Finite Group Databasebeta

← #11764869

Subgroups — #11764869

Order 1120.

188 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 62 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×C4×C5×D7C211yesmaximal, characteristic, complemented
2C2×#63306C211yesmaximal, characteristic
3C2×#63304C211yesmaximal, characteristic, complemented
4#10587902C211yesmaximal, characteristic, complemented
5C7×#683C211yesmaximal, characteristic, complemented
6(C2×D7)⋊Dic5C211yesmaximal, characteristic, complemented
7Dic5×Dic7C211yesmaximal, characteristic, complemented
8C22×D35C2211yescharacteristic
9C22×C5×D7C2211yescharacteristic
10C2×C4×C5×C7C2211yescharacteristic
11C2×Dic35C2211yescharacteristic
12C2×C7×Dic5C2211yescharacteristic
13C2×C7×Dic5C2211yescharacteristic
14C2×C5×Dic7C2211yescharacteristic
15C4×C5×D7—22no—
16#63306C414yescomplemented
17#63304—22no—
18#6456—51nomaximal, Hall
19C4×C22⋊D5—71nomaximal, Hall
20C22×C5×C7C2311yescharacteristic
21C2×D35—21no—
22C2×D35—21no—
23C2×D35C2×C412yescomplemented
24C2×C5×D7—21no—
25C2×C5×D7—21no—
26C2×C5×D7C2×C412yescomplemented
27C4×C5×C7—21no—
28Dic35—21no—
29C5×Dic7D412yescomplemented
30C7×Dic5—21no—
31C7×Dic5C2×C412yescomplemented
32C2×D28—51no—
33C2×C4×D7—51no—
34C2×C4×D7D511yescharacteristic, complemented
35C7×C4⋊C4—51no—
36(C2×D7)⋊C4—51no—
37(C2×D7)⋊C4—51no—
38C4×Dic7—51no—
39C22×C4×C5—71no—
40C2×C22⋊D5—71no—
41C2×C4×D5—71no—
42C22⋊Dic5—71no—
43#685—71no—
44#683D711yescharacteristic, complemented
45C4×Dic5—71no—
46C2×C5×C7C22×C411yescharacteristic
47C2×C5×C7C2×D411yescharacteristic
48C2×C5×C7#4111yescharacteristic
49D35—22no—
50C5×D7—22no—
51C22×D7—51no—
52C22×D7C2×D511yescharacteristic
53C2×C4×C7—51no—
54C2×C4×C7—51no—
55C2×C4×C7C2×D511yescharacteristic
56C2×Dic7—51no—
57C2×Dic7C2×D511yescharacteristic
58D28—54no—
59C4×D7—22no—
60C4×D7—102no—
61C23×C5—71no—
62C22×D5—71no—
63C2×C4×C5—71no—
64C2×C4×C5—142no—
65C2×C4×C5C2×D711yescharacteristic
66C22⋊D5—74no—
67C2×Dic5—71no—
68C2×Dic5C2×D711yescharacteristic
69C2×Dic5C2×D711yescharacteristic
70C4×D5—142no—
71C5×C7C4×D411yescharacteristic, complemented, Hall
72C4×D4—351noSylow
73C22×C7C22×D511yescharacteristic
74C2×D7—21no—
75C2×D7—21no—
76C2×D7—52no—
77C2×D7—101no—
78C2×D7—101no—
79C2×D7C4×D512yescomplemented
80C4×C7—21no—
81C4×C7—52no—
82C4×C7—101no—
83Dic7—101no—
84Dic7C22⋊D512yescomplemented
85C22×C5—72no—
86C22×C5—141no—
87C22×C5—141no—
88C22×C5C22×D711yescharacteristic
89C2×D5—72no—
90C2×D5—141no—
91C2×D5—141no—
92C4×C5—21no—
93C4×C5—72no—
94Dic5—21no—
95Dic5—141no—
96Dic5C4×D712yescomplemented
97C2×D4—351no—
98C22×C4—71no—
99C22×C4—351no—
100C4⋊C4—51no—
101C22⋊C4—351no—
102C22⋊C4—351no—
103C42—351no—
104C2×C7C2×C4×D511yescharacteristic
105C2×C7#70911yescharacteristic
106C2×C7C2×C22⋊D511yescharacteristic
107D7—22no—
108D7—102no—
109C2×C5—142no—
110C2×C5C2×C4×D711yescharacteristic
111C2×C5D4×D711yescharacteristic
112C2×C5#116111yescharacteristic
113D5—142no—
114C23—71no—
115C23—351no—
116D4—354no—
117C2×C4—51no—
118C2×C4—51no—
119C2×C4—71no—
120C2×C4—142no—
121C2×C4—351no—
122C2×C4—702no—
123C2×C4D5×D711yescharacteristic
124C7C4×C22⋊D511yescharacteristic, complemented, Sylow
125C5#645611yescharacteristic, complemented, Sylow
126C22—72no—
127C22—141no—
128C22—141no—
129C22—352no—
130C22—701no—
131C22—701no—
132C22C2×D5×D711yescharacteristic
133C4—21no—
134C4—52no—
135C4—72no—
136C4—101no—
137C4—701no—
138C2—142no—
139C2—702no—
140C2#1058794611yescharacteristic
141C2C4×D5×D711yescharacteristic
142C2D7×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×D7
commutatorC2×C5×C7C22×C4
FittingC2×C4×C5×C7C22
socle, cosocleC22×C5×C7C23
prime radicalC2×#63306C2
hypercenterC2×C4D5×D7
hypocenterC5×C7C4×D4
LCSG ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C5×D7C2semidirect
3. C2×#63304C2semidirect
4. #10587902C2semidirect
5. C7×#683C2semidirect
6. (C2×D7)⋊Dic5C2semidirect
7. Dic5×Dic7C2semidirect
16. #63306C4semidirect
23. C2×D35C2×C4semidirect
26. C2×C5×D7C2×C4semidirect
29. C5×Dic7D4semidirect
31. C7×Dic5C2×C4semidirect
34. C2×C4×D7D5semidirect
44. #683D7semidirect
71. C5×C7C4×D4semidirect
79. C2×D7C4×D5semidirect
84. Dic7C22⋊D5semidirect
96. Dic5C4×D7semidirect
124. C7C4×C22⋊D5semidirect
125. C5#6456semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×D72
C2×#633062
C2×#633042
#105879022
C7×#6832
(C2×D7)⋊Dic52
Dic5×Dic72
#64565
C4×C22⋊D57