Finite Group Databasebeta

← #81589

Subgroups — #81589

Order 384.

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

normal subgroups only

This group has 348 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#5721C211yesmaximal, characteristic, complemented
2#5713C211yesmaximal, characteristic
3C3×#486C211yesmaximal, characteristic
4#5094C211yesmaximal, characteristic, complemented
5#5075C211yesmaximal, characteristic
6#4768C212yesmaximal, complemented
7#4767C212yesmaximal, complemented
8#4766C212yesmaximal, complemented
9#4758C212yesmaximal, complemented
10C4×Dic12C211yesmaximal, characteristic, complemented
11C8×Dic6C211yesmaximal, characteristic, complemented
12#3365—31nomaximal, Sylow
13C3×C4⋊Q8C2211yescharacteristic
14C3×#127C2211yescharacteristic
15Q8×Dic3—21no—
16#944—21no—
17#936—21no—
18#936C2212yes—
19#935—22no—
20D4×Dic3—21no—
21D4×Dic3C2212yes—
22C2×#214C2212yes—
23C2×Dic12C2211yescharacteristic
24#890C2212yes—
25#889—22no—
26#887C2212yes—
27C4×Dic6C2211yescharacteristic
28C4×Dic6C2211yescharacteristic
29C4×Dic6C2211yescharacteristic
30C3×#102C2212yes—
31C3×#102C2212yes—
32C3×C4×C8C2211yescharacteristic
33#832C2212yes—
34#818C2211yescharacteristic
35#816C2211yescharacteristic
36#816C2211yescharacteristic
37Dic3⋊C8C2212yes—
38C8×Dic3C2212yes—
39#810C2212yes—
40#808C2212yes—
41C4⋊(C3⋊C8)C2211yescharacteristic
42#559—31no—
43#557—31no—
44#488—32no—
45#486D311yescharacteristic
46#478—32no—
47#475—31no—
48#464—32no—
49#460—31no—
50C8×Q8—31no—
51C4×Q16—31no—
52C4×SD16—32no—
53C2×C3×Q8—21no—
54C2×C3×D4—21no—
55C2×C3×D4—21no—
56C2×C3×D4C2312yes—
57C22×Dic3—22no—
58C2×Dic6D411yescharacteristic
59C2×Dic6C2311yescharacteristic
60C2×Dic6C2311yescharacteristic
61C2×C3×C8C2311yescharacteristic
62C2×C3×C8C2311yescharacteristic
63C3×C4⋊C4—21no—
64C3×C4⋊C4C2312yes—
65C3×C42C2311yescharacteristic
66#217—22no—
67#217—22no—
68#217—22no—
69#214—24no—
70C4⋊Dic3—22no—
71C4⋊Dic3D411yescharacteristic
72C4⋊Dic3C2311yescharacteristic
73C4⋊Dic3C2311yescharacteristic
74Dic3⋊C4—21no—
75Dic3⋊C4—21no—
76Dic3⋊C4—22no—
77Dic3⋊C4—22no—
78Dic3⋊C4D412yes—
79C4×Dic3—21no—
80C4×Dic3—21no—
81C4×Dic3—22no—
82C4×Dic3C2312yes—
83C2×C3⋊C8C2312yes—
84Dic12—22no—
85C2×Q16—31no—
86C2×SD16—32no—
87C4⋊Q8—61no—
88C4⋊Q8C2×D311yescharacteristic
89#127C2×D311yescharacteristic
90#125—32no—
91#125—62no—
92#124—32no—
93#124—61no—
94#123—62no—
95C4×Q8—31no—
96C4×Q8—32no—
97C4×Q8—31no—
98C4×Q8—31no—
99C4×Q8—61no—
100C4×D4—32no—
101C4×D4—61no—
102#107—31no—
103#106—32no—
104C4⋊C8—32no—
105C4⋊C8—31no—
106#103—31no—
107#103—31no—
108#103—32no—
109#102—32no—
110#102C2×D312yes—
111#102C2×D312yes—
112C4×C8—32no—
113C4×C8C2×D311yescharacteristic
114C23×C3—22no—
115C3×Q8—42no—
116C3×D4—22no—
117C3×D4—22no—
118C3×D4—42no—
119C3×D4—81no—
120C2×C3×C4—22no—
121C2×C3×C4C2×D411yescharacteristic
122C2×C3×C4C2×D411yescharacteristic
123C2×C3×C4C2411yescharacteristic
124C2×Dic3—21no—
125C2×Dic3—21no—
126C2×Dic3—21no—
127C2×Dic3—21no—
128C2×Dic3—82no—
129C2×Dic3C2×D412yes—
130C2×Dic3C2×D412yes—
131Dic6—22no—
132Dic6—21no—
133Dic6—21no—
134Dic6—21no—
135Dic6#4112yes—
136C3×C8—21no—
137C3×C8—21no—
138C3⋊C8—22no—
139C2×Q8—21no—
140C2×Q8—31no—
141C2×Q8—31no—
142C2×Q8—31no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4C22×D312yes—
146C22×C4—62no—
147Q16—62no—
148SD16—64no—
149C2×C8—32no—
150C2×C8C22×D311yescharacteristic
151C2×C8C22×D311yescharacteristic
152C4⋊C4—21no—
153C4⋊C4—31no—
154C4⋊C4—32no—
155C4⋊C4—31no—
156C4⋊C4—31no—
157C4⋊C4—62no—
158C4⋊C4—62no—
159C4⋊C4—62no—
160C4⋊C4—61no—
161C4⋊C4—61no—
162C4⋊C4C22×D312yes—
163C22⋊C4—62no—
164C22⋊C4—62no—
165C22⋊C4—62no—
166C42—32no—
167C42—62no—
168C42—61no—
169C42—61no—
170C42C22×D311yescharacteristic
171C22×C3—42no—
172C22×C3—42no—
173C22×C3—42no—
174C22×C3C22×D411yescharacteristic
175C3×C4—21no—
176C3×C4—42no—
177C3×C4#13512yes—
178C3×C4C2×#4111yescharacteristic
179C3×C42−1+411yescharacteristic
180Dic3—22no—
181Dic3—22no—
182Dic3—22no—
183Dic3—41no—
184Dic3—41no—
185Dic3—41no—
186C23—22no—
187Q8—32no—
188Q8—42no—
189Q8—62no—
190Q8—61no—
191Q8—61no—
192Q8—61no—
193D4—22no—
194D4—22no—
195D4—42no—
196D4—81no—
197C2×C4—22no—
198C2×C4—32no—
199C2×C4—32no—
200C2×C4—61no—
201C2×C4—61no—
202C2×C4—61no—
203C2×C4—61no—
204C2×C4—242no—
205C2×C4D3×D411yescharacteristic
206C2×C4D3×D411yescharacteristic
207C2×C4C23×D311yescharacteristic
208C8—21no—
209C8—21no—
210C8—62no—
211C2×C3—82no—
212C2×C3#54811yescharacteristic
213C2×C3C2×#13511yescharacteristic
214C2×C3#57711yescharacteristic
215C22—42no—
216C22—42no—
217C22—42no—
218C22C2×D3×D411yescharacteristic
219C4—21no—
220C4—42no—
221C4—62no—
222C4—62no—
223C4—62no—
224C4—121no—
225C4—121no—
226C4—121no—
227C4#91212yes—
228C4D3×#4111yescharacteristic
229C4#101011yescharacteristic
230C3#336511yescharacteristic, complemented, Sylow
231C2—82no—
232C2#567711yescharacteristic
233C2C2×#91211yescharacteristic
234C2#576211yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#486C2
socleC22×C3C22×D4
prime radicalC3×#127C22
hypercenter#486D3
hypocenterC3#3365
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. #5721C2semidirect
4. #5094C2semidirect
6. #4768C2semidirect
7. #4767C2semidirect
8. #4766C2semidirect
9. #4758C2semidirect
10. C4×Dic12C2semidirect
11. C8×Dic6C2semidirect
230. C3#3365semidirect

Maximal subgroups

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

subgroupindex
#57212
#57132
C3×#4862
#50942
#50752
#47682
#47672
#47662
#47582
C4×Dic122
C8×Dic62
#33653