Finite Group Databasebeta

← C3×#85827 #11906016

Subgroups — C3×#85827 #11906016

Order 1152.

3107 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×#1010C212yesmaximal, complemented
2C32×C4×#41C211yesmaximal, characteristic, complemented
3C3×Q8×D12C214yesmaximal, complemented
4C3×#5555C2112yesmaximal, complemented
5C3×#5526C216yesmaximal, complemented
6C3×#5477C213yesmaximal, complemented
7C2×C3×#869C213yesmaximal, complemented
8C3×#3499—31nomaximal
9#85827C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C3×#1010—216no—
12C2×C3×D3×Q8C2214yes—
13C2×C3×#237C22112yes—
14C2×C3×#235C2216yes—
15C22×C3×Dic6C2216yes—
16C32×C4×Q8C2212yes—
17C32×C4×D4C2216yes—
18C32×#117C2213yes—
19C2×C32×C42C2213yes—
20C3×#930C22112yes—
21C2×C3×C4⋊Dic3C22112yes—
22C3×#897C22124yes—
23C3×#886C22124yes—
24C3×#875C2216yes—
25C3×#874C2211yescharacteristic
26C3×C4×D12C22112yes—
27C3×#869C2216yes—
28C3×#869C22112yes—
29C3×#869C2213yes—
30C2×C3×2−1+4—32no—
31C2×#1010C2×C312yescomplemented
32C3×D4×Q8—34no—
33C3×#547—312no—
34C3×#536—36no—
35C3×#532—33no—
36C2×C3×C4⋊Q8—33no—
37C3×C4×#41—21no—
38C3×C4×#41D311yescharacteristic, complemented
39C3×C4×#41C2×C311yescharacteristic, complemented
40Q8×D12C2×C314yescomplemented
41#5555C2×C3112yescomplemented
42#5526C2×C316yescomplemented
43#5477C2×C313yescomplemented
44C2×#869C2×C313yescomplemented
45C32×#41D418yescomplemented
46C2×C32×Q8C2311yescharacteristic
47C2×C32×D4C2313yes—
48C22×C32×C4C2316yes—
49C22×C32×C4C2313yes—
50C2×C3×#67C23112yes—
51C22×C3×Dic3C23112yes—
52C3×D3×Q8—216no—
53C3×#237—248no—
54C3×#235—224no—
55C2×C3×D12C2314yes—
56C2×C3×D12C2312yes—
57C2×C3×C4×D3C23112yes—
58C2×C3×Dic6—224no—
59C2×C3×Dic6C23112yes—
60C2×C3×Dic6C2316yes—
61C32×C4⋊C4C2316yes—
62C32×C22⋊C4C2316yes—
63C32×C42C2311yescharacteristic
64C32×C42C2313yes—
65C32×C42C2316yes—
66C3×(C2×D3)⋊C4C23124yes—
67C3×C4⋊Dic3C23124yes—
68C3×C4⋊Dic3C23112yes—
69#3499—31noSylow
70C3×2−1+4—616no—
71C2×C3×#41—21no—
72C2×C3×#41—312no—
73C2×C3×#41—36no—
74C2×C3×#41C2×D311yescharacteristic
75C2×C3×#41C22×C311yescharacteristic
76C22×C3×Q8—34no—
77C22×C3×Q8—36no—
78#1010—216no—
79C2×D3×Q8C22×C314yes—
80C2×#237C22×C3112yes—
81C2×#235C22×C316yes—
82C22×Dic6C22×C316yes—
83C3×C4⋊Q8—33no—
84C3×C4⋊Q8—36no—
85C3×C4⋊Q8—312no—
86C3×#127—31no—
87C3×#124—36no—
88C3×#123—324no—
89C3×C22⋊Q8—324no—
90C3×#121—312no—
91C3×C4×Q8—22no—
92C3×C4×Q8C2×D312yes—
93C3×C4×Q8C22×C312yes—
94C3×C4×D4—26no—
95C3×C4×D4—312no—
96C3×C4×D4C2×D316yes—
97C3×C4×D4C22×C316yes—
98C3×#117—23no—
99C3×#117C2×D313yes—
100C3×#117C22×C313yes—
101C2×C3×C4⋊C4—312no—
102C2×C3×C42—23no—
103C2×C3×C42C2×D313yes—
104C2×C3×C42C22×C313yes—
105#930C22×C3112yes—
106C2×C4⋊Dic3C22×C3112yes—
107#897C22×C3124yes—
108#886C22×C3124yes—
109#875C22×C316yes—
110#874C22×C311yescharacteristic
111C4×D12C22×C3112yes—
112#869C22×C313yes—
113#869C22×C316yes—
114#869C22×C3112yes—
115C23×C32C2413yes—
116C22×C3×D3C2414yes—
117C32×Q8C2×D414yes—
118C32×D4C2×D4112yes—
119C2×C32×C4—212no—
120C2×C32×C4C2×D4112yes—
121C2×C32×C4C2416yes—
122C2×C32×C4C2411yescharacteristic
123C2×C32×C4C2413yes—
124C2×C32×C4C2412yes—
125C3×#67—224no—
126C2×C3×Dic3—224no—
127C2×C3×Dic3C24112yes—
128C3×D12—24no—
129C3×D12—28no—
130C3×C4×D3—224no—
131C3×Dic6—212no—
132C3×Dic6—224no—
133C2×2−1+4—32no—
134D4×Q8—34no—
135#547—312no—
136#536—36no—
137#532—33no—
138C2×C4⋊Q8—33no—
139C4×#41C3×D311yescharacteristic, complemented
140C3×#41—28no—
141C3×#41—648no—
142C3×#41—624no—
143C3×#41D1218yescomplemented
144C3×#41C3×D418yescomplemented
145C2×C3×Q8—21no—
146C2×C3×Q8—312no—
147C2×C3×Q8—36no—
148C2×C3×Q8—616no—
149C2×C3×Q8—624no—
150C2×C3×Q8C22×D311yescharacteristic
151C2×C3×Q8C23×C311yescharacteristic
152C2×C3×D4—23no—
153C2×C3×D4—312no—
154C2×C3×D4—34no—
155C2×C3×D4—32no—
156C2×C3×D4C22×D313yes—
157C2×C3×D4C23×C313yes—
158C22×C3×C4—23no—
159C22×C3×C4—26no—
160C22×C3×C4—312no—
161C22×C3×C4—312no—
162C22×C3×C4C22×D316yes—
163C22×C3×C4C22×D313yes—
164C22×C3×C4C23×C316yes—
165C22×C3×C4C23×C313yes—
166C2×#67C23×C3112yes—
167C22×Dic3C23×C3112yes—
168D3×Q8—216no—
169#237—248no—
170#235—224no—
171C2×D12C23×C314yes—
172C2×D12C23×C312yes—
173C2×C4×D3C23×C3112yes—
174C2×Dic6—224no—
175C2×Dic6C23×C316yes—
176C2×Dic6C23×C3112yes—
177C3×C4⋊C4—26no—
178C3×C4⋊C4—312no—
179C3×C4⋊C4—324no—
180C3×C4⋊C4C22×D316yes—
181C3×C4⋊C4C23×C316yes—
182C3×C22⋊C4—26no—
183C3×C22⋊C4—324no—
184C3×C22⋊C4C22×D316yes—
185C3×C22⋊C4C23×C316yes—
186C3×C42—21no—
187C3×C42—23no—
188C3×C42—26no—
189C3×C42C22×D311yescharacteristic
190C3×C42C22×D313yes—
191C3×C42C22×D316yes—
192C3×C42C23×C311yescharacteristic
193C3×C42C23×C316yes—
194C3×C42C23×C313yes—
195(C2×D3)⋊C4C23×C3124yes—
196C4⋊Dic3C23×C3112yes—
197C4⋊Dic3C23×C3124yes—
198C22×C32—26no—
199C22×C32C22×D416yes—
200C22×C32C2511yescharacteristic
201C2×C3×D3—24no—
202C2×C3×D3—28no—
203C32×C4—26no—
204C32×C4C22×D412yes—
205C32×C4C22×D416yes—
206C32×C42−1+414yescomplemented
207C3×Dic3—212no—
2082−1+4—616no—
209C2×#41—312no—
210C2×#41—36no—
211C2×#41C2×C3×D311yescharacteristic
212C22×Q8—34no—
213C22×Q8—36no—
214C4⋊Q8—33no—
215C4⋊Q8—36no—
216C4⋊Q8—312no—
217#127—31no—
218#124—36no—
219#123—324no—
220C22⋊Q8—324no—
221#121—312no—
222C4×Q8C2×C3×D312yes—
223C4×D4—312no—
224C4×D4C2×C3×D316yes—
225#117C2×C3×D313yes—
226C2×C4⋊C4—312no—
227C2×C42C2×C3×D313yes—
228C23×C3—23no—
229C23×C3—34no—
230C23×C3C23×D313yes—
231C23×C3C24×C313yes—
232C22×D3C24×C314yes—
233C3×Q8—24no—
234C3×Q8—624no—
235C3×Q8—612no—
236C3×Q8C2×D1214yes—
237C3×Q8C2×C3×D414yes—
238C3×D4—212no—
239C3×D4—624no—
240C3×D4—64no—
241C3×D4—68no—
242C3×D4C2×D12112yes—
243C3×D4C2×C3×D4112yes—
244C2×C3×C4—212no—
245C2×C3×C4—212no—
246C2×C3×C4—21no—
247C2×C3×C4—22no—
248C2×C3×C4—23no—
249C2×C3×C4—26no—
250C2×C3×C4—212no—
251C2×C3×C4—312no—
252C2×C3×C4—412no—
253C2×C3×C4—624no—
254C2×C3×C4—624no—
255C2×C3×C4C2×D12112yes—
256C2×C3×C4C2×C3×D4112yes—
257C2×C3×C4C23×D316yes—
258C2×C3×C4C23×D311yescharacteristic
259C2×C3×C4C23×D313yes—
260C2×C3×C4C23×D312yes—
261C2×C3×C4C24×C316yes—
262C2×C3×C4C24×C311yescharacteristic
263C2×C3×C4C24×C313yes—
264C2×C3×C4C24×C312yes—
265#67—224no—
266C2×Dic3—224no—
267C2×Dic3C24×C3112yes—
268D12—24no—
269D12—28no—
270C4×D3—224no—
271Dic6—212no—
272Dic6—224no—
273C2×C32—26no—
274C2×C32C23×D411yescharacteristic
275C2×C32C2×2−1+412yes—
276C3×D3—44no—
277#41—648no—
278#41—624no—
279#41C3×D1218yescomplemented
280C2×Q8—312no—
281C2×Q8—36no—
282C2×Q8—616no—
283C2×Q8—624no—
284C2×Q8C22×C3×D311yescharacteristic
285C2×D4—312no—
286C2×D4—34no—
287C2×D4—32no—
288C2×D4C22×C3×D313yes—
289C22×C4—312no—
290C22×C4—312no—
291C22×C4C22×C3×D316yes—
292C22×C4C22×C3×D313yes—
293C4⋊C4—312no—
294C4⋊C4—324no—
295C4⋊C4C22×C3×D316yes—
296C22⋊C4—324no—
297C22⋊C4C22×C3×D316yes—
298C42C22×C3×D311yescharacteristic
299C42C22×C3×D313yes—
300C42C22×C3×D316yes—
301C22×C3—26no—
302C22×C3—26no—
303C22×C3—26no—
304C22×C3—21no—
305C22×C3—46no—
306C22×C3—64no—
307C22×C3—68no—
308C22×C3C22×D1216yes—
309C22×C3C22×C3×D416yes—
310C22×C3C24×D311yescharacteristic
311C22×C3C25×C311yescharacteristic
312C2×D3—24no—
313C2×D3—28no—
314C3×C4—26no—
315C3×C4—26no—
316C3×C4—22no—
317C3×C4—26no—
318C3×C4—24no—
319C3×C4—46no—
320C3×C4—612no—
321C3×C4C22×D1216yes—
322C3×C4C22×D1212yes—
323C3×C4#101014yescomplemented
324C3×C4C22×C3×D412yes—
325C3×C4C22×C3×D416yes—
326C3×C4C3×2−1+414yescomplemented
327Dic3—212no—
328C32#349911yescharacteristic, complemented, Sylow
329C23—34no—
330C23C23×C3×D313yes—
331Q8—624no—
332Q8—612no—
333Q8C2×C3×D1214yes—
334D4—624no—
335D4—64no—
336D4—68no—
337D4C2×C3×D12112yes—
338C2×C4—212no—
339C2×C4—312no—
340C2×C4—624no—
341C2×C4—624no—
342C2×C4C2×C3×D12112yes—
343C2×C4C23×C3×D316yes—
344C2×C4C23×C3×D311yescharacteristic
345C2×C4C23×C3×D313yes—
346C2×C4C23×C3×D312yes—
347C2×C3—26no—
348C2×C3—26no—
349C2×C3—21no—
350C2×C3—22no—
351C2×C3—46no—
352C2×C3—124no—
353C2×C3C23×D1211yescharacteristic
354C2×C3C2×#101012yes—
355C2×C3C23×C3×D411yescharacteristic
356C2×C3C2×C3×2−1+412yes—
357D3—44no—
358C22—26no—
359C22—64no—
360C22—68no—
361C22C22×C3×D1216yes—
362C22C24×C3×D311yescharacteristic
363C4—26no—
364C4—612no—
365C4C22×C3×D1216yes—
366C4C22×C3×D1212yes—
367C4C3×#101014yescomplemented
368C3—21no—
369C3#8582711yescharacteristic, direct product factor
370C3C3×#349911yescharacteristic, complemented
371C2—26no—
372C2—124no—
373C2C23×C3×D1211yescharacteristic
374C2C2×C3×#101012yes—
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×C4×#41C2
socleC22×C32C25
hypercenterC3×C4×#41D3
hypocenterC3C3×#3499
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C32×C4×#41C2semidirect
3. C3×Q8×D12C2semidirect
4. C3×#5555C2semidirect
5. C3×#5526C2semidirect
6. C3×#5477C2semidirect
7. C2×C3×#869C2semidirect
9. #85827C3direct (N × H)
31. C2×#1010C2×C3semidirect
38. C3×C4×#41D3semidirect
39. C3×C4×#41C2×C3semidirect
40. Q8×D12C2×C3semidirect
41. #5555C2×C3semidirect
42. #5526C2×C3semidirect
43. #5477C2×C3semidirect
44. C2×#869C2×C3semidirect
45. C32×#41D4semidirect
139. C4×#41C3×D3semidirect
143. C3×#41D12semidirect
144. C3×#41C3×D4semidirect
206. C32×C42−1+4semidirect
279. #41C3×D12semidirect
323. C3×C4#1010semidirect
326. C3×C4C3×2−1+4semidirect
328. C32#3499semidirect
367. C4C3×#1010semidirect
369. C3#85827direct (N × H)
370. C3C3×#3499semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C32×C4×#412
C3×Q8×D122
C3×#55552
C3×#55262
C3×#54772
C2×C3×#8692
C3×#34993
#858273