Finite Group Databasebeta

← C17×#10516 #16868260

Subgroups — C17×#10516 #16868260

Order 4352.

364 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 94 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×#3249C211yesmaximal, characteristic
2C17×#1843C211yesmaximal, characteristic
3C17×#1552C212yesmaximal
4C17×#1506C212yesmaximal
5C17×#1290C211yesmaximal, characteristic
6C17×#533C2212yes—
7C17×#477—22no—
8C17×#467—22no—
9C17×#462—22no—
10C17×#432C2212yes—
11C2×C17×C4⋊C8—22no—
12C2×C17×C4⋊C8C2211yescharacteristic
13C2×C17×C4⋊C8C2211yescharacteristic
14C17×#376C2211yescharacteristic
15C17×#332—22no—
16C17×#332—22no—
17C17×#328—24no—
18C2×Q16×C17—22no—
19C22×C8×C17—21no—
20C22×C8×C17D412yes—
21C17×C4⋊Q8D412yes—
22C17×C4⋊Q8D412yes—
23C17×#125—22no—
24C17×C22⋊Q8—22no—
25C17×C22⋊Q8—22no—
26C4×Q8×C17—22no—
27C4×Q8×C17—22no—
28C17×#117—22no—
29C2×C42×C17—21no—
30C2×C42×C17C2311yescharacteristic
31C17×#107—22no—
32C17×C4⋊C8—22no—
33C17×C4⋊C8—22no—
34C17×C4⋊C8—22no—
35C17×C4⋊C8—44no—
36C17×#103—24no—
37C17×C22⋊C8—22no—
38C17×#97—22no—
39C17×#95—21no—
40C17×#95D412yes—
41C2×Q8×C17—22no—
42C2×Q8×C17—22no—
43C22×C4×C17—22no—
44C22×C4×C17C2×D411yescharacteristic
45C22×C4×C17C2×D411yescharacteristic
46C22×C4×C17#4111yescharacteristic
47Q16×C17—82no—
48C2×C8×C17—22no—
49C2×C8×C17—42no—
50C2×C8×C17—42no—
51C2×C8×C17—41no—
52C2×C8×C17—42no—
53C4⋊C4×C17—22no—
54C4⋊C4×C17—22no—
55C4⋊C4×C17—22no—
56C4⋊C4×C17—22no—
57C4⋊C4×C17—42no—
58C4⋊C4×C17—42no—
59C22⋊C4×C17—42no—
60C42×C17—22no—
61C42×C17—22no—
62C42×C17—42no—
63C42×C17C2×D412yes—
64C42×C17#4112yes—
65#10516C1711yesmaximal, characteristic, direct product factor, Sylow
66C23×C17#12111yescharacteristic
67Q8×C17—42no—
68Q8×C17—42no—
69Q8×C17—82no—
70C2×C4×C17—22no—
71C2×C4×C17—21no—
72C2×C4×C17—21no—
73C2×C4×C17—24no—
74C2×C4×C17—41no—
75C2×C4×C17—42no—
76C2×C4×C17—42no—
77C2×C4×C17—42no—
78C2×C4×C17—42no—
79C2×C4×C17#12011yescharacteristic
80C2×C4×C17#12112yes—
81C2×C4×C17#12312yes—
82C2×C4×C17#12411yescharacteristic
83C8×C17—42no—
84C8×C17—82no—
85C8×C17—81no—
86#3249C2×C1711yescharacteristic
87#1843C2×C1711yescharacteristic
88#1552C2×C1712yes—
89#1506C2×C1712yes—
90#1290C2×C1711yescharacteristic
91C22×C17—21no—
92C22×C17—21no—
93C22×C17#39411yescharacteristic
94C22×C17#47312yes—
95C4×C17—22no—
96C4×C17—21no—
97C4×C17—22no—
98C4×C17—44no—
99C4×C17—82no—
100C4×C17—82no—
101C4×C17#45311yescharacteristic
102C4×C17#45611yescharacteristic
103#533C22×C1712yes—
104#477—22no—
105#467—22no—
106#462—22no—
107#432C22×C1712yes—
108C2×C4⋊C8—22no—
109C2×C4⋊C8C22×C1711yescharacteristic
110C2×C4⋊C8C22×C1711yescharacteristic
111#376C22×C1711yescharacteristic
112#332—22no—
113#332—22no—
114#328—24no—
115C2×C17—22no—
116C2×C17#203911yescharacteristic
117C2×C17#204711yescharacteristic
118C2×C17#205311yescharacteristic
119C2×Q16—22no—
120C22×C8—21no—
121C22×C8D4×C1712yes—
122C4⋊Q8D4×C1712yes—
123C4⋊Q8D4×C1712yes—
124#125—22no—
125C22⋊Q8—22no—
126C22⋊Q8—22no—
127C4×Q8—22no—
128C4×Q8—22no—
129#117—22no—
130C2×C42—21no—
131C2×C42C23×C1711yescharacteristic
132#107—22no—
133C4⋊C8—22no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—44no—
137#103—24no—
138C22⋊C8—22no—
139#97—22no—
140#95—21no—
141#95D4×C1712yes—
142C17#1051611yescharacteristic, direct product factor, Sylow
143C2×Q8—22no—
144C2×Q8—22no—
145C22×C4—22no—
146C22×C4C2×D4×C1711yescharacteristic
147C22×C4C2×D4×C1711yescharacteristic
148C22×C4#41×C1711yescharacteristic
149Q16—82no—
150C2×C8—22no—
151C2×C8—42no—
152C2×C8—42no—
153C2×C8—41no—
154C2×C8—42no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—22no—
158C4⋊C4—22no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C22⋊C4—42no—
162C42—22no—
163C42—22no—
164C42—42no—
165C42C2×D4×C1712yes—
166C42#41×C1712yes—
167C23C17×#12111yescharacteristic
168Q8—42no—
169Q8—42no—
170Q8—82no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4C17×#12011yescharacteristic
181C2×C4C17×#12112yes—
182C2×C4C17×#12312yes—
183C2×C4C17×#12411yescharacteristic
184C8—42no—
185C8—82no—
186C8—81no—
187C22—21no—
188C22—21no—
189C22C17×#39411yescharacteristic
190C22C17×#47312yes—
191C4—21no—
192C4—22no—
193C4—22no—
194C4—44no—
195C4—82no—
196C4—82no—
197C4C17×#45311yescharacteristic
198C4C17×#45611yescharacteristic
199C2—22no—
200C2C17×#203911yescharacteristic
201C2C17×#204711yescharacteristic
202C2C17×#205311yescharacteristic
subgroupG/H
center, socleC22×C17#394
commutator, Frattini, cosocleC2×C42C23×C17
prime radicalC23×C17#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
65. #10516C17direct (N × H)
142. C17#10516direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#32492
C17×#18432
C17×#15522
C17×#15062
C17×#12902
#1051617