Finite Group Databasebeta

← #17950007

Subgroups — #17950007

Order 4352.

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

normal subgroups only

This group has 426 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#14544701C211yesmaximal, characteristic
2C4×#10587544C211yesmaximal, characteristic
3#14543603C214yesmaximal
4#14537145C211yesmaximal, characteristic
5C2×#10587544—21no—
6C2×C4⋊#3624—21no—
7C2×C4×#3624—21no—
8#11763675—21no—
9#11763675C2212yes—
10#11763675C2212yes—
11C2×#10587576—21no—
12#11762708—21no—
13#11762708C412yes—
14#11762705—21no—
15#11762705C2212yes—
16#11762679C411yescharacteristic
17#11762674—21no—
18C42×Dic17C2211yescharacteristic
19C17×#384C411yescharacteristic
20C22×#3624—22no—
21C22×#3624—22no—
22C2×C4⋊C4×C17—21no—
23C2×C4⋊C4×C17—21no—
24C2×C4⋊C4×C17C2×C412yes—
25C2×C42×C17C2×C411yescharacteristic
26C2×C4⋊Dic17—21no—
27C2×C4⋊Dic17—21no—
28C2×C4⋊Dic17—22no—
29C2×C4⋊Dic17C2×C412yes—
30C2×#63225—22no—
31C2×C4×Dic17C2×C411yescharacteristic
32C2×C4×Dic17D411yescharacteristic
33C2×C4×Dic17D411yescharacteristic
34C2×C4×Dic17D411yescharacteristic
35C2×C4×Dic17D411yescharacteristic
36C2×C4×Dic17C2311yescharacteristic
37#10587576—42no—
38#10587576—42no—
39#10587544—24no—
40C4⋊#3624—42no—
41C4×#3624—42no—
42#10587502—22no—
43#10587502—22no—
44C22×C4×C17—22no—
45C22×C4×C17C22⋊C411yescharacteristic
46C22×C4×C17C22⋊C411yescharacteristic
47C22×C4×C17C22×C411yescharacteristic
48C22×Dic17—22no—
49C22×Dic17C22⋊C411yescharacteristic
50C22×Dic17C22⋊C411yescharacteristic
51C22×Dic17C2×D411yescharacteristic
52C22×Dic17C2×D411yescharacteristic
53C2×#3624—24no—
54C2×#3624—42no—
55C2×#3624—42no—
56C2×#3624—42no—
57C2×#3624—42no—
58C2×#3624—42no—
59C4⋊C4×C17—42no—
60C4⋊C4×C17—42no—
61C4⋊C4×C17—42no—
62C42×C17—22no—
63C4⋊Dic17—24no—
64C4⋊Dic17—42no—
65C4⋊Dic17—42no—
66C4⋊Dic17—44no—
67#63225—42no—
68#63225—42no—
69C4×Dic17—22no—
70C4×Dic17—22no—
71C4×Dic17—41no—
72C4×Dic17—41no—
73C4×Dic17D812yes—
74C4×Dic17SD1612yes—
75C4×Dic17SD1612yes—
76C4×Dic17Q1612yes—
77#7663—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—42no—
84C2×C4×C17—42no—
85C2×C4×C17—42no—
86C2×C4×C17#10112yes—
87C2×C4×C17#10212yes—
88C2×C4×C17#10312yes—
89C2×C4×C17#10412yes—
90C2×C4×C17#13112yes—
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—42no—
100C2×Dic17—42no—
101C2×Dic17—42no—
102C2×Dic17#10212yes—
103C2×Dic17#10312yes—
104C2×Dic17C2×D811yescharacteristic
105C2×Dic17C2×SD1611yescharacteristic
106C2×Dic17C2×SD1611yescharacteristic
107C2×Dic17C2×Q1611yescharacteristic
108#3624—44no—
109#3624—82no—
110#2859—171no—
111#1831—171no—
112C4×C4⋊C8—171no—
113#1271—174no—
114C22×C17#40811yescharacteristic
115C22×C17#41011yescharacteristic
116C22×C17C2×#10111yescharacteristic
117C22×C17C2×#10211yescharacteristic
118C22×C17C2×#10311yescharacteristic
119C22×C17C2×#10411yescharacteristic
120C22×C17#42111yescharacteristic
121C4×C17—22no—
122C4×C17—22no—
123C4×C17—82no—
124C4×C17#33214yes—
125Dic17—22no—
126Dic17—22no—
127Dic17—21no—
128Dic17—21no—
129Dic17—21no—
130Dic17—21no—
131Dic17—82no—
132C2×#125—341no—
133C2×C4⋊C8—341no—
134C2×C4⋊C8—341no—
135C2×C4×C8—341no—
136#389—172no—
137#389—172no—
138#389—341no—
139#389—341no—
140#384—171no—
141#384#59511yescharacteristic
142#382—341no—
143C43—171no—
144#336—172no—
145#336—172no—
146#336—341no—
147C2×C17#147011yescharacteristic
148C2×C17#148011yescharacteristic
149C2×C17#149311yescharacteristic
150C2×C17#150211yescharacteristic
151C2×C17#151811yescharacteristic
152C2×C17#152811yescharacteristic
153C2×C17C2×#33211yescharacteristic
154C22×C8—342no—
155C22×C8—342no—
156#125—682no—
157#125—682no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—172no—
161C2×C4⋊C4—342no—
162C2×C4⋊C4—342no—
163C2×C4⋊C4—341no—
164C2×C4⋊C4—341no—
165C2×C4⋊C4C2×#59512yes—
166C2×C42—171no—
167C2×C42—171no—
168C2×C42—171no—
169C2×C42—171no—
170C2×C42—171no—
171C2×C42—171no—
172C2×C42C2×#59511yescharacteristic
173C4⋊C8—344no—
174C4⋊C8—682no—
175C4×C8—682no—
176#95—342no—
177#95—342no—
178C17#766311yescharacteristic, complemented, Sylow
179C22×C4—22no—
180C22×C4—171no—
181C22×C4—171no—
182C22×C4—171no—
183C22×C4—171no—
184C22×C4—342no—
185C22×C4C22⋊#59511yescharacteristic
186C22×C4C22⋊#59511yescharacteristic
187C22×C4C22×#59511yescharacteristic
188C2×C8—344no—
189C2×C8—682no—
190C2×C8—682no—
191C2×C8—682no—
192C2×C8—682no—
193C2×C8—682no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—344no—
198C4⋊C4—682no—
199C4⋊C4—682no—
200C4⋊C4—682no—
201C4⋊C4—684no—
202C4⋊C4—682no—
203C42—22no—
204C42—172no—
205C42—172no—
206C42—172no—
207C42—172no—
208C42—342no—
209C42—342no—
210C42—681no—
211C42—681no—
212C23C2×C22⋊#59511yescharacteristic
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—171no—
221C2×C4—172no—
222C2×C4—171no—
223C2×C4—171no—
224C2×C4—172no—
225C2×C4—171no—
226C2×C4—341no—
227C2×C4—341no—
228C2×C4—341no—
229C2×C4—341no—
230C2×C4—341no—
231C2×C4—341no—
232C2×C4—341no—
233C2×C4—341no—
234C2×C4—682no—
235C2×C4—682no—
236C2×C4—682no—
237C2×C4#1058754512yes—
238C2×C4#1058754712yes—
239C2×C4#1058754812yes—
240C2×C4#1058754912yes—
241C2×C4#1058768012yes—
242C8—684no—
243C8—1362no—
244C22#1176378411yescharacteristic
245C22#1176378911yescharacteristic
246C22C2×#1058754511yescharacteristic
247C22C2×#1058754711yescharacteristic
248C22C2×#1058754911yescharacteristic
249C22C2×#1058754811yescharacteristic
250C22#1176380811yescharacteristic
251C4—22no—
252C4—22no—
253C4—82no—
254C4—342no—
255C4—341no—
256C4—341no—
257C4—341no—
258C4—341no—
259C4—342no—
260C4—1362no—
261C4#1176366814yes—
262C2#1454405811yescharacteristic
263C2#1454409111yescharacteristic
264C2#1454413411yescharacteristic
265C2#1454416411yescharacteristic
266C2#1454421811yescharacteristic
267C2#1454424611yescharacteristic
268C2C2×#1176366811yescharacteristic
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#7663
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
178. C17#7663semidirect

Maximal subgroups

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

subgroupindex
#145447012
C4×#105875442
#145436032
#145371452
#766317