Finite Group Databasebeta

← #79395

Subgroups — #79395

Order 384.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#5535C211yesmaximal, characteristic
2#5516C211yesmaximal, characteristic, complemented
3C3×#433C211yesmaximal, characteristic, complemented
4#4848C212yesmaximal, complemented
5#4829C212yesmaximal, complemented
6#4738C212yesmaximal, complemented
7#4737C212yesmaximal, complemented
8#4710C212yesmaximal, complemented
9C4×#204C212yesmaximal, complemented
10#3126—31nomaximal, Sylow
11C22×Dic6C2211yescharacteristic
12C3×#117C2211yescharacteristic
13#930C2212yes—
14#926C2211yescharacteristic
15C2×#204C2212yes—
16C2×#204C2212yes—
17#894—22no—
18#887—22no—
19#884—22no—
20#877—22no—
21#874C2211yescharacteristic
22C4×D12C2212yes—
23#870C2211yescharacteristic
24C4×Dic6C2212yes—
25C4×Dic6C2212yes—
26C3×C4⋊C8C2212yes—
27C3×C22⋊C8C2212yes—
28C3×#97C2211yescharacteristic
29C3×C4×C8C2211yescharacteristic
30#821C2212yes—
31#821C2212yes—
32#818C2212yes—
33#817C2212yes—
34#816C2212yes—
35#816C2212yes—
36#540—31no—
37#519—31no—
38#482—32no—
39#479—32no—
40#460—32no—
41#448—32no—
42#440—32no—
43C4×SD16—32no—
44#433D311yescharacteristic, complemented
45C22×C3×C4C2311yescharacteristic
46C2×#67—22no—
47C22×Dic3—21no—
48C2×D12—22no—
49C2×D12C2312yes—
50C2×C4×D3—22no—
51C2×Dic6—21no—
52C2×Dic6—24no—
53C2×Dic6C2312yes—
54C2×C3×C8C2312yes—
55C2×C3×C8C2312yes—
56C3×C4⋊C4D412yes—
57C3×C22⋊C4D412yes—
58C3×C42C2311yescharacteristic
59C3×C42C2311yescharacteristic
60#217—21no—
61(C2×D3)⋊C4—22no—
62(C2×D3)⋊C4—22no—
63C4⋊Dic3C2312yes—
64C4⋊Dic3C2312yes—
65Dic3⋊C4—22no—
66Dic3⋊C4—22no—
67Dic3⋊C4—22no—
68C4×Dic3—22no—
69C4×Dic3—22no—
70C4×Dic3—21no—
71#204—24no—
72#204—24no—
73C22×Q8—31no—
74C2×SD16—32no—
75C2×SD16—32no—
76#127—31no—
77#125—31no—
78#123—62no—
79#121—32no—
80#121—62no—
81C4×Q8—32no—
82C4×Q8—32no—
83C4×Q8—62no—
84C4×D4—32no—
85#117—31no—
86#117—62no—
87#117C2×D311yescharacteristic
88#107—32no—
89#106—32no—
90C4⋊C8C2×D312yes—
91#103—32no—
92#103—32no—
93#102—32no—
94#102—32no—
95C22⋊C8C2×D312yes—
96#97C2×D311yescharacteristic
97C4×C8C2×D311yescharacteristic
98C23×C3C2×D411yescharacteristic
99C22×D3—22no—
100C2×C3×C4—22no—
101C2×C3×C4C2×D412yes—
102C2×C3×C4C2×D412yes—
103C2×C3×C4C2×D411yescharacteristic
104C2×C3×C4C2411yescharacteristic
105#67—82no—
106C2×Dic3—24no—
107C2×Dic3—22no—
108C2×Dic3—22no—
109C2×Dic3—22no—
110D12—22no—
111D12—22no—
112D12—82no—
113C4×D3—82no—
114Dic6—24no—
115Dic6—22no—
116Dic6#4114yes—
117C3×C8—22no—
118C3×C8—22no—
119C2×Q8—32no—
120C2×Q8—64no—
121C2×Q8—61no—
122C2×D4—32no—
123C2×D4—62no—
124C2×D4—62no—
125C22×C4—61no—
126C22×C4—62no—
127C22×C4C22×D311yescharacteristic
128SD16—64no—
129SD16—64no—
130C2×C8C22×D312yes—
131C2×C8C22×D312yes—
132C4⋊C4—32no—
133C4⋊C4—32no—
134C4⋊C4—62no—
135C4⋊C4—62no—
136C4⋊C4—62no—
137C4⋊C4D1212yes—
138C22⋊C4—61no—
139C22⋊C4—62no—
140C22⋊C4—62no—
141C22⋊C4D1212yes—
142C42—61no—
143C42—62no—
144C42—62no—
145C42C22×D311yescharacteristic
146C42C22×D311yescharacteristic
147C22×C3—21no—
148C22×C3—22no—
149C22×C3C22×D411yescharacteristic
150C2×D3—42no—
151C2×D3—42no—
152C2×D3—42no—
153C3×C4—21no—
154C3×C4—22no—
155C3×C4—22no—
156C3×C4C2×#4112yes—
157Dic3—24no—
158Dic3—42no—
159Dic3—42no—
160C23—62no—
161C23C2×D1211yescharacteristic
162Q8—34no—
163Q8—64no—
164Q8—62no—
165D4—62no—
166D4—62no—
167D4—242no—
168D4—242no—
169C2×C4—22no—
170C2×C4—64no—
171C2×C4—62no—
172C2×C4—62no—
173C2×C4—62no—
174C2×C4—242no—
175C2×C4C2×D1212yes—
176C2×C4C2×D1212yes—
177C2×C4C2×D1211yescharacteristic
178C2×C4C23×D311yescharacteristic
179C8—22no—
180C8—22no—
181C2×C3—41no—
182C2×C3#52511yescharacteristic
183C2×C3#57712yes—
184D3—82no—
185C22—22no—
186C22—21no—
187C22—122no—
188C22—122no—
189C22—122no—
190C22C22×D1211yescharacteristic
191C4—22no—
192C4—22no—
193C4—21no—
194C4—64no—
195C4—122no—
196C4—122no—
197C4D3×#4112yes—
198C3#312611yescharacteristic, complemented, Sylow
199C2—41no—
200C2—242no—
201C2#552411yescharacteristic
202C2#575112yes—
subgroupG/H
centerC22C22×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#433C2
socleC22×C3C22×D4
prime radical#5535C2
hypercenter#433D3
hypocenterC3#3126
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #5516C2semidirect
3. C3×#433C2semidirect
4. #4848C2semidirect
5. #4829C2semidirect
6. #4738C2semidirect
7. #4737C2semidirect
8. #4710C2semidirect
9. C4×#204C2semidirect
44. #433D3semidirect
198. C3#3126semidirect

Maximal subgroups

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

subgroupindex
#55352
#55162
C3×#4332
#48482
#48292
#47382
#47372
#47102
C4×#2042
#31263