Finite Group Databasebeta

← C3×D7×2−1+4 #13062344

Subgroups — C3×D7×2−1+4 #13062344

Order 1344.

1588 conjugacy classes of subgroups; only the 890 normal subgroups are shown.

normal subgroups only

This group has 1588 conjugacy classes of subgroups — too many to draw. Only its 890 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×C7×2−1+4C211yesmaximal, characteristic, complemented
2C3×#6554C2110yesmaximal, complemented
3C3×D7×#41C2110yesmaximal, complemented
4C3×#6551C215yesmaximal, complemented
5C2×C3×Q8×D7C215yesmaximal, complemented
6D7×2−1+4C311yesmaximal, characteristic, direct product factor, Hall
7C3×C7×#41C22110yescomplemented
8C2×C3×C7×Q8C2215yescomplemented
9C3×#1161C22110yescomplemented
10C3×Q8×D7C22110yes—
11C3×Q8×D7C22120yescomplemented
12C3×#1159C22130yescomplemented
13C3×D4×D7C22110yes—
14C3×#1157C22130yescomplemented
15C2×C3×C4×D7C22115yes—
16C2×C3×Dic14C22115yescomplemented
17C7×2−1+4C2×C311yescharacteristic, complemented
18#6554C2×C3110yescomplemented
19D7×#41C2×C3110yescomplemented
20#6551C2×C315yescomplemented
21C2×Q8×D7C2×C315yescomplemented
22C2×C3×2−1+4—71nomaximal, Hall
23C22×C3×D7C2315yes—
24C3×C7×Q8C23110yes—
25C3×C7×D4C23110yes—
26C2×C3×C4×C7C23115yes—
27C3×C22⋊D7C23120yes—
28C2×C3×Dic7C23115yes—
29C3×D28C23110yes—
30C3×C4×D7C23110yes—
31C3×C4×D7C23130yes—
32C3×Dic14C23130yes—
33C7×#41C22×C3110yescomplemented
34C2×C7×Q8C22×C315yescomplemented
35#1161C22×C3110yescomplemented
36Q8×D7C22×C3110yes—
37Q8×D7C22×C3120yescomplemented
38#1159C22×C3130yescomplemented
39D4×D7C22×C3110yes—
40#1157C22×C3130yescomplemented
41C2×C4×D7C22×C3115yes—
42C2×Dic14C22×C3115yescomplemented
43C3×2−1+4—710no—
44C3×2−1+4—75no—
45C3×2−1+4D711yescharacteristic, direct product factor
46C2×C3×#41—710no—
47C22×C3×Q8—75no—
48C22×C3×C7C2415yes—
49C2×C3×D7—210no—
50C2×C3×D7C2415yes—
51C2×C3×D7C2411yescharacteristic
52C3×C4×C7C24110yes—
53C3×Dic7C24110yes—
54C2×2−1+4—71noSylow
55C22×D7C23×C315yes—
56C7×Q8C23×C3110yes—
57C7×D4C23×C3110yes—
58C2×C4×C7C23×C3115yes—
59C22⋊D7C23×C3120yes—
60C2×Dic7C23×C3115yes—
61D28C23×C3110yes—
62C4×D7C23×C3110yes—
63C4×D7C23×C3130yes—
64Dic14C23×C3130yes—
65C3×#41—710no—
66C3×#41—730no—
67C3×#41—730no—
68C3×#41C2×D7110yescomplemented
69C2×C3×Q8—710no—
70C2×C3×Q8—720no—
71C2×C3×Q8—715no—
72C2×C3×Q8C2×D715yescomplemented
73C2×C3×D4—710no—
74C22×C3×C4—715no—
75C2×C3×C7—25no—
76C2×C3×C7C2511yescharacteristic
77C3×D7—25no—
78C3×D72−1+412yesdirect product factor
792−1+4—710no—
802−1+4—75no—
812−1+4C3×D711yescharacteristic, direct product factor
82C2×#41—710no—
83C22×Q8—75no—
84C22×C7C24×C315yes—
85C2×D7—210no—
86C2×D7C24×C315yes—
87C2×D7C24×C311yescharacteristic
88C4×C7C24×C3110yes—
89Dic7C24×C3110yes—
90C23×C3—75no—
91C3×Q8—730no—
92C3×Q8C22×D7110yes—
93C3×D4—720no—
94C3×D4—710no—
95C3×D4C22×D7110yes—
96C2×C3×C4—715no—
97C2×C3×C4—710no—
98C2×C3×C4—730no—
99C2×C3×C4C22×D7115yes—
100C3×C7C2×2−1+411yescharacteristic, complemented, Hall
101#41—710no—
102#41—730no—
103#41—730no—
104#41C2×C3×D7110yescomplemented
105C2×Q8—710no—
106C2×Q8—720no—
107C2×Q8—715no—
108C2×Q8C2×C3×D715yescomplemented
109C2×D4—710no—
110C22×C4—715no—
111C2×C7—25no—
112C2×C7C25×C311yescharacteristic
113D7—25no—
114D7C3×2−1+412yesdirect product factor
115C22×C3—71no—
116C22×C3—75no—
117C22×C3—1410no—
118C22×C3C23×D715yes—
119C3×C4—710no—
120C3×C4C23×D7110yes—
121C23—75no—
122Q8—730no—
123Q8C22×C3×D7110yes—
124D4—720no—
125D4—710no—
126D4C22×C3×D7110yes—
127C2×C4—715no—
128C2×C4—710no—
129C2×C4—730no—
130C2×C4C22×C3×D7115yes—
131C7C2×C3×2−1+411yescharacteristic, complemented, Sylow
132C2×C3—25no—
133C2×C3—72no—
134C2×C3—145no—
135C2×C3C24×D711yescharacteristic
136C22—71no—
137C22—75no—
138C22—1410no—
139C22C23×C3×D715yes—
140C4—710no—
141C4C23×C3×D7110yes—
142C3D7×2−1+411yescharacteristic, direct product factor, Sylow
143C2—25no—
144C2—72no—
145C2—145no—
146C2C24×C3×D711yescharacteristic
subgroupG/H
centerC2×C3C24×D7
commutator, cosocleC2×C7C25×C3
FrattiniC2C24×C3×D7
FittingC3×C7×2−1+4C2
socleC2×C3×C7C25
hypercenterC3×2−1+4D7
hypocenterC7C2×C3×2−1+4
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C3 ◁ C3×2−1+4

Complements

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

NH ≅ G/Ntype
1. C3×C7×2−1+4C2semidirect
2. C3×#6554C2semidirect
3. C3×D7×#41C2semidirect
4. C3×#6551C2semidirect
5. C2×C3×Q8×D7C2semidirect
6. D7×2−1+4C3direct (N × H)
7. C3×C7×#41C22semidirect
8. C2×C3×C7×Q8C22semidirect
9. C3×#1161C22semidirect
11. C3×Q8×D7C22semidirect
12. C3×#1159C22semidirect
14. C3×#1157C22semidirect
16. C2×C3×Dic14C22semidirect
17. C7×2−1+4C2×C3semidirect
18. #6554C2×C3semidirect
19. D7×#41C2×C3semidirect
20. #6551C2×C3semidirect
21. C2×Q8×D7C2×C3semidirect
33. C7×#41C22×C3semidirect
34. C2×C7×Q8C22×C3semidirect
35. #1161C22×C3semidirect
37. Q8×D7C22×C3semidirect
38. #1159C22×C3semidirect
40. #1157C22×C3semidirect
42. C2×Dic14C22×C3semidirect
45. C3×2−1+4D7direct (N × H)
68. C3×#41C2×D7semidirect
72. C2×C3×Q8C2×D7semidirect
78. C3×D72−1+4direct (N × H)
81. 2−1+4C3×D7direct (N × H)
100. C3×C7C2×2−1+4semidirect
104. #41C2×C3×D7semidirect
108. C2×Q8C2×C3×D7semidirect
114. D7C3×2−1+4direct (N × H)
131. C7C2×C3×2−1+4semidirect
142. C3D7×2−1+4direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C7×2−1+42
C3×#65542
C3×D7×#412
C3×#65512
C2×C3×Q8×D72
D7×2−1+43
C2×C3×2−1+47