Finite Group Databasebeta

← C3×D3×(C3⋊Dic3)⋊C3 #14518622

Subgroups — C3×D3×(C3⋊Dic3)⋊C3 #14518622

Order 1944.

751 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 751 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C2×C3×D3×H(3,𝔽3)C211yesmaximal, characteristic
2C3×C3⋊((C3⋊Dic3)⋊C3)C211yesmaximal, characteristic, complemented
3C32×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
4C3×D3×C3⋊Dic3C311yesmaximal, characteristic, complemented
5C32×D3×Dic3—31nomaximal
6C2×C3×(C3⋊Dic3)⋊C3—31nomaximal
7D3×(C3⋊Dic3)⋊C3C313yesmaximal, direct product factor
8C2×C32×H(3,𝔽3)C2211yescharacteristic
9C3×D3×H(3,𝔽3)C412yescomplemented
10C2×C33×D3—21no—
11C2×C33×D3D311yescharacteristic
12C2×C33×D3C2×C311yescharacteristic
13C3×C3⋊(C3⋊Dic3)C2×C311yescharacteristic, complemented
14C32×C3⋊Dic3—31no—
15C32×C3⋊Dic3C2×C311yescharacteristic, complemented
16C33×Dic3—31no—
17C22×C3×H(3,𝔽3)—31no—
18C2×D3×H(3,𝔽3)—23no—
19C2×D3×H(3,𝔽3)C2×C313yes—
20C3⋊((C3⋊Dic3)⋊C3)C2×C313yescomplemented
21C3×(C3⋊Dic3)⋊C3—21no—
22C3×(C3⋊Dic3)⋊C3—23no—
23C3×(C3⋊Dic3)⋊C3—31no—
24C3×(C3⋊Dic3)⋊C3—61no—
25C3×(C3⋊Dic3)⋊C3D311yescharacteristic, direct product factor
26C3×(C3⋊Dic3)⋊C3C2×C313yescomplemented
27C32×H(3,𝔽3)C2×C411yescharacteristic, complemented, Sylow
28C2×C3×C3⋊Dic3—31no—
29C2×C32×Dic3—91no—
30C32×C4×D3—91no—
31D3×C3⋊Dic3C3211yescharacteristic, complemented
32C3×D3×Dic3—33no—
33C3×D3×Dic3—31no—
34C3×D3×Dic3—91no—
35C2×(C3⋊Dic3)⋊C3—33no—
36C2×C34—21no—
37C2×C34C2×D311yescharacteristic
38C2×C34C22×C311yescharacteristic
39C33×D3—22no—
40C33×D3Dic312yescomplemented
41C33×D3C3×C412yescomplemented
42C2×C3×H(3,𝔽3)—21no—
43C2×C3×H(3,𝔽3)—21no—
44C2×C3×H(3,𝔽3)—23no—
45C2×C3×H(3,𝔽3)—23no—
46C2×C3×H(3,𝔽3)—32no—
47C2×C3×H(3,𝔽3)—43no—
48C2×C3×H(3,𝔽3)—41no—
49C2×C3×H(3,𝔽3)C2×D311yescharacteristic
50C2×C3×H(3,𝔽3)C22×C313yes—
51D3×H(3,𝔽3)—26no—
52D3×H(3,𝔽3)C3×C416yescomplemented
53C22×C33—31no—
54C22×C33—31no—
55C22×C33—61no—
56C2×C32×D3—21no—
57C2×C32×D3—23no—
58C2×C32×D3—31no—
59C2×C32×D3—31no—
60C2×C32×D3—61no—
61C2×C32×D3—61no—
62C2×C32×D3—62no—
63C2×C32×D3—61no—
64C2×C32×D3C3×D311yescharacteristic
65C2×C32×D3C3×D313yes—
66C2×C32×D3C2×C3211yescharacteristic
67C33×C4—91no—
68C3⋊(C3⋊Dic3)C2×C3211yescharacteristic, complemented
69C3×C3⋊Dic3—21no—
70C3×C3⋊Dic3—33no—
71C3×C3⋊Dic3—31no—
72C3×C3⋊Dic3—31no—
73C3×C3⋊Dic3—61no—
74C3×C3⋊Dic3—91no—
75C3×C3⋊Dic3—181no—
76C3×C3⋊Dic3C3×D311yescharacteristic, complemented
77C3×C3⋊Dic3C2×C3211yescharacteristic, complemented
78C32×Dic3—31no—
79C32×Dic3—33no—
80C32×Dic3—31no—
81C32×Dic3—63no—
82C32×Dic3—61no—
83C32×Dic3—91no—
84C32×Dic3—91no—
85C32×Dic3—91no—
86C32×Dic3—181no—
87C22×H(3,𝔽3)—33no—
88C22×H(3,𝔽3)—63no—
89(C3⋊Dic3)⋊C3—23no—
90(C3⋊Dic3)⋊C3—33no—
91(C3⋊Dic3)⋊C3—63no—
92(C3⋊Dic3)⋊C3C3×D313yesdirect product factor
93C34—21no—
94C34C2×Dic311yescharacteristic, complemented
95C34C2×C3×C411yescharacteristic, complemented
96C3×H(3,𝔽3)—21no—
97C3×H(3,𝔽3)—21no—
98C3×H(3,𝔽3)—23no—
99C3×H(3,𝔽3)—23no—
100C3×H(3,𝔽3)—43no—
101C3×H(3,𝔽3)—41no—
102C3×H(3,𝔽3)C4×D311yescharacteristic, complemented
103C3×H(3,𝔽3)C2×C3×C413yescomplemented
104C2×C32×C4—271no—
105C2×C3⋊Dic3—31no—
106C2×C3×Dic3—93no—
107C2×C3×Dic3—91no—
108C2×C3×Dic3—271no—
109C3×C4×D3—93no—
110C3×C4×D3—91no—
111D3×Dic3—31no—
112D3×Dic3—91no—
113C2×C33—21no—
114C2×C33—23no—
115C2×C33—21no—
116C2×C33—21no—
117C2×C33—21no—
118C2×C33—21no—
119C2×C33—23no—
120C2×C33—31no—
121C2×C33—32no—
122C2×C33—31no—
123C2×C33—32no—
124C2×C33—41no—
125C2×C33—43no—
126C2×C33—41no—
127C2×C33—61no—
128C2×C33—61no—
129C2×C33—61no—
130C2×C33—61no—
131C2×C33—62no—
132C2×C33—62no—
133C2×C33—61no—
134C2×C33—121no—
135C2×C33—121no—
136C2×C33—121no—
137C2×C33—122no—
138C2×C33D3211yescharacteristic
139C2×C33C2×C3×D311yescharacteristic
140C2×C33C2×C3×D311yescharacteristic
141C2×C33C2×C3×D313yes—
142C2×C33C22×C3211yescharacteristic
143C32×D3—22no—
144C32×D3—26no—
145C32×D3—32no—
146C32×D3—32no—
147C32×D3—62no—
148C32×D3—62no—
149C32×D3—64no—
150C32×D3—62no—
151C32×D3C3×Dic312yes—
152C32×D3C3×Dic316yescomplemented
153C32×D3C32×C412yescomplemented
154C2×H(3,𝔽3)—23no—
155C2×H(3,𝔽3)—23no—
156C2×H(3,𝔽3)—23no—
157C2×H(3,𝔽3)—36no—
158C2×H(3,𝔽3)—43no—
159C2×H(3,𝔽3)—43no—
160C2×H(3,𝔽3)—46no—
161C2×H(3,𝔽3)—43no—
162C2×H(3,𝔽3)—66no—
163C2×H(3,𝔽3)C2×C3×D313yes—
164C22×C32—31no—
165C22×C32—33no—
166C22×C32—31no—
167C22×C32—63no—
168C22×C32—61no—
169C22×C32—91no—
170C22×C32—91no—
171C22×C32—181no—
172C22×C32—181no—
173C22×C32—181no—
174C22×C32—182no—
175C2×C3×D3—21no—
176C2×C3×D3—33no—
177C2×C3×D3—31no—
178C2×C3×D3—61no—
179C2×C3×D3—63no—
180C2×C3×D3(C3⋊D3)⋊C311yescharacteristic
181C2×C3×D3C32×D311yescharacteristic
182C32×C4—91no—
183C32×C4—93no—
184C32×C4—91no—
185C32×C4—183no—
186C32×C4—181no—
187C32×C4—271no—
188C3⋊Dic3—31no—
189C3⋊Dic3—31no—
190C3⋊Dic3—61no—
191C3⋊Dic3—91no—
192C3⋊Dic3—181no—
193C3⋊Dic3C32×D311yescharacteristic, complemented
194C3×Dic3—33no—
195C3×Dic3—31no—
196C3×Dic3—31no—
197C3×Dic3—63no—
198C3×Dic3—61no—
199C3×Dic3—91no—
200C3×Dic3—91no—
201C3×Dic3—93no—
202C3×Dic3—91no—
203C3×Dic3—93no—
204C3×Dic3—91no—
205C3×Dic3—181no—
206C3×Dic3—181no—
207C3×Dic3—183no—
208C3×Dic3—271no—
209C3×Dic3—541no—
210C33—21no—
211C33—21no—
212C33—23no—
213C33—21no—
214C33—21no—
215C33—21no—
216C33—23no—
217C33—31no—
218C33—31no—
219C33—41no—
220C33—43no—
221C33—41no—
222C33—61no—
223C33—61no—
224C33—61no—
225C33—61no—
226C33—62no—
227C33—61no—
228C33—121no—
229C33—121no—
230C33—121no—
231C33—122no—
232C33D3×Dic311yescharacteristic, complemented
233C33C3×C4×D311yescharacteristic, complemented
234C33C2×C3×Dic311yescharacteristic
235C33C2×C3×Dic313yescomplemented
236C33C2×C32×C411yescharacteristic, complemented
237H(3,𝔽3)—23no—
238H(3,𝔽3)—23no—
239H(3,𝔽3)—23no—
240H(3,𝔽3)—43no—
241H(3,𝔽3)—43no—
242H(3,𝔽3)—46no—
243H(3,𝔽3)—43no—
244H(3,𝔽3)C3×C4×D313yescomplemented
245C2×C3×C4—271no—
246C2×C3×C4—273no—
247C2×Dic3—91no—
248C2×Dic3—271no—
249C4×D3—91no—
250C2×C32—21no—
251C2×C32—21no—
252C2×C32—21no—
253C2×C32—21no—
254C2×C32—21no—
255C2×C32—23no—
256C2×C32—23no—
257C2×C32—31no—
258C2×C32—32no—
259C2×C32—31no—
260C2×C32—33no—
261C2×C32—31no—
262C2×C32—36no—
263C2×C32—32no—
264C2×C32—41no—
265C2×C32—43no—
266C2×C32—41no—
267C2×C32—61no—
268C2×C32—63no—
269C2×C32—63no—
270C2×C32—61no—
271C2×C32—61no—
272C2×C32—61no—
273C2×C32—62no—
274C2×C32—66no—
275C2×C32—62no—
276C2×C32—61no—
277C2×C32—61no—
278C2×C32—61no—
279C2×C32—61no—
280C2×C32—63no—
281C2×C32—92no—
282C2×C32—92no—
283C2×C32—121no—
284C2×C32—121no—
285C2×C32—123no—
286C2×C32—121no—
287C2×C32—121no—
288C2×C32—123no—
289C2×C32—122no—
290C2×C32—123no—
291C2×C32—121no—
292C2×C32—122no—
293C2×C32—126no—
294C2×C32—121no—
295C2×C32—182no—
296C2×C32—182no—
297C2×C32—182no—
298C2×C32—184no—
299C2×C32C2×(C3⋊D3)⋊C311yescharacteristic
300C2×C32C3×D3211yescharacteristic
301C2×C32C3×D3213yes—
302C2×C32C2×C32×D311yescharacteristic
303C2×C32C2×C32×D311yescharacteristic
304C3×D3—22no—
305C3×D3—36no—
306C3×D3—32no—
307C3×D3—62no—
308C3×D3—66no—
309C3×D3(C3⋊Dic3)⋊C312yesdirect product factor
310C3×D3C32×Dic312yes—
311C22×C3—31no—
312C22×C3—31no—
313C22×C3—61no—
314C22×C3—91no—
315C22×C3—93no—
316C22×C3—181no—
317C22×C3—183no—
318C2×D3C3×(C3⋊D3)⋊C311yescharacteristic
319C3×C4—93no—
320C3×C4—91no—
321C3×C4—91no—
322C3×C4—181no—
323C3×C4—183no—
324C3×C4—273no—
325C3×C4—271no—
326Dic3—31no—
327Dic3—91no—
328Dic3—91no—
329Dic3—91no—
330Dic3—181no—
331Dic3—271no—
332Dic3—541no—
333C32—21no—
334C32—21no—
335C32—21no—
336C32—21no—
337C32—23no—
338C32—21no—
339C32—23no—
340C32—31no—
341C32—33no—
342C32—31no—
343C32—31no—
344C32—41no—
345C32—43no—
346C32—41no—
347C32—61no—
348C32—61no—
349C32—63no—
350C32—61no—
351C32—63no—
352C32—61no—
353C32—62no—
354C32—61no—
355C32—61no—
356C32—61no—
357C32—63no—
358C32—61no—
359C32—121no—
360C32—121no—
361C32—121no—
362C32—121no—
363C32—123no—
364C32—123no—
365C32—122no—
366C32—123no—
367C32—121no—
368C32—122no—
369C32—126no—
370C32—121no—
371C32C2×(C3⋊Dic3)⋊C311yescharacteristic, complemented
372C32C3×D3×Dic311yescharacteristic
373C32C3×D3×Dic313yescomplemented
374C32C32×C4×D311yescharacteristic, complemented
375C32C2×C32×Dic311yescharacteristic
376C2×C4—271noSylow
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—32no—
381C2×C3—32no—
382C2×C3—31no—
383C2×C3—33no—
384C2×C3—41no—
385C2×C3—62no—
386C2×C3—61no—
387C2×C3—63no—
388C2×C3—61no—
389C2×C3—63no—
390C2×C3—96no—
391C2×C3—92no—
392C2×C3—121no—
393C2×C3—123no—
394C2×C3—182no—
395C2×C3—186no—
396C2×C3D3×(C3⋊D3)⋊C311yescharacteristic
397C2×C3C2×C3×(C3⋊D3)⋊C311yescharacteristic
398C2×C3C32×D3211yescharacteristic
399D3C3×(C3⋊Dic3)⋊C312yesdirect product factor
400C22—31no—
401C4—91no—
402C4—271no—
403C3—21no—
404C3—21no—
405C3—21no—
406C3—33no—
407C3—31no—
408C3—41no—
409C3—61no—
410C3—63no—
411C3—63no—
412C3—61no—
413C3—121no—
414C3—123no—
415C3D3×(C3⋊Dic3)⋊C311yescharacteristic, direct product factor
416C3C2×C3×(C3⋊Dic3)⋊C311yescharacteristic, complemented
417C3C32×D3×Dic311yescharacteristic
418C2—32no—
419C2C3×D3×(C3⋊D3)⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2×C3D3×(C3⋊D3)⋊C3
commutator, hypocenterC33C2×C32×C4
FrattiniC2×C3C32×D32
FittingC2×C32×H(3,𝔽3)C22
socleC2×C33C2×C3×D3
prime radicalC2×C3×D3×H(3,𝔽3)C2
cosocleC2×C33C22×C32
LCSG ▷ C33
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. C3×C3⋊((C3⋊Dic3)⋊C3)C2semidirect
3. C32×(C3⋊Dic3)⋊C3C2semidirect
4. C3×D3×C3⋊Dic3C3semidirect
7. D3×(C3⋊Dic3)⋊C3C3direct (N × H)
9. C3×D3×H(3,𝔽3)C4semidirect
13. C3×C3⋊(C3⋊Dic3)C2×C3semidirect
15. C32×C3⋊Dic3C2×C3semidirect
20. C3⋊((C3⋊Dic3)⋊C3)C2×C3semidirect
25. C3×(C3⋊Dic3)⋊C3D3direct (N × H)
26. C3×(C3⋊Dic3)⋊C3C2×C3semidirect
27. C32×H(3,𝔽3)C2×C4semidirect
31. D3×C3⋊Dic3C32semidirect
40. C33×D3Dic3semidirect
41. C33×D3C3×C4semidirect
52. D3×H(3,𝔽3)C3×C4semidirect
68. C3⋊(C3⋊Dic3)C2×C32semidirect
76. C3×C3⋊Dic3C3×D3semidirect
77. C3×C3⋊Dic3C2×C32semidirect
92. (C3⋊Dic3)⋊C3C3×D3direct (N × H)
94. C34C2×Dic3semidirect
95. C34C2×C3×C4semidirect
102. C3×H(3,𝔽3)C4×D3semidirect
103. C3×H(3,𝔽3)C2×C3×C4semidirect
152. C32×D3C3×Dic3semidirect
153. C32×D3C32×C4semidirect
193. C3⋊Dic3C32×D3semidirect
232. C33D3×Dic3semidirect
233. C33C3×C4×D3semidirect
235. C33C2×C3×Dic3semidirect
236. C33C2×C32×C4semidirect
244. H(3,𝔽3)C3×C4×D3semidirect
309. C3×D3(C3⋊Dic3)⋊C3direct (N × H)
371. C32C2×(C3⋊Dic3)⋊C3semidirect
373. C32C3×D3×Dic3semidirect
374. C32C32×C4×D3semidirect
399. D3C3×(C3⋊Dic3)⋊C3direct (N × H)
415. C3D3×(C3⋊Dic3)⋊C3direct (N × H)
416. C3C2×C3×(C3⋊Dic3)⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×H(3,𝔽3)2
C3×C3⋊((C3⋊Dic3)⋊C3)2
C32×(C3⋊Dic3)⋊C32
C3×D3×C3⋊Dic33
C32×D3×Dic33
C2×C3×(C3⋊Dic3)⋊C33
D3×(C3⋊Dic3)⋊C33