Finite Group Databasebeta

← C17×#1607 #14524613

Subgroups — C17×#1607 #14524613

Order 2176.

280 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 68 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×#534C211yesmaximal, characteristic
2C17×#480C212yesmaximal, complemented
3C17×#397C211yesmaximal, characteristic, complemented
4C17×#327C212yesmaximal, complemented
5C17×#323C211yesmaximal, characteristic, complemented
6C22×D4×C17—21no—
7C17×#123—22no—
8C17×#121—21no—
9C17×#121C2212yes—
10C17×#120—22no—
11C2×C4⋊C4×C17C2211yescharacteristic, complemented
12C2×C22⋊C4×C17—21no—
13C2×C22⋊C4×C17C2211yescharacteristic
14C17×#107—22no—
15C17×#102—22no—
16C17×C22⋊C8C2212yescomplemented
17C17×#95—21no—
18C17×#95C2211yescharacteristic, complemented
19C24×C17—21no—
20C24×C17D411yescharacteristic
21C2×D4×C17—22no—
22C2×D4×C17—22no—
23C2×D4×C17—21no—
24C2×D4×C17—42no—
25C2×D4×C17—42no—
26C2×D4×C17D412yes—
27C22×C4×C17—21no—
28C22×C4×C17—21no—
29C22×C4×C17—21no—
30C22×C4×C17D411yescharacteristic
31C22×C4×C17C2311yescharacteristic
32C2×C8×C17—22no—
33C4⋊C4×C17—21no—
34C4⋊C4×C17—22no—
35C4⋊C4×C17D412yes—
36C22⋊C4×C17—22no—
37C22⋊C4×C17—22no—
38C22⋊C4×C17—22no—
39C22⋊C4×C17—42no—
40C23×C17—21no—
41C23×C17—21no—
42C23×C17—22no—
43C23×C17—41no—
44C23×C17—41no—
45C23×C17—42no—
46C23×C17—81no—
47C23×C17—81no—
48C23×C17D812yes—
49C23×C17C2×D411yescharacteristic
50D4×C17—42no—
51D4×C17—44no—
52D4×C17—42no—
53D4×C17—42no—
54D4×C17—81no—
55C2×C4×C17—21no—
56C2×C4×C17—22no—
57C2×C4×C17—41no—
58C2×C4×C17—42no—
59C2×C4×C17—41no—
60C2×C4×C17—41no—
61C2×C4×C17—41no—
62C2×C4×C17—41no—
63C2×C4×C17—41no—
64C2×C4×C17—41no—
65C2×C4×C17—41no—
66C2×C4×C17C2×D412yes—
67C8×C17—42no—
68#1607C1711yesmaximal, characteristic, direct product factor, Sylow
69C22×C17—21no—
70C22×C17—21no—
71C22×C17—22no—
72C22×C17—42no—
73C22×C17—41no—
74C22×C17—41no—
75C22×C17—42no—
76C22×C17—42no—
77C22×C17—42no—
78C22×C17—81no—
79C22×C17—84no—
80C22×C17#12011yescharacteristic
81C22×C17C2×D811yescharacteristic
82C22×C17AGL(1,ℤ/8)11yescharacteristic
83C4×C17—22no—
84C4×C17—42no—
85C4×C17—41no—
86C4×C17—81no—
87C4×C17—81no—
88#534C2×C1711yescharacteristic
89#480C2×C1712yescomplemented
90#397C2×C1711yescharacteristic, complemented
91#327C2×C1712yescomplemented
92#323C2×C1711yescharacteristic, complemented
93C2×C17—21no—
94C2×C17—21no—
95C2×C17—42no—
96C2×C17—82no—
97C2×C17#44711yescharacteristic
98C2×C17#45511yescharacteristic
99C2×C17#45811yescharacteristic
100C22×D4—21no—
101#123—22no—
102#121—21no—
103#121C22×C1712yes—
104#120—22no—
105C2×C4⋊C4C22×C1711yescharacteristic, complemented
106C2×C22⋊C4—21no—
107C2×C22⋊C4C22×C1711yescharacteristic
108#107—22no—
109#102—22no—
110C22⋊C8C22×C1712yescomplemented
111#95—21no—
112#95C22×C1711yescharacteristic, complemented
113C17#160711yescharacteristic, direct product factor, Sylow
114C24—21no—
115C24D4×C1711yescharacteristic
116C2×D4—22no—
117C2×D4—22no—
118C2×D4—21no—
119C2×D4—42no—
120C2×D4—42no—
121C2×D4D4×C1712yes—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4D4×C1711yescharacteristic
126C22×C4C23×C1711yescharacteristic
127C2×C8—22no—
128C4⋊C4—21no—
129C4⋊C4—22no—
130C4⋊C4D4×C1712yes—
131C22⋊C4—22no—
132C22⋊C4—22no—
133C22⋊C4—22no—
134C22⋊C4—42no—
135C23—21no—
136C23—21no—
137C23—22no—
138C23—41no—
139C23—41no—
140C23—42no—
141C23—81no—
142C23—81no—
143C23D8×C1712yes—
144C23C2×D4×C1711yescharacteristic
145D4—42no—
146D4—44no—
147D4—42no—
148D4—42no—
149D4—81no—
150C2×C4—21no—
151C2×C4—22no—
152C2×C4—41no—
153C2×C4—42no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4C2×D4×C1712yes—
162C8—42no—
163C22—21no—
164C22—21no—
165C22—22no—
166C22—42no—
167C22—41no—
168C22—41no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—81no—
173C22—84no—
174C22C17×#12011yescharacteristic
175C22C2×D8×C1711yescharacteristic
176C22C17×AGL(1,ℤ/8)11yescharacteristic
177C4—22no—
178C4—42no—
179C4—41no—
180C4—81no—
181C4—81no—
182C2—21no—
183C2—21no—
184C2—42no—
185C2—82no—
186C2C17×#44711yescharacteristic
187C2C17×#45511yescharacteristic
188C2C17×#45811yescharacteristic
subgroupG/H
center, socleC22×C17#120
commutator, Frattini, cosocleC22×C4C23×C17
prime radicalC17×#534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#480C2semidirect
3. C17×#397C2semidirect
4. C17×#327C2semidirect
5. C17×#323C2semidirect
11. C2×C4⋊C4×C17C22semidirect
16. C17×C22⋊C8C22semidirect
18. C17×#95C22semidirect
68. #1607C17direct (N × H)
89. #480C2×C17semidirect
90. #397C2×C17semidirect
91. #327C2×C17semidirect
92. #323C2×C17semidirect
105. C2×C4⋊C4C22×C17semidirect
110. C22⋊C8C22×C17semidirect
112. #95C22×C17semidirect
113. C17#1607direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#5342
C17×#4802
C17×#3972
C17×#3272
C17×#3232
#160717