Finite Group Databasebeta

← #13051034

Subgroups — #13051034

Order 1344.

172 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 38 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×#6503C211yesmaximal, characteristic
2#10620673C211yesmaximal, characteristic, complemented
3C7×#834C211yesmaximal, characteristic, complemented
4#89269—31nomaximal, Hall
5C2×C3×C7×D4C2211yescharacteristic
6C2×C3×C22⋊D7—21no—
7C2×C3×C22⋊D7—21no—
8C2×C3×D28C411yescharacteristic, complemented
9#66636—21no—
10C7×#217—21no—
11C3×C4×Dic7C411yescharacteristic, complemented
12#6503D311yescharacteristic
13C7×#99—31no—
14#6408—31no—
15#4545—71nomaximal, Hall
16C23×C3×C7D411yescharacteristic
17C23×C3×C7D411yescharacteristic
18C22×C3×D7—21no—
19C3×C7×D4—41no—
20C2×C3×C4×C7C2×C411yescharacteristic
21C2×Dic21—41no—
22C2×C7×Dic3—41no—
23C3×C22⋊D7—42no—
24C3×C22⋊D7—42no—
25C2×C3×Dic7—21no—
26C3×D28—41no—
27C2×C7×D4C2×D311yescharacteristic
28C2×C22⋊D7—21no—
29C2×C22⋊D7—21no—
30C2×D28Dic311yescharacteristic, complemented
31C7×C22⋊C4—61no—
32C22⋊Dic7—61no—
33C4×Dic7Dic311yescharacteristic, complemented
34C3×#127—71no—
35#834—71no—
36#834D711yescharacteristic, complemented
37C22×C3×C7—21no—
38C22×C3×C7—21no—
39C22×C3×C7—41no—
40C22×C3×C7—41no—
41C22×C3×C7C22⋊C411yescharacteristic
42C2×C3×D7—41no—
43C2×C3×D7—41no—
44C2×C3×D7—41no—
45C3×C4×C7—21no—
46Dic21—81no—
47C3×Dic7—22no—
48C7×Dic3—81no—
49#353—211noSylow
50C23×C7#6711yescharacteristic
51C23×C7#6711yescharacteristic
52C22×D7—21no—
53C7×D4—41no—
54C2×C4×C7—121no—
55C2×C4×C7C2×Dic311yescharacteristic
56C22⋊D7—42no—
57C22⋊D7—42no—
58C2×Dic7—21no—
59C2×Dic7—121no—
60D28—41no—
61C2×C3×D4—71no—
62C2×C3×D4—141no—
63C2×C3×D4—141no—
64C2×C3×D4C2×D711yescharacteristic
65C3×C42—71no—
66#217—21no—
67#217—141no—
68C2×C3×C7—21no—
69C2×C3×C7—41no—
70C2×C3×C7—41no—
71C2×C3×C7#9911yescharacteristic
72C3×D7—81no—
73#127—71no—
74#99—31no—
75#99—211no—
76C22×C7—21no—
77C22×C7—21no—
78C22×C7—41no—
79C22×C7—41no—
80C22×C7#21711yescharacteristic
81C2×D7—41no—
82C2×D7—41no—
83C2×D7—41no—
84C4×C7—21no—
85C4×C7—241no—
86Dic7—22no—
87Dic7—241no—
88C23×C3—141no—
89C23×C3D2811yescharacteristic
90C23×C3C22⋊D711yescharacteristic
91C3×D4—41no—
92C3×D4—281no—
93C3×D4—282no—
94C3×D4—282no—
95C2×C3×C4—141no—
96C2×C3×C4C4×D711yescharacteristic
97C2×Dic3—41no—
98C2×Dic3—281no—
99C3×C7#35311yescharacteristic, complemented, Hall
100C2×D4—71no—
101C2×D4—141no—
102C2×D4—141no—
103C2×D4D3×D711yescharacteristic
104C22⋊C4—61no—
105C22⋊C4—421no—
106C42—71no—
107C2×C7—21no—
108C2×C7—41no—
109C2×C7—41no—
110C2×C7#83411yescharacteristic
111D7—81no—
112C22×C3—21no—
113C22×C3—21no—
114C22×C3—41no—
115C22×C3—41no—
116C22×C3—281no—
117C22×C3—281no—
118C22×C3—281no—
119C22×C3(C2×D7)⋊C411yescharacteristic
120C3×C4—21no—
121C3×C4—142no—
122Dic3—81no—
123Dic3—561no—
124C23—141no—
125C23#424511yescharacteristic
126C23#424611yescharacteristic
127D4—41no—
128D4—281no—
129D4—282no—
130D4—282no—
131C2×C4—121no—
132C2×C4—141no—
133C2×C4—841no—
134C2×C4Dic3×D711yescharacteristic
135C7#454511yescharacteristic, complemented, Sylow
136C2×C3—21no—
137C2×C3—41no—
138C2×C3—41no—
139C2×C3—561no—
140C2×C3#638011yescharacteristic
141C22—21no—
142C22—21no—
143C22—41no—
144C22—41no—
145C22—281no—
146C22—281no—
147C22—281no—
148C22(C2×D7)⋊Dic311yescharacteristic
149C4—21no—
150C4—142no—
151C4—241no—
152C4—1681no—
153C3#8926911yescharacteristic, complemented, Sylow
154C2—21no—
155C2—41no—
156C2—41no—
157C2—561no—
158C2#1062053011yescharacteristic
subgroupG/H
centerC2#10620530
commutatorC2×C3×C4×C7C2×C4
Frattini, hypercenterC2×D4D3×D7
Fitting, cosocleC2×C3×C7×D4C22
socleC2×C3×C7#99
prime radicalC3×#6503C2
hypocenterC3×C7#353
LCSG ▷ C2×C3×C4×C7 ▷ C22×C3×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #10620673C2semidirect
3. C7×#834C2semidirect
8. C2×C3×D28C4semidirect
11. C3×C4×Dic7C4semidirect
30. C2×D28Dic3semidirect
33. C4×Dic7Dic3semidirect
36. #834D7semidirect
99. C3×C7#353semidirect
135. C7#4545semidirect
153. C3#89269semidirect

Maximal subgroups

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

subgroupindex
C3×#65032
#106206732
C7×#8342
#892693
#45457