Finite Group Databasebeta

← C3×D32×C3⋊D3 #14519539

Subgroups — C3×D32×C3⋊D3 #14519539

Order 1944.

2028 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 2028 conjugacy classes of subgroups — too many to draw. Only its 156 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⋊#1113C211yesmaximal, characteristic, complemented
2C3×C3⋊D32C211yesmaximal, characteristic, complemented
3C3×D3×C3⋊(C3⋊D3)C212yesmaximal, complemented
4C32×D3×C3⋊D3C212yesmaximal, complemented
5C33×D32C211yesmaximal, characteristic, complemented
6C2×C3×D3×C3⋊D3—32nomaximal
7D32×C3⋊D3C311yesmaximal, characteristic, direct product factor
8C3×D33—34nomaximal
9C3×C3⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
10C32×C3⋊(C3⋊D3)C2212yescomplemented
11C33×C3⋊D3C2211yescharacteristic, complemented
12C33×C3⋊D3C2211yescharacteristic, complemented
13C34×D3C2212yescomplemented
14C2×C3×C3⋊(C3⋊D3)—32no—
15C2×C32×C3⋊D3—32no—
16C2×C33×D3—32no—
17C3⋊#1113C2×C311yescharacteristic, complemented
18C3⋊D32C2×C311yescharacteristic, complemented
19D3×C3⋊(C3⋊D3)C2×C312yescomplemented
20C3×#1113—34no—
21C3×D3×C3⋊D3—22no—
22C3×D3×C3⋊D3—32no—
23C3×D3×C3⋊D3—32no—
24C3×D3×C3⋊D3—32no—
25C3×D3×C3⋊D3—34no—
26C3×D3×C3⋊D3—38no—
27C3×D3×C3⋊D3—68no—
28C3×D3×C3⋊D3—61no—
29C3×D3×C3⋊D3D312yesdirect product factor
30C3×D3×C3⋊D3C2×C312yescomplemented
31C32×D32—24no—
32C32×D32—38no—
33C32×D32D314yescomplemented
34C32×D32C2×C311yescharacteristic, complemented
35C35C2311yescharacteristic, complemented, Sylow
36C22×C3×C3⋊D3—91no—
37C2×D3×C3⋊D3—32no—
38C2×C3×D32—98no—
39C2×C3×D32—91no—
40D33—34no—
41C2×C34—32no—
42C3⋊(C3⋊(C3⋊D3))C22×C311yescharacteristic, complemented
43C3×C3⋊(C3⋊D3)—22no—
44C3×C3⋊(C3⋊D3)—32no—
45C3×C3⋊(C3⋊D3)—34no—
46C3×C3⋊(C3⋊D3)—61no—
47C3×C3⋊(C3⋊D3)—68no—
48C3×C3⋊(C3⋊D3)—124no—
49C3×C3⋊(C3⋊D3)C2×D312yescomplemented
50C3×C3⋊(C3⋊D3)C22×C312yescomplemented
51C32×C3⋊D3—21no—
52C32×C3⋊D3—22no—
53C32×C3⋊D3—24no—
54C32×C3⋊D3—32no—
55C32×C3⋊D3—38no—
56C32×C3⋊D3—41no—
57C32×C3⋊D3—68no—
58C32×C3⋊D3C2×D312yescomplemented
59C32×C3⋊D3C2×D314yescomplemented
60C32×C3⋊D3C22×C311yescharacteristic, complemented
61C32×C3⋊D3C22×C311yescharacteristic, complemented
62C33×D3—28no—
63C33×D3—28no—
64C33×D3—22no—
65C33×D3—32no—
66C33×D3—34no—
67C33×D3—48no—
68C33×D3—61no—
69C33×D3C2×D312yescomplemented
70C33×D3C2×D318yescomplemented
71C33×D3C22×C312yescomplemented
72C22×C33—91no—
73C2×C3⋊(C3⋊D3)—32no—
74C2×C3×C3⋊D3—32no—
75C2×C3×C3⋊D3—32no—
76C2×C3×C3⋊D3—62no—
77C2×C3×C3⋊D3—91no—
78C2×C3×C3⋊D3—92no—
79C2×C3×C3⋊D3—98no—
80C2×C3×C3⋊D3—91no—
81C2×C3×C3⋊D3—91no—
82C2×C3×C3⋊D3—188no—
83C2×C32×D3—38no—
84C2×C32×D3—32no—
85C2×C32×D3—68no—
86C2×C32×D3—98no—
87C2×C32×D3—92no—
88#1113—34no—
89D3×C3⋊D3—32no—
90D3×C3⋊D3—32no—
91D3×C3⋊D3—34no—
92D3×C3⋊D3—32no—
93D3×C3⋊D3—38no—
94D3×C3⋊D3—68no—
95D3×C3⋊D3—61no—
96D3×C3⋊D3C3×D312yesdirect product factor
97C3×D32—24no—
98C3×D32—38no—
99C3×D32—38no—
100C3×D32—68no—
101C3×D32—98no—
102C3×D32—98no—
103C3×D32—91no—
104C3×D32—98no—
105C3×D32—92no—
106C3×D32—188no—
107C3×D32—184no—
108C3×D32C3×D314yescomplemented
109C3×D32C3⋊D311yescharacteristic, direct product factor
110C34—28no—
111C34—21no—
112C34—24no—
113C34—22no—
114C34—48no—
115C34—44no—
116C34—41no—
117C34—84no—
118C34C22×D312yescomplemented
119C34C22×D314yescomplemented
120C34C23×C311yescharacteristic, complemented
121C22×C3⋊D3—91no—
122C22×C3×D3—272no—
123C22×C3×D3—274no—
124C2×D32—98no—
125C2×D32—91no—
126C2×C33—32no—
127C2×C33—32no—
128C2×C33—38no—
129C2×C33—68no—
130C2×C33—62no—
131C2×C33—68no—
132C2×C33—91no—
133C2×C33—91no—
134C2×C33—128no—
135C3⋊(C3⋊D3)—32no—
136C3⋊(C3⋊D3)—34no—
137C3⋊(C3⋊D3)—61no—
138C3⋊(C3⋊D3)—68no—
139C3⋊(C3⋊D3)—124no—
140C3⋊(C3⋊D3)C2×C3×D312yescomplemented
141C3×C3⋊D3—21no—
142C3×C3⋊D3—22no—
143C3×C3⋊D3—24no—
144C3×C3⋊D3—32no—
145C3×C3⋊D3—32no—
146C3×C3⋊D3—38no—
147C3×C3⋊D3—38no—
148C3×C3⋊D3—41no—
149C3×C3⋊D3—68no—
150C3×C3⋊D3—68no—
151C3×C3⋊D3—62no—
152C3×C3⋊D3—68no—
153C3×C3⋊D3—91no—
154C3×C3⋊D3—98no—
155C3×C3⋊D3—91no—
156C3×C3⋊D3—128no—
157C3×C3⋊D3—188no—
158C3×C3⋊D3—188no—
159C3×C3⋊D3—184no—
160C3×C3⋊D3—364no—
161C3×C3⋊D3—364no—
162C3×C3⋊D3—3612no—
163C3×C3⋊D3D3211yescharacteristic, direct product factor
164C3×C3⋊D3C2×C3×D312yescomplemented
165C3×C3⋊D3C2×C3×D314yescomplemented
166C3×C3⋊D3C2×C3⋊D311yescharacteristic, complemented
167C32×D3—28no—
168C32×D3—28no—
169C32×D3—28no—
170C32×D3—28no—
171C32×D3—28no—
172C32×D3—32no—
173C32×D3—38no—
174C32×D3—38no—
175C32×D3—34no—
176C32×D3—48no—
177C32×D3—424no—
178C32×D3—48no—
179C32×D3—68no—
180C32×D3—68no—
181C32×D3—64no—
182C32×D3—61no—
183C32×D3—64no—
184C32×D3—98no—
185C32×D3—92no—
186C32×D3—124no—
187C32×D3—124no—
188C32×D3—188no—
189C32×D3D3218yescomplemented
190C32×D3C2×C3×D318yescomplemented
191C32×D3C2×C3×D312yescomplemented
192C32×D3C2×C3⋊D312yescomplemented
193C22×C32—91no—
194C22×C32—94no—
195C22×C32—184no—
196C22×C32—272no—
197C2×C3⋊D3—32no—
198C2×C3⋊D3—91no—
199C2×C3⋊D3—92no—
200C2×C3⋊D3—91no—
201C2×C3⋊D3—98no—
202C2×C3⋊D3—91no—
203C2×C3⋊D3—188no—
204C2×C3×D3—38no—
205C2×C3×D3—32no—
206C2×C3×D3—68no—
207C2×C3×D3—98no—
208C2×C3×D3—98no—
209C2×C3×D3—92no—
210C2×C3×D3—92no—
211C2×C3×D3—182no—
212C2×C3×D3—188no—
213C2×C3×D3—272no—
214C2×C3×D3—272no—
215C2×C3×D3—274no—
216C2×C3×D3—274no—
217C2×C3×D3—272no—
218C2×C3×D3—278no—
219C2×C3×D3—272no—
220C2×C3×D3—541no—
221C2×C3×D3—548no—
222D32—38no—
223D32—98no—
224D32—98no—
225D32—91no—
226D32—98no—
227D32—92no—
228D32—188no—
229D32—184no—
230D32C3×C3⋊D311yescharacteristic, direct product factor
231C33—28no—
232C33—28no—
233C33—28no—
234C33—21no—
235C33—22no—
236C33—24no—
237C33—28no—
238C33—28no—
239C33—24no—
240C33—44no—
241C33—48no—
242C33—48no—
243C33—44no—
244C33—44no—
245C33—424no—
246C33—44no—
247C33—48no—
248C33—412no—
249C33—44no—
250C33—48no—
251C33—41no—
252C33—88no—
253C33—84no—
254C33—84no—
255C33—88no—
256C33—84no—
257C33—812no—
258C33—824no—
259C33—84no—
260C33—824no—
261C33C2×D3211yescharacteristic, complemented
262C33C2×D3218yescomplemented
263C33C22×C3×D312yescomplemented
264C33C22×C3×D314yescomplemented
265C33C22×C3⋊D311yescharacteristic, complemented
266C23×C3—811no—
267C22×D3—272no—
268C22×D3—274no—
269C2×C32—32no—
270C2×C32—38no—
271C2×C32—38no—
272C2×C32—32no—
273C2×C32—68no—
274C2×C32—68no—
275C2×C32—68no—
276C2×C32—68no—
277C2×C32—68no—
278C2×C32—91no—
279C2×C32—94no—
280C2×C32—92no—
281C2×C32—91no—
282C2×C32—128no—
283C2×C32—128no—
284C2×C32—1224no—
285C2×C32—184no—
286C2×C32—182no—
287C2×C32—181no—
288C2×C32—272no—
289C2×C32—361no—
290C3⋊D3—32no—
291C3⋊D3—38no—
292C3⋊D3—68no—
293C3⋊D3—91no—
294C3⋊D3—98no—
295C3⋊D3—91no—
296C3⋊D3—188no—
297C3⋊D3—188no—
298C3⋊D3—184no—
299C3⋊D3—364no—
300C3⋊D3—364no—
301C3⋊D3—3612no—
302C3⋊D3C3×D3211yescharacteristic, direct product factor
303C3⋊D3C2×C3×C3⋊D311yescharacteristic, complemented
304C3×D3—28no—
305C3×D3—28no—
306C3×D3—22no—
307C3×D3—34no—
308C3×D3—38no—
309C3×D3—38no—
310C3×D3—32no—
311C3×D3—48no—
312C3×D3—68no—
313C3×D3—64no—
314C3×D3—68no—
315C3×D3—61no—
316C3×D3—64no—
317C3×D3—98no—
318C3×D3—98no—
319C3×D3—92no—
320C3×D3—92no—
321C3×D3—124no—
322C3×D3—124no—
323C3×D3—182no—
324C3×D3—188no—
325C3×D3—188no—
326C3×D3—188no—
327C3×D3—274no—
328C3×D3—272no—
329C3×D3—368no—
330C3×D3—541no—
331C3×D3—548no—
332C3×D3—1084no—
333C3×D3C3×D3218yescomplemented
334C3×D3D3×C3⋊D312yesdirect product factor
335C3×D3C2×C3×C3⋊D312yescomplemented
336C22×C3—94no—
337C22×C3—91no—
338C22×C3—184no—
339C22×C3—272no—
340C22×C3—272no—
341C22×C3—542no—
342C22×C3—812no—
343C22×C3—811no—
344C22×C3—811no—
345C2×D3—32no—
346C2×D3—98no—
347C2×D3—92no—
348C2×D3—272no—
349C2×D3—272no—
350C2×D3—274no—
351C2×D3—274no—
352C2×D3—272no—
353C2×D3—278no—
354C2×D3—272no—
355C2×D3—541no—
356C2×D3—548no—
357C32—28no—
358C32—24no—
359C32—24no—
360C32—28no—
361C32—21no—
362C32—28no—
363C32—28no—
364C32—28no—
365C32—22no—
366C32—44no—
367C32—48no—
368C32—41no—
369C32—412no—
370C32—424no—
371C32—44no—
372C32—48no—
373C32—44no—
374C32—48no—
375C32—44no—
376C32—44no—
377C32—48no—
378C32—84no—
379C32—88no—
380C32—84no—
381C32—88no—
382C32—824no—
383C32—812no—
384C32—84no—
385C32—824no—
386C32—84no—
387C32D3314yescomplemented
388C32C2×C3×D3218yescomplemented
389C32C2×C3×D3211yescharacteristic, complemented
390C32C2×D3×C3⋊D312yescomplemented
391C32C22×C3×C3⋊D311yescharacteristic, complemented
392C23—811noSylow
393C2×C3—38no—
394C2×C3—32no—
395C2×C3—32no—
396C2×C3—68no—
397C2×C3—68no—
398C2×C3—62no—
399C2×C3—94no—
400C2×C3—91no—
401C2×C3—91no—
402C2×C3—92no—
403C2×C3—128no—
404C2×C3—181no—
405C2×C3—184no—
406C2×C3—182no—
407C2×C3—272no—
408C2×C3—272no—
409C2×C3—361no—
410C2×C3—542no—
411C2×C3—811no—
412D3—34no—
413D3—32no—
414D3—61no—
415D3—98no—
416D3—92no—
417D3—188no—
418D3—274no—
419D3—272no—
420D3—541no—
421D3—548no—
422D3—1084no—
423D3C3×D3×C3⋊D312yesdirect product factor
424C22—91no—
425C22—272no—
426C22—812no—
427C22—811no—
428C22—811no—
429C3—21no—
430C3—28no—
431C3—24no—
432C3—22no—
433C3—44no—
434C3—48no—
435C3—41no—
436C3—84no—
437C3C3×D3314yescomplemented
438C3D32×C3⋊D311yescharacteristic, direct product factor
439C3C2×C3×D3×C3⋊D312yescomplemented
440C2—32no—
441C2—91no—
442C2—91no—
443C2—272no—
444C2—811no—
subgroupG/H
center, hypercenterC3D32×C3⋊D3
commutator, cosocle, hypocenterC34C23×C3
FrattiniC1G
Fitting, socleC35C23
LCSG ▷ C34
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C3⋊#1113C2semidirect
2. C3×C3⋊D32C2semidirect
3. C3×D3×C3⋊(C3⋊D3)C2semidirect
4. C32×D3×C3⋊D3C2semidirect
5. C33×D32C2semidirect
7. D32×C3⋊D3C3direct (N × H)
9. C3×C3⋊(C3⋊(C3⋊D3))C22semidirect
10. C32×C3⋊(C3⋊D3)C22semidirect
11. C33×C3⋊D3C22semidirect
12. C33×C3⋊D3C22semidirect
13. C34×D3C22semidirect
17. C3⋊#1113C2×C3semidirect
18. C3⋊D32C2×C3semidirect
19. D3×C3⋊(C3⋊D3)C2×C3semidirect
29. C3×D3×C3⋊D3D3direct (N × H)
30. C3×D3×C3⋊D3C2×C3semidirect
33. C32×D32D3semidirect
34. C32×D32C2×C3semidirect
35. C35C23semidirect
42. C3⋊(C3⋊(C3⋊D3))C22×C3semidirect
49. C3×C3⋊(C3⋊D3)C2×D3semidirect
50. C3×C3⋊(C3⋊D3)C22×C3semidirect
58. C32×C3⋊D3C2×D3semidirect
59. C32×C3⋊D3C2×D3semidirect
60. C32×C3⋊D3C22×C3semidirect
61. C32×C3⋊D3C22×C3semidirect
69. C33×D3C2×D3semidirect
70. C33×D3C2×D3semidirect
71. C33×D3C22×C3semidirect
96. D3×C3⋊D3C3×D3direct (N × H)
108. C3×D32C3×D3semidirect
109. C3×D32C3⋊D3direct (N × H)
118. C34C22×D3semidirect
119. C34C22×D3semidirect
120. C34C23×C3semidirect
140. C3⋊(C3⋊D3)C2×C3×D3semidirect
163. C3×C3⋊D3D32direct (N × H)
164. C3×C3⋊D3C2×C3×D3semidirect
165. C3×C3⋊D3C2×C3×D3semidirect
166. C3×C3⋊D3C2×C3⋊D3semidirect
189. C32×D3D32semidirect
190. C32×D3C2×C3×D3semidirect
191. C32×D3C2×C3×D3semidirect
192. C32×D3C2×C3⋊D3semidirect
230. D32C3×C3⋊D3direct (N × H)
261. C33C2×D32semidirect
262. C33C2×D32semidirect
263. C33C22×C3×D3semidirect
264. C33C22×C3×D3semidirect
265. C33C22×C3⋊D3semidirect
302. C3⋊D3C3×D32direct (N × H)
303. C3⋊D3C2×C3×C3⋊D3semidirect
333. C3×D3C3×D32semidirect
334. C3×D3D3×C3⋊D3direct (N × H)
335. C3×D3C2×C3×C3⋊D3semidirect
387. C32D33semidirect
388. C32C2×C3×D32semidirect
389. C32C2×C3×D32semidirect
390. C32C2×D3×C3⋊D3semidirect
391. C32C22×C3×C3⋊D3semidirect
423. D3C3×D3×C3⋊D3direct (N × H)
437. C3C3×D33semidirect
438. C3D32×C3⋊D3direct (N × H)
439. C3C2×C3×D3×C3⋊D3semidirect

Maximal subgroups

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

subgroupindex
C3×C3⋊#11132
C3×C3⋊D322
C3×D3×C3⋊(C3⋊D3)2
C32×D3×C3⋊D32
C33×D322
C2×C3×D3×C3⋊D33
D32×C3⋊D33
C3×D333