Finite Group Databasebeta

← #81587

Subgroups — #81587

Order 384.

384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 115 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#5727C211yesmaximal, characteristic, complemented
2#5713C211yesmaximal, characteristic, complemented
3C3×#486C211yesmaximal, characteristic, complemented
4#5094C211yesmaximal, characteristic, complemented
5#5072C211yesmaximal, characteristic
6#4787C212yesmaximal, complemented
7#4785C212yesmaximal, complemented
8#4765C212yesmaximal, complemented
9#4761C212yesmaximal, complemented
10C4×#204C211yesmaximal, characteristic, complemented
11#4679C211yesmaximal, characteristic, complemented
12#3373—31nomaximal, Sylow
13C2×D3×Q8—21no—
14C3×C4⋊Q8C2211yescharacteristic
15C3×#127C2211yescharacteristic
16#946—21no—
17#936—21no—
18#936C2212yes—
19#935—22no—
20D4×Dic3—21no—
21D4×Dic3C2212yes—
22C2×#213C2212yes—
23C2×#204C2211yescharacteristic
24#896—22no—
25#893C2212yes—
26#888C2212yes—
27C4×D12C2211yescharacteristic
28C4×Dic6C2211yescharacteristic
29C4×Dic6C2211yescharacteristic
30C3×#102C2212yes—
31C3×#102C2212yes—
32C3×C4×C8C2211yescharacteristic
33#832C2212yes—
34#821C2211yescharacteristic
35#817C2211yescharacteristic
36#816C2211yescharacteristic
37#815C2212yes—
38Dic3⋊C8C2212yes—
39#810C2212yes—
40#808C2212yes—
41C4⋊(C3⋊C8)C2211yescharacteristic
42#559—31no—
43D4×Q8—31no—
44#489—32no—
45#486D311yescharacteristic, complemented
46#476—32no—
47#475—31no—
48#463—32no—
49#459—31no—
50#446—31no—
51#442—32no—
52C4×SD16—31no—
53C2×C3×Q8—21no—
54C2×C3×D4—21no—
55C2×C3×D4—21no—
56C2×C3×D4C2312yes—
57C22×Dic3—22no—
58D3×Q8—44no—
59C2×D12C2311yescharacteristic
60C2×C4×D3—21no—
61C2×C4×D3—22no—
62C2×Dic6—22no—
63C2×Dic6D411yescharacteristic
64C2×Dic6C2311yescharacteristic
65C2×C3×C8C2311yescharacteristic
66C2×C3×C8C2311yescharacteristic
67C3×C4⋊C4—21no—
68C3×C4⋊C4C2312yes—
69C3×C42C2311yescharacteristic
70#217—22no—
71#217—22no—
72#217—22no—
73#213—24no—
74(C2×D3)⋊C4—21no—
75(C2×D3)⋊C4—22no—
76C4⋊Dic3D411yescharacteristic
77C4⋊Dic3C2311yescharacteristic
78C4⋊Dic3C2311yescharacteristic
79Dic3⋊C4—21no—
80Dic3⋊C4—22no—
81Dic3⋊C4D412yes—
82C4×Dic3—21no—
83C4×Dic3C2312yes—
84C2×C3⋊C8C2312yes—
85#204—22no—
86C22×Q8—61no—
87C2×SD16—31no—
88C2×D8—32no—
89C4⋊Q8—32no—
90C4⋊Q8C2×D311yescharacteristic
91#127C2×D311yescharacteristic
92#124—32no—
93#124—61no—
94#123—62no—
95C22⋊Q8—62no—
96C22⋊Q8—61no—
97C4×Q8—31no—
98C4×Q8—31no—
99C4×D4—32no—
100C4×D4—32no—
101C4×D4—31no—
102C4×D4—61no—
103#106—31no—
104#106—32no—
105C4⋊C8—32no—
106C4⋊C8—31no—
107#103—31no—
108#103—32no—
109#102—32no—
110#102—31no—
111#102C2×D312yes—
112#102C2×D312yes—
113#97—32no—
114C4×C8C2×D311yescharacteristic
115C23×C3—22no—
116C22×D3—21no—
117C3×Q8—42no—
118C3×D4—22no—
119C3×D4—22no—
120C3×D4—42no—
121C3×D4—81no—
122C2×C3×C4—22no—
123C2×C3×C4C2×D411yescharacteristic
124C2×C3×C4C2×D411yescharacteristic
125C2×C3×C4C2411yescharacteristic
126C2×Dic3—21no—
127C2×Dic3—21no—
128C2×Dic3—21no—
129C2×Dic3—82no—
130C2×Dic3C2×D412yes—
131C2×Dic3C2×D412yes—
132D12—21no—
133D12#4112yes—
134C4×D3—44no—
135C4×D3—42no—
136Dic6—22no—
137Dic6—21no—
138Dic6—21no—
139Dic6—44no—
140C3×C8—21no—
141C3×C8—21no—
142C3⋊C8—22no—
143C2×Q8—21no—
144C2×Q8—31no—
145C2×Q8—31no—
146C2×Q8—62no—
147C2×Q8—124no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4—31no—
151C2×D4C22×D312yes—
152C22×C4—62no—
153C22×C4—62no—
154C22×C4—61no—
155SD16—62no—
156D8—64no—
157C2×C8—32no—
158C2×C8C22×D311yescharacteristic
159C2×C8C22×D311yescharacteristic
160C4⋊C4—21no—
161C4⋊C4—31no—
162C4⋊C4—32no—
163C4⋊C4—31no—
164C4⋊C4—31no—
165C4⋊C4—62no—
166C4⋊C4—61no—
167C4⋊C4C22×D312yes—
168C22⋊C4—62no—
169C22⋊C4—62no—
170C22⋊C4—62no—
171C22⋊C4—62no—
172C22⋊C4—61no—
173C42—32no—
174C42—61no—
175C42C22×D311yescharacteristic
176C22×C3—42no—
177C22×C3—42no—
178C22×C3—42no—
179C22×C3C22×D411yescharacteristic
180C2×D3—22no—
181C2×D3—41no—
182C2×D3—41no—
183C3×C4—21no—
184C3×C4—42no—
185C3×C4AGL(1,ℤ/8)12yes—
186C3×C4C2×#4111yescharacteristic
187C3×C42−1+411yescharacteristic
188Dic3—22no—
189Dic3—22no—
190Dic3—41no—
191Dic3—41no—
192Dic3—41no—
193C23—22no—
194C23—61no—
195Q8—42no—
196Q8—62no—
197Q8—61no—
198Q8—61no—
199Q8—124no—
200D4—22no—
201D4—22no—
202D4—32no—
203D4—42no—
204D4—61no—
205D4—81no—
206C2×C4—22no—
207C2×C4—32no—
208C2×C4—32no—
209C2×C4—61no—
210C2×C4—61no—
211C2×C4—61no—
212C2×C4—124no—
213C2×C4—122no—
214C2×C4—242no—
215C2×C4D3×D411yescharacteristic
216C2×C4D3×D411yescharacteristic
217C2×C4C23×D311yescharacteristic
218C8—21no—
219C8—21no—
220C8—62no—
221C2×C3—82no—
222C2×C3#54811yescharacteristic
223C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
224C2×C3#57711yescharacteristic
225D3—42no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—62no—
230C22—121no—
231C22—121no—
232C22C2×D3×D411yescharacteristic
233C4—21no—
234C4—42no—
235C4—62no—
236C4—62no—
237C4—121no—
238C4—121no—
239C4—121no—
240C4#91112yes—
241C4D3×#4111yescharacteristic
242C4#101011yescharacteristic
243C3#337311yescharacteristic, complemented, Sylow
244C2—82no—
245C2—122no—
246C2#567711yescharacteristic
247C2C2×#91111yescharacteristic
248C2#576211yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#486C2
socleC22×C3C22×D4
prime radical#5072C2
hypercenter#486D3
hypocenterC3#3373
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #5727C2semidirect
2. #5713C2semidirect
3. C3×#486C2semidirect
4. #5094C2semidirect
6. #4787C2semidirect
7. #4785C2semidirect
8. #4765C2semidirect
9. #4761C2semidirect
10. C4×#204C2semidirect
11. #4679C2semidirect
45. #486D3semidirect
243. C3#3373semidirect

Maximal subgroups

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

subgroupindex
#57272
#57132
C3×#4862
#50942
#50722
#47872
#47852
#47652
#47612
C4×#2042
#46792
#33733