Finite Group Databasebeta

← D3×#448 #80037

Subgroups — D3×#448 #80037

Order 384.

792 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×Q8C211yesmaximal, characteristic, complemented
2C2×D3×SD16C212yesmaximal, complemented
3D3×#121C211yesmaximal, characteristic
4C3×#448C211yesmaximal, characteristic, complemented
5#5227C211yesmaximal, characteristic, complemented
6#5170C212yesmaximal, complemented
7#5040C211yesmaximal, characteristic, complemented
8#4806C212yesmaximal, complemented
9D3×#103C212yesmaximal, complemented
10#4738C211yesmaximal, characteristic, complemented
11D3×C22⋊C8C211yesmaximal, characteristic, complemented
12C2×#448—31nomaximal, Sylow
13C22×C3×Q8C2211yescharacteristic, complemented
14C2×D3×Q8—28no—
15C2×D3×Q8—21no—
16C2×D3×Q8—21no—
17C2×D3×Q8C2212yes—
18C2×D3×Q8C2212yescomplemented
19C2×D3×D4—21no—
20C2×D3×D4C2211yescharacteristic
21C22×C4×D3—21no—
22C22×C4×D3C2211yescharacteristic
23C22×Dic6—21no—
24C22×Dic6C2211yescharacteristic, complemented
25C2×C3×SD16C2212yescomplemented
26C3×#121C2211yescharacteristic
27C2×#215C2212yescomplemented
28#939—21no—
29#938C2211yescharacteristic
30C2×#214C2212yescomplemented
31#930C2211yescharacteristic
32D3×SD16—28no—
33C2×#204C2212yescomplemented
34C2×D3×C8C2212yes—
35#895C2211yescharacteristic
36D3×C4⋊C4C2211yescharacteristic
37#884—21no—
38D3×C22⋊C4—21no—
39C3×#103C2212yescomplemented
40C3×C22⋊C8C2211yescharacteristic, complemented
41#835C2212yescomplemented
42#830C2211yescharacteristic, complemented
43(C2×D3)⋊C8C2212yescomplemented
44#816C2212yescomplemented
45#810C2212yescomplemented
46C23×Q8—31no—
47C22×SD16—32no—
48C2×#121—31no—
49#448—31no—
50#448—32no—
51#448—31no—
52#448—32no—
53#448—31no—
54#448D311yescharacteristic, direct product factor
55C2×#103—32no—
56C2×C22⋊C8—31no—
57C23×D3—21no—
58C23×D3D411yescharacteristic
59C2×C3×Q8—24no—
60C2×C3×Q8—21no—
61C2×C3×Q8C2312yes—
62C2×C3×D4—21no—
63C2×C3×D4C2311yescharacteristic
64C22×C3×C4—21no—
65C22×C3×C4C2311yescharacteristic
66C2×#67—21no—
67C2×#67—21no—
68C2×#67—21no—
69C22×Dic3—21no—
70C22×Dic3D411yescharacteristic
71D3×Q8—28no—
72D3×Q8—28no—
73D3×Q8—24no—
74D3×Q8—24no—
75D3×Q8—24no—
76D3×Q8D418yescomplemented
77D3×D4—24no—
78D3×D4—44no—
79C2×D12—21no—
80C2×D12C2311yescharacteristic
81C2×C4×D3—28no—
82C2×C4×D3—22no—
83C2×C4×D3—22no—
84C2×C4×D3—24no—
85C2×C4×D3—21no—
86C2×C4×D3D411yescharacteristic
87C2×C4×D3D411yescharacteristic
88C2×C4×D3C2311yescharacteristic
89C2×C4×D3C2311yescharacteristic
90C2×Dic6—28no—
91C2×Dic6—21no—
92C2×Dic6—22no—
93C2×Dic6—22no—
94C2×Dic6—24no—
95C2×Dic6C2312yes—
96C3×SD16—24no—
97C2×C3×C8C2312yes—
98C3×C4⋊C4C2311yescharacteristic
99C3×C22⋊C4—21no—
100#217—21no—
101#215—24no—
102#214—24no—
103(C2×D3)⋊C4—21no—
104(C2×D3)⋊C4—21no—
105C4⋊Dic3C2311yescharacteristic
106Dic3⋊C4—21no—
107C2×C3⋊C8C2312yes—
108#204—24no—
109D3×C8—24no—
110C22×Q8—32no—
111C22×Q8—32no—
112C22×Q8—31no—
113C22×Q8—61no—
114C22×Q8—61no—
115C22×Q8—61no—
116C22×Q8—68no—
117C22×Q8C2×D311yescharacteristic, complemented
118C22×D4—31no—
119C22×D4—61no—
120C23×C4—31no—
121C23×C4—61no—
122C2×SD16—32no—
123C2×SD16—32no—
124C2×SD16—32no—
125C2×SD16—68no—
126C2×SD16C2×D312yescomplemented
127C22×C8—32no—
128#121—31no—
129#121—31no—
130#121—31no—
131#121—61no—
132#121—61no—
133#121C2×D311yescharacteristic
134C2×C4⋊C4—31no—
135C2×C22⋊C4—61no—
136#103—32no—
137#103—32no—
138#103—32no—
139#103C2×D312yescomplemented
140C22⋊C8—31no—
141C22⋊C8—32no—
142C22⋊C8C2×D311yescharacteristic, complemented
143C23×C3—21no—
144C23×C3C2×D411yescharacteristic
145C22×D3—22no—
146C22×D3—22no—
147C22×D3—21no—
148C22×D3—42no—
149C22×D3—42no—
150C22×D3—42no—
151C22×D3SD1614yescomplemented
152C22×D3C2×D411yescharacteristic
153C22×D3C2×D411yescharacteristic
154C3×Q8—24no—
155C3×Q8—22no—
156C3×Q8C2×D414yescomplemented
157C3×D4—22no—
158C3×D4—42no—
159C2×C3×C4—24no—
160C2×C3×C4—22no—
161C2×C3×C4—22no—
162C2×C3×C4—21no—
163C2×C3×C4C2×D411yescharacteristic
164C2×C3×C4C2411yescharacteristic
165#67—42no—
166#67—42no—
167#67—42no—
168C2×Dic3—24no—
169C2×Dic3—22no—
170C2×Dic3—22no—
171C2×Dic3—21no—
172C2×Dic3C2×D411yescharacteristic
173C2×Dic3C2×D411yescharacteristic
174D12—22no—
175D12—42no—
176C4×D3—28no—
177C4×D3—28no—
178C4×D3—22no—
179C4×D3—22no—
180C4×D3—22no—
181C4×D3—42no—
182C4×D3C2×D414yes—
183Dic6—28no—
184Dic6—24no—
185Dic6—22no—
186Dic6—28no—
187Dic6C2×D414yescomplemented
188C3×C8—22no—
189C3⋊C8—22no—
190C24—31no—
191C24—61no—
192C2×Q8—24no—
193C2×Q8—21no—
194C2×Q8—38no—
195C2×Q8—32no—
196C2×Q8—62no—
197C2×Q8—62no—
198C2×Q8—64no—
199C2×Q8—68no—
200C2×Q8—64no—
201C2×Q8—64no—
202C2×Q8—68no—
203C2×Q8—68no—
204C2×Q8—64no—
205C2×Q8—61no—
206C2×Q8C22×D312yes—
207C2×D4—21no—
208C2×D4—31no—
209C2×D4—61no—
210C2×D4—64no—
211C2×D4—61no—
212C2×D4—61no—
213C2×D4—61no—
214C2×D4—124no—
215C2×D4C22×D311yescharacteristic
216C22×C4—21no—
217C22×C4—31no—
218C22×C4—31no—
219C22×C4—31no—
220C22×C4—31no—
221C22×C4—31no—
222C22×C4—64no—
223C22×C4—62no—
224C22×C4—62no—
225C22×C4—68no—
226C22×C4—61no—
227C22×C4—61no—
228C22×C4C22×D311yescharacteristic
229SD16—24no—
230SD16—64no—
231SD16—64no—
232SD16—64no—
233C2×C8—32no—
234C2×C8—64no—
235C2×C8C22×D312yes—
236C4⋊C4—31no—
237C4⋊C4—61no—
238C4⋊C4C22×D311yescharacteristic
239C22⋊C4—21no—
240C22⋊C4—61no—
241C22⋊C4—61no—
242C22⋊C4—61no—
243C22×C3—21no—
244C22×C3—21no—
245C22×C3—41no—
246C22×C3—41no—
247C22×C3—41no—
248C22×C3C2×SD1612yescomplemented
249C22×C3C22×D411yescharacteristic
250C2×D3—21no—
251C2×D3—21no—
252C2×D3—28no—
253C2×D3—41no—
254C2×D3—41no—
255C2×D3—41no—
256C2×D3—84no—
257C2×D3#12012yes—
258C2×D3C2×SD1612yes—
259C2×D3C2×SD1612yescomplemented
260C2×D3#13712yes—
261C3×C4—24no—
262C3×C4—21no—
263C3×C4—41no—
264C3×C4C22×D412yes—
265Dic3—21no—
266Dic3—24no—
267Dic3—41no—
268Dic3#12012yes—
269C23—21no—
270C23—31no—
271C23—34no—
272C23—31no—
273C23—62no—
274C23—62no—
275C23—61no—
276C23—122no—
277C23—122no—
278C23—122no—
279C23D3×D411yescharacteristic
280Q8—24no—
281Q8—22no—
282Q8—34no—
283Q8—68no—
284Q8—68no—
285Q8—64no—
286Q8—62no—
287Q8D3×D414yescomplemented
288D4—22no—
289D4—42no—
290D4—62no—
291D4—122no—
292D4—122no—
293D4—122no—
294D4—122no—
295C2×C4—24no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—31no—
300C2×C4—34no—
301C2×C4—31no—
302C2×C4—62no—
303C2×C4—62no—
304C2×C4—68no—
305C2×C4—68no—
306C2×C4—62no—
307C2×C4—64no—
308C2×C4—62no—
309C2×C4—62no—
310C2×C4—61no—
311C2×C4—122no—
312C2×C4D3×D411yescharacteristic
313C2×C4C23×D311yescharacteristic
314C8—22no—
315C8—62no—
316C2×C3—22no—
317C2×C3—81no—
318C2×C3C2×#12011yescharacteristic
319C2×C3C22×SD1611yescharacteristic
320C2×C3C2×#13711yescharacteristic
321D3—22no—
322D3—81no—
323D3#44814yesdirect product factor
324C22—21no—
325C22—21no—
326C22—32no—
327C22—32no—
328C22—32no—
329C22—32no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—68no—
334C22—61no—
335C22—61no—
336C22—121no—
337C22—121no—
338C22—121no—
339C22—244no—
340C22D3×SD1612yescomplemented
341C22C2×D3×D411yescharacteristic
342C4—24no—
343C4—21no—
344C4—32no—
345C4—41no—
346C4—61no—
347C4—64no—
348C4—121no—
349C4C2×D3×D412yes—
350C3C2×#44811yescharacteristic, complemented, Sylow
351C2—22no—
352C2—34no—
353C2—62no—
354C2—81no—
355C2—241no—
356C2D3×#12011yescharacteristic
357C2C2×D3×SD1611yescharacteristic
358C2D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#448C2
socleC22×C3C22×D4
prime radicalD3×#121C2
hypercenter#448D3
hypocenterC3C2×#448
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C22×D3×Q8C2semidirect
2. C2×D3×SD16C2semidirect
4. C3×#448C2semidirect
5. #5227C2semidirect
6. #5170C2semidirect
7. #5040C2semidirect
8. #4806C2semidirect
9. D3×#103C2semidirect
10. #4738C2semidirect
11. D3×C22⋊C8C2semidirect
13. C22×C3×Q8C22semidirect
18. C2×D3×Q8C22semidirect
24. C22×Dic6C22semidirect
25. C2×C3×SD16C22semidirect
27. C2×#215C22semidirect
30. C2×#214C22semidirect
33. C2×#204C22semidirect
39. C3×#103C22semidirect
40. C3×C22⋊C8C22semidirect
41. #835C22semidirect
42. #830C22semidirect
43. (C2×D3)⋊C8C22semidirect
44. #816C22semidirect
45. #810C22semidirect
54. #448D3direct (N × H)
76. D3×Q8D4semidirect
117. C22×Q8C2×D3semidirect
126. C2×SD16C2×D3semidirect
139. #103C2×D3semidirect
142. C22⋊C8C2×D3semidirect
151. C22×D3SD16semidirect
156. C3×Q8C2×D4semidirect
187. Dic6C2×D4semidirect
248. C22×C3C2×SD16semidirect
259. C2×D3C2×SD16semidirect
287. Q8D3×D4semidirect
323. D3#448direct (N × H)
340. C22D3×SD16semidirect
350. C3C2×#448semidirect

Maximal subgroups

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

subgroupindex
C22×D3×Q82
C2×D3×SD162
D3×#1212
C3×#4482
#52272
#51702
#50402
#48062
D3×#1032
#47382
D3×C22⋊C82
C2×#4483