Finite Group Databasebeta

← #17956531

Subgroups — #17956531

Order 4352.

424 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 102 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#14544569C211yesmaximal, characteristic
2#14544501C211yesmaximal, characteristic
3#14543660C214yesmaximal
4#14537145C211yesmaximal, characteristic
5C2×#10587544—21no—
6C2×#10587542C2212yes—
7C2×#10587542C2212yes—
8#11763675—21no—
9#11763675—21no—
10#11763675—21no—
11C2×#10587576C412yes—
12#11762708—21no—
13#11762708—21no—
14#11762705—21no—
15#11762705—21no—
16#11762679C411yescharacteristic
17#11762674C2212yes—
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#10587544—24no—
39#10587542—22no—
40#10587542—24no—
41#10587542Q814yes—
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—44no—
64C4⋊Dic17—42no—
65C4⋊Dic17—42no—
66C4⋊Dic17—42no—
67#63225—44no—
68C4×Dic17—22no—
69C4×Dic17—22no—
70C4×Dic17—41no—
71C4×Dic17—41no—
72C4×Dic17—41no—
73C4×Dic17C2×Q812yes—
74C4×Dic17#4112yes—
75#9894—171nomaximal, Sylow
76C23×C17C2×C22⋊C411yescharacteristic
77C2×C4×C17—21no—
78C2×C4×C17—21no—
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#10412yes—
88C2×C4×C17C4×Q812yes—
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—21no—
98C2×Dic17—42no—
99C2×Dic17—42no—
100C2×Dic17—42no—
101C2×Dic17#10012yes—
102C2×Dic17C22⋊Q812yes—
103C2×Dic17#12411yescharacteristic
104C2×Dic17C4⋊Q811yescharacteristic
105#3624—44no—
106#3624—44no—
107#2859—171no—
108#1767—171no—
109#1745—171no—
110#1295—174no—
111C22×C17#39111yescharacteristic
112C22×C17C2×#10011yescharacteristic
113C22×C17C2×#10111yescharacteristic
114C22×C17C2×#10411yescharacteristic
115C22×C17#42111yescharacteristic
116C22×C17#42111yescharacteristic
117C22×C17#42111yescharacteristic
118C4×C17—22no—
119C4×C17—22no—
120C4×C17—22no—
121C4×C17—82no—
122Dic17—21no—
123Dic17—21no—
124Dic17—22no—
125Dic17—22no—
126Dic17—41no—
127Dic17—82no—
128C2×#125—172no—
129C2×C4⋊C8—341no—
130C2×#97—172no—
131C2×#97—172no—
132#389—341no—
133#389—341no—
134#389—341no—
135#389—341no—
136#384—171no—
137#384#59511yescharacteristic
138#382—172no—
139C43—171no—
140#336—341no—
141#336—341no—
142#336—341no—
143C2×C17#152811yescharacteristic
144C2×C17#153011yescharacteristic
145C2×C17#153411yescharacteristic
146C2×C17#153611yescharacteristic
147C2×C17#198611yescharacteristic
148C2×C17#199511yescharacteristic
149C2×C17#199711yescharacteristic
150C22×C8—342no—
151C22×C8—342no—
152#125—684no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—172no—
156C2×C4⋊C4—342no—
157C2×C4⋊C4—342no—
158C2×C4⋊C4—341no—
159C2×C4⋊C4—341no—
160C2×C4⋊C4C2×#59512yes—
161C2×C42—171no—
162C2×C42—171no—
163C2×C42—171no—
164C2×C42—171no—
165C2×C42—171no—
166C2×C42—171no—
167C2×C42C2×#59511yescharacteristic
168C4⋊C8—344no—
169#97—174no—
170#97—342no—
171#97—344no—
172#95—342no—
173#95—342no—
174C17#989411yescharacteristic, complemented, Sylow
175C22×C4—22no—
176C22×C4—171no—
177C22×C4—171no—
178C22×C4—171no—
179C22×C4—171no—
180C22×C4—342no—
181C22×C4C22⋊#59511yescharacteristic
182C22×C4C22⋊#59511yescharacteristic
183C22×C4C22×#59511yescharacteristic
184C2×C8—344no—
185C2×C8—344no—
186C2×C8—682no—
187C2×C8—682no—
188C2×C8—682no—
189C2×C8—682no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—682no—
194C4⋊C4—682no—
195C4⋊C4—682no—
196C4⋊C4—684no—
197C4⋊C4—684no—
198C42—22no—
199C42—172no—
200C42—172no—
201C42—342no—
202C42—342no—
203C42—681no—
204C42—681no—
205C42—681no—
206C23C2×C22⋊#59511yescharacteristic
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—172no—
217C2×C4—171no—
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#1058754812yes—
234C2×C4Q8×#59512yes—
235C8—684no—
236C8—684no—
237C22(C2×#595)⋊Q811yescharacteristic
238C22D17⋊#10011yescharacteristic
239C22C2×#1058754511yescharacteristic
240C22C2×#1058754811yescharacteristic
241C22#1176380711yescharacteristic
242C22#1176380811yescharacteristic
243C22#1176380811yescharacteristic
244C4—22no—
245C4—22no—
246C4—22no—
247C4—82no—
248C4—341no—
249C4—341no—
250C4—342no—
251C4—342no—
252C4—681no—
253C4—1362no—
254C2#1454424611yescharacteristic
255C2#1454425411yescharacteristic
256C2#1454426611yescharacteristic
257C2#1454427411yescharacteristic
258C2#1454496011yescharacteristic
259C2#1454497211yescharacteristic
260C2#1454497711yescharacteristic
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#9894
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
174. C17#9894semidirect

Maximal subgroups

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

subgroupindex
#145445692
#145445012
#145436602
#145371452
#989417