Finite Group Databasebeta

← #17949865

Subgroups — #17949865

Order 4352.

462 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 104 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#14544712C211yesmaximal, characteristic
2#14544569C211yesmaximal, characteristic
3#14543603C214yesmaximal
4#14531351C211yesmaximal, characteristic
5C2×#10587544—21no—
6C2×#10587542—21no—
7#11763675—21no—
8#11763675—21no—
9#11763675C2212yes—
10#11763675C2212yes—
11C2×#10587555C411yescharacteristic
12C2×#10587573—21no—
13#11762714—21no—
14#11762705—21no—
15#11762705C2212yes—
16C4⋊C4×Dic17—21no—
17C4⋊C4×Dic17C412yes—
18C42×Dic17C2211yescharacteristic
19C17×#384C411yescharacteristic
20C22×Dic34—21no—
21C22×#3624—22no—
22C22×#3624—22no—
23C2×C4⋊C4×C17—21no—
24C2×C4⋊C4×C17—21no—
25C2×C4⋊C4×C17C2×C412yes—
26C2×C42×C17C2×C411yescharacteristic
27C2×C4⋊Dic17—21no—
28C2×C4⋊Dic17C2×C412yes—
29C2×#63225—22no—
30C2×C4×Dic17—22no—
31C2×C4×Dic17C2×C411yescharacteristic
32C2×C4×Dic17D411yescharacteristic
33C2×C4×Dic17D411yescharacteristic
34C2×C4×Dic17D411yescharacteristic
35C2×C4×Dic17D411yescharacteristic
36C2×C4×Dic17C2311yescharacteristic
37#10587573—44no—
38#10587555—24no—
39#10587544—24no—
40#10587542—42no—
41#10587502—22no—
42#10587502—22no—
43C22×C4×C17—22no—
44C22×C4×C17C22⋊C411yescharacteristic
45C22×C4×C17C22⋊C411yescharacteristic
46C22×C4×C17C22×C411yescharacteristic
47C22×Dic17—22no—
48C22×Dic17C22⋊C411yescharacteristic
49C22×Dic17C22⋊C411yescharacteristic
50C22×Dic17C2×D411yescharacteristic
51C22×Dic17C2×D411yescharacteristic
52C2×Dic34—24no—
53C2×Dic34—42no—
54C2×Dic34—42no—
55C2×#3624—24no—
56C2×#3624—42no—
57C2×#3624—42no—
58C2×#3624—42no—
59C2×#3624—42no—
60C2×#3624—42no—
61C4⋊C4×C17—42no—
62C4⋊C4×C17—42no—
63C4⋊C4×C17—42no—
64C42×C17—22no—
65C4⋊Dic17—24no—
66C4⋊Dic17—22no—
67C4⋊Dic17M1614yes—
68#63225—44no—
69C4×Dic17—22no—
70C4×Dic17—22no—
71C4×Dic17—22no—
72C4×Dic17—41no—
73C4×Dic17—41no—
74C4×Dic17—44no—
75C4×Dic17SD1612yes—
76C4×Dic17Q1612yes—
77#7622—171nomaximal, Sylow
78C23×C17C2×C22⋊C411yescharacteristic
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17—21no—
82C2×C4×C17—21no—
83C2×C4×C17—21no—
84C2×C4×C17—21no—
85C2×C4×C17—42no—
86C2×C4×C17—42no—
87C2×C4×C17—42no—
88C2×C4×C17#10312yes—
89C2×C4×C17#10412yes—
90C2×C4×C17C2×M1612yes—
91C2×Dic17—21no—
92C2×Dic17—21no—
93C2×Dic17—21no—
94C2×Dic17—21no—
95C2×Dic17—21no—
96C2×Dic17—21no—
97C2×Dic17—21no—
98C2×Dic17—21no—
99C2×Dic17—24no—
100C2×Dic17—42no—
101C2×Dic17—42no—
102C2×Dic17#10112yes—
103C2×Dic17#10312yes—
104C2×Dic17C2×SD1611yescharacteristic
105C2×Dic17C2×Q1611yescharacteristic
106C2×Dic17AGL(1,ℤ/8)12yes—
107Dic34—48no—
108#3624—44no—
109#3624—82no—
110C4×C4⋊Q8—171no—
111#1839—171no—
112#1767—171no—
113#1271—174no—
114C22×C17#40711yescharacteristic
115C22×C17#41011yescharacteristic
116C22×C17C2×#10111yescharacteristic
117C22×C17C2×#10311yescharacteristic
118C22×C17#41811yescharacteristic
119C22×C17C2×#10411yescharacteristic
120C22×C17#42111yescharacteristic
121C4×C17—22no—
122C4×C17—22no—
123C4×C17—22no—
124C4×C17—82no—
125Dic17—22no—
126Dic17—21no—
127Dic17—21no—
128Dic17—22no—
129Dic17—22no—
130Dic17—44no—
131C2×C4⋊Q8—171no—
132C2×C4×Q8—341no—
133C2×C4⋊C8—341no—
134C2×#97—341no—
135#391—341no—
136#389—172no—
137#389—341no—
138#384#59511yescharacteristic
139C4×C4⋊C4—172no—
140C4×C4⋊C4—341no—
141C43—171no—
142#336—172no—
143#336—172no—
144#336—341no—
145#336—341no—
146C2×C17#146711yescharacteristic
147C2×C17#148711yescharacteristic
148C2×C17#149011yescharacteristic
149C2×C17#150311yescharacteristic
150C2×C17#151411yescharacteristic
151C2×C17#153111yescharacteristic
152C2×C17#154911yescharacteristic
153C22×Q8—341no—
154C22×C8—342no—
155C22×C8—342no—
156C4⋊Q8—344no—
157C4×Q8—684no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—172no—
161C2×C4⋊C4—341no—
162C2×C4⋊C4—342no—
163C2×C4⋊C4C2×#59512yes—
164C2×C42—171no—
165C2×C42—171no—
166C2×C42—171no—
167C2×C42—171no—
168C2×C42—171no—
169C2×C42—171no—
170C2×C42—342no—
171C2×C42C2×#59511yescharacteristic
172C4⋊C8—344no—
173#97—682no—
174#95—342no—
175#95—342no—
176C17#762211yescharacteristic, complemented, Sylow
177C2×Q8—344no—
178C2×Q8—682no—
179C2×Q8—682no—
180C22×C4—22no—
181C22×C4—171no—
182C22×C4—171no—
183C22×C4—171no—
184C22×C4—171no—
185C22×C4—342no—
186C22×C4C22⋊#59511yescharacteristic
187C22×C4C22⋊#59511yescharacteristic
188C22×C4C22×#59511yescharacteristic
189C2×C8—344no—
190C2×C8—682no—
191C2×C8—682no—
192C2×C8—682no—
193C2×C8—682no—
194C2×C8—682no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—42no—
198C4⋊C4—174no—
199C4⋊C4—344no—
200C4⋊C4—342no—
201C4⋊C4—684no—
202C42—22no—
203C42—172no—
204C42—172no—
205C42—342no—
206C42—342no—
207C42—342no—
208C42—681no—
209C42—681no—
210C42—684no—
211C23C2×C22⋊#59511yescharacteristic
212Q8—688no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—172no—
223C2×C4—171no—
224C2×C4—172no—
225C2×C4—171no—
226C2×C4—172no—
227C2×C4—341no—
228C2×C4—341no—
229C2×C4—341no—
230C2×C4—341no—
231C2×C4—341no—
232C2×C4—341no—
233C2×C4—341no—
234C2×C4—341no—
235C2×C4—344no—
236C2×C4—682no—
237C2×C4—682no—
238C2×C4#1058754912yes—
239C2×C4#1058755012yes—
240C2×C4D17⋊M1612yes—
241C8—684no—
242C8—1362no—
243C22#1176378111yescharacteristic
244C22#1176378911yescharacteristic
245C22D17⋊#10111yescharacteristic
246C22C2×#1058754911yescharacteristic
247C22#1176380111yescharacteristic
248C22C2×#1058755011yescharacteristic
249C22#1176380711yescharacteristic
250C4—22no—
251C4—22no—
252C4—22no—
253C4—82no—
254C4—341no—
255C4—341no—
256C4—342no—
257C4—342no—
258C4—342no—
259C4—684no—
260C2#1454404811yescharacteristic
261C2#1454411411yescharacteristic
262C2#1454412511yescharacteristic
263C2#1454416811yescharacteristic
264C2#1454420411yescharacteristic
265C2#1454425811yescharacteristic
266C2#1454430011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#384C4
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#384#595
hypocenterC17#7622
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
176. C17#7622semidirect

Maximal subgroups

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

subgroupindex
#145447122
#145445692
#145436032
#145313512
#762217