Finite Group Databasebeta

← C17×#1464 #14524470

Subgroups — C17×#1464 #14524470

Order 2176.

252 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 96 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×C17×#117C211yesmaximal, characteristic
2C17×#432C212yesmaximal, complemented
3C17×#324C212yesmaximal, complemented
4C17×#323C212yesmaximal
5C23×C4×C17C411yescharacteristic
6C17×#117—22no—
7C17×#117—22no—
8C2×C4⋊C4×C17C411yescharacteristic
9C2×C4⋊C4×C17C2211yescharacteristic
10C2×C22⋊C4×C17C411yescharacteristic
11C2×C22⋊C4×C17C2211yescharacteristic
12C2×C42×C17C411yescharacteristic
13C2×C42×C17C2211yescharacteristic
14C17×C4⋊C8—22no—
15C17×C22⋊C8C2214yes—
16C17×#97—22no—
17C24×C17C2×C411yescharacteristic
18C22×C4×C17—22no—
19C22×C4×C17—21no—
20C22×C4×C17—21no—
21C22×C4×C17—22no—
22C22×C4×C17C2×C411yescharacteristic
23C22×C4×C17C2×C411yescharacteristic
24C22×C4×C17C2×C411yescharacteristic
25C22×C4×C17C2×C411yescharacteristic
26C22×C4×C17C2×C411yescharacteristic
27C22×C4×C17C2311yescharacteristic
28C2×C8×C17—24no—
29C4⋊C4×C17—22no—
30C4⋊C4×C17—22no—
31C22⋊C4×C17—22no—
32C22⋊C4×C17—22no—
33C42×C17—21no—
34C42×C17—21no—
35C42×C17D412yes—
36C42×C17D412yes—
37C23×C17—21no—
38C23×C17—21no—
39C23×C17—41no—
40C23×C17—41no—
41C23×C17M1612yes—
42C23×C17C22×C411yescharacteristic
43C2×C4×C17—24no—
44C2×C4×C17—24no—
45C2×C4×C17—21no—
46C2×C4×C17—21no—
47C2×C4×C17—21no—
48C2×C4×C17—21no—
49C2×C4×C17—21no—
50C2×C4×C17—21no—
51C2×C4×C17—41no—
52C2×C4×C17—41no—
53C2×C4×C17—41no—
54C2×C4×C17—41no—
55C2×C4×C17C22⋊C411yescharacteristic
56C2×C4×C17C22⋊C411yescharacteristic
57C2×C4×C17C22⋊C412yes—
58C2×C4×C17M1612yes—
59C2×C4×C17C2×D412yes—
60C8×C17—44no—
61#1464C1711yesmaximal, characteristic, direct product factor, Sylow
62C22×C17—21no—
63C22×C17—21no—
64C22×C17—22no—
65C22×C17—42no—
66C22×C17—42no—
67C22×C17—41no—
68C22×C17—41no—
69C22×C17C2×C22⋊C411yescharacteristic
70C22×C17C2×M1611yescharacteristic
71C22×C17C2×M1611yescharacteristic
72C4×C17—21no—
73C4×C17—21no—
74C4×C17—22no—
75C4×C17—22no—
76C4×C17—22no—
77C4×C17—41no—
78C4×C17—41no—
79C2×#117C2×C1711yescharacteristic
80#432C2×C1712yescomplemented
81#324C2×C1712yescomplemented
82#323C2×C1712yes—
83C2×C17—21no—
84C2×C17—21no—
85C2×C17—42no—
86C2×C17#40711yescharacteristic
87C2×C17#41011yescharacteristic
88C2×C17#41311yescharacteristic
89C23×C4C4×C1711yescharacteristic
90#117—22no—
91#117—22no—
92C2×C4⋊C4C4×C1711yescharacteristic
93C2×C4⋊C4C22×C1711yescharacteristic
94C2×C22⋊C4C4×C1711yescharacteristic
95C2×C22⋊C4C22×C1711yescharacteristic
96C2×C42C4×C1711yescharacteristic
97C2×C42C22×C1711yescharacteristic
98C4⋊C8—22no—
99C22⋊C8C22×C1714yes—
100#97—22no—
101C17#146411yescharacteristic, direct product factor, Sylow
102C24C2×C4×C1711yescharacteristic
103C22×C4—22no—
104C22×C4—21no—
105C22×C4—21no—
106C22×C4—22no—
107C22×C4C2×C4×C1711yescharacteristic
108C22×C4C2×C4×C1711yescharacteristic
109C22×C4C2×C4×C1711yescharacteristic
110C22×C4C2×C4×C1711yescharacteristic
111C22×C4C2×C4×C1711yescharacteristic
112C22×C4C23×C1711yescharacteristic
113C2×C8—24no—
114C4⋊C4—22no—
115C4⋊C4—22no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C42—21no—
119C42—21no—
120C42D4×C1712yes—
121C42D4×C1712yes—
122C23—21no—
123C23—21no—
124C23—41no—
125C23—41no—
126C23M16×C1712yes—
127C23C22×C4×C1711yescharacteristic
128C2×C4—24no—
129C2×C4—24no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4C22⋊C4×C1711yescharacteristic
141C2×C4C22⋊C4×C1711yescharacteristic
142C2×C4C22⋊C4×C1712yes—
143C2×C4M16×C1712yes—
144C2×C4C2×D4×C1712yes—
145C8—44no—
146C22—21no—
147C22—21no—
148C22—22no—
149C22—42no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22C2×C22⋊C4×C1711yescharacteristic
154C22C2×M16×C1711yescharacteristic
155C22C2×M16×C1711yescharacteristic
156C4—21no—
157C4—21no—
158C4—22no—
159C4—22no—
160C4—22no—
161C4—41no—
162C4—41no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2C17×#40711yescharacteristic
167C2C17×#41011yescharacteristic
168C2C17×#41311yescharacteristic
subgroupG/H
center, socleC22×C17C2×C22⋊C4
commutatorC23C22×C4×C17
Frattini, cosocleC22×C4C23×C17
prime radicalC24×C17C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#432C2semidirect
3. C17×#324C2semidirect
61. #1464C17direct (N × H)
80. #432C2×C17semidirect
81. #324C2×C17semidirect
101. C17#1464direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#1172
C17×#4322
C17×#3242
C17×#3232
#146417