Finite Group Databasebeta

← #16938420

Subgroups — #16938420

Order 4352.

344 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 81 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#14528903C211yesmaximal, characteristic
2#14527484C212yesmaximal
3#14527296C212yesmaximal
4#14526654C211yesmaximal, characteristic
5C17×#3249C211yesmaximal, characteristic
6#11762866C2212yes—
7C2×C4⋊#3622C2211yescharacteristic
8#11762655C2211yescharacteristic
9#11762563—22no—
10#11762555—22no—
11#11762555—22no—
12#11762546—24no—
13C17×#533C2212yes—
14C17×#477—22no—
15C17×#467—22no—
16C17×#462—22no—
17C2×C17×C4⋊C8C2211yescharacteristic
18C2×Q16×C17—22no—
19C22×C8×C17D412yes—
20C17×C4⋊Q8D412yes—
21C17×C4⋊Q8D412yes—
22C17×#125—22no—
23C17×C22⋊Q8—22no—
24C17×C22⋊Q8—22no—
25C4×Q8×C17—22no—
26C4×Q8×C17—22no—
27C17×#117—22no—
28C2×C42×C17C2311yescharacteristic
29C2×C4×Dic17—21no—
30C22×#3622—21no—
31C17×#107—22no—
32C17×C4⋊C8—22no—
33C17×#103—24no—
34#10587502—21no—
35#10587502D412yes—
36C22⋊#3622—22no—
37C4⋊#3622—22no—
38C4⋊#3622—22no—
39#10587474—22no—
40C2×Q8×C17—22no—
41C2×Q8×C17—22no—
42C22×C4×C17C2×D411yescharacteristic
43C22×C4×C17C2×D411yescharacteristic
44C22×C4×C17#4111yescharacteristic
45C22×Dic17—22no—
46Q16×C17—82no—
47C2×C8×C17—22no—
48C2×C8×C17—42no—
49C4⋊C4×C17—22no—
50C4⋊C4×C17—22no—
51C4⋊C4×C17—22no—
52C4⋊C4×C17—22no—
53C4⋊C4×C17—42no—
54C4⋊C4×C17—42no—
55C22⋊C4×C17—42no—
56C42×C17—42no—
57C42×C17C2×D412yes—
58C42×C17#4112yes—
59C4×Dic17—41no—
60C4×Dic17—41no—
61C2×#3622—42no—
62C2×#3622—41no—
63C2×#3622—42no—
64#10517—171nomaximal, 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#12011yescharacteristic
76C2×C4×C17#12112yes—
77C2×C4×C17#12312yes—
78C2×C4×C17#12411yescharacteristic
79C2×Dic17—42no—
80C2×Dic17—42no—
81C2×Dic17—42no—
82C8×C17—42no—
83#3622—82no—
84#3622—81no—
85#3249D1711yescharacteristic
86#1832—171no—
87#1552—172no—
88#1506—172no—
89#1290—171no—
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#45411yescharacteristic
100C4×C17#45511yescharacteristic
101Dic17—82no—
102#533C2×D1712yes—
103#477—22no—
104#467—22no—
105#462—22no—
106#432—172no—
107C2×C4⋊C8—171no—
108C2×C4⋊C8C2×D1711yescharacteristic
109#376—171no—
110#336—342no—
111#332—342no—
112#332—342no—
113#328—344no—
114C2×C17—22no—
115C2×C17#204011yescharacteristic
116C2×C17#204711yescharacteristic
117C2×C17#205311yescharacteristic
118C2×Q16—22no—
119C22×C8—341no—
120C22×C8C22⋊D1712yes—
121C4⋊Q8C22⋊D1712yes—
122C4⋊Q8C22⋊D1712yes—
123#125—22no—
124C22⋊Q8—22no—
125C22⋊Q8—22no—
126C4×Q8—22no—
127C4×Q8—22no—
128#117—22no—
129C2×C42—341no—
130C2×C42C22×D1711yescharacteristic
131#107—22no—
132C4⋊C8—22no—
133C4⋊C8—342no—
134C4⋊C8—342no—
135#103—24no—
136C22⋊C8—342no—
137#97—342no—
138#95—172no—
139#95—341no—
140C17#1051711yescharacteristic, complemented, Sylow
141C2×Q8—22no—
142C2×Q8—22no—
143C22×C4—342no—
144C22×C4D4×D1711yescharacteristic
145C22×C4#6325411yescharacteristic
146C22×C4C2×C22⋊D1711yescharacteristic
147Q16—82no—
148C2×C8—22no—
149C2×C8—42no—
150C2×C8—682no—
151C2×C8—682no—
152C2×C8—681no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—42no—
158C4⋊C4—42no—
159C22⋊C4—42no—
160C42—42no—
161C42—681no—
162C42—681no—
163C42#6325412yes—
164C42C2×C22⋊D1712yes—
165C23#1058762411yescharacteristic
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—682no—
176C2×C4—682no—
177C2×C4—682no—
178C2×C4#1058762112yes—
179C2×C4#1058762211yescharacteristic
180C2×C4#1058762512yes—
181C2×C4#1058763911yescharacteristic
182C8—42no—
183C8—1362no—
184C8—1361no—
185C22—21no—
186C22—21no—
187C22#1176272311yescharacteristic
188C22#1176308112yes—
189C4—22no—
190C4—22no—
191C4—21no—
192C4—82no—
193C4—82no—
194C4—1362no—
195C4#1176298211yescharacteristic
196C4#1176298711yescharacteristic
197C2—22no—
198C2#1453001011yescharacteristic
199C2#1453004911yescharacteristic
200C2#1453008711yescharacteristic
subgroupG/H
centerC22#11762723
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#3249C2
socleC22×C17#394
prime radicalC23×C17#121
hypercenter#3249D17
hypocenterC17#10517
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

Complements

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

NH ≅ G/Ntype
140. C17#10517semidirect

Maximal subgroups

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

subgroupindex
#145289032
#145274842
#145272962
#145266542
C17×#32492
#1051717