Finite Group Databasebeta

← #17952546

Subgroups — #17952546

Order 4352.

826 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 826 conjugacy classes of subgroups — too many to draw. Only its 120 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#14544511C212yesmaximal
2C2×#11763666C214yesmaximal, complemented
3C2×#125×D17C211yesmaximal, characteristic
4C2×#10587543—22no—
5C2×#10587542C2214yes—
6#11763675—22no—
7#11763666—28no—
8C2×#10587556C411yescharacteristic
9C2×#10587576C2212yes—
10C2×#10587575—22no—
11#125×D17—28no—
12C2×C4⋊C4×D17—22no—
13C2×C4⋊C4×D17C412yes—
14C2×C42×D17C2211yescharacteristic
15C2×C17×#125C411yescharacteristic
16C22×C4×D17—22no—
17C22×C4×D17C2×C411yescharacteristic
18C22×C4×D17D412yes—
19C22×#3624—24no—
20C17×#125—24no—
21C2×C4⋊C4×C17—22no—
22C2×C4⋊C4×C17C2×C412yes—
23C2×C42×C17C2×C411yescharacteristic
24C2×C4⋊Dic17—22no—
25C2×C4⋊Dic17C2×C412yes—
26C2×#63225—22no—
27C2×#63225—22no—
28C2×#63225—22no—
29C2×C4×Dic17D412yes—
30C2×C4×Dic17C2311yescharacteristic
31C4⋊C4×D17—216no—
32C4⋊C4×D17—24no—
33C4⋊C4×D17—24no—
34#10587576—24no—
35#10587576D418yes—
36#10587575—216no—
37C42×D17—24no—
38#10587556—24no—
39#10587543—28no—
40#10587542—28no—
41C23×D17C22⋊C411yescharacteristic
42C22×C4×C17—22no—
43C22×C4×C17C22⋊C412yes—
44C22×C4×C17C22×C411yescharacteristic
45C22×Dic17—22no—
46C22×Dic17C22⋊C411yescharacteristic
47C22×Dic17C2×D412yes—
48C2×C4×D17—22no—
49C2×C4×D17—22no—
50C2×C4×D17—22no—
51C2×C4×D17—28no—
52C2×C4×D17—24no—
53C2×C4×D17—24no—
54C2×C4×D17—42no—
55C2×C4×D17—44no—
56C2×C4×D17—44no—
57C2×#3624—28no—
58C2×#3624—44no—
59C2×#3624—44no—
60C4⋊C4×C17—28no—
61C4⋊C4×C17—22no—
62C4⋊C4×C17C22⋊C414yes—
63C42×C17—22no—
64C4⋊Dic17—22no—
65C4⋊Dic17—28no—
66C4⋊Dic17C22⋊C414yes—
67#63225—28no—
68#63225—28no—
69#63225—28no—
70C4×Dic17—24no—
71C4×Dic17C2×D414yes—
72#8335—171nomaximal, Sylow
73C23×C17C2×C22⋊C411yescharacteristic
74C22×D17—21no—
75C22×D17—21no—
76C22×D17—22no—
77C22×D17#10112yes—
78C22×D17#10414yes—
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17—22no—
82C2×C4×C17—24no—
83C2×C4×C17—22no—
84C2×C4×C17—22no—
85C2×C4×C17—42no—
86C2×C4×C17—42no—
87C2×C4×C17C2×C22⋊C412yes—
88C2×Dic17—21no—
89C2×Dic17—21no—
90C2×Dic17—22no—
91C2×Dic17—22no—
92C2×Dic17—24no—
93C2×Dic17—42no—
94C2×Dic17—42no—
95C2×Dic17#10112yes—
96C2×Dic17#12014yes—
97C4×D17—28no—
98C4×D17—48no—
99C4×D17—416no—
100#3624—48no—
101C22×#125—171no—
102#1749—172no—
103C2×#330—174no—
104C22×C17#37911yescharacteristic
105C22×C17C2×#10111yescharacteristic
106C22×C17C2×#10111yescharacteristic
107C22×C17C2×#10412yes—
108C22×C17#42112yes—
109C2×D17—24no—
110C2×D17—22no—
111C2×D17—24no—
112C2×D17—22no—
113C2×D17#33014yescomplemented
114C4×C17—22no—
115C4×C17—42no—
116C4×C17—44no—
117Dic17—22no—
118Dic17—24no—
119Dic17—44no—
120C2×#125—172no—
121C2×#125—171no—
122C2×#125—342no—
123C2×#125—348no—
124C2×#125#59511yescharacteristic
125C22×C4⋊C4—172no—
126C22×C4⋊C4—342no—
127C22×C42—171no—
128C2×C22⋊C8—342no—
129C2×#97—174no—
130#336—342no—
131#330—348no—
132C2×C17C2×#33011yescharacteristic
133C2×C17#152812yes—
134C2×C17#153411yescharacteristic
135C2×C17#178411yescharacteristic
136C2×C17#178912yes—
137D17—24no—
138C23×C4—171no—
139C23×C4—172no—
140C23×C4—342no—
141C22×C8—344no—
142#125—24no—
143#125—178no—
144#125—344no—
145#125—344no—
146#125—3416no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—172no—
149C2×C4⋊C4—344no—
150C2×C4⋊C4—3416no—
151C2×C4⋊C4—342no—
152C2×C4⋊C4—342no—
153C2×C4⋊C4—342no—
154C2×C4⋊C4—342no—
155C2×C4⋊C4—344no—
156C2×C4⋊C4C2×#59512yes—
157C2×C42—171no—
158C2×C42—172no—
159C2×C42—344no—
160C2×C42C2×#59511yescharacteristic
161C22⋊C8—348no—
162#97—348no—
163C17#833511yescharacteristic, complemented, Sylow
164C24—171no—
165C22×C4—22no—
166C22×C4—171no—
167C22×C4—172no—
168C22×C4—342no—
169C22×C4—344no—
170C22×C4—342no—
171C22×C4—344no—
172C22×C4—348no—
173C22×C4—342no—
174C22×C4—342no—
175C22×C4—682no—
176C22×C4—684no—
177C22×C4—684no—
178C22×C4C22⋊#59512yes—
179C22×C4C22×#59511yescharacteristic
180C2×C8—348no—
181C2×C8—684no—
182C2×C8—684no—
183C4⋊C4—28no—
184C4⋊C4—22no—
185C4⋊C4—174no—
186C4⋊C4—348no—
187C4⋊C4—348no—
188C4⋊C4—348no—
189C4⋊C4—348no—
190C4⋊C4—342no—
191C4⋊C4C22⋊#59514yes—
192C42—22no—
193C42—174no—
194C42—344no—
195C23—172no—
196C23—174no—
197C23—341no—
198C23—341no—
199C23—342no—
200C23C2×C22⋊#59511yescharacteristic
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—24no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—174no—
210C2×C4—172no—
211C2×C4—348no—
212C2×C4—341no—
213C2×C4—341no—
214C2×C4—342no—
215C2×C4—342no—
216C2×C4—344no—
217C2×C4—688no—
218C2×C4—6816no—
219C2×C4—682no—
220C2×C4—682no—
221C2×C4C2×C22⋊#59512yes—
222C8—688no—
223C22—174no—
224C22—344no—
225C22—342no—
226C22—342no—
227C22—344no—
228C22#1176375011yescharacteristic
229C22D17⋊#10111yescharacteristic
230C22D17⋊#10111yescharacteristic
231C22D17⋊#10412yes—
232C22#1176380612yes—
233C4—22no—
234C4—42no—
235C4—44no—
236C4—342no—
237C4—344no—
238C4—684no—
239C2—344no—
240C2D17⋊#33011yescharacteristic
241C2#1454424712yes—
242C2#1454426711yescharacteristic
243C2#1454461911yescharacteristic
244C2#1454462612yes—
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×#125C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×#125#595
hypocenterC17#8335
LCSG ▷ C22×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. C2×#11763666C2semidirect
113. C2×D17#330semidirect
163. C17#8335semidirect

Maximal subgroups

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

subgroupindex
#145445112
C2×#117636662
C2×#125×D172
#833517