Finite Group Databasebeta

← C17×#1598 #14524604

Subgroups — C17×#1598 #14524604

Order 2176.

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

normal subgroups only

This group has 310 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×#537C211yesmaximal, characteristic, complemented
2C17×#447C212yesmaximal, complemented
3C17×#394C211yesmaximal, characteristic, complemented
4C17×#327C212yesmaximal, complemented
5C17×#324C211yesmaximal, characteristic, complemented
6C2×#41×C17—21no—
7C22×D4×C17C2211yescharacteristic
8C2×D8×C17—22no—
9C17×C22⋊Q8—22no—
10C17×#121—22no—
11C17×#121—21no—
12C17×#121C2212yes—
13C2×C4⋊C4×C17C2211yescharacteristic
14C2×C22⋊C4×C17—21no—
15C2×C22⋊C4×C17—21no—
16C17×#102—22no—
17C17×C22⋊C8C2212yes—
18C17×#95C2211yescharacteristic
19C24×C17—21no—
20#41×C17—42no—
21#41×C17—42no—
22C2×Q8×C17—21no—
23C2×D4×C17—21no—
24C2×D4×C17—22no—
25C2×D4×C17—21no—
26C2×D4×C17—22no—
27C2×D4×C17—42no—
28C2×D4×C17D412yes—
29C22×C4×C17—22no—
30C22×C4×C17—21no—
31C22×C4×C17D411yescharacteristic
32C22×C4×C17D411yescharacteristic
33C22×C4×C17C2311yescharacteristic
34D8×C17—44no—
35C2×C8×C17—22no—
36C4⋊C4×C17—21no—
37C4⋊C4×C17—22no—
38C4⋊C4×C17D412yes—
39C22⋊C4×C17—22no—
40C22⋊C4×C17—22no—
41C22⋊C4×C17—42no—
42C22⋊C4×C17—42no—
43C23×C17—22no—
44C23×C17—22no—
45C23×C17—41no—
46C23×C17—41no—
47C23×C17—41no—
48C23×C17—41no—
49C23×C17—41no—
50C23×C17—41no—
51C23×C17C2×D411yescharacteristic
52Q8×C17—42no—
53D4×C17—24no—
54D4×C17—42no—
55D4×C17—42no—
56D4×C17—42no—
57D4×C17—42no—
58D4×C17—42no—
59D4×C17—81no—
60C2×C4×C17—21no—
61C2×C4×C17—21no—
62C2×C4×C17—21no—
63C2×C4×C17—22no—
64C2×C4×C17—41no—
65C2×C4×C17—44no—
66C2×C4×C17—41no—
67C2×C4×C17—41no—
68C2×C4×C17—41no—
69C2×C4×C17—41no—
70C2×C4×C17D812yescomplemented
71C2×C4×C17C2×D412yes—
72C8×C17—42no—
73#1598C1711yesmaximal, characteristic, direct product factor, Sylow
74C22×C17—21no—
75C22×C17—21no—
76C22×C17—42no—
77C22×C17—42no—
78C22×C17—42no—
79C22×C17—42no—
80C22×C17—42no—
81C22×C17—42no—
82C22×C17—81no—
83C22×C17—81no—
84C22×C17—81no—
85C22×C17—81no—
86C22×C17#12011yescharacteristic
87C22×C17C2×D811yescharacteristic
88C22×C17AGL(1,ℤ/8)11yescharacteristic
89C4×C17—22no—
90C4×C17—22no—
91C4×C17—42no—
92C4×C17—41no—
93C4×C17—81no—
94#537C2×C1711yescharacteristic, complemented
95#447C2×C1712yescomplemented
96#394C2×C1711yescharacteristic, complemented
97#327C2×C1712yescomplemented
98#324C2×C1711yescharacteristic, complemented
99C2×C17—21no—
100C2×C17—21no—
101C2×C17—82no—
102C2×C17—82no—
103C2×C17#44711yescharacteristic
104C2×C17#45411yescharacteristic
105C2×C17B(4,𝔽2)11yescharacteristic
106C2×#41—21no—
107C22×D4C22×C1711yescharacteristic
108C2×D8—22no—
109C22⋊Q8—22no—
110#121—22no—
111#121—21no—
112#121C22×C1712yes—
113C2×C4⋊C4C22×C1711yescharacteristic
114C2×C22⋊C4—21no—
115C2×C22⋊C4—21no—
116#102—22no—
117C22⋊C8C22×C1712yes—
118#95C22×C1711yescharacteristic
119C17#159811yescharacteristic, direct product factor, Sylow
120C24—21no—
121#41—42no—
122#41—42no—
123C2×Q8—21no—
124C2×D4—21no—
125C2×D4—22no—
126C2×D4—21no—
127C2×D4—22no—
128C2×D4—42no—
129C2×D4D4×C1712yes—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4D4×C1711yescharacteristic
133C22×C4D4×C1711yescharacteristic
134C22×C4C23×C1711yescharacteristic
135D8—44no—
136C2×C8—22no—
137C4⋊C4—21no—
138C4⋊C4—22no—
139C4⋊C4D4×C1712yes—
140C22⋊C4—22no—
141C22⋊C4—22no—
142C22⋊C4—42no—
143C22⋊C4—42no—
144C23—22no—
145C23—22no—
146C23—41no—
147C23—41no—
148C23—41no—
149C23—41no—
150C23—41no—
151C23—41no—
152C23C2×D4×C1711yescharacteristic
153Q8—42no—
154D4—24no—
155D4—42no—
156D4—42no—
157D4—42no—
158D4—42no—
159D4—42no—
160D4—81no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—41no—
166C2×C4—44no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4D8×C1712yescomplemented
172C2×C4C2×D4×C1712yes—
173C8—42no—
174C22—21no—
175C22—21no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—42no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—81no—
186C22C17×#12011yescharacteristic
187C22C2×D8×C1711yescharacteristic
188C22C17×AGL(1,ℤ/8)11yescharacteristic
189C4—22no—
190C4—22no—
191C4—42no—
192C4—41no—
193C4—81no—
194C2—21no—
195C2—21no—
196C2—82no—
197C2—82no—
198C2C17×#44711yescharacteristic
199C2C17×#45411yescharacteristic
200C2C17×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C17#120
commutator, Frattini, cosocleC22×C4C23×C17
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
1. C17×#537C2semidirect
2. C17×#447C2semidirect
3. C17×#394C2semidirect
4. C17×#327C2semidirect
5. C17×#324C2semidirect
70. C2×C4×C17D8semidirect
73. #1598C17direct (N × H)
94. #537C2×C17semidirect
95. #447C2×C17semidirect
96. #394C2×C17semidirect
97. #327C2×C17semidirect
98. #324C2×C17semidirect
119. C17#1598direct (N × H)
171. C2×C4D8×C17semidirect

Maximal subgroups

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

subgroupindex
C17×#5372
C17×#4472
C17×#3942
C17×#3272
C17×#3242
#159817