Finite Group Databasebeta

← C2×D3×C22⋊Q8 #85974

Subgroups — C2×D3×C22⋊Q8 #85974

Order 384.

1840 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×Q8C211yesmaximal, characteristic, complemented
2C23×C4×D3C211yesmaximal, characteristic
3C2×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
4C2×#946C211yesmaximal, characteristic, complemented
5C2×#924C211yesmaximal, characteristic, complemented
6D3×C22⋊Q8C2116yesmaximal, direct product factor
7C2×#897C211yesmaximal, characteristic, complemented
8C2×#896C212yesmaximal, complemented
9C2×D3×C4⋊C4C211yesmaximal, characteristic, complemented
10C2×D3×C4⋊C4C212yesmaximal, complemented
11C2×D3×C22⋊C4C212yesmaximal
12C2×#878C212yesmaximal, complemented
13C22×C22⋊Q8—31nomaximal, Sylow
14C24×D3C2211yescharacteristic
15C22×C3×Q8C2211yescharacteristic, complemented
16C23×C3×C4C2211yescharacteristic
17C23×Dic3C2211yescharacteristic
18C2×D3×Q8—28no—
19C2×D3×Q8C2218yescomplemented
20C22×C4×D3—28no—
21C22×C4×D3C2211yescharacteristic
22C22×C4×D3C2211yescharacteristic
23C22×C4×D3C2211yescharacteristic
24C22×C4×D3C2218yes—
25C22×C4×D3C2212yes—
26C22×C4×D3C2212yes—
27C22×C4×D3C2211yescharacteristic
28C22×Dic6C2212yescomplemented
29C22×Dic6C2211yescharacteristic, complemented
30C3×C22⋊Q8C2218yescomplemented
31C2×C3×C4⋊C4C2212yescomplemented
32C2×C3×C4⋊C4C2211yescharacteristic, complemented
33C2×C3×C22⋊C4C2212yes—
34C2×#217C2212yes—
35#946C2218yescomplemented
36C2×(C2×D3)⋊C4C2212yes—
37C2×(C2×D3)⋊C4C2212yes—
38C2×C4⋊Dic3C2212yescomplemented
39C2×C4⋊Dic3C2211yescharacteristic, complemented
40#924C2218yescomplemented
41C2×Dic3⋊C4C2212yescomplemented
42C2×Dic3⋊C4C2212yescomplemented
43C2×Dic3⋊C4C2212yescomplemented
44#897C2218yescomplemented
45#896C22116yescomplemented
46D3×C4⋊C4C2218yescomplemented
47D3×C4⋊C4C22116yescomplemented
48D3×C22⋊C4C22116yes—
49#878C22116yescomplemented
50C23×Q8—31no—
51C24×C4—31no—
52C2×C22⋊Q8—31no—
53C2×C22⋊Q8—31no—
54C2×C22⋊Q8—316no—
55C2×C22⋊Q8—32no—
56C2×C22⋊Q8—31no—
57C2×C22⋊Q8—32no—
58C2×C22⋊Q8D311yescharacteristic, direct product factor
59C22×C4⋊C4—31no—
60C22×C4⋊C4—32no—
61C22×C22⋊C4—32no—
62C24×C3C2311yescharacteristic
63C23×D3—24no—
64C23×D3—24no—
65C23×D3Q818yescomplemented
66C23×D3C2314yes—
67C23×D3C2311yescharacteristic
68C23×D3C2311yescharacteristic
69C2×C3×Q8—24no—
70C2×C3×Q8C2314yescomplemented
71C22×C3×C4—24no—
72C22×C3×C4C2311yescharacteristic
73C22×C3×C4C2312yes—
74C22×C3×C4C2312yes—
75C22×C3×C4C2314yes—
76C22×C3×C4C2311yescharacteristic
77C22×Dic3—24no—
78C22×Dic3C2314yes—
79C22×Dic3C2312yes—
80C22×Dic3C2311yescharacteristic
81C22×Dic3C2312yes—
82C22×Dic3C2311yescharacteristic
83D3×Q8—232no—
84C2×C4×D3—24no—
85C2×C4×D3—28no—
86C2×C4×D3—28no—
87C2×C4×D3—24no—
88C2×C4×D3—24no—
89C2×C4×D3—232no—
90C2×C4×D3D418yes—
91C2×C4×D3C2318yes—
92C2×C4×D3C2318yes—
93C2×C4×D3C2314yes—
94C2×C4×D3C2314yes—
95C2×C4×D3C2314yes—
96C2×C4×D3C2314yes—
97C2×Dic6—24no—
98C2×Dic6—28no—
99C2×Dic6C2318yescomplemented
100C2×Dic6C2314yescomplemented
101C3×C4⋊C4C2318yescomplemented
102C3×C4⋊C4C2314yescomplemented
103C3×C22⋊C4C2318yes—
104#217C2318yes—
105(C2×D3)⋊C4C2318yes—
106(C2×D3)⋊C4C2318yes—
107C4⋊Dic3C2318yescomplemented
108C4⋊Dic3C2314yescomplemented
109Dic3⋊C4C2318yescomplemented
110Dic3⋊C4C2318yescomplemented
111Dic3⋊C4C2318yescomplemented
112C25—31no—
113C22×Q8—38no—
114C22×Q8—32no—
115C22×Q8—31no—
116C22×Q8—68no—
117C22×Q8C2×D311yescharacteristic, complemented
118C23×C4—31no—
119C23×C4—31no—
120C23×C4—32no—
121C23×C4—32no—
122C23×C4—31no—
123C23×C4—31no—
124C23×C4—38no—
125C23×C4—31no—
126C23×C4—68no—
127C23×C4C2×D311yescharacteristic
128C22⋊Q8—38no—
129C22⋊Q8—38no—
130C22⋊Q8—316no—
131C22⋊Q8—38no—
132C22⋊Q8—316no—
133C22⋊Q8C2×D318yesdirect product factor
134C2×C4⋊C4—32no—
135C2×C4⋊C4—32no—
136C2×C4⋊C4—32no—
137C2×C4⋊C4—31no—
138C2×C4⋊C4—32no—
139C2×C4⋊C4—38no—
140C2×C4⋊C4—316no—
141C2×C4⋊C4C2×D311yescharacteristic, complemented
142C2×C4⋊C4C2×D312yescomplemented
143C2×C22⋊C4—32no—
144C2×C22⋊C4—32no—
145C2×C22⋊C4—32no—
146C2×C22⋊C4—316no—
147C2×C22⋊C4C2×D312yes—
148C23×C3—22no—
149C23×C3—22no—
150C23×C3C2×Q814yescomplemented
151C23×C3C2412yes—
152C23×C3C2411yescharacteristic
153C22×D3—22no—
154C22×D3—22no—
155C22×D3—232no—
156C22×D3—28no—
157C22×D3—28no—
158C22×D3C2×D414yes—
159C22×D3C2×Q814yes—
160C22×D3C2×Q8116yescomplemented
161C22×D3C2×Q814yescomplemented
162C22×D3#4114yes—
163C22×D3C2412yes—
164C22×D3C2412yes—
165C3×Q8—28no—
166C2×C3×C4—24no—
167C2×C3×C4—22no—
168C2×C3×C4—24no—
169C2×C3×C4—28no—
170C2×C3×C4C2×D414yes—
171C2×C3×C4C2412yes—
172C2×C3×C4C2414yes—
173C2×C3×C4C2414yes—
174C2×C3×C4C2412yes—
175C2×Dic3—24no—
176C2×Dic3—22no—
177C2×Dic3—24no—
178C2×Dic3—28no—
179C2×Dic3C2×D414yes—
180C2×Dic3C2414yes—
181C2×Dic3C2412yes—
182C2×Dic3C2414yes—
183C2×Dic3C2412yes—
184C4×D3—28no—
185C4×D3—216no—
186C4×D3—216no—
187C4×D3—28no—
188C4×D3—28no—
189C4×D3C2×D4116yes—
190Dic6—28no—
191Dic6—216no—
192C24—31no—
193C24—38no—
194C24—34no—
195C24—31no—
196C24—64no—
197C24—64no—
198C24C22×D311yescharacteristic
199C2×Q8—24no—
200C2×Q8—38no—
201C2×Q8—34no—
202C2×Q8—68no—
203C2×Q8—632no—
204C2×Q8—64no—
205C2×Q8C22×D314yescomplemented
206C22×C4—24no—
207C22×C4—31no—
208C22×C4—38no—
209C22×C4—34no—
210C22×C4—34no—
211C22×C4—32no—
212C22×C4—32no—
213C22×C4—31no—
214C22×C4—38no—
215C22×C4—38no—
216C22×C4—34no—
217C22×C4—34no—
218C22×C4—34no—
219C22×C4—64no—
220C22×C4—632no—
221C22×C4—64no—
222C22×C4—68no—
223C22×C4—68no—
224C22×C4—64no—
225C22×C4—64no—
226C22×C4C22×D314yes—
227C22×C4C22×D312yes—
228C22×C4C22×D312yes—
229C22×C4C22×D311yescharacteristic
230C22×C4C22×D311yescharacteristic
231C4⋊C4—38no—
232C4⋊C4—38no—
233C4⋊C4—38no—
234C4⋊C4—34no—
235C4⋊C4—38no—
236C4⋊C4C22×D314yescomplemented
237C4⋊C4C22×D318yescomplemented
238C22⋊C4—38no—
239C22⋊C4—38no—
240C22⋊C4—38no—
241C22⋊C4C22×D318yes—
242C22×C3—28no—
243C22×C3—22no—
244C22×C3—22no—
245C22×C3C22×D412yes—
246C22×C3C22×Q812yes—
247C22×C3C22×Q814yescomplemented
248C22×C3C2×#4112yes—
249C22×C3C2511yescharacteristic
250C2×D3—28no—
251C2×D3—22no—
252C2×D3—22no—
253C2×D3—232no—
254C2×D3C22⋊Q8116yesdirect product factor
255C2×D3C22×D414yes—
256C2×D3C22×Q814yes—
257C2×D3C22×Q814yescomplemented
258C2×D3C2×#4114yes—
259C3×C4—24no—
260C3×C4—22no—
261C3×C4—24no—
262C3×C4C22×D414yes—
263Dic3—24no—
264Dic3—22no—
265Dic3—24no—
266Dic3C22×D414yes—
267C23—22no—
268C23—22no—
269C23—34no—
270C23—34no—
271C23—34no—
272C23—32no—
273C23—34no—
274C23—316no—
275C23—32no—
276C23—68no—
277C23—68no—
278C23—632no—
279C23—62no—
280C23—62no—
281C23D3×Q814yescomplemented
282C23C23×D312yes—
283C23C23×D311yescharacteristic
284Q8—28no—
285Q8—616no—
286Q8—68no—
287C2×C4—22no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—28no—
291C2×C4—34no—
292C2×C4—32no—
293C2×C4—316no—
294C2×C4—34no—
295C2×C4—34no—
296C2×C4—32no—
297C2×C4—68no—
298C2×C4—68no—
299C2×C4—616no—
300C2×C4—616no—
301C2×C4—68no—
302C2×C4—62no—
303C2×C4—64no—
304C2×C4—64no—
305C2×C4—68no—
306C2×C4D3×D414yes—
307C2×C4C23×D314yes—
308C2×C4C23×D314yes—
309C2×C4C23×D312yes—
310C2×C4C23×D312yes—
311C2×C3—24no—
312C2×C3C2×C22⋊Q814yescomplemented
313C2×C3C23×D411yescharacteristic
314C2×C3C23×Q811yescharacteristic
315C2×C3C22×#4111yescharacteristic
316D3—24no—
317D3C2×C22⋊Q818yesdirect product factor
318C22—22no—
319C22—22no—
320C22—28no—
321C22—34no—
322C22—34no—
323C22—34no—
324C22—316no—
325C22—34no—
326C22—632no—
327C22—62no—
328C22—62no—
329C22—68no—
330C22C2×D3×D412yes—
331C22C2×D3×Q812yes—
332C22C2×D3×Q814yescomplemented
333C22D3×#4112yes—
334C22C24×D311yescharacteristic
335C4—22no—
336C4—24no—
337C4—24no—
338C4—34no—
339C4—62no—
340C4—64no—
341C4—64no—
342C4C2×D3×D414yes—
343C3C22×C22⋊Q811yescharacteristic, complemented, Sylow
344C2—24no—
345C2—38no—
346C2—64no—
347C2D3×C22⋊Q814yesdirect product factor
348C2C22×D3×D411yescharacteristic
349C2C22×D3×Q811yescharacteristic
350C2C2×D3×#4111yescharacteristic
subgroupG/H
centerC23C23×D3
commutator, cosocleC22×C3C25
FrattiniC22C24×D3
FittingC2×C3×C22⋊Q8C2
socleC23×C3C24
prime radicalC24×D3C22
hypercenterC2×C22⋊Q8D3
hypocenterC3C22×C22⋊Q8
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×D3×Q8C2semidirect
3. C2×C3×C22⋊Q8C2semidirect
4. C2×#946C2semidirect
5. C2×#924C2semidirect
6. D3×C22⋊Q8C2direct (N × H)
7. C2×#897C2semidirect
8. C2×#896C2semidirect
9. C2×D3×C4⋊C4C2semidirect
10. C2×D3×C4⋊C4C2semidirect
12. C2×#878C2semidirect
15. C22×C3×Q8C22semidirect
19. C2×D3×Q8C22semidirect
28. C22×Dic6C22semidirect
29. C22×Dic6C22semidirect
30. C3×C22⋊Q8C22semidirect
31. C2×C3×C4⋊C4C22semidirect
32. C2×C3×C4⋊C4C22semidirect
35. #946C22semidirect
38. C2×C4⋊Dic3C22semidirect
39. C2×C4⋊Dic3C22semidirect
40. #924C22semidirect
41. C2×Dic3⋊C4C22semidirect
42. C2×Dic3⋊C4C22semidirect
43. C2×Dic3⋊C4C22semidirect
44. #897C22semidirect
45. #896C22semidirect
46. D3×C4⋊C4C22semidirect
47. D3×C4⋊C4C22semidirect
49. #878C22semidirect
58. C2×C22⋊Q8D3direct (N × H)
65. C23×D3Q8semidirect
70. C2×C3×Q8C23semidirect
99. C2×Dic6C23semidirect
100. C2×Dic6C23semidirect
101. C3×C4⋊C4C23semidirect
102. C3×C4⋊C4C23semidirect
107. C4⋊Dic3C23semidirect
108. C4⋊Dic3C23semidirect
109. Dic3⋊C4C23semidirect
110. Dic3⋊C4C23semidirect
111. Dic3⋊C4C23semidirect
117. C22×Q8C2×D3semidirect
133. C22⋊Q8C2×D3direct (N × H)
141. C2×C4⋊C4C2×D3semidirect
142. C2×C4⋊C4C2×D3semidirect
150. C23×C3C2×Q8semidirect
160. C22×D3C2×Q8semidirect
161. C22×D3C2×Q8semidirect
205. C2×Q8C22×D3semidirect
236. C4⋊C4C22×D3semidirect
237. C4⋊C4C22×D3semidirect
247. C22×C3C22×Q8semidirect
254. C2×D3C22⋊Q8direct (N × H)
257. C2×D3C22×Q8semidirect
281. C23D3×Q8semidirect
312. C2×C3C2×C22⋊Q8semidirect
317. D3C2×C22⋊Q8direct (N × H)
332. C22C2×D3×Q8semidirect
343. C3C22×C22⋊Q8semidirect
347. C2D3×C22⋊Q8direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×Q82
C23×C4×D32
C2×C3×C22⋊Q82
C2×#9462
C2×#9242
D3×C22⋊Q82
C2×#8972
C2×#8962
C2×D3×C4⋊C42
C2×D3×C22⋊C42
C2×#8782
C22×C22⋊Q83