Finite Group Databasebeta

← C2×D17⋊#330 #17965728

Subgroups — C2×D17⋊#330 #17965728

Order 4352.

1158 conjugacy classes of subgroups; only the 272 normal subgroups are shown.

normal subgroups only

This group has 1158 conjugacy classes of subgroups — too many to draw. Only its 272 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
1C2×#11763768C212yesmaximal
2D17⋊#330C218yesmaximal, direct product factor
3C2×#11763666C214yesmaximal, complemented
4C2×#125×D17C211yesmaximal, characteristic
5C22×#63242—22no—
6#11763768—24no—
7#11763768C2218yes—
8C2×#10587542—22no—
9C2×#10587542C2214yes—
10#11763666C22116yescomplemented
11C2×#10587556C411yescharacteristic
12C2×#10587576C2212yes—
13C2×#10587575—22no—
14#125×D17—24no—
15#125×D17C414yes—
16#125×D17C2214yes—
17C2×C4⋊C4×D17—22no—
18C2×C4⋊C4×D17C412yes—
19C2×C42×D17C2211yescharacteristic
20C2×C17×#125C411yescharacteristic
21C22×C4×D17—22no—
22C22×C4×D17C2×C411yescharacteristic
23C22×C4×D17D412yes—
24C22×#3624—24no—
25C2×#63242—216no—
26C2×#63242—28no—
27C17×#125—22no—
28C17×#125C2×C414yes—
29C2×C4⋊C4×C17—22no—
30C2×C4⋊C4×C17C2×C412yes—
31C2×C42×C17C2×C411yescharacteristic
32C2×C4⋊Dic17—22no—
33C2×C4⋊Dic17C2×C412yes—
34C2×#63225—22no—
35C2×#63225—22no—
36C2×#63225—22no—
37C2×C4×Dic17D412yes—
38C2×C4×Dic17C2311yescharacteristic
39C4⋊C4×D17—28no—
40C4⋊C4×D17—24no—
41C4⋊C4×D17—28no—
42C4⋊C4×D17C2×C418yes—
43#10587576—22no—
44#10587576—22no—
45#10587576C2×C414yes—
46#10587576C2314yes—
47#10587575—28no—
48#10587575—28no—
49C42×D17C2×C412yes—
50C42×D17D414yes—
51C42×D17C2312yes—
52#10587556—22no—
53#10587556C2×C414yes—
54#10587542—28no—
55#10587542—24no—
56#10587542C2318yes—
57C23×D17C22⋊C411yescharacteristic
58C22×C4×C17—22no—
59C22×C4×C17C22⋊C412yes—
60C22×C4×C17C22×C411yescharacteristic
61C22×Dic17—22no—
62C22×Dic17C22⋊C411yescharacteristic
63C22×Dic17C2×D412yes—
64C2×C4×D17—24no—
65C2×C4×D17—28no—
66C2×C4×D17—28no—
67C2×C4×D17—48no—
68C2×C4×D17C22⋊C412yes—
69C2×C4×D17C22⋊C414yes—
70C2×C4×D17C22×C412yes—
71C2×C4×D17C2×D414yes—
72C2×#3624—216no—
73C2×#3624—28no—
74#63242—232no—
75C4⋊C4×C17—22no—
76C4⋊C4×C17—28no—
77C4⋊C4×C17C22×C414yes—
78C42×C17C22⋊C412yes—
79C42×C17C22×C412yes—
80C4⋊Dic17—22no—
81C4⋊Dic17—24no—
82C4⋊Dic17—24no—
83C4⋊Dic17C22×C414yes—
84#63225—28no—
85#63225—28no—
86#63225—24no—
87#63225—24no—
88C4×Dic17C22⋊C414yes—
89C4×Dic17C22×C411yescharacteristic
90C4×Dic17C2×D412yes—
91C4×Dic17C2×D414yes—
92C4×Dic17C2411yescharacteristic
93C22×#330—171nomaximal, Sylow
94C23×C17C2×C22⋊C411yescharacteristic
95C22×D17#10114yes—
96C22×D17#10418yes—
97C22×D17C2×C22⋊C412yes—
98C2×C4×C17—22no—
99C2×C4×C17—24no—
100C2×C4×C17—24no—
101C2×C4×C17—44no—
102C2×C4×C17C2×C22⋊C411yescharacteristic
103C2×C4×C17C2×C22⋊C414yes—
104C2×C4×C17C23×C411yescharacteristic
105C2×Dic17—22no—
106C2×Dic17—24no—
107C2×Dic17—24no—
108C2×Dic17—44no—
109C2×Dic17C2×C22⋊C412yes—
110C2×Dic17C2×C22⋊C412yes—
111C2×Dic17C22×D412yes—
112C4×D17—24no—
113C4×D17—24no—
114C4×D17—28no—
115C4×D17—28no—
116C4×D17—416no—
117#3624—216no—
118C22×#125—171no—
119C22×#97—172no—
120C2×#330—174no—
121C2×#330—178no—
122C22×C17C2×#10112yes—
123C22×C17C2×#10414yes—
124C22×C17C22×C22⋊C411yescharacteristic
125C2×D17#330116yescomplemented
126C2×D17C2×#10114yes—
127C2×D17C2×#10418yes—
128C4×C17—21no—
129C4×C17—21no—
130C4×C17—24no—
131C4×C17—44no—
132Dic17—22no—
133Dic17—22no—
134Dic17—22no—
135Dic17—44no—
136C23×C8—342no—
137C2×#125—174no—
138C2×#125—174no—
139C2×#125—172no—
140C2×#125—171no—
141C2×#125—342no—
142C2×#125—344no—
143C2×#125#59511yescharacteristic
144C22×C4⋊C4—172no—
145C22×C4⋊C4—342no—
146C22×C42—171no—
147C2×#97—174no—
148C2×#97—178no—
149C2×#97—342no—
150C2×#97—344no—
151#330—1716no—
152C2×C17C2×#33014yescomplemented
153C2×C17C22×#10111yescharacteristic
154C2×C17C22×#10412yes—
155D17C2×#33018yescomplemented
156C23×C4—172no—
157C23×C4—171no—
158C23×C4—342no—
159C22×C8—348no—
160C22×C8—344no—
161C22×C8—3416no—
162#125—22no—
163#125—174no—
164#125—174no—
165#125—174no—
166#125—348no—
167#125—348no—
168#125—342no—
169#125—342no—
170#125—342no—
171#125C2×#59514yes—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—172no—
174C2×C4⋊C4—178no—
175C2×C4⋊C4—344no—
176C2×C4⋊C4—348no—
177C2×C4⋊C4—348no—
178C2×C4⋊C4—342no—
179C2×C4⋊C4—342no—
180C2×C4⋊C4—342no—
181C2×C4⋊C4—342no—
182C2×C4⋊C4C2×#59512yes—
183C2×C42—172no—
184C2×C42—171no—
185C2×C42—174no—
186C2×C42—172no—
187C2×C42—172no—
188C2×C42C2×#59511yescharacteristic
189#97—178no—
190#97—344no—
191#97—348no—
192C17C22×#33011yescharacteristic, complemented, Sylow
193C24—171no—
194C22×C4—22no—
195C22×C4—171no—
196C22×C4—172no—
197C22×C4—172no—
198C22×C4—174no—
199C22×C4—174no—
200C22×C4—172no—
201C22×C4—348no—
202C22×C4—344no—
203C22×C4—348no—
204C22×C4—342no—
205C22×C4—688no—
206C22×C4C22⋊#59512yes—
207C22×C4C22×#59511yescharacteristic
208C2×C8—348no—
209C2×C8—3432no—
210C2×C8—3416no—
211C4⋊C4—28no—
212C4⋊C4—22no—
213C4⋊C4—174no—
214C4⋊C4—348no—
215C4⋊C4—344no—
216C4⋊C4—344no—
217C4⋊C4—344no—
218C4⋊C4—344no—
219C4⋊C4—342no—
220C4⋊C4—348no—
221C4⋊C4C22×#59514yes—
222C42—172no—
223C42—174no—
224C42—174no—
225C42—171no—
226C42—171no—
227C42C22⋊#59512yes—
228C42C22×#59512yes—
229C23—174no—
230C23—178no—
231C23—172no—
232C23C2×C22⋊#59511yescharacteristic
233C2×C4—22no—
234C2×C4—24no—
235C2×C4—24no—
236C2×C4—44no—
237C2×C4—172no—
238C2×C4—172no—
239C2×C4—172no—
240C2×C4—348no—
241C2×C4—348no—
242C2×C4—344no—
243C2×C4—344no—
244C2×C4—342no—
245C2×C4—344no—
246C2×C4—344no—
247C2×C4—6816no—
248C2×C4—684no—
249C2×C4C2×C22⋊#59511yescharacteristic
250C2×C4C2×C22⋊#59514yes—
251C2×C4C23×#59511yescharacteristic
252C8—3416no—
253C22—178no—
254C22—1716no—
255C22—174no—
256C22D17⋊#10112yes—
257C22D17⋊#10414yes—
258C22C22×C22⋊#59511yescharacteristic
259C4—24no—
260C4—21no—
261C4—21no—
262C4—44no—
263C4—342no—
264C4—342no—
265C4—342no—
266C4—684no—
267C2—178no—
268C2D17⋊#33014yesdirect product factor
269C2C2×D17⋊#10111yescharacteristic
270C2C2×D17⋊#10412yes—
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC2×C17×#125C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC4×Dic17C24
hypercenterC2×#125#595
hypocenterC17C22×#330
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. D17⋊#330C2direct (N × H)
3. C2×#11763666C2semidirect
10. #11763666C22semidirect
125. C2×D17#330semidirect
152. C2×C17C2×#330semidirect
155. D17C2×#330semidirect
192. C17C22×#330semidirect
268. C2D17⋊#330direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117637682
D17⋊#3302
C2×#117636662
C2×#125×D172
C22×#33017