Finite Group Databasebeta

← C3×#63964 #11723289

Subgroups — C3×#63964 #11723289

Order 864.

450 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×Dic3C211yesmaximal, characteristic
2C2×C3×#627C211yesmaximal, characteristic, complemented
3C3×#3757C211yesmaximal, characteristic
4C32×#217C211yesmaximal, characteristic
5C3×#3724C211yesmaximal, characteristic, complemented
6C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
7C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
8C3×#924—31nomaximal
9C3×#878—31nomaximal
10#63964C311yesmaximal, characteristic, direct product factor
11C23×C33C2211yescharacteristic
12C2×C3×C3⋊Dic3C2211yescharacteristic
13C2×C3×C3⋊Dic3C2211yescharacteristic
14C2×C32×Dic3—22no—
15C2×C32×Dic3C2211yescharacteristic
16C2×C32×Dic3C2211yescharacteristic
17C2×C32×Dic3C2211yescharacteristic
18C2×C32×Dic3C2211yescharacteristic
19C3×#627—22no—
20C22×C32×C4—31no—
21C22×C3×Dic3—21no—
22C22×C3×Dic3D311yescharacteristic
23C22×C3×Dic3C2×C311yescharacteristic
24C2×C3×Dic6—31no—
25C2×C3×Dic6—31no—
26C2×#627C2×C311yescharacteristic, complemented
27C32×C22⋊C4—31no—
28#3757C2×C311yescharacteristic
29C3×#217—21no—
30C3×#217—31no—
31C3×#217—31no—
32C3×#217—61no—
33C3×#217D311yescharacteristic
34C3×#217C2×C311yescharacteristic
35C3×C4⋊Dic3—31no—
36C3×C4⋊Dic3—31no—
37C3×Dic3⋊C4—31no—
38C3×Dic3⋊C4—31no—
39C3×Dic3⋊C4—31no—
40C3×Dic3⋊C4—31no—
41#3724C2×C311yescharacteristic, complemented
42Dic3⋊Dic3C2×C311yescharacteristic, complemented
43Dic3⋊Dic3C2×C311yescharacteristic, complemented
44C22×C33—21no—
45C22×C33—21no—
46C22×C33Q812yescomplemented
47C22×C33C2311yescharacteristic
48C3×C3⋊Dic3—21no—
49C3×C3⋊Dic3—21no—
50C32×Dic3—21no—
51C32×Dic3—21no—
52C32×Dic3—21no—
53C32×Dic3D412yes—
54C3×C22⋊Q8—91no—
55#924—31no—
56#878—31no—
57C23×C32—21no—
58C23×C32—21no—
59C23×C32—21no—
60C23×C32—41no—
61C23×C32C2×D311yescharacteristic
62C23×C32C2×D311yescharacteristic
63C23×C32C22×C311yescharacteristic
64C2×C32×C4—31no—
65C2×C32×C4—31no—
66C2×C32×C4—31no—
67C2×C32×C4—31no—
68C2×C32×C4—62no—
69C2×C3⋊Dic3C22×C311yescharacteristic
70C2×C3⋊Dic3C22×C311yescharacteristic
71C2×C3×Dic3—24no—
72C2×C3×Dic3—22no—
73C2×C3×Dic3—22no—
74C2×C3×Dic3—21no—
75C2×C3×Dic3—21no—
76C2×C3×Dic3—21no—
77C2×C3×Dic3—21no—
78C2×C3×Dic3—31no—
79C2×C3×Dic3—31no—
80C2×C3×Dic3—31no—
81C2×C3×Dic3—31no—
82C2×C3×Dic3—61no—
83C2×C3×Dic3—61no—
84C2×C3×Dic3C2×D311yescharacteristic
85C2×C3×Dic3C2×D311yescharacteristic
86C2×C3×Dic3C2×D311yescharacteristic
87C2×C3×Dic3C2×D311yescharacteristic
88C2×C3×Dic3C22×C311yescharacteristic
89C2×C3×Dic3C22×C311yescharacteristic
90C2×C3×Dic3C22×C311yescharacteristic
91C2×C3×Dic3C22×C311yescharacteristic
92C3×Dic6—62no—
93C3×Dic6—62no—
94#627—22no—
95C2×C33—22no—
96C2×C33C2×D411yescharacteristic
97C2×C33C2×Q811yescharacteristic
98C2×C33#4111yescharacteristic
99C2×C3×Q8—91no—
100C22×C3×C4—31no—
101C22×C3×C4—31no—
102C22×C3×C4—61no—
103C22×Dic3C3×D311yescharacteristic
104C2×Dic6—31no—
105C2×Dic6—31no—
106C3×C4⋊C4—91no—
107C3×C4⋊C4—91no—
108C3×C4⋊C4—91no—
109C3×C22⋊C4—31no—
110C3×C22⋊C4—31no—
111C3×C22⋊C4—61no—
112C3×C22⋊C4—91no—
113#217—31no—
114#217—31no—
115#217—61no—
116#217C3×D311yescharacteristic
117C4⋊Dic3—31no—
118C4⋊Dic3—31no—
119Dic3⋊C4—31no—
120Dic3⋊C4—31no—
121Dic3⋊C4—31no—
122Dic3⋊C4—31no—
123C22×C32—21no—
124C22×C32—21no—
125C22×C32—22no—
126C22×C32—22no—
127C22×C32—21no—
128C22×C32—21no—
129C22×C32—21no—
130C22×C32—21no—
131C22×C32—22no—
132C22×C32—22no—
133C22×C32—22no—
134C22×C32—21no—
135C22×C32—21no—
136C22×C32—21no—
137C22×C32—42no—
138C22×C32—41no—
139C22×C32—41no—
140C22×C32—41no—
141C22×C32—41no—
142C22×C32—41no—
143C22×C32—42no—
144C22×C32—42no—
145C22×C32Dic612yescomplemented
146C22×C32Dic612yescomplemented
147C22×C32C3×Q812yescomplemented
148C22×C32C22×D311yescharacteristic
149C22×C32C22×D311yescharacteristic
150C22×C32C23×C311yescharacteristic
151C32×C4—32no—
152C32×C4—61no—
153C32×C4—61no—
154C32×C4—61no—
155C3⋊Dic3—21no—
156C3⋊Dic3—21no—
157C3×Dic3—22no—
158C3×Dic3—21no—
159C3×Dic3—21no—
160C3×Dic3—21no—
161C3×Dic3—21no—
162C3×Dic3—21no—
163C3×Dic3—21no—
164C3×Dic3—22no—
165C3×Dic3—41no—
166C3×Dic3—41no—
167C3×Dic3—61no—
168C3×Dic3—61no—
169C3×Dic3—61no—
170C3×Dic3—61no—
171C3×Dic3—121no—
172C3×Dic3—121no—
173C3×Dic3#6712yes—
174C3×Dic3C3×D412yes—
175C22⋊Q8—91noSylow
176C33C22⋊Q811yescharacteristic, complemented, Sylow
177C23×C3—21no—
178C23×C3—21no—
179C23×C3—21no—
180C23×C3—41no—
181C23×C3D3211yescharacteristic
182C23×C3C2×C3×D311yescharacteristic
183C23×C3C2×C3×D311yescharacteristic
184C3×Q8—182no—
185C2×C3×C4—31no—
186C2×C3×C4—31no—
187C2×C3×C4—31no—
188C2×C3×C4—31no—
189C2×C3×C4—31no—
190C2×C3×C4—31no—
191C2×C3×C4—31no—
192C2×C3×C4—31no—
193C2×C3×C4—61no—
194C2×C3×C4—61no—
195C2×C3×C4—61no—
196C2×C3×C4—61no—
197C2×C3×C4—62no—
198C2×C3×C4—62no—
199C2×C3×C4—64no—
200C2×C3×C4—91no—
201C2×C3×C4—91no—
202C2×Dic3—22no—
203C2×Dic3—31no—
204C2×Dic3—31no—
205C2×Dic3—31no—
206C2×Dic3—31no—
207C2×Dic3—61no—
208C2×Dic3—61no—
209C2×Dic3C2×C3×D311yescharacteristic
210C2×Dic3C2×C3×D311yescharacteristic
211C2×Dic3C2×C3×D311yescharacteristic
212C2×Dic3C2×C3×D311yescharacteristic
213Dic6—62no—
214Dic6—62no—
215C2×C32—22no—
216C2×C32—24no—
217C2×C32—22no—
218C2×C32—22no—
219C2×C32—21no—
220C2×C32—21no—
221C2×C32—21no—
222C2×C32—21no—
223C2×C32—21no—
224C2×C32—21no—
225C2×C32—21no—
226C2×C32—21no—
227C2×C32—21no—
228C2×C32—41no—
229C2×C32—41no—
230C2×C32—41no—
231C2×C32—42no—
232C2×C32—42no—
233C2×C32—44no—
234C2×C32C2×Dic611yescharacteristic
235C2×C32C2×Dic611yescharacteristic
236C2×C32#23511yescharacteristic
237C2×C32D3×D411yescharacteristic
238C2×C32#23711yescharacteristic
239C2×C32C2×#6711yescharacteristic
240C2×C32C2×C3×D411yescharacteristic
241C2×C32C2×C3×Q811yescharacteristic
242C2×C32C3×#4111yescharacteristic
243C2×Q8—91no—
244C22×C4—31no—
245C4⋊C4—91no—
246C4⋊C4—91no—
247C4⋊C4—91no—
248C22⋊C4—31no—
249C22⋊C4—91no—
250C22×C3—22no—
251C22×C3—22no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—22no—
259C22×C3—22no—
260C22×C3—22no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—42no—
269C22×C3—42no—
270C22×C3—42no—
271C22×C3—41no—
272C22×C3#62712yescomplemented
273C22×C3C3×Dic612yescomplemented
274C22×C3C3×Dic612yescomplemented
275C22×C3C2×D3211yescharacteristic
276C22×C3C22×C3×D311yescharacteristic
277C22×C3C22×C3×D311yescharacteristic
278C3×C4—32no—
279C3×C4—32no—
280C3×C4—62no—
281C3×C4—62no—
282C3×C4—61no—
283C3×C4—61no—
284C3×C4—61no—
285C3×C4—61no—
286C3×C4—61no—
287C3×C4—61no—
288C3×C4—121no—
289C3×C4—121no—
290C3×C4—181no—
291C3×C4—181no—
292Dic3—21no—
293Dic3—21no—
294Dic3—21no—
295Dic3—61no—
296Dic3—61no—
297Dic3—61no—
298Dic3—61no—
299Dic3—121no—
300Dic3—121no—
301Dic3C3×#6712yes—
302C32—21no—
303C32—21no—
304C32—21no—
305C32—41no—
306C32#87811yescharacteristic, complemented
307C32#92411yescharacteristic, complemented
308C32C3×C22⋊Q811yescharacteristic, complemented
309C23C3×D3211yescharacteristic
310Q8—182no—
311C2×C4—31no—
312C2×C4—31no—
313C2×C4—31no—
314C2×C4—31no—
315C2×C4—62no—
316C2×C4—91no—
317C2×C4—91no—
318C2×C3—24no—
319C2×C3—22no—
320C2×C3—22no—
321C2×C3—22no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—42no—
332C2×C3—42no—
333C2×C3—44no—
334C2×C3—41no—
335C2×C3—41no—
336C2×C3—41no—
337C2×C3#380411yescharacteristic
338C2×C3C2×#62711yescharacteristic
339C2×C3D3×#6711yescharacteristic
340C2×C3C2×C3×Dic611yescharacteristic
341C2×C3C2×C3×Dic611yescharacteristic
342C2×C3C3×#23511yescharacteristic
343C2×C3C3×D3×D411yescharacteristic
344C2×C3C3×#23711yescharacteristic
345C2×C3C2×C3×#6711yescharacteristic
346C22—21no—
347C22—21no—
348C22C3×#62712yescomplemented
349C22C2×C3×D3211yescharacteristic
350C4—32no—
351C4—61no—
352C4—61no—
353C4—61no—
354C4—181no—
355C4—181no—
356C3—21no—
357C3—21no—
358C3—21no—
359C3—41no—
360C3#6396411yescharacteristic, direct product factor
361C3C3×#87811yescharacteristic, complemented
362C3C3×#92411yescharacteristic, complemented
363C2—22no—
364C2C3×#380411yescharacteristic
365C2C2×C3×#62711yescharacteristic
366C2C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C2×D32
commutator, cosocleC22×C32C23×C3
FrattiniC22C2×C3×D32
Fitting, prime radicalC23×C33C22
socleC22×C33C23
hypercenterC23×C3D32
hypocenterC32C3×C22⋊Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
2. C2×C3×#627C2semidirect
5. C3×#3724C2semidirect
6. C3×Dic3⋊Dic3C2semidirect
7. C3×Dic3⋊Dic3C2semidirect
10. #63964C3direct (N × H)
26. C2×#627C2×C3semidirect
41. #3724C2×C3semidirect
42. Dic3⋊Dic3C2×C3semidirect
43. Dic3⋊Dic3C2×C3semidirect
46. C22×C33Q8semidirect
145. C22×C32Dic6semidirect
146. C22×C32Dic6semidirect
147. C22×C32C3×Q8semidirect
176. C33C22⋊Q8semidirect
272. C22×C3#627semidirect
273. C22×C3C3×Dic6semidirect
274. C22×C3C3×Dic6semidirect
306. C32#878semidirect
307. C32#924semidirect
308. C32C3×C22⋊Q8semidirect
348. C22C3×#627semidirect
360. C3#63964direct (N × H)
361. C3C3×#878semidirect
362. C3C3×#924semidirect

Maximal subgroups

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

subgroupindex
C22×C32×Dic32
C2×C3×#6272
C3×#37572
C32×#2172
C3×#37242
C3×Dic3⋊Dic32
C3×#9243
C3×#8783
#639643