Finite Group Databasebeta

← #17950069

Subgroups — #17950069

Order 4352.

432 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 114 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#14544570C211yesmaximal, characteristic
2#14544499C211yesmaximal, characteristic
3#14543603C214yesmaximal
4#14537145C211yesmaximal, characteristic
5C2×C4⋊#3624—21no—
6C2×#10587542—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#10587542—42no—
40C4⋊#3624—24no—
41C4×#3624—24no—
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—24no—
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—22no—
72C4×Dic17—22no—
73C4×Dic17—41no—
74C4×Dic17D812yes—
75C4×Dic17SD1612yes—
76#7680—171nomaximal, Sylow
77C23×C17C2×C22⋊C411yescharacteristic
78C2×C4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17—21no—
82C2×C4×C17—42no—
83C2×C4×C17—42no—
84C2×C4×C17—42no—
85C2×C4×C17#10112yes—
86C2×C4×C17#10212yes—
87C2×C4×C17#10412yes—
88C2×C4×C17#10412yes—
89C2×C4×C17#13112yes—
90C2×Dic17—21no—
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×Dic17C2×D811yescharacteristic
104C2×Dic17C2×SD1611yescharacteristic
105C2×Dic17#13712yes—
106#3624—44no—
107#3624—44no—
108#2859—171no—
109#1767—171no—
110#1744—171no—
111#1271—174no—
112C22×C17#40811yescharacteristic
113C22×C17#41011yescharacteristic
114C22×C17C2×#10111yescharacteristic
115C22×C17C2×#10211yescharacteristic
116C22×C17#41911yescharacteristic
117C22×C17C2×#10411yescharacteristic
118C22×C17C2×#10411yescharacteristic
119C4×C17—22no—
120C4×C17—22no—
121C4×C17—82no—
122C4×C17#33014yes—
123Dic17—22no—
124Dic17—21no—
125Dic17—21no—
126Dic17—22no—
127Dic17—41no—
128Dic17—82no—
129C2×#125—341no—
130C2×C4⋊C8—341no—
131C2×#97—341no—
132C2×C4×C8—341no—
133#389—172no—
134#389—172no—
135#389—341no—
136#389—341no—
137#384—171no—
138#384#59511yescharacteristic
139#382—341no—
140C43—171no—
141#336—172no—
142#336—172no—
143#336—341no—
144C2×C17#147011yescharacteristic
145C2×C17#148511yescharacteristic
146C2×C17#149211yescharacteristic
147C2×C17#150211yescharacteristic
148C2×C17#150611yescharacteristic
149C2×C17C2×#33011yescharacteristic
150C2×C17#154611yescharacteristic
151C22×C8—342no—
152C22×C8—342no—
153#125—682no—
154#125—682no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—172no—
158C2×C4⋊C4—342no—
159C2×C4⋊C4—342no—
160C2×C4⋊C4—341no—
161C2×C4⋊C4—341no—
162C2×C4⋊C4C2×#59512yes—
163C2×C42—171no—
164C2×C42—171no—
165C2×C42—171no—
166C2×C42—171no—
167C2×C42—171no—
168C2×C42—171no—
169C2×C42C2×#59511yescharacteristic
170C4⋊C8—344no—
171#97—682no—
172C4×C8—344no—
173#95—342no—
174#95—342no—
175C17#768011yescharacteristic, complemented, Sylow
176C22×C4—22no—
177C22×C4—171no—
178C22×C4—171no—
179C22×C4—171no—
180C22×C4—171no—
181C22×C4—342no—
182C22×C4C22⋊#59511yescharacteristic
183C22×C4C22⋊#59511yescharacteristic
184C22×C4C22×#59511yescharacteristic
185C2×C8—344no—
186C2×C8—344no—
187C2×C8—682no—
188C2×C8—682no—
189C2×C8—682no—
190C2×C8—682no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—344no—
195C4⋊C4—682no—
196C4⋊C4—682no—
197C4⋊C4—684no—
198C4⋊C4—682no—
199C4⋊C4—682no—
200C42—22no—
201C42—172no—
202C42—172no—
203C42—342no—
204C42—342no—
205C42—342no—
206C42—342no—
207C42—681no—
208C23C2×C22⋊#59511yescharacteristic
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—171no—
217C2×C4—172no—
218C2×C4—171no—
219C2×C4—172no—
220C2×C4—341no—
221C2×C4—341no—
222C2×C4—341no—
223C2×C4—341no—
224C2×C4—341no—
225C2×C4—341no—
226C2×C4—341no—
227C2×C4—341no—
228C2×C4—341no—
229C2×C4—682no—
230C2×C4—682no—
231C2×C4—682no—
232C2×C4#1058754512yes—
233C2×C4#1058754712yes—
234C2×C4#1058754812yes—
235C2×C4#1058755012yes—
236C2×C4#1058768012yes—
237C8—684no—
238C8—684no—
239C22#1176378411yescharacteristic
240C22#1176378911yescharacteristic
241C22C2×#1058754511yescharacteristic
242C22C2×#1058754711yescharacteristic
243C22#1176380211yescharacteristic
244C22C2×#1058754811yescharacteristic
245C22C2×#1058755011yescharacteristic
246C4—22no—
247C4—22no—
248C4—82no—
249C4—342no—
250C4—341no—
251C4—341no—
252C4—342no—
253C4—681no—
254C4—1362no—
255C4#1176366614yes—
256C2#1454405811yescharacteristic
257C2#1454410811yescharacteristic
258C2#1454413111yescharacteristic
259C2#1454416411yescharacteristic
260C2#1454417811yescharacteristic
261C2C2×#1176366611yescharacteristic
262C2#1454429311yescharacteristic
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#7680
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
175. C17#7680semidirect

Maximal subgroups

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

subgroupindex
#145445702
#145444992
#145436032
#145371452
#768017