Finite Group Databasebeta

← #16945170

Subgroups — #16945170

Order 4352.

324 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 71 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#14539522C211yesmaximal, characteristic
2#14530596C211yesmaximal, characteristic, complemented
3#14526774C212yesmaximal, complemented
4#14526768C212yesmaximal, complemented
5C17×#1841C211yesmaximal, characteristic, complemented
6#11763359—21no—
7#11763207C411yescharacteristic, complemented
8#11763186C411yescharacteristic, complemented
9#11763156—21no—
10#11763062—21no—
11#11763062C2212yes—
12#11762922—21no—
13#11762922C412yescomplemented
14#11762630—21no—
15#11762591C2212yes—
16#11762587—21no—
17C4×M16×C17C2211yescharacteristic
18C17×#344—21no—
19C17×#339—21no—
20C17×#338C2211yescharacteristic
21C17×H(3,ℤ/4)C2211yescharacteristic
22C2×#63252—41no—
23C2×M16×C17—21no—
24C2×M16×C17D411yescharacteristic
25C2×M16×C17C2311yescharacteristic
26C17×#117—21no—
27C2×C42×C17D411yescharacteristic
28#10587616—22no—
29#10587616—41no—
30C2×D136—21no—
31C2×D136C2×C412yes—
32#10587561—41no—
33#10587560—21no—
34C4×D68—22no—
35C4×D68—41no—
36#10587555—21no—
37C17×#97C2×C411yescharacteristic
38C17×#97D411yescharacteristic
39C4×C8×C17C2×C411yescharacteristic
40C4×C8×C17D411yescharacteristic
41#10587492—22no—
42#10587492—22no—
43#10587488—21no—
44#10587488C2×C412yes—
45#10587483—22no—
46C22×C4×C17—21no—
47C22×C4×C17C2×D411yescharacteristic
48C2×C22⋊D17—42no—
49#63252—84no—
50C2×D68—22no—
51C2×D68—41no—
52C2×D68—41no—
53C2×C4×D17—42no—
54C2×Dic34—41no—
55M16×C17—41no—
56M16×C17—41no—
57M16×C17—41no—
58M16×C17—41no—
59C2×C8×C17—41no—
60C2×C8×C17C22⋊C411yescharacteristic
61C2×C8×C17C22⋊C411yescharacteristic
62C2×C8×C17C22×C411yescharacteristic
63C2×C8×C17C2×D411yescharacteristic
64C4⋊C4×C17—41no—
65C22⋊C4×C17—41no—
66C42×C17—21no—
67C42×C17—41no—
68C42×C17C22⋊C411yescharacteristic
69C42×C17C22⋊C411yescharacteristic
70#63227—42no—
71#63227—42no—
72C4⋊Dic17—22no—
73C4⋊Dic17—41no—
74D136—42no—
75D136—42no—
76#63214—42no—
77#11837—171nomaximal, Sylow
78C23×C17AGL(1,ℤ/8)11yescharacteristic
79C22×D17—42no—
80C2×C4×C17—21no—
81C2×C4×C17—21no—
82C2×C4×C17—21no—
83C2×C4×C17—21no—
84C2×C4×C17—42no—
85C2×C4×C17—81no—
86C2×C4×C17C2×C22⋊C411yescharacteristic
87C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
88C22⋊D17—84no—
89C2×Dic17—42no—
90D68—42no—
91D68—42no—
92D68—82no—
93D68—82no—
94C4×D17—84no—
95Dic34—82no—
96C8×C17—21no—
97C8×C17—21no—
98C8×C17—21no—
99C8×C17—21no—
100C8×C17—81no—
101#3184—171no—
102#2165—171no—
103#1841D1711yescharacteristic, complemented
104#1341—172no—
105#1339—172no—
106C22×C17—21no—
107C22×C17—41no—
108C22×C17#41811yescharacteristic
109C2×D17—82no—
110C2×D17—82no—
111C2×D17—82no—
112C4×C17—22no—
113C4×C17—21no—
114C4×C17—41no—
115C4×C17—161no—
116C4×C17#41011yescharacteristic
117C4×C17#42111yescharacteristic
118Dic17—82no—
119#532—341no—
120#498—171no—
121#493—171no—
122#486—341no—
123#469—172no—
124#469—341no—
125#442—172no—
126#442—341no—
127C4×M16C2×D1711yescharacteristic
128#364—341no—
129#349—172no—
130#347—341no—
131#344—21no—
132#339—21no—
133#338C2×D1711yescharacteristic
134H(3,ℤ/4)C2×D1711yescharacteristic
135C2×C17—21no—
136C2×C17—41no—
137C2×C17#151411yescharacteristic
138D17—162no—
139C2×#41—681no—
140C2×D8—172no—
141C2×D8—341no—
142C2×M16—21no—
143C2×M16C22⋊D1711yescharacteristic
144C2×M16C22×D1711yescharacteristic
145C4⋊Q8—341no—
146#127—341no—
147#124—681no—
148#121—342no—
149#121—681no—
150C4×D4—342no—
151C4×D4—681no—
152#117—21no—
153C2×C42C22⋊D1711yescharacteristic
154M32—342no—
155#106—172no—
156#106—341no—
157#102—342no—
158#102—342no—
159#97C4×D1711yescharacteristic
160#97D6811yescharacteristic
161C4×C8C4×D1711yescharacteristic
162C4×C8D6811yescharacteristic
163C17#1183711yescharacteristic, complemented, Sylow
164#41—1364no—
165C2×Q8—681no—
166C2×D4—342no—
167C2×D4—681no—
168C2×D4—681no—
169C2×D4—682no—
170C22×C4—21no—
171C22×C4—682no—
172C22×C4C2×C22⋊D1711yescharacteristic
173D8—682no—
174D8—682no—
175M16—41no—
176M16—41no—
177M16—41no—
178M16—41no—
179C2×C8—41no—
180C2×C8#6322711yescharacteristic
181C2×C8#6322711yescharacteristic
182C2×C8C2×C4×D1711yescharacteristic
183C2×C8C2×D6811yescharacteristic
184C4⋊C4—41no—
185C4⋊C4—342no—
186C4⋊C4—681no—
187C22⋊C4—41no—
188C22⋊C4—682no—
189C22⋊C4—682no—
190C42—21no—
191C42—41no—
192C42#6322711yescharacteristic
193C42#6322711yescharacteristic
194C16—682no—
195C23—682no—
196C23#1058763511yescharacteristic
197Q8—1362no—
198D4—682no—
199D4—682no—
200D4—1362no—
201D4—1362no—
202D4—1364no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—42no—
208C2×C4—81no—
209C2×C4—682no—
210C2×C4—1364no—
211C2×C4C2×#6322711yescharacteristic
212C2×C4#1058763511yescharacteristic
213C8—21no—
214C8—21no—
215C8—21no—
216C8—21no—
217C8—81no—
218C22—21no—
219C22—41no—
220C22—1362no—
221C22—1362no—
222C22—1362no—
223C22#1176281311yescharacteristic
224C4—22no—
225C4—21no—
226C4—41no—
227C4—161no—
228C4—1362no—
229C4#1176278211yescharacteristic
230C4#1176282711yescharacteristic
231C2—21no—
232C2—41no—
233C2—2722no—
234C2#1452733011yescharacteristic
subgroupG/H
centerC2#14527330
commutatorC2×C8×C17C22×C4
FrattiniC2×M16C22×D17
FittingC17×#1841C2
socleC2×C17#1514
prime radical#14539522C2
cosocleC2×M16×C17C23
hypercenter#1841D17
hypocenterC17#11837
LCSG ▷ C2×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #1841

Complements

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

NH ≅ G/Ntype
2. #14530596C2semidirect
3. #14526774C2semidirect
4. #14526768C2semidirect
5. C17×#1841C2semidirect
7. #11763207C4semidirect
8. #11763186C4semidirect
13. #11762922C4semidirect
103. #1841D17semidirect
163. C17#11837semidirect

Maximal subgroups

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

subgroupindex
#145395222
#145305962
#145267742
#145267682
C17×#18412
#1183717