Finite Group Databasebeta

← #81593

Subgroups — #81593

Order 384.

368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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#5728C211yesmaximal, characteristic
2#5728C211yesmaximal, characteristic
3C3×#487C211yesmaximal, characteristic, complemented
4#5092C211yesmaximal, characteristic, complemented
5#5078C211yesmaximal, characteristic, complemented
6#4813C214yesmaximal
7#4790C214yesmaximal, complemented
8C4×D3×C8C211yesmaximal, characteristic
9#4681C211yesmaximal, characteristic, complemented
10#3170—31nomaximal, Sylow
11C3×C4⋊Q8C2211yescharacteristic
12C3×C4⋊Q8C2211yescharacteristic
13#946—21no—
14#946C2212yes—
15Q8×Dic3—21no—
16Q8×Dic3C2212yes—
17C2×#216C2214yes—
18C2×D3×C8C2212yes—
19#897—21no—
20#897C2212yes—
21#892—21no—
22#892—21no—
23#890—21no—
24#890—21no—
25#887—21no—
26#887C2212yes—
27C42×D3C2211yescharacteristic
28#869C2211yescharacteristic
29#869C2211yescharacteristic
30C3×#103C2214yes—
31C3×C4×C8C2211yescharacteristic
32#816C2214yes—
33C8×Dic3C2212yes—
34#807C2214yes—
35C4×C3⋊C8C2211yescharacteristic
36#533—31no—
37#533—31no—
38#500—31no—
39#494—31no—
40#487—31no—
41#487D311yescharacteristic, complemented
42#467—34no—
43C4×Q16—34no—
44C2×C4×C8—31no—
45C2×C3×Q8—21no—
46C2×C3×Q8C2312yes—
47C2×C4×D3D411yescharacteristic
48C2×C4×D3D411yescharacteristic
49C2×C4×D3C2311yescharacteristic
50C2×Dic6—21no—
51C2×Dic6C2312yes—
52C2×C3×C8C2312yes—
53C3×C4⋊C4—21no—
54C3×C4⋊C4—21no—
55C3×C4⋊C4—21no—
56C3×C4⋊C4C2312yes—
57C3×C42C2311yescharacteristic
58#216—28no—
59(C2×D3)⋊C4—22no—
60(C2×D3)⋊C4—22no—
61C4⋊Dic3—21no—
62C4⋊Dic3—21no—
63C4⋊Dic3—21no—
64C4⋊Dic3—22no—
65C4⋊Dic3—22no—
66C4⋊Dic3C2312yes—
67Dic3⋊C4—22no—
68Dic3⋊C4—22no—
69C4×Dic3—22no—
70C4×Dic3—22no—
71C4×Dic3D411yescharacteristic
72C4×Dic3D411yescharacteristic
73C4×Dic3C2311yescharacteristic
74C2×C3⋊C8C2312yes—
75D3×C8—24no—
76C2×Q16—34no—
77C22×C8—32no—
78C4⋊Q8—31no—
79C4⋊Q8—31no—
80C4⋊Q8C2×D311yescharacteristic
81C4⋊Q8C2×D311yescharacteristic
82#125—61no—
83#125—61no—
84C22⋊Q8—32no—
85C22⋊Q8—32no—
86C22⋊Q8—61no—
87C22⋊Q8—61no—
88C4×Q8—32no—
89C4×Q8—32no—
90C4×Q8—61no—
91C4×Q8—61no—
92#117—61no—
93#117—61no—
94C2×C42—31no—
95#107—34no—
96#103—34no—
97#103C2×D314yes—
98C4×C8—32no—
99C4×C8—31no—
100C4×C8C2×D311yescharacteristic
101C22×D3C2×D411yescharacteristic
102C3×Q8—24no—
103C3×Q8—42no—
104C2×C3×C4—22no—
105C2×C3×C4—22no—
106C2×C3×C4C2×D411yescharacteristic
107C2×C3×C4C2×D411yescharacteristic
108C2×C3×C4C2411yescharacteristic
109C2×Dic3—22no—
110C2×Dic3—22no—
111C2×Dic3C2×D411yescharacteristic
112C2×Dic3C2×D411yescharacteristic
113C2×Dic3C2×D411yescharacteristic
114C4×D3—22no—
115C4×D3—22no—
116C4×D3Q1614yescomplemented
117Dic6—24no—
118Dic6—42no—
119C3×C8—22no—
120C3⋊C8#4114yes—
121C2×Q8—21no—
122C2×Q8—32no—
123C2×Q8—61no—
124C2×Q8C22×D312yes—
125C22×C4—31no—
126C22×C4—31no—
127C22×C4—31no—
128Q16—68no—
129C2×C8—32no—
130C2×C8—64no—
131C2×C8C22×D312yes—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—32no—
136C4⋊C4—62no—
137C4⋊C4—62no—
138C4⋊C4—62no—
139C4⋊C4—62no—
140C4⋊C4—61no—
141C4⋊C4—61no—
142C4⋊C4—61no—
143C4⋊C4C22×D312yes—
144C22⋊C4—62no—
145C22⋊C4—62no—
146C42—31no—
147C42—31no—
148C42—31no—
149C42—62no—
150C42—62no—
151C42C22×D311yescharacteristic
152C22×C3C22×D411yescharacteristic
153C2×D3—21no—
154C2×D3—21no—
155C2×D3C2×Q1612yes—
156C3×C4—42no—
157C3×C4—42no—
158C3×C4C2×Q1612yes—
159C3×C4#13512yes—
160C3×C4C2×#4112yes—
161Dic3—21no—
162Dic3—21no—
163Dic3—42no—
164Dic3—42no—
165Dic3C2×Q1612yes—
166C23—31no—
167Q8—24no—
168Q8—42no—
169Q8—64no—
170Q8—122no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—31no—
174C2×C4—34no—
175C2×C4—31no—
176C2×C4—31no—
177C2×C4—62no—
178C2×C4—62no—
179C2×C4—62no—
180C2×C4—62no—
181C2×C4D3×D411yescharacteristic
182C2×C4D3×D411yescharacteristic
183C2×C4C23×D311yescharacteristic
184C8—22no—
185C8—34no—
186C2×C3#53211yescharacteristic
187C2×C3C22×Q1611yescharacteristic
188C2×C3C2×#13511yescharacteristic
189D3—22no—
190C22—32no—
191C22—61no—
192C22—61no—
193C22C2×D3×D411yescharacteristic
194C4—32no—
195C4—42no—
196C4—42no—
197C4—61no—
198C4—61no—
199C4—122no—
200C4—122no—
201C4#91612yes—
202C4D3×Q1612yes—
203C4D3×#4112yes—
204C3#317011yescharacteristic, complemented, Sylow
205C2—62no—
206C2#566811yescharacteristic
207C2C2×#91611yescharacteristic
208C2C2×D3×Q1611yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#487C2
socleC22×C3C22×D4
prime radicalC22×D3C2×D4
hypercenter#487D3
hypocenterC3#3170
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. C3×#487C2semidirect
4. #5092C2semidirect
5. #5078C2semidirect
7. #4790C2semidirect
9. #4681C2semidirect
41. #487D3semidirect
116. C4×D3Q16semidirect
204. C3#3170semidirect

Maximal subgroups

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

subgroupindex
#57282
C3×#4872
#50922
#50782
#48132
#47902
C4×D3×C82
#46812
#31703