Finite Group Databasebeta

← D17⋊#1412 #17962697

Subgroups — D17⋊#1412 #17962697

Order 4352.

390 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 58 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
1D17⋊#353C212yesmaximal
2#14543925C212yesmaximal, complemented
3#14543924C211yesmaximal, characteristic, complemented
4#14543923C211yesmaximal, characteristic, complemented
5D17×#490C211yesmaximal, characteristic
6D17⋊#99—22no—
7#11763714C2212yes—
8#11763714C2212yes—
9#11763713—22no—
10#127×D17C2211yescharacteristic
11#125×D17C411yescharacteristic, complemented
12#11763175C2211yescharacteristic
13#11763174C2211yescharacteristic
14#11763173C411yescharacteristic, complemented
15#11763172—22no—
16#102×D17—22no—
17#97×D17C411yescharacteristic, complemented
18C17×#490C411yescharacteristic, complemented
19C2×D4×D17—41no—
20C2×D4×D17D412yes—
21C2×C22⋊#595—42no—
22C17×#127C2×C411yescharacteristic
23C17×#125C2×C411yescharacteristic, complemented
24#10587626—41no—
25#10587626D412yes—
26C2×C8×D17—21no—
27C4⋊C4×D17—21no—
28C4⋊C4×D17—41no—
29#10587576—21no—
30#10587575—41no—
31#10587560C2311yescharacteristic
32C42×D17C2×C411yescharacteristic
33#10587556C2×C411yescharacteristic, complemented
34#10587551—42no—
35#10587539—22no—
36#10587539—22no—
37C17×#102—22no—
38C17×#97C2×C411yescharacteristic, complemented
39#10587503—22no—
40#10587492—22no—
41#10587486—21no—
42#10587480—22no—
43#10587474C2×C411yescharacteristic, complemented
44C23×D17—22no—
45C22×#595—82no—
46C2×D4×C17—41no—
47C2×D4×C17C22⋊C412yes—
48C2×C22⋊D17—22no—
49C2×C22⋊D17—42no—
50D4×D17—42no—
51D4×D17—42no—
52D4×D17—84no—
53C2×D68—41no—
54C2×D68C2×D412yes—
55C2×C4×D17—21no—
56C2×C4×D17—41no—
57C2×C4×D17C22⋊C411yescharacteristic
58C22⋊#595—42no—
59C22⋊#595—42no—
60C22⋊#595—82no—
61C2×C8×C17—21no—
62C4⋊C4×C17—21no—
63C4⋊C4×C17—41no—
64C42×C17C22×C411yescharacteristic
65C4⋊Dic17—21no—
66C4⋊Dic17—41no—
67#63225—41no—
68#63225—41no—
69#63225—41no—
70C4×Dic17—21no—
71C4×Dic17C22⋊C411yescharacteristic
72C2×#3622—21no—
73C8×D17—41no—
74C8×D17—41no—
75C2×#1412—171nomaximal, Sylow
76C23×C17—22no—
77C22×D17—22no—
78C22×D17—42no—
79C22×D17—42no—
80C22×D17—84no—
81C22×D17#9911yescharacteristic
82C2×#595—82no—
83C2×#595—82no—
84C2×#595—164no—
85D4×C17—42no—
86D4×C17—82no—
87C2×C4×C17—21no—
88C2×C4×C17—41no—
89C2×C4×C17C2×C22⋊C411yescharacteristic
90C22⋊D17—82no—
91C22⋊D17—84no—
92C2×Dic17—21no—
93C2×Dic17—41no—
94C2×Dic17#9911yescharacteristic
95D68—42no—
96D68—82no—
97C4×D17—21no—
98C4×D17—21no—
99C4×D17—42no—
100C4×D17—82no—
101C8×C17—41no—
102#3622—41no—
103C2×#490—171no—
104C2×#353—172no—
105#1412—171no—
106#1412—171no—
107#1412—172no—
108C22×C17—42no—
109C22×C17—82no—
110C22×C17C2×#9911yescharacteristic
111C2×D17—22no—
112C2×D17—42no—
113C2×D17—84no—
114C2×D17—82no—
115C2×D17—162no—
116C2×D17#35411yescharacteristic
117C2×D17#35411yescharacteristic
118#595—162no—
119#595—162no—
120C4×C17—21no—
121C4×C17—41no—
122C4×C17—81no—
123Dic17—21no—
124Dic17—41no—
125Dic17—81no—
126C2×#127—171no—
127C2×#125—171no—
128#490—171no—
129#490—171no—
130#490—171no—
131#490—342no—
132#490#59511yescharacteristic, complemented
133C2×#102—342no—
134C2×#99—342no—
135C2×#97—171no—
136#353—172no—
137#353—172no—
138#353—342no—
139C2×C17—21no—
140C2×C17—82no—
141C2×C17C2×#35411yescharacteristic
142D17—21no—
143D17—82no—
144D17#141212yescomplemented
145C22×D4—172no—
146C22×D4—681no—
147C22×C8—341no—
148#127—172no—
149#127—171no—
150#127—681no—
151#127C2×#59511yescharacteristic
152#125—171no—
153#125—341no—
154#125—681no—
155#125C2×#59511yescharacteristic, complemented
156C2×C4⋊C4—341no—
157C2×C4⋊C4—681no—
158C2×C22⋊C4—682no—
159C2×C42—171no—
160#102—22no—
161#102—342no—
162#102—342no—
163#102—342no—
164#99—342no—
165#99—342no—
166#99—682no—
167#97—171no—
168#97—341no—
169#97C2×#59511yescharacteristic, complemented
170C17C2×#141211yescharacteristic, complemented, Sylow
171C24—342no—
172C2×D4—41no—
173C2×D4—172no—
174C2×D4—342no—
175C2×D4—681no—
176C2×D4—682no—
177C2×D4—682no—
178C2×D4—682no—
179C2×D4—1364no—
180C2×D4C22⋊#59512yes—
181C22×C4—171no—
182C22×C4—341no—
183C22×C4—681no—
184C22×C4—1362no—
185C2×C8—21no—
186C2×C8—341no—
187C2×C8—681no—
188C2×C8—681no—
189C4⋊C4—21no—
190C4⋊C4—41no—
191C4⋊C4—341no—
192C4⋊C4—681no—
193C4⋊C4—681no—
194C4⋊C4—681no—
195C4⋊C4—681no—
196C22⋊C4—682no—
197C22⋊C4—682no—
198C22⋊C4—1362no—
199C42—171no—
200C42—341no—
201C42C22×#59511yescharacteristic
202C23—22no—
203C23—171no—
204C23—342no—
205C23—682no—
206C23—682no—
207C23—1364no—
208D4—42no—
209D4—82no—
210D4—682no—
211D4—1362no—
212D4—1362no—
213D4—1364no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—2724no—
217C2×C4—171no—
218C2×C4—341no—
219C2×C4—341no—
220C2×C4—341no—
221C2×C4—682no—
222C2×C4—681no—
223C2×C4—1362no—
224C2×C4—1362no—
225C2×C4—1362no—
226C2×C4C2×C22⋊#59511yescharacteristic
227C8—41no—
228C8—681no—
229C22—42no—
230C22—82no—
231C22—2722no—
232C22—171no—
233C22—171no—
234C22—342no—
235C22—682no—
236C22—1362no—
237C22—1364no—
238C22D17⋊#9911yescharacteristic
239C4—21no—
240C4—41no—
241C4—81no—
242C4—2722no—
243C4—2722no—
244C4—341no—
245C4—681no—
246C4—1361no—
247C2—21no—
248C2—82no—
249C2—172no—
250C2—341no—
251C2—1362no—
252C2D17⋊#35411yescharacteristic
subgroupG/H
centerC2D17⋊#354
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC17×#490C4
socleC2×C17C2×#354
prime radical#127×D17C22
cosocle#10587560C23
hypercenter#490#595
hypocenterC17C2×#1412
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #14543925C2semidirect
3. #14543924C2semidirect
4. #14543923C2semidirect
11. #125×D17C4semidirect
14. #11763173C4semidirect
17. #97×D17C4semidirect
18. C17×#490C4semidirect
23. C17×#125C2×C4semidirect
33. #10587556C2×C4semidirect
38. C17×#97C2×C4semidirect
43. #10587474C2×C4semidirect
132. #490#595semidirect
144. D17#1412semidirect
155. #125C2×#595semidirect
169. #97C2×#595semidirect
170. C17C2×#1412semidirect

Maximal subgroups

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

subgroupindex
D17⋊#3532
#145439252
#145439242
#145439232
D17×#4902
C2×#141217