Finite Group Databasebeta

← #17950078

Subgroups — #17950078

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#14543602C214yesmaximal
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#11762708C2212yes—
14#11762705—21no—
15#11762705C412yes—
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—44no—
38#10587542—42no—
39C4⋊#3624—24no—
40C4×#3624—24no—
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×#3624—24no—
53C2×#3624—24no—
54C2×#3624—42no—
55C2×#3624—42no—
56C2×#3624—42no—
57C2×#3624—42no—
58C4⋊C4×C17—24no—
59C4⋊C4×C17—42no—
60C4⋊C4×C17—42no—
61C42×C17—22no—
62C4⋊Dic17—42no—
63C4⋊Dic17—42no—
64C4⋊Dic17—44no—
65C4⋊Dic17—42no—
66#63225—44no—
67C4×Dic17—22no—
68C4×Dic17—22no—
69C4×Dic17—22no—
70C4×Dic17—22no—
71C4×Dic17—41no—
72C4×Dic17SD1612yes—
73C4×Dic17Q1612yes—
74#7683—171nomaximal, Sylow
75C23×C17C2×C22⋊C411yescharacteristic
76C2×C4×C17—21no—
77C2×C4×C17—21no—
78C2×C4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—42no—
81C2×C4×C17—42no—
82C2×C4×C17—42no—
83C2×C4×C17#10112yes—
84C2×C4×C17#10312yes—
85C2×C4×C17#10412yes—
86C2×C4×C17#10412yes—
87C2×C4×C17#13112yes—
88C2×Dic17—21no—
89C2×Dic17—21no—
90C2×Dic17—21no—
91C2×Dic17—21no—
92C2×Dic17—21no—
93C2×Dic17—21no—
94C2×Dic17—21no—
95C2×Dic17—21no—
96C2×Dic17—21no—
97C2×Dic17—42no—
98C2×Dic17—42no—
99C2×Dic17—42no—
100C2×Dic17#10312yes—
101C2×Dic17C2×SD1611yescharacteristic
102C2×Dic17C2×Q1611yescharacteristic
103C2×Dic17AGL(1,ℤ/8)12yes—
104#3624—44no—
105#3624—44no—
106#2859—171no—
107#1767—171no—
108#1744—171no—
109#1271—174no—
110C22×C17#40811yescharacteristic
111C22×C17#41011yescharacteristic
112C22×C17C2×#10111yescharacteristic
113C22×C17C2×#10311yescharacteristic
114C22×C17#41811yescharacteristic
115C22×C17C2×#10411yescharacteristic
116C22×C17C2×#10411yescharacteristic
117C4×C17—22no—
118C4×C17—22no—
119C4×C17—82no—
120C4×C17#33014yes—
121Dic17—22no—
122Dic17—21no—
123Dic17—21no—
124Dic17—22no—
125Dic17—41no—
126Dic17—82no—
127C2×#125—341no—
128C2×C4⋊C8—341no—
129C2×#97—341no—
130C2×C4×C8—341no—
131#389—172no—
132#389—172no—
133#389—341no—
134#389—341no—
135#384—171no—
136#384#59511yescharacteristic
137#382—341no—
138C43—171no—
139#336—172no—
140#336—172no—
141#336—341no—
142C2×C17#147011yescharacteristic
143C2×C17#148411yescharacteristic
144C2×C17#149311yescharacteristic
145C2×C17#150311yescharacteristic
146C2×C17#150511yescharacteristic
147C2×C17C2×#33011yescharacteristic
148C2×C17#154911yescharacteristic
149C22×C8—342no—
150C22×C8—342no—
151#125—684no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—172no—
155C2×C4⋊C4—342no—
156C2×C4⋊C4—342no—
157C2×C4⋊C4—341no—
158C2×C4⋊C4—341no—
159C2×C4⋊C4C2×#59512yes—
160C2×C42—171no—
161C2×C42—171no—
162C2×C42—171no—
163C2×C42—171no—
164C2×C42—171no—
165C2×C42—171no—
166C2×C42C2×#59511yescharacteristic
167C4⋊C8—344no—
168#97—682no—
169C4×C8—344no—
170#95—342no—
171#95—342no—
172C17#768311yescharacteristic, complemented, Sylow
173C22×C4—22no—
174C22×C4—171no—
175C22×C4—171no—
176C22×C4—171no—
177C22×C4—171no—
178C22×C4—342no—
179C22×C4C22⋊#59511yescharacteristic
180C22×C4C22⋊#59511yescharacteristic
181C22×C4C22×#59511yescharacteristic
182C2×C8—344no—
183C2×C8—344no—
184C2×C8—682no—
185C2×C8—682no—
186C2×C8—682no—
187C2×C8—682no—
188C4⋊C4—24no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—682no—
192C4⋊C4—682no—
193C4⋊C4—684no—
194C4⋊C4—684no—
195C4⋊C4—682no—
196C42—22no—
197C42—172no—
198C42—172no—
199C42—342no—
200C42—342no—
201C42—342no—
202C42—342no—
203C42—681no—
204C23C2×C22⋊#59511yescharacteristic
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—171no—
213C2×C4—172no—
214C2×C4—171no—
215C2×C4—172no—
216C2×C4—341no—
217C2×C4—341no—
218C2×C4—341no—
219C2×C4—341no—
220C2×C4—341no—
221C2×C4—341no—
222C2×C4—341no—
223C2×C4—341no—
224C2×C4—341no—
225C2×C4—682no—
226C2×C4—682no—
227C2×C4—682no—
228C2×C4#1058754512yes—
229C2×C4#1058754812yes—
230C2×C4#1058754912yes—
231C2×C4#1058755012yes—
232C2×C4#1058767812yes—
233C8—684no—
234C8—684no—
235C22#1176378311yescharacteristic
236C22#1176379011yescharacteristic
237C22C2×#1058754511yescharacteristic
238C22C2×#1058754911yescharacteristic
239C22#1176380111yescharacteristic
240C22C2×#1058754811yescharacteristic
241C22C2×#1058755011yescharacteristic
242C4—22no—
243C4—22no—
244C4—82no—
245C4—342no—
246C4—341no—
247C4—341no—
248C4—342no—
249C4—681no—
250C4—1362no—
251C4#1176366614yes—
252C2#1454405711yescharacteristic
253C2#1454410411yescharacteristic
254C2#1454413311yescharacteristic
255C2#1454416711yescharacteristic
256C2#1454417511yescharacteristic
257C2C2×#1176366611yescharacteristic
258C2#1454429911yescharacteristic
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#7683
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
172. C17#7683semidirect

Maximal subgroups

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

subgroupindex
#145445702
#145444992
#145436022
#145371452
#768317