Finite Group Databasebeta

← C3×#74148 #11801212

Subgroups — C3×#74148 #11801212

Order 1152.

1389 conjugacy classes of subgroups.

The subgroup lattice has 361 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#892C212yesmaximal
2C2×C3×C42×D3C211yesmaximal, characteristic
3C32×#382C211yesmaximal, characteristic, complemented
4C3×#4975C212yesmaximal, complemented
5C3×#4936C211yesmaximal, characteristic, complemented
6C3×#4667C214yesmaximal
7C3×#4649C214yesmaximal, complemented
8C3×#2285—31nomaximal
9#74148C311yesmaximal, characteristic, direct product factor
10C22×C3×C4×D3C2212yes—
11C22×C3×C4×D3C2211yescharacteristic
12C2×C32×C4⋊C4C2212yes—
13C2×C32×C42C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4C2214yes—
15C2×C3×C4⋊Dic3C2212yes—
16C2×C3×Dic3⋊C4C2218yes—
17C2×C3×C4×Dic3C2214yes—
18C2×C3×C4×Dic3C2212yes—
19C2×C3×C4×Dic3C2211yescharacteristic
20C3×#892—28no—
21C3×C42×D3C418yescomplemented
22C32×#95C2214yes—
23C3×C3⋊#95C2214yes—
24C2×C3×#117—32no—
25C22×C3×C42—31no—
26C2×#892C2×C312yes—
27C2×C42×D3C2×C311yescharacteristic
28C3×#384—32no—
29C3×#382—21no—
30C3×#382—31no—
31C3×#382D311yescharacteristic, complemented
32C3×#382C2×C311yescharacteristic, complemented
33C3×#380—34no—
34C3×C4×C4⋊C4—34no—
35#4975C2×C312yescomplemented
36#4936C2×C311yescharacteristic, complemented
37#4667C2×C314yes—
38#4649C2×C314yescomplemented
39C23×C3×D3C2311yescharacteristic
40C22×C32×C4C2314yes—
41C22×C32×C4C2312yes—
42C22×C32×C4C2311yescharacteristic
43C22×C3×Dic3C2314yes—
44C22×C3×Dic3C2311yescharacteristic
45C22×C3×Dic3C2312yes—
46C2×C3×C4×D3—28no—
47C2×C3×C4×D3C2×C418yes—
48C2×C3×C4×D3C2×C414yes—
49C2×C3×C4×D3D414yes—
50C2×C3×C4×D3Q814yes—
51C32×C4⋊C4—24no—
52C32×C42C2×C414yes—
53C3×(C2×D3)⋊C4—28no—
54C3×C4⋊Dic3—24no—
55C3×Dic3⋊C4—216no—
56C3×C4×Dic3—28no—
57C3×C4×Dic3C2×C418yes—
58C3×C4×Dic3C2×C414yes—
59#2285—31noSylow
60C23×C3×C4—31no—
61C23×C3×C4—32no—
62C22×C4×D3C22×C312yes—
63C22×C4×D3C22×C311yescharacteristic
64C3×#117—68no—
65C2×C3×C4⋊C4—22no—
66C2×C3×C4⋊C4—38no—
67C2×C3×C4⋊C4—32no—
68C2×C3×C4⋊C4C2×D312yes—
69C2×C3×C4⋊C4C22×C312yes—
70C2×C3×C22⋊C4—34no—
71C2×C3×C42—21no—
72C2×C3×C42—32no—
73C2×C3×C42—31no—
74C2×C3×C42—38no—
75C2×C3×C42—34no—
76C2×C3×C42C2×D311yescharacteristic
77C2×C3×C42C22×C311yescharacteristic
78C2×(C2×D3)⋊C4C22×C314yes—
79C2×C4⋊Dic3C22×C312yes—
80C2×Dic3⋊C4C22×C318yes—
81C2×C4×Dic3C22×C314yes—
82C2×C4×Dic3C22×C312yes—
83C2×C4×Dic3C22×C311yescharacteristic
84#892—28no—
85C42×D3C3×C418yescomplemented
86C3×#95—24no—
87C3×#95—34no—
88C3×#95C2×D314yes—
89C3×#95C22×C314yes—
90C3⋊#95C22×C314yes—
91C23×C32C2411yescharacteristic
92C22×C3×D3—24no—
93C22×C3×D3C22×C412yes—
94C22×C3×D3C2×D412yes—
95C22×C3×D3C2×Q812yes—
96C2×C32×C4—24no—
97C2×C32×C4—24no—
98C2×C32×C4—28no—
99C2×C32×C4C22×C414yes—
100C2×C32×C4C22×C412yes—
101C2×C32×C4C2×D412yes—
102C2×C32×C4C2×Q812yes—
103C2×C3×Dic3—24no—
104C2×C3×Dic3—28no—
105C2×C3×Dic3C22×C412yes—
106C2×C3×Dic3C22×C414yes—
107C2×C3×Dic3C2×D412yes—
108C2×C3×Dic3C2×Q812yes—
109C2×C3×Dic3#4118yes—
110C3×C4×D3—216no—
111C3×C4×D3C4⋊C4116yescomplemented
112C2×#117—32no—
113C22×C42—31no—
114#384—32no—
115#382—31no—
116#382C3×D311yescharacteristic, complemented
117#380—34no—
118C4×C4⋊C4—34no—
119C24×C3—31no—
120C23×D3C23×C311yescharacteristic
121C22×C3×C4—21no—
122C22×C3×C4—22no—
123C22×C3×C4—24no—
124C22×C3×C4—31no—
125C22×C3×C4—32no—
126C22×C3×C4—34no—
127C22×C3×C4—34no—
128C22×C3×C4—34no—
129C22×C3×C4—38no—
130C22×C3×C4—34no—
131C22×C3×C4—68no—
132C22×C3×C4C22×D314yes—
133C22×C3×C4C22×D312yes—
134C22×C3×C4C22×D311yescharacteristic
135C22×C3×C4C23×C314yes—
136C22×C3×C4C23×C312yes—
137C22×C3×C4C23×C311yescharacteristic
138C22×Dic3C23×C314yes—
139C22×Dic3C23×C311yescharacteristic
140C22×Dic3C23×C312yes—
141C2×C4×D3—28no—
142C2×C4×D3C2×C3×C418yes—
143C2×C4×D3C2×C3×C414yes—
144C2×C4×D3C3×D414yes—
145C2×C4×D3C3×Q814yes—
146C3×C4⋊C4—24no—
147C3×C4⋊C4—24no—
148C3×C4⋊C4—44no—
149C3×C4⋊C4—616no—
150C3×C4⋊C4—64no—
151C3×C22⋊C4—68no—
152C3×C42—24no—
153C3×C42—38no—
154C3×C42—34no—
155C3×C42—68no—
156C3×C42C4×D314yes—
157C3×C42C2×C3×C414yes—
158(C2×D3)⋊C4—28no—
159C4⋊Dic3—24no—
160Dic3⋊C4—216no—
161C4×Dic3—28no—
162C4×Dic3C2×C3×C418yes—
163C4×Dic3C2×C3×C414yes—
164C22×C32C23×C411yescharacteristic
165C22×C32C22×D411yescharacteristic
166C22×C32C22×Q811yescharacteristic
167C22×C32C2×#4114yes—
168C2×C3×D3—24no—
169C2×C3×D3—24no—
170C2×C3×D3—24no—
171C2×C3×D3C2×C4⋊C414yes—
172C32×C4—24no—
173C32×C4—44no—
174C32×C4C2×C4⋊C414yes—
175C3×Dic3—44no—
176C3×Dic3C2×C4⋊C414yes—
177C3×Dic3#11718yescomplemented
178C23×C4—31no—
179C23×C4—32no—
180#117—68no—
181C2×C4⋊C4—32no—
182C2×C4⋊C4—38no—
183C2×C4⋊C4C2×C3×D312yes—
184C2×C22⋊C4—34no—
185C2×C42—32no—
186C2×C42—31no—
187C2×C42—38no—
188C2×C42—34no—
189C2×C42C2×C3×D311yescharacteristic
190#95—34no—
191#95C2×C3×D314yes—
192C23×C3—21no—
193C23×C3—32no—
194C23×C3—32no—
195C23×C3—32no—
196C23×C3—64no—
197C23×C3C23×D311yescharacteristic
198C23×C3C24×C311yescharacteristic
199C22×D3—24no—
200C22×D3C22×C3×C412yes—
201C22×D3C2×C3×D412yes—
202C22×D3C2×C3×Q812yes—
203C2×C3×C4—24no—
204C2×C3×C4—24no—
205C2×C3×C4—24no—
206C2×C3×C4—28no—
207C2×C3×C4—24no—
208C2×C3×C4—28no—
209C2×C3×C4—22no—
210C2×C3×C4—24no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4—32no—
214C2×C3×C4—34no—
215C2×C3×C4—32no—
216C2×C3×C4—32no—
217C2×C3×C4—38no—
218C2×C3×C4—316no—
219C2×C3×C4—44no—
220C2×C3×C4—44no—
221C2×C3×C4—48no—
222C2×C3×C4—616no—
223C2×C3×C4—64no—
224C2×C3×C4—68no—
225C2×C3×C4C2×C4×D314yes—
226C2×C3×C4C2×C4×D312yes—
227C2×C3×C4D3×D412yes—
228C2×C3×C4D3×Q812yes—
229C2×C3×C4C22×C3×C414yes—
230C2×C3×C4C22×C3×C412yes—
231C2×C3×C4C2×C3×D412yes—
232C2×C3×C4C2×C3×Q812yes—
233C2×Dic3—24no—
234C2×Dic3—28no—
235C2×Dic3C22×C3×C412yes—
236C2×Dic3C22×C3×C414yes—
237C2×Dic3C2×C3×D412yes—
238C2×Dic3C2×C3×Q812yes—
239C2×Dic3C3×#4118yes—
240C4×D3—216no—
241C4×D3C3×C4⋊C4116yescomplemented
242C2×C32C22×C4⋊C411yescharacteristic
243C2×C32C2×#11712yes—
244C2×C32#53212yes—
245C2×C32#53312yes—
246C3×D3—24no—
247C24—31no—
248C22×C4—31no—
249C22×C4—32no—
250C22×C4—34no—
251C22×C4—34no—
252C22×C4—34no—
253C22×C4—38no—
254C22×C4—34no—
255C22×C4—68no—
256C22×C4C22×C3×D314yes—
257C22×C4C22×C3×D312yes—
258C22×C4C22×C3×D311yescharacteristic
259C4⋊C4—24no—
260C4⋊C4—616no—
261C4⋊C4—64no—
262C22⋊C4—68no—
263C42—38no—
264C42—34no—
265C42—68no—
266C42C3×C4×D314yes—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—24no—
271C22×C3—34no—
272C22×C3—64no—
273C22×C3—64no—
274C22×C3—64no—
275C22×C3C22×C4×D311yescharacteristic
276C22×C3C2×D3×D411yescharacteristic
277C22×C3C2×D3×Q811yescharacteristic
278C22×C3D3×#4114yes—
279C22×C3C23×C3×C411yescharacteristic
280C22×C3C22×C3×D411yescharacteristic
281C22×C3C22×C3×Q811yescharacteristic
282C22×C3C2×C3×#4114yes—
283C2×D3—24no—
284C2×D3—24no—
285C2×D3—24no—
286C2×D3C2×C3×C4⋊C414yes—
287C3×C4—24no—
288C3×C4—24no—
289C3×C4—24no—
290C3×C4—34no—
291C3×C4—38no—
292C3×C4—44no—
293C3×C4—44no—
294C3×C4—44no—
295C3×C4—84no—
296C3×C4—124no—
297C3×C4D3×C4⋊C414yes—
298C3×C4C2×C3×C4⋊C414yes—
299Dic3—44no—
300Dic3C2×C3×C4⋊C414yes—
301Dic3C3×#11718yescomplemented
302C32#228511yescharacteristic, complemented, Sylow
303C23—32no—
304C23—32no—
305C23—32no—
306C23—64no—
307C23C23×C3×D311yescharacteristic
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—28no—
311C2×C4—32no—
312C2×C4—34no—
313C2×C4—32no—
314C2×C4—32no—
315C2×C4—38no—
316C2×C4—316no—
317C2×C4—616no—
318C2×C4—64no—
319C2×C4—68no—
320C2×C4C2×C3×C4×D314yes—
321C2×C4C2×C3×C4×D312yes—
322C2×C4C3×D3×D412yes—
323C2×C4C3×D3×Q812yes—
324C2×C3—21no—
325C2×C3—22no—
326C2×C3—22no—
327C2×C3—22no—
328C2×C3—64no—
329C2×C3C2×D3×C4⋊C411yescharacteristic
330C2×C3D3×#11712yes—
331C2×C3#566812yes—
332C2×C3#568812yes—
333C2×C3C22×C3×C4⋊C411yescharacteristic
334C2×C3C2×C3×#11712yes—
335C2×C3C3×#53212yes—
336C2×C3C3×#53312yes—
337D3—24no—
338C22—34no—
339C22—64no—
340C22—64no—
341C22—64no—
342C22C22×C3×C4×D311yescharacteristic
343C22C2×C3×D3×D411yescharacteristic
344C22C2×C3×D3×Q811yescharacteristic
345C22C3×D3×#4114yes—
346C4—24no—
347C4—34no—
348C4—38no—
349C4—44no—
350C4—124no—
351C4C3×D3×C4⋊C414yes—
352C3—21no—
353C3#7414811yescharacteristic, direct product factor
354C3C3×#228511yescharacteristic, complemented
355C2—64no—
356C2C2×C3×D3×C4⋊C411yescharacteristic
357C2C3×D3×#11712yes—
358C2C3×#566812yes—
359C2C3×#568812yes—
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#382C2
socleC23×C32C24
prime radicalC23×C3×D3C23
cosocleC23×C3C24×C3
hypercenterC3×#382D3
hypocenterC3C3×#2285
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#382

Complements

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

NH ≅ G/Ntype
3. C32×#382C2semidirect
4. C3×#4975C2semidirect
5. C3×#4936C2semidirect
7. C3×#4649C2semidirect
9. #74148C3direct (N × H)
21. C3×C42×D3C4semidirect
31. C3×#382D3semidirect
32. C3×#382C2×C3semidirect
35. #4975C2×C3semidirect
36. #4936C2×C3semidirect
38. #4649C2×C3semidirect
85. C42×D3C3×C4semidirect
111. C3×C4×D3C4⋊C4semidirect
116. #382C3×D3semidirect
177. C3×Dic3#117semidirect
241. C4×D3C3×C4⋊C4semidirect
301. Dic3C3×#117semidirect
302. C32#2285semidirect
353. C3#74148direct (N × H)
354. C3C3×#2285semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8922
C2×C3×C42×D32
C32×#3822
C3×#49752
C3×#49362
C3×#46672
C3×#46492
C3×#22853
#741483