Finite Group Databasebeta

← C3×#63879 #11723204

Subgroups — C3×#63879 #11723204

Order 864.

506 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D3C211yesmaximal, characteristic, complemented
2C2×C3×#625C211yesmaximal, characteristic
3C2×C3×D3×Dic3C211yesmaximal, characteristic, complemented
4C3×#3750C211yesmaximal, characteristic, complemented
5C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
7C3×Dic32C211yesmaximal, characteristic, complemented
8C3×C4×#67—31nomaximal
9C3×#67⋊C4—31nomaximal
10#63879C311yesmaximal, characteristic, direct product factor
11C22×C32×D3C2211yescharacteristic
12C22×C32×D3C2211yescharacteristic
13C2×C33×C4C2211yescharacteristic
14C2×C3×C3⋊Dic3C2211yescharacteristic
15C2×C3×C3⋊Dic3C2211yescharacteristic
16C2×C32×Dic3C2211yescharacteristic
17C2×C32×Dic3C2211yescharacteristic
18C32×C4×D3—22no—
19C3×#625C414yescomplemented
20C3×D3×Dic3—22no—
21C22×C32×C4—31no—
22C2×C3×#67—31no—
23C2×C3×#67—31no—
24C22×C3×Dic3—31no—
25C2×C3×C4×D3—21no—
26C2×C3×C4×D3—31no—
27C2×C3×C4×D3D311yescharacteristic, complemented
28C2×C3×C4×D3C2×C311yescharacteristic, complemented
29C2×#625C2×C311yescharacteristic
30C2×D3×Dic3C2×C311yescharacteristic, complemented
31C32×C22⋊C4—31no—
32#3750C2×C311yescharacteristic, complemented
33C3×#217—31no—
34C3×(C2×D3)⋊C4—21no—
35C3×(C2×D3)⋊C4—31no—
36C3×(C2×D3)⋊C4D311yescharacteristic, complemented
37C3×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
38C3×Dic3⋊C4—31no—
39C3×Dic3⋊C4—31no—
40C3×Dic3⋊C4—61no—
41C3×C4×Dic3—31no—
42C3×C4×Dic3—31no—
43(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
44Dic32C2×C311yescharacteristic, complemented
45C22×C33C2311yescharacteristic
46C2×C32×D3—21no—
47C2×C32×D3—21no—
48C2×C32×D3—21no—
49C2×C32×D3—21no—
50C2×C32×D3C2×C412yescomplemented
51C2×C32×D3C2×C412yescomplemented
52C33×C4—21no—
53C3×C3⋊Dic3—21no—
54C3×C3⋊Dic3C2×C412yescomplemented
55C32×Dic3—21no—
56C32×Dic3D412yescomplemented
57C3×C4×D4—91no—
58C4×#67—31no—
59#67⋊C4—31no—
60C23×C32—31no—
61C23×C32—31no—
62C22×C3×D3—21no—
63C22×C3×D3—21no—
64C22×C3×D3C2×D311yescharacteristic
65C22×C3×D3C2×D311yescharacteristic
66C22×C3×D3C22×C311yescharacteristic
67C22×C3×D3C22×C311yescharacteristic
68C2×C32×C4—21no—
69C2×C32×C4—21no—
70C2×C32×C4—21no—
71C2×C32×C4—31no—
72C2×C32×C4—31no—
73C2×C32×C4—41no—
74C2×C32×C4—62no—
75C2×C32×C4C2×D311yescharacteristic
76C2×C32×C4C2×D311yescharacteristic
77C2×C32×C4C22×C311yescharacteristic
78C2×C3⋊Dic3C22×C311yescharacteristic
79C2×C3⋊Dic3C22×C311yescharacteristic
80C3×#67—34no—
81C3×#67—34no—
82C2×C3×Dic3—21no—
83C2×C3×Dic3—21no—
84C2×C3×Dic3—31no—
85C2×C3×Dic3—31no—
86C2×C3×Dic3—31no—
87C2×C3×Dic3—31no—
88C2×C3×Dic3—61no—
89C2×C3×Dic3—61no—
90C2×C3×Dic3—62no—
91C2×C3×Dic3C2×D311yescharacteristic
92C2×C3×Dic3C2×D311yescharacteristic
93C2×C3×Dic3C22×C311yescharacteristic
94C2×C3×Dic3C22×C311yescharacteristic
95C3×C4×D3—24no—
96C3×C4×D3—22no—
97C3×C4×D3—22no—
98C3×C4×D3—62no—
99#625C3×C414yescomplemented
100D3×Dic3—22no—
101C2×C33C22×C411yescharacteristic
102C2×C33C2×D411yescharacteristic
103C2×C33#4111yescharacteristic
104C32×D3—22no—
105C32×D3—22no—
106C2×C3×D4—91no—
107C22×C3×C4—31no—
108C22×C3×C4—31no—
109C22×C3×C4—61no—
110C22×C3×C4—91no—
111C2×#67—31no—
112C2×#67—31no—
113C22×Dic3—31no—
114C2×C4×D3—31no—
115C2×C4×D3C3×D311yescharacteristic, complemented
116C3×C4⋊C4—91no—
117C3×C22⋊C4—31no—
118C3×C22⋊C4—31no—
119C3×C22⋊C4—61no—
120C3×C22⋊C4—91no—
121C3×C42—91no—
122#217—31no—
123(C2×D3)⋊C4—31no—
124(C2×D3)⋊C4C3×D311yescharacteristic, complemented
125Dic3⋊C4—31no—
126Dic3⋊C4—31no—
127Dic3⋊C4—61no—
128C4×Dic3—31no—
129C4×Dic3—31no—
130C22×C32—21no—
131C22×C32—21no—
132C22×C32—21no—
133C22×C32—32no—
134C22×C32—32no—
135C22×C32—41no—
136C22×C32—61no—
137C22×C32—61no—
138C22×C32—61no—
139C22×C32—61no—
140C22×C32C22×D311yescharacteristic
141C22×C32C22×D311yescharacteristic
142C22×C32C23×C311yescharacteristic
143C2×C3×D3—22no—
144C2×C3×D3—22no—
145C2×C3×D3—21no—
146C2×C3×D3—21no—
147C2×C3×D3—21no—
148C2×C3×D3—21no—
149C2×C3×D3—21no—
150C2×C3×D3—21no—
151C2×C3×D3—21no—
152C2×C3×D3—21no—
153C2×C3×D3—22no—
154C2×C3×D3—22no—
155C2×C3×D3—41no—
156C2×C3×D3—41no—
157C2×C3×D3C4×D312yescomplemented
158C2×C3×D3C4×D312yescomplemented
159C2×C3×D3C2×C3×C412yescomplemented
160C2×C3×D3C2×C3×C412yescomplemented
161C32×C4—21no—
162C32×C4—22no—
163C32×C4—21no—
164C32×C4—21no—
165C32×C4—32no—
166C32×C4—41no—
167C32×C4—41no—
168C32×C4—42no—
169C32×C4—61no—
170C3⋊Dic3—21no—
171C3⋊Dic3C2×C3×C412yescomplemented
172C3×Dic3—21no—
173C3×Dic3—21no—
174C3×Dic3—22no—
175C3×Dic3—32no—
176C3×Dic3—32no—
177C3×Dic3—41no—
178C3×Dic3—62no—
179C3×Dic3—61no—
180C3×Dic3—61no—
181C3×Dic3—121no—
182C3×Dic3#6712yescomplemented
183C3×Dic3C3×D412yescomplemented
184C4×D4—91noSylow
185C33C4×D411yescharacteristic, complemented, Sylow
186C23×C3—31no—
187C23×C3—31no—
188C23×C3—31no—
189C23×C3—31no—
190C23×C3—61no—
191C23×C3—61no—
192C22×D3C2×C3×D311yescharacteristic
193C22×D3C2×C3×D311yescharacteristic
194C3×D4—94no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—31no—
199C2×C3×C4—31no—
200C2×C3×C4—31no—
201C2×C3×C4—31no—
202C2×C3×C4—41no—
203C2×C3×C4—61no—
204C2×C3×C4—61no—
205C2×C3×C4—62no—
206C2×C3×C4—62no—
207C2×C3×C4—64no—
208C2×C3×C4—91no—
209C2×C3×C4—91no—
210C2×C3×C4—182no—
211C2×C3×C4D3211yescharacteristic
212C2×C3×C4C2×C3×D311yescharacteristic
213C2×C3×C4C2×C3×D311yescharacteristic
214#67—34no—
215#67—34no—
216C2×Dic3—31no—
217C2×Dic3—31no—
218C2×Dic3—31no—
219C2×Dic3—31no—
220C2×Dic3—61no—
221C2×Dic3—61no—
222C2×Dic3—62no—
223C2×Dic3C2×C3×D311yescharacteristic
224C2×Dic3C2×C3×D311yescharacteristic
225C4×D3—22no—
226C4×D3—62no—
227C2×C32—21no—
228C2×C32—21no—
229C2×C32—21no—
230C2×C32—21no—
231C2×C32—21no—
232C2×C32—21no—
233C2×C32—21no—
234C2×C32—21no—
235C2×C32—21no—
236C2×C32—41no—
237C2×C32—41no—
238C2×C32—41no—
239C2×C32—62no—
240C2×C32—62no—
241C2×C32C2×C4×D311yescharacteristic
242C2×C32C2×C4×D311yescharacteristic
243C2×C32#23511yescharacteristic
244C2×C32D3×D411yescharacteristic
245C2×C32#23711yescharacteristic
246C2×C32C2×#6711yescharacteristic
247C2×C32C22×C3×C411yescharacteristic
248C2×C32C2×C3×D411yescharacteristic
249C2×C32C3×#4111yescharacteristic
250C3×D3—24no—
251C3×D3—22no—
252C3×D3—22no—
253C3×D3—22no—
254C3×D3—22no—
255C3×D3—42no—
256C2×D4—91no—
257C22×C4—31no—
258C22×C4—91no—
259C4⋊C4—91no—
260C22⋊C4—31no—
261C22⋊C4—91no—
262C42—91no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—32no—
267C22×C3—32no—
268C22×C3—32no—
269C22×C3—32no—
270C22×C3—41no—
271C22×C3—62no—
272C22×C3—62no—
273C22×C3—62no—
274C22×C3—62no—
275C22×C3—61no—
276C22×C3—61no—
277C22×C3—61no—
278C22×C3—61no—
279C22×C3—61no—
280C22×C3—61no—
281C22×C3—61no—
282C22×C3—61no—
283C22×C3—121no—
284C22×C3—121no—
285C22×C3C2×D3211yescharacteristic
286C22×C3C22×C3×D311yescharacteristic
287C22×C3C22×C3×D311yescharacteristic
288C2×D3—21no—
289C2×D3—21no—
290C2×D3—21no—
291C2×D3—21no—
292C2×D3C3×C4×D312yescomplemented
293C2×D3C3×C4×D312yescomplemented
294C3×C4—22no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—32no—
299C3×C4—32no—
300C3×C4—41no—
301C3×C4—41no—
302C3×C4—42no—
303C3×C4—62no—
304C3×C4—61no—
305C3×C4—61no—
306C3×C4—92no—
307C3×C4—121no—
308C3×C4—181no—
309Dic3—21no—
310Dic3—32no—
311Dic3—32no—
312Dic3—62no—
313Dic3—61no—
314Dic3—61no—
315Dic3—121no—
316Dic3C3×#6712yescomplemented
317C32—21no—
318C32—21no—
319C32—21no—
320C32—41no—
321C32#67⋊C411yescharacteristic, complemented
322C32C4×#6711yescharacteristic, complemented
323C32C3×C4×D411yescharacteristic, complemented
324C23—31no—
325C23—31no—
326D4—94no—
327C2×C4—31no—
328C2×C4—31no—
329C2×C4—62no—
330C2×C4—91no—
331C2×C4—91no—
332C2×C4—182no—
333C2×C4C3×D3211yescharacteristic
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—41no—
344C2×C3—41no—
345C2×C3—41no—
346C2×C3—64no—
347C2×C3—62no—
348C2×C3—62no—
349C2×C3—62no—
350C2×C3—62no—
351C2×C3—122no—
352C2×C3#379511yescharacteristic
353C2×C3C4×D3211yescharacteristic
354C2×C3D3×#6711yescharacteristic
355C2×C3C2×C3×C4×D311yescharacteristic
356C2×C3C2×C3×C4×D311yescharacteristic
357C2×C3C3×#23511yescharacteristic
358C2×C3C3×D3×D411yescharacteristic
359C2×C3C3×#23711yescharacteristic
360C2×C3C2×C3×#6711yescharacteristic
361D3—22no—
362D3—22no—
363C22—32no—
364C22—32no—
365C22—61no—
366C22—61no—
367C22—61no—
368C22—61no—
369C22C2×C3×D3211yescharacteristic
370C4—21no—
371C4—32no—
372C4—61no—
373C4—92no—
374C4—181no—
375C3—21no—
376C3—21no—
377C3—21no—
378C3—41no—
379C3#6387911yescharacteristic, direct product factor
380C3C3×#67⋊C411yescharacteristic, complemented
381C3C3×C4×#6711yescharacteristic, complemented
382C2—62no—
383C2—62no—
384C2C3×#379511yescharacteristic
385C2C3×C4×D3211yescharacteristic
386C2C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C2×D32
commutatorC2×C32C22×C3×C4
FrattiniC22C2×C3×D32
FittingC2×C33×C4C22
socleC22×C33C23
prime radicalC2×C3×#625C2
cosocleC22×C32C23×C3
hypercenterC2×C3×C4D32
hypocenterC32C3×C4×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D3C2semidirect
3. C2×C3×D3×Dic3C2semidirect
4. C3×#3750C2semidirect
5. C32×(C2×D3)⋊C4C2semidirect
6. C3×(C2×D3)⋊Dic3C2semidirect
7. C3×Dic32C2semidirect
10. #63879C3direct (N × H)
19. C3×#625C4semidirect
27. C2×C3×C4×D3D3semidirect
28. C2×C3×C4×D3C2×C3semidirect
30. C2×D3×Dic3C2×C3semidirect
32. #3750C2×C3semidirect
36. C3×(C2×D3)⋊C4D3semidirect
37. C3×(C2×D3)⋊C4C2×C3semidirect
43. (C2×D3)⋊Dic3C2×C3semidirect
44. Dic32C2×C3semidirect
50. C2×C32×D3C2×C4semidirect
51. C2×C32×D3C2×C4semidirect
54. C3×C3⋊Dic3C2×C4semidirect
56. C32×Dic3D4semidirect
99. #625C3×C4semidirect
115. C2×C4×D3C3×D3semidirect
124. (C2×D3)⋊C4C3×D3semidirect
157. C2×C3×D3C4×D3semidirect
158. C2×C3×D3C4×D3semidirect
159. C2×C3×D3C2×C3×C4semidirect
160. C2×C3×D3C2×C3×C4semidirect
171. C3⋊Dic3C2×C3×C4semidirect
182. C3×Dic3#67semidirect
183. C3×Dic3C3×D4semidirect
185. C33C4×D4semidirect
292. C2×D3C3×C4×D3semidirect
293. C2×D3C3×C4×D3semidirect
316. Dic3C3×#67semidirect
321. C32#67⋊C4semidirect
322. C32C4×#67semidirect
323. C32C3×C4×D4semidirect
379. C3#63879direct (N × H)
380. C3C3×#67⋊C4semidirect
381. C3C3×C4×#67semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D32
C2×C3×#6252
C2×C3×D3×Dic32
C3×#37502
C32×(C2×D3)⋊C42
C3×(C2×D3)⋊Dic32
C3×Dic322
C3×C4×#673
C3×#67⋊C43
#638793