Finite Group Databasebeta

← #82039

Subgroups — #82039

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×#919C211yesmaximal, characteristic, complemented
3C3×#510C211yesmaximal, characteristic, complemented
4#5193C211yesmaximal, characteristic, complemented
5#5179C211yesmaximal, characteristic, complemented
6#4919C212yesmaximal, complemented
7#4918C212yesmaximal, complemented
8#4916C212yesmaximal, complemented
9#4914C212yesmaximal, complemented
10#4908C211yesmaximal, characteristic, complemented
11D3×M32C211yesmaximal, characteristic, complemented
12#3414—31nomaximal, Sylow
13D3×#41—21no—
14C2×#239—21no—
15C3×#135C2211yescharacteristic
16C2×C3×Q16C2211yescharacteristic, complemented
17#950—21no—
18C2×#215—21no—
19#919—21no—
20#919—21no—
21#919C2212yes—
22#919C2212yescomplemented
23#919C2211yescharacteristic, complemented
24D3×Q16C2211yescharacteristic, complemented
25#916—21no—
26D3×SD16—21no—
27#912C2211yescharacteristic, complemented
28D3×D8C2211yescharacteristic, complemented
29#904C2211yescharacteristic
30C2×D24C2211yescharacteristic, complemented
31C2×D3×C8C2211yescharacteristic
32C3×Q32C2212yescomplemented
33C3×SD32C2212yescomplemented
34C3×M32C2211yescharacteristic, complemented
35#829C2212yescomplemented
36#828C2212yescomplemented
37#828C2212yescomplemented
38#826C2212yescomplemented
39#812C2211yescharacteristic, complemented
40#800C2212yescomplemented
41D48C2212yescomplemented
42#798C2212yescomplemented
43D3×C16C2212yescomplemented
44C2×#135—31no—
45C2×#135—31no—
46#510—31no—
47#510—32no—
48#510D311yescharacteristic, complemented
49#509—31no—
50#509—32no—
51#509—31no—
52#508—32no—
53#508—32no—
54C2×M32—31no—
55C3×#41—21no—
56C2×C3×Q8—21no—
57#239—21no—
58#239—22no—
59#239—22no—
60#239—41no—
61#239—41no—
62D3×Q8—21no—
63#237—21no—
64#237—41no—
65D3×D4—21no—
66D3×D4—41no—
67#235—21no—
68#235—41no—
69C2×D12—21no—
70C2×D12—41no—
71C2×C4×D3—41no—
72C2×C4×D3—41no—
73C2×C4×D3D411yescharacteristic
74C3×Q16—21no—
75C3×Q16C2311yescharacteristic
76C3×Q16C2312yes—
77C3×SD16—21no—
78C3×D8C2311yescharacteristic
79C2×C3×C8C2311yescharacteristic
80#216—21no—
81#215—21no—
82#215—22no—
83#215—22no—
84#214—21no—
85#213—21no—
86C2×C3⋊C8D411yescharacteristic
87Dic12C2311yescharacteristic
88D24—21no—
89D24C2311yescharacteristic
90D24C2312yes—
91#204—21no—
92D3×C8D411yescharacteristic
93D3×C8D411yescharacteristic
94D3×C8C2311yescharacteristic
95D3×C8C2311yescharacteristic
96C3×C16C2312yes—
97C3⋊C16C2312yes—
98C2×#41—61no—
99C2×#41—61no—
100#135—32no—
101#135—31no—
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×Q16C2×D311yescharacteristic, complemented
112C2×SD16—61no—
113C2×SD16—61no—
114C2×D8—31no—
115C2×D8—31no—
116C22×C8—31no—
117Q32—32no—
118Q32C2×D312yescomplemented
119SD32—32no—
120SD32—32no—
121SD32—32no—
122SD32C2×D312yescomplemented
123D16—32no—
124D16—32no—
125M32—31no—
126M32—32no—
127M32C2×D311yescharacteristic, complemented
128C2×C16—32no—
129C22×D3—41no—
130C22×D3—41no—
131C22×D3D811yescharacteristic
132C3×Q8—22no—
133C3×Q8—21no—
134C3×Q8—41no—
135C3×D4—21no—
136C3×D4—41no—
137C2×C3×C4—41no—
138C2×C3×C4—41no—
139C2×C3×C4C2×D411yescharacteristic
140#67—41no—
141#67—41no—
142#67—41no—
143C2×Dic3—41no—
144C2×Dic3D811yescharacteristic
145D12—21no—
146D12—22no—
147D12—42no—
148D12—42no—
149D12—41no—
150D12—41no—
151C4×D3—41no—
152C4×D3—41no—
153C4×D3—41no—
154C4×D3—42no—
155C4×D3—42no—
156C4×D3D811yescharacteristic
157C4×D3D811yescharacteristic
158C4×D3C2×D411yescharacteristic
159C4×D3C2×D411yescharacteristic
160Dic6—21no—
161Dic6—41no—
162C3×C8C2×D411yescharacteristic
163C3×C8C2411yescharacteristic
164C3⋊C8C2×D411yescharacteristic
165C3⋊C8C2×D411yescharacteristic
166#41—21no—
167#41—61no—
168#41—62no—
169#41—61no—
170#41—62no—
171#41—61no—
172#41—121no—
173#41—121no—
174#41—121no—
175#41—121no—
176C2×Q8—21no—
177C2×Q8—61no—
178C2×D4—61no—
179C2×D4—61no—
180C2×D4—121no—
181C2×D4—121no—
182C22×C4—31no—
183C22×C4—121no—
184C22×C4—121no—
185Q16—21no—
186Q16—31no—
187Q16—61no—
188Q16C22×D311yescharacteristic
189Q16C22×D312yes—
190SD16—21no—
191SD16—61no—
192SD16—62no—
193SD16—61no—
194SD16—62no—
195SD16—61no—
196D8—32no—
197D8—31no—
198D8—61no—
199D8—61no—
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—41no—
210C22×C3C2×D811yescharacteristic
211C2×D3—41no—
212C2×D3—42no—
213C2×D3—41no—
214C2×D3—82no—
215C2×D3—82no—
216C2×D3C2×D811yescharacteristic
217C2×D3C2×D811yescharacteristic
218C3×C4—41no—
219C3×C4—42no—
220C3×C4C2×D811yescharacteristic
221C3×C4C22×D411yescharacteristic
222Dic3—41no—
223Dic3C2×D811yescharacteristic
224Dic3C2×D811yescharacteristic
225C23—31no—
226C23—121no—
227C23—121no—
228Q8—21no—
229Q8—22no—
230Q8—41no—
231Q8—61no—
232Q8—121no—
233D4—21no—
234D4—41no—
235D4—61no—
236D4—62no—
237D4—121no—
238D4—121no—
239D4—122no—
240D4—122no—
241D4—121no—
242D4—121no—
243D4—121no—
244C2×C4—31no—
245C2×C4—31no—
246C2×C4—31no—
247C2×C4—31no—
248C2×C4—31no—
249C2×C4—41no—
250C2×C4—41no—
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×C3C22×D811yescharacteristic
265D3—21no—
266D3—21no—
267D3—82no—
268D3—81no—
269C22—31no—
270C22—31no—
271C22—41no—
272C22—121no—
273C22—122no—
274C22—121no—
275C22—242no—
276C22—242no—
277C22D3×D811yescharacteristic
278C4—31no—
279C4—31no—
280C4—41no—
281C4—42no—
282C4—121no—
283C4D3×D811yescharacteristic
284C4C2×D3×D411yescharacteristic
285C3#341411yescharacteristic, complemented, Sylow
286C2—21no—
287C2—61no—
288C2—61no—
289C2—81no—
290C2—242no—
291C2—241no—
292C2C2×D3×D811yescharacteristic
subgroupG/H
centerC2C2×D3×D8
commutator, cosocleC3×C8C24
FrattiniC8C23×D3
FittingC3×#510C2
socleC2×C3C22×D8
hypercenter#510D3
hypocenterC3#3414
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
1. D3×#135C2semidirect
2. C2×#919C2semidirect
3. C3×#510C2semidirect
4. #5193C2semidirect
5. #5179C2semidirect
6. #4919C2semidirect
7. #4918C2semidirect
8. #4916C2semidirect
9. #4914C2semidirect
10. #4908C2semidirect
11. D3×M32C2semidirect
16. C2×C3×Q16C22semidirect
22. #919C22semidirect
23. #919C22semidirect
24. D3×Q16C22semidirect
27. #912C22semidirect
28. D3×D8C22semidirect
30. C2×D24C22semidirect
32. C3×Q32C22semidirect
33. C3×SD32C22semidirect
34. C3×M32C22semidirect
35. #829C22semidirect
36. #828C22semidirect
37. #828C22semidirect
38. #826C22semidirect
39. #812C22semidirect
40. #800C22semidirect
41. D48C22semidirect
42. #798C22semidirect
43. D3×C16C22semidirect
48. #510D3semidirect
111. C2×Q16C2×D3semidirect
118. Q32C2×D3semidirect
122. SD32C2×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×#9192
C3×#5102
#51932
#51792
#49192
#49182
#49162
#49142
#49082
D3×M322
#34143