Finite Group Databasebeta

← C3×#87294 #11904467

Subgroups — C3×#87294 #11904467

Order 1152.

3381 conjugacy classes of subgroups.

The subgroup lattice has 394 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×D3×Q8C211yesmaximal, characteristic, complemented
3C3×#5831C218yesmaximal, complemented
4C3×#5828C216yesmaximal, complemented
5C3×#5825C216yesmaximal, complemented
6C3×Q8×#67C218yesmaximal, complemented
7C3×#5812C211yesmaximal, characteristic, complemented
8C3×#3486—31nomaximal
9#87294C311yesmaximal, characteristic, direct product factor
10C32×2−1+4—28no—
11C2×C32×#41C2216yes—
12C2×C32×#41C2214yescomplemented
13C22×C32×Q8C2211yescharacteristic
14C22×C32×Q8C2214yescomplemented
15C2×C3×D3×Q8—28no—
16C2×C3×D3×Q8C2218yes—
17C22×C3×C4×D3C2213yes—
18C22×C3×Dic6C2213yes—
19C3×#946C22112yes—
20C3×Q8×Dic3C2218yescomplemented
21C3×#944C22112yescomplemented
22C3×#938C22112yes—
23C3×#937C2214yes—
24C3×#936C22112yescomplemented
25C3×#935C22112yes—
26C3×C4×#67C22124yes—
27C3×#926C2216yes—
28C3×#924C22124yescomplemented
29C2×C3×2−1+4—21no—
30C2×C3×2−1+4D311yescharacteristic, complemented
31C2×C3×2−1+4C2×C311yescharacteristic, complemented
32C23×C3×Q8—31no—
33C22×D3×Q8C2×C311yescharacteristic, complemented
34C3×D4×Q8—38no—
35C3×#548—38no—
36C3×#536—36no—
37C3×#525—36no—
38C3×#519—31no—
39#5831C2×C318yescomplemented
40#5828C2×C316yescomplemented
41#5825C2×C316yescomplemented
42Q8×#67C2×C318yescomplemented
43#5812C2×C311yescharacteristic, complemented
44C23×C3×D3C2311yescharacteristic
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×#67C2318yes—
56C22×C3×Dic3C2313yes—
57C3×D3×Q8—232no—
58C2×C3×C4×D3—212no—
59C2×C3×C4×D3C23112yes—
60C2×C3×Dic6—212no—
61C2×C3×Dic6C23112yes—
62C3×#217C23124yes—
63C3×#217C2314yes—
64C3×(C2×D3)⋊C4C2318yes—
65C3×C4⋊Dic3C23112yes—
66C3×Dic3⋊C4C23124yes—
67C3×C4×Dic3C23112yes—
68#3486—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×#41C2×D316yes—
75C2×C3×#41C2×D314yescomplemented
76C2×C3×#41C22×C316yes—
77C2×C3×#41C22×C314yescomplemented
78C22×C3×Q8—21no—
79C22×C3×Q8—24no—
80C22×C3×Q8—38no—
81C22×C3×Q8—33no—
82C22×C3×Q8—68no—
83C22×C3×Q8C2×D311yescharacteristic
84C22×C3×Q8C2×D314yescomplemented
85C22×C3×Q8C22×C311yescharacteristic
86C22×C3×Q8C22×C314yescomplemented
87C23×C3×C4—33no—
88C2×D3×Q8—28no—
89C2×D3×Q8C22×C318yes—
90C22×C4×D3C22×C313yes—
91C22×Dic6C22×C313yes—
92C3×C4⋊Q8—312no—
93C3×#124—312no—
94C3×#123—312no—
95C3×C22⋊Q8—312no—
96C3×C22⋊Q8—324no—
97C3×#121—312no—
98C3×#120—34no—
99C3×C4×Q8—38no—
100C3×C4×D4—324no—
101C3×#117—36no—
102#946C22×C3112yes—
103Q8×Dic3C22×C318yescomplemented
104#944C22×C3112yescomplemented
105#938C22×C3112yes—
106#937C22×C314yes—
107#936C22×C3112yescomplemented
108#935C22×C3112yes—
109C4×#67C22×C3124yes—
110#926C22×C316yes—
111#924C22×C3124yescomplemented
112C23×C32C2414yes—
113C23×C32C2411yescharacteristic
114C22×C3×D3—22no—
115C22×C3×D3—24no—
116C22×C3×D3C2412yes—
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—216no—
126C2×C3×Dic3—26no—
127C2×C3×Dic3C2418yes—
128C2×C3×Dic3C2416yes—
129C3×C4×D3—224no—
130C3×Dic6—224no—
131C2×2−1+4C3×D311yescharacteristic, complemented
132C23×Q8—31no—
133D4×Q8—38no—
134#548—38no—
135#536—36no—
136#525—36no—
137#519—31no—
138C24×C3—31no—
139C23×D3C23×C311yescharacteristic
140C3×#41—232no—
141C3×#41—248no—
142C3×#41—216no—
143C3×#41—216no—
144C3×#41—224no—
145C3×#41—224no—
146C2×C3×Q8—232no—
147C2×C3×Q8—216no—
148C2×C3×Q8—216no—
149C2×C3×Q8—28no—
150C2×C3×Q8—26no—
151C2×C3×Q8—24no—
152C2×C3×Q8—312no—
153C2×C3×Q8—632no—
154C2×C3×Q8—612no—
155C2×C3×Q8#6718yescomplemented
156C2×C3×Q8C3×D418yescomplemented
157C2×C3×Q8C22×D316yes—
158C2×C3×Q8C22×D314yes—
159C2×C3×Q8C23×C316yes—
160C2×C3×Q8C23×C314yes—
161C2×C3×D4—24no—
162C2×C3×D4—26no—
163C2×C3×D4—38no—
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—33no—
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×C318yes—
178C22×Dic3C23×C313yes—
179D3×Q8—232no—
180C2×C4×D3—212no—
181C2×C4×D3C23×C3112yes—
182C2×Dic6—212no—
183C2×Dic6C23×C3112yes—
184C3×C4⋊C4—324no—
185C3×C4⋊C4—312no—
186C3×C22⋊C4—34no—
187C3×C22⋊C4—324no—
188C3×C22⋊C4—38no—
189C3×C42—312no—
190#217C23×C3124yes—
191#217C23×C314yes—
192(C2×D3)⋊C4C23×C318yes—
193C4⋊Dic3C23×C3112yes—
194Dic3⋊C4C23×C3124yes—
195C4×Dic3C23×C3112yes—
196C22×C32—24no—
197C22×C32—22no—
198C22×C32—28no—
199C22×C32C22×D412yes—
200C22×C32C2511yescharacteristic
201C2×C3×D3—28no—
202C2×C3×D3—22no—
203C2×C3×D3—22no—
204C2×C3×D32−1+414yescomplemented
205C32×C4—24no—
206C32×C4C22×D4112yes—
207C3×Dic3—26no—
208C3×Dic3—28no—
2092−1+4—28no—
210C2×#41C2×C3×D316yes—
211C2×#41C2×C3×D314yescomplemented
212C22×Q8—38no—
213C22×Q8—33no—
214C22×Q8—68no—
215C22×Q8C2×C3×D311yescharacteristic
216C22×Q8C2×C3×D314yescomplemented
217C23×C4—33no—
218C4⋊Q8—312no—
219#124—312no—
220#123—312no—
221C22⋊Q8—312no—
222C22⋊Q8—324no—
223#121—312no—
224#120—34no—
225C4×Q8—38no—
226C4×D4—324no—
227#117—36no—
228C23×C3—24no—
229C23×C3—21no—
230C23×C3—32no—
231C23×C3—64no—
232C23×C3—62no—
233C23×C3C23×D314yes—
234C23×C3C23×D311yescharacteristic
235C23×C3C24×C314yes—
236C23×C3C24×C311yescharacteristic
237C22×D3—22no—
238C22×D3—24no—
239C22×D3C24×C312yes—
240C3×Q8—224no—
241C3×Q8—212no—
242C3×Q8—212no—
243C3×Q8—216no—
244C3×Q8—624no—
245C3×Q8C2×#67116yes—
246C3×Q8C2×C3×D4116yes—
247C3×D4—216no—
248C3×D4—224no—
249C3×D4—28no—
250C3×D4—28no—
251C3×D4—212no—
252C3×D4—212no—
253C3×D4—616no—
254C2×C3×C4—248no—
255C2×C3×C4—224no—
256C2×C3×C4—224no—
257C2×C3×C4—24no—
258C2×C3×C4—26no—
259C2×C3×C4—212no—
260C2×C3×C4—38no—
261C2×C3×C4—36no—
262C2×C3×C4—66no—
263C2×C3×C4—624no—
264C2×C3×C4C2×#67112yes—
265C2×C3×C4C2×C3×D4112yes—
266C2×C3×C4C23×D314yes—
267C2×C3×C4C23×D316yes—
268C2×C3×C4C24×C314yes—
269C2×C3×C4C24×C316yes—
270#67—216no—
271C2×Dic3—26no—
272C2×Dic3C24×C318yes—
273C2×Dic3C24×C316yes—
274C4×D3—224no—
275Dic6—224no—
276C2×C32—22no—
277C2×C32—44no—
278C2×C32C23×D411yescharacteristic
279C2×C32C2×2−1+412yes—
280C3×D3—24no—
281C24—31no—
282#41—216no—
283#41—224no—
284C2×Q8—216no—
285C2×Q8—312no—
286C2×Q8—632no—
287C2×Q8—612no—
288C2×Q8C3×#6718yescomplemented
289C2×Q8C22×C3×D316yes—
290C2×Q8C22×C3×D314yes—
291C2×D4—38no—
292C2×D4C22×C3×D314yes—
293C2×D4C22×C3×D316yes—
294C22×C4—33no—
295C22×C4—312no—
296C22×C4—612no—
297C22×C4C22×C3×D3112yes—
298C22×C4C22×C3×D313yes—
299C4⋊C4—312no—
300C4⋊C4—324no—
301C22⋊C4—34no—
302C22⋊C4—324no—
303C22⋊C4—38no—
304C42—312no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—28no—
308C22×C3—28no—
309C22×C3—24no—
310C22×C3—24no—
311C22×C3—28no—
312C22×C3—22no—
313C22×C3—21no—
314C22×C3—34no—
315C22×C3—42no—
316C22×C3—48no—
317C22×C3—68no—
318C22×C3—62no—
319C22×C3—62no—
320C22×C3C22×#6712yes—
321C22×C3C22×C3×D412yes—
322C22×C3C24×D311yescharacteristic
323C22×C3C25×C311yescharacteristic
324C2×D3—28no—
325C2×D3—22no—
326C2×D3—22no—
327C2×D3C3×2−1+414yescomplemented
328C3×C4—28no—
329C3×C4—24no—
330C3×C4—24no—
331C3×C4—212no—
332C3×C4—68no—
333C3×C4—66no—
334C3×C4C22×#67112yes—
335C3×C4C22×C3×D4112yes—
336Dic3—26no—
337Dic3—28no—
338C32#348611yescharacteristic, complemented, Sylow
339C23—32no—
340C23—64no—
341C23—62no—
342C23C23×C3×D314yes—
343C23C23×C3×D311yescharacteristic
344Q8—212no—
345Q8—624no—
346Q8C2×C3×#67116yes—
347D4—28no—
348D4—212no—
349D4—616no—
350C2×C4—224no—
351C2×C4—38no—
352C2×C4—36no—
353C2×C4—66no—
354C2×C4—624no—
355C2×C4C2×C3×#67112yes—
356C2×C4C23×C3×D314yes—
357C2×C4C23×C3×D316yes—
358C2×C3—22no—
359C2×C3—22no—
360C2×C3—22no—
361C2×C3—21no—
362C2×C3—42no—
363C2×C3—48no—
364C2×C3—44no—
365C2×C3—44no—
366C2×C3—64no—
367C2×C3D3×2−1+412yes—
368C2×C3C23×#6711yescharacteristic
369C2×C3C23×C3×D411yescharacteristic
370C2×C3C2×C3×2−1+412yes—
371D3—24no—
372C22—22no—
373C22—28no—
374C22—24no—
375C22—34no—
376C22—68no—
377C22—62no—
378C22—62no—
379C22C22×C3×#6712yes—
380C22C24×C3×D311yescharacteristic
381C4—24no—
382C4—68no—
383C4—66no—
384C4C22×C3×#67112yes—
385C3—21no—
386C3#8729411yescharacteristic, direct product factor
387C3C3×#348611yescharacteristic, complemented
388C2—22no—
389C2—44no—
390C2—64no—
391C2C3×D3×2−1+412yes—
392C2C23×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×#3486
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×D3×Q8C2semidirect
3. C3×#5831C2semidirect
4. C3×#5828C2semidirect
5. C3×#5825C2semidirect
6. C3×Q8×#67C2semidirect
7. C3×#5812C2semidirect
9. #87294C3direct (N × H)
12. C2×C32×#41C22semidirect
14. C22×C32×Q8C22semidirect
20. C3×Q8×Dic3C22semidirect
21. C3×#944C22semidirect
24. C3×#936C22semidirect
28. C3×#924C22semidirect
30. C2×C3×2−1+4D3semidirect
31. C2×C3×2−1+4C2×C3semidirect
33. C22×D3×Q8C2×C3semidirect
39. #5831C2×C3semidirect
40. #5828C2×C3semidirect
41. #5825C2×C3semidirect
42. Q8×#67C2×C3semidirect
43. #5812C2×C3semidirect
48. C2×C32×Q8D4semidirect
75. C2×C3×#41C2×D3semidirect
77. C2×C3×#41C22×C3semidirect
84. C22×C3×Q8C2×D3semidirect
86. C22×C3×Q8C22×C3semidirect
103. Q8×Dic3C22×C3semidirect
104. #944C22×C3semidirect
107. #936C22×C3semidirect
111. #924C22×C3semidirect
131. C2×2−1+4C3×D3semidirect
155. C2×C3×Q8#67semidirect
156. C2×C3×Q8C3×D4semidirect
204. C2×C3×D32−1+4semidirect
211. C2×#41C2×C3×D3semidirect
216. C22×Q8C2×C3×D3semidirect
288. C2×Q8C3×#67semidirect
327. C2×D3C3×2−1+4semidirect
338. C32#3486semidirect
386. C3#87294direct (N × H)
387. C3C3×#3486semidirect

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×D3×Q82
C3×#58312
C3×#58282
C3×#58252
C3×Q8×#672
C3×#58122
C3×#34863
#872943