Finite Group Databasebeta

← C17×#7525 #16865269

Subgroups — C17×#7525 #16865269

Order 4352.

138 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 30 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
1C17×#1662C211yesmaximal, characteristic
2C17×#1413C211yesmaximal, characteristic, complemented
3C17×#1356C211yesmaximal, characteristic, complemented
4C17×#562C411yescharacteristic
5C17×#491C2211yescharacteristic
6C17×#489—21no—
7C17×#356—21no—
8C17×#347—21no—
9C17×#330C411yescharacteristic
10C17×#329—21no—
11C17×C4⋊Q8D411yescharacteristic
12C17×#125C2×C411yescharacteristic
13C17×#124—21no—
14C17×#123—41no—
15C17×C22⋊Q8—41no—
16C17×#121—41no—
17C17×M32—41no—
18C17×#103—41no—
19C17×#103—41no—
20C17×#102—41no—
21C17×#101—41no—
22C17×#97—21no—
23C17×#97D411yescharacteristic
24C2×Q8×C17—21no—
25C2×Q8×C17—21no—
26C2×D4×C17—21no—
27C2×D4×C17—41no—
28C22×C4×C17—41no—
29M16×C17—81no—
30C2×C8×C17—21no—
31C2×C8×C17—41no—
32C4⋊C4×C17—21no—
33C4⋊C4×C17—41no—
34C4⋊C4×C17—41no—
35C4⋊C4×C17—41no—
36C22⋊C4×C17—41no—
37C22⋊C4×C17—41no—
38C22⋊C4×C17—41no—
39C42×C17C22⋊C411yescharacteristic
40C16×C17—42no—
41#7525C1711yesmaximal, characteristic, direct product factor, Sylow
42C23×C17—41no—
43Q8×C17—81no—
44Q8×C17—81no—
45D4×C17—81no—
46D4×C17—161no—
47C2×C4×C17—21no—
48C2×C4×C17—41no—
49C2×C4×C17—41no—
50C2×C4×C17—41no—
51C2×C4×C17—161no—
52C2×C4×C17#9911yescharacteristic
53C8×C17—41no—
54C8×C17—81no—
55C8×C17—161no—
56#1662C2×C1711yescharacteristic
57#1413C2×C1711yescharacteristic, complemented
58#1356C2×C1711yescharacteristic, complemented
59C22×C17—81no—
60C22×C17—81no—
61C22×C17—81no—
62C22×C17AΣL(1,𝔽16)11yescharacteristic
63C4×C17—21no—
64C4×C17—41no—
65C4×C17—81no—
66C4×C17—81no—
67C4×C17—81no—
68#562C4×C1711yescharacteristic
69#491C22×C1711yescharacteristic
70#489—21no—
71#356—21no—
72#347—21no—
73#330C4×C1711yescharacteristic
74#329—21no—
75C2×C17—21no—
76C2×C17—161no—
77C2×C17#140411yescharacteristic
78C4⋊Q8D4×C1711yescharacteristic
79#125C2×C4×C1711yescharacteristic
80#124—21no—
81#123—41no—
82C22⋊Q8—41no—
83#121—41no—
84M32—41no—
85#103—41no—
86#103—41no—
87#102—41no—
88#101—41no—
89#97—21no—
90#97D4×C1711yescharacteristic
91C17#752511yescharacteristic, direct product factor, Sylow
92C2×Q8—21no—
93C2×Q8—21no—
94C2×D4—21no—
95C2×D4—41no—
96C22×C4—41no—
97M16—81no—
98C2×C8—21no—
99C2×C8—41no—
100C4⋊C4—21no—
101C4⋊C4—41no—
102C4⋊C4—41no—
103C4⋊C4—41no—
104C22⋊C4—41no—
105C22⋊C4—41no—
106C22⋊C4—41no—
107C42C22⋊C4×C1711yescharacteristic
108C16—42no—
109C23—41no—
110Q8—81no—
111Q8—81no—
112D4—81no—
113D4—161no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—161no—
119C2×C4C17×#9911yescharacteristic
120C8—41no—
121C8—81no—
122C8—161no—
123C22—81no—
124C22—81no—
125C22—81no—
126C22C17×AΣL(1,𝔽16)11yescharacteristic
127C4—21no—
128C4—41no—
129C4—81no—
130C4—81no—
131C4—81no—
132C2—21no—
133C2—161no—
134C2C17×#140411yescharacteristic
subgroupG/H
center, socleC2×C17#1404
commutator#125C2×C4×C17
Frattini, cosocle#491C22×C17
prime radicalC17×#562C4
LCSG ▷ #125 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C17 ◁ C22×C17 ◁ C2×C4×C17 ◁ C42×C17 ◁ C17×#491 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#1413C2semidirect
3. C17×#1356C2semidirect
41. #7525C17direct (N × H)
57. #1413C2×C17semidirect
58. #1356C2×C17semidirect
91. C17#7525direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#16622
C17×#14132
C17×#13562
#752517