Finite Group Databasebeta

← #17958401

Subgroups — #17958401

Order 4352.

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

normal subgroups only

This group has 510 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#14544036C212yesmaximal
2#14543711C212yesmaximal
3#14543710C212yesmaximal
4#14531369C211yesmaximal, characteristic
5#11763830—22no—
6#11763655—22no—
7#11763652C2214yes—
8C23×Dic34C411yescharacteristic
9C2×#10587563C411yescharacteristic
10C2×#10587563C2211yescharacteristic
11#11762713—22no—
12#11762713—22no—
13#11762672C2211yescharacteristic
14#11762670C411yescharacteristic
15#11762670C2211yescharacteristic
16C17×#381C411yescharacteristic
17C23×C4×C17C2×C411yescharacteristic
18C23×Dic17C2×C411yescharacteristic
19C23×Dic17C2×C411yescharacteristic
20C22×Dic34—22no—
21C22×Dic34—21no—
22C22×Dic34—21no—
23C22×Dic34—22no—
24C22×Dic34—41no—
25C22×Dic34—41no—
26C22×Dic34—42no—
27C2×C22⋊C4×C17C2×C411yescharacteristic
28C2×C22⋊C4×C17C2×C411yescharacteristic
29C2×C22⋊Dic17C2×C411yescharacteristic
30C2×C22⋊Dic17C2311yescharacteristic
31C2×#63225—21no—
32C2×#63225D412yes—
33C2×C4×Dic17—21no—
34C2×C4×Dic17D412yes—
35#10587563—41no—
36#10587563—41no—
37#10587563—42no—
38C22⋊#3624—24no—
39#10587542—42no—
40C4⋊#3624—42no—
41C17×#95—22no—
42#10587502—22no—
43#10587502—22no—
44#10587502—22no—
45C24×C17C22×C411yescharacteristic
46C22×C4×C17—21no—
47C22×C4×C17—21no—
48C22×C4×C17—21no—
49C22×C4×C17—41no—
50C22×C4×C17—41no—
51C22×C4×C17C22⋊C412yes—
52C22×C4×C17M1612yes—
53C22×Dic17—21no—
54C22×Dic17—21no—
55C22×Dic17—21no—
56C22×Dic17—21no—
57C22×Dic17—22no—
58C22×Dic17—21no—
59C22×Dic17—21no—
60C22×Dic17—21no—
61C22×Dic17—41no—
62C22×Dic17—41no—
63C22×Dic17C22⋊C411yescharacteristic
64C22×Dic17C22⋊C411yescharacteristic
65C22×Dic17M1612yes—
66C22×Dic17C2×D412yes—
67C2×Dic34—24no—
68C2×Dic34—24no—
69C2×Dic34—44no—
70C2×Dic34—44no—
71C2×Dic34—44no—
72C2×Dic34—44no—
73C2×Dic34—42no—
74C2×Dic34—42no—
75C2×Dic34—41no—
76C2×Dic34—41no—
77C2×Dic34—42no—
78C2×#3624—44no—
79C22⋊C4×C17—41no—
80C22⋊C4×C17—41no—
81C22⋊Dic17—41no—
82C22⋊Dic17—41no—
83#63225—42no—
84#63225—42no—
85C4×Dic17—22no—
86C4×Dic17—22no—
87C4×Dic17—42no—
88#11504—171nomaximal, Sylow
89C23×C17—21no—
90C23×C17—21no—
91C23×C17—42no—
92C23×C17C2×C22⋊C411yescharacteristic
93C23×C17C2×M1611yescharacteristic
94C23×C17C2×M1611yescharacteristic
95C2×C4×C17—22no—
96C2×C4×C17—22no—
97C2×C4×C17—42no—
98C2×C4×C17—41no—
99C2×C4×C17—41no—
100C2×C4×C17—42no—
101C2×C4×C17—42no—
102C2×C4×C17—42no—
103C2×C4×C17—41no—
104C2×Dic17—22no—
105C2×Dic17—22no—
106C2×Dic17—22no—
107C2×Dic17—22no—
108C2×Dic17—21no—
109C2×Dic17—21no—
110C2×Dic17—21no—
111C2×Dic17—21no—
112C2×Dic17—22no—
113C2×Dic17—22no—
114C2×Dic17—42no—
115C2×Dic17—41no—
116C2×Dic17—41no—
117C2×Dic17—42no—
118C2×Dic17—42no—
119C2×Dic17—42no—
120C2×Dic17—41no—
121C2×Dic17#9911yescharacteristic
122C2×Dic17#9911yescharacteristic
123C2×Dic17#10012yes—
124Dic34—44no—
125Dic34—44no—
126Dic34—48no—
127#3624—84no—
128#2310—171no—
129#1464—172no—
130#1317—172no—
131#1317—172no—
132C22×C17—22no—
133C22×C17—21no—
134C22×C17—21no—
135C22×C17—41no—
136C22×C17—41no—
137C22×C17—42no—
138C22×C17—42no—
139C22×C17#40711yescharacteristic
140C22×C17C2×#9911yescharacteristic
141C22×C17C2×#10011yescharacteristic
142C4×C17—42no—
143C4×C17—42no—
144C4×C17—81no—
145Dic17—21no—
146Dic17—21no—
147Dic17—22no—
148Dic17—42no—
149Dic17—42no—
150Dic17—81no—
151C23×Q8—171no—
152C2×#117—171no—
153C2×#117—171no—
154#432—342no—
155#391—342no—
156#391—342no—
157#381—171no—
158#381—171no—
159#381—171no—
160#381#59511yescharacteristic
161#324—342no—
162#323—174no—
163C2×C17—21no—
164C2×C17—21no—
165C2×C17—41no—
166C2×C17—41no—
167C2×C17#146211yescharacteristic
168C2×C17#212312yes—
169C22×Q8—342no—
170C22×Q8—341no—
171C22×Q8—341no—
172C22×Q8—342no—
173C22×Q8—681no—
174C22×Q8—681no—
175C22×Q8—682no—
176C23×C4—171no—
177C23×C4—171no—
178C23×C4C2×#59511yescharacteristic
179#117—681no—
180#117—681no—
181#117—682no—
182C2×C4⋊C4—172no—
183C2×C4⋊C4—341no—
184C2×C22⋊C4—171no—
185C2×C22⋊C4—171no—
186C2×C22⋊C4C2×#59511yescharacteristic
187C2×C22⋊C4C2×#59511yescharacteristic
188C2×C42—172no—
189C2×C42—341no—
190C4⋊C8—682no—
191C22⋊C8—344no—
192#97—682no—
193#95—22no—
194#95—342no—
195#95—342no—
196#95—342no—
197C17#1150411yescharacteristic, complemented, Sylow
198C24C22×#59511yescharacteristic
199C2×Q8—344no—
200C2×Q8—344no—
201C2×Q8—681no—
202C2×Q8—681no—
203C2×Q8—682no—
204C2×Q8—684no—
205C2×Q8—684no—
206C2×Q8—682no—
207C2×Q8—682no—
208C2×Q8—684no—
209C2×Q8—684no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—171no—
216C22×C4—171no—
217C22×C4—172no—
218C22×C4—172no—
219C22×C4—341no—
220C22×C4—341no—
221C22×C4—342no—
222C22×C4—341no—
223C22×C4—341no—
224C22×C4—341no—
225C22×C4—341no—
226C22×C4—341no—
227C22×C4—681no—
228C22×C4—681no—
229C22×C4#6324312yes—
230C22×C4C22⋊#59512yes—
231C2×C8—684no—
232C4⋊C4—682no—
233C4⋊C4—682no—
234C22⋊C4—41no—
235C22⋊C4—41no—
236C22⋊C4—681no—
237C22⋊C4—681no—
238C42—342no—
239C42—342no—
240C42—682no—
241C23—21no—
242C23—21no—
243C23—42no—
244C23C2×#6324311yescharacteristic
245C23D17⋊M1611yescharacteristic
246C23C2×C22⋊#59511yescharacteristic
247Q8—684no—
248Q8—684no—
249Q8—688no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—171no—
260C2×C4—171no—
261C2×C4—172no—
262C2×C4—342no—
263C2×C4—342no—
264C2×C4—342no—
265C2×C4—342no—
266C2×C4—341no—
267C2×C4—341no—
268C2×C4—341no—
269C2×C4—341no—
270C2×C4—342no—
271C2×C4—342no—
272C2×C4—682no—
273C2×C4—681no—
274C2×C4—681no—
275C2×C4—682no—
276C2×C4—682no—
277C2×C4—682no—
278C2×C4—681no—
279C8—1364no—
280C22—22no—
281C22—21no—
282C22—21no—
283C22—41no—
284C22—41no—
285C22—42no—
286C22—42no—
287C22#1176378011yescharacteristic
288C22D17⋊#9911yescharacteristic
289C22D17⋊#10011yescharacteristic
290C4—42no—
291C4—42no—
292C4—81no—
293C4—341no—
294C4—341no—
295C4—342no—
296C4—682no—
297C4—682no—
298C4—1361no—
299C2—21no—
300C2—21no—
301C2—41no—
302C2—41no—
303C2#1454403011yescharacteristic
304C2#1454504712yes—
subgroupG/H
centerC22D17⋊#99
commutator, prime radicalC24×C17C22×C4
FrattiniC24C22×#595
FittingC17×#381C4
socleC22×C17C2×#99
cosocleC2×C22⋊Dic17C23
hypercenter#381#595
hypocenterC17#11504
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #381

Complements

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

NH ≅ G/Ntype
197. C17#11504semidirect

Maximal subgroups

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

subgroupindex
#145440362
#145437112
#145437102
#145313692
#1150417