Finite Group Databasebeta

← #16938419

Subgroups — #16938419

Order 4352.

364 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 77 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
1#14540129C211yesmaximal, characteristic
2#14528937C211yesmaximal, characteristic
3#14527485C212yesmaximal
4#14527297C212yesmaximal
5C17×#1290C211yesmaximal, characteristic
6#11763366C2212yes—
7#11763105—22no—
8#11763050—22no—
9#11763020—22no—
10C2×C4⋊#3622C2211yescharacteristic
11C2×#10587485—22no—
12#11762655C2211yescharacteristic
13#11762556—22no—
14#11762554—22no—
15#11762547—24no—
16C17×#432C2212yes—
17C2×C17×C4⋊C8C2211yescharacteristic
18C22×C8×C17D412yes—
19C2×C42×C17C2311yescharacteristic
20#10587612—22no—
21#10587610—22no—
22#10587610—22no—
23C2×C4×Dic17—21no—
24C22×#3622—21no—
25C2×Dic68—22no—
26#10587556—22no—
27#10587555D412yes—
28#10587555D412yes—
29C4×Dic34—22no—
30C4×Dic34—22no—
31C17×C4⋊C8—22no—
32C17×C4⋊C8—22no—
33C17×C22⋊C8—22no—
34C17×#97—22no—
35#10587502—21no—
36#10587502D412yes—
37#10587489—22no—
38#10587487—24no—
39#10587485—44no—
40C4⋊#3622—22no—
41C22×C4×C17C2×D411yescharacteristic
42C22×C4×C17C2×D411yescharacteristic
43C22×C4×C17#4111yescharacteristic
44C22×Dic17—22no—
45C2×Dic34—22no—
46C2×Dic34—22no—
47C2×C8×C17—22no—
48C2×C8×C17—42no—
49C2×C8×C17—42no—
50C42×C17C2×D412yes—
51C42×C17#4112yes—
52C22⋊Dic17—42no—
53C4⋊Dic17—22no—
54C4⋊Dic17—22no—
55C4⋊Dic17—22no—
56C4⋊Dic17—22no—
57#63225—42no—
58#63225—42no—
59C4×Dic17—22no—
60C4×Dic17—22no—
61C4×Dic17—42no—
62C2×#3622—42no—
63C2×#3622—41no—
64Dic68—82no—
65#10516—171nomaximal, Sylow
66C23×C17#12111yescharacteristic
67C2×C4×C17—22no—
68C2×C4×C17—21no—
69C2×C4×C17—21no—
70C2×C4×C17—41no—
71C2×C4×C17#12011yescharacteristic
72C2×C4×C17#12112yes—
73C2×C4×C17#12312yes—
74C2×C4×C17#12411yescharacteristic
75C2×Dic17—24no—
76C2×Dic17—42no—
77C2×Dic17—42no—
78C2×Dic17—42no—
79C2×Dic17—42no—
80Dic34—42no—
81Dic34—42no—
82Dic34—82no—
83C8×C17—42no—
84C8×C17—82no—
85#3622—81no—
86#3249—171no—
87#1843—171no—
88#1552—172no—
89#1506—172no—
90#1290D1711yescharacteristic
91C22×C17—21no—
92C22×C17—21no—
93C22×C17#39411yescharacteristic
94C22×C17#47312yes—
95C4×C17—22no—
96C4×C17—21no—
97C4×C17—22no—
98C4×C17#45311yescharacteristic
99C4×C17#45611yescharacteristic
100Dic17—44no—
101Dic17—82no—
102Dic17—82no—
103#533—172no—
104#477—342no—
105#467—342no—
106#462—342no—
107#432C2×D1712yes—
108C2×C4⋊C8—171no—
109C2×C4⋊C8—342no—
110C2×C4⋊C8C2×D1711yescharacteristic
111#376—171no—
112#332—342no—
113#332—342no—
114#328—344no—
115C2×C17—22no—
116C2×C17#203911yescharacteristic
117C2×C17#204711yescharacteristic
118C2×C17#205311yescharacteristic
119C2×Q16—342no—
120C22×C8—341no—
121C22×C8D6812yes—
122C4⋊Q8—172no—
123C4⋊Q8—172no—
124#125—342no—
125C22⋊Q8—342no—
126C22⋊Q8—342no—
127C4×Q8—342no—
128C4×Q8—342no—
129#117—342no—
130C2×C42—341no—
131C2×C42C22×D1711yescharacteristic
132#107—342no—
133C4⋊C8—22no—
134C4⋊C8—22no—
135C4⋊C8—342no—
136C4⋊C8—684no—
137#103—344no—
138C22⋊C8—22no—
139#97—22no—
140#95—172no—
141#95—341no—
142C17#1051611yescharacteristic, complemented, Sylow
143C2×Q8—342no—
144C2×Q8—342no—
145C22×C4—342no—
146C22×C4C2×D6811yescharacteristic
147C22×C4D4×D1711yescharacteristic
148C22×C4#6325611yescharacteristic
149Q16—1362no—
150C2×C8—22no—
151C2×C8—42no—
152C2×C8—42no—
153C2×C8—682no—
154C2×C8—681no—
155C4⋊C4—342no—
156C4⋊C4—342no—
157C4⋊C4—342no—
158C4⋊C4—342no—
159C4⋊C4—682no—
160C4⋊C4—682no—
161C22⋊C4—682no—
162C42—342no—
163C42—342no—
164C42—682no—
165C42#6325212yes—
166C42D4×D1712yes—
167C23#1058758111yescharacteristic
168Q8—682no—
169Q8—682no—
170Q8—1362no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—344no—
176C2×C4—682no—
177C2×C4—682no—
178C2×C4—682no—
179C2×C4—682no—
180C2×C4#1058756111yescharacteristic
181C2×C4#1058756811yescharacteristic
182C2×C4#1058757012yes—
183C2×C4#1058758012yes—
184C8—42no—
185C8—82no—
186C8—1361no—
187C22—21no—
188C22—21no—
189C22#1176272711yescharacteristic
190C22#1176308512yes—
191C4—22no—
192C4—22no—
193C4—21no—
194C4—684no—
195C4—1362no—
196C4—1362no—
197C4#1176297911yescharacteristic
198C4#1176299411yescharacteristic
199C2—22no—
200C2#1453000911yescharacteristic
201C2#1453005311yescharacteristic
202C2#1453009111yescharacteristic
subgroupG/H
centerC22#11762727
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1290C2
socleC22×C17#394
prime radicalC23×C17#121
hypercenter#1290D17
hypocenterC17#10516
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
142. C17#10516semidirect

Maximal subgroups

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

subgroupindex
#145401292
#145289372
#145274852
#145272972
C17×#12902
#1051617