Finite Group Databasebeta

← C3×#87290 #11904529

Subgroups — C3×#87290 #11904529

Order 1152.

3469 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×2−1+4C211yesmaximal, characteristic, complemented
2C22×C3×#239C211yesmaximal, characteristic, complemented
3C3×#5834C218yesmaximal, complemented
4C3×#5830C216yesmaximal, complemented
5C3×#5828C216yesmaximal, complemented
6C3×#5817C218yesmaximal, complemented
7C3×#5812C211yesmaximal, characteristic, complemented
8C3×#3487—31nomaximal
9#87290C311yesmaximal, characteristic, direct product factor
10C32×2−1+4—28no—
11C2×C32×#41C2216yes—
12C2×C32×#41C2214yescomplemented
13C22×C32×Q8C2211yescharacteristic
14C22×C32×Q8C2214yescomplemented
15C2×C3×#239—28no—
16C2×C3×#239C2218yes—
17C22×C3×D12C2213yes—
18C22×C3×C4×D3C2213yes—
19C3×#947C22112yescomplemented
20C3×#946C22112yescomplemented
21C3×Q8×Dic3C2218yescomplemented
22C3×#940C22112yescomplemented
23C3×#938C22112yescomplemented
24C3×#937C22112yes—
25C3×#935C2214yes—
26C3×#930C22124yescomplemented
27C3×C4×#67C22124yescomplemented
28C3×#926C2216yes—
29C2×C3×2−1+4—21no—
30C2×C3×2−1+4D311yescharacteristic, complemented
31C2×C3×2−1+4C2×C311yescharacteristic, complemented
32C22×C3×#41—31no—
33C22×#239C2×C311yescharacteristic, complemented
34C3×#550—38no—
35C3×#548—38no—
36C3×#535—36no—
37C3×#525—36no—
38C3×#519—31no—
39#5834C2×C318yescomplemented
40#5830C2×C316yescomplemented
41#5828C2×C316yescomplemented
42#5817C2×C318yescomplemented
43#5812C2×C311yescharacteristic, complemented
44C23×C3×D3C2313yes—
45C32×#41—216no—
46C32×#41—224no—
47C2×C32×Q8—216no—
48C2×C32×Q8D418yescomplemented
49C2×C32×Q8C2316yes—
50C2×C32×Q8C2314yes—
51C2×C32×D4C2314yes—
52C2×C32×D4C2316yes—
53C22×C32×C4C23112yes—
54C22×C32×C4C2313yes—
55C2×C3×#67C23124yes—
56C22×C3×Dic3C2311yescharacteristic
57C3×#239—232no—
58C2×C3×D12—212no—
59C2×C3×D12C23112yes—
60C2×C3×C4×D3—212no—
61C2×C3×C4×D3C23112yes—
62C3×#217C2314yes—
63C3×#217C2318yes—
64C3×(C2×D3)⋊C4C23124yes—
65C3×C4⋊Dic3C23112yes—
66C3×Dic3⋊C4C2318yes—
67C3×C4×Dic3C23112yes—
68#3487—31noSylow
69C3×2−1+4—216no—
70C3×2−1+4—28no—
71C3×2−1+4—28no—
72C2×C3×#41—26no—
73C2×C3×#41—24no—
74C2×C3×#41—38no—
75C2×C3×#41—68no—
76C2×C3×#41C2×D316yes—
77C2×C3×#41C2×D314yescomplemented
78C2×C3×#41C22×C316yes—
79C2×C3×#41C22×C314yescomplemented
80C22×C3×Q8—21no—
81C22×C3×Q8—24no—
82C22×C3×Q8C2×D311yescharacteristic
83C22×C3×Q8C2×D314yescomplemented
84C22×C3×Q8C22×C311yescharacteristic
85C22×C3×Q8C22×C314yescomplemented
86C22×C3×D4—33no—
87C23×C3×C4—33no—
88C2×#239—28no—
89C2×#239C22×C318yes—
90C22×D12C22×C313yes—
91C22×C4×D3C22×C313yes—
92C3×#127—312no—
93C3×#124—312no—
94C3×#123—34no—
95C3×C22⋊Q8—312no—
96C3×#121—312no—
97C3×#121—324no—
98C3×#120—312no—
99C3×C4×Q8—38no—
100C3×C4×D4—324no—
101C3×#117—36no—
102#947C22×C3112yescomplemented
103#946C22×C3112yescomplemented
104Q8×Dic3C22×C318yescomplemented
105#940C22×C3112yescomplemented
106#938C22×C3112yescomplemented
107#937C22×C3112yes—
108#935C22×C314yes—
109#930C22×C3124yescomplemented
110C4×#67C22×C3124yescomplemented
111#926C22×C316yes—
112C23×C32C2414yes—
113C23×C32C2411yescharacteristic
114C22×C3×D3—26no—
115C22×C3×D3—46no—
116C22×C3×D3C2416yes—
117C32×Q8—212no—
118C32×Q8C2×D4116yes—
119C32×D4—28no—
120C32×D4—212no—
121C2×C32×C4—224no—
122C2×C32×C4C2×D4112yes—
123C2×C32×C4C2414yes—
124C2×C32×C4C2416yes—
125C3×#67—424no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3C2418yes—
128C2×C3×Dic3C2412yes—
129C3×D12—224no—
130C3×C4×D3—224no—
131C2×2−1+4C3×D311yescharacteristic, complemented
132C22×#41—31no—
133#550—38no—
134#548—38no—
135#535—36no—
136#525—36no—
137#519—31no—
138C24×C3—33no—
139C23×D3C23×C313yes—
140C3×#41—232no—
141C3×#41—248no—
142C3×#41—216no—
143C3×#41—216no—
144C3×#41—224no—
145C3×#41—224no—
146C3×#41—632no—
147C2×C3×Q8—232no—
148C2×C3×Q8—216no—
149C2×C3×Q8—216no—
150C2×C3×Q8—28no—
151C2×C3×Q8—26no—
152C2×C3×Q8—24no—
153C2×C3×Q8#6718yescomplemented
154C2×C3×Q8C3×D418yescomplemented
155C2×C3×Q8C22×D316yes—
156C2×C3×Q8C22×D314yes—
157C2×C3×Q8C23×C316yes—
158C2×C3×Q8C23×C314yes—
159C2×C3×D4—24no—
160C2×C3×D4—26no—
161C2×C3×D4—324no—
162C2×C3×D4—312no—
163C2×C3×D4—612no—
164C2×C3×D4C22×D314yes—
165C2×C3×D4C22×D316yes—
166C2×C3×D4C23×C314yes—
167C2×C3×D4C23×C316yes—
168C22×C3×C4—212no—
169C22×C3×C4—23no—
170C22×C3×C4—31no—
171C22×C3×C4—312no—
172C22×C3×C4—612no—
173C22×C3×C4C22×D3112yes—
174C22×C3×C4C22×D313yes—
175C22×C3×C4C23×C3112yes—
176C22×C3×C4C23×C313yes—
177C2×#67C23×C3124yes—
178C22×Dic3C23×C311yescharacteristic
179#239—232no—
180C2×D12—212no—
181C2×D12C23×C3112yes—
182C2×C4×D3—212no—
183C2×C4×D3C23×C3112yes—
184C3×C4⋊C4—38no—
185C3×C4⋊C4—312no—
186C3×C22⋊C4—34no—
187C3×C22⋊C4—38no—
188C3×C22⋊C4—324no—
189C3×C42—312no—
190#217C23×C314yes—
191#217C23×C318yes—
192(C2×D3)⋊C4C23×C3124yes—
193C4⋊Dic3C23×C3112yes—
194Dic3⋊C4C23×C318yes—
195C4×Dic3C23×C3112yes—
196C22×C32—24no—
197C22×C32—22no—
198C22×C32—28no—
199C22×C32C22×D412yes—
200C22×C32C2511yescharacteristic
201C2×C3×D3—26no—
202C2×C3×D3—212no—
203C2×C3×D3—412no—
204C32×C4—24no—
205C32×C4C22×D4112yes—
206C3×Dic3—22no—
207C3×Dic3—28no—
2082−1+4—28no—
209C2×#41—38no—
210C2×#41—68no—
211C2×#41C2×C3×D316yes—
212C2×#41C2×C3×D314yescomplemented
213C22×Q8C2×C3×D311yescharacteristic
214C22×Q8C2×C3×D314yescomplemented
215C22×D4—33no—
216C23×C4—33no—
217#127—312no—
218#124—312no—
219#123—34no—
220C22⋊Q8—312no—
221#121—312no—
222#121—324no—
223#120—312no—
224C4×Q8—38no—
225C4×D4—324no—
226#117—36no—
227C23×C3—24no—
228C23×C3—21no—
229C23×C3—36no—
230C23×C3—66no—
231C23×C3—126no—
232C23×C3C23×D314yes—
233C23×C3C23×D311yescharacteristic
234C23×C3C24×C314yes—
235C23×C3C24×C311yescharacteristic
236C22×D3—26no—
237C22×D3—46no—
238C22×D3C24×C316yes—
239C3×Q8—224no—
240C3×Q8—212no—
241C3×Q8—212no—
242C3×Q8—216no—
243C3×Q8C2×#67116yes—
244C3×Q8C2×C3×D4116yes—
245C3×D4—216no—
246C3×D4—224no—
247C3×D4—28no—
248C3×D4—28no—
249C3×D4—212no—
250C3×D4—212no—
251C3×D4—624no—
252C3×D4—1224no—
253C2×C3×C4—248no—
254C2×C3×C4—224no—
255C2×C3×C4—224no—
256C2×C3×C4—24no—
257C2×C3×C4—26no—
258C2×C3×C4—212no—
259C2×C3×C4—38no—
260C2×C3×C4—32no—
261C2×C3×C4—62no—
262C2×C3×C4—624no—
263C2×C3×C4C2×#67112yes—
264C2×C3×C4C2×C3×D4112yes—
265C2×C3×C4C23×D314yes—
266C2×C3×C4C23×D316yes—
267C2×C3×C4C24×C314yes—
268C2×C3×C4C24×C316yes—
269#67—424no—
270C2×Dic3—22no—
271C2×Dic3C24×C318yes—
272C2×Dic3C24×C312yes—
273D12—224no—
274C4×D3—224no—
275C2×C32—22no—
276C2×C32—44no—
277C2×C32C23×D411yescharacteristic
278C2×C32#58512yes—
279C3×D3—46no—
280C24—33no—
281#41—216no—
282#41—224no—
283#41—632no—
284C2×Q8—216no—
285C2×Q8C3×#6718yescomplemented
286C2×Q8C22×C3×D316yes—
287C2×Q8C22×C3×D314yes—
288C2×D4—324no—
289C2×D4—312no—
290C2×D4—612no—
291C2×D4C22×C3×D314yes—
292C2×D4C22×C3×D316yes—
293C22×C4—31no—
294C22×C4—312no—
295C22×C4—612no—
296C22×C4C22×C3×D3112yes—
297C22×C4C22×C3×D313yes—
298C4⋊C4—312no—
299C4⋊C4—38no—
300C22⋊C4—34no—
301C22⋊C4—38no—
302C22⋊C4—324no—
303C42—312no—
304C22×C3—22no—
305C22×C3—22no—
306C22×C3—28no—
307C22×C3—28no—
308C22×C3—24no—
309C22×C3—24no—
310C22×C3—28no—
311C22×C3—22no—
312C22×C3—21no—
313C22×C3—42no—
314C22×C3—48no—
315C22×C3—612no—
316C22×C3—66no—
317C22×C3—1212no—
318C22×C3C22×#6712yes—
319C22×C3C22×C3×D412yes—
320C22×C3C24×D311yescharacteristic
321C22×C3C25×C311yescharacteristic
322C2×D3—26no—
323C2×D3—212no—
324C2×D3—412no—
325C3×C4—28no—
326C3×C4—24no—
327C3×C4—24no—
328C3×C4—212no—
329C3×C4—68no—
330C3×C4—62no—
331C3×C4C22×#67112yes—
332C3×C4C22×C3×D4112yes—
333Dic3—22no—
334Dic3—28no—
335C32#348711yescharacteristic, complemented, Sylow
336C23—36no—
337C23—66no—
338C23—126no—
339C23C23×C3×D314yes—
340C23C23×C3×D311yescharacteristic
341Q8—212no—
342Q8C2×C3×#67116yes—
343D4—28no—
344D4—212no—
345D4—624no—
346D4—1224no—
347C2×C4—224no—
348C2×C4—38no—
349C2×C4—32no—
350C2×C4—62no—
351C2×C4—624no—
352C2×C4C2×C3×#67112yes—
353C2×C4C23×C3×D314yes—
354C2×C4C23×C3×D316yes—
355C2×C3—22no—
356C2×C3—22no—
357C2×C3—22no—
358C2×C3—21no—
359C2×C3—42no—
360C2×C3—48no—
361C2×C3—44no—
362C2×C3—44no—
363C2×C3—126no—
364C2×C3#596812yes—
365C2×C3C23×#6711yescharacteristic
366C2×C3C23×C3×D411yescharacteristic
367C2×C3C3×#58512yes—
368D3—46no—
369C22—22no—
370C22—28no—
371C22—24no—
372C22—612no—
373C22—66no—
374C22—1212no—
375C22C22×C3×#6712yes—
376C22C24×C3×D311yescharacteristic
377C4—24no—
378C4—68no—
379C4—62no—
380C4C22×C3×#67112yes—
381C3—21no—
382C3#8729011yescharacteristic, direct product factor
383C3C3×#348711yescharacteristic, complemented
384C2—22no—
385C2—44no—
386C2—126no—
387C2C3×#596812yes—
388C2C23×C3×#6711yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×2−1+4C2
socleC22×C32C25
hypercenterC2×C3×2−1+4D3
hypocenterC3C3×#3487
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×C32×2−1+4C2semidirect
2. C22×C3×#239C2semidirect
3. C3×#5834C2semidirect
4. C3×#5830C2semidirect
5. C3×#5828C2semidirect
6. C3×#5817C2semidirect
7. C3×#5812C2semidirect
9. #87290C3direct (N × H)
12. C2×C32×#41C22semidirect
14. C22×C32×Q8C22semidirect
19. C3×#947C22semidirect
20. C3×#946C22semidirect
21. C3×Q8×Dic3C22semidirect
22. C3×#940C22semidirect
23. C3×#938C22semidirect
26. C3×#930C22semidirect
27. C3×C4×#67C22semidirect
30. C2×C3×2−1+4D3semidirect
31. C2×C3×2−1+4C2×C3semidirect
33. C22×#239C2×C3semidirect
39. #5834C2×C3semidirect
40. #5830C2×C3semidirect
41. #5828C2×C3semidirect
42. #5817C2×C3semidirect
43. #5812C2×C3semidirect
48. C2×C32×Q8D4semidirect
77. C2×C3×#41C2×D3semidirect
79. C2×C3×#41C22×C3semidirect
83. C22×C3×Q8C2×D3semidirect
85. C22×C3×Q8C22×C3semidirect
102. #947C22×C3semidirect
103. #946C22×C3semidirect
104. Q8×Dic3C22×C3semidirect
105. #940C22×C3semidirect
106. #938C22×C3semidirect
109. #930C22×C3semidirect
110. C4×#67C22×C3semidirect
131. C2×2−1+4C3×D3semidirect
153. C2×C3×Q8#67semidirect
154. C2×C3×Q8C3×D4semidirect
212. C2×#41C2×C3×D3semidirect
214. C22×Q8C2×C3×D3semidirect
285. C2×Q8C3×#67semidirect
335. C32#3487semidirect
382. C3#87290direct (N × H)
383. C3C3×#3487semidirect

Maximal subgroups

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

subgroupindex
C2×C32×2−1+42
C22×C3×#2392
C3×#58342
C3×#58302
C3×#58282
C3×#58172
C3×#58122
C3×#34873
#872903