Finite Group Databasebeta

← C3×#87274 #11904538

Subgroups — C3×#87274 #11904538

Order 1152.

3517 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×#41C211yesmaximal, characteristic, complemented
2C2×C3×#1007C211yesmaximal, characteristic, complemented
3C3×#5834C218yesmaximal, complemented
4C3×#5831C218yesmaximal, complemented
5C3×#5812C211yesmaximal, characteristic, complemented
6C3×#5805C216yesmaximal, complemented
7C3×#5791C216yesmaximal, complemented
8C3×#3487—31nomaximal
9#87274C311yesmaximal, characteristic, direct product factor
10C2×C32×#41—28no—
11C2×C32×#41C2218yes—
12C22×C32×Q8C2211yescharacteristic
13C22×C32×D4C2213yes—
14C23×C32×C4C2213yes—
15C3×#1007—28no—
16C2×C3×#239C2214yescomplemented
17C2×C3×D3×Q8C2214yescomplemented
18C2×C3×#235C2216yes—
19C3×#953C22112yes—
20C3×Q8×Dic3C2218yescomplemented
21C3×#940C22112yescomplemented
22C3×#938C22124yescomplemented
23C3×#936C22112yescomplemented
24C3×#930C22112yescomplemented
25C3×#929C2214yes—
26C3×C4×#67C22124yescomplemented
27C3×#926C2216yes—
28C3×#924C22112yescomplemented
29C2×C3×2−1+4—31no—
30C22×C3×#41—21no—
31C22×C3×#41D311yescharacteristic, complemented
32C22×C3×#41C2×C311yescharacteristic, complemented
33C2×#1007C2×C311yescharacteristic, complemented
34C3×#550—38no—
35C3×#548—38no—
36C3×#535—36no—
37C3×#525—36no—
38C3×#519—31no—
39#5834C2×C318yescomplemented
40#5831C2×C318yescomplemented
41#5812C2×C311yescharacteristic, complemented
42#5805C2×C316yescomplemented
43#5791C2×C316yescomplemented
44C24×C32C2313yes—
45C32×#41—232no—
46C2×C32×Q8D418yescomplemented
47C2×C32×Q8C2314yes—
48C2×C32×D4—212no—
49C2×C32×D4C23112yes—
50C22×C32×C4—212no—
51C22×C32×C4C23112yes—
52C22×C32×C4C2311yescharacteristic
53C22×C32×C4C2313yes—
54C2×C3×#67C2314yes—
55C2×C3×#67C23124yes—
56C3×#239—216no—
57C3×D3×Q8—216no—
58C3×#235—224no—
59C2×C3×D12C2316yes—
60C2×C3×C4×D3C23112yes—
61C2×C3×Dic6C2316yes—
62C3×#217C23124yes—
63C3×#217C2314yes—
64C3×(C2×D3)⋊C4C2318yes—
65C3×C4⋊Dic3C23112yes—
66C3×Dic3⋊C4C2318yes—
67C3×C4×Dic3C23112yes—
68#3487—31noSylow
69C3×2−1+4—68no—
70C2×C3×#41—216no—
71C2×C3×#41—28no—
72C2×C3×#41—28no—
73C2×C3×#41—28no—
74C2×C3×#41—34no—
75C2×C3×#41—36no—
76C2×C3×#41C2×D318yes—
77C2×C3×#41C22×C318yes—
78C22×C3×Q8—21no—
79C22×C3×Q8—34no—
80C22×C3×Q8C2×D311yescharacteristic
81C22×C3×Q8C22×C311yescharacteristic
82C22×C3×D4—23no—
83C22×C3×D4C2×D313yes—
84C22×C3×D4C22×C313yes—
85C23×C3×C4—23no—
86C23×C3×C4C2×D313yes—
87C23×C3×C4C22×C313yes—
88#1007—28no—
89C2×#239C22×C314yescomplemented
90C2×D3×Q8C22×C314yescomplemented
91C2×#235C22×C316yes—
92C3×#127—312no—
93C3×#124—312no—
94C3×#123—34no—
95C3×C22⋊Q8—312no—
96C3×#121—324no—
97C3×#121—312no—
98C3×#120—312no—
99C3×C4×Q8—38no—
100C3×C4×D4—324no—
101C3×#117—36no—
102#953C22×C3112yes—
103Q8×Dic3C22×C318yescomplemented
104#940C22×C3112yescomplemented
105#938C22×C3124yescomplemented
106#936C22×C3112yescomplemented
107#930C22×C3112yescomplemented
108#929C22×C314yes—
109C4×#67C22×C3124yescomplemented
110#926C22×C316yes—
111#924C22×C3112yescomplemented
112C23×C32—26no—
113C23×C32—46no—
114C23×C32C2416yes—
115C23×C32C2411yescharacteristic
116C22×C3×D3C2414yes—
117C32×Q8C2×D4116yes—
118C32×D4—224no—
119C2×C32×C4—22no—
120C2×C32×C4—224no—
121C2×C32×C4C2×D4112yes—
122C2×C32×C4C2412yes—
123C2×C32×C4C2416yes—
124C3×#67—28no—
125C3×#67—424no—
126C2×C3×Dic3C2418yes—
127C2×C3×Dic3C2414yes—
128C3×D12—212no—
129C3×C4×D3—224no—
130C3×Dic6—212no—
131C2×2−1+4—31no—
132C22×#41C3×D311yescharacteristic, complemented
133#550—38no—
134#548—38no—
135#535—36no—
136#525—36no—
137#519—31no—
138C24×C3—23no—
139C24×C3C22×D313yes—
140C24×C3C23×C313yes—
141C3×#41—264no—
142C3×#41—232no—
143C3×#41—232no—
144C3×#41—616no—
145C3×#41—624no—
146C2×C3×Q8—28no—
147C2×C3×Q8—24no—
148C2×C3×Q8—36no—
149C2×C3×Q8—616no—
150C2×C3×Q8#6718yescomplemented
151C2×C3×Q8C3×D418yescomplemented
152C2×C3×Q8C22×D314yes—
153C2×C3×Q8C23×C314yes—
154C2×C3×D4—224no—
155C2×C3×D4—212no—
156C2×C3×D4—212no—
157C2×C3×D4—212no—
158C2×C3×D4—34no—
159C2×C3×D4—324no—
160C2×C3×D4—36no—
161C2×C3×D4C22×D3112yes—
162C2×C3×D4C23×C3112yes—
163C22×C3×C4—224no—
164C22×C3×C4—212no—
165C22×C3×C4—212no—
166C22×C3×C4—21no—
167C22×C3×C4—23no—
168C22×C3×C4—212no—
169C22×C3×C4—312no—
170C22×C3×C4C22×D3112yes—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D313yes—
173C22×C3×C4C23×C3112yes—
174C22×C3×C4C23×C311yescharacteristic
175C22×C3×C4C23×C313yes—
176C2×#67C23×C314yes—
177C2×#67C23×C3124yes—
178#239—216no—
179D3×Q8—216no—
180#235—224no—
181C2×D12C23×C316yes—
182C2×C4×D3C23×C3112yes—
183C2×Dic6C23×C316yes—
184C3×C4⋊C4—38no—
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×C318yes—
195C4×Dic3C23×C3112yes—
196C22×C32—22no—
197C22×C32—26no—
198C22×C32—212no—
199C22×C32—412no—
200C22×C32C22×D412yes—
201C22×C32C2511yescharacteristic
202C2×C3×D3—24no—
203C2×C3×D3—28no—
204C32×C4—22no—
205C32×C4C22×D4112yes—
206C3×Dic3—24no—
207C3×Dic3—28no—
2082−1+4—68no—
209C2×#41—28no—
210C2×#41—34no—
211C2×#41—36no—
212C2×#41C2×C3×D318yes—
213C22×Q8—34no—
214C22×Q8C2×C3×D311yescharacteristic
215C22×D4C2×C3×D313yes—
216C23×C4C2×C3×D313yes—
217#127—312no—
218#124—312no—
219#123—34no—
220C22⋊Q8—312no—
221#121—324no—
222#121—312no—
223#120—312no—
224C4×Q8—38no—
225C4×D4—324no—
226#117—36no—
227C23×C3—212no—
228C23×C3—26no—
229C23×C3—26no—
230C23×C3—21no—
231C23×C3—26no—
232C23×C3—34no—
233C23×C3—46no—
234C23×C3—46no—
235C23×C3—412no—
236C23×C3C23×D316yes—
237C23×C3C23×D311yescharacteristic
238C23×C3C24×C316yes—
239C23×C3C24×C311yescharacteristic
240C22×D3C24×C314yes—
241C3×Q8—216no—
242C3×Q8—612no—
243C3×Q8C2×#67116yes—
244C3×Q8C2×C3×D4116yes—
245C3×D4—248no—
246C3×D4—224no—
247C3×D4—224no—
248C3×D4—68no—
249C3×D4—612no—
250C3×D4—1224no—
251C2×C3×C4—24no—
252C2×C3×C4—248no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—224no—
256C2×C3×C4—224no—
257C2×C3×C4—22no—
258C2×C3×C4—26no—
259C2×C3×C4—212no—
260C2×C3×C4—38no—
261C2×C3×C4—34no—
262C2×C3×C4—624no—
263C2×C3×C4C2×#67112yes—
264C2×C3×C4C2×C3×D4112yes—
265C2×C3×C4C23×D312yes—
266C2×C3×C4C23×D316yes—
267C2×C3×C4C24×C312yes—
268C2×C3×C4C24×C316yes—
269#67—28no—
270#67—424no—
271C2×Dic3C24×C318yes—
272C2×Dic3C24×C314yes—
273D12—212no—
274C4×D3—224no—
275Dic6—212no—
276C2×C32—22no—
277C2×C32—46no—
278C2×C32C23×D411yescharacteristic
279C2×C32#58512yes—
280C3×D3—44no—
281C24C22×C3×D313yes—
282#41—232no—
283#41—616no—
284#41—624no—
285C2×Q8—36no—
286C2×Q8—616no—
287C2×Q8C3×#6718yescomplemented
288C2×Q8C22×C3×D314yes—
289C2×D4—212no—
290C2×D4—34no—
291C2×D4—324no—
292C2×D4—36no—
293C2×D4C22×C3×D3112yes—
294C22×C4—212no—
295C22×C4—312no—
296C22×C4C22×C3×D3112yes—
297C22×C4C22×C3×D311yescharacteristic
298C22×C4C22×C3×D313yes—
299C4⋊C4—312no—
300C4⋊C4—38no—
301C22⋊C4—34no—
302C22⋊C4—324no—
303C22⋊C4—38no—
304C42—312no—
305C22×C3—24no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—212no—
309C22×C3—212no—
310C22×C3—26no—
311C22×C3—26no—
312C22×C3—212no—
313C22×C3—22no—
314C22×C3—21no—
315C22×C3—412no—
316C22×C3—424no—
317C22×C3—412no—
318C22×C3—412no—
319C22×C3—68no—
320C22×C3—64no—
321C22×C3C22×#6712yes—
322C22×C3C22×C3×D412yes—
323C22×C3C24×D311yescharacteristic
324C22×C3C25×C311yescharacteristic
325C2×D3—24no—
326C2×D3—28no—
327C3×C4—24no—
328C3×C4—22no—
329C3×C4—22no—
330C3×C4—212no—
331C3×C4—68no—
332C3×C4—64no—
333C3×C4C22×#67112yes—
334C3×C4C22×C3×D4112yes—
335Dic3—24no—
336Dic3—28no—
337C32#348711yescharacteristic, complemented, Sylow
338C23—26no—
339C23—34no—
340C23—46no—
341C23C23×C3×D316yes—
342C23C23×C3×D311yescharacteristic
343Q8—612no—
344Q8C2×C3×#67116yes—
345D4—224no—
346D4—68no—
347D4—612no—
348D4—1224no—
349C2×C4—22no—
350C2×C4—224no—
351C2×C4—38no—
352C2×C4—34no—
353C2×C4—624no—
354C2×C4C2×C3×#67112yes—
355C2×C4C23×C3×D312yes—
356C2×C4C23×C3×D316yes—
357C2×C3—24no—
358C2×C3—22no—
359C2×C3—22no—
360C2×C3—22no—
361C2×C3—21no—
362C2×C3—412no—
363C2×C3—46no—
364C2×C3—46no—
365C2×C3—124no—
366C2×C3#596412yes—
367C2×C3C23×#6711yescharacteristic
368C2×C3C23×C3×D411yescharacteristic
369C2×C3C3×#58512yes—
370D3—44no—
371C22—22no—
372C22—212no—
373C22—26no—
374C22—412no—
375C22—68no—
376C22—64no—
377C22C22×C3×#6712yes—
378C22C24×C3×D311yescharacteristic
379C4—22no—
380C4—68no—
381C4—64no—
382C4C22×C3×#67112yes—
383C3—21no—
384C3#8727411yescharacteristic, direct product factor
385C3C3×#348711yescharacteristic, complemented
386C2—22no—
387C2—46no—
388C2—124no—
389C2C3×#596412yes—
390C2C23×C3×#6711yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC22×C32×#41C2
socleC22×C32C25
hypercenterC22×C3×#41D3
hypocenterC3C3×#3487
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×#41

Complements

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

NH ≅ G/Ntype
1. C22×C32×#41C2semidirect
2. C2×C3×#1007C2semidirect
3. C3×#5834C2semidirect
4. C3×#5831C2semidirect
5. C3×#5812C2semidirect
6. C3×#5805C2semidirect
7. C3×#5791C2semidirect
9. #87274C3direct (N × H)
16. C2×C3×#239C22semidirect
17. C2×C3×D3×Q8C22semidirect
20. C3×Q8×Dic3C22semidirect
21. C3×#940C22semidirect
22. C3×#938C22semidirect
23. C3×#936C22semidirect
24. C3×#930C22semidirect
26. C3×C4×#67C22semidirect
28. C3×#924C22semidirect
31. C22×C3×#41D3semidirect
32. C22×C3×#41C2×C3semidirect
33. C2×#1007C2×C3semidirect
39. #5834C2×C3semidirect
40. #5831C2×C3semidirect
41. #5812C2×C3semidirect
42. #5805C2×C3semidirect
43. #5791C2×C3semidirect
46. C2×C32×Q8D4semidirect
89. C2×#239C22×C3semidirect
90. C2×D3×Q8C22×C3semidirect
103. Q8×Dic3C22×C3semidirect
104. #940C22×C3semidirect
105. #938C22×C3semidirect
106. #936C22×C3semidirect
107. #930C22×C3semidirect
109. C4×#67C22×C3semidirect
111. #924C22×C3semidirect
132. C22×#41C3×D3semidirect
150. C2×C3×Q8#67semidirect
151. C2×C3×Q8C3×D4semidirect
287. C2×Q8C3×#67semidirect
337. C32#3487semidirect
384. C3#87274direct (N × H)
385. C3C3×#3487semidirect

Maximal subgroups

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

subgroupindex
C22×C32×#412
C2×C3×#10072
C3×#58342
C3×#58312
C3×#58122
C3×#58052
C3×#57912
C3×#34873
#872743