Finite Group Databasebeta

← C17×#10517 #16868261

Subgroups — C17×#10517 #16868261

Order 4352.

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

normal subgroups only

This group has 344 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×#1832C211yesmaximal, characteristic
3C17×#1552C212yesmaximal
4C17×#1506C212yesmaximal
5C17×#1290C211yesmaximal, characteristic
6C17×#533C2212yes—
7C17×#477—22no—
8C17×#467—22no—
9C17×#462—22no—
10C17×#432C2212yes—
11C2×C17×C4⋊C8C2211yescharacteristic
12C2×C17×C4⋊C8C2211yescharacteristic
13C17×#376C2211yescharacteristic
14C17×#336—22no—
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×#103—24no—
36C17×C22⋊C8—22no—
37C17×#97—22no—
38C17×#95—21no—
39C17×#95D412yes—
40C2×Q8×C17—22no—
41C2×Q8×C17—22no—
42C22×C4×C17—22no—
43C22×C4×C17C2×D411yescharacteristic
44C22×C4×C17C2×D411yescharacteristic
45C22×C4×C17#4111yescharacteristic
46Q16×C17—82no—
47C2×C8×C17—22no—
48C2×C8×C17—42no—
49C2×C8×C17—42no—
50C2×C8×C17—41no—
51C2×C8×C17—42no—
52C4⋊C4×C17—22no—
53C4⋊C4×C17—22no—
54C4⋊C4×C17—22no—
55C4⋊C4×C17—22no—
56C4⋊C4×C17—42no—
57C4⋊C4×C17—42no—
58C22⋊C4×C17—42no—
59C42×C17—41no—
60C42×C17—41no—
61C42×C17—42no—
62C42×C17C2×D412yes—
63C42×C17#4112yes—
64#10517C1711yesmaximal, characteristic, direct product factor, Sylow
65C23×C17#12111yescharacteristic
66Q8×C17—42no—
67Q8×C17—42no—
68Q8×C17—82no—
69C2×C4×C17—22no—
70C2×C4×C17—21no—
71C2×C4×C17—21no—
72C2×C4×C17—41no—
73C2×C4×C17—42no—
74C2×C4×C17—42no—
75C2×C4×C17—42no—
76C2×C4×C17—42no—
77C2×C4×C17—42no—
78C2×C4×C17#12011yescharacteristic
79C2×C4×C17#12112yes—
80C2×C4×C17#12312yes—
81C2×C4×C17#12411yescharacteristic
82C8×C17—42no—
83C8×C17—82no—
84C8×C17—81no—
85#3249C2×C1711yescharacteristic
86#1832C2×C1711yescharacteristic
87#1552C2×C1712yes—
88#1506C2×C1712yes—
89#1290C2×C1711yescharacteristic
90C22×C17—21no—
91C22×C17—21no—
92C22×C17#39411yescharacteristic
93C22×C17#47312yes—
94C4×C17—22no—
95C4×C17—21no—
96C4×C17—22no—
97C4×C17—82no—
98C4×C17—82no—
99C4×C17—82no—
100C4×C17#45411yescharacteristic
101C4×C17#45511yescharacteristic
102#533C22×C1712yes—
103#477—22no—
104#467—22no—
105#462—22no—
106#432C22×C1712yes—
107C2×C4⋊C8C22×C1711yescharacteristic
108C2×C4⋊C8C22×C1711yescharacteristic
109#376C22×C1711yescharacteristic
110#336—22no—
111#332—22no—
112#332—22no—
113#328—24no—
114C2×C17—22no—
115C2×C17#204011yescharacteristic
116C2×C17#204711yescharacteristic
117C2×C17#205311yescharacteristic
118C2×Q16—22no—
119C22×C8—21no—
120C22×C8D4×C1712yes—
121C4⋊Q8D4×C1712yes—
122C4⋊Q8D4×C1712yes—
123#125—22no—
124C22⋊Q8—22no—
125C22⋊Q8—22no—
126C4×Q8—22no—
127C4×Q8—22no—
128#117—22no—
129C2×C42—21no—
130C2×C42C23×C1711yescharacteristic
131#107—22no—
132C4⋊C8—22no—
133C4⋊C8—22no—
134C4⋊C8—22no—
135#103—24no—
136C22⋊C8—22no—
137#97—22no—
138#95—21no—
139#95D4×C1712yes—
140C17#1051711yescharacteristic, direct product factor, Sylow
141C2×Q8—22no—
142C2×Q8—22no—
143C22×C4—22no—
144C22×C4C2×D4×C1711yescharacteristic
145C22×C4C2×D4×C1711yescharacteristic
146C22×C4#41×C1711yescharacteristic
147Q16—82no—
148C2×C8—22no—
149C2×C8—42no—
150C2×C8—42no—
151C2×C8—41no—
152C2×C8—42no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—42no—
158C4⋊C4—42no—
159C22⋊C4—42no—
160C42—41no—
161C42—41no—
162C42—42no—
163C42C2×D4×C1712yes—
164C42#41×C1712yes—
165C23C17×#12111yescharacteristic
166Q8—42no—
167Q8—42no—
168Q8—82no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4C17×#12011yescharacteristic
179C2×C4C17×#12112yes—
180C2×C4C17×#12312yes—
181C2×C4C17×#12411yescharacteristic
182C8—42no—
183C8—82no—
184C8—81no—
185C22—21no—
186C22—21no—
187C22C17×#39411yescharacteristic
188C22C17×#47312yes—
189C4—21no—
190C4—22no—
191C4—22no—
192C4—82no—
193C4—82no—
194C4—82no—
195C4C17×#45411yescharacteristic
196C4C17×#45511yescharacteristic
197C2—22no—
198C2C17×#204011yescharacteristic
199C2C17×#204711yescharacteristic
200C2C17×#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
64. #10517C17direct (N × H)
140. C17#10517direct (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×#18322
C17×#15522
C17×#15062
C17×#12902
#1051717