Finite Group Databasebeta

← #17958220

Subgroups — #17958220

Order 4352.

434 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 112 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#14544015C211yesmaximal, characteristic
2#14544015C211yesmaximal, characteristic
3#14543728C214yesmaximal
4#14531407C211yesmaximal, characteristic
5#11763825—21no—
6#11763825—21no—
7#11763654—21no—
8#11763654—21no—
9#11763652C2212yes—
10#11763652C2212yes—
11C2×#10587612C2211yescharacteristic
12C22×C4⋊Dic17C411yescharacteristic
13#11762708—21no—
14#11762708—21no—
15#11762684C412yes—
16#11762684C2212yes—
17#11762679—21no—
18#11762675—21no—
19C2×C17×#117C411yescharacteristic
20C23×C4×C17C2×C411yescharacteristic
21C23×Dic17C2×C412yes—
22C17×#117—22no—
23C17×#117C814yescomplemented
24C2×C4⋊C4×C17—21no—
25C2×C22⋊C4×C17C2×C412yes—
26C2×C42×C17—21no—
27C2×C22⋊Dic17C2×C411yescharacteristic
28C2×C22⋊Dic17C2311yescharacteristic
29#10587612—41no—
30#10587612—41no—
31C2×C4⋊Dic17—21no—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—22no—
34C2×C4⋊Dic17—22no—
35C2×C4⋊Dic17—41no—
36C2×C4⋊Dic17—41no—
37C2×C4⋊Dic17D411yescharacteristic
38C2×C4⋊Dic17D411yescharacteristic
39C2×C4×Dic17D411yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41C22⋊#3624—22no—
42C22⋊#3624—22no—
43C4⋊#3624—41no—
44C4⋊#3624—41no—
45C4×#3624—41no—
46C4×#3624—41no—
47#10587502—22no—
48#10587502—22no—
49C24×C17C22×C411yescharacteristic
50C22×C4×C17—21no—
51C22×C4×C17—21no—
52C22×C4×C17—22no—
53C22×C4×C17—22no—
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C2×C812yes—
57C22×C4×C17M1612yes—
58C22×Dic17—22no—
59C22×Dic17—42no—
60C22×Dic17—82no—
61C22×Dic17C22⋊C411yescharacteristic
62C22×Dic17C22⋊C411yescharacteristic
63C22×Dic17C2×D411yescharacteristic
64C22×Dic17C2×D411yescharacteristic
65C2×#3624—42no—
66C2×#3624—42no—
67C4⋊C4×C17—24no—
68C22⋊C4×C17—22no—
69C22⋊C4×C17C2×C814yes—
70C42×C17—24no—
71C22⋊Dic17—41no—
72C22⋊Dic17—41no—
73C4⋊Dic17—41no—
74C4⋊Dic17—41no—
75C4⋊Dic17—42no—
76C4⋊Dic17—41no—
77C4⋊Dic17—41no—
78C4⋊Dic17—82no—
79C4⋊Dic17—82no—
80C4×Dic17—21no—
81C4×Dic17—21no—
82C4×Dic17—21no—
83C4×Dic17—21no—
84#11454—171nomaximal, Sylow
85C23×C17—21no—
86C23×C17—21no—
87C23×C17—41no—
88C23×C17—41no—
89C23×C17C2×C22⋊C411yescharacteristic
90C23×C17C22×C811yescharacteristic
91C23×C17C2×M1611yescharacteristic
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—22no—
95C2×C4×C17—22no—
96C2×C4×C17—22no—
97C2×C4×C17—22no—
98C2×C4×C17—24no—
99C2×C4×C17—42no—
100C2×C4×C17—42no—
101C2×C4×C17C22⋊C812yes—
102C2×C4×C17C22⋊C812yes—
103C2×C4×C17#9911yescharacteristic
104C2×C4×C17#9911yescharacteristic
105C2×C4×C17#10112yes—
106C2×Dic17—21no—
107C2×Dic17—21no—
108C2×Dic17—21no—
109C2×Dic17—21no—
110C2×Dic17—41no—
111C2×Dic17—41no—
112C2×Dic17—41no—
113C2×Dic17—41no—
114C2×Dic17—42no—
115C2×Dic17—42no—
116C2×Dic17—42no—
117C2×Dic17—84no—
118#3624—82no—
119#3624—82no—
120#2317—171no—
121#1458—171no—
122#1458—171no—
123#1326—174no—
124C22×C17—21no—
125C22×C17—21no—
126C22×C17—21no—
127C22×C17—21no—
128C22×C17—41no—
129C22×C17—41no—
130C22×C17—42no—
131C22×C17—41no—
132C22×C17—41no—
133C22×C17C2×C22⋊C811yescharacteristic
134C22×C17C2×#9911yescharacteristic
135C22×C17C2×#10111yescharacteristic
136C4×C17—22no—
137C4×C17—44no—
138C4×C17#32412yes—
139C4×C17#32412yes—
140Dic17—41no—
141Dic17—41no—
142Dic17—41no—
143Dic17—41no—
144Dic17—82no—
145C2×#117—171no—
146C2×#117#59511yescharacteristic
147C22×C4⋊C4—171no—
148#431—341no—
149#431—341no—
150#389—341no—
151#389—341no—
152#385—172no—
153#385—172no—
154#384—341no—
155#382—341no—
156#324—341no—
157#324—341no—
158#323—172no—
159#323—172no—
160C2×C17—21no—
161C2×C17—21no—
162C2×C17—41no—
163C2×C17—41no—
164C2×C17C2×#32411yescharacteristic
165C2×C17#212211yescharacteristic
166C2×C17#212311yescharacteristic
167C23×C4—172no—
168C23×C4C2×#59511yescharacteristic
169#117—22no—
170#117—681no—
171#117—681no—
172#117#362414yescomplemented
173C2×C4⋊C4—21no—
174C2×C4⋊C4—171no—
175C2×C4⋊C4—171no—
176C2×C4⋊C4—341no—
177C2×C4⋊C4—341no—
178C2×C4⋊C4—342no—
179C2×C4⋊C4—342no—
180C2×C4⋊C4—681no—
181C2×C4⋊C4—681no—
182C2×C22⋊C4—171no—
183C2×C22⋊C4—171no—
184C2×C22⋊C4C2×#59512yes—
185C2×C42—21no—
186C2×C42—171no—
187C2×C42—171no—
188C4⋊C8—681no—
189C4⋊C8—681no—
190C22⋊C8—342no—
191C22⋊C8—342no—
192C4×C8—681no—
193C4×C8—681no—
194#95—342no—
195#95—342no—
196C17#1145411yescharacteristic, complemented, Sylow
197C24C22×#59511yescharacteristic
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—171no—
203C22×C4—171no—
204C22×C4—171no—
205C22×C4—171no—
206C22×C4—342no—
207C22×C4—682no—
208C22×C4—1362no—
209C22×C4C2×#362412yes—
210C22×C4#6324712yes—
211C22×C4C22⋊#59511yescharacteristic
212C22×C4C22⋊#59511yescharacteristic
213C2×C8—682no—
214C2×C8—682no—
215C4⋊C4—24no—
216C4⋊C4—681no—
217C4⋊C4—681no—
218C4⋊C4—682no—
219C4⋊C4—681no—
220C4⋊C4—681no—
221C4⋊C4—1362no—
222C4⋊C4—1362no—
223C22⋊C4—22no—
224C22⋊C4—681no—
225C22⋊C4—681no—
226C22⋊C4C2×#362414yes—
227C42—24no—
228C42—341no—
229C42—341no—
230C42—341no—
231C42—341no—
232C23—21no—
233C23—21no—
234C23—41no—
235C23—41no—
236C23C22×#362411yescharacteristic
237C23C2×#6324711yescharacteristic
238C23C2×C22⋊#59511yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—24no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—341no—
249C2×C4—341no—
250C2×C4—341no—
251C2×C4—341no—
252C2×C4—681no—
253C2×C4—681no—
254C2×C4—681no—
255C2×C4—681no—
256C2×C4—682no—
257C2×C4—682no—
258C2×C4—682no—
259C2×C4—1364no—
260C2×C4#1058753911yescharacteristic
261C2×C4#1058753911yescharacteristic
262C2×C4#1058754512yes—
263C2×C4C22⋊#362412yes—
264C2×C4C22⋊#362412yes—
265C8—1362no—
266C8—1362no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—41no—
272C22—41no—
273C22—42no—
274C22—41no—
275C22—41no—
276C22C2×C22⋊#362411yescharacteristic
277C22C2×#1058753911yescharacteristic
278C22C2×#1058754511yescharacteristic
279C4—22no—
280C4—44no—
281C4—681no—
282C4—681no—
283C4—681no—
284C4—681no—
285C4—1362no—
286C4#1176365412yes—
287C4#1176365412yes—
288C2—21no—
289C2—21no—
290C2—41no—
291C2—41no—
292C2C2×#1176365411yescharacteristic
293C2#1454504511yescharacteristic
294C2#1454504811yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC23×C17C22×C8
FrattiniC24C22×#595
FittingC2×C17×#117C4
socleC22×C17C2×#99
prime radicalC24×C17C22×C4
cosocleC2×C22⋊Dic17C23
hypercenterC2×#117#595
hypocenterC17#11454
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
23. C17×#117C8semidirect
172. #117#3624semidirect
196. C17#11454semidirect

Maximal subgroups

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

subgroupindex
#145440152
#145437282
#145314072
#1145417