Finite Group Databasebeta

← #83482

Subgroups — #83482

Order 384.

494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C3×D42C211yesmaximal, characteristic, complemented
2#5555C211yesmaximal, characteristic, complemented
3#5217C212yesmaximal, complemented
4C2×#832C212yesmaximal, complemented
5#5072C211yesmaximal, characteristic, complemented
6#5070C211yesmaximal, characteristic, complemented
7#5038C212yesmaximal, complemented
8#5033C212yesmaximal, complemented
9C4×#213C211yesmaximal, characteristic, complemented
10D4×C3⋊C8C211yesmaximal, characteristic, complemented
11#5007C211yesmaximal, characteristic, complemented
12#3294—31nomaximal, Sylow
13C22×C3×D4—21no—
14C22×C3×D4C2212yes—
15C2×#237—21no—
16C3×#127C2211yescharacteristic
17C3×#121—21no—
18C3×#121C2212yes—
19C3×#120—22no—
20C3×C4×D4C2211yescharacteristic
21C3×C4×D4C2211yescharacteristic
22C2×#213C2211yescharacteristic
23C2×#213C2212yescomplemented
24#930C2212yescomplemented
25C2×C4⋊Dic3C2212yescomplemented
26C22×C3⋊C8C2212yescomplemented
27#897—21no—
28#886—22no—
29C4×D12C2211yescharacteristic, complemented
30#869C2211yescharacteristic, complemented
31#832C2211yescharacteristic
32#832C2212yes—
33#832C2212yescomplemented
34#832C2212yescomplemented
35#832C2212yescomplemented
36#830C2212yescomplemented
37#809C2211yescharacteristic, complemented
38#807C2212yescomplemented
39#807C2211yescharacteristic, complemented
40C4⋊(C3⋊C8)C2211yescharacteristic, complemented
41C4×C3⋊C8C2211yescharacteristic, complemented
42#547—31no—
43D42D311yescharacteristic, complemented
44#486—31no—
45#480—32no—
46#474—31no—
47#466—32no—
48#459—31no—
49#447—32no—
50C4×D8—31no—
51C8×D4—31no—
52C2×#102—32no—
53C24×C3—22no—
54C2×C3×D4—24no—
55C2×C3×D4—22no—
56C2×C3×D4—22no—
57C2×C3×D4—21no—
58C2×C3×D4—21no—
59C2×C3×D4—42no—
60C2×C3×D4—44no—
61C2×C3×D4D411yescharacteristic
62C2×C3×D4C2312yes—
63C2×C3×D4C2311yescharacteristic
64C22×C3×C4—21no—
65C22×C3×C4C2312yes—
66C2×#67—22no—
67C22×Dic3—22no—
68#237—44no—
69C2×D12C2311yescharacteristic
70C2×C4×D3—21no—
71C2×Dic6—21no—
72C3×C4⋊C4D411yescharacteristic
73C3×C4⋊C4C2311yescharacteristic
74C3×C22⋊C4—21no—
75C3×C22⋊C4—22no—
76C3×C22⋊C4D412yes—
77C3×C42C2311yescharacteristic
78#213—22no—
79#213—42no—
80(C2×D3)⋊C4—21no—
81(C2×D3)⋊C4—22no—
82C4⋊Dic3—21no—
83C4⋊Dic3—22no—
84C4⋊Dic3C2312yes—
85C4⋊Dic3C2311yescharacteristic
86C2×C3⋊C8—42no—
87C2×C3⋊C8C2311yescharacteristic
88C2×C3⋊C8C2311yescharacteristic
89C2×C3⋊C8C2312yes—
90C2×#41—61no—
91C22×D4—21no—
92C22×D4C2×D312yes—
93C2×D8—31no—
94C2×D8—32no—
95C22×C8—32no—
96C4⋊Q8—31no—
97#127C2×D311yescharacteristic
98#123—62no—
99C22⋊Q8—61no—
100#121—21no—
101#121—32no—
102#121C2×D312yes—
103#120—22no—
104C4×D4—31no—
105C4×D4C2×D311yescharacteristic
106C4×D4C2×D311yescharacteristic
107C2×C4⋊C4—32no—
108#107—31no—
109#107—32no—
110C4⋊C8—31no—
111#102—31no—
112#102—32no—
113#102—32no—
114#102—32no—
115#102—32no—
116#102—31no—
117C22⋊C8—32no—
118C4×C8—31no—
119C23×C3—21no—
120C23×C3—22no—
121C23×C3—44no—
122C23×C3—44no—
123C23×C3—82no—
124C23×C3C2×D412yes—
125C22×D3—21no—
126C3×D4—22no—
127C3×D4—21no—
128C3×D4—22no—
129C3×D4—44no—
130C3×D4—44no—
131C3×D4—42no—
132C3×D4—81no—
133C3×D4D814yescomplemented
134C3×D4#4112yescomplemented
135C2×C3×C4—22no—
136C2×C3×C4—22no—
137C2×C3×C4—21no—
138C2×C3×C4—42no—
139C2×C3×C4C2×D411yescharacteristic
140C2×C3×C4C2×D412yes—
141C2×C3×C4C2×D411yescharacteristic
142C2×C3×C4C2411yescharacteristic
143#67—44no—
144C2×Dic3—22no—
145C2×Dic3—21no—
146C2×Dic3—44no—
147D12—21no—
148D12—21no—
149C4×D3—42no—
150Dic6—42no—
151C3⋊C8—21no—
152C3⋊C8—21no—
153C3⋊C8—22no—
154C24—22no—
155#41—124no—
156C2×Q8—61no—
157C2×D4—24no—
158C2×D4—22no—
159C2×D4—22no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—31no—
163C2×D4—42no—
164C2×D4—44no—
165C2×D4—62no—
166C2×D4#6711yescharacteristic
167C2×D4C22×D312yes—
168C2×D4C22×D311yescharacteristic
169C22×C4—21no—
170C22×C4—62no—
171C22×C4—61no—
172C22×C4C22×D312yes—
173D8—62no—
174D8—122no—
175C2×C8—31no—
176C2×C8—31no—
177C2×C8—32no—
178C2×C8—122no—
179C4⋊C4—31no—
180C4⋊C4—32no—
181C4⋊C4—62no—
182C4⋊C4—61no—
183C4⋊C4#6711yescharacteristic
184C4⋊C4C22×D311yescharacteristic
185C22⋊C4—21no—
186C22⋊C4—22no—
187C22⋊C4—61no—
188C22⋊C4—62no—
189C22⋊C4#6712yes—
190C42C22×D311yescharacteristic
191C22×C3—22no—
192C22×C3—22no—
193C22×C3—22no—
194C22×C3—41no—
195C22×C3—41no—
196C22×C3—42no—
197C22×C3—42no—
198C22×C3—42no—
199C22×C3—88no—
200C22×C3C2×D814yes—
201C22×C3C22×D411yescharacteristic
202C2×D3—41no—
203C2×D3—41no—
204C2×D3—41no—
205C3×C4—22no—
206C3×C4—21no—
207C3×C4—41no—
208C3×C4C2×D812yes—
209C3×C4C2×#4111yescharacteristic
210C3×C4H(5,𝔽2)11yescharacteristic
211Dic3—42no—
212Dic3—41no—
213C23—21no—
214C23—22no—
215C23—44no—
216C23—44no—
217C23—61no—
218C23—82no—
219C23C2×#6712yes—
220Q8—122no—
221D4—22no—
222D4—21no—
223D4—22no—
224D4—44no—
225D4—44no—
226D4—42no—
227D4—61no—
228D4—61no—
229D4—81no—
230D4—124no—
231D4#21314yescomplemented
232D4#23712yescomplemented
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—42no—
237C2×C4—61no—
238C2×C4—62no—
239C2×C4—124no—
240C2×C4—122no—
241C2×C4C2×#6711yescharacteristic
242C2×C4C2×#6712yes—
243C2×C4C2×#6711yescharacteristic
244C2×C4C23×D311yescharacteristic
245C8—61no—
246C8—61no—
247C8—62no—
248C2×C3—24no—
249C2×C3—42no—
250C2×C3—82no—
251C2×C3#54611yescharacteristic
252C2×C3C22×D811yescharacteristic
253C2×C3#57711yescharacteristic
254D3—81no—
255C22—22no—
256C22—22no—
257C22—22no—
258C22—41no—
259C22—41no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—88no—
264C22—121no—
265C22—121no—
266C22—121no—
267C22C2×#21314yes—
268C22C22×#6711yescharacteristic
269C4—22no—
270C4—21no—
271C4—41no—
272C4—121no—
273C4—122no—
274C4C2×#21312yes—
275C4C2×#23711yescharacteristic
276C4#100411yescharacteristic
277C3#329411yescharacteristic, complemented, Sylow
278C2—24no—
279C2—42no—
280C2—82no—
281C2—241no—
282C2C22×#21311yescharacteristic
283C2#580611yescharacteristic
284C2#583611yescharacteristic
subgroupG/H
centerC22C22×#67
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×D42C2
socleC22×C3C22×D4
hypercenterD42D3
hypocenterC3#3294
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C3×D42C2semidirect
2. #5555C2semidirect
3. #5217C2semidirect
4. C2×#832C2semidirect
5. #5072C2semidirect
6. #5070C2semidirect
7. #5038C2semidirect
8. #5033C2semidirect
9. C4×#213C2semidirect
10. D4×C3⋊C8C2semidirect
11. #5007C2semidirect
23. C2×#213C22semidirect
24. #930C22semidirect
25. C2×C4⋊Dic3C22semidirect
26. C22×C3⋊C8C22semidirect
29. C4×D12C22semidirect
30. #869C22semidirect
33. #832C22semidirect
34. #832C22semidirect
35. #832C22semidirect
36. #830C22semidirect
37. #809C22semidirect
38. #807C22semidirect
39. #807C22semidirect
40. C4⋊(C3⋊C8)C22semidirect
41. C4×C3⋊C8C22semidirect
43. D42D3semidirect
133. C3×D4D8semidirect
134. C3×D4#41semidirect
231. D4#213semidirect
232. D4#237semidirect
277. C3#3294semidirect

Maximal subgroups

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

subgroupindex
C3×D422
#55552
#52172
C2×#8322
#50722
#50702
#50382
#50332
C4×#2132
D4×C3⋊C82
#50072
#32943