Finite Group Databasebeta

← #17959475

Subgroups — #17959475

Order 4352.

434 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 74 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#14544683C211yesmaximal, characteristic
2#14544034C211yesmaximal, characteristic
3#14543782C214yesmaximal, complemented
4C2×#11762749C211yesmaximal, characteristic
5#11763779—21no—
6#11763779—21no—
7#11763689—21no—
8#11763689C2212yes—
9#11763655—21no—
10#11763655C2212yes—
11C22×C4⋊Dic17C411yescharacteristic
12C22×#63225C2211yescharacteristic
13#11762749—21no—
14#11762749—21no—
15#11762749C412yes—
16#11762749C2212yes—
17C2×#10587502—21no—
18C2×#10587502—21no—
19C2×C17×#95C411yescharacteristic
20C23×C4×C17—21no—
21C23×C4×C17C2×C411yescharacteristic
22C23×Dic17—21no—
23C23×Dic17D411yescharacteristic
24C23×Dic17D411yescharacteristic
25C2×#63247—22no—
26C2×#63247—41no—
27C2×C4⋊Dic17—21no—
28C2×C4⋊Dic17—41no—
29C2×C4⋊Dic17—41no—
30C2×C4⋊Dic17C2×C412yes—
31C2×#63225—41no—
32C2×#63225—41no—
33C2×#63225C2×C411yescharacteristic
34C2×#63225D411yescharacteristic
35C2×#63225D411yescharacteristic
36C2×#63225C2311yescharacteristic
37C22⋊#3624—22no—
38C22⋊#3624—41no—
39C22⋊#3624—41no—
40C22⋊#3624—41no—
41C17×#95—21no—
42C17×#95C2×C412yes—
43#10587502—22no—
44#10587502—22no—
45#10587502—22no—
46#10587502—22no—
47C24×C17C22⋊C411yescharacteristic
48C22×C4×C17—21no—
49C22×C4×C17—21no—
50C22×C4×C17—22no—
51C22×C4×C17—42no—
52C22×C4×C17—42no—
53C22×C4×C17—42no—
54C22×C4×C17—42no—
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C22×C411yescharacteristic
57C22×Dic17—21no—
58C22×Dic17—21no—
59C22×Dic17—21no—
60C22×Dic17—21no—
61C22×Dic17—22no—
62C22×Dic17—22no—
63C22×Dic17—41no—
64C22×Dic17—42no—
65C22×Dic17—44no—
66C22×Dic17—41no—
67C22×Dic17—41no—
68C22×Dic17C22⋊C411yescharacteristic
69C22×Dic17C22⋊C411yescharacteristic
70C22×Dic17C2×D411yescharacteristic
71C22×Dic17C2×D411yescharacteristic
72#63247—42no—
73#63247—42no—
74#63247—82no—
75C2×#3624—42no—
76C2×#3624—42no—
77C4⋊Dic17—42no—
78C4⋊Dic17—42no—
79#63225—41no—
80#63225—41no—
81#63225—41no—
82#63225—41no—
83#11814—171nomaximal, Sylow
84C23×C17—22no—
85C23×C17—22no—
86C23×C17—21no—
87C23×C17—21no—
88C23×C17#9911yescharacteristic
89C23×C17#9911yescharacteristic
90C23×C17C2×C22⋊C411yescharacteristic
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—42no—
94C2×C4×C17—42no—
95C2×C4×C17—41no—
96C2×C4×C17—41no—
97C2×C4×C17—42no—
98C2×C4×C17—42no—
99C2×C4×C17—42no—
100C2×C4×C17—84no—
101C2×Dic17—21no—
102C2×Dic17—21no—
103C2×Dic17—21no—
104C2×Dic17—21no—
105C2×Dic17—21no—
106C2×Dic17—21no—
107C2×Dic17—21no—
108C2×Dic17—42no—
109C2×Dic17—42no—
110C2×Dic17—42no—
111C2×Dic17—41no—
112C2×Dic17—41no—
113C2×Dic17—44no—
114C2×Dic17—42no—
115C2×Dic17—81no—
116C2×Dic17—82no—
117C2×Dic17—82no—
118C2×Dic17#13712yes—
119#3624—82no—
120#3624—82no—
121C2×#400—171no—
122#1821—171no—
123#1463—171no—
124#1353—174no—
125C22×C17—24no—
126C22×C17—24no—
127C22×C17—21no—
128C22×C17—21no—
129C22×C17—21no—
130C22×C17—21no—
131C22×C17—21no—
132C22×C17—21no—
133C22×C17#35212yes—
134C22×C17#35512yes—
135C22×C17C2×#9911yescharacteristic
136C22×C17#41911yescharacteristic
137C22×C17#42111yescharacteristic
138C4×C17—41no—
139C4×C17—41no—
140C4×C17—82no—
141Dic17—22no—
142Dic17—41no—
143Dic17—41no—
144Dic17—41no—
145Dic17—82no—
146C22×C4⋊C4—171no—
147C22×C4⋊C4—171no—
148#407—341no—
149#407—341no—
150#400—172no—
151#400—172no—
152#400—341no—
153#400—341no—
154C2×#95—341no—
155C2×#95—341no—
156C2×#95#59511yescharacteristic
157#343—172no—
158#343—341no—
159#324—172no—
160#324—341no—
161C2×C17—21no—
162C2×C17—22no—
163C2×C17—22no—
164C2×C17—21no—
165C2×C17#151111yescharacteristic
166C2×C17C2×#35211yescharacteristic
167C2×C17C2×#35511yescharacteristic
168C23×C4—21no—
169C23×C4—171no—
170C23×C4—171no—
171C23×C4—341no—
172C23×C4C2×#59511yescharacteristic
173C2×M16—342no—
174C2×M16—681no—
175C2×C4⋊C4—171no—
176C2×C4⋊C4—171no—
177C2×C4⋊C4—171no—
178C2×C4⋊C4—171no—
179C2×C4⋊C4—172no—
180C2×C4⋊C4—341no—
181C2×C4⋊C4—681no—
182C2×C4⋊C4—681no—
183C2×C4⋊C4—681no—
184C2×C4⋊C4—681no—
185C22⋊C8—342no—
186C22⋊C8—681no—
187C22⋊C8—681no—
188C22⋊C8—681no—
189#95—21no—
190#95—342no—
191#95—342no—
192#95—342no—
193#95—342no—
194#95C2×#59512yes—
195C17#1181411yescharacteristic, complemented, Sylow
196C24C22⋊#59511yescharacteristic
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—22no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—171no—
205C22×C4—171no—
206C22×C4—171no—
207C22×C4—171no—
208C22×C4—342no—
209C22×C4—341no—
210C22×C4—341no—
211C22×C4—341no—
212C22×C4—341no—
213C22×C4—342no—
214C22×C4—681no—
215C22×C4—682no—
216C22×C4—684no—
217C22×C4—681no—
218C22×C4—681no—
219C22×C4C22⋊#59511yescharacteristic
220C22×C4C22×#59511yescharacteristic
221M16—682no—
222M16—682no—
223M16—1362no—
224C2×C8—682no—
225C2×C8—682no—
226C4⋊C4—681no—
227C4⋊C4—681no—
228C4⋊C4—681no—
229C4⋊C4—681no—
230C4⋊C4—682no—
231C4⋊C4—682no—
232C23—22no—
233C23—22no—
234C23—21no—
235C23—21no—
236C23#1058753911yescharacteristic
237C23#1058753911yescharacteristic
238C23C2×C22⋊#59511yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—84no—
249C2×C4—172no—
250C2×C4—341no—
251C2×C4—341no—
252C2×C4—341no—
253C2×C4—341no—
254C2×C4—341no—
255C2×C4—341no—
256C2×C4—341no—
257C2×C4—682no—
258C2×C4—682no—
259C2×C4—682no—
260C2×C4—681no—
261C2×C4—681no—
262C2×C4—684no—
263C2×C4—682no—
264C2×C4—1361no—
265C2×C4—1362no—
266C2×C4—1362no—
267C8—1362no—
268C8—1362no—
269C22—24no—
270C22—24no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22#1176371212yes—
278C22#1176371812yes—
279C22C2×#1058753911yescharacteristic
280C22#1176380211yescharacteristic
281C22#1176380711yescharacteristic
282C4—41no—
283C4—41no—
284C4—82no—
285C4—342no—
286C4—681no—
287C4—681no—
288C4—681no—
289C4—1362no—
290C2—21no—
291C2—22no—
292C2—22no—
293C2—21no—
294C2#1454419211yescharacteristic
295C2C2×#1176371211yescharacteristic
296C2C2×#1176371811yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×#95C4
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC2×#63225C23
hypercenterC2×#95#595
hypocenterC17#11814
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. #14543782C2semidirect
195. C17#11814semidirect

Maximal subgroups

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

subgroupindex
#145446832
#145440342
#145437822
C2×#117627492
#1181417