Finite Group Databasebeta

← C3×D3×(C2×D3)⋊C4 #11723245

Subgroups — C3×D3×(C2×D3)⋊C4 #11723245

Order 864.

666 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D32C211yesmaximal, characteristic
2C2×C32×C4×D3C211yesmaximal, characteristic, complemented
3C2×C3×D3×Dic3C211yesmaximal, characteristic, complemented
4C3×#3752C211yesmaximal, characteristic, complemented
5C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C3×#3722C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8C2×C3×(C2×D3)⋊C4—31nomaximal
9C3×D3×C22⋊C4—31nomaximal
10D3×(C2×D3)⋊C4C311yesmaximal, characteristic, direct product factor
11C22×C3×C3⋊D3C2211yescharacteristic
12C22×C32×D3C2211yescharacteristic
13C22×C32×D3C2211yescharacteristic
14C2×C3×D32—22no—
15C2×C3×D32—22no—
16C2×C3×D32C414yescomplemented
17C2×C33×C4C2211yescharacteristic, complemented
18C2×C3×C3⋊Dic3C2211yescharacteristic, complemented
19C2×C32×Dic3C2211yescharacteristic, complemented
20C2×C32×Dic3C2211yescharacteristic, complemented
21C32×C4×D3—22no—
22C3×D3×Dic3—22no—
23C23×C3×D3—31no—
24C23×C3×D3—31no—
25C22×D32C2×C311yescharacteristic
26C22×C32×C4—31no—
27C22×C3×Dic3—31no—
28C2×C3×C4×D3—21no—
29C2×C3×C4×D3—31no—
30C2×C3×C4×D3D311yescharacteristic, complemented
31C2×C3×C4×D3C2×C311yescharacteristic, complemented
32C2×D3×Dic3C2×C311yescharacteristic, complemented
33C32×C22⋊C4—31no—
34#3752C2×C311yescharacteristic, complemented
35C3×#217—31no—
36C3×(C2×D3)⋊C4—21no—
37C3×(C2×D3)⋊C4—31no—
38C3×(C2×D3)⋊C4—31no—
39C3×(C2×D3)⋊C4—31no—
40C3×(C2×D3)⋊C4—31no—
41C3×(C2×D3)⋊C4—31no—
42C3×(C2×D3)⋊C4—61no—
43C3×(C2×D3)⋊C4D311yescharacteristic, direct product factor
44C3×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
45#3722C2×C311yescharacteristic, complemented
46(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
47C22×C33C2311yescharacteristic
48C2×C3×C3⋊D3—21no—
49C2×C3×C3⋊D3—21no—
50C2×C3×C3⋊D3C2×C412yescomplemented
51C2×C32×D3—21no—
52C2×C32×D3—21no—
53C2×C32×D3C2×C412yes—
54C2×C32×D3C2×C412yescomplemented
55C2×C32×D3D412yes—
56C2×C32×D3D412yes—
57C3×D32—28no—
58C33×C4—21no—
59C3×C3⋊Dic3—21no—
60C32×Dic3—21no—
61C32×Dic3—21no—
62C2×C3×C22⋊C4—91no—
63C2×(C2×D3)⋊C4—31no—
64D3×C22⋊C4—31no—
65C23×C32—31no—
66C23×C32—31no—
67C22×C3⋊D3C22×C311yescharacteristic
68C22×C3×D3—21no—
69C22×C3×D3—21no—
70C22×C3×D3—31no—
71C22×C3×D3—31no—
72C22×C3×D3—34no—
73C22×C3×D3—34no—
74C22×C3×D3—61no—
75C22×C3×D3—62no—
76C22×C3×D3—62no—
77C22×C3×D3—62no—
78C22×C3×D3—62no—
79C22×C3×D3C2×D311yescharacteristic
80C22×C3×D3C2×D311yescharacteristic
81C22×C3×D3C22×C311yescharacteristic
82C22×C3×D3C22×C311yescharacteristic
83C2×D32—22no—
84C2×D32—22no—
85C2×D32C3×C414yescomplemented
86C2×C32×C4—21no—
87C2×C32×C4—21no—
88C2×C32×C4—21no—
89C2×C32×C4—31no—
90C2×C32×C4—31no—
91C2×C32×C4—41no—
92C2×C32×C4—62no—
93C2×C32×C4C2×D311yescharacteristic, complemented
94C2×C32×C4C2×D311yescharacteristic, complemented
95C2×C32×C4C22×C311yescharacteristic, complemented
96C2×C3⋊Dic3C22×C311yescharacteristic, complemented
97C2×C3×Dic3—21no—
98C2×C3×Dic3—21no—
99C2×C3×Dic3—31no—
100C2×C3×Dic3—31no—
101C2×C3×Dic3—61no—
102C2×C3×Dic3—62no—
103C2×C3×Dic3C2×D311yescharacteristic, complemented
104C2×C3×Dic3C2×D311yescharacteristic, complemented
105C2×C3×Dic3C22×C311yescharacteristic, complemented
106C2×C3×Dic3C22×C311yescharacteristic, complemented
107C3×C4×D3—24no—
108C3×C4×D3—22no—
109C3×C4×D3—22no—
110C3×C4×D3—62no—
111D3×Dic3—22no—
112C2×C33C22×C411yescharacteristic
113C2×C33C2×D411yescharacteristic
114C2×C33C2×D411yescharacteristic
115C3×C3⋊D3—22no—
116C32×D3—22no—
117C32×D3C22⋊C414yescomplemented
118C24×C3—91no—
119C23×D3—31no—
120C23×D3—31no—
121C22×C3×C4—31no—
122C22×C3×C4—31no—
123C22×C3×C4—61no—
124C22×C3×C4—91no—
125C22×Dic3—31no—
126C2×C4×D3—31no—
127C2×C4×D3C3×D311yescharacteristic, complemented
128C3×C22⋊C4—31no—
129C3×C22⋊C4—31no—
130C3×C22⋊C4—61no—
131C3×C22⋊C4—91no—
132C3×C22⋊C4—91no—
133C3×C22⋊C4—91no—
134#217—31no—
135(C2×D3)⋊C4—31no—
136(C2×D3)⋊C4—31no—
137(C2×D3)⋊C4—31no—
138(C2×D3)⋊C4—31no—
139(C2×D3)⋊C4—31no—
140(C2×D3)⋊C4—61no—
141(C2×D3)⋊C4C3×D311yescharacteristic, direct product factor
142C22×C32—21no—
143C22×C32—21no—
144C22×C32—21no—
145C22×C32—32no—
146C22×C32—32no—
147C22×C32—32no—
148C22×C32—32no—
149C22×C32—41no—
150C22×C32—61no—
151C22×C32—61no—
152C22×C32C22×D311yescharacteristic
153C22×C32C22×D311yescharacteristic
154C22×C32C23×C311yescharacteristic
155C2×C3⋊D3—21no—
156C2×C3⋊D3—21no—
157C2×C3⋊D3C2×C3×C412yescomplemented
158C2×C3×D3—21no—
159C2×C3×D3—21no—
160C2×C3×D3—21no—
161C2×C3×D3—21no—
162C2×C3×D3—22no—
163C2×C3×D3—22no—
164C2×C3×D3—22no—
165C2×C3×D3—22no—
166C2×C3×D3—32no—
167C2×C3×D3—32no—
168C2×C3×D3—41no—
169C2×C3×D3—41no—
170C2×C3×D3—62no—
171C2×C3×D3—68no—
172C2×C3×D3—61no—
173C2×C3×D3—61no—
174C2×C3×D3—61no—
175C2×C3×D3—61no—
176C2×C3×D3—68no—
177C2×C3×D3—121no—
178C2×C3×D3—121no—
179C2×C3×D3C4×D312yes—
180C2×C3×D3C4×D312yescomplemented
181C2×C3×D3D1212yes—
182C2×C3×D3#6712yes—
183C2×C3×D3C2×C3×C412yes—
184C2×C3×D3C2×C3×C412yescomplemented
185C2×C3×D3C3×D412yes—
186C2×C3×D3C3×D412yes—
187D32—28no—
188C32×C4—21no—
189C32×C4—22no—
190C32×C4—21no—
191C32×C4—21no—
192C32×C4—41no—
193C32×C4—41no—
194C32×C4—42no—
195C32×C4—61no—
196C32×C4—61no—
197C3⋊Dic3—21no—
198C3×Dic3—22no—
199C3×Dic3—21no—
200C3×Dic3—21no—
201C3×Dic3—21no—
202C3×Dic3—21no—
203C3×Dic3—41no—
204C3×Dic3—61no—
205C3×Dic3—61no—
206C3×Dic3—121no—
207C2×C22⋊C4—91noSylow
208C33C2×C22⋊C411yescharacteristic, complemented, Sylow
209C23×C3—31no—
210C23×C3—31no—
211C23×C3—31no—
212C23×C3—31no—
213C23×C3—61no—
214C23×C3—61no—
215C23×C3—94no—
216C23×C3—91no—
217C23×C3—182no—
218C23×C3—182no—
219C22×D3—31no—
220C22×D3—31no—
221C22×D3—34no—
222C22×D3—34no—
223C22×D3—61no—
224C22×D3—62no—
225C22×D3—62no—
226C22×D3—62no—
227C22×D3—62no—
228C22×D3C2×C3×D311yescharacteristic
229C22×D3C2×C3×D311yescharacteristic
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—31no—
234C2×C3×C4—31no—
235C2×C3×C4—31no—
236C2×C3×C4—31no—
237C2×C3×C4—41no—
238C2×C3×C4—61no—
239C2×C3×C4—61no—
240C2×C3×C4—62no—
241C2×C3×C4—62no—
242C2×C3×C4—64no—
243C2×C3×C4—91no—
244C2×C3×C4—182no—
245C2×C3×C4D3211yescharacteristic, complemented
246C2×C3×C4C2×C3×D311yescharacteristic, complemented
247C2×C3×C4C2×C3×D311yescharacteristic, complemented
248C2×Dic3—31no—
249C2×Dic3—31no—
250C2×Dic3—61no—
251C2×Dic3—62no—
252C2×Dic3C2×C3×D311yescharacteristic, complemented
253C2×Dic3C2×C3×D311yescharacteristic, complemented
254C4×D3—22no—
255C4×D3—62no—
256C2×C32—21no—
257C2×C32—21no—
258C2×C32—21no—
259C2×C32—21no—
260C2×C32—21no—
261C2×C32—21no—
262C2×C32—21no—
263C2×C32—21no—
264C2×C32—21no—
265C2×C32—34no—
266C2×C32—41no—
267C2×C32—41no—
268C2×C32—41no—
269C2×C32—62no—
270C2×C32C2×C4×D311yescharacteristic
271C2×C32C2×C4×D311yescharacteristic
272C2×C32C2×D1211yescharacteristic
273C2×C32D3×D411yescharacteristic
274C2×C32D3×D411yescharacteristic
275C2×C32C2×#6711yescharacteristic
276C2×C32C22×C3×C411yescharacteristic
277C2×C32C2×C3×D411yescharacteristic
278C2×C32C2×C3×D411yescharacteristic
279C3⋊D3—22no—
280C3×D3—22no—
281C3×D3—22no—
282C3×D3—24no—
283C3×D3—42no—
284C3×D3—62no—
285C3×D3—62no—
286C3×D3—122no—
287C3×D3(C2×D3)⋊C414yesdirect product factor
288C3×D3C3×C22⋊C414yescomplemented
289C24—91no—
290C22×C4—31no—
291C22×C4—91no—
292C22⋊C4—31no—
293C22⋊C4—91no—
294C22⋊C4—91no—
295C22⋊C4—91no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—32no—
300C22×C3—32no—
301C22×C3—32no—
302C22×C3—32no—
303C22×C3—32no—
304C22×C3—32no—
305C22×C3—32no—
306C22×C3—32no—
307C22×C3—41no—
308C22×C3—62no—
309C22×C3—62no—
310C22×C3—62no—
311C22×C3—62no—
312C22×C3—61no—
313C22×C3—61no—
314C22×C3—61no—
315C22×C3—61no—
316C22×C3—92no—
317C22×C3—121no—
318C22×C3—121no—
319C22×C3—188no—
320C22×C3—181no—
321C22×C3—181no—
322C22×C3C2×D3211yescharacteristic
323C22×C3C22×C3×D311yescharacteristic
324C22×C3C22×C3×D311yescharacteristic
325C2×D3—21no—
326C2×D3—21no—
327C2×D3—32no—
328C2×D3—32no—
329C2×D3—62no—
330C2×D3—68no—
331C2×D3—61no—
332C2×D3—61no—
333C2×D3—61no—
334C2×D3—61no—
335C2×D3—68no—
336C2×D3—121no—
337C2×D3—121no—
338C2×D3C3×C4×D312yes—
339C2×D3C3×C4×D312yescomplemented
340C2×D3C3×D1212yes—
341C2×D3C3×#6712yes—
342C3×C4—22no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—41no—
347C3×C4—41no—
348C3×C4—42no—
349C3×C4—62no—
350C3×C4—61no—
351C3×C4—61no—
352C3×C4—61no—
353C3×C4—61no—
354C3×C4—121no—
355C3×C4—181no—
356Dic3—21no—
357Dic3—21no—
358Dic3—61no—
359Dic3—61no—
360Dic3—121no—
361C32—21no—
362C32—21no—
363C32—21no—
364C32—41no—
365C32D3×C22⋊C411yescharacteristic, complemented
366C32C2×(C2×D3)⋊C411yescharacteristic, complemented
367C32C2×C3×C22⋊C411yescharacteristic, complemented
368C23—31no—
369C23—31no—
370C23—94no—
371C23—91no—
372C23—182no—
373C23—182no—
374C2×C4—31no—
375C2×C4—31no—
376C2×C4—62no—
377C2×C4—91no—
378C2×C4—182no—
379C2×C4C3×D3211yescharacteristic, complemented
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—34no—
390C2×C3—34no—
391C2×C3—41no—
392C2×C3—41no—
393C2×C3—41no—
394C2×C3—64no—
395C2×C3—62no—
396C2×C3—62no—
397C2×C3—122no—
398C2×C3—182no—
399C2×C3C4×D3211yescharacteristic
400C2×C3D3×D1211yescharacteristic
401C2×C3D3×#6711yescharacteristic
402C2×C3C2×C3×C4×D311yescharacteristic
403C2×C3C2×C3×C4×D311yescharacteristic
404C2×C3C2×C3×D1211yescharacteristic
405C2×C3C3×D3×D411yescharacteristic
406C2×C3C3×D3×D411yescharacteristic
407C2×C3C2×C3×#6711yescharacteristic
408D3—22no—
409D3—62no—
410D3—62no—
411D3—122no—
412D3C3×(C2×D3)⋊C414yesdirect product factor
413C22—32no—
414C22—32no—
415C22—32no—
416C22—32no—
417C22—61no—
418C22—61no—
419C22—92no—
420C22—188no—
421C22—181no—
422C22—181no—
423C22C2×C3×D3211yescharacteristic
424C4—21no—
425C4—61no—
426C4—61no—
427C4—181no—
428C3—21no—
429C3—21no—
430C3—21no—
431C3—41no—
432C3D3×(C2×D3)⋊C411yescharacteristic, direct product factor
433C3C3×D3×C22⋊C411yescharacteristic, complemented
434C3C2×C3×(C2×D3)⋊C411yescharacteristic, complemented
435C2—34no—
436C2—62no—
437C2—182no—
438C2C3×C4×D3211yescharacteristic
439C2C3×D3×D1211yescharacteristic
440C2C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C2×D32
commutatorC2×C32C22×C3×C4
FrattiniC22C2×C3×D32
FittingC2×C33×C4C22
socleC22×C33C23
prime radicalC22×C3×D32C2
cosocleC22×C32C23×C3
hypercenterC2×C3×C4D32
hypocenterC32C2×C3×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C32×C4×D3C2semidirect
3. C2×C3×D3×Dic3C2semidirect
4. C3×#3752C2semidirect
5. C32×(C2×D3)⋊C4C2semidirect
6. C3×#3722C2semidirect
7. C3×(C2×D3)⋊Dic3C2semidirect
10. D3×(C2×D3)⋊C4C3direct (N × H)
16. C2×C3×D32C4semidirect
17. C2×C33×C4C22semidirect
18. C2×C3×C3⋊Dic3C22semidirect
19. C2×C32×Dic3C22semidirect
20. C2×C32×Dic3C22semidirect
30. C2×C3×C4×D3D3semidirect
31. C2×C3×C4×D3C2×C3semidirect
32. C2×D3×Dic3C2×C3semidirect
34. #3752C2×C3semidirect
43. C3×(C2×D3)⋊C4D3direct (N × H)
44. C3×(C2×D3)⋊C4C2×C3semidirect
45. #3722C2×C3semidirect
46. (C2×D3)⋊Dic3C2×C3semidirect
50. C2×C3×C3⋊D3C2×C4semidirect
54. C2×C32×D3C2×C4semidirect
85. C2×D32C3×C4semidirect
93. C2×C32×C4C2×D3semidirect
94. C2×C32×C4C2×D3semidirect
95. C2×C32×C4C22×C3semidirect
96. C2×C3⋊Dic3C22×C3semidirect
103. C2×C3×Dic3C2×D3semidirect
104. C2×C3×Dic3C2×D3semidirect
105. C2×C3×Dic3C22×C3semidirect
106. C2×C3×Dic3C22×C3semidirect
117. C32×D3C22⋊C4semidirect
127. C2×C4×D3C3×D3semidirect
141. (C2×D3)⋊C4C3×D3direct (N × H)
157. C2×C3⋊D3C2×C3×C4semidirect
180. C2×C3×D3C4×D3semidirect
184. C2×C3×D3C2×C3×C4semidirect
208. C33C2×C22⋊C4semidirect
245. C2×C3×C4D32semidirect
246. C2×C3×C4C2×C3×D3semidirect
247. C2×C3×C4C2×C3×D3semidirect
252. C2×Dic3C2×C3×D3semidirect
253. C2×Dic3C2×C3×D3semidirect
287. C3×D3(C2×D3)⋊C4direct (N × H)
288. C3×D3C3×C22⋊C4semidirect
339. C2×D3C3×C4×D3semidirect
365. C32D3×C22⋊C4semidirect
366. C32C2×(C2×D3)⋊C4semidirect
367. C32C2×C3×C22⋊C4semidirect
379. C2×C4C3×D32semidirect
412. D3C3×(C2×D3)⋊C4direct (N × H)
432. C3D3×(C2×D3)⋊C4direct (N × H)
433. C3C3×D3×C22⋊C4semidirect
434. C3C2×C3×(C2×D3)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D322
C2×C32×C4×D32
C2×C3×D3×Dic32
C3×#37522
C32×(C2×D3)⋊C42
C3×#37222
C3×(C2×D3)⋊Dic32
C2×C3×(C2×D3)⋊C43
C3×D3×C22⋊C43
D3×(C2×D3)⋊C43