Finite Group Databasebeta

← C22×C3×#946 #11900313

Subgroups — C22×C3×#946 #11900313

Order 1152.

4105 conjugacy classes of subgroups.

The subgroup lattice has 345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C32×Q8C211yesmaximal, characteristic, complemented
2C23×C3×C4×D3C211yesmaximal, characteristic
3C2×C3×#946C2124yesmaximal, direct product factor
4C22×C3×(C2×D3)⋊C4C212yesmaximal
5C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
6C22×C3×Dic3⋊C4C212yesmaximal, complemented
7C22×C3×C22⋊Q8—31nomaximal
8C22×#946C311yesmaximal, characteristic, direct product factor
9C24×C3×D3C2211yescharacteristic
10C22×C32×Q8—28no—
11C22×C32×Q8C22112yescomplemented
12C23×C32×C4C2212yes—
13C23×C32×C4C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2212yes—
16C22×C3×C4×D3—28no—
17C22×C3×C4×D3C22112yes—
18C3×#946C22164yesdirect product factor
19C2×C3×(C2×D3)⋊C4C22124yes—
20C2×C3×C4⋊Dic3C22112yescomplemented
21C2×C3×Dic3⋊C4C22124yescomplemented
22C23×C3×Q8—21no—
23C23×C3×Q8D311yescharacteristic, complemented
24C23×C3×Q8C2×C311yescharacteristic, complemented
25C24×C3×C4—31no—
26C23×C4×D3C2×C311yescharacteristic
27C2×C3×C22⋊Q8—324no—
28C22×C3×C4⋊C4—32no—
29C22×C3×C4⋊C4—31no—
30C22×C3×C22⋊C4—32no—
31C2×#946C2×C3124yesdirect product factor
32C22×(C2×D3)⋊C4C2×C312yes—
33C22×C4⋊Dic3C2×C311yescharacteristic, complemented
34C22×Dic3⋊C4C2×C312yescomplemented
35C24×C32C2311yescharacteristic
36C23×C3×D3—24no—
37C23×C3×D3—24no—
38C23×C3×D3Q818yescomplemented
39C23×C3×D3C2316yes—
40C2×C32×Q8—248no—
41C2×C32×Q8C23116yescomplemented
42C22×C32×C4—28no—
43C22×C32×C4D418yes—
44C22×C32×C4C23112yes—
45C22×C32×C4C2316yes—
46C22×C3×Dic3—24no—
47C22×C3×Dic3—28no—
48C22×C3×Dic3C2316yes—
49C22×C3×Dic3C23112yes—
50C2×C3×C4×D3—248no—
51C2×C3×C4×D3C23116yes—
52C3×(C2×D3)⋊C4C23132yes—
53C3×C4⋊Dic3C23116yescomplemented
54C3×Dic3⋊C4C23132yescomplemented
55C22×C22⋊Q8—31noSylow
56C25×C3—31no—
57C24×D3C22×C311yescharacteristic
58C22×C3×Q8—216no—
59C22×C3×Q8—28no—
60C22×C3×Q8—28no—
61C22×C3×Q8—212no—
62C22×C3×Q8C2×D3112yescomplemented
63C22×C3×Q8C22×C3112yescomplemented
64C23×C3×C4—22no—
65C23×C3×C4—21no—
66C23×C3×C4—31no—
67C23×C3×C4—32no—
68C23×C3×C4—312no—
69C23×C3×C4—68no—
70C23×C3×C4C2×D312yes—
71C23×C3×C4C2×D311yescharacteristic
72C23×C3×C4C22×C312yes—
73C23×C3×C4C22×C311yescharacteristic
74C23×Dic3C22×C311yescharacteristic
75C23×Dic3C22×C312yes—
76C22×C4×D3—28no—
77C22×C4×D3C22×C3112yes—
78C3×C22⋊Q8—364no—
79C2×C3×C4⋊C4—324no—
80C2×C3×C4⋊C4—312no—
81C2×C3×C22⋊C4—324no—
82#946C22×C3164yesdirect product factor
83C2×(C2×D3)⋊C4C22×C3124yes—
84C2×C4⋊Dic3C22×C3112yescomplemented
85C2×Dic3⋊C4C22×C3124yescomplemented
86C23×C32C2×D414yes—
87C23×C32C2×Q814yes—
88C23×C32#4114yes—
89C23×C32C2413yes—
90C22×C3×D3—232no—
91C22×C3×D3—212no—
92C22×C3×D3—212no—
93C22×C3×D3C2×Q8124yescomplemented
94C22×C3×D3C2414yes—
95C32×Q8—232no—
96C2×C32×C4—224no—
97C2×C32×C4C2×D4124yes—
98C2×C32×C4C2418yes—
99C2×C32×C4C2414yes—
100C2×C3×Dic3—212no—
101C2×C3×Dic3—224no—
102C2×C3×Dic3C2414yes—
103C2×C3×Dic3C2418yes—
104C3×C4×D3—232no—
105C23×Q8C3×D311yescharacteristic, complemented
106C24×C4—31no—
107C2×C22⋊Q8—324no—
108C22×C4⋊C4—32no—
109C22×C4⋊C4—31no—
110C22×C22⋊C4—32no—
111C24×C3—21no—
112C24×C3—38no—
113C24×C3—36no—
114C24×C3—64no—
115C24×C3—64no—
116C24×C3C22×D311yescharacteristic
117C24×C3C23×C311yescharacteristic
118C23×D3—24no—
119C23×D3—24no—
120C23×D3C3×Q818yescomplemented
121C23×D3C23×C316yes—
122C2×C3×Q8—296no—
123C2×C3×Q8—248no—
124C2×C3×Q8—248no—
125C2×C3×Q8—216no—
126C2×C3×Q8C22×D3116yescomplemented
127C2×C3×Q8C23×C3116yescomplemented
128C22×C3×C4—216no—
129C22×C3×C4—28no—
130C22×C3×C4—28no—
131C22×C3×C4—28no—
132C22×C3×C4—212no—
133C22×C3×C4—26no—
134C22×C3×C4—312no—
135C22×C3×C4—36no—
136C22×C3×C4—316no—
137C22×C3×C4—68no—
138C22×C3×C4—64no—
139C22×C3×C4—648no—
140C22×C3×C4#6718yes—
141C22×C3×C4C3×D418yes—
142C22×C3×C4C22×D3112yes—
143C22×C3×C4C22×D316yes—
144C22×C3×C4C23×C3112yes—
145C22×C3×C4C23×C316yes—
146C22×Dic3—24no—
147C22×Dic3—28no—
148C22×Dic3C23×C316yes—
149C22×Dic3C23×C3112yes—
150C2×C4×D3—248no—
151C2×C4×D3C23×C3116yes—
152C3×C4⋊C4—332no—
153C3×C4⋊C4—316no—
154C3×C22⋊C4—332no—
155(C2×D3)⋊C4C23×C3132yes—
156C4⋊Dic3C23×C3116yescomplemented
157Dic3⋊C4C23×C3132yescomplemented
158C22×C32C22⋊Q8116yescomplemented
159C22×C32C22×D416yes—
160C22×C32C22×Q816yes—
161C22×C32C2×#4116yes—
162C22×C32C2511yescharacteristic
163C2×C3×D3—248no—
164C2×C3×D3—24no—
165C2×C3×D3—24no—
166C2×C3×D3C22×Q818yescomplemented
167C32×C4—28no—
168C32×C4C22×D418yes—
169C3×Dic3—24no—
170C3×Dic3—28no—
171C25—31no—
172C22×Q8—28no—
173C22×Q8C2×C3×D3112yescomplemented
174C23×C4—32no—
175C23×C4—31no—
176C23×C4—312no—
177C23×C4—68no—
178C23×C4C2×C3×D312yes—
179C23×C4C2×C3×D311yescharacteristic
180C22⋊Q8—364no—
181C2×C4⋊C4—324no—
182C2×C4⋊C4—312no—
183C2×C22⋊C4—324no—
184C23×C3—23no—
185C23×C3—24no—
186C23×C3—24no—
187C23×C3—24no—
188C23×C3—324no—
189C23×C3—34no—
190C23×C3—632no—
191C23×C3—612no—
192C23×C3—612no—
193C23×C3D3×Q814yes—
194C23×C3#23914yes—
195C23×C3C2×#6714yes—
196C23×C3C2×C3×D414yes—
197C23×C3C2×C3×Q814yes—
198C23×C3C3×#4114yes—
199C23×C3C23×D313yes—
200C23×C3C24×C313yes—
201C22×D3—232no—
202C22×D3—212no—
203C22×D3—212no—
204C22×D3C2×C3×Q8124yescomplemented
205C22×D3C24×C314yes—
206C3×Q8—264no—
207C3×Q8—232no—
208C3×Q8—232no—
209C2×C3×C4—248no—
210C2×C3×C4—224no—
211C2×C3×C4—224no—
212C2×C3×C4—28no—
213C2×C3×C4—24no—
214C2×C3×C4—224no—
215C2×C3×C4—38no—
216C2×C3×C4—34no—
217C2×C3×C4—624no—
218C2×C3×C4—612no—
219C2×C3×C4—632no—
220C2×C3×C4C2×#67124yes—
221C2×C3×C4C2×C3×D4124yes—
222C2×C3×C4C23×D318yes—
223C2×C3×C4C23×D314yes—
224C2×C3×C4C24×C318yes—
225C2×C3×C4C24×C314yes—
226C2×Dic3—212no—
227C2×Dic3—224no—
228C2×Dic3C24×C314yes—
229C2×Dic3C24×C318yes—
230C4×D3—232no—
231C2×C32C2×C22⋊Q8112yescomplemented
232C2×C32C23×D411yescharacteristic
233C2×C32C23×Q811yescharacteristic
234C2×C32C22×#4111yescharacteristic
235C3×D3—28no—
236C24—36no—
237C24—38no—
238C24—64no—
239C24—64no—
240C24C22×C3×D311yescharacteristic
241C2×Q8—248no—
242C2×Q8C22×C3×D3116yescomplemented
243C22×C4—28no—
244C22×C4—312no—
245C22×C4—36no—
246C22×C4—316no—
247C22×C4—68no—
248C22×C4—64no—
249C22×C4—648no—
250C22×C4C3×#6718yes—
251C22×C4C22×C3×D3112yes—
252C22×C4C22×C3×D316yes—
253C4⋊C4—332no—
254C4⋊C4—316no—
255C22⋊C4—332no—
256C22×C3—216no—
257C22×C3—26no—
258C22×C3—26no—
259C22×C3—26no—
260C22×C3—21no—
261C22×C3—38no—
262C22×C3—64no—
263C22×C3—64no—
264C22×C3—648no—
265C22×C3#946116yesdirect product factor
266C22×C3C3×C22⋊Q8116yescomplemented
267C22×C3C2×D3×Q816yes—
268C22×C3C2×#23916yes—
269C22×C3C22×#6716yes—
270C22×C3C22×C3×D416yes—
271C22×C3C22×C3×Q816yes—
272C22×C3C2×C3×#4116yes—
273C22×C3C24×D311yescharacteristic
274C22×C3C25×C311yescharacteristic
275C2×D3—24no—
276C2×D3—24no—
277C2×D3—248no—
278C2×D3C22×C3×Q818yescomplemented
279C3×C4—216no—
280C3×C4—28no—
281C3×C4—28no—
282C3×C4—28no—
283C3×C4—68no—
284C3×C4—64no—
285C3×C4C22×#6718yes—
286C3×C4C22×C3×D418yes—
287Dic3—24no—
288Dic3—28no—
289C32C22×C22⋊Q811yescharacteristic, complemented, Sylow
290C23—324no—
291C23—34no—
292C23—632no—
293C23—612no—
294C23—612no—
295C23C3×D3×Q814yes—
296C23C3×#23914yes—
297C23C2×C3×#6714yes—
298C23C23×C3×D313yes—
299Q8—232no—
300C2×C4—224no—
301C2×C4—38no—
302C2×C4—34no—
303C2×C4—624no—
304C2×C4—612no—
305C2×C4—632no—
306C2×C4C2×C3×#67124yes—
307C2×C4C23×C3×D318yes—
308C2×C4C23×C3×D314yes—
309C2×C3—212no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—68no—
314C2×C3C2×#946112yesdirect product factor
315C2×C3C2×C3×C22⋊Q8112yescomplemented
316C2×C3C22×D3×Q811yescharacteristic
317C2×C3C22×#23911yescharacteristic
318C2×C3C23×#6711yescharacteristic
319C2×C3C23×C3×D411yescharacteristic
320C2×C3C23×C3×Q811yescharacteristic
321C2×C3C22×C3×#4111yescharacteristic
322D3—28no—
323C22—38no—
324C22—648no—
325C22—64no—
326C22—64no—
327C22C3×#946116yesdirect product factor
328C22C2×C3×D3×Q816yes—
329C22C2×C3×#23916yes—
330C22C22×C3×#6716yes—
331C22C24×C3×D311yescharacteristic
332C4—28no—
333C4—68no—
334C4—64no—
335C4C22×C3×#6718yes—
336C3—21no—
337C3C22×#94611yescharacteristic, direct product factor
338C3C22×C3×C22⋊Q811yescharacteristic, complemented
339C2—68no—
340C2C2×C3×#946112yesdirect product factor
341C2C22×C3×D3×Q811yescharacteristic
342C2C22×C3×#23911yescharacteristic
343C2C23×C3×#6711yescharacteristic
subgroupG/H
centerC24×C3C22×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC23×C32×Q8C2
socleC24×C32C23
prime radicalC24×C3×D3C22
hypercenterC23×C3×Q8D3
hypocenterC3C22×C3×C22⋊Q8
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C23×C3×Q8

Complements

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

NH ≅ G/Ntype
1. C23×C32×Q8C2semidirect
3. C2×C3×#946C2direct (N × H)
5. C22×C3×C4⋊Dic3C2semidirect
6. C22×C3×Dic3⋊C4C2semidirect
8. C22×#946C3direct (N × H)
11. C22×C32×Q8C22semidirect
18. C3×#946C22direct (N × H)
20. C2×C3×C4⋊Dic3C22semidirect
21. C2×C3×Dic3⋊C4C22semidirect
23. C23×C3×Q8D3semidirect
24. C23×C3×Q8C2×C3semidirect
31. C2×#946C2×C3direct (N × H)
33. C22×C4⋊Dic3C2×C3semidirect
34. C22×Dic3⋊C4C2×C3semidirect
38. C23×C3×D3Q8semidirect
41. C2×C32×Q8C23semidirect
53. C3×C4⋊Dic3C23semidirect
54. C3×Dic3⋊C4C23semidirect
62. C22×C3×Q8C2×D3semidirect
63. C22×C3×Q8C22×C3semidirect
82. #946C22×C3direct (N × H)
84. C2×C4⋊Dic3C22×C3semidirect
85. C2×Dic3⋊C4C22×C3semidirect
93. C22×C3×D3C2×Q8semidirect
105. C23×Q8C3×D3semidirect
120. C23×D3C3×Q8semidirect
126. C2×C3×Q8C22×D3semidirect
127. C2×C3×Q8C23×C3semidirect
156. C4⋊Dic3C23×C3semidirect
157. Dic3⋊C4C23×C3semidirect
158. C22×C32C22⋊Q8semidirect
166. C2×C3×D3C22×Q8semidirect
173. C22×Q8C2×C3×D3semidirect
204. C22×D3C2×C3×Q8semidirect
231. C2×C32C2×C22⋊Q8semidirect
242. C2×Q8C22×C3×D3semidirect
265. C22×C3#946direct (N × H)
266. C22×C3C3×C22⋊Q8semidirect
278. C2×D3C22×C3×Q8semidirect
289. C32C22×C22⋊Q8semidirect
314. C2×C3C2×#946direct (N × H)
315. C2×C3C2×C3×C22⋊Q8semidirect
327. C22C3×#946direct (N × H)
337. C3C22×#946direct (N × H)
338. C3C22×C3×C22⋊Q8semidirect
340. C2C2×C3×#946direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C32×Q82
C23×C3×C4×D32
C2×C3×#9462
C22×C3×(C2×D3)⋊C42
C22×C3×C4⋊Dic32
C22×C3×Dic3⋊C42
C22×C3×C22⋊Q83
C22×#9463