Finite Group Databasebeta

← #17950157

Subgroups — #17950157

Order 4352.

500 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 94 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#14544676C211yesmaximal, characteristic
2#14544511C211yesmaximal, characteristic
3#14543603C214yesmaximal, complemented
4#14537131C211yesmaximal, characteristic
5C2×#10587543—21no—
6C2×#10587543—21no—
7C2×#10587542—21no—
8#11763675—21no—
9#11763675C2212yes—
10#11763675C2212yes—
11C2×#10587632—21no—
12C2×C42×D17C2211yescharacteristic
13#11762716—21no—
14#11762705—21no—
15#11762705C2212yes—
16#11762679C411yescharacteristic
17#11762666—21no—
18#11762666C412yes—
19C2×C17×C4⋊Q8C411yescharacteristic
20C22×Q8×C17—21no—
21C22×C4×D17C2×C411yescharacteristic
22C22×C4×D17D411yescharacteristic
23C22×C4×D17D411yescharacteristic
24C22×#3624—22no—
25C22×#3624—22no—
26C17×C4⋊Q8—42no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17C2×C412yes—
29C2×C42×C17C2×C411yescharacteristic
30#10587632—44no—
31C2×#63227—22no—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17C2×C412yes—
35C2×#63225—22no—
36C2×C4×Dic17D411yescharacteristic
37C2×C4×Dic17D411yescharacteristic
38C2×C4×Dic17C2311yescharacteristic
39C42×D17—42no—
40#10587543—24no—
41#10587543—42no—
42#10587542—42no—
43#10587502—22no—
44#10587502—22no—
45C23×D17C22⋊C411yescharacteristic
46C2×Q8×C17—42no—
47C2×Q8×C17—42no—
48C2×Q8×C17—42no—
49C22×C4×C17—22no—
50C22×C4×C17C22⋊C411yescharacteristic
51C22×C4×C17C22⋊C411yescharacteristic
52C22×C4×C17C22×C411yescharacteristic
53C22×Dic17—22no—
54C22×Dic17C22⋊C411yescharacteristic
55C22×Dic17C2×D411yescharacteristic
56C22×Dic17C2×D411yescharacteristic
57C2×C4×D17—22no—
58C2×C4×D17—22no—
59C2×C4×D17—22no—
60C2×C4×D17—22no—
61C2×C4×D17—22no—
62C2×C4×D17—22no—
63C2×C4×D17—41no—
64C2×C4×D17—41no—
65C2×C4×D17—41no—
66C2×#3624—24no—
67C2×#3624—42no—
68C2×#3624—42no—
69C2×#3624—42no—
70C2×#3624—42no—
71C2×#3624—42no—
72C4⋊C4×C17—42no—
73C4⋊C4×C17—42no—
74C42×C17—22no—
75#63227—44no—
76C4⋊Dic17—24no—
77C4⋊Dic17—42no—
78C4⋊Dic17—42no—
79#63225—44no—
80C4×Dic17—22no—
81C4×Dic17—41no—
82C4×Dic17—41no—
83#7705—171nomaximal, Sylow
84C23×C17C2×C22⋊C411yescharacteristic
85C22×D17—21no—
86C22×D17—21no—
87C22×D17—21no—
88C22×D17—21no—
89C22×D17—21no—
90C22×D17—21no—
91C22×D17#10112yes—
92Q8×C17—84no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—21no—
99C2×C4×C17—42no—
100C2×C4×C17—42no—
101C2×C4×C17—42no—
102C2×C4×C17#9912yes—
103C2×C4×C17#10412yes—
104C2×C4×C17#13112yes—
105C2×Dic17—21no—
106C2×Dic17—21no—
107C2×Dic17—21no—
108C2×Dic17—21no—
109C2×Dic17—21no—
110C2×Dic17—21no—
111C2×Dic17—21no—
112C2×Dic17—42no—
113C2×Dic17—42no—
114C2×Dic17—42no—
115C2×Dic17AGL(1,ℤ/8)12yes—
116C2×Dic17#13712yes—
117C4×D17—44no—
118C4×D17—44no—
119C4×D17—44no—
120#3624—44no—
121#3624—82no—
122#2857—171no—
123#1817—171no—
124#1749—171no—
125#1271—174no—
126C22×C17#40811yescharacteristic
127C22×C17C2×#9911yescharacteristic
128C22×C17C2×#10111yescharacteristic
129C22×C17#41811yescharacteristic
130C22×C17#41911yescharacteristic
131C22×C17C2×#10411yescharacteristic
132C22×C17#42111yescharacteristic
133C2×D17—22no—
134C2×D17—22no—
135C2×D17—22no—
136C2×D17—41no—
137C2×D17—41no—
138C2×D17—41no—
139C2×D17—41no—
140C4×C17—22no—
141C4×C17—22no—
142C4×C17—22no—
143C4×C17—82no—
144Dic17—22no—
145Dic17—22no—
146Dic17—41no—
147Dic17—82no—
148C2×C4⋊Q8#59511yescharacteristic
149C2×C22⋊Q8—341no—
150C22×C42—171no—
151C2×C22⋊C8—341no—
152C2×C22⋊C8—341no—
153C2×#97—341no—
154#391—341no—
155#389—172no—
156#389—341no—
157#384—171no—
158#380—172no—
159#380—341no—
160#336—172no—
161#336—172no—
162#336—341no—
163C2×C17#147211yescharacteristic
164C2×C17#148511yescharacteristic
165C2×C17#149611yescharacteristic
166C2×C17#150711yescharacteristic
167C2×C17#151111yescharacteristic
168C2×C17#153111yescharacteristic
169C2×C17#155611yescharacteristic
170D17—42no—
171C22×Q8—21no—
172C23×C4—171no—
173C23×C4—171no—
174C23×C4—171no—
175C22×C8—342no—
176C22×C8—342no—
177C4⋊Q8—42no—
178C22⋊Q8—684no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—172no—
181C2×C4⋊C4—342no—
182C2×C4⋊C4—341no—
183C2×C4⋊C4—341no—
184C2×C4⋊C4C2×#59512yes—
185C2×C22⋊C4—342no—
186C2×C42—171no—
187C2×C42—171no—
188C2×C42—171no—
189C2×C42—682no—
190C2×C42C2×#59511yescharacteristic
191C22⋊C8—344no—
192C22⋊C8—682no—
193#97—682no—
194#95—342no—
195#95—342no—
196C17#770511yescharacteristic, complemented, Sylow
197C24—171no—
198C2×Q8—42no—
199C2×Q8—42no—
200C2×Q8—42no—
201C22×C4—22no—
202C22×C4—171no—
203C22×C4—171no—
204C22×C4—171no—
205C22×C4—342no—
206C22×C4—342no—
207C22×C4—342no—
208C22×C4—342no—
209C22×C4—342no—
210C22×C4—342no—
211C22×C4—342no—
212C22×C4—681no—
213C22×C4—681no—
214C22×C4—681no—
215C22×C4C22⋊#59511yescharacteristic
216C22×C4C22⋊#59511yescharacteristic
217C22×C4C22×#59511yescharacteristic
218C2×C8—344no—
219C2×C8—682no—
220C2×C8—682no—
221C2×C8—682no—
222C2×C8—682no—
223C2×C8—682no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—344no—
227C4⋊C4—682no—
228C4⋊C4—682no—
229C4⋊C4—684no—
230C22⋊C4—684no—
231C42—22no—
232C42—342no—
233C42—681no—
234C42—681no—
235C23—172no—
236C23—341no—
237C23—341no—
238C23—341no—
239C23—341no—
240C23—341no—
241C23—341no—
242C23C2×C22⋊#59511yescharacteristic
243Q8—84no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—172no—
254C2×C4—172no—
255C2×C4—341no—
256C2×C4—341no—
257C2×C4—341no—
258C2×C4—341no—
259C2×C4—341no—
260C2×C4—341no—
261C2×C4—341no—
262C2×C4—684no—
263C2×C4—684no—
264C2×C4—684no—
265C2×C4—682no—
266C2×C4—682no—
267C2×C4—682no—
268C2×C4#1058754812yes—
269C2×C4#1058755112yes—
270C2×C4#1058768012yes—
271C8—684no—
272C8—1362no—
273C22—342no—
274C22—342no—
275C22—342no—
276C22—681no—
277C22—681no—
278C22—681no—
279C22—681no—
280C22#1176378411yescharacteristic
281C22C2×#1058755111yescharacteristic
282C22D17⋊#10111yescharacteristic
283C22#1176380111yescharacteristic
284C22#1176380211yescharacteristic
285C22C2×#1058754811yescharacteristic
286C22#1176380811yescharacteristic
287C4—22no—
288C4—22no—
289C4—22no—
290C4—82no—
291C4—342no—
292C4—342no—
293C4—681no—
294C4—1362no—
295C2—682no—
296C2#1454406411yescharacteristic
297C2#1454410811yescharacteristic
298C2#1454414511yescharacteristic
299C2#1454418011yescharacteristic
300C2#1454419411yescharacteristic
301C2#1454425711yescharacteristic
302C2#1454431411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×C4⋊Q8C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×C4⋊Q8#595
hypocenterC17#7705
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #14543603C2semidirect
196. C17#7705semidirect

Maximal subgroups

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

subgroupindex
#145446762
#145445112
#145436032
#145371312
#770517