Finite Group Databasebeta

← C3×#89493 #13055155

Subgroups — C3×#89493 #13055155

Order 1344.

208 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 86 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⋊Dic7C211yesmaximal, characteristic
2C3×#6487C211yesmaximal, characteristic
3C3×C7×C22⋊C8C211yesmaximal, characteristic
4C3×#6391C212yesmaximal, complemented
5C3×#6390C212yesmaximal, complemented
6#89493C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C4×C7C2211yescharacteristic
8C22×C3×Dic7—21no—
9C2×C3×Dic14C2211yescharacteristic
10C2×C3×C7×C8C2212yes—
11C3×C22⋊Dic7—21no—
12C3×C4⋊Dic7—21no—
13C3×C4⋊Dic7C2211yescharacteristic
14C3×C4⋊Dic7C2212yes—
15C3×Dic7⋊C4—21no—
16C2×C4⋊Dic7C2×C311yescharacteristic
17#6487C2×C311yescharacteristic
18C7×C22⋊C8C2×C311yescharacteristic
19#6391C2×C312yescomplemented
20#6390C2×C312yescomplemented
21C3×#483—71nomaximal, Hall
22C23×C3×C7D411yescharacteristic
23C2×C3×C4×C7—22no—
24C2×C3×C4×C7D411yescharacteristic
25C2×C3×C4×C7C2311yescharacteristic
26C2×C3×Dic7—21no—
27C2×C3×Dic7—21no—
28C2×C3×Dic7—22no—
29C2×C3×Dic7—42no—
30C3×Dic14—22no—
31C3×C7×C8—22no—
32C22×C4×C7C22×C311yescharacteristic
33C22×Dic7—21no—
34C2×Dic14C22×C311yescharacteristic
35C2×C7×C8C22×C312yes—
36C22⋊Dic7—21no—
37C4⋊Dic7—21no—
38C4⋊Dic7C22×C311yescharacteristic
39C4⋊Dic7C22×C312yes—
40Dic7⋊C4—21no—
41C3×C22⋊Q8—71no—
42C2×C3×C4⋊C4—71no—
43C3×#106—72no—
44C3×#103—72no—
45C3×C22⋊C8D711yescharacteristic
46C22×C3×C7—21no—
47C22×C3×C7—21no—
48C22×C3×C7SD1612yes—
49C22×C3×C7C2×D411yescharacteristic
50C3×C4×C7—21no—
51C3×C4×C7#4112yes—
52C3×Dic7—41no—
53C3×Dic7—42no—
54C3×Dic7—41no—
55#483—71noSylow
56C23×C7C3×D411yescharacteristic
57C2×C4×C7—22no—
58C2×C4×C7C3×D411yescharacteristic
59C2×C4×C7C23×C311yescharacteristic
60C2×Dic7—21no—
61C2×Dic7—21no—
62C2×Dic7—22no—
63C2×Dic7—42no—
64Dic14—22no—
65C7×C8—22no—
66C2×C3×Q8—71no—
67C22×C3×C4—141no—
68C22×C3×C4C2×D711yescharacteristic
69C2×C3×C8C2×D712yes—
70C3×C4⋊C4—72no—
71C3×C4⋊C4—71no—
72C3×C4⋊C4—141no—
73C3×C4⋊C4—141no—
74C3×C22⋊C4—141no—
75C2×C3×C7—22no—
76C2×C3×C7#12311yescharacteristic
77C2×C3×C7C2×SD1611yescharacteristic
78C2×C3×C7#13711yescharacteristic
79C22⋊Q8—71no—
80C2×C4⋊C4—71no—
81#106—72no—
82#103—72no—
83C22⋊C8C3×D711yescharacteristic
84C22×C7—21no—
85C22×C7—21no—
86C22×C7C3×SD1612yes—
87C22×C7C2×C3×D411yescharacteristic
88C4×C7—21no—
89C4×C7C3×#4112yes—
90Dic7—41no—
91Dic7—42no—
92Dic7—41no—
93C23×C3D2811yescharacteristic
94C3×Q8—142no—
95C2×C3×C4—22no—
96C2×C3×C4—141no—
97C2×C3×C4—141no—
98C2×C3×C4—142no—
99C2×C3×C4—282no—
100C2×C3×C4D2811yescharacteristic
101C2×C3×C4C22×D711yescharacteristic
102C3×C8—22no—
103C3×C7#48311yescharacteristic, complemented, Hall
104C2×Q8—71no—
105C22×C4—141no—
106C22×C4C2×C3×D711yescharacteristic
107C2×C8C2×C3×D712yes—
108C4⋊C4—72no—
109C4⋊C4—71no—
110C4⋊C4—141no—
111C4⋊C4—141no—
112C22⋊C4—141no—
113C2×C7—22no—
114C2×C7C3×#12311yescharacteristic
115C2×C7C2×C3×SD1611yescharacteristic
116C2×C7C3×#13711yescharacteristic
117C22×C3—21no—
118C22×C3—21no—
119C22×C3#113212yes—
120C22×C3C2×D2811yescharacteristic
121C3×C4—21no—
122C3×C4—281no—
123C3×C4—282no—
124C3×C4—281no—
125C3×C4#115912yes—
126C23C3×D2811yescharacteristic
127Q8—142no—
128C2×C4—22no—
129C2×C4—141no—
130C2×C4—141no—
131C2×C4—142no—
132C2×C4—282no—
133C2×C4C3×D2811yescharacteristic
134C2×C4C22×C3×D711yescharacteristic
135C8—22no—
136C7C3×#48311yescharacteristic, complemented, Sylow
137C2×C3—22no—
138C2×C3#644911yescharacteristic
139C2×C3C2×#113211yescharacteristic
140C2×C3#647211yescharacteristic
141C22—21no—
142C22—21no—
143C22C3×#113212yes—
144C22C2×C3×D2811yescharacteristic
145C4—21no—
146C4—281no—
147C4—282no—
148C4—281no—
149C4C3×#115912yes—
150C3#8949311yescharacteristic, direct product factor, Sylow
151C2—22no—
152C2C3×#644911yescharacteristic
153C2C2×C3×#113211yescharacteristic
154C2C3×#647211yescharacteristic
subgroupG/H
centerC22×C3C2×D28
commutator, cosocleC2×C4×C7C23×C3
FrattiniC2×C4C22×C3×D7
FittingC3×C7×C22⋊C8C2
socleC22×C3×C7C2×D4
prime radicalC23×C3×C7D4
hypercenterC3×C22⋊C8D7
hypocenterC7C3×#483
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. C3×#6391C2semidirect
5. C3×#6390C2semidirect
6. #89493C3direct (N × H)
19. #6391C2×C3semidirect
20. #6390C2×C3semidirect
103. C3×C7#483semidirect
136. C7C3×#483semidirect
150. C3#89493direct (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⋊Dic72
C3×#64872
C3×C7×C22⋊C82
C3×#63912
C3×#63902
#894933
C3×#4837