Finite Group Databasebeta

← C3×#6289⋊C3 #14518618

Subgroups — C3×#6289⋊C3 #14518618

Order 1944.

711 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 711 conjugacy classes of subgroups — too many to draw. Only its 106 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×C3⋊((C3⋊D3)⋊C3)C211yesmaximal, characteristic
2C3×Dic3×H(3,𝔽3)C211yesmaximal, characteristic, complemented
3C32×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
4C3×#6289C311yesmaximal, characteristic, complemented
5C32×#624—31nomaximal
6C3×C4×(C3⋊D3)⋊C3—31nomaximal
7#6289⋊C3C313yesmaximal, direct product factor
8C2×C32×H(3,𝔽3)C2211yescharacteristic
9C3×C3⋊((C3⋊D3)⋊C3)C412yescomplemented
10C2×C3×C3⋊(C3⋊D3)C2×C311yescharacteristic
11C2×C32×C3⋊D3—31no—
12C32×C3⋊Dic3C2×C311yescharacteristic, complemented
13C33×Dic3—21no—
14C33×Dic3—31no—
15C33×Dic3D311yescharacteristic, complemented
16C33×Dic3C2×C311yescharacteristic, complemented
17C2×C3⋊((C3⋊D3)⋊C3)C2×C313yes—
18C2×C3×(C3⋊D3)⋊C3—31no—
19C2×C3×(C3⋊D3)⋊C3—61no—
20C3×C4×H(3,𝔽3)—31no—
21Dic3×H(3,𝔽3)—23no—
22Dic3×H(3,𝔽3)C2×C313yescomplemented
23C3×(C3⋊Dic3)⋊C3—21no—
24C3×(C3⋊Dic3)⋊C3—23no—
25C3×(C3⋊Dic3)⋊C3D311yescharacteristic, complemented
26C3×(C3⋊Dic3)⋊C3C2×C313yescomplemented
27C32×H(3,𝔽3)C2×C411yescharacteristic, complemented, Sylow
28C3×C4×C3⋊D3—31no—
29C32×C4×D3—91no—
30C32×C4×D3—91no—
31#6289C3211yescharacteristic, complemented
32C3×#624—31no—
33C3×#624—33no—
34C3×#624—91no—
35C4×(C3⋊D3)⋊C3—33no—
36C2×C34—21no—
37C2×C34C2×D311yescharacteristic
38C2×C34C22×C311yescharacteristic
39C3×C3⋊(C3⋊D3)C3×C412yescomplemented
40C32×C3⋊D3—32no—
41C2×C3×H(3,𝔽3)—21no—
42C2×C3×H(3,𝔽3)—21no—
43C2×C3×H(3,𝔽3)—23no—
44C2×C3×H(3,𝔽3)—23no—
45C2×C3×H(3,𝔽3)—43no—
46C2×C3×H(3,𝔽3)—41no—
47C2×C3×H(3,𝔽3)C2×D311yescharacteristic
48C2×C3×H(3,𝔽3)C22×C313yes—
49C3⋊((C3⋊D3)⋊C3)C3×C416yescomplemented
50C3×(C3⋊D3)⋊C3—32no—
51C3×(C3⋊D3)⋊C3—62no—
52C2×C3⋊(C3⋊D3)C2×C3211yescharacteristic
53C2×C3×C3⋊D3—33no—
54C2×C3×C3⋊D3—31no—
55C2×C3×C3⋊D3—31no—
56C2×C3×C3⋊D3—61no—
57C2×C3×C3⋊D3—91no—
58C2×C3×C3⋊D3—181no—
59C2×C32×D3—91no—
60C2×C32×D3—91no—
61C2×C32×D3—181no—
62C33×C4—31no—
63C33×C4—31no—
64C33×C4—61no—
65C33×C4—91no—
66C3×C3⋊Dic3—21no—
67C3×C3⋊Dic3C3×D311yescharacteristic, complemented
68C3×C3⋊Dic3C2×C3211yescharacteristic, complemented
69C32×Dic3—21no—
70C32×Dic3—23no—
71C32×Dic3—31no—
72C32×Dic3—31no—
73C32×Dic3—31no—
74C32×Dic3—33no—
75C32×Dic3—31no—
76C32×Dic3—63no—
77C32×Dic3—61no—
78C32×Dic3—61no—
79C32×Dic3—61no—
80C32×Dic3—62no—
81C32×Dic3—61no—
82C32×Dic3—91no—
83C32×Dic3C3×D311yescharacteristic
84C32×Dic3C3×D313yescomplemented
85C32×Dic3C2×C3211yescharacteristic, complemented
86C2×(C3⋊D3)⋊C3—33no—
87C2×(C3⋊D3)⋊C3—63no—
88C4×H(3,𝔽3)—33no—
89C4×H(3,𝔽3)—63no—
90(C3⋊Dic3)⋊C3—23no—
91(C3⋊Dic3)⋊C3C3×D313yescomplemented
92C34—21no—
93C34C4×D311yescharacteristic, complemented
94C34C2×C3×C411yescharacteristic, complemented
95C3×H(3,𝔽3)—21no—
96C3×H(3,𝔽3)—21no—
97C3×H(3,𝔽3)—23no—
98C3×H(3,𝔽3)—23no—
99C3×H(3,𝔽3)—43no—
100C3×H(3,𝔽3)—41no—
101C3×H(3,𝔽3)C4×D311yescharacteristic, complemented
102C3×H(3,𝔽3)C2×C3×C413yescomplemented
103C2×C32×C4—271no—
104C4×C3⋊D3—31no—
105C3×C4×D3—93no—
106C3×C4×D3—91no—
107C3×C4×D3—93no—
108C3×C4×D3—91no—
109C3×C4×D3—271no—
110#624—31no—
111#624—91no—
112C2×C33—21no—
113C2×C33—23no—
114C2×C33—21no—
115C2×C33—21no—
116C2×C33—21no—
117C2×C33—23no—
118C2×C33—21no—
119C2×C33—31no—
120C2×C33—31no—
121C2×C33—41no—
122C2×C33—43no—
123C2×C33—41no—
124C2×C33—61no—
125C2×C33—61no—
126C2×C33—61no—
127C2×C33—61no—
128C2×C33—62no—
129C2×C33—61no—
130C2×C33—121no—
131C2×C33—121no—
132C2×C33—121no—
133C2×C33—122no—
134C2×C33D3211yescharacteristic
135C2×C33C2×C3×D311yescharacteristic
136C2×C33C2×C3×D313yes—
137C2×C33C2×C3×D311yescharacteristic
138C2×C33C22×C3211yescharacteristic
139C3⋊(C3⋊D3)C32×C412yescomplemented
140C3×C3⋊D3—32no—
141C3×C3⋊D3—36no—
142C3×C3⋊D3—32no—
143C3×C3⋊D3—62no—
144C3×C3⋊D3—92no—
145C3×C3⋊D3—182no—
146C32×D3—92no—
147C32×D3—92no—
148C32×D3—182no—
149C2×H(3,𝔽3)—23no—
150C2×H(3,𝔽3)—23no—
151C2×H(3,𝔽3)—23no—
152C2×H(3,𝔽3)—43no—
153C2×H(3,𝔽3)—43no—
154C2×H(3,𝔽3)—46no—
155C2×H(3,𝔽3)—43no—
156C2×H(3,𝔽3)C2×C3×D313yes—
157(C3⋊D3)⋊C3—36no—
158(C3⋊D3)⋊C3—66no—
159C22×C32—271no—
160C2×C3⋊D3—31no—
161C2×C3⋊D3—31no—
162C2×C3⋊D3—61no—
163C2×C3⋊D3—91no—
164C2×C3⋊D3—181no—
165C2×C3×D3—93no—
166C2×C3×D3—91no—
167C2×C3×D3—93no—
168C2×C3×D3—91no—
169C2×C3×D3—181no—
170C2×C3×D3—183no—
171C2×C3×D3—271no—
172C2×C3×D3—541no—
173C32×C4—31no—
174C32×C4—33no—
175C32×C4—31no—
176C32×C4—63no—
177C32×C4—61no—
178C32×C4—91no—
179C32×C4—91no—
180C32×C4—91no—
181C32×C4—93no—
182C32×C4—91no—
183C32×C4—181no—
184C32×C4—181no—
185C32×C4—181no—
186C32×C4—182no—
187C32×C4—183no—
188C32×C4—181no—
189C3⋊Dic3C32×D311yescharacteristic, complemented
190C3×Dic3—21no—
191C3×Dic3—33no—
192C3×Dic3—31no—
193C3×Dic3—31no—
194C3×Dic3—33no—
195C3×Dic3—31no—
196C3×Dic3—63no—
197C3×Dic3—61no—
198C3×Dic3—61no—
199C3×Dic3—63no—
200C3×Dic3—91no—
201C3×Dic3—91no—
202C3×Dic3—181no—
203C3×Dic3(C3⋊D3)⋊C311yescharacteristic, complemented
204C3×Dic3C32×D311yescharacteristic
205C33—21no—
206C33—21no—
207C33—23no—
208C33—21no—
209C33—21no—
210C33—23no—
211C33—21no—
212C33—31no—
213C33—31no—
214C33—41no—
215C33—43no—
216C33—41no—
217C33—61no—
218C33—61no—
219C33—61no—
220C33—61no—
221C33—62no—
222C33—61no—
223C33—121no—
224C33—121no—
225C33—121no—
226C33—122no—
227C33#62411yescharacteristic, complemented
228C33C3×C4×D311yescharacteristic
229C33C3×C4×D311yescharacteristic, complemented
230C33C3×C4×D313yescomplemented
231C33C2×C32×C411yescharacteristic, complemented
232H(3,𝔽3)—23no—
233H(3,𝔽3)—23no—
234H(3,𝔽3)—23no—
235H(3,𝔽3)—43no—
236H(3,𝔽3)—43no—
237H(3,𝔽3)—46no—
238H(3,𝔽3)—43no—
239H(3,𝔽3)C3×C4×D313yescomplemented
240C2×C3×C4—271no—
241C2×C3×C4—273no—
242C4×D3—91no—
243C4×D3—91no—
244C4×D3—271no—
245C2×C32—21no—
246C2×C32—21no—
247C2×C32—21no—
248C2×C32—21no—
249C2×C32—21no—
250C2×C32—23no—
251C2×C32—23no—
252C2×C32—31no—
253C2×C32—31no—
254C2×C32—33no—
255C2×C32—31no—
256C2×C32—41no—
257C2×C32—43no—
258C2×C32—41no—
259C2×C32—61no—
260C2×C32—63no—
261C2×C32—61no—
262C2×C32—63no—
263C2×C32—61no—
264C2×C32—61no—
265C2×C32—62no—
266C2×C32—61no—
267C2×C32—61no—
268C2×C32—61no—
269C2×C32—61no—
270C2×C32—63no—
271C2×C32—121no—
272C2×C32—121no—
273C2×C32—123no—
274C2×C32—121no—
275C2×C32—121no—
276C2×C32—123no—
277C2×C32—122no—
278C2×C32—123no—
279C2×C32—121no—
280C2×C32—122no—
281C2×C32—126no—
282C2×C32—121no—
283C2×C32—272no—
284C2×C32C2×(C3⋊D3)⋊C311yescharacteristic
285C2×C32C3×D3211yescharacteristic
286C2×C32C3×D3213yes—
287C2×C32C2×C32×D311yescharacteristic
288C2×C32C2×C32×D311yescharacteristic
289C3⋊D3—32no—
290C3⋊D3—32no—
291C3⋊D3—62no—
292C3⋊D3—92no—
293C3⋊D3—182no—
294C3×D3—96no—
295C3×D3—92no—
296C3×D3—92no—
297C3×D3—96no—
298C3×D3—182no—
299C3×D3—186no—
300C3×D3—272no—
301C3×D3—542no—
302C22×C3—273no—
303C22×C3—271no—
304C2×D3—91no—
305C2×D3—91no—
306C2×D3—181no—
307C2×D3—271no—
308C2×D3—541no—
309C3×C4—31no—
310C3×C4—31no—
311C3×C4—61no—
312C3×C4—91no—
313C3×C4—93no—
314C3×C4—93no—
315C3×C4—91no—
316C3×C4—91no—
317C3×C4—181no—
318C3×C4—183no—
319C3×C4—181no—
320C3×C4—183no—
321Dic3—31no—
322Dic3—91no—
323Dic3C3×(C3⋊D3)⋊C311yescharacteristic, complemented
324C32—21no—
325C32—21no—
326C32—21no—
327C32—21no—
328C32—21no—
329C32—23no—
330C32—23no—
331C32—31no—
332C32—33no—
333C32—31no—
334C32—31no—
335C32—41no—
336C32—43no—
337C32—41no—
338C32—61no—
339C32—63no—
340C32—61no—
341C32—61no—
342C32—63no—
343C32—61no—
344C32—62no—
345C32—61no—
346C32—61no—
347C32—61no—
348C32—63no—
349C32—61no—
350C32—121no—
351C32—121no—
352C32—121no—
353C32—121no—
354C32—123no—
355C32—123no—
356C32—122no—
357C32—123no—
358C32—121no—
359C32—122no—
360C32—126no—
361C32—121no—
362C32C4×(C3⋊D3)⋊C311yescharacteristic, complemented
363C32C3×#62411yescharacteristic
364C32C3×#62413yescomplemented
365C32C32×C4×D311yescharacteristic
366C32C32×C4×D311yescharacteristic, complemented
367C2×C4—271noSylow
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—31no—
372C2×C3—33no—
373C2×C3—41no—
374C2×C3—63no—
375C2×C3—61no—
376C2×C3—63no—
377C2×C3—61no—
378C2×C3—121no—
379C2×C3—123no—
380C2×C3—276no—
381C2×C3—272no—
382C2×C3D3×(C3⋊D3)⋊C311yescharacteristic
383C2×C3C2×C3×(C3⋊D3)⋊C311yescharacteristic
384C2×C3C32×D3211yescharacteristic
385D3—92no—
386D3—92no—
387D3—182no—
388D3—272no—
389D3—542no—
390C22—271no—
391C4—31no—
392C4—91no—
393C3—21no—
394C3—21no—
395C3—21no—
396C3—31no—
397C3—33no—
398C3—41no—
399C3—61no—
400C3—63no—
401C3—61no—
402C3—63no—
403C3—121no—
404C3—123no—
405C3#6289⋊C311yescharacteristic, direct product factor
406C3C3×C4×(C3⋊D3)⋊C311yescharacteristic, complemented
407C3C32×#62411yescharacteristic
408C2—272no—
409C2C3×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×C3⋊((C3⋊D3)⋊C3)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×Dic3×H(3,𝔽3)C2semidirect
3. C32×(C3⋊Dic3)⋊C3C2semidirect
4. C3×#6289C3semidirect
7. #6289⋊C3C3direct (N × H)
9. C3×C3⋊((C3⋊D3)⋊C3)C4semidirect
12. C32×C3⋊Dic3C2×C3semidirect
15. C33×Dic3D3semidirect
16. C33×Dic3C2×C3semidirect
22. Dic3×H(3,𝔽3)C2×C3semidirect
25. C3×(C3⋊Dic3)⋊C3D3semidirect
26. C3×(C3⋊Dic3)⋊C3C2×C3semidirect
27. C32×H(3,𝔽3)C2×C4semidirect
31. #6289C32semidirect
39. C3×C3⋊(C3⋊D3)C3×C4semidirect
49. C3⋊((C3⋊D3)⋊C3)C3×C4semidirect
67. C3×C3⋊Dic3C3×D3semidirect
68. C3×C3⋊Dic3C2×C32semidirect
84. C32×Dic3C3×D3semidirect
85. C32×Dic3C2×C32semidirect
91. (C3⋊Dic3)⋊C3C3×D3semidirect
93. C34C4×D3semidirect
94. C34C2×C3×C4semidirect
101. C3×H(3,𝔽3)C4×D3semidirect
102. C3×H(3,𝔽3)C2×C3×C4semidirect
139. C3⋊(C3⋊D3)C32×C4semidirect
189. C3⋊Dic3C32×D3semidirect
203. C3×Dic3(C3⋊D3)⋊C3semidirect
227. C33#624semidirect
229. C33C3×C4×D3semidirect
230. C33C3×C4×D3semidirect
231. C33C2×C32×C4semidirect
239. H(3,𝔽3)C3×C4×D3semidirect
323. Dic3C3×(C3⋊D3)⋊C3semidirect
362. C32C4×(C3⋊D3)⋊C3semidirect
364. C32C3×#624semidirect
366. C32C32×C4×D3semidirect
405. C3#6289⋊C3direct (N × H)
406. C3C3×C4×(C3⋊D3)⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C3⋊((C3⋊D3)⋊C3)2
C3×Dic3×H(3,𝔽3)2
C32×(C3⋊Dic3)⋊C32
C3×#62893
C32×#6243
C3×C4×(C3⋊D3)⋊C33
#6289⋊C33