Finite Group Databasebeta

← C3×#2190 #72905

Subgroups — C3×#2190 #72905

Order 384.

226 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 64 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
1C3×#575C211yesmaximal, characteristic, complemented
2C3×#509C212yesmaximal, complemented
3C3×#469C211yesmaximal, characteristic, complemented
4C3×#360C212yesmaximal, complemented
5C3×#349C211yesmaximal, characteristic, complemented
6#2190C311yesmaximal, characteristic, direct product factor, Sylow
7C2×C3×#41—21no—
8C3×#137—22no—
9C3×AGL(1,ℤ/8)—22no—
10C3×#135—21no—
11C3×#135C2212yes—
12C2×C3×D8C2211yescharacteristic, complemented
13C2×C3×M16C2211yescharacteristic
14C3×#121—21no—
15C3×SD32—22no—
16C3×D16—22no—
17C3×M32C2212yescomplemented
18C3×#106C2211yescharacteristic, complemented
19C3×#102—21no—
20#575C2×C311yescharacteristic, complemented
21#509C2×C312yescomplemented
22#469C2×C311yescharacteristic, complemented
23#360C2×C312yescomplemented
24#349C2×C311yescharacteristic, complemented
25C3×#41—22no—
26C3×#41—22no—
27C3×#41—41no—
28C3×#41—41no—
29C2×C3×Q8—21no—
30C2×C3×D4—21no—
31C2×C3×D4—21no—
32C2×C3×D4—41no—
33C2×C3×D4—41no—
34C22×C3×C4—41no—
35C22×C3×C4D411yescharacteristic
36C3×Q16—21no—
37C3×Q16D412yescomplemented
38C3×SD16—22no—
39C3×SD16—22no—
40C3×D8—21no—
41C3×D8—22no—
42C3×D8D412yescomplemented
43C3×M16—22no—
44C2×C3×C8D411yescharacteristic
45C2×C3×C8C2311yescharacteristic
46C3×C4⋊C4—21no—
47C3×C22⋊C4—41no—
48C3×C16—22no—
49C2×#41—21no—
50#137—22no—
51AGL(1,ℤ/8)—22no—
52#135—21no—
53#135C22×C312yes—
54C2×D8C22×C311yescharacteristic, complemented
55C2×M16C22×C311yescharacteristic
56#121—21no—
57SD32—22no—
58D16—22no—
59M32C22×C312yescomplemented
60#106C22×C311yescharacteristic, complemented
61#102—21no—
62C23×C3—41no—
63C23×C3—41no—
64C23×C3D811yescharacteristic
65C3×Q8—22no—
66C3×Q8—41no—
67C3×D4—22no—
68C3×D4—41no—
69C3×D4—42no—
70C3×D4—42no—
71C3×D4—41no—
72C3×D4—41no—
73C3×D4—82no—
74C2×C3×C4—21no—
75C2×C3×C4—21no—
76C2×C3×C4—42no—
77C2×C3×C4—41no—
78C2×C3×C4—42no—
79C2×C3×C4—41no—
80C2×C3×C4D811yescharacteristic
81C2×C3×C4C2×D411yescharacteristic
82C3×C8—21no—
83C3×C8C2×D412yes—
84#41—22no—
85#41—22no—
86#41—41no—
87#41—41no—
88C2×Q8—21no—
89C2×D4—21no—
90C2×D4—21no—
91C2×D4—41no—
92C2×D4—41no—
93C22×C4—41no—
94C22×C4C3×D411yescharacteristic
95Q16—21no—
96Q16C3×D412yescomplemented
97SD16—22no—
98SD16—22no—
99D8—21no—
100D8—22no—
101D8C3×D412yescomplemented
102M16—22no—
103C2×C8C3×D411yescharacteristic
104C2×C8C23×C311yescharacteristic
105C4⋊C4—21no—
106C22⋊C4—41no—
107C16—22no—
108C22×C3—21no—
109C22×C3—41no—
110C22×C3—42no—
111C22×C3—81no—
112C22×C3—81no—
113C22×C3—82no—
114C22×C3—81no—
115C22×C3C2×D811yescharacteristic
116C3×C4—21no—
117C3×C4—42no—
118C3×C4—81no—
119C3×C4#12011yescharacteristic
120C3×C4AGL(1,ℤ/8)11yescharacteristic
121C23—41no—
122C23—41no—
123C23C3×D811yescharacteristic
124Q8—22no—
125Q8—41no—
126D4—22no—
127D4—41no—
128D4—42no—
129D4—42no—
130D4—41no—
131D4—41no—
132D4—82no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—42no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—41no—
139C2×C4C3×D811yescharacteristic
140C2×C4C2×C3×D411yescharacteristic
141C8—21no—
142C8C2×C3×D412yes—
143C2×C3—21no—
144C2×C3—41no—
145C2×C3—82no—
146C2×C3—161no—
147C2×C3#44711yescharacteristic
148C22—21no—
149C22—41no—
150C22—42no—
151C22—81no—
152C22—81no—
153C22—82no—
154C22—81no—
155C22C2×C3×D811yescharacteristic
156C4—21no—
157C4—42no—
158C4—81no—
159C4C3×#12011yescharacteristic
160C4C3×AGL(1,ℤ/8)11yescharacteristic
161C3#219011yescharacteristic, direct product factor, Sylow
162C2—21no—
163C2—41no—
164C2—82no—
165C2—161no—
166C2C3×#44711yescharacteristic
subgroupG/H
center, socleC2×C3#447
commutator, Frattini, cosocleC2×C8C23×C3
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×M16 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#575C2semidirect
2. C3×#509C2semidirect
3. C3×#469C2semidirect
4. C3×#360C2semidirect
5. C3×#349C2semidirect
6. #2190C3direct (N × H)
12. C2×C3×D8C22semidirect
17. C3×M32C22semidirect
18. C3×#106C22semidirect
20. #575C2×C3semidirect
21. #509C2×C3semidirect
22. #469C2×C3semidirect
23. #360C2×C3semidirect
24. #349C2×C3semidirect
37. C3×Q16D4semidirect
42. C3×D8D4semidirect
54. C2×D8C22×C3semidirect
59. M32C22×C3semidirect
60. #106C22×C3semidirect
96. Q16C3×D4semidirect
101. D8C3×D4semidirect
161. C3#2190direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#5752
C3×#5092
C3×#4692
C3×#3602
C3×#3492
#21903