Finite Group Databasebeta

← #16938400

Subgroups — #16938400

Order 4352.

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

normal subgroups only

This group has 388 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#14540094C211yesmaximal, characteristic
2#14528903C211yesmaximal, characteristic, complemented
3#14527480C212yesmaximal, complemented
4#14527293C212yesmaximal, complemented
5C17×#1290C211yesmaximal, characteristic, complemented
6#11763359C2212yes—
7#11763090—22no—
8#11763045—22no—
9#11763005—22no—
10C2×C4⋊#3622C2211yescharacteristic
11#11762655C2211yescharacteristic
12#11762563—22no—
13#11762557—22no—
14#11762552—22no—
15#11762544—24no—
16C17×#432C2212yes—
17C2×C17×C4⋊C8C2211yescharacteristic
18C2×#63252—22no—
19C22×C8×C17D412yes—
20C2×C42×C17C2311yescharacteristic
21#10587616—22no—
22#10587616—22no—
23C2×C4×Dic17—21no—
24C22×#3622—21no—
25C2×D136—22no—
26#10587561—22no—
27#10587560D412yes—
28C4×D68—22no—
29C4×D68—22no—
30#10587555D412yes—
31C17×C4⋊C8—22no—
32C17×C4⋊C8—22no—
33C17×C22⋊C8—22no—
34C17×#97—22no—
35#10587502—21no—
36#10587502D412yes—
37#10587492—24no—
38#10587489—22no—
39C4⋊#3622—22no—
40C22×C4×C17C2×D411yescharacteristic
41C22×C4×C17C2×D411yescharacteristic
42C22×C4×C17#4111yescharacteristic
43C2×C22⋊D17—42no—
44C22×Dic17—22no—
45#63252—84no—
46C2×D68—22no—
47C2×D68—22no—
48C2×D68—22no—
49C2×C4×D17—42no—
50C2×Dic34—22no—
51C2×C8×C17—22no—
52C2×C8×C17—42no—
53C2×C8×C17—42no—
54C42×C17C2×D412yes—
55C42×C17#4112yes—
56#63227—42no—
57#63227—42no—
58C4⋊Dic17—22no—
59C4⋊Dic17—22no—
60C4×Dic17—41no—
61C4×Dic17—41no—
62C2×#3622—42no—
63C2×#3622—41no—
64D136—82no—
65#10513—171nomaximal, Sylow
66C23×C17#12111yescharacteristic
67C22×D17—42no—
68C2×C4×C17—22no—
69C2×C4×C17—21no—
70C2×C4×C17—21no—
71C2×C4×C17—41no—
72C2×C4×C17#12011yescharacteristic
73C2×C4×C17#12112yes—
74C2×C4×C17#12312yes—
75C2×C4×C17#12411yescharacteristic
76C22⋊D17—84no—
77C2×Dic17—42no—
78C2×Dic17—42no—
79C2×Dic17—42no—
80C2×Dic17—42no—
81D68—42no—
82D68—42no—
83D68—82no—
84D68—82no—
85C4×D17—84no—
86Dic34—82no—
87C8×C17—42no—
88C8×C17—82no—
89#3622—81no—
90#3245—171no—
91#1832—171no—
92#1551—172no—
93#1505—172no—
94#1290D1711yescharacteristic, complemented
95C22×C17—21no—
96C22×C17—21no—
97C22×C17#39411yescharacteristic
98C22×C17#47212yes—
99C2×D17—82no—
100C2×D17—82no—
101C2×D17—82no—
102C4×C17—22no—
103C4×C17—21no—
104C4×C17—22no—
105C4×C17#45411yescharacteristic
106C4×C17#45511yescharacteristic
107Dic17—82no—
108Dic17—82no—
109#532—172no—
110#474—342no—
111#466—342no—
112#459—342no—
113#432C2×D1712yes—
114C2×C4⋊C8—171no—
115C2×C4⋊C8C2×D1711yescharacteristic
116#376—171no—
117#336—342no—
118#333—342no—
119#331—342no—
120#327—344no—
121C2×C17—22no—
122C2×C17#204011yescharacteristic
123C2×C17#204511yescharacteristic
124C2×C17#205311yescharacteristic
125D17—162no—
126C2×#41—342no—
127C2×D8—342no—
128C22×C8—341no—
129C22×C8D6812yes—
130C4⋊Q8—172no—
131#127—172no—
132#124—342no—
133#121—342no—
134#121—342no—
135C4×D4—342no—
136C4×D4—342no—
137C2×C42—341no—
138C2×C42C22×D1711yescharacteristic
139#107—342no—
140C4⋊C8—22no—
141C4⋊C8—22no—
142C4⋊C8—342no—
143#102—344no—
144C22⋊C8—22no—
145#97—22no—
146#95—172no—
147#95—341no—
148C17#1051311yescharacteristic, complemented, Sylow
149#41—1364no—
150C2×Q8—342no—
151C2×D4—342no—
152C2×D4—342no—
153C2×D4—342no—
154C2×D4—682no—
155C22×C4—342no—
156C22×C4—682no—
157C22×C4C2×D6811yescharacteristic
158C22×C4D4×D1711yescharacteristic
159C22×C4#6325611yescharacteristic
160D8—1362no—
161C2×C8—22no—
162C2×C8—42no—
163C2×C8—42no—
164C2×C8—682no—
165C2×C8—681no—
166C4⋊C4—342no—
167C4⋊C4—342no—
168C22⋊C4—682no—
169C22⋊C4—682no—
170C42—681no—
171C42—681no—
172C42#6325212yes—
173C42D4×D1712yes—
174C23—682no—
175C23#1058758111yescharacteristic
176Q8—1362no—
177D4—682no—
178D4—682no—
179D4—1362no—
180D4—1362no—
181D4—1364no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—682no—
187C2×C4—682no—
188C2×C4—682no—
189C2×C4—682no—
190C2×C4—1364no—
191C2×C4#1058756111yescharacteristic
192C2×C4#1058756811yescharacteristic
193C2×C4#1058757012yes—
194C2×C4#1058758012yes—
195C8—42no—
196C8—82no—
197C8—1361no—
198C22—21no—
199C22—21no—
200C22—1362no—
201C22—1362no—
202C22—1362no—
203C22#1176272711yescharacteristic
204C22#1176308012yes—
205C4—22no—
206C4—21no—
207C4—22no—
208C4—1362no—
209C4—1362no—
210C4#1176298411yescharacteristic
211C4#1176298911yescharacteristic
212C2—22no—
213C2—2722no—
214C2#1453001411yescharacteristic
215C2#1453004111yescharacteristic
216C2#1453009111yescharacteristic
subgroupG/H
centerC22#11762727
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1290C2
socleC22×C17#394
prime radical#14540094C2
hypercenter#1290D17
hypocenterC17#10513
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
2. #14528903C2semidirect
3. #14527480C2semidirect
4. #14527293C2semidirect
5. C17×#1290C2semidirect
94. #1290D17semidirect
148. C17#10513semidirect

Maximal subgroups

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

subgroupindex
#145400942
#145289032
#145274802
#145272932
C17×#12902
#1051317