Finite Group Databasebeta

← #16947383

Subgroups — #16947383

Order 4352.

342 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 59 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#14534026C211yesmaximal, characteristic
2#14527826C212yesmaximal
3#14526810C212yesmaximal
4#14526730C211yesmaximal, characteristic
5C17×#2060C211yesmaximal, characteristic
6#11763142—22no—
7#11762748—21no—
8#11762748C2212yes—
9#11762708—22no—
10#11762674—22no—
11C4×C4⋊Dic17—21no—
12#11762546—22no—
13#11762535C2212yes—
14C17×#544C2211yescharacteristic
15C17×#428—21no—
16C17×#384C2211yescharacteristic
17C17×#343C2211yescharacteristic
18C17×#339—21no—
19C2×M16×C17—21no—
20C17×C4⋊Q8—41no—
21C17×#125—41no—
22C17×C22⋊Q8—22no—
23C17×#117—21no—
24C2×C4⋊C4×C17—22no—
25C2×C4⋊C4×C17D411yescharacteristic
26C2×C4⋊C4×C17C2311yescharacteristic
27C2×C42×C17D411yescharacteristic
28C2×C4⋊Dic17—21no—
29C2×C4⋊Dic17—21no—
30C2×C4⋊Dic17—21no—
31C2×C4⋊Dic17D412yes—
32C2×C4×Dic17—22no—
33C17×#107—41no—
34C17×#106—41no—
35#10587506—42no—
36#10587502—22no—
37#10587502—21no—
38#10587502—22no—
39#10587502—22no—
40#10587502D412yes—
41C22⋊#3622—22no—
42#10587478—42no—
43C2×Q8×C17—22no—
44C22×C4×C17—21no—
45C22×C4×C17—21no—
46C22×C4×C17C2×D412yes—
47C22×C4×C17C2×D411yescharacteristic
48C22×Dic17—22no—
49C22×Dic17—22no—
50M16×C17—22no—
51M16×C17—41no—
52C2×C8×C17—41no—
53C4⋊C4×C17—22no—
54C4⋊C4×C17—21no—
55C4⋊C4×C17—21no—
56C4⋊C4×C17—41no—
57C4⋊C4×C17—41no—
58C4⋊C4×C17—42no—
59C4⋊C4×C17—44no—
60C22⋊C4×C17—41no—
61C42×C17—21no—
62C42×C17—41no—
63C42×C17Q1612yes—
64C4⋊Dic17—42no—
65C4⋊Dic17—42no—
66C4⋊Dic17—42no—
67C4⋊Dic17—81no—
68C4×Dic17—44no—
69C2×#3622—42no—
70#12257—171nomaximal, Sylow
71C23×C17#12011yescharacteristic
72Q8×C17—82no—
73C2×C4×C17—22no—
74C2×C4×C17—22no—
75C2×C4×C17—22no—
76C2×C4×C17—21no—
77C2×C4×C17—21no—
78C2×C4×C17—22no—
79C2×C4×C17—42no—
80C2×C4×C17—42no—
81C2×C4×C17—41no—
82C2×C4×C17—41no—
83C2×C4×C17—41no—
84C2×C4×C17C2×Q1611yescharacteristic
85C2×C4×C17#13711yescharacteristic
86C2×Dic17—42no—
87C2×Dic17—42no—
88C2×Dic17—42no—
89C2×Dic17—42no—
90C2×Dic17—42no—
91C2×Dic17—42no—
92C8×C17—42no—
93#3622—82no—
94#2571—171no—
95#2060D1711yescharacteristic
96#1617—172no—
97#1353—172no—
98#1325—171no—
99C22×C17—21no—
100C22×C17—21no—
101C22×C17#45111yescharacteristic
102C22×C17#45611yescharacteristic
103C22×C17B(4,𝔽2)11yescharacteristic
104C4×C17—24no—
105C4×C17—21no—
106C4×C17—21no—
107C4×C17—42no—
108C4×C17—81no—
109C4×C17—81no—
110C4×C17—81no—
111Dic17—82no—
112Dic17—82no—
113#544C2×D1711yescharacteristic
114#484—342no—
115#428—21no—
116#400—172no—
117#400—341no—
118#389—342no—
119#384C2×D1711yescharacteristic
120#382—342no—
121C4×C4⋊C4—341no—
122#343C2×D1711yescharacteristic
123#339—21no—
124#328—342no—
125#324—172no—
126C2×C17—21no—
127C2×C17—21no—
128C2×C17#160511yescharacteristic
129C2×C17#219811yescharacteristic
130C2×C17#220411yescharacteristic
131C2×M16—21no—
132C4⋊Q8—41no—
133#125—41no—
134C22⋊Q8—22no—
135#117—21no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—172no—
138C2×C4⋊C4—341no—
139C2×C4⋊C4—341no—
140C2×C4⋊C4—341no—
141C2×C4⋊C4C22⋊D1711yescharacteristic
142C2×C4⋊C4C22×D1711yescharacteristic
143C2×C42—342no—
144C2×C42C22⋊D1711yescharacteristic
145#107—41no—
146#107—682no—
147#106—41no—
148#103—682no—
149C22⋊C8—342no—
150#95—172no—
151#95—341no—
152#95—342no—
153#95—342no—
154#95—342no—
155C17#1225711yescharacteristic, complemented, Sylow
156C2×Q8—22no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—342no—
160C22×C4—342no—
161C22×C4D4×D1712yes—
162C22×C4C2×C22⋊D1711yescharacteristic
163M16—22no—
164M16—41no—
165C2×C8—41no—
166C2×C8—682no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—22no—
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—44no—
173C4⋊C4—42no—
174C4⋊C4—682no—
175C4⋊C4—682no—
176C4⋊C4—682no—
177C4⋊C4—1361no—
178C22⋊C4—41no—
179C42—21no—
180C42—41no—
181C42—684no—
182C42#6323112yes—
183C23#1058762311yescharacteristic
184Q8—82no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—682no—
197C2×C4—682no—
198C2×C4—682no—
199C2×C4—682no—
200C2×C4—682no—
201C2×C4—682no—
202C2×C4C2×#6323111yescharacteristic
203C2×C4#1058763711yescharacteristic
204C8—42no—
205C8—1362no—
206C22—21no—
207C22—21no—
208C22#1176296411yescharacteristic
209C22#1176299111yescharacteristic
210C22#1176299511yescharacteristic
211C4—24no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—81no—
216C4—81no—
217C4—81no—
218C4—1362no—
219C4—1362no—
220C2—21no—
221C2—21no—
222C2#1452775711yescharacteristic
223C2#1453077911yescharacteristic
224C2#1453080911yescharacteristic
subgroupG/H
centerC22#11762995
commutator, cosocleC2×C4⋊C4×C17C23
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2060C2
socleC22×C17B(4,𝔽2)
prime radicalC23×C17#120
hypercenter#2060D17
hypocenterC17#12257
LCSG ▷ C2×C4⋊C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2060

Complements

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

NH ≅ G/Ntype
155. C17#12257semidirect

Maximal subgroups

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

subgroupindex
#145340262
#145278262
#145268102
#145267302
C17×#20602
#1225717