
354D3—31no—
355D3—31no—
356D3—32no—
357D3—91no—
358D3—811no—
359D3—811no—
360D3—812no—
361D3—811no—
362D3—1621no—
363D3—1621no—
364D3—1622no—
365C22—2431noSylow
366C3—21no—
367C3—21no—
368C3—22no—
369C3—61no—
370C3—121no—
371C3—121no—
372C3—122no—
373C3D3×D27⋊C311yescharacteristic, complemented
374C3D3×D27⋊C311yescharacteristic, complemented
375C3D3×D27⋊C312yescomplemented
376C3C3×D9×C3⋊D311yescharacteristic
377C2—91no—
378C2—271no—
379C2—2431no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC32×C27C22×C3
FrattiniC9C3×D3×C3⋊D3
FittingC32×C27⋊C3C22
socleC33C2×C3×D9
LCSG ▷ C32×C27
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C3⋊(D27⋊C3))C2semidirect
2. C32×D27⋊C3C2semidirect
3. C3⋊D3×C27⋊C3C2semidirect
5. C3⋊D3×D27C3semidirect
9. C32×C27⋊C3C22semidirect
13. C3⋊(C3⋊D27)C2×C3semidirect
21. C3⋊D3×C27C2×C3semidirect
28. C3×D27⋊C3D3semidirect
29. C3×D27⋊C3D3semidirect
30. C3×D27⋊C3D3semidirect
31. C32×D27C2×C3semidirect
51. C3×C27⋊C3C2×D3semidirect
52. C3×C27⋊C3C2×D3semidirect
53. C3×C27⋊C3C2×D3semidirect
55. C32×C27C22×C3semidirect
92. D27⋊C3C3⋊D3direct (N × H)
99. C3×D27C3×D3semidirect
100. C3×D27C3×D3semidirect
101. C3×D27C3×D3semidirect
143. C27⋊C3C2×C3⋊D3semidirect
153. C3×C27C2×C3×D3semidirect
154. C3×C27C2×C3×D3semidirect
155. C3×C27C2×C3×D3semidirect
207. D27C3×C3⋊D3semidirect
264. C27C2×C3×C3⋊D3semidirect
280. C3⋊D3D27⋊C3direct (N × H)
331. C32C2×D27⋊C3semidirect
373. C3D3×D27⋊C3semidirect
374. C3D3×D27⋊C3semidirect
375. C3D3×D27⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C3⋊(D27⋊C3))2
C32×D27⋊C32
C3⋊D3×C27⋊C32
C3×D9×C3⋊D33
C3⋊D3×D273
D3×D27⋊C33