Finite Group Databasebeta

← #16943418

Subgroups — #16943418

Order 4352.

526 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 93 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#14531369C211yesmaximal, characteristic
2#14527095C212yesmaximal
3#14526714C211yesmaximal, characteristic
4#14526713C212yesmaximal
5C17×#1317C211yesmaximal, characteristic
6C23×Dic34C411yescharacteristic
7C2×#10587563C411yescharacteristic
8C2×#10587563C2211yescharacteristic
9#11762859—22no—
10#11762713—22no—
11#11762713—22no—
12#11762672C411yescharacteristic
13#11762670C411yescharacteristic
14#11762670C2211yescharacteristic
15#11762534—22no—
16#11762533C2212yes—
17C17×#381C2211yescharacteristic
18C17×#323C2212yes—
19C23×C4×C17C2×C411yescharacteristic
20C23×Dic17C2×C411yescharacteristic
21C23×Dic17C2×C411yescharacteristic
22C22×Dic34—21no—
23C22×Dic34—21no—
24C22×Dic34—22no—
25C22×Dic34—42no—
26C22×Dic34—42no—
27C22×Dic34C814yescomplemented
28C2×C22⋊C4×C17C2×C411yescharacteristic
29C2×C22⋊C4×C17C2311yescharacteristic
30C2×C22⋊Dic17C2×C411yescharacteristic
31C2×C22⋊Dic17C2×C411yescharacteristic
32C2×#63225—21no—
33C2×#63225D412yes—
34C2×C4×Dic17—21no—
35C2×C4×Dic17D412yes—
36#10587563—42no—
37#10587563—42no—
38C17×C22⋊C8—22no—
39C17×#95—22no—
40#10587502—22no—
41#10587502—22no—
42#10587502—22no—
43C22⋊#3622—22no—
44#10587485—42no—
45C8×Dic17—42no—
46C24×C17C22×C411yescharacteristic
47C22×C4×C17—21no—
48C22×C4×C17—21no—
49C22×C4×C17—21no—
50C22×C4×C17—41no—
51C22×C4×C17—41no—
52C22×C4×C17C2×C812yes—
53C22×C4×C17C2×D412yes—
54C22×Dic17—22no—
55C22×Dic17—22no—
56C22×Dic17—21no—
57C22×Dic17—21no—
58C22×Dic17—21no—
59C22×Dic17—41no—
60C22×Dic17—41no—
61C22×Dic17C22⋊C411yescharacteristic
62C22×Dic17C22⋊C412yes—
63C22×Dic17C22⋊C411yescharacteristic
64C22×Dic17C2×C812yes—
65C22×Dic17C2×C812yes—
66C22×Dic17M1612yes—
67C2×Dic34—24no—
68C2×Dic34—24no—
69C2×Dic34—42no—
70C2×Dic34—42no—
71C2×Dic34—48no—
72C2×Dic34—42no—
73C2×Dic34—42no—
74C2×Dic34—48no—
75C2×C8×C17—42no—
76C22⋊C4×C17—41no—
77C22⋊C4×C17—41no—
78C22⋊Dic17—41no—
79C22⋊Dic17—41no—
80#63225—42no—
81#63225—42no—
82C4×Dic17—22no—
83C4×Dic17—22no—
84C4×Dic17—42no—
85C2×#3622—42no—
86#11428—171nomaximal, Sylow
87C23×C17—21no—
88C23×C17—21no—
89C23×C17—42no—
90C23×C17C2×C22⋊C411yescharacteristic
91C23×C17C22×C811yescharacteristic
92C23×C17C2×M1611yescharacteristic
93C2×C4×C17—22no—
94C2×C4×C17—22no—
95C2×C4×C17—42no—
96C2×C4×C17—41no—
97C2×C4×C17—41no—
98C2×C4×C17—42no—
99C2×C4×C17—42no—
100C2×C4×C17—42no—
101C2×C4×C17—41no—
102C2×Dic17—21no—
103C2×Dic17—21no—
104C2×Dic17—24no—
105C2×Dic17—24no—
106C2×Dic17—22no—
107C2×Dic17—22no—
108C2×Dic17—42no—
109C2×Dic17—41no—
110C2×Dic17—41no—
111C2×Dic17—42no—
112C2×Dic17—42no—
113C2×Dic17—42no—
114C2×Dic17—41no—
115C2×Dic17C22⋊C812yes—
116C2×Dic17C22⋊C812yes—
117C2×Dic17#9912yes—
118C2×Dic17#10012yes—
119Dic34—48no—
120Dic34—48no—
121C8×C17—82no—
122#3622—82no—
123#2310—171no—
124#1458—172no—
125#1317—171no—
126#1317—172no—
127#1317D1711yescharacteristic
128C22×C17—22no—
129C22×C17—21no—
130C22×C17—21no—
131C22×C17—41no—
132C22×C17—41no—
133C22×C17—42no—
134C22×C17—42no—
135C22×C17C2×C22⋊C811yescharacteristic
136C22×C17C2×#9911yescharacteristic
137C22×C17C2×#10011yescharacteristic
138C4×C17—42no—
139C4×C17—42no—
140C4×C17—81no—
141Dic17—22no—
142Dic17—42no—
143Dic17—42no—
144Dic17—81no—
145Dic17#32314yes—
146C23×Q8—171no—
147C2×#117—171no—
148C2×#117—171no—
149#431—342no—
150#391—342no—
151#391—342no—
152#381—171no—
153#381—171no—
154#381—171no—
155#381C2×D1711yescharacteristic
156#324—342no—
157#323—172no—
158#323C2×D1712yes—
159C2×C17—21no—
160C2×C17—21no—
161C2×C17—41no—
162C2×C17—41no—
163C2×C17C2×#32311yescharacteristic
164C2×C17#212312yes—
165C22×Q8—174no—
166C22×Q8—342no—
167C22×Q8—341no—
168C22×Q8—341no—
169C22×Q8—682no—
170C22×Q8—682no—
171C23×C4—171no—
172C23×C4—171no—
173C23×C4C4×D1711yescharacteristic
174#117—682no—
175#117—682no—
176C2×C4⋊C4—172no—
177C2×C4⋊C4—341no—
178C2×C22⋊C4—171no—
179C2×C22⋊C4—171no—
180C2×C22⋊C4C4×D1711yescharacteristic
181C2×C22⋊C4C22×D1711yescharacteristic
182C2×C42—172no—
183C2×C42—341no—
184C4⋊C8—682no—
185C22⋊C8—22no—
186C22⋊C8—342no—
187C4×C8—682no—
188#95—22no—
189#95—342no—
190#95—342no—
191#95—342no—
192C17#1142811yescharacteristic, complemented, Sylow
193C24C2×C4×D1711yescharacteristic
194C2×Q8—344no—
195C2×Q8—344no—
196C2×Q8—682no—
197C2×Q8—682no—
198C2×Q8—688no—
199C2×Q8—688no—
200C2×Q8—682no—
201C2×Q8—682no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—171no—
208C22×C4—171no—
209C22×C4—172no—
210C22×C4—172no—
211C22×C4—172no—
212C22×C4—172no—
213C22×C4—342no—
214C22×C4—342no—
215C22×C4—341no—
216C22×C4—341no—
217C22×C4—341no—
218C22×C4—681no—
219C22×C4—681no—
220C22×C4C8×D1712yes—
221C22×C4D4×D1712yes—
222C2×C8—42no—
223C2×C8—682no—
224C4⋊C4—682no—
225C4⋊C4—682no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—681no—
229C22⋊C4—681no—
230C42—342no—
231C42—342no—
232C42—682no—
233C23—21no—
234C23—21no—
235C23—42no—
236C23C22⋊C4×D1711yescharacteristic
237C23C2×C8×D1711yescharacteristic
238C23M16×D1711yescharacteristic
239Q8—688no—
240Q8—688no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—172no—
251C2×C4—172no—
252C2×C4—172no—
253C2×C4—172no—
254C2×C4—344no—
255C2×C4—344no—
256C2×C4—341no—
257C2×C4—341no—
258C2×C4—342no—
259C2×C4—342no—
260C2×C4—682no—
261C2×C4—681no—
262C2×C4—681no—
263C2×C4—682no—
264C2×C4—682no—
265C2×C4—682no—
266C2×C4—681no—
267C8—82no—
268C8—1362no—
269C22—22no—
270C22—21no—
271C22—21no—
272C22—41no—
273C22—41no—
274C22—42no—
275C22—42no—
276C22C22⋊C8×D1711yescharacteristic
277C22#99×D1711yescharacteristic
278C22#100×D1711yescharacteristic
279C4—42no—
280C4—42no—
281C4—81no—
282C4—174no—
283C4—342no—
284C4—682no—
285C4—682no—
286C4—1361no—
287C2—21no—
288C2—21no—
289C2—41no—
290C2—41no—
291C2D17×#32311yescharacteristic
292C2#1453043612yes—
subgroupG/H
centerC22#99×D17
commutatorC23×C17C22×C8
FrattiniC2×C22⋊C4C22×D17
FittingC17×#1317C2
socleC22×C17C2×#99
prime radicalC24×C17C22×C4
cosocleC2×C22⋊C4×C17C23
hypercenter#1317D17
hypocenterC17#11428
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
27. C22×Dic34C8semidirect
192. C17#11428semidirect

Maximal subgroups

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

subgroupindex
#145313692
#145270952
#145267142
#145267132
C17×#13172
#1142817