Finite Group Databasebeta

← #80948

Subgroups — #80948

Order 384.

492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 127 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
1#5725C211yesmaximal, characteristic, complemented
2C4×D3×D4C211yesmaximal, characteristic, complemented
3C3×#474C211yesmaximal, characteristic, complemented
4#5087C211yesmaximal, characteristic, complemented
5#5015C211yesmaximal, characteristic, complemented
6#4882C212yesmaximal, complemented
7#4872C212yesmaximal, complemented
8#4843C211yesmaximal, characteristic, complemented
9#4833C211yesmaximal, characteristic, complemented
10#4773C212yesmaximal, complemented
11#4756C212yesmaximal, complemented
12#3100—31nomaximal, Sylow
13C2×#239—21no—
14C2×D3×D4C2211yescharacteristic
15C22×C4×D3—21no—
16C3×C4⋊Q8C2211yescharacteristic, complemented
17C3×C4×D4C2211yescharacteristic
18#947—21no—
19D4×Dic3C2211yescharacteristic
20C2×#213C2212yes—
21C4×#67—21no—
22C2×D24C2212yes—
23#895—21no—
24#895C2212yes—
25#893—21no—
26#893C2211yescharacteristic
27#893C2212yescomplemented
28D3×C4⋊C4C2211yescharacteristic
29#67⋊C4—21no—
30D3×C22⋊C4—21no—
31#874C2211yescharacteristic, complemented
32C4×D12C2211yescharacteristic
33C42×D3C2211yescharacteristic
34C3×#107C2212yescomplemented
35C3×C4⋊C8C2211yescharacteristic, complemented
36C3×#102C2212yes—
37#821C2212yescomplemented
38(C2×D3)⋊C8C2212yes—
39C8×Dic3C2212yescomplemented
40#809C2212yes—
41#809C2212yescomplemented
42#807C2212yescomplemented
43C4⋊(C3⋊C8)C2211yescharacteristic, complemented
44#532—31no—
45C2×C4×D4—31no—
46#480—32no—
47#474—31no—
48#474D311yescharacteristic, complemented
49#459—31no—
50#459—31no—
51#447—32no—
52C4×D8—32no—
53C4×D8—32no—
54#431—31no—
55C23×D3—21no—
56C2×C3×Q8—21no—
57C2×C3×D4C2311yescharacteristic
58C22×C3×C4—21no—
59C2×#67—21no—
60C22×Dic3—21no—
61#239—44no—
62D3×D4—22no—
63D3×D4—22no—
64C2×D12—22no—
65C2×D12—21no—
66C2×D12—21no—
67C2×D12C2312yes—
68C2×D12C2311yescharacteristic
69C2×C4×D3—21no—
70C2×C4×D3—21no—
71C2×C4×D3—21no—
72C2×C4×D3—22no—
73C2×C4×D3—44no—
74C2×C4×D3D411yescharacteristic
75C2×C4×D3D411yescharacteristic
76C2×C4×D3C2311yescharacteristic
77C2×C3×C8C2312yes—
78C3×C4⋊C4—21no—
79C3×C4⋊C4C2312yes—
80C3×C4⋊C4C2311yescharacteristic
81C3×C22⋊C4—21no—
82C3×C42C2311yescharacteristic
83#217—21no—
84#213—24no—
85(C2×D3)⋊C4—21no—
86(C2×D3)⋊C4—21no—
87(C2×D3)⋊C4—22no—
88(C2×D3)⋊C4—22no—
89C4⋊Dic3C2311yescharacteristic
90Dic3⋊C4—21no—
91C4×Dic3D411yescharacteristic
92C4×Dic3D411yescharacteristic
93C4×Dic3C2311yescharacteristic
94C2×C3⋊C8C2312yes—
95D24—24no—
96C2×#41—61no—
97C22×D4—31no—
98C23×C4—61no—
99C2×D8—32no—
100C2×D8—32no—
101C4⋊Q8C2×D311yescharacteristic, complemented
102#127—31no—
103#124—61no—
104#121—32no—
105#121—61no—
106C4×D4—31no—
107C4×D4—31no—
108C4×D4—32no—
109C4×D4—31no—
110C4×D4—61no—
111C4×D4—61no—
112C4×D4—61no—
113C4×D4C2×D311yescharacteristic
114C2×C4⋊C4—31no—
115C2×C22⋊C4—61no—
116C2×C42—31no—
117#107—32no—
118#107C2×D312yescomplemented
119C4⋊C8—31no—
120C4⋊C8C2×D311yescharacteristic, complemented
121#102—32no—
122#102—32no—
123#102—32no—
124#102C2×D312yes—
125C22⋊C8—32no—
126C4×C8—32no—
127C23×C3—21no—
128C22×D3—24no—
129C22×D3—21no—
130C22×D3—22no—
131C22×D3—42no—
132C22×D3—42no—
133C22×D3C2×D411yescharacteristic
134C3×Q8—42no—
135C3×D4—21no—
136C3×D4#4112yescomplemented
137C2×C3×C4—21no—
138C2×C3×C4—22no—
139C2×C3×C4—42no—
140C2×C3×C4C2×D411yescharacteristic
141C2×C3×C4C2×D411yescharacteristic
142C2×C3×C4C2411yescharacteristic
143#67—24no—
144C2×Dic3—21no—
145C2×Dic3—42no—
146C2×Dic3C2×D411yescharacteristic
147C2×Dic3C2×D411yescharacteristic
148C2×Dic3C2×D411yescharacteristic
149D12—21no—
150D12—22no—
151D12—22no—
152D12—42no—
153D12—44no—
154D12—42no—
155D12#4112yescomplemented
156C4×D3—21no—
157C4×D3—21no—
158C4×D3—41no—
159C4×D3—42no—
160C4×D3—42no—
161C4×D3—42no—
162C4×D3—44no—
163C4×D3D814yescomplemented
164C3×C8—22no—
165C3⋊C8—22no—
166C24—61no—
167#41—124no—
168C2×Q8—21no—
169C2×D4—31no—
170C2×D4—32no—
171C2×D4—62no—
172C2×D4—61no—
173C2×D4—62no—
174C2×D4—62no—
175C2×D4—61no—
176C2×D4—61no—
177C2×D4C22×D311yescharacteristic
178C22×C4—21no—
179C22×C4—31no—
180C22×C4—31no—
181C22×C4—31no—
182C22×C4—61no—
183C22×C4—62no—
184C22×C4—61no—
185C22×C4—61no—
186C22×C4—61no—
187C22×C4—124no—
188D8—64no—
189D8—64no—
190C2×C8—32no—
191C2×C8C22×D312yes—
192C4⋊C4—21no—
193C4⋊C4—31no—
194C4⋊C4—61no—
195C4⋊C4C22×D311yescharacteristic
196C4⋊C4C22×D312yes—
197C22⋊C4—21no—
198C22⋊C4—61no—
199C22⋊C4—62no—
200C22⋊C4—62no—
201C22⋊C4—61no—
202C22⋊C4—61no—
203C42—31no—
204C42—31no—
205C42—31no—
206C42C22×D311yescharacteristic
207C22×C3—22no—
208C22×C3—41no—
209C22×C3—41no—
210C22×C3C22×D411yescharacteristic
211C2×D3—21no—
212C2×D3—21no—
213C2×D3—22no—
214C2×D3—48no—
215C2×D3—41no—
216C2×D3—41no—
217C2×D3—42no—
218C2×D3—42no—
219C2×D3—42no—
220C2×D3C2×D812yes—
221C3×C4—21no—
222C3×C4—41no—
223C3×C4—42no—
224C3×C4C2×D812yes—
225C3×C4C2×#4111yescharacteristic
226C3×C4C2×#4111yescharacteristic
227Dic3—21no—
228Dic3—21no—
229Dic3—41no—
230Dic3C2×D812yes—
231C23—21no—
232C23—31no—
233C23—64no—
234C23—61no—
235C23—62no—
236C23—122no—
237C23—122no—
238Q8—42no—
239D4—21no—
240D4—32no—
241D4—64no—
242D4—61no—
243D4—62no—
244D4—62no—
245D4—122no—
246D4—124no—
247D4—122no—
248D4#23912yescomplemented
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—31no—
252C2×C4—34no—
253C2×C4—31no—
254C2×C4—31no—
255C2×C4—42no—
256C2×C4—61no—
257C2×C4—61no—
258C2×C4—61no—
259C2×C4—121no—
260C2×C4—122no—
261C2×C4—124no—
262C2×C4—122no—
263C2×C4—122no—
264C2×C4—122no—
265C2×C4D3×D411yescharacteristic
266C2×C4D3×D411yescharacteristic
267C2×C4C23×D311yescharacteristic
268C8—22no—
269C8—62no—
270C2×C3—42no—
271C2×C3#52511yescharacteristic
272C2×C3C22×D811yescharacteristic
273C2×C3#57511yescharacteristic
274D3—22no—
275D3—42no—
276D3—82no—
277C22—22no—
278C22—32no—
279C22—41no—
280C22—41no—
281C22—61no—
282C22—61no—
283C22—62no—
284C22—128no—
285C22—121no—
286C22—121no—
287C22—122no—
288C22—122no—
289C22—122no—
290C22C2×D3×D411yescharacteristic
291C4—21no—
292C4—32no—
293C4—41no—
294C4—42no—
295C4—61no—
296C4—61no—
297C4—121no—
298C4D3×D812yes—
299C4C2×#23911yescharacteristic
300C4D3×#4111yescharacteristic
301C3#310011yescharacteristic, complemented, Sylow
302C2—42no—
303C2—62no—
304C2—122no—
305C2—242no—
306C2#562711yescharacteristic
307C2C2×D3×D811yescharacteristic
308C2#577711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#474C2
socleC22×C3C22×D4
hypercenter#474D3
hypocenterC3#3100
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #5725C2semidirect
2. C4×D3×D4C2semidirect
3. C3×#474C2semidirect
4. #5087C2semidirect
5. #5015C2semidirect
6. #4882C2semidirect
7. #4872C2semidirect
8. #4843C2semidirect
9. #4833C2semidirect
10. #4773C2semidirect
11. #4756C2semidirect
16. C3×C4⋊Q8C22semidirect
27. #893C22semidirect
31. #874C22semidirect
34. C3×#107C22semidirect
35. C3×C4⋊C8C22semidirect
37. #821C22semidirect
39. C8×Dic3C22semidirect
41. #809C22semidirect
42. #807C22semidirect
43. C4⋊(C3⋊C8)C22semidirect
48. #474D3semidirect
101. C4⋊Q8C2×D3semidirect
118. #107C2×D3semidirect
120. C4⋊C8C2×D3semidirect
136. C3×D4#41semidirect
155. D12#41semidirect
163. C4×D3D8semidirect
248. D4#239semidirect
301. C3#3100semidirect

Maximal subgroups

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

subgroupindex
#57252
C4×D3×D42
C3×#4742
#50872
#50152
#48822
#48722
#48432
#48332
#47732
#47562
#31003