Finite Group Databasebeta

← C3×#90620 #13062345

Subgroups — C3×#90620 #13062345

Order 1344.

1620 conjugacy classes of subgroups; only the 886 normal subgroups are shown.

normal subgroups only

This group has 1620 conjugacy classes of subgroups — too many to draw. Only its 886 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×#6553C2110yesmaximal, complemented
3C3×D7×#41C2110yesmaximal, complemented
4C3×#6551C215yesmaximal, complemented
5C2×C3×#1161C215yesmaximal, complemented
6#90620C311yesmaximal, characteristic, direct product factor, Hall
7C3×C7×#41C22110yescomplemented
8C2×C3×C7×Q8C2215yescomplemented
9C3×#1161C22110yescomplemented
10C3×#1161C22120yescomplemented
11C3×Q8×D7C22110yescomplemented
12C3×#1159C22110yescomplemented
13C3×D4×D7C22130yescomplemented
14C3×#1157C22130yescomplemented
15C2×C3×D28C22115yescomplemented
16C2×C3×C4×D7C22115yescomplemented
17C7×2−1+4C2×C311yescharacteristic, complemented
18#6553C2×C3110yescomplemented
19D7×#41C2×C3110yescomplemented
20#6551C2×C315yescomplemented
21C2×#1161C2×C315yescomplemented
22C3×#585—71nomaximal, Hall
23C22×C3×D7C23115yes—
24C3×C7×Q8C23110yes—
25C3×C7×D4C23110yes—
26C2×C3×C4×C7C23115yes—
27C3×C22⋊D7C23120yes—
28C2×C3×Dic7C2315yes—
29C3×D28C23130yes—
30C3×C4×D7C23110yes—
31C3×C4×D7C23130yes—
32C3×Dic14C23110yes—
33C7×#41C22×C3110yescomplemented
34C2×C7×Q8C22×C315yescomplemented
35#1161C22×C3110yescomplemented
36#1161C22×C3120yescomplemented
37Q8×D7C22×C3110yescomplemented
38#1159C22×C3110yescomplemented
39D4×D7C22×C3130yescomplemented
40#1157C22×C3130yescomplemented
41C2×D28C22×C3115yescomplemented
42C2×C4×D7C22×C3115yescomplemented
43C3×2−1+4—75no—
44C3×2−1+4D711yescharacteristic, complemented
45C3×H(5,𝔽2)—710no—
46C2×C3×#41—710no—
47C2×C3×#41—75no—
48C22×C3×C7C2415yes—
49C2×C3×D7—415no—
50C2×C3×D7C24110yes—
51C3×C4×C7C24110yes—
52C3×Dic7C2415yes—
53C3×Dic7C2411yescharacteristic
54#585—71noSylow
55C22×D7C23×C3115yes—
56C7×Q8C23×C3110yes—
57C7×D4C23×C3110yes—
58C2×C4×C7C23×C3115yes—
59C22⋊D7C23×C3120yes—
60C2×Dic7C23×C315yes—
61D28C23×C3130yes—
62C4×D7C23×C3110yes—
63C4×D7C23×C3130yes—
64Dic14C23×C3110yes—
65C3×#41—710no—
66C3×#41—720no—
67C3×#41—710no—
68C3×#41—730no—
69C3×#41C2×D7110yescomplemented
70C2×C3×Q8—710no—
71C2×C3×Q8C2×D715yescomplemented
72C2×C3×D4—730no—
73C2×C3×D4—715no—
74C22×C3×C4—715no—
75C2×C3×C7—25no—
76C2×C3×C7C2511yescharacteristic
77C3×D7—210no—
782−1+4—75no—
792−1+4C3×D711yescharacteristic, complemented
80H(5,𝔽2)—710no—
81C2×#41—710no—
82C2×#41—75no—
83C22×C7C24×C315yes—
84C2×D7—415no—
85C2×D7C24×C3110yes—
86C4×C7C24×C3110yes—
87Dic7C24×C315yes—
88Dic7C24×C311yescharacteristic
89C23×C3—715no—
90C3×Q8—710no—
91C3×Q8C22×D7110yes—
92C3×D4—720no—
93C3×D4—730no—
94C3×D4C22×D7110yes—
95C2×C3×C4—75no—
96C2×C3×C4—710no—
97C2×C3×C4—730no—
98C2×C3×C4C22×D7115yes—
99C3×C7#58511yescharacteristic, complemented, Hall
100#41—710no—
101#41—720no—
102#41—710no—
103#41—730no—
104#41C2×C3×D7110yescomplemented
105C2×Q8—710no—
106C2×Q8C2×C3×D715yescomplemented
107C2×D4—730no—
108C2×D4—715no—
109C22×C4—715no—
110C2×C7—25no—
111C2×C7C25×C311yescharacteristic
112D7—210no—
113C22×C3—710no—
114C22×C3—2815no—
115C22×C3C23×D715yes—
116C3×C4—71no—
117C3×C4—75no—
118C3×C4C23×D7110yes—
119C23—715no—
120Q8—710no—
121Q8C22×C3×D7110yes—
122D4—720no—
123D4—730no—
124D4C22×C3×D7110yes—
125C2×C4—75no—
126C2×C4—710no—
127C2×C4—730no—
128C2×C4C22×C3×D7115yes—
129C7C3×#58511yescharacteristic, complemented, Sylow
130C2×C3—25no—
131C2×C3—1410no—
132C2×C3C24×D711yescharacteristic
133C22—710no—
134C22—2815no—
135C22C23×C3×D715yes—
136C4—71no—
137C4—75no—
138C4C23×C3×D7110yes—
139C3#9062011yescharacteristic, direct product factor, Sylow
140C2—25no—
141C2—1410no—
142C2C24×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
hypocenterC7C3×#585
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×#6553C2semidirect
3. C3×D7×#41C2semidirect
4. C3×#6551C2semidirect
5. C2×C3×#1161C2semidirect
6. #90620C3direct (N × H)
7. C3×C7×#41C22semidirect
8. C2×C3×C7×Q8C22semidirect
9. C3×#1161C22semidirect
10. C3×#1161C22semidirect
11. C3×Q8×D7C22semidirect
12. C3×#1159C22semidirect
13. C3×D4×D7C22semidirect
14. C3×#1157C22semidirect
15. C2×C3×D28C22semidirect
16. C2×C3×C4×D7C22semidirect
17. C7×2−1+4C2×C3semidirect
18. #6553C2×C3semidirect
19. D7×#41C2×C3semidirect
20. #6551C2×C3semidirect
21. C2×#1161C2×C3semidirect
33. C7×#41C22×C3semidirect
34. C2×C7×Q8C22×C3semidirect
35. #1161C22×C3semidirect
36. #1161C22×C3semidirect
37. Q8×D7C22×C3semidirect
38. #1159C22×C3semidirect
39. D4×D7C22×C3semidirect
40. #1157C22×C3semidirect
41. C2×D28C22×C3semidirect
42. C2×C4×D7C22×C3semidirect
44. C3×2−1+4D7semidirect
69. C3×#41C2×D7semidirect
71. C2×C3×Q8C2×D7semidirect
79. 2−1+4C3×D7semidirect
99. C3×C7#585semidirect
104. #41C2×C3×D7semidirect
106. C2×Q8C2×C3×D7semidirect
129. C7C3×#585semidirect
139. C3#90620direct (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×#65532
C3×D7×#412
C3×#65512
C2×C3×#11612
#906203
C3×#5857