Finite Group Databasebeta

← #17958202

Subgroups — #17958202

Order 4352.

454 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 90 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#14544013C212yesmaximal
2#14543727C212yesmaximal, complemented
3#14543724C212yesmaximal, complemented
4#14531405C211yesmaximal, characteristic
5#11763777—22no—
6#11763655—22no—
7#11763654C2214yes—
8C2×#10587578C411yescharacteristic
9C2×#10587558C411yescharacteristic
10C2×C4⋊C4×D17C2211yescharacteristic
11#11762704—22no—
12#11762680—22no—
13#11762678C2211yescharacteristic
14#11762675C2211yescharacteristic
15#11762674C411yescharacteristic
16C17×#384C411yescharacteristic
17C22×C4×D17C2×C411yescharacteristic
18C22×C4×D17D412yes—
19C2×#63242—42no—
20C2×C4⋊C4×C17—22no—
21C2×C4⋊C4×C17C2×C411yescharacteristic
22C2×C4⋊C4×C17C2×C411yescharacteristic
23C2×C42×C17C2×C411yescharacteristic
24C2×#63227—21no—
25C2×#63227—21no—
26C2×C4⋊Dic17C2×C411yescharacteristic
27C2×C4⋊Dic17C2311yescharacteristic
28C2×#63225—21no—
29C2×#63225—22no—
30C2×#63225D412yes—
31C2×C4×Dic17—21no—
32C2×C4×Dic17C2×C411yescharacteristic
33#10587578—42no—
34C4⋊C4×D17—42no—
35#10587558—22no—
36#10587558C814yescomplemented
37C22⋊#3624—24no—
38#10587543—42no—
39#10587502—22no—
40#10587502—22no—
41C23×D17C22⋊C411yescharacteristic
42C22×C4×C17—21no—
43C22×C4×C17—21no—
44C22×C4×C17C22⋊C412yes—
45C22×C4×C17C22×C411yescharacteristic
46C22×Dic17—21no—
47C22×Dic17—21no—
48C22×Dic17C22⋊C411yescharacteristic
49C22×Dic17C2×D412yes—
50C2×C4×D17—22no—
51C2×C4×D17—22no—
52C2×C4×D17—22no—
53C2×C4×D17—22no—
54C2×C4×D17—82no—
55C2×C4×D17C2×C812yes—
56C2×C4×D17M1612yes—
57C2×#3624—44no—
58#63242—84no—
59C4⋊C4×C17—41no—
60C4⋊C4×C17—41no—
61C4⋊C4×C17—82no—
62C42×C17—21no—
63C42×C17C2×C812yescomplemented
64#63227—24no—
65#63227—42no—
66C4⋊Dic17—41no—
67C4⋊Dic17—41no—
68#63225—24no—
69#63225—42no—
70#63225—82no—
71C4×Dic17—21no—
72C4×Dic17—42no—
73C4×Dic17C2×C812yescomplemented
74#11448—171nomaximal, Sylow
75C23×C17C2×C22⋊C411yescharacteristic
76C22×D17—41no—
77C22×D17—41no—
78C22×D17C22⋊C812yes—
79C22×D17#9912yes—
80C22×D17#10112yes—
81C2×C4×C17—21no—
82C2×C4×C17—21no—
83C2×C4×C17—22no—
84C2×C4×C17—22no—
85C2×C4×C17—41no—
86C2×C4×C17—41no—
87C2×C4×C17—42no—
88C2×C4×C17—42no—
89C2×C4×C17—41no—
90C2×C4×C17C22×C811yescharacteristic
91C2×C4×C17C2×M1611yescharacteristic
92C2×Dic17—21no—
93C2×Dic17—21no—
94C2×Dic17—22no—
95C2×Dic17—22no—
96C2×Dic17—41no—
97C2×Dic17—41no—
98C2×Dic17—42no—
99C2×Dic17—42no—
100C2×Dic17—41no—
101C2×Dic17C22⋊C812yes—
102C4×D17—24no—
103C4×D17—24no—
104C4×D17—44no—
105C4×D17—82no—
106#3624—84no—
107#2317—171no—
108C2×#324—172no—
109#1325—172no—
110#1324—172no—
111C22×C17—21no—
112C22×C17—21no—
113C22×C17C2×C22⋊C811yescharacteristic
114C22×C17C2×#9911yescharacteristic
115C22×C17C2×#10111yescharacteristic
116C2×D17—22no—
117C2×D17—22no—
118C2×D17—42no—
119C2×D17—42no—
120C2×D17#32414yes—
121C4×C17—21no—
122C4×C17—21no—
123C4×C17—42no—
124C4×C17—42no—
125C4×C17—81no—
126Dic17—22no—
127Dic17—42no—
128Dic17—42no—
129Dic17—81no—
130C2×#117—171no—
131C2×#117—171no—
132C22×C4⋊C4—171no—
133C2×C22⋊C8—342no—
134#389—342no—
135#385—342no—
136#384—171no—
137#384#59511yescharacteristic
138#382—171no—
139#382—171no—
140#324—174no—
141#324—342no—
142C2×C17—21no—
143C2×C17—21no—
144C2×C17C2×#32411yescharacteristic
145C2×C17#212711yescharacteristic
146C2×C17#213311yescharacteristic
147D17—24no—
148C23×C4—171no—
149C23×C4—172no—
150C22×C8—682no—
151#117—174no—
152#117—342no—
153#117—682no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—172no—
156C2×C4⋊C4—171no—
157C2×C4⋊C4—171no—
158C2×C4⋊C4—341no—
159C2×C4⋊C4—342no—
160C2×C4⋊C4—682no—
161C2×C4⋊C4C2×#59511yescharacteristic
162C2×C4⋊C4C2×#59511yescharacteristic
163C2×C22⋊C4—341no—
164C2×C22⋊C4—341no—
165C2×C42—171no—
166C2×C42—341no—
167C2×C42C2×#59511yescharacteristic
168C22⋊C8—344no—
169C22⋊C8—682no—
170#95—342no—
171#95—342no—
172C17#1144811yescharacteristic, complemented, Sylow
173C24—171no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—171no—
177C22×C4—172no—
178C22×C4—172no—
179C22×C4—172no—
180C22×C4—342no—
181C22×C4—342no—
182C22×C4—342no—
183C22×C4—342no—
184C22×C4—341no—
185C22×C4—341no—
186C22×C4—1362no—
187C22×C4C22⋊#59512yes—
188C22×C4C22×#59511yescharacteristic
189C2×C8—684no—
190C2×C8—1364no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—82no—
194C4⋊C4—344no—
195C4⋊C4—682no—
196C4⋊C4—681no—
197C4⋊C4—681no—
198C4⋊C4—1362no—
199C22⋊C4—344no—
200C22⋊C4—682no—
201C42—21no—
202C42—172no—
203C42—341no—
204C42—682no—
205C42#6324212yescomplemented
206C23—172no—
207C23—172no—
208C23—172no—
209C23—681no—
210C23—681no—
211C23C2×C22⋊#59511yescharacteristic
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—41no—
221C2×C4—172no—
222C2×C4—344no—
223C2×C4—344no—
224C2×C4—341no—
225C2×C4—341no—
226C2×C4—342no—
227C2×C4—342no—
228C2×C4—684no—
229C2×C4—681no—
230C2×C4—681no—
231C2×C4—682no—
232C2×C4—682no—
233C2×C4—681no—
234C2×C4—1362no—
235C2×C4C2×#6324211yescharacteristic
236C2×C4D17⋊M1611yescharacteristic
237C8—1364no—
238C22—21no—
239C22—21no—
240C22—174no—
241C22—342no—
242C22—342no—
243C22—682no—
244C22—682no—
245C22#1176377711yescharacteristic
246C22D17⋊#9911yescharacteristic
247C22D17⋊#10111yescharacteristic
248C4—21no—
249C4—21no—
250C4—42no—
251C4—42no—
252C4—81no—
253C4—342no—
254C4—682no—
255C4—682no—
256C4—1361no—
257C2—21no—
258C2—21no—
259C2—344no—
260C2#1454401311yescharacteristic
261C2#1454506011yescharacteristic
262C2#1454508211yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#384C4
socleC22×C17C2×#99
prime radicalC23×D17C22⋊C4
cosocleC2×C4⋊Dic17C23
hypercenter#384#595
hypocenterC17#11448
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #384

Complements

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

NH ≅ G/Ntype
2. #14543727C2semidirect
3. #14543724C2semidirect
36. #10587558C8semidirect
63. C42×C17C2×C8semidirect
73. C4×Dic17C2×C8semidirect
172. C17#11448semidirect
205. C42#63242semidirect

Maximal subgroups

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

subgroupindex
#145440132
#145437272
#145437242
#145314052
#1144817