Finite Group Databasebeta

← #17948903

Subgroups — #17948903

Order 4352.

336 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 68 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#14545012C211yesmaximal, characteristic
2#14544660C211yesmaximal, characteristic
3D17×#341C211yesmaximal, characteristic
4C2×#10587530—21no—
5C2×#10587533C412yes—
6#11763751—21no—
7#11763704C412yescomplemented
8C22⋊#63216—21no—
9#11763683—21no—
10C2×M16×D17—21no—
11C22×C8×D17C2211yescharacteristic
12#11762574C411yescharacteristic, complemented
13#11762573—21no—
14C17×#341C411yescharacteristic, complemented
15C22×C4×D17D411yescharacteristic
16C2×C22⋊#595—41no—
17C2×C4⋊#595—22no—
18C2×M16×C17—21no—
19C22×C8×C17C2×C411yescharacteristic
20C2×#63223—21no—
21C22×#3622D411yescharacteristic
22M16×D17—24no—
23M16×D17—42no—
24C2×#63218—41no—
25C2×C8×D17—42no—
26C2×C8×D17—41no—
27C2×C8×D17C2×C411yescharacteristic
28C2×C8×D17C2×C411yescharacteristic
29C2×C8×D17D411yescharacteristic
30C2×C8×D17Q811yescharacteristic
31(C2×#595)⋊C4—41no—
32C2×#63216—22no—
33#10587533—42no—
34#10587530—42no—
35C23×D17SD1611yescharacteristic
36C22×#595—42no—
37C22×C4×C17C22⋊C411yescharacteristic
38C22×Dic17Q1611yescharacteristic
39C2×C4×D17—22no—
40C2×C4×D17—22no—
41C2×C4×D17C22⋊C411yescharacteristic
42C2×C4×D17C4⋊C411yescharacteristic
43C2×C4×D17D811yescharacteristic
44C2×C4×D17SD1611yescharacteristic
45C22⋊#595—82no—
46C4⋊#595—42no—
47C4⋊#595—42no—
48M16×C17—22no—
49M16×C17—41no—
50C2×C8×C17—41no—
51C2×C8×C17—41no—
52C2×C8×C17C4211yescharacteristic
53C2×C8×C17C4⋊C411yescharacteristic
54#63223—22no—
55#63223—41no—
56C2×#3622—41no—
57C2×#3622—41no—
58C2×#3622C22⋊C411yescharacteristic
59C2×#3622C4⋊C411yescharacteristic
60#63218—44no—
61C8×D17—22no—
62C8×D17—22no—
63C8×D17—41no—
64C8×D17—41no—
65C8×D17—44no—
66#63216—42no—
67#7263—171nomaximal, Sylow
68C23×C17#10311yescharacteristic
69C22×D17—22no—
70C22×D17—22no—
71C22×D17—41no—
72C22×D17#10211yescharacteristic
73C22×D17#10611yescharacteristic
74C2×#595—82no—
75C2×#595—82no—
76C2×#595—82no—
77C2×C4×C17—21no—
78C2×C4×C17—21no—
79C2×C4×C17#9511yescharacteristic
80C2×C4×C17#10211yescharacteristic
81C2×Dic17—22no—
82C2×Dic17#10311yescharacteristic
83C2×Dic17#10711yescharacteristic
84C4×D17—22no—
85C4×D17—21no—
86C4×D17—21no—
87C4×D17—22no—
88C4×D17#9912yes—
89C4×D17#10412yes—
90C8×C17—21no—
91C8×C17—21no—
92C8×C17—42no—
93#3622—21no—
94#3622—21no—
95#3622—42no—
96#2112—171no—
97#1807—171no—
98C2×#341—171no—
99C22×C17—21no—
100C22×C17—21no—
101C22×C17—21no—
102C22×C17#34011yescharacteristic
103C2×D17—21no—
104C2×D17—21no—
105C2×D17—21no—
106C2×D17—21no—
107C2×D17—44no—
108C2×D17#32712yes—
109C2×D17#36512yes—
110#595—162no—
111C4×C17—21no—
112C4×C17#33911yescharacteristic
113C4×C17#34211yescharacteristic
114Dic17—21no—
115Dic17#32812yes—
116C22×M16—341no—
117C23×C8—171no—
118C2×M32—341no—
119C2×#106—172no—
120#380—341no—
121C22⋊C16—172no—
122C22⋊C16—341no—
123#341—171no—
124#341—341no—
125#341#59511yescharacteristic, complemented
126#340—341no—
127C2×C17—41no—
128C2×C17#129411yescharacteristic
129C2×C17#138311yescharacteristic
130C2×C17#138911yescharacteristic
131D17—22no—
132D17—22no—
133C23×C4—171no—
134C2×M16—21no—
135C2×M16—344no—
136C2×M16—341no—
137C2×M16—681no—
138C2×M16—682no—
139C22×C8—171no—
140C22×C8—171no—
141C22×C8—171no—
142C22×C8—171no—
143C22×C8—171no—
144C22×C8—682no—
145C22×C8—681no—
146C22×C8C2×#59511yescharacteristic
147C2×C4⋊C4—342no—
148C2×C22⋊C4—681no—
149M32—682no—
150C2×C16—342no—
151#106—682no—
152#95—681no—
153C17#726311yescharacteristic, complemented, Sylow
154C24—171no—
155C22×C4—171no—
156C22×C4—171no—
157C22×C4—171no—
158C22×C4—171no—
159C22×C4—171no—
160C22×C4—342no—
161C22×C4—342no—
162C22×C4—682no—
163C22×C4C22⋊#59511yescharacteristic
164M16—22no—
165M16—41no—
166M16—342no—
167M16—684no—
168M16—681no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—171no—
172C2×C8—171no—
173C2×C8—342no—
174C2×C8—342no—
175C2×C8—681no—
176C2×C8—681no—
177C2×C8—684no—
178C2×C8—681no—
179C2×C8—681no—
180C2×C8C4×#59511yescharacteristic
181C2×C8C4⋊#59511yescharacteristic
182C4⋊C4—682no—
183C4⋊C4—682no—
184C22⋊C4—1362no—
185C16—682no—
186C23—171no—
187C23—171no—
188C23—342no—
189C23—342no—
190C23—681no—
191C23#1058754911yescharacteristic
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—171no—
195C2×C4—172no—
196C2×C4—172no—
197C2×C4—171no—
198C2×C4—342no—
199C2×C4—342no—
200C2×C4—342no—
201C2×C4—341no—
202C2×C4—341no—
203C2×C4—1362no—
204C2×C4—1362no—
205C2×C4—1362no—
206C2×C4(C2×#595)⋊C411yescharacteristic
207C2×C4#1058754711yescharacteristic
208C8—21no—
209C8—21no—
210C8—42no—
211C8—341no—
212C8—341no—
213C8—682no—
214C22—21no—
215C22—21no—
216C22—21no—
217C22—172no—
218C22—172no—
219C22—341no—
220C22—341no—
221C22—341no—
222C22—341no—
223C22—684no—
224C22#1176368211yescharacteristic
225C4—21no—
226C4—2722no—
227C4—172no—
228C4—341no—
229C4#1176368011yescharacteristic
230C4#1176368611yescharacteristic
231C2—41no—
232C2—342no—
233C2—342no—
234C2#1454365811yescharacteristic
235C2#1454385011yescharacteristic
236C2#1454386411yescharacteristic
subgroupG/H
centerC22#11763682
commutatorC2×C8×C17C42
FrattiniC22×C8C2×#595
FittingC17×#341C4
socleC22×C17#340
prime radicalC23×D17SD16
cosocleC22×C8×D17C22
hypercenter#341#595
hypocenterC17#7263
LCSG ▷ C2×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #341

Complements

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

NH ≅ G/Ntype
7. #11763704C4semidirect
12. #11762574C4semidirect
14. C17×#341C4semidirect
125. #341#595semidirect
153. C17#7263semidirect

Maximal subgroups

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

subgroupindex
#145450122
#145446602
D17×#3412
#726317