Finite Group Databasebeta

← #16938423

Subgroups — #16938423

Order 4352.

344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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#14527482C212yesmaximal
3#14527295C212yesmaximal
4#14526654C211yesmaximal, characteristic
5C17×#1832C211yesmaximal, characteristic
6#11763366C2212yes—
7#11763105—22no—
8#11763050—22no—
9#11763020—22no—
10#11762866C2212yes—
11#11762556—22no—
12#11762554—22no—
13#11762545—24no—
14C2×C17×C4⋊C8C2211yescharacteristic
15C2×C17×C4⋊C8C2211yescharacteristic
16C17×#376C2211yescharacteristic
17C17×#336—22no—
18C22×C8×C17—21no—
19C22×C8×C17D412yes—
20C2×C42×C17—21no—
21C2×C42×C17C2311yescharacteristic
22#10587612—22no—
23#10587610—22no—
24#10587610—22no—
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×#95—21no—
34C17×#95D412yes—
35C22⋊#3622—22no—
36#10587489—22no—
37#10587487—24no—
38C4⋊#3622—22no—
39#10587474—22no—
40C22×C4×C17—22no—
41C22×C4×C17C2×D411yescharacteristic
42C22×C4×C17C2×D411yescharacteristic
43C22×C4×C17#4111yescharacteristic
44C2×Dic34—22no—
45C2×Dic34—22no—
46C2×C8×C17—22no—
47C2×C8×C17—42no—
48C2×C8×C17—42no—
49C2×C8×C17—41no—
50C42×C17—41no—
51C42×C17—41no—
52C42×C17C2×D412yes—
53C42×C17#4112yes—
54C22⋊Dic17—42no—
55C4⋊Dic17—22no—
56C4⋊Dic17—22no—
57C4⋊Dic17—22no—
58C4⋊Dic17—22no—
59#63225—42no—
60#63225—42no—
61C4×Dic17—42no—
62C2×#3622—42no—
63Dic68—82no—
64#10517—171nomaximal, Sylow
65C23×C17#12111yescharacteristic
66C2×C4×C17—22no—
67C2×C4×C17—21no—
68C2×C4×C17—21no—
69C2×C4×C17—41no—
70C2×C4×C17—42no—
71C2×C4×C17—42no—
72C2×C4×C17—42no—
73C2×C4×C17#12011yescharacteristic
74C2×C4×C17#12112yes—
75C2×C4×C17#12312yes—
76C2×C4×C17#12411yescharacteristic
77C2×Dic17—42no—
78C2×Dic17—42no—
79Dic34—42no—
80Dic34—42no—
81Dic34—82no—
82C8×C17—42no—
83C8×C17—81no—
84#3622—82no—
85#3249—171no—
86#1832D1711yescharacteristic
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#45411yescharacteristic
99C4×C17#45511yescharacteristic
100Dic17—82no—
101Dic17—82no—
102#533—172no—
103#477—342no—
104#467—342no—
105#462—342no—
106#432—172no—
107C2×C4⋊C8C2×D1711yescharacteristic
108C2×C4⋊C8C2×D1711yescharacteristic
109#376C2×D1711yescharacteristic
110#336—22no—
111#332—342no—
112#332—342no—
113#328—344no—
114C2×C17—22no—
115C2×C17#204011yescharacteristic
116C2×C17#204711yescharacteristic
117C2×C17#205311yescharacteristic
118C2×Q16—342no—
119C22×C8—21no—
120C22×C8C22⋊D1712yes—
121C4⋊Q8—172no—
122C4⋊Q8—172no—
123#125—342no—
124C22⋊Q8—342no—
125C22⋊Q8—342no—
126C4×Q8—342no—
127C4×Q8—342no—
128#117—342no—
129C2×C42—21no—
130C2×C42C22×D1711yescharacteristic
131#107—342no—
132C4⋊C8—22no—
133C4⋊C8—22no—
134C4⋊C8—342no—
135#103—344no—
136C22⋊C8—342no—
137#97—342no—
138#95—21no—
139#95D6812yes—
140C17#1051711yescharacteristic, complemented, Sylow
141C2×Q8—342no—
142C2×Q8—342no—
143C22×C4—22no—
144C22×C4C2×D6811yescharacteristic
145C22×C4#6325211yescharacteristic
146C22×C4C2×C22⋊D1711yescharacteristic
147Q16—1362no—
148C2×C8—22no—
149C2×C8—42no—
150C2×C8—42no—
151C2×C8—41no—
152C2×C8—682no—
153C4⋊C4—342no—
154C4⋊C4—342no—
155C4⋊C4—342no—
156C4⋊C4—342no—
157C4⋊C4—682no—
158C4⋊C4—682no—
159C22⋊C4—682no—
160C42—41no—
161C42—41no—
162C42—682no—
163C42D4×D1712yes—
164C42#6325612yes—
165C23#1058761611yescharacteristic
166Q8—682no—
167Q8—682no—
168Q8—1362no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—682no—
177C2×C4—682no—
178C2×C4#1058758012yes—
179C2×C4#1058758112yes—
180C2×C4#1058762311yescharacteristic
181C2×C4#1058763311yescharacteristic
182C8—42no—
183C8—81no—
184C8—1362no—
185C22—21no—
186C22—21no—
187C22#1176272611yescharacteristic
188C22#1176308412yes—
189C4—22no—
190C4—22no—
191C4—21no—
192C4—82no—
193C4—1362no—
194C4—1362no—
195C4#1176298111yescharacteristic
196C4#1176298611yescharacteristic
197C2—22no—
198C2#1453001311yescharacteristic
199C2#1453005211yescharacteristic
200C2#1453009011yescharacteristic
subgroupG/H
centerC22#11762726
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1832C2
socleC22×C17#394
prime radicalC23×C17#121
hypercenter#1832D17
hypocenterC17#10517
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1832

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
#145401292
#145274822
#145272952
#145266542
C17×#18322
#1051717