Finite Group Databasebeta

← C3×#2058 #72773

Subgroups — C3×#2058 #72773

Order 384.

282 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 116 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
1C2×C3×C4⋊Q8C211yesmaximal, characteristic
2C2×C3×#106C212yesmaximal
3C3×#389C211yesmaximal, characteristic
4C3×#340C212yesmaximal
5C3×#336C211yesmaximal, characteristic
6#2058C311yesmaximal, characteristic, direct product factor, Sylow
7C22×C3×Q8—21no—
8C22×C3×C8C2212yes—
9C3×C4⋊Q8—24no—
10C2×C3×C4⋊C4—21no—
11C2×C3×C4⋊C4—21no—
12C2×C3×C4⋊C4C2211yescharacteristic
13C2×C3×C4⋊C4C2212yes—
14C2×C3×C4⋊C4C2211yescharacteristic
15C2×C3×C42C2211yescharacteristic
16C3×#106—24no—
17C3×#95—21no—
18C2×C4⋊Q8C2×C311yescharacteristic
19C2×#106C2×C312yes—
20#389C2×C311yescharacteristic
21#340C2×C312yes—
22#336C2×C311yescharacteristic
23C2×C3×Q8—24no—
24C2×C3×Q8—42no—
25C2×C3×Q8—42no—
26C22×C3×C4—21no—
27C22×C3×C4—22no—
28C22×C3×C4—21no—
29C22×C3×C4D411yescharacteristic
30C22×C3×C4D411yescharacteristic
31C22×C3×C4C2311yescharacteristic
32C2×C3×C8—22no—
33C2×C3×C8—22no—
34C2×C3×C8Q814yescomplemented
35C3×C4⋊C4—24no—
36C3×C4⋊C4—22no—
37C3×C4⋊C4—21no—
38C3×C4⋊C4—22no—
39C3×C4⋊C4—42no—
40C3×C4⋊C4D414yes—
41C3×C4⋊C4Q812yescomplemented
42C3×C42—22no—
43C22×Q8—21no—
44C22×C8C22×C312yes—
45C4⋊Q8—24no—
46C2×C4⋊C4—21no—
47C2×C4⋊C4—21no—
48C2×C4⋊C4C22×C311yescharacteristic
49C2×C4⋊C4C22×C312yes—
50C2×C4⋊C4C22×C311yescharacteristic
51C2×C42C22×C311yescharacteristic
52#106—24no—
53#95—21no—
54C23×C3C2×D411yescharacteristic
55C3×Q8—48no—
56C2×C3×C4—21no—
57C2×C3×C4—21no—
58C2×C3×C4—21no—
59C2×C3×C4—21no—
60C2×C3×C4—24no—
61C2×C3×C4—22no—
62C2×C3×C4—41no—
63C2×C3×C4—42no—
64C2×C3×C4—41no—
65C2×C3×C4—42no—
66C2×C3×C4—41no—
67C2×C3×C4—41no—
68C2×C3×C4—41no—
69C2×C3×C4SD1612yes—
70C2×C3×C4SD1612yes—
71C2×C3×C4C2×D412yes—
72C2×C3×C4C2×Q812yes—
73C2×C3×C4C2×Q811yescharacteristic
74C2×C3×C4#4111yescharacteristic
75C3×C8—24no—
76C2×Q8—24no—
77C2×Q8—42no—
78C2×Q8—42no—
79C22×C4—21no—
80C22×C4—22no—
81C22×C4—21no—
82C22×C4C3×D411yescharacteristic
83C22×C4C3×D411yescharacteristic
84C22×C4C23×C311yescharacteristic
85C2×C8—22no—
86C2×C8—22no—
87C2×C8C3×Q814yescomplemented
88C4⋊C4—24no—
89C4⋊C4—22no—
90C4⋊C4—21no—
91C4⋊C4—22no—
92C4⋊C4—42no—
93C4⋊C4C3×D414yes—
94C4⋊C4C3×Q812yescomplemented
95C42—22no—
96C22×C3#12011yescharacteristic
97C22×C3C22⋊Q811yescharacteristic
98C22×C3C4⋊Q811yescharacteristic
99C22×C3C2×SD1611yescharacteristic
100C22×C3C2×SD1611yescharacteristic
101C22×C3AGL(1,ℤ/8)11yescharacteristic
102C22×C3#13711yescharacteristic
103C3×C4—22no—
104C3×C4—22no—
105C3×C4—44no—
106C3×C4—42no—
107C3×C4—81no—
108C3×C4C22⋊Q812yes—
109C3×C4C4⋊Q812yes—
110C23C2×C3×D411yescharacteristic
111Q8—48no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—24no—
117C2×C4—22no—
118C2×C4—41no—
119C2×C4—42no—
120C2×C4—42no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4C3×SD1612yes—
126C2×C4C3×SD1612yes—
127C2×C4C2×C3×D412yes—
128C2×C4C2×C3×Q812yes—
129C2×C4C2×C3×Q811yescharacteristic
130C2×C4C3×#4111yescharacteristic
131C8—24no—
132C2×C3#39511yescharacteristic
133C2×C3#44811yescharacteristic
134C2×C3#45011yescharacteristic
135C2×C3#47511yescharacteristic
136C2×C3#47611yescharacteristic
137C2×C3#49811yescharacteristic
138C2×C3#50111yescharacteristic
139C22C3×#12011yescharacteristic
140C22C3×C22⋊Q811yescharacteristic
141C22C3×C4⋊Q811yescharacteristic
142C22C2×C3×SD1611yescharacteristic
143C22C2×C3×SD1611yescharacteristic
144C22C3×AGL(1,ℤ/8)11yescharacteristic
145C22C3×#13711yescharacteristic
146C4—22no—
147C4—22no—
148C4—44no—
149C4—42no—
150C4—81no—
151C4C3×C22⋊Q812yes—
152C4C3×C4⋊Q812yes—
153C3#205811yescharacteristic, direct product factor, Sylow
154C2C3×#39511yescharacteristic
155C2C3×#44811yescharacteristic
156C2C3×#45011yescharacteristic
157C2C3×#47511yescharacteristic
158C2C3×#47611yescharacteristic
159C2C3×#49811yescharacteristic
160C2C3×#50111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C3C2×D4
commutator, Frattini, cosocleC22×C4C23×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
6. #2058C3direct (N × H)
34. C2×C3×C8Q8semidirect
41. C3×C4⋊C4Q8semidirect
87. C2×C8C3×Q8semidirect
94. C4⋊C4C3×Q8semidirect
153. C3#2058direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4⋊Q82
C2×C3×#1062
C3×#3892
C3×#3402
C3×#3362
#20583