Finite Group Databasebeta

← C2×C3×Q8×D12 #11902655

Subgroups — C2×C3×Q8×D12 #11902655

Order 1152.

3285 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Q8C212yesmaximal, complemented
2C2×C32×C4×Q8C211yesmaximal, characteristic, complemented
3C3×Q8×D12C2116yesmaximal, direct product factor
4C2×C3×#897C216yesmaximal, complemented
5C2×C3×C4×D12C213yesmaximal
6C2×C3×#869C213yesmaximal, complemented
7C2×C3×D4×Q8—31nomaximal
8C2×Q8×D12C311yesmaximal, characteristic, direct product factor
9C22×C32×Q8C2211yescharacteristic
10C2×C3×D3×Q8—216no—
11C2×C3×D3×Q8C22116yescomplemented
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3C2216yes—
14C22×C3×Dic6C2216yes—
15C32×C4×Q8C2218yescomplemented
16C2×C32×C4⋊C4C2213yes—
17C2×C32×C42C2213yes—
18C2×C3×(C2×D3)⋊C4C2216yes—
19C2×C3×C4⋊Dic3C2216yes—
20C2×C3×C4⋊Dic3C2213yes—
21C3×#897C22148yescomplemented
22C3×C4×D12C22124yes—
23C3×#869C22124yescomplemented
24C23×C3×Q8—32no—
25C22×D3×Q8C2×C312yescomplemented
26C3×D4×Q8—316no—
27C2×C3×C4⋊Q8—33no—
28C2×C3×C22⋊Q8—36no—
29C2×C3×C4×Q8—21no—
30C2×C3×C4×Q8D311yescharacteristic, complemented
31C2×C3×C4×Q8C2×C311yescharacteristic, complemented
32C2×C3×C4×D4—33no—
33Q8×D12C2×C3116yesdirect product factor
34C2×#897C2×C316yescomplemented
35C2×C4×D12C2×C313yes—
36C2×#869C2×C313yescomplemented
37C23×C3×D3C2312yes—
38C2×C32×Q8D418yescomplemented
39C2×C32×Q8C2314yes—
40C22×C32×C4C2313yes—
41C22×C32×C4C2313yes—
42C22×C32×C4C2311yescharacteristic
43C22×C3×Dic3C2316yes—
44C3×D3×Q8—264no—
45C2×C3×D12Q818yesdirect product factor
46C2×C3×D12C2314yes—
47C2×C3×C4×D3—224no—
48C2×C3×C4×D3C23124yes—
49C2×C3×Dic6—224no—
50C2×C3×Dic6C23124yes—
51C32×C4⋊C4C23112yes—
52C32×C42C23112yes—
53C3×(C2×D3)⋊C4C23124yes—
54C3×C4⋊Dic3C23124yes—
55C3×C4⋊Dic3C23112yes—
56C2×D4×Q8—31noSylow
57C22×C3×Q8—21no—
58C22×C3×Q8—316no—
59C22×C3×Q8—36no—
60C22×C3×Q8—616no—
61C22×C3×Q8C2×D311yescharacteristic
62C22×C3×Q8C22×C311yescharacteristic
63C22×C3×D4—31no—
64C23×C3×C4—36no—
65C2×D3×Q8—216no—
66C2×D3×Q8C22×C3116yescomplemented
67C22×D12C22×C311yescharacteristic
68C22×C4×D3C22×C316yes—
69C22×Dic6C22×C316yes—
70C3×C4⋊Q8—324no—
71C3×C22⋊Q8—348no—
72C3×C4×Q8—28no—
73C3×C4×Q8C2×D318yescomplemented
74C3×C4×Q8C22×C318yescomplemented
75C3×C4×D4—324no—
76C2×C3×C4⋊C4—23no—
77C2×C3×C4⋊C4—33no—
78C2×C3×C4⋊C4—36no—
79C2×C3×C4⋊C4C2×D313yes—
80C2×C3×C4⋊C4C22×C313yes—
81C2×C3×C22⋊C4—36no—
82C2×C3×C42—23no—
83C2×C3×C42C2×D313yes—
84C2×C3×C42C22×C313yes—
85C2×(C2×D3)⋊C4C22×C316yes—
86C2×C4⋊Dic3C22×C313yes—
87C2×C4⋊Dic3C22×C316yes—
88#897C22×C3148yescomplemented
89C4×D12C22×C3124yes—
90#869C22×C3124yescomplemented
91C23×C32C2411yescharacteristic
92C22×C3×D3—24no—
93C22×C3×D3—24no—
94C22×C3×D3C2×Q818yescomplemented
95C22×C3×D3C2414yes—
96C32×Q8C2×D4116yescomplemented
97C2×C32×C4—26no—
98C2×C32×C4C2×D4112yes—
99C2×C32×C4C2×Q814yescomplemented
100C2×C32×C4C2416yes—
101C2×C32×C4C2416yes—
102C2×C32×C4C2412yes—
103C2×C3×Dic3—212no—
104C2×C3×Dic3C24112yes—
105C3×D12C2×Q8116yesdirect product factor
106C3×C4×D3—248no—
107C3×Dic6—248no—
108C23×Q8—32no—
109D4×Q8—316no—
110C2×C4⋊Q8—33no—
111C2×C22⋊Q8—36no—
112C2×C4×Q8C3×D311yescharacteristic, complemented
113C2×C4×D4—33no—
114C24×C3—32no—
115C23×D3C23×C312yes—
116C2×C3×Q8—28no—
117C2×C3×Q8—24no—
118C2×C3×Q8—324no—
119C2×C3×Q8—664no—
120C2×C3×Q8—624no—
121C2×C3×Q8D1218yesdirect product factor
122C2×C3×Q8C3×D418yescomplemented
123C2×C3×Q8C22×D314yes—
124C2×C3×Q8C23×C314yes—
125C2×C3×D4—38no—
126C2×C3×D4—34no—
127C22×C3×C4—21no—
128C22×C3×C4—23no—
129C22×C3×C4—23no—
130C22×C3×C4—36no—
131C22×C3×C4—324no—
132C22×C3×C4—624no—
133C22×C3×C4C22×D313yes—
134C22×C3×C4C22×D313yes—
135C22×C3×C4C22×D311yescharacteristic
136C22×C3×C4C23×C313yes—
137C22×C3×C4C23×C313yes—
138C22×C3×C4C23×C311yescharacteristic
139C22×Dic3C23×C316yes—
140D3×Q8—264no—
141C2×D12C3×Q818yesdirect product factor
142C2×D12C23×C314yes—
143C2×C4×D3—224no—
144C2×C4×D3C23×C3124yes—
145C2×Dic6—224no—
146C2×Dic6C23×C3124yes—
147C3×C4⋊C4—212no—
148C3×C4⋊C4—312no—
149C3×C4⋊C4—324no—
150C3×C4⋊C4C22×D3112yes—
151C3×C4⋊C4C23×C3112yes—
152C3×C22⋊C4—324no—
153C3×C42—212no—
154C3×C42C22×D3112yes—
155C3×C42C23×C3112yes—
156(C2×D3)⋊C4C23×C3124yes—
157C4⋊Dic3C23×C3112yes—
158C4⋊Dic3C23×C3124yes—
159C22×C32C22×D412yes—
160C22×C32C22×Q812yes—
161C22×C322−1+412yes—
162C22×C32C2511yescharacteristic
163C2×C3×D3—216no—
164C2×C3×D3—24no—
165C2×C3×D3—24no—
166C2×C3×D3C22×Q818yescomplemented
167C32×C4—26no—
168C32×C4C22×D4112yes—
169C32×C4C22×Q814yescomplemented
170C3×Dic3—212no—
171C22×Q8—316no—
172C22×Q8—36no—
173C22×Q8—616no—
174C22×Q8C2×C3×D311yescharacteristic
175C22×D4—31no—
176C23×C4—36no—
177C4⋊Q8—324no—
178C22⋊Q8—348no—
179C4×Q8C2×C3×D318yescomplemented
180C4×D4—324no—
181C2×C4⋊C4—33no—
182C2×C4⋊C4—36no—
183C2×C4⋊C4C2×C3×D313yes—
184C2×C22⋊C4—36no—
185C2×C42C2×C3×D313yes—
186C23×C3—21no—
187C23×C3—38no—
188C23×C3—34no—
189C23×C3—64no—
190C23×C3—64no—
191C23×C3C23×D311yescharacteristic
192C23×C3C24×C311yescharacteristic
193C22×D3—24no—
194C22×D3—24no—
195C22×D3C2×C3×Q818yescomplemented
196C22×D3C24×C314yes—
197C3×Q8—216no—
198C3×Q8—648no—
199C3×Q8C2×D12116yesdirect product factor
200C3×Q8C2×C3×D4116yescomplemented
201C3×D4—316no—
202C2×C3×C4—26no—
203C2×C3×C4—26no—
204C2×C3×C4—22no—
205C2×C3×C4—26no—
206C2×C3×C4—26no—
207C2×C3×C4—212no—
208C2×C3×C4—24no—
209C2×C3×C4—312no—
210C2×C3×C4—46no—
211C2×C3×C4—612no—
212C2×C3×C4—648no—
213C2×C3×C4C2×D12112yes—
214C2×C3×C4D3×Q814yescomplemented
215C2×C3×C4C2×C3×D4112yes—
216C2×C3×C4C2×C3×Q814yescomplemented
217C2×C3×C4C23×D316yes—
218C2×C3×C4C23×D316yes—
219C2×C3×C4C23×D312yes—
220C2×C3×C4C24×C316yes—
221C2×C3×C4C24×C316yes—
222C2×C3×C4C24×C312yes—
223C2×Dic3—212no—
224C2×Dic3C24×C3112yes—
225D12C2×C3×Q8116yesdirect product factor
226C4×D3—248no—
227Dic6—248no—
228C2×C32D4×Q814yescomplemented
229C2×C32C23×D411yescharacteristic
230C2×C32C23×Q811yescharacteristic
231C2×C32C2×2−1+411yescharacteristic
232C3×D3—28no—
233C24—32no—
234C2×Q8—324no—
235C2×Q8—664no—
236C2×Q8—624no—
237C2×Q8C3×D1218yesdirect product factor
238C2×Q8C22×C3×D314yes—
239C2×D4—34no—
240C2×D4—38no—
241C22×C4—36no—
242C22×C4—324no—
243C22×C4—624no—
244C22×C4C22×C3×D313yes—
245C22×C4C22×C3×D313yes—
246C22×C4C22×C3×D311yescharacteristic
247C4⋊C4—312no—
248C4⋊C4—324no—
249C4⋊C4C22×C3×D3112yes—
250C22⋊C4—324no—
251C42C22×C3×D3112yes—
252C22×C3—22no—
253C22×C3—22no—
254C22×C3—22no—
255C22×C3—21no—
256C22×C3—38no—
257C22×C3—64no—
258C22×C3—64no—
259C22×C3—616no—
260C22×C3C22×D1212yes—
261C22×C3C2×D3×Q812yes—
262C22×C3#101012yes—
263C22×C3C22×C3×D412yes—
264C22×C3C22×C3×Q812yes—
265C22×C3C3×2−1+412yes—
266C22×C3C24×D311yescharacteristic
267C22×C3C25×C311yescharacteristic
268C2×D3—24no—
269C2×D3—24no—
270C2×D3—216no—
271C2×D3C22×C3×Q818yescomplemented
272C3×C4—26no—
273C3×C4—26no—
274C3×C4—212no—
275C3×C4—24no—
276C3×C4—46no—
277C3×C4—612no—
278C3×C4C22×D12112yes—
279C3×C4C2×D3×Q814yescomplemented
280C3×C4C22×C3×D4112yes—
281C3×C4C22×C3×Q814yescomplemented
282Dic3—212no—
283C32C2×D4×Q811yescharacteristic, complemented, Sylow
284C23—38no—
285C23—34no—
286C23—64no—
287C23—64no—
288C23C23×C3×D311yescharacteristic
289Q8—648no—
290Q8C2×C3×D12116yesdirect product factor
291D4—316no—
292C2×C4—26no—
293C2×C4—312no—
294C2×C4—612no—
295C2×C4—648no—
296C2×C4C2×C3×D12112yes—
297C2×C4C3×D3×Q814yescomplemented
298C2×C4C23×C3×D316yes—
299C2×C4C23×C3×D316yes—
300C2×C4C23×C3×D312yes—
301C2×C3—24no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—68no—
306C2×C3Q8×D1214yesdirect product factor
307C2×C3C3×D4×Q814yescomplemented
308C2×C3C23×D1211yescharacteristic
309C2×C3C22×D3×Q811yescharacteristic
310C2×C3C2×#101011yescharacteristic
311C2×C3C23×C3×D411yescharacteristic
312C2×C3C23×C3×Q811yescharacteristic
313C2×C3C2×C3×2−1+411yescharacteristic
314D3—28no—
315C22—38no—
316C22—616no—
317C22—64no—
318C22—64no—
319C22C22×C3×D1212yes—
320C22C2×C3×D3×Q812yes—
321C22C3×#101012yes—
322C22C24×C3×D311yescharacteristic
323C4—26no—
324C4—612no—
325C4C22×C3×D12112yes—
326C4C2×C3×D3×Q814yescomplemented
327C3—21no—
328C3C2×Q8×D1211yescharacteristic, direct product factor
329C3C2×C3×D4×Q811yescharacteristic, complemented
330C2—68no—
331C2C3×Q8×D1214yesdirect product factor
332C2C23×C3×D1211yescharacteristic
333C2C22×C3×D3×Q811yescharacteristic
334C2C2×C3×#101011yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C4×Q8C2
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C3×C4×Q8D3
hypocenterC3C2×C3×D4×Q8
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×Q8C2semidirect
2. C2×C32×C4×Q8C2semidirect
3. C3×Q8×D12C2direct (N × H)
4. C2×C3×#897C2semidirect
6. C2×C3×#869C2semidirect
8. C2×Q8×D12C3direct (N × H)
11. C2×C3×D3×Q8C22semidirect
15. C32×C4×Q8C22semidirect
21. C3×#897C22semidirect
23. C3×#869C22semidirect
25. C22×D3×Q8C2×C3semidirect
30. C2×C3×C4×Q8D3semidirect
31. C2×C3×C4×Q8C2×C3semidirect
33. Q8×D12C2×C3direct (N × H)
34. C2×#897C2×C3semidirect
36. C2×#869C2×C3semidirect
38. C2×C32×Q8D4semidirect
45. C2×C3×D12Q8direct (N × H)
66. C2×D3×Q8C22×C3semidirect
73. C3×C4×Q8C2×D3semidirect
74. C3×C4×Q8C22×C3semidirect
88. #897C22×C3semidirect
90. #869C22×C3semidirect
94. C22×C3×D3C2×Q8semidirect
96. C32×Q8C2×D4semidirect
99. C2×C32×C4C2×Q8semidirect
105. C3×D12C2×Q8direct (N × H)
112. C2×C4×Q8C3×D3semidirect
121. C2×C3×Q8D12direct (N × H)
122. C2×C3×Q8C3×D4semidirect
141. C2×D12C3×Q8direct (N × H)
166. C2×C3×D3C22×Q8semidirect
169. C32×C4C22×Q8semidirect
179. C4×Q8C2×C3×D3semidirect
195. C22×D3C2×C3×Q8semidirect
199. C3×Q8C2×D12direct (N × H)
200. C3×Q8C2×C3×D4semidirect
214. C2×C3×C4D3×Q8semidirect
216. C2×C3×C4C2×C3×Q8semidirect
225. D12C2×C3×Q8direct (N × H)
228. C2×C32D4×Q8semidirect
237. C2×Q8C3×D12direct (N × H)
271. C2×D3C22×C3×Q8semidirect
279. C3×C4C2×D3×Q8semidirect
281. C3×C4C22×C3×Q8semidirect
283. C32C2×D4×Q8semidirect
290. Q8C2×C3×D12direct (N × H)
297. C2×C4C3×D3×Q8semidirect
306. C2×C3Q8×D12direct (N × H)
307. C2×C3C3×D4×Q8semidirect
326. C4C2×C3×D3×Q8semidirect
328. C3C2×Q8×D12direct (N × H)
329. C3C2×C3×D4×Q8semidirect
331. C2C3×Q8×D12direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C2×C32×C4×Q82
C3×Q8×D122
C2×C3×#8972
C2×C3×C4×D122
C2×C3×#8692
C2×C3×D4×Q83
C2×Q8×D123