Finite Group Databasebeta

← #17958318

Subgroups — #17958318

Order 4352.

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

normal subgroups only

This group has 524 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#14544020C212yesmaximal, complemented
2#14543725C212yesmaximal, complemented
3#14543713C212yesmaximal, complemented
4#14531508C211yesmaximal, characteristic
5C2×C22⋊#3624—22no—
6#11763654C2214yes—
7#11763652—22no—
8C2×#10587626C411yescharacteristic
9C2×D4×Dic17C2211yescharacteristic
10C2×#10587579C411yescharacteristic
11#11762711C2211yescharacteristic
12#11762686—22no—
13#11762685—22no—
14#11762674C2211yescharacteristic
15#11762655C411yescharacteristic
16C17×#390C411yescharacteristic
17C22×D4×C17C2×C411yescharacteristic
18C22×C22⋊D17—22no—
19C23×Dic17D412yes—
20C22×D68C2×C411yescharacteristic
21C22×C4×D17—21no—
22C22×#3624—42no—
23C2×C4⋊C4×C17C2×C411yescharacteristic
24C2×C22⋊C4×C17—22no—
25C2×C42×C17C2×C411yescharacteristic
26C2×C22⋊Dic17D412yes—
27#10587626—22no—
28#10587626C814yescomplemented
29D4×Dic17—42no—
30C2×#63227—21no—
31C2×#63227—22no—
32C2×C4⋊Dic17C2311yescharacteristic
33C2×C4×Dic17C2×C411yescharacteristic
34C2×C4×Dic17C2×C411yescharacteristic
35#10587579—42no—
36C22⋊#3624—24no—
37C22⋊#3624—42no—
38#10587502—21no—
39#10587502—21no—
40#10587502—22no—
41C24×C17C22⋊C412yes—
42C23×D17—21no—
43C2×D4×C17—41no—
44C2×D4×C17—41no—
45C2×D4×C17C2×C812yes—
46C2×D4×C17M1612yes—
47C22×C4×C17—21no—
48C22×C4×C17—21no—
49C22×C4×C17C22×C411yescharacteristic
50C2×C22⋊D17—28no—
51C2×C22⋊D17—82no—
52C2×C22⋊D17—82no—
53C22×Dic17—21no—
54C22×Dic17—22no—
55C22×Dic17—22no—
56C22×Dic17—82no—
57C22×Dic17C22⋊C411yescharacteristic
58C22×Dic17C22⋊C411yescharacteristic
59C22×Dic17C2×D412yes—
60C2×D68—21no—
61C2×D68—41no—
62C2×D68—41no—
63C2×D68C2×C812yescomplemented
64C2×C4×D17—42no—
65C2×C4×D17—82no—
66C2×#3624—44no—
67C2×#3624—84no—
68C4⋊C4×C17—41no—
69C22⋊C4×C17—82no—
70C42×C17—41no—
71C22⋊Dic17—42no—
72#63227—42no—
73#63227—82no—
74C4⋊Dic17—41no—
75C4×Dic17—21no—
76C4×Dic17—22no—
77C4×Dic17C2×C812yescomplemented
78#11479—171nomaximal, Sylow
79C23×C17—22no—
80C23×C17—22no—
81C23×C17—42no—
82C23×C17—42no—
83C23×C17C22⋊C814yes—
84C23×C17C2×C22⋊C411yescharacteristic
85C22×D17—22no—
86C22×D17—42no—
87C22×D17—42no—
88C22×D17—41no—
89C22×D17—41no—
90D4×C17—42no—
91D4×C17—42no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—41no—
95C2×C4×C17—42no—
96C2×C4×C17—41no—
97C2×C4×C17—41no—
98C2×C4×C17—41no—
99C2×C4×C17C22×C811yescharacteristic
100C2×C4×C17C2×M1611yescharacteristic
101C22⋊D17—88no—
102C2×Dic17—22no—
103C2×Dic17—21no—
104C2×Dic17—22no—
105C2×Dic17—41no—
106C2×Dic17—44no—
107C2×Dic17—41no—
108C2×Dic17—41no—
109C2×Dic17—41no—
110C2×Dic17—42no—
111C2×Dic17—82no—
112C2×Dic17#9912yes—
113D68—42no—
114D68—42no—
115C4×D17—84no—
116#3624—84no—
117#2328—171no—
118#1459—172no—
119#1324—172no—
120#1318—172no—
121C22×C17—21no—
122C22×C17—21no—
123C22×C17—24no—
124C22×C17—44no—
125C22×C17—42no—
126C22×C17—42no—
127C22×C17—82no—
128C22×C17C2×C22⋊C811yescharacteristic
129C22×C17C2×#9911yescharacteristic
130C22×C17#41311yescharacteristic
131C2×D17—44no—
132C2×D17—42no—
133C2×D17—82no—
134C2×D17—81no—
135C2×D17—81no—
136C4×C17—21no—
137C4×C17—21no—
138C4×C17—81no—
139C4×C17—81no—
140Dic17—22no—
141Dic17—42no—
142Dic17—42no—
143Dic17—41no—
144C2×#127—171no—
145C2×C4×D4—171no—
146C2×C4×D4—171no—
147C2×C22⋊C8—342no—
148#390—171no—
149#390#59511yescharacteristic
150#386—342no—
151#386—342no—
152#382—171no—
153#376—171no—
154#324—174no—
155#323—342no—
156C2×C17—21no—
157C2×C17—21no—
158C2×C17—44no—
159C2×C17#145911yescharacteristic
160C2×C17#212711yescharacteristic
161C2×C17#213411yescharacteristic
162D17—82no—
163C22×D4—171no—
164C22×D4—342no—
165C22×D4C2×#59511yescharacteristic
166C23×C4—172no—
167C23×C4—341no—
168C22×C8—682no—
169#127—174no—
170#127—342no—
171C4×D4—682no—
172C4×D4—682no—
173C2×C4⋊C4—171no—
174C2×C4⋊C4C2×#59511yescharacteristic
175C2×C22⋊C4—22no—
176C2×C22⋊C4—172no—
177C2×C22⋊C4—341no—
178C2×C22⋊C4—342no—
179C2×C42—171no—
180C2×C42—171no—
181C2×C42C2×#59511yescharacteristic
182C22⋊C8—344no—
183C22⋊C8—682no—
184#95—341no—
185#95—341no—
186#95—342no—
187C17#1147911yescharacteristic, complemented, Sylow
188C24—341no—
189C24C22⋊#59512yes—
190C2×D4—41no—
191C2×D4—41no—
192C2×D4—172no—
193C2×D4—348no—
194C2×D4—341no—
195C2×D4—681no—
196C2×D4—681no—
197C2×D4—1362no—
198C2×D4—1362no—
199C2×D4#6324212yes—
200C2×D4#6324312yes—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—171no—
204C22×C4—171no—
205C22×C4—172no—
206C22×C4—342no—
207C22×C4—342no—
208C22×C4—341no—
209C22×C4—682no—
210C22×C4—1362no—
211C22×C4—1362no—
212C22×C4C22×#59511yescharacteristic
213C2×C8—684no—
214C2×C8—1364no—
215C4⋊C4—41no—
216C4⋊C4—681no—
217C22⋊C4—82no—
218C22⋊C4—682no—
219C22⋊C4—682no—
220C22⋊C4—1362no—
221C42—41no—
222C42—172no—
223C42—342no—
224C42—341no—
225C23—22no—
226C23—22no—
227C23—42no—
228C23—42no—
229C23—342no—
230C23—682no—
231C23—682no—
232C23—681no—
233C23—681no—
234C23#1058754314yes—
235C23C2×C22⋊#59511yescharacteristic
236D4—42no—
237D4—42no—
238D4—682no—
239D4—682no—
240D4—1368no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—172no—
249C2×C4—342no—
250C2×C4—341no—
251C2×C4—342no—
252C2×C4—681no—
253C2×C4—684no—
254C2×C4—681no—
255C2×C4—681no—
256C2×C4—682no—
257C2×C4—681no—
258C2×C4—1364no—
259C2×C4—1362no—
260C2×C4C2×#6324211yescharacteristic
261C2×C4C2×#6324311yescharacteristic
262C8—1364no—
263C22—21no—
264C22—21no—
265C22—24no—
266C22—44no—
267C22—42no—
268C22—42no—
269C22—82no—
270C22—684no—
271C22—682no—
272C22—1362no—
273C22—1361no—
274C22—1361no—
275C22C2×#1058754311yescharacteristic
276C22D17⋊#9911yescharacteristic
277C22#1176379611yescharacteristic
278C4—21no—
279C4—21no—
280C4—81no—
281C4—81no—
282C4—342no—
283C4—682no—
284C4—682no—
285C4—681no—
286C2—21no—
287C2—21no—
288C2—44no—
289C2—1362no—
290C2#1454402211yescharacteristic
291C2#1454506211yescharacteristic
292C2#1454508411yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#390C4
socleC22×C17C2×#99
prime radicalC2×#10587626C4
cosocleC2×C4⋊Dic17C23
hypercenter#390#595
hypocenterC17#11479
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #14544020C2semidirect
2. #14543725C2semidirect
3. #14543713C2semidirect
28. #10587626C8semidirect
63. C2×D68C2×C8semidirect
77. C4×Dic17C2×C8semidirect
187. C17#11479semidirect

Maximal subgroups

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

subgroupindex
#145440202
#145437252
#145437132
#145315082
#1147917