Finite Group Databasebeta

← #17950032

Subgroups — #17950032

Order 4352.

468 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 92 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
2C4×#10587543C211yesmaximal, characteristic
3#14543602C212yesmaximal, complemented
4#14543602C212yesmaximal, complemented
5#14537095C211yesmaximal, characteristic
6C2×#10587543—21no—
7C2×#10587543—21no—
8C2×C4×#3624—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587556C411yescharacteristic
13C2×C42×D17C2211yescharacteristic
14#11762708C2211yescharacteristic
15#11762708C2211yescharacteristic
16#11762694—21no—
17#11762694—21no—
18#11762683—21no—
19#11762683—21no—
20#11762666C411yescharacteristic
21#11762666C411yescharacteristic
22C17×#382C411yescharacteristic
23C22×C4×D17C2×C411yescharacteristic
24C22×C4×D17D411yescharacteristic
25C22×C4×D17D411yescharacteristic
26C22×#3624—22no—
27C22×#3624—22no—
28C2×C4⋊C4×C17C2×C411yescharacteristic
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C42×C17C2×C411yescharacteristic
31C2×#63227—21no—
32C2×#63227—21no—
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17C2×C411yescharacteristic
36C2×C4⋊Dic17C2×C411yescharacteristic
37C2×#63225—21no—
38C2×#63225—21no—
39C2×C4×Dic17D411yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41C2×C4×Dic17C2311yescharacteristic
42C42×D17—42no—
43#10587556—42no—
44#10587543—24no—
45#10587543—42no—
46C4×#3624—42no—
47C17×#95—21no—
48C17×#95—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53C23×D17C22⋊C411yescharacteristic
54C22×C4×C17—21no—
55C22×C4×C17—21no—
56C22×C4×C17C22⋊C411yescharacteristic
57C22×C4×C17C22⋊C411yescharacteristic
58C22×C4×C17C22×C411yescharacteristic
59C22×Dic17—21no—
60C22×Dic17—21no—
61C22×Dic17C22⋊C411yescharacteristic
62C22×Dic17C2×D411yescharacteristic
63C22×Dic17C2×D411yescharacteristic
64C2×C4×D17—22no—
65C2×C4×D17—22no—
66C2×C4×D17—22no—
67C2×C4×D17—22no—
68C2×C4×D17—22no—
69C2×C4×D17—22no—
70C2×C4×D17—41no—
71C2×C4×D17—41no—
72C2×C4×D17—41no—
73C2×#3624—24no—
74C2×#3624—42no—
75C2×#3624—42no—
76C2×#3624—42no—
77C2×#3624—42no—
78C2×#3624—42no—
79C4⋊C4×C17—22no—
80C4⋊C4×C17—22no—
81C42×C17—22no—
82#63227—42no—
83#63227—42no—
84C4⋊Dic17—42no—
85C4⋊Dic17—42no—
86C4⋊Dic17—41no—
87C4⋊Dic17—41no—
88#63225—42no—
89#63225—42no—
90C4×Dic17—22no—
91C4×Dic17—41no—
92C4×Dic17—41no—
93#7671—171nomaximal, Sylow
94C23×C17C2×C22⋊C411yescharacteristic
95C22×D17—21no—
96C22×D17—21no—
97C22×D17—21no—
98C22×D17—21no—
99C22×D17—21no—
100C22×D17—21no—
101C22×D17#10412yes—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17#9912yes—
116C2×C4×C17#13112yes—
117C2×Dic17—21no—
118C2×Dic17—21no—
119C2×Dic17—21no—
120C2×Dic17—21no—
121C2×Dic17—21no—
122C2×Dic17—21no—
123C2×Dic17—41no—
124C2×Dic17—41no—
125C2×Dic17—41no—
126C2×Dic17—41no—
127C2×Dic17—41no—
128C2×Dic17—41no—
129C2×Dic17#10112yes—
130C2×Dic17#13512yes—
131C2×Dic17#13512yes—
132C4×D17—44no—
133C4×D17—44no—
134C4×D17—44no—
135#3624—44no—
136#3624—82no—
137#2851—171no—
138#1817—171no—
139C4×C22⋊C8—171no—
140#1271—172no—
141#1271—172no—
142C22×C17#40811yescharacteristic
143C22×C17C2×#9911yescharacteristic
144C22×C17C2×#10111yescharacteristic
145C22×C17#41611yescharacteristic
146C22×C17#41611yescharacteristic
147C22×C17C2×#10411yescharacteristic
148C22×C17#42111yescharacteristic
149C2×D17—22no—
150C2×D17—22no—
151C2×D17—22no—
152C2×D17—41no—
153C2×D17—41no—
154C2×D17—41no—
155C2×D17—41no—
156C4×C17—22no—
157C4×C17—22no—
158C4×C17—41no—
159C4×C17—81no—
160C4×C17—81no—
161Dic17—22no—
162Dic17—22no—
163Dic17—22no—
164Dic17—81no—
165Dic17—81no—
166C2×#125—171no—
167C22×C42—171no—
168C2×C22⋊C8—341no—
169C2×C22⋊C8—341no—
170C2×C4×C8—341no—
171#389—171no—
172#389—171no—
173#387—341no—
174#387—341no—
175#385—341no—
176#385—341no—
177#382#59511yescharacteristic
178#380—171no—
179#380—171no—
180#336—172no—
181#336—172no—
182#336—341no—
183C2×C17#147211yescharacteristic
184C2×C17#148211yescharacteristic
185C2×C17#149411yescharacteristic
186C2×C17#150111yescharacteristic
187C2×C17#151611yescharacteristic
188C2×C17#152811yescharacteristic
189C2×C17#154411yescharacteristic
190D17—42no—
191C23×C4—171no—
192C23×C4—171no—
193C23×C4—171no—
194C22×C8—342no—
195C22×C8—342no—
196#125—682no—
197C2×C4⋊C4—171no—
198C2×C4⋊C4—171no—
199C2×C4⋊C4—341no—
200C2×C4⋊C4—341no—
201C2×C4⋊C4—341no—
202C2×C4⋊C4—341no—
203C2×C4⋊C4C2×#59511yescharacteristic
204C2×C4⋊C4C2×#59511yescharacteristic
205C2×C22⋊C4—341no—
206C2×C22⋊C4—341no—
207C2×C42—171no—
208C2×C42—171no—
209C2×C42—171no—
210C2×C42—682no—
211C2×C42C2×#59511yescharacteristic
212C22⋊C8—344no—
213C22⋊C8—682no—
214C4×C8—682no—
215#95—21no—
216#95—21no—
217#95—341no—
218#95—341no—
219#95—341no—
220#95—341no—
221C17#767111yescharacteristic, complemented, Sylow
222C24—171no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—171no—
226C22×C4—171no—
227C22×C4—171no—
228C22×C4—342no—
229C22×C4—342no—
230C22×C4—342no—
231C22×C4—342no—
232C22×C4—342no—
233C22×C4—342no—
234C22×C4—341no—
235C22×C4—341no—
236C22×C4—681no—
237C22×C4—681no—
238C22×C4—681no—
239C22×C4C22⋊#59511yescharacteristic
240C22×C4C22⋊#59511yescharacteristic
241C22×C4C22×#59511yescharacteristic
242C2×C8—344no—
243C2×C8—682no—
244C2×C8—682no—
245C2×C8—682no—
246C2×C8—682no—
247C2×C8—682no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—681no—
251C4⋊C4—681no—
252C4⋊C4—682no—
253C4⋊C4—682no—
254C4⋊C4—682no—
255C4⋊C4—682no—
256C22⋊C4—682no—
257C22⋊C4—682no—
258C42—22no—
259C42—342no—
260C42—681no—
261C42—681no—
262C23—172no—
263C23—341no—
264C23—341no—
265C23—341no—
266C23—341no—
267C23—341no—
268C23—341no—
269C23C2×C22⋊#59511yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—172no—
284C2×C4—172no—
285C2×C4—172no—
286C2×C4—341no—
287C2×C4—341no—
288C2×C4—341no—
289C2×C4—341no—
290C2×C4—341no—
291C2×C4—341no—
292C2×C4—684no—
293C2×C4—684no—
294C2×C4—684no—
295C2×C4—681no—
296C2×C4—681no—
297C2×C4—681no—
298C2×C4—681no—
299C2×C4—681no—
300C2×C4—681no—
301C2×C4#1058753912yes—
302C2×C4#1058767812yes—
303C8—684no—
304C8—1362no—
305C22—342no—
306C22—342no—
307C22—342no—
308C22—681no—
309C22—681no—
310C22—681no—
311C22—681no—
312C22#1176378311yescharacteristic
313C22C2×#1058753911yescharacteristic
314C22D17⋊#10111yescharacteristic
315C22#1176379911yescharacteristic
316C22#1176379911yescharacteristic
317C22D17⋊#10411yescharacteristic
318C22#1176380611yescharacteristic
319C4—22no—
320C4—22no—
321C4—41no—
322C4—81no—
323C4—81no—
324C4—342no—
325C4—342no—
326C4—342no—
327C4—1361no—
328C4—1361no—
329C2—682no—
330C2#1454406211yescharacteristic
331C2#1454409611yescharacteristic
332C2#1454413611yescharacteristic
333C2#1454416111yescharacteristic
334C2#1454421211yescharacteristic
335C2#1454424711yescharacteristic
336C2#1454429011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#382C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#382#595
hypocenterC17#7671
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
3. #14543602C2semidirect
4. #14543602C2semidirect
221. C17#7671semidirect

Maximal subgroups

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

subgroupindex
#145446762
C4×#105875432
#145436022
#145370952
#767117