Finite Group Databasebeta

← #17950139

Subgroups — #17950139

Order 4352.

394 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 88 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#14544711C211yesmaximal, characteristic
2#14544501C211yesmaximal, characteristic
3#14543603C212yesmaximal
4#14543602C212yesmaximal
5#14537143C211yesmaximal, characteristic
6C2×#10587542—21no—
7#11763675—21no—
8#11763675—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587575—21no—
13#11762708C2211yescharacteristic
14#11762707C411yescharacteristic
15#11762706—21no—
16#11762705C2211yescharacteristic
17#11762704—21no—
18#11762678C411yescharacteristic
19#11762678C411yescharacteristic
20#11762673—21no—
21C42×Dic17C2211yescharacteristic
22C17×#389C411yescharacteristic
23C22×#3624—22no—
24C22×#3624—22no—
25C2×C4⋊C4×C17—21no—
26C2×C4⋊C4×C17C2×C411yescharacteristic
27C2×C4⋊C4×C17C2×C411yescharacteristic
28C2×C42×C17C2×C411yescharacteristic
29C2×C4⋊Dic17—21no—
30C2×C4⋊Dic17C2×C411yescharacteristic
31C2×C4⋊Dic17C2×C411yescharacteristic
32C2×#63225—21no—
33C2×#63225—21no—
34C2×#63225—21no—
35C2×#63225—21no—
36C2×#63225—21no—
37C2×#63225—21no—
38C2×C4×Dic17C2×C411yescharacteristic
39C2×C4×Dic17D411yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17D411yescharacteristic
43C2×C4×Dic17C2311yescharacteristic
44#10587575—44no—
45#10587542—24no—
46C17×#95—21no—
47#10587502—21no—
48#10587502—21no—
49#10587502—21no—
50C22×C4×C17—21no—
51C22×C4×C17—21no—
52C22×C4×C17C22⋊C411yescharacteristic
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22×C411yescharacteristic
55C22×Dic17—21no—
56C22×Dic17—21no—
57C22×Dic17C22⋊C411yescharacteristic
58C22×Dic17C22⋊C411yescharacteristic
59C22×Dic17C2×D411yescharacteristic
60C22×Dic17C2×D411yescharacteristic
61C2×#3624—24no—
62C2×#3624—42no—
63C2×#3624—42no—
64C2×#3624—42no—
65C2×#3624—42no—
66C2×#3624—42no—
67C4⋊C4×C17—22no—
68C4⋊C4×C17—41no—
69C4⋊C4×C17—42no—
70C42×C17—22no—
71C4⋊Dic17—22no—
72C4⋊Dic17—42no—
73C4⋊Dic17—41no—
74#63225—42no—
75#63225—42no—
76#63225—42no—
77#63225—42no—
78#63225—42no—
79#63225—42no—
80C4×Dic17—22no—
81C4×Dic17—22no—
82C4×Dic17—22no—
83C4×Dic17—22no—
84C4×Dic17—41no—
85C4×Dic17—41no—
86#7700—171nomaximal, Sylow
87C23×C17C2×C22⋊C411yescharacteristic
88C2×C4×C17—21no—
89C2×C4×C17—21no—
90C2×C4×C17—21no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—41no—
97C2×C4×C17—41no—
98C2×C4×C17—41no—
99C2×C4×C17—41no—
100C2×C4×C17—41no—
101C2×C4×C17—41no—
102C2×C4×C17#13112yes—
103C2×Dic17—21no—
104C2×Dic17—21no—
105C2×Dic17—21no—
106C2×Dic17—21no—
107C2×Dic17—21no—
108C2×Dic17—21no—
109C2×Dic17—21no—
110C2×Dic17—21no—
111C2×Dic17—41no—
112C2×Dic17—41no—
113C2×Dic17—41no—
114C2×Dic17—41no—
115C2×Dic17—41no—
116C2×Dic17—41no—
117C2×Dic17#10112yes—
118C2×Dic17#10412yes—
119C2×Dic17AGL(1,ℤ/8)12yes—
120C2×Dic17#13712yes—
121#3624—44no—
122#3624—82no—
123#2859—171no—
124#1839—171no—
125#1745—171no—
126#1271—172no—
127#1271—172no—
128C22×C17#40811yescharacteristic
129C22×C17#41011yescharacteristic
130C22×C17C2×#10111yescharacteristic
131C22×C17#41811yescharacteristic
132C22×C17#41911yescharacteristic
133C22×C17C2×#10411yescharacteristic
134C22×C17#42111yescharacteristic
135C4×C17—22no—
136C4×C17—41no—
137C4×C17—41no—
138C4×C17—81no—
139C4×C17—81no—
140Dic17—22no—
141Dic17—22no—
142Dic17—22no—
143Dic17—22no—
144Dic17—81no—
145Dic17—81no—
146C2×#125—341no—
147C2×#97—341no—
148#389—171no—
149#389—171no—
150#389—171no—
151#389—341no—
152#389—341no—
153#389#59511yescharacteristic
154#384—171no—
155#384—171no—
156#382—341no—
157C43—171no—
158#336—172no—
159#336—172no—
160#336—341no—
161#336—341no—
162#336—341no—
163C2×C17#147011yescharacteristic
164C2×C17#148511yescharacteristic
165C2×C17#149611yescharacteristic
166C2×C17#150511yescharacteristic
167C2×C17#151511yescharacteristic
168C2×C17#152811yescharacteristic
169C2×C17#155611yescharacteristic
170C22×C8—342no—
171C22×C8—342no—
172#125—684no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—171no—
175C2×C4⋊C4—171no—
176C2×C4⋊C4—341no—
177C2×C4⋊C4—341no—
178C2×C4⋊C4—341no—
179C2×C4⋊C4—341no—
180C2×C4⋊C4—341no—
181C2×C4⋊C4—341no—
182C2×C4⋊C4—341no—
183C2×C4⋊C4C2×#59511yescharacteristic
184C2×C4⋊C4C2×#59511yescharacteristic
185C2×C42—171no—
186C2×C42—171no—
187C2×C42—171no—
188C2×C42—171no—
189C2×C42—171no—
190C2×C42—171no—
191C2×C42C2×#59511yescharacteristic
192#97—344no—
193#95—21no—
194#95—341no—
195#95—341no—
196#95—341no—
197C17#770011yescharacteristic, complemented, Sylow
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—171no—
201C22×C4—171no—
202C22×C4—171no—
203C22×C4—171no—
204C22×C4—341no—
205C22×C4—341no—
206C22×C4C22⋊#59511yescharacteristic
207C22×C4C22⋊#59511yescharacteristic
208C22×C4C22×#59511yescharacteristic
209C2×C8—344no—
210C2×C8—682no—
211C2×C8—682no—
212C2×C8—682no—
213C2×C8—682no—
214C2×C8—682no—
215C4⋊C4—22no—
216C4⋊C4—41no—
217C4⋊C4—42no—
218C4⋊C4—342no—
219C4⋊C4—681no—
220C4⋊C4—682no—
221C4⋊C4—682no—
222C4⋊C4—682no—
223C4⋊C4—682no—
224C4⋊C4—682no—
225C4⋊C4—682no—
226C4⋊C4—682no—
227C42—22no—
228C42—342no—
229C42—342no—
230C42—342no—
231C42—342no—
232C42—681no—
233C42—681no—
234C23C2×C22⋊#59511yescharacteristic
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—172no—
250C2×C4—172no—
251C2×C4—172no—
252C2×C4—172no—
253C2×C4—341no—
254C2×C4—341no—
255C2×C4—341no—
256C2×C4—341no—
257C2×C4—341no—
258C2×C4—341no—
259C2×C4—341no—
260C2×C4—341no—
261C2×C4—681no—
262C2×C4—681no—
263C2×C4—681no—
264C2×C4—681no—
265C2×C4—681no—
266C2×C4—681no—
267C2×C4#1058767812yes—
268C8—684no—
269C8—1362no—
270C22#1176378211yescharacteristic
271C22#1176378811yescharacteristic
272C22D17⋊#10111yescharacteristic
273C22#1176380111yescharacteristic
274C22#1176380211yescharacteristic
275C22D17⋊#10411yescharacteristic
276C22#1176380611yescharacteristic
277C4—22no—
278C4—41no—
279C4—41no—
280C4—81no—
281C4—81no—
282C4—342no—
283C4—342no—
284C4—342no—
285C4—342no—
286C4—1361no—
287C4—1361no—
288C2#1454405611yescharacteristic
289C2#1454410611yescharacteristic
290C2#1454414311yescharacteristic
291C2#1454417411yescharacteristic
292C2#1454420611yescharacteristic
293C2#1454424711yescharacteristic
294C2#1454431411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#389C4
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#389#595
hypocenterC17#7700
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
197. C17#7700semidirect

Maximal subgroups

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

subgroupindex
#145447112
#145445012
#145436032
#145436022
#145371432
#770017