Finite Group Databasebeta

← #82035

Subgroups — #82035

Order 384.

364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 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
1D3×#135C211yesmaximal, characteristic, complemented
2C2×#912C211yesmaximal, characteristic, complemented
3C3×#509C211yesmaximal, characteristic, complemented
4#5195C211yesmaximal, characteristic, complemented
5#5147C211yesmaximal, characteristic, complemented
6#4916C212yesmaximal, complemented
7#4915C212yesmaximal, complemented
8#4912C212yesmaximal, complemented
9#4911C212yesmaximal, complemented
10#4909C211yesmaximal, characteristic, complemented
11D3×M32C211yesmaximal, characteristic, complemented
12#3414—31nomaximal, Sylow
13D3×#41—21no—
14C2×#237—21no—
15C3×#135C2211yescharacteristic
16C2×C3×D8C2211yescharacteristic, complemented
17#950—21no—
18C2×#214—21no—
19#919C2211yescharacteristic, complemented
20D3×Q16C2211yescharacteristic, complemented
21#916—21no—
22D3×SD16—21no—
23#912—21no—
24#912—21no—
25#912C2212yes—
26#912C2211yescharacteristic, complemented
27#912C2212yescomplemented
28D3×D8C2211yescharacteristic, complemented
29C2×Dic12C2211yescharacteristic, complemented
30#904C2211yescharacteristic
31C2×D3×C8C2211yescharacteristic
32C3×SD32C2212yescomplemented
33C3×D16C2212yescomplemented
34C3×M32C2211yescharacteristic, complemented
35#829C2212yescomplemented
36#827C2212yescomplemented
37#827C2212yescomplemented
38#826C2212yescomplemented
39#812C2211yescharacteristic, complemented
40Dic24C2212yescomplemented
41#800C2212yescomplemented
42#798C2212yescomplemented
43D3×C16C2212yescomplemented
44C2×#135—31no—
45C2×#135—31no—
46#510—31no—
47#510—32no—
48#510—31no—
49#509—31no—
50#509—32no—
51#509D311yescharacteristic, complemented
52#508—32no—
53#508—32no—
54C2×M32—31no—
55C3×#41—21no—
56C2×C3×D4—21no—
57C2×#67—41no—
58C22×Dic3—41no—
59#239—21no—
60D3×Q8—21no—
61#237—22no—
62#237—22no—
63#237—21no—
64#237—41no—
65#237—41no—
66#237—41no—
67D3×D4—21no—
68D3×D4—41no—
69#235—21no—
70#235—41no—
71C2×C4×D3—41no—
72C2×C4×D3D411yescharacteristic
73C2×Dic6—21no—
74C3×Q16C2311yescharacteristic
75C3×SD16—21no—
76C3×D8—21no—
77C3×D8C2312yes—
78C3×D8C2311yescharacteristic
79C2×C3×C8C2311yescharacteristic
80#216—21no—
81#215—21no—
82#214—22no—
83#214—22no—
84#214—21no—
85#213—21no—
86C2×C3⋊C8D411yescharacteristic
87Dic12—21no—
88Dic12C2312yes—
89Dic12C2311yescharacteristic
90D24C2311yescharacteristic
91#204—21no—
92D3×C8D411yescharacteristic
93D3×C8D411yescharacteristic
94D3×C8C2311yescharacteristic
95D3×C8C2311yescharacteristic
96C3×C16C2312yes—
97C3⋊C16C2312yes—
98C2×#41—61no—
99C2×#41—61no—
100#135—31no—
101#135—32no—
102#135—32no—
103#135—31no—
104#135—31no—
105#135—61no—
106#135—61no—
107#135—61no—
108#135—61no—
109#135C2×D311yescharacteristic
110C2×Q16—31no—
111C2×Q16—31no—
112C2×SD16—61no—
113C2×SD16—61no—
114C2×D8—31no—
115C2×D8C2×D311yescharacteristic, complemented
116C22×C8—31no—
117Q32—32no—
118Q32—32no—
119SD32—32no—
120SD32—32no—
121SD32—32no—
122SD32C2×D312yescomplemented
123D16—32no—
124D16C2×D312yescomplemented
125M32—31no—
126M32—32no—
127M32C2×D311yescharacteristic, complemented
128C2×C16—32no—
129C23×C3—41no—
130C22×D3—41no—
131C22×D3D811yescharacteristic
132C3×Q8—21no—
133C3×D4—21no—
134C3×D4—22no—
135C3×D4—41no—
136C3×D4—41no—
137C2×C3×C4—41no—
138C2×C3×C4C2×D411yescharacteristic
139#67—41no—
140#67—41no—
141#67—42no—
142#67—42no—
143#67—41no—
144C2×Dic3—41no—
145C2×Dic3—41no—
146C2×Dic3—42no—
147C2×Dic3—42no—
148C2×Dic3D811yescharacteristic
149D12—21no—
150D12—41no—
151C4×D3—41no—
152C4×D3—41no—
153C4×D3—41no—
154C4×D3D811yescharacteristic
155C4×D3D811yescharacteristic
156C4×D3C2×D411yescharacteristic
157C4×D3C2×D411yescharacteristic
158Dic6—21no—
159Dic6—22no—
160Dic6—41no—
161Dic6—41no—
162C3×C8C2×D411yescharacteristic
163C3×C8C2411yescharacteristic
164C3⋊C8C2×D411yescharacteristic
165C3⋊C8C2×D411yescharacteristic
166#41—21no—
167#41—62no—
168#41—62no—
169#41—61no—
170#41—61no—
171#41—61no—
172#41—121no—
173#41—121no—
174#41—121no—
175#41—121no—
176C2×Q8—61no—
177C2×Q8—61no—
178C2×D4—21no—
179C2×D4—61no—
180C2×D4—121no—
181C2×D4—121no—
182C22×C4—31no—
183C22×C4—121no—
184C22×C4—121no—
185Q16—31no—
186Q16—32no—
187Q16—61no—
188Q16—61no—
189Q16C22×D311yescharacteristic
190SD16—21no—
191SD16—62no—
192SD16—62no—
193SD16—61no—
194SD16—61no—
195SD16—61no—
196D8—21no—
197D8—31no—
198D8—61no—
199D8C22×D312yes—
200D8C22×D311yescharacteristic
201C2×C8—31no—
202C2×C8—31no—
203C2×C8—31no—
204C2×C8—31no—
205C2×C8—31no—
206C2×C8C22×D311yescharacteristic
207C16—32no—
208C16C22×D312yes—
209C22×C3—42no—
210C22×C3—41no—
211C22×C3—82no—
212C22×C3C2×D811yescharacteristic
213C2×D3—41no—
214C2×D3—41no—
215C2×D3—82no—
216C2×D3C2×D811yescharacteristic
217C2×D3C2×D811yescharacteristic
218C3×C4—41no—
219C3×C4C2×D811yescharacteristic
220C3×C4C22×D411yescharacteristic
221Dic3—41no—
222Dic3—42no—
223Dic3C2×D811yescharacteristic
224Dic3C2×D811yescharacteristic
225C23—31no—
226C23—41no—
227C23—121no—
228Q8—21no—
229Q8—62no—
230Q8—61no—
231Q8—121no—
232Q8—121no—
233D4—22no—
234D4—21no—
235D4—41no—
236D4—41no—
237D4—61no—
238D4—121no—
239D4—121no—
240D4—122no—
241D4—121no—
242D4—122no—
243D4—121no—
244C2×C4—31no—
245C2×C4—31no—
246C2×C4—31no—
247C2×C4—31no—
248C2×C4—31no—
249C2×C4—41no—
250C2×C4—121no—
251C2×C4—121no—
252C2×C4—122no—
253C2×C4—122no—
254C2×C4—121no—
255C2×C4—121no—
256C2×C4—121no—
257C2×C4D3×D411yescharacteristic
258C8—31no—
259C8—31no—
260C8D3×D411yescharacteristic
261C8C23×D311yescharacteristic
262C2×C3—21no—
263C2×C3—81no—
264C2×C3—82no—
265C2×C3C22×D811yescharacteristic
266D3—21no—
267D3—21no—
268D3—81no—
269C22—31no—
270C22—31no—
271C22—41no—
272C22—42no—
273C22—82no—
274C22—121no—
275C22—121no—
276C22—242no—
277C22D3×D811yescharacteristic
278C4—31no—
279C4—31no—
280C4—41no—
281C4—122no—
282C4—121no—
283C4D3×D811yescharacteristic
284C4C2×D3×D411yescharacteristic
285C3#341411yescharacteristic, complemented, Sylow
286C2—21no—
287C2—61no—
288C2—61no—
289C2—82no—
290C2—81no—
291C2—241no—
292C2C2×D3×D811yescharacteristic
subgroupG/H
centerC2C2×D3×D8
commutator, cosocleC3×C8C24
FrattiniC8C23×D3
FittingC3×#509C2
socleC2×C3C22×D8
hypercenter#509D3
hypocenterC3#3414
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. D3×#135C2semidirect
2. C2×#912C2semidirect
3. C3×#509C2semidirect
4. #5195C2semidirect
5. #5147C2semidirect
6. #4916C2semidirect
7. #4915C2semidirect
8. #4912C2semidirect
9. #4911C2semidirect
10. #4909C2semidirect
11. D3×M32C2semidirect
16. C2×C3×D8C22semidirect
19. #919C22semidirect
20. D3×Q16C22semidirect
26. #912C22semidirect
27. #912C22semidirect
28. D3×D8C22semidirect
29. C2×Dic12C22semidirect
32. C3×SD32C22semidirect
33. C3×D16C22semidirect
34. C3×M32C22semidirect
35. #829C22semidirect
36. #827C22semidirect
37. #827C22semidirect
38. #826C22semidirect
39. #812C22semidirect
40. Dic24C22semidirect
41. #800C22semidirect
42. #798C22semidirect
43. D3×C16C22semidirect
51. #509D3semidirect
115. C2×D8C2×D3semidirect
122. SD32C2×D3semidirect
124. D16C2×D3semidirect
127. M32C2×D3semidirect
285. C3#3414semidirect

Maximal subgroups

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

subgroupindex
D3×#1352
C2×#9122
C3×#5092
#51952
#51472
#49162
#49152
#49122
#49112
#49092
D3×M322
#34143