Finite Group Databasebeta

← #16945828

Subgroups — #16945828

Order 4352.

300 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 83 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#14539368C211yesmaximal, characteristic
2#14530538C211yesmaximal, characteristic
3#14527546C211yesmaximal, characteristic
4#14526843C211yesmaximal, characteristic, complemented
5#14526841C211yesmaximal, characteristic, complemented
6#14526833C211yesmaximal, characteristic, complemented
7C17×#1362C211yesmaximal, characteristic, complemented
8#11763364—21no—
9C2×#10587469—21no—
10#11763214C2211yescharacteristic
11#11763159—21no—
12#11763047—21no—
13#11763047C412yes—
14Q16×Dic17—21no—
15Q16×Dic17C412yes—
16#11762865—21no—
17C4×C8×D17C2211yescharacteristic
18C4⋊#63214C2211yescharacteristic
19#11762627—21no—
20#11762562C2211yescharacteristic
21#11762559—21no—
22C17×#494C2211yescharacteristic
23C17×C4⋊C16C2211yescharacteristic
24C17×#335C2211yescharacteristic
25C2×Q16×C17—21no—
26C2×Q16×C17C2×C412yes—
27C17×C4⋊Q8—21no—
28#10587632—22no—
29Q8×Dic17—22no—
30C2×C8×D17C2×C411yescharacteristic
31C2×C8×D17D411yescharacteristic
32#10587583—41no—
33#10587578—41no—
34#10587576—41no—
35#10587573—41no—
36C42×D17D411yescharacteristic
37#10587555—21no—
38C2×C16×C17—21no—
39C17×C4⋊C8—21no—
40C4×C8×C17C2311yescharacteristic
41#10587506—22no—
42#10587506—22no—
43#10587491—41no—
44#10587489—21no—
45#10587489C2×C412yes—
46#10587486—41no—
47C8×Dic17C2×C411yescharacteristic
48C8×Dic17D411yescharacteristic
49C2×#63214—21no—
50C4⋊#3622—21no—
51C4×#3622D411yescharacteristic
52#10587469—42no—
53C2×Q8×C17—22no—
54C2×C4×D17C22⋊C411yescharacteristic
55C2×C4×D17D811yescharacteristic
56C2×C4×D17SD1611yescharacteristic
57C2×Dic34—41no—
58Q16×C17—42no—
59Q16×C17—41no—
60Q16×C17—41no—
61C2×C8×C17—41no—
62C2×C8×C17C22×C411yescharacteristic
63C2×C8×C17C2×D411yescharacteristic
64C4⋊C4×C17—41no—
65C4⋊C4×C17—41no—
66C42×C17C2×D411yescharacteristic
67#63227—42no—
68C4⋊Dic17—22no—
69C4⋊Dic17—41no—
70C4⋊Dic17—42no—
71#63225—42no—
72C4×Dic17—42no—
73C4×Dic17C22⋊C411yescharacteristic
74C4×Dic17D811yescharacteristic
75C4×Dic17SD1611yescharacteristic
76C2×#3622—41no—
77C2×#3622C22⋊C411yescharacteristic
78C2×#3622C22⋊C411yescharacteristic
79C8×D17—21no—
80C8×D17—21no—
81C8×D17—41no—
82C16×C17—41no—
83#63214—41no—
84#11987—171nomaximal, Sylow
85C22×D17#10211yescharacteristic
86Q8×C17—42no—
87Q8×C17—42no—
88C2×C4×C17—42no—
89C2×C4×C17C2×C22⋊C411yescharacteristic
90C2×C4×C17C2×D811yescharacteristic
91C2×C4×C17C2×SD1611yescharacteristic
92C2×Dic17—42no—
93C2×Dic17#10211yescharacteristic
94C2×Dic17#10211yescharacteristic
95C2×Dic17#10211yescharacteristic
96C4×D17—21no—
97C4×D17—21no—
98C4×D17—21no—
99C4×D17—21no—
100C4×D17—41no—
101Dic34—82no—
102C8×C17—21no—
103C8×C17—81no—
104C8×C17AGL(1,ℤ/8)11yescharacteristic
105C8×C17#13711yescharacteristic
106#3622—21no—
107#3622—21no—
108#3622—81no—
109#3170—171no—
110#2150—171no—
111#1568—171no—
112#1365—171no—
113#1365—171no—
114#1362—171no—
115#1362D1711yescharacteristic, complemented
116C22×C17C2×#10211yescharacteristic
117C2×D17—21no—
118C2×D17—21no—
119C2×D17—21no—
120C4×C17—21no—
121C4×C17—82no—
122C4×C17#41311yescharacteristic
123C4×C17#41711yescharacteristic
124C4×C17#51011yescharacteristic
125C4×C17#51011yescharacteristic
126Dic17—21no—
127Dic17—21no—
128Dic17—21no—
129Dic17—82no—
130#533—341no—
131C2×M32—341no—
132#500—171no—
133#494C2×D1711yescharacteristic
134#487—341no—
135#467—172no—
136#467—341no—
137C4×Q16—172no—
138C4×Q16—341no—
139#432—341no—
140C2×C4×C8—171no—
141C4⋊C16—171no—
142C4⋊C16—341no—
143C4⋊C16C2×D1711yescharacteristic
144#335—171no—
145#335C2×D1711yescharacteristic
146#334—341no—
147C2×C17#154711yescharacteristic
148C2×C17#214111yescharacteristic
149C2×C17#214811yescharacteristic
150D17—41no—
151C2×Q16—21no—
152C2×Q16C4×D1712yes—
153C22×C8—171no—
154C22×C8—171no—
155C4⋊Q8—21no—
156C4⋊Q8—341no—
157#125—681no—
158C22⋊Q8—342no—
159C22⋊Q8—681no—
160C4×Q8—342no—
161C4×Q8—681no—
162#117—681no—
163C2×C42—171no—
164M32—682no—
165C2×C16—21no—
166C2×C16—341no—
167#107—172no—
168#107—341no—
169C4⋊C8—21no—
170C4⋊C8—341no—
171#103—342no—
172#103—342no—
173C22⋊C8—681no—
174#97—681no—
175C4×C8—171no—
176C4×C8—171no—
177C4×C8—171no—
178C4×C8C22×D1711yescharacteristic
179C17#1198711yescharacteristic, complemented, Sylow
180C2×Q8—22no—
181C2×Q8—681no—
182C22×C4—171no—
183C22×C4—171no—
184C22×C4—171no—
185Q16—42no—
186Q16—41no—
187Q16—41no—
188C2×C8—41no—
189C2×C8—171no—
190C2×C8—171no—
191C2×C8—341no—
192C2×C8—341no—
193C2×C8—681no—
194C2×C8—681no—
195C2×C8C2×C4×D1711yescharacteristic
196C2×C8D4×D1711yescharacteristic
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—342no—
200C4⋊C4—682no—
201C4⋊C4—682no—
202C4⋊C4—681no—
203C22⋊C4—682no—
204C42—171no—
205C42—171no—
206C42—171no—
207C42—682no—
208C42D4×D1711yescharacteristic
209C16—41no—
210C16—681no—
211C23—171no—
212Q8—42no—
213Q8—42no—
214Q8—1362no—
215C2×C4—42no—
216C2×C4—171no—
217C2×C4—171no—
218C2×C4—171no—
219C2×C4—341no—
220C2×C4—341no—
221C2×C4—341no—
222C2×C4—341no—
223C2×C4—681no—
224C2×C4—682no—
225C2×C4C22⋊C4×D1711yescharacteristic
226C2×C4D8×D1711yescharacteristic
227C2×C4SD16×D1711yescharacteristic
228C8—21no—
229C8—81no—
230C8—341no—
231C8—341no—
232C8—1361no—
233C8#1058759711yescharacteristic
234C8#1058760111yescharacteristic
235C22—341no—
236C22—341no—
237C22—341no—
238C22#102×D1711yescharacteristic
239C4—21no—
240C4—82no—
241C4—341no—
242C4—341no—
243C4—341no—
244C4—1362no—
245C4#1176279011yescharacteristic
246C4#1176280711yescharacteristic
247C4#1176324811yescharacteristic
248C4#1176325111yescharacteristic
249C2—681no—
250C2#1452745811yescharacteristic
251C2#1453050211yescharacteristic
252C2#1453053211yescharacteristic
subgroupG/H
centerC22#102×D17
commutatorC2×C8×C17C22×C4
FrattiniC4×C8C22×D17
FittingC17×#1362C2
socleC22×C17C2×#102
prime radicalC22×D17#102
cosocleC4×C8×C17C23
hypercenter#1362D17
hypocenterC17#11987
LCSG ▷ C2×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
4. #14526843C2semidirect
5. #14526841C2semidirect
6. #14526833C2semidirect
7. C17×#1362C2semidirect
115. #1362D17semidirect
179. C17#11987semidirect

Maximal subgroups

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

subgroupindex
#145393682
#145305382
#145275462
#145268432
#145268412
#145268332
C17×#13622
#1198717