Finite Group Databasebeta

← C3×#85874 #11904541

Subgroups — C3×#85874 #11904541

Order 1152.

3205 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic, complemented
2C22×C3×#239C211yesmaximal, characteristic, complemented
3C32×#519C211yesmaximal, characteristic, complemented
4C3×#5577C218yesmaximal, complemented
5C3×#5576C218yesmaximal, complemented
6C3×#5525C216yesmaximal, complemented
7C3×#5524C216yesmaximal, complemented
8C3×#3487—31nomaximal
9#85874C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C3×#1007—28no—
12C2×C3×#239—28no—
13C2×C3×#239C2218yes—
14C2×C3×#239C2214yescomplemented
15C2×C3×D3×Q8C2214yescomplemented
16C2×C3×#235C2216yes—
17C22×C3×D12C2213yes—
18C22×C3×C4×D3C2213yes—
19C32×C4×Q8C2218yescomplemented
20C32×#117C2216yes—
21C3×#897C22112yescomplemented
22C3×#895C22112yescomplemented
23C3×#895C22124yescomplemented
24C3×#886C2214yes—
25C3×#882C22112yes—
26C3×#875C22112yescomplemented
27C3×#874C22112yescomplemented
28C3×C4×D12C22124yescomplemented
29C2×C3×2−1+4—31no—
30C22×C3×#41—31no—
31C2×#1007C2×C311yescharacteristic, complemented
32C22×#239C2×C311yescharacteristic, complemented
33C3×#550—38no—
34C3×#548—38no—
35C3×#535—36no—
36C3×#525—36no—
37C3×#519—21no—
38C3×#519D311yescharacteristic, complemented
39C3×#519C2×C311yescharacteristic, complemented
40#5577C2×C318yescomplemented
41#5576C2×C318yescomplemented
42#5525C2×C316yescomplemented
43#5524C2×C316yescomplemented
44C23×C3×D3C2313yes—
45C2×C32×Q8D418yescomplemented
46C2×C32×Q8C2314yes—
47C22×C32×C4C2313yes—
48C2×C3×#67C2314yes—
49C22×C3×Dic3C2311yescharacteristic
50C3×#239—232no—
51C3×#239—216no—
52C3×D3×Q8—216no—
53C3×#235—224no—
54C2×C3×D12—212no—
55C2×C3×D12C23112yes—
56C2×C3×D12C2316yes—
57C2×C3×D12C23124yes—
58C2×C3×C4×D3—212no—
59C2×C3×C4×D3C23112yes—
60C2×C3×C4×D3C23112yes—
61C2×C3×Dic6C2316yes—
62C32×C4⋊C4C23112yes—
63C32×C22⋊C4C2314yes—
64C32×C42C23112yes—
65C3×(C2×D3)⋊C4C23124yes—
66C3×(C2×D3)⋊C4C2318yes—
67C3×C4⋊Dic3C2318yes—
68#3487—31noSylow
69C3×2−1+4—68no—
70C2×C3×#41—38no—
71C2×C3×#41—34no—
72C2×C3×#41—36no—
73C2×C3×#41—68no—
74C22×C3×Q8—21no—
75C22×C3×Q8—34no—
76C22×C3×Q8C2×D311yescharacteristic
77C22×C3×Q8C22×C311yescharacteristic
78C22×C3×D4—33no—
79C23×C3×C4—33no—
80#1007—28no—
81C2×#239—28no—
82C2×#239C22×C318yes—
83C2×#239C22×C314yescomplemented
84C2×D3×Q8C22×C314yescomplemented
85C2×#235C22×C316yes—
86C22×D12C22×C313yes—
87C22×C4×D3C22×C313yes—
88C3×#127—312no—
89C3×#124—312no—
90C3×#123—34no—
91C3×C22⋊Q8—312no—
92C3×#121—312no—
93C3×#121—324no—
94C3×#120—312no—
95C3×C4×Q8—28no—
96C3×C4×Q8C2×D318yescomplemented
97C3×C4×Q8C22×C318yescomplemented
98C3×C4×D4—324no—
99C3×#117—26no—
100C3×#117C2×D316yes—
101C3×#117C22×C316yes—
102#897C22×C3112yescomplemented
103#895C22×C3112yescomplemented
104#895C22×C3124yescomplemented
105#886C22×C314yes—
106#882C22×C3112yes—
107#875C22×C3112yescomplemented
108#874C22×C3112yescomplemented
109C4×D12C22×C3124yescomplemented
110C23×C32C2411yescharacteristic
111C22×C3×D3—26no—
112C22×C3×D3—46no—
113C22×C3×D3C2416yes—
114C22×C3×D3C2414yes—
115C32×Q8C2×D4116yes—
116C2×C32×C4C2×D4112yes—
117C2×C32×C4C2418yes—
118C2×C32×C4C2416yes—
119C3×#67—28no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3C2412yes—
122C2×C3×Dic3C2414yes—
123C3×D12—224no—
124C3×D12—212no—
125C3×D12—424no—
126C3×C4×D3—224no—
127C3×C4×D3—224no—
128C3×Dic6—212no—
129C2×2−1+4—31no—
130C22×#41—31no—
131#550—38no—
132#548—38no—
133#535—36no—
134#525—36no—
135#519C3×D311yescharacteristic, complemented
136C24×C3—33no—
137C23×D3C23×C313yes—
138C3×#41—632no—
139C3×#41—616no—
140C3×#41—624no—
141C2×C3×Q8—28no—
142C2×C3×Q8—24no—
143C2×C3×Q8—36no—
144C2×C3×Q8—616no—
145C2×C3×Q8D1218yescomplemented
146C2×C3×Q8C3×D418yescomplemented
147C2×C3×Q8C22×D314yes—
148C2×C3×Q8C23×C314yes—
149C2×C3×D4—34no—
150C2×C3×D4—312no—
151C2×C3×D4—36no—
152C2×C3×D4—324no—
153C2×C3×D4—612no—
154C22×C3×C4—23no—
155C22×C3×C4—31no—
156C22×C3×C4—312no—
157C22×C3×C4—312no—
158C22×C3×C4—612no—
159C22×C3×C4C22×D313yes—
160C22×C3×C4C23×C313yes—
161C2×#67C23×C314yes—
162C22×Dic3C23×C311yescharacteristic
163#239—232no—
164#239—216no—
165D3×Q8—216no—
166#235—224no—
167C2×D12—212no—
168C2×D12C23×C316yes—
169C2×D12C23×C3112yes—
170C2×D12C23×C3124yes—
171C2×C4×D3—212no—
172C2×C4×D3C23×C3112yes—
173C2×C4×D3C23×C3112yes—
174C2×Dic6C23×C316yes—
175C3×C4⋊C4—212no—
176C3×C4⋊C4—38no—
177C3×C4⋊C4C22×D3112yes—
178C3×C4⋊C4C23×C3112yes—
179C3×C22⋊C4—24no—
180C3×C22⋊C4—38no—
181C3×C22⋊C4—324no—
182C3×C22⋊C4C22×D314yes—
183C3×C22⋊C4C23×C314yes—
184C3×C42—212no—
185C3×C42C22×D3112yes—
186C3×C42C23×C3112yes—
187(C2×D3)⋊C4C23×C318yes—
188(C2×D3)⋊C4C23×C3124yes—
189C4⋊Dic3C23×C318yes—
190C22×C32—22no—
191C22×C32C22×D412yes—
192C22×C32C2511yescharacteristic
193C2×C3×D3—24no—
194C2×C3×D3—26no—
195C2×C3×D3—28no—
196C2×C3×D3—212no—
197C2×C3×D3—412no—
198C32×C4—28no—
199C32×C4C22×D4112yes—
200C3×Dic3—24no—
201C3×Dic3—22no—
2022−1+4—68no—
203C2×#41—38no—
204C2×#41—34no—
205C2×#41—36no—
206C2×#41—68no—
207C22×Q8—34no—
208C22×Q8C2×C3×D311yescharacteristic
209C22×D4—33no—
210C23×C4—33no—
211#127—312no—
212#124—312no—
213#123—34no—
214C22⋊Q8—312no—
215#121—312no—
216#121—324no—
217#120—312no—
218C4×Q8C2×C3×D318yescomplemented
219C4×D4—324no—
220#117C2×C3×D316yes—
221C23×C3—21no—
222C23×C3—36no—
223C23×C3—34no—
224C23×C3—66no—
225C23×C3—126no—
226C23×C3C23×D311yescharacteristic
227C23×C3C24×C311yescharacteristic
228C22×D3—26no—
229C22×D3—46no—
230C22×D3C24×C316yes—
231C22×D3C24×C314yes—
232C3×Q8—216no—
233C3×Q8—612no—
234C3×Q8C2×D12116yes—
235C3×Q8C2×C3×D4116yes—
236C3×D4—68no—
237C3×D4—624no—
238C3×D4—612no—
239C3×D4—1224no—
240C2×C3×C4—26no—
241C2×C3×C4—28no—
242C2×C3×C4—212no—
243C2×C3×C4—34no—
244C2×C3×C4—32no—
245C2×C3×C4—62no—
246C2×C3×C4—624no—
247C2×C3×C4—624no—
248C2×C3×C4C2×D12112yes—
249C2×C3×C4C2×C3×D4112yes—
250C2×C3×C4C23×D318yes—
251C2×C3×C4C23×D316yes—
252C2×C3×C4C24×C318yes—
253C2×C3×C4C24×C316yes—
254#67—28no—
255C2×Dic3—22no—
256C2×Dic3C24×C312yes—
257C2×Dic3C24×C314yes—
258D12—224no—
259D12—212no—
260D12—424no—
261C4×D3—224no—
262C4×D3—224no—
263Dic6—212no—
264C2×C32—22no—
265C2×C32C23×D411yescharacteristic
266C2×C32#58512yes—
267C3×D3—44no—
268C3×D3—46no—
269C24—33no—
270#41—632no—
271#41—616no—
272#41—624no—
273C2×Q8—36no—
274C2×Q8—616no—
275C2×Q8C3×D1218yescomplemented
276C2×Q8C22×C3×D314yes—
277C2×D4—34no—
278C2×D4—312no—
279C2×D4—36no—
280C2×D4—324no—
281C2×D4—612no—
282C22×C4—31no—
283C22×C4—312no—
284C22×C4—312no—
285C22×C4—612no—
286C22×C4C22×C3×D313yes—
287C4⋊C4—38no—
288C4⋊C4C22×C3×D3112yes—
289C22⋊C4—38no—
290C22⋊C4—324no—
291C22⋊C4C22×C3×D314yes—
292C42C22×C3×D3112yes—
293C22×C3—22no—
294C22×C3—22no—
295C22×C3—22no—
296C22×C3—21no—
297C22×C3—42no—
298C22×C3—64no—
299C22×C3—66no—
300C22×C3—68no—
301C22×C3—612no—
302C22×C3—1212no—
303C22×C3C22×D1212yes—
304C22×C3C22×C3×D412yes—
305C22×C3C24×D311yescharacteristic
306C22×C3C25×C311yescharacteristic
307C2×D3—24no—
308C2×D3—26no—
309C2×D3—28no—
310C2×D3—212no—
311C2×D3—412no—
312C3×C4—28no—
313C3×C4—28no—
314C3×C4—212no—
315C3×C4—48no—
316C3×C4—62no—
317C3×C4—64no—
318C3×C4C22×D12112yes—
319C3×C4C22×C3×D4112yes—
320Dic3—24no—
321Dic3—22no—
322C32#348711yescharacteristic, complemented, Sylow
323C23—36no—
324C23—34no—
325C23—66no—
326C23—126no—
327C23C23×C3×D311yescharacteristic
328Q8—612no—
329Q8C2×C3×D12116yes—
330D4—68no—
331D4—624no—
332D4—612no—
333D4—1224no—
334C2×C4—34no—
335C2×C4—32no—
336C2×C4—62no—
337C2×C4—624no—
338C2×C4—624no—
339C2×C4C2×C3×D12112yes—
340C2×C4C23×C3×D318yes—
341C2×C4C23×C3×D316yes—
342C2×C3—22no—
343C2×C3—22no—
344C2×C3—21no—
345C2×C3—22no—
346C2×C3—42no—
347C2×C3—126no—
348C2×C3—124no—
349C2×C3C23×D1211yescharacteristic
350C2×C3#596812yes—
351C2×C3C23×C3×D411yescharacteristic
352C2×C3C3×#58512yes—
353D3—46no—
354D3—44no—
355C22—22no—
356C22—64no—
357C22—66no—
358C22—68no—
359C22—612no—
360C22—1212no—
361C22C22×C3×D1212yes—
362C22C24×C3×D311yescharacteristic
363C4—28no—
364C4—62no—
365C4—64no—
366C4C22×C3×D12112yes—
367C3—21no—
368C3#8587411yescharacteristic, direct product factor
369C3C3×#348711yescharacteristic, complemented
370C2—22no—
371C2—126no—
372C2—124no—
373C2C23×C3×D1211yescharacteristic
374C2C3×#596812yes—
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#519C2
socleC22×C32C25
hypercenterC3×#519D3
hypocenterC3C3×#3487
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#519

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1007C2semidirect
2. C22×C3×#239C2semidirect
3. C32×#519C2semidirect
4. C3×#5577C2semidirect
5. C3×#5576C2semidirect
6. C3×#5525C2semidirect
7. C3×#5524C2semidirect
9. #85874C3direct (N × H)
14. C2×C3×#239C22semidirect
15. C2×C3×D3×Q8C22semidirect
19. C32×C4×Q8C22semidirect
21. C3×#897C22semidirect
22. C3×#895C22semidirect
23. C3×#895C22semidirect
26. C3×#875C22semidirect
27. C3×#874C22semidirect
28. C3×C4×D12C22semidirect
31. C2×#1007C2×C3semidirect
32. C22×#239C2×C3semidirect
38. C3×#519D3semidirect
39. C3×#519C2×C3semidirect
40. #5577C2×C3semidirect
41. #5576C2×C3semidirect
42. #5525C2×C3semidirect
43. #5524C2×C3semidirect
45. C2×C32×Q8D4semidirect
83. C2×#239C22×C3semidirect
84. C2×D3×Q8C22×C3semidirect
96. C3×C4×Q8C2×D3semidirect
97. C3×C4×Q8C22×C3semidirect
102. #897C22×C3semidirect
103. #895C22×C3semidirect
104. #895C22×C3semidirect
107. #875C22×C3semidirect
108. #874C22×C3semidirect
109. C4×D12C22×C3semidirect
135. #519C3×D3semidirect
145. C2×C3×Q8D12semidirect
146. C2×C3×Q8C3×D4semidirect
218. C4×Q8C2×C3×D3semidirect
275. C2×Q8C3×D12semidirect
322. C32#3487semidirect
368. C3#85874direct (N × H)
369. C3C3×#3487semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C22×C3×#2392
C32×#5192
C3×#55772
C3×#55762
C3×#55252
C3×#55242
C3×#34873
#858743