Finite Group Databasebeta

← #79956

Subgroups — #79956

Order 384.

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

normal subgroups only

This group has 380 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#5585C212yesmaximal, complemented
2C3×#446C211yesmaximal, characteristic, complemented
3#4845C212yesmaximal, complemented
4#4844C212yesmaximal, complemented
5#4843C212yesmaximal, complemented
6#4712C212yesmaximal, complemented
7#4710C212yesmaximal, complemented
8#4696C211yesmaximal, characteristic, complemented
9C4×D24C211yesmaximal, characteristic, complemented
10#3403—31nomaximal, Sylow
11C3×C4×Q8C2211yescharacteristic
12#947—22no—
13C2×Dic12C2211yescharacteristic
14C2×D24C2211yescharacteristic
15C2×D24C2211yescharacteristic
16C2×D24C2212yes—
17C2×#204C2212yes—
18C2×#204C2212yes—
19#894—22no—
20#894—22no—
21#893—22no—
22#875C2212yes—
23#875C2212yes—
24#874C2212yes—
25C4×D12C2212yes—
26C4×D12C2212yes—
27C4×Dic6C2212yes—
28C3×C4⋊C8C2212yes—
29C3×C4⋊C8C2211yescharacteristic
30C3×#97C2212yes—
31C3×C4×C8C2211yescharacteristic
32#821C2212yes—
33#821C2212yes—
34#818C2211yescharacteristic
35#816C2212yes—
36#559—32no—
37#496—32no—
38#495—31no—
39#464—32no—
40#463—32no—
41#459—32no—
42#446D311yescharacteristic, complemented
43#440—32no—
44C4×D8—31no—
45C2×C3×Q8D411yescharacteristic
46C2×D12—22no—
47C2×D12—22no—
48C2×D12C2312yes—
49C2×D12C2312yes—
50C2×C4×D3—22no—
51C2×C4×D3—22no—
52C2×Dic6C2312yes—
53C2×C3×C8C2312yes—
54C2×C3×C8C2311yescharacteristic
55C2×C3×C8C2311yescharacteristic
56C3×C4⋊C4D412yes—
57C3×C4⋊C4D411yescharacteristic
58C3×C42C2311yescharacteristic
59C3×C42C2312yes—
60(C2×D3)⋊C4—22no—
61(C2×D3)⋊C4—22no—
62(C2×D3)⋊C4—22no—
63(C2×D3)⋊C4—22no—
64(C2×D3)⋊C4—22no—
65(C2×D3)⋊C4—22no—
66C4⋊Dic3C2312yes—
67Dic3⋊C4—22no—
68C4×Dic3—22no—
69Dic12—41no—
70D24—22no—
71D24—42no—
72D24—41no—
73#204—24no—
74#204—42no—
75C2×Q16—31no—
76C2×SD16—32no—
77C2×SD16—32no—
78C2×D8—31no—
79C2×D8—31no—
80C2×D8—32no—
81#127—32no—
82#124—32no—
83#124—32no—
84#124—62no—
85#123—62no—
86#123—62no—
87C4×Q8—32no—
88C4×Q8C2×D311yescharacteristic
89C4×D4—32no—
90C4×D4—32no—
91C4×D4—62no—
92#107—31no—
93C4⋊C8C2×D312yes—
94C4⋊C8C2×D311yescharacteristic
95#103—32no—
96#102—32no—
97#102—32no—
98#97C2×D312yes—
99C4×C8C2×D311yescharacteristic
100C22×D3—22no—
101C22×D3—22no—
102C3×Q8—41no—
103C2×C3×C4C2×D412yes—
104C2×C3×C4C2×D412yes—
105C2×C3×C4C2×D411yescharacteristic
106C2×C3×C4C2×D411yescharacteristic
107C2×C3×C4C2411yescharacteristic
108C2×Dic3—22no—
109C2×Dic3—22no—
110D12—22no—
111D12—22no—
112D12—22no—
113D12—22no—
114D12—44no—
115D12—82no—
116C4×D3—82no—
117C4×D3—82no—
118Dic6—22no—
119Dic6—22no—
120C3×C8—22no—
121C3×C8—21no—
122C3×C8#4112yes—
123C2×Q8—32no—
124C2×Q8D1211yescharacteristic
125C2×D4—32no—
126C2×D4—32no—
127C2×D4—62no—
128C2×D4—62no—
129C22×C4—62no—
130C22×C4—62no—
131Q16—121no—
132SD16—64no—
133SD16—122no—
134D8—62no—
135D8—122no—
136D8—121no—
137C2×C8C22×D311yescharacteristic
138C2×C8C22×D312yes—
139C2×C8C22×D311yescharacteristic
140C4⋊C4—32no—
141C4⋊C4—62no—
142C4⋊C4D1212yes—
143C4⋊C4D1211yescharacteristic
144C22⋊C4—62no—
145C22⋊C4—62no—
146C22⋊C4—62no—
147C22⋊C4—62no—
148C22⋊C4—62no—
149C22⋊C4—62no—
150C42—62no—
151C42C22×D311yescharacteristic
152C42C22×D312yes—
153C22×C3C22×D411yescharacteristic
154C2×D3—42no—
155C2×D3—42no—
156C2×D3—42no—
157C2×D3—42no—
158C2×D3—42no—
159C2×D3—42no—
160C3×C4—22no—
161C3×C4—21no—
162C3×C4—21no—
163C3×C4—22no—
164C3×C4C2×#4111yescharacteristic
165C3×C4H(5,𝔽2)11yescharacteristic
166Dic3—42no—
167Dic3—42no—
168C23—62no—
169C23—62no—
170Q8—41no—
171Q8—62no—
172Q8—62no—
173D4—62no—
174D4—62no—
175D4—62no—
176D4—62no—
177D4—124no—
178D4—242no—
179C2×C4—62no—
180C2×C4—62no—
181C2×C4—242no—
182C2×C4—242no—
183C2×C4C2×D1212yes—
184C2×C4C2×D1211yescharacteristic
185C2×C4C2×D1211yescharacteristic
186C2×C4C2×D1212yes—
187C2×C4C23×D311yescharacteristic
188C8—22no—
189C8—21no—
190C8#23912yes—
191C2×C3#55011yescharacteristic
192C2×C3#57511yescharacteristic
193C2×C3#57611yescharacteristic
194D3—82no—
195D3—82no—
196C22—122no—
197C22—122no—
198C22—122no—
199C22—122no—
200C22—122no—
201C22—122no—
202C22C22×D1211yescharacteristic
203C4—22no—
204C4—21no—
205C4—21no—
206C4—22no—
207C4—122no—
208C4—122no—
209C4C2×#23911yescharacteristic
210C4#100911yescharacteristic
211C3#340311yescharacteristic, complemented, Sylow
212C2—242no—
213C2—242no—
214C2#557711yescharacteristic
215C2#574811yescharacteristic
216C2#575211yescharacteristic
subgroupG/H
centerC22C22×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#446C2
socleC22×C3C22×D4
hypercenter#446D3
hypocenterC3#3403
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #5585C2semidirect
2. C3×#446C2semidirect
3. #4845C2semidirect
4. #4844C2semidirect
5. #4843C2semidirect
6. #4712C2semidirect
7. #4710C2semidirect
8. #4696C2semidirect
9. C4×D24C2semidirect
42. #446D3semidirect
211. C3#3403semidirect

Maximal subgroups

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

subgroupindex
#55852
C3×#4462
#48452
#48442
#48432
#47122
#47102
#46962
C4×D242
#34033