Finite Group Databasebeta

← C3×#85818 #11905889

Subgroups — C3×#85818 #11905889

Order 1152.

3133 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C212yesmaximal, complemented
2C2×C32×C4×Q8C211yesmaximal, characteristic, complemented
3C3×#5577C214yesmaximal, complemented
4C3×#5576C218yesmaximal, complemented
5C3×Q8×D12C214yesmaximal, complemented
6C3×#5510C216yesmaximal, complemented
7C3×#5477C216yesmaximal, complemented
8C3×#3497—31nomaximal
9#85818C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C3×#1007—216no—
12C2×C3×#239C2218yes—
13C2×C3×D3×Q8C2218yes—
14C2×C3×#235C22112yes—
15C32×C4×Q8C2214yes—
16C32×C4×Q8C2214yes—
17C2×C32×C4⋊C4C2213yes—
18C2×C32×C42C2213yes—
19C3×#930C22112yes—
20C3×#930C2214yes—
21C3×#897C22124yes—
22C3×#895C22124yes—
23C3×#875C22112yes—
24C3×#874C2216yes—
25C3×C4×D12C22112yes—
26C3×C4×D12C22112yes—
27C3×#869C2216yes—
28C2×C3×2−1+4—32no—
29C2×#1007C2×C312yescomplemented
30C3×#550—34no—
31C3×D4×Q8—34no—
32C3×#548—38no—
33C3×#537—36no—
34C3×#532—36no—
35C2×C3×C4×Q8—21no—
36C2×C3×C4×Q8D311yescharacteristic, complemented
37C2×C3×C4×Q8C2×C311yescharacteristic, complemented
38#5577C2×C314yescomplemented
39#5576C2×C318yescomplemented
40Q8×D12C2×C314yescomplemented
41#5510C2×C316yescomplemented
42#5477C2×C316yescomplemented
43C2×C32×Q8D418yescomplemented
44C2×C32×Q8C2314yes—
45C22×C32×C4C2311yescharacteristic
46C22×C32×C4C2313yes—
47C22×C32×C4C2313yes—
48C2×C3×#67C2318yes—
49C3×#239—232no—
50C3×D3×Q8—232no—
51C3×#235—248no—
52C2×C3×D12C23112yes—
53C2×C3×D12C2314yes—
54C2×C3×D12C23112yes—
55C2×C3×C4×D3C23124yes—
56C2×C3×Dic6C23112yes—
57C32×C4⋊C4C23112yes—
58C32×C42C2316yes—
59C32×C42C2316yes—
60C3×(C2×D3)⋊C4C23124yes—
61C3×(C2×D3)⋊C4C2318yes—
62C3×C4⋊Dic3C23112yes—
63C3×C4⋊Dic3C2314yes—
64#3497—31noSylow
65C3×2−1+4—616no—
66C2×C3×#41—38no—
67C2×C3×#41—312no—
68C22×C3×Q8—21no—
69C22×C3×Q8—38no—
70C22×C3×Q8C2×D311yescharacteristic
71C22×C3×Q8C22×C311yescharacteristic
72#1007—216no—
73C2×#239C22×C318yes—
74C2×D3×Q8C22×C318yes—
75C2×#235C22×C3112yes—
76C3×C4⋊Q8—36no—
77C3×#127—36no—
78C3×#124—312no—
79C3×C22⋊Q8—324no—
80C3×#121—34no—
81C3×#121—312no—
82C3×#121—324no—
83C3×C4×Q8—24no—
84C3×C4×Q8—24no—
85C3×C4×Q8C2×D314yes—
86C3×C4×Q8C2×D314yes—
87C3×C4×Q8C22×C314yes—
88C3×C4×Q8C22×C314yes—
89C3×C4×D4—312no—
90C3×C4×D4—312no—
91C2×C3×C4⋊C4—23no—
92C2×C3×C4⋊C4C2×D313yes—
93C2×C3×C4⋊C4C22×C313yes—
94C2×C3×C42—23no—
95C2×C3×C42C2×D313yes—
96C2×C3×C42C22×C313yes—
97#930C22×C314yes—
98#930C22×C3112yes—
99#897C22×C3124yes—
100#895C22×C3124yes—
101#875C22×C3112yes—
102#874C22×C316yes—
103C4×D12C22×C3112yes—
104C4×D12C22×C3112yes—
105#869C22×C316yes—
106C23×C32C2411yescharacteristic
107C22×C3×D3C2418yes—
108C32×Q8C2×D4116yes—
109C2×C32×C4—22no—
110C2×C32×C4—43no—
111C2×C32×C4C2×D4112yes—
112C2×C32×C4C2416yes—
113C2×C32×C4C2411yescharacteristic
114C2×C32×C4C2416yes—
115C2×C32×C4C2411yescharacteristic
116C3×#67—216no—
117C2×C3×Dic3C2418yes—
118C3×D12—224no—
119C3×D12—28no—
120C3×D12—412no—
121C3×C4×D3—248no—
122C3×Dic6—224no—
123C2×2−1+4—32no—
124#550—34no—
125D4×Q8—34no—
126#548—38no—
127#537—36no—
128#532—36no—
129C2×C4×Q8C3×D311yescharacteristic, complemented
130C3×#41—632no—
131C3×#41—648no—
132C2×C3×Q8—28no—
133C2×C3×Q8—24no—
134C2×C3×Q8—312no—
135C2×C3×Q8—632no—
136C2×C3×Q8D1218yescomplemented
137C2×C3×Q8C3×D418yescomplemented
138C2×C3×Q8C22×D314yes—
139C2×C3×Q8C23×C314yes—
140C2×C3×D4—38no—
141C2×C3×D4—34no—
142C2×C3×D4—312no—
143C2×C3×D4—312no—
144C22×C3×C4—21no—
145C22×C3×C4—23no—
146C22×C3×C4—23no—
147C22×C3×C4—324no—
148C22×C3×C4C22×D311yescharacteristic
149C22×C3×C4C22×D313yes—
150C22×C3×C4C22×D313yes—
151C22×C3×C4C23×C311yescharacteristic
152C22×C3×C4C23×C313yes—
153C22×C3×C4C23×C313yes—
154C2×#67C23×C318yes—
155#239—232no—
156D3×Q8—232no—
157#235—248no—
158C2×D12C23×C314yes—
159C2×D12C23×C3112yes—
160C2×D12C23×C3112yes—
161C2×C4×D3C23×C3124yes—
162C2×Dic6C23×C3112yes—
163C3×C4⋊C4—212no—
164C3×C4⋊C4—34no—
165C3×C4⋊C4—312no—
166C3×C4⋊C4C22×D3112yes—
167C3×C4⋊C4C23×C3112yes—
168C3×C22⋊C4—38no—
169C3×C22⋊C4—324no—
170C3×C42—26no—
171C3×C42—26no—
172C3×C42C22×D316yes—
173C3×C42C22×D316yes—
174C3×C42C23×C316yes—
175C3×C42C23×C316yes—
176(C2×D3)⋊C4C23×C318yes—
177(C2×D3)⋊C4C23×C3124yes—
178C4⋊Dic3C23×C314yes—
179C4⋊Dic3C23×C3112yes—
180C22×C32—21no—
181C22×C32—21no—
182C22×C32C22×D412yes—
183C22×C32C2511yescharacteristic
184C2×C3×D3—28no—
185C2×C3×D3—28no—
186C2×C3×D3—28no—
187C32×C4—21no—
188C32×C4—26no—
189C32×C4C22×D4112yes—
190C32×C42−1+412yescomplemented
191C3×Dic3—28no—
1922−1+4—616no—
193C2×#41—38no—
194C2×#41—312no—
195C22×Q8—38no—
196C22×Q8C2×C3×D311yescharacteristic
197C4⋊Q8—36no—
198#127—36no—
199#124—312no—
200C22⋊Q8—324no—
201#121—34no—
202#121—312no—
203#121—324no—
204C4×Q8C2×C3×D314yes—
205C4×Q8C2×C3×D314yes—
206C4×D4—312no—
207C4×D4—312no—
208C2×C4⋊C4C2×C3×D313yes—
209C2×C42C2×C3×D313yes—
210C23×C3—21no—
211C23×C3—38no—
212C23×C3C23×D311yescharacteristic
213C23×C3C24×C311yescharacteristic
214C22×D3C24×C318yes—
215C3×Q8—216no—
216C3×Q8—624no—
217C3×Q8C2×D12116yes—
218C3×Q8C2×C3×D4116yes—
219C3×D4—616no—
220C3×D4—624no—
221C3×D4—68no—
222C3×D4—1212no—
223C2×C3×C4—24no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—26no—
229C2×C3×C4—26no—
230C2×C3×C4—212no—
231C2×C3×C4—38no—
232C2×C3×C4—43no—
233C2×C3×C4—43no—
234C2×C3×C4—46no—
235C2×C3×C4—648no—
236C2×C3×C4C2×D12112yes—
237C2×C3×C4C2×C3×D4112yes—
238C2×C3×C4C23×D311yescharacteristic
239C2×C3×C4C23×D316yes—
240C2×C3×C4C23×D316yes—
241C2×C3×C4C23×D311yescharacteristic
242C2×C3×C4C24×C316yes—
243C2×C3×C4C24×C311yescharacteristic
244C2×C3×C4C24×C316yes—
245C2×C3×C4C24×C311yescharacteristic
246#67—216no—
247C2×Dic3C24×C318yes—
248D12—224no—
249D12—28no—
250D12—412no—
251C4×D3—248no—
252Dic6—224no—
253C2×C32—22no—
254C2×C32C23×D411yescharacteristic
255C2×C32C2×2−1+411yescharacteristic
256C2×C32#58511yescharacteristic
257C3×D3—48no—
258#41—632no—
259#41—648no—
260C2×Q8—312no—
261C2×Q8—632no—
262C2×Q8C3×D1218yescomplemented
263C2×Q8C22×C3×D314yes—
264C2×D4—38no—
265C2×D4—34no—
266C2×D4—312no—
267C2×D4—312no—
268C22×C4—324no—
269C22×C4C22×C3×D311yescharacteristic
270C22×C4C22×C3×D313yes—
271C22×C4C22×C3×D313yes—
272C4⋊C4—34no—
273C4⋊C4—312no—
274C4⋊C4C22×C3×D3112yes—
275C22⋊C4—38no—
276C22⋊C4—324no—
277C42C22×C3×D316yes—
278C42C22×C3×D316yes—
279C22×C3—22no—
280C22×C3—22no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—21no—
284C22×C3—21no—
285C22×C3—22no—
286C22×C3—21no—
287C22×C3—68no—
288C22×C3—68no—
289C22×C3—68no—
290C22×C3C22×D1212yes—
291C22×C3C22×C3×D412yes—
292C22×C3C24×D311yescharacteristic
293C22×C3C25×C311yescharacteristic
294C2×D3—28no—
295C2×D3—28no—
296C2×D3—28no—
297C3×C4—22no—
298C3×C4—21no—
299C3×C4—26no—
300C3×C4—21no—
301C3×C4—26no—
302C3×C4—212no—
303C3×C4—22no—
304C3×C4—46no—
305C3×C4—68no—
306C3×C4C22×D12112yes—
307C3×C4#100712yescomplemented
308C3×C4C22×C3×D4112yes—
309C3×C4C3×2−1+412yescomplemented
310Dic3—28no—
311C32#349711yescharacteristic, complemented, Sylow
312C23—38no—
313C23C23×C3×D311yescharacteristic
314Q8—624no—
315Q8C2×C3×D12116yes—
316D4—616no—
317D4—624no—
318D4—68no—
319D4—1212no—
320C2×C4—22no—
321C2×C4—38no—
322C2×C4—43no—
323C2×C4—648no—
324C2×C4C2×C3×D12112yes—
325C2×C4C23×C3×D311yescharacteristic
326C2×C4C23×C3×D316yes—
327C2×C4C23×C3×D316yes—
328C2×C4C23×C3×D311yescharacteristic
329C2×C3—24no—
330C2×C3—22no—
331C2×C3—22no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—128no—
336C2×C3C23×D1211yescharacteristic
337C2×C3C2×#100711yescharacteristic
338C2×C3#596411yescharacteristic
339C2×C3C23×C3×D411yescharacteristic
340C2×C3C2×C3×2−1+411yescharacteristic
341C2×C3C3×#58511yescharacteristic
342D3—48no—
343C22—21no—
344C22—21no—
345C22—68no—
346C22—68no—
347C22—68no—
348C22C22×C3×D1212yes—
349C22C24×C3×D311yescharacteristic
350C4—21no—
351C4—26no—
352C4—68no—
353C4C22×C3×D12112yes—
354C4C3×#100712yescomplemented
355C3—21no—
356C3#8581811yescharacteristic, direct product factor
357C3C3×#349711yescharacteristic, complemented
358C2—22no—
359C2—128no—
360C2C23×C3×D1211yescharacteristic
361C2C2×C3×#100711yescharacteristic
362C2C3×#596411yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C4×Q8C2
socleC22×C32C25
hypercenterC2×C3×C4×Q8D3
hypocenterC3C3×#3497
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1007C2semidirect
2. C2×C32×C4×Q8C2semidirect
3. C3×#5577C2semidirect
4. C3×#5576C2semidirect
5. C3×Q8×D12C2semidirect
6. C3×#5510C2semidirect
7. C3×#5477C2semidirect
9. #85818C3direct (N × H)
29. C2×#1007C2×C3semidirect
36. C2×C3×C4×Q8D3semidirect
37. C2×C3×C4×Q8C2×C3semidirect
38. #5577C2×C3semidirect
39. #5576C2×C3semidirect
40. Q8×D12C2×C3semidirect
41. #5510C2×C3semidirect
42. #5477C2×C3semidirect
43. C2×C32×Q8D4semidirect
129. C2×C4×Q8C3×D3semidirect
136. C2×C3×Q8D12semidirect
137. C2×C3×Q8C3×D4semidirect
190. C32×C42−1+4semidirect
262. C2×Q8C3×D12semidirect
307. C3×C4#1007semidirect
309. C3×C4C3×2−1+4semidirect
311. C32#3497semidirect
354. C4C3×#1007semidirect
356. C3#85818direct (N × H)
357. C3C3×#3497semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C2×C32×C4×Q82
C3×#55772
C3×#55762
C3×Q8×D122
C3×#55102
C3×#54772
C3×#34973
#858183