Finite Group Databasebeta

← #17950250

Subgroups — #17950250

Order 4352.

450 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 90 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#14544639C211yesmaximal, characteristic
3#14543603C212yesmaximal, complemented
4#14543603C212yesmaximal, complemented
5#14537089C211yesmaximal, characteristic
6C2×C4⋊#3624—21no—
7C2×#10587543—21no—
8C2×#10587543—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×C42×D17C2211yescharacteristic
13#11762705C2211yescharacteristic
14#11762705C2211yescharacteristic
15#11762690—21no—
16#11762690—21no—
17#11762680—21no—
18#11762680—21no—
19#11762675C411yescharacteristic
20#11762666C411yescharacteristic
21#11762666C411yescharacteristic
22C2×C17×#125C411yescharacteristic
23C22×C4×D17C2×C411yescharacteristic
24C22×C4×D17D411yescharacteristic
25C22×C4×D17D411yescharacteristic
26C22×#3624—22no—
27C22×#3624—22no—
28C17×#125—42no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17C2×C411yescharacteristic
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C42×C17C2×C411yescharacteristic
34C2×#63227—21no—
35C2×#63227—21no—
36C2×C4⋊Dic17C2×C411yescharacteristic
37C2×C4⋊Dic17C2×C411yescharacteristic
38C2×#63225—21no—
39C2×#63225—21no—
40C2×C4×Dic17D411yescharacteristic
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17C2311yescharacteristic
43C42×D17—42no—
44#10587543—42no—
45#10587543—42no—
46C4⋊#3624—42no—
47#10587502—21no—
48#10587502—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—21no—
69C2×C4×D17—21no—
70C2×C4×D17—41no—
71C2×C4×D17—41no—
72C2×C4×D17—41no—
73C2×C4×D17—41no—
74C2×#3624—42no—
75C2×#3624—42no—
76C2×#3624—42no—
77C2×#3624—42no—
78C2×#3624—42no—
79C2×#3624—42no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—41no—
82C4⋊C4×C17—42no—
83C4⋊C4×C17—42no—
84C42×C17—22no—
85#63227—42no—
86#63227—42no—
87C4⋊Dic17—22no—
88C4⋊Dic17—22no—
89#63225—42no—
90#63225—41no—
91#63225—41no—
92C4×Dic17—22no—
93C4×Dic17—41no—
94C4×Dic17—41no—
95#7731—171nomaximal, Sylow
96C23×C17C2×C22⋊C411yescharacteristic
97C22×D17—21no—
98C22×D17—21no—
99C22×D17—21no—
100C22×D17—21no—
101C22×D17—21no—
102C22×D17—21no—
103C22×D17#10112yes—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—21no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—41no—
117C2×C4×C17#9912yes—
118C2×C4×C17#13112yes—
119C2×Dic17—21no—
120C2×Dic17—21no—
121C2×Dic17—21no—
122C2×Dic17—21no—
123C2×Dic17—21no—
124C2×Dic17—21no—
125C2×Dic17—21no—
126C2×Dic17—41no—
127C2×Dic17—41no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131C2×Dic17—41no—
132C2×Dic17#13512yes—
133C2×Dic17AGL(1,ℤ/8)11yescharacteristic
134C2×Dic17#13711yescharacteristic
135C4×D17—44no—
136C4×D17—42no—
137C4×D17—42no—
138C4×D17—44no—
139#3624—82no—
140#3624—82no—
141#2851—171no—
142#1817—171no—
143#1797—171no—
144#1271—172no—
145#1271—172no—
146C22×C17#40811yescharacteristic
147C22×C17C2×#9911yescharacteristic
148C22×C17C2×#10111yescharacteristic
149C22×C17#41611yescharacteristic
150C22×C17#41711yescharacteristic
151C22×C17#42111yescharacteristic
152C22×C17#42111yescharacteristic
153C2×D17—22no—
154C2×D17—22no—
155C2×D17—22no—
156C2×D17—41no—
157C2×D17—41no—
158C2×D17—41no—
159C2×D17—41no—
160C4×C17—22no—
161C4×C17—22no—
162C4×C17—41no—
163C4×C17—81no—
164C4×C17—81no—
165Dic17—21no—
166Dic17—21no—
167Dic17—22no—
168Dic17—41no—
169Dic17—81no—
170Dic17—81no—
171C2×#125#59511yescharacteristic
172C22×C42—171no—
173C2×C4⋊C8—341no—
174C2×C22⋊C8—341no—
175C2×C22⋊C8—341no—
176#389—171no—
177#389—171no—
178#387—341no—
179#387—341no—
180#385—341no—
181#385—341no—
182#382—171no—
183#380—171no—
184#380—171no—
185#336—172no—
186#336—172no—
187#336—341no—
188C2×C17#147211yescharacteristic
189C2×C17#148211yescharacteristic
190C2×C17#149511yescharacteristic
191C2×C17#151311yescharacteristic
192C2×C17#151611yescharacteristic
193C2×C17#153411yescharacteristic
194C2×C17#155211yescharacteristic
195D17—42no—
196C23×C4—171no—
197C23×C4—171no—
198C23×C4—171no—
199C22×C8—342no—
200C22×C8—342no—
201#125—42no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—171no—
205C2×C4⋊C4—171no—
206C2×C4⋊C4—341no—
207C2×C4⋊C4—341no—
208C2×C4⋊C4C2×#59511yescharacteristic
209C2×C4⋊C4C2×#59511yescharacteristic
210C2×C22⋊C4—341no—
211C2×C22⋊C4—341no—
212C2×C42—171no—
213C2×C42—171no—
214C2×C42—171no—
215C2×C42—682no—
216C2×C42C2×#59511yescharacteristic
217C4⋊C8—682no—
218C22⋊C8—682no—
219C22⋊C8—682no—
220#95—341no—
221#95—341no—
222#95—341no—
223#95—341no—
224#95—341no—
225#95—341no—
226C17#773111yescharacteristic, complemented, Sylow
227C24—171no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—171no—
231C22×C4—171no—
232C22×C4—171no—
233C22×C4—341no—
234C22×C4—342no—
235C22×C4—341no—
236C22×C4—342no—
237C22×C4—342no—
238C22×C4—342no—
239C22×C4—341no—
240C22×C4—341no—
241C22×C4—681no—
242C22×C4—681no—
243C22×C4—681no—
244C22×C4—681no—
245C22×C4C22⋊#59511yescharacteristic
246C22×C4C22⋊#59511yescharacteristic
247C22×C4C22×#59511yescharacteristic
248C2×C8—682no—
249C2×C8—682no—
250C2×C8—682no—
251C2×C8—682no—
252C2×C8—682no—
253C2×C8—682no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—342no—
259C4⋊C4—342no—
260C4⋊C4—682no—
261C4⋊C4—681no—
262C4⋊C4—681no—
263C22⋊C4—682no—
264C22⋊C4—682no—
265C42—22no—
266C42—342no—
267C42—681no—
268C42—681no—
269C23—172no—
270C23—341no—
271C23—341no—
272C23—341no—
273C23—341no—
274C23—341no—
275C23—341no—
276C23C2×C22⋊#59511yescharacteristic
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—172no—
291C2×C4—171no—
292C2×C4—171no—
293C2×C4—341no—
294C2×C4—341no—
295C2×C4—341no—
296C2×C4—341no—
297C2×C4—341no—
298C2×C4—341no—
299C2×C4—341no—
300C2×C4—684no—
301C2×C4—684no—
302C2×C4—682no—
303C2×C4—682no—
304C2×C4—681no—
305C2×C4—681no—
306C2×C4—681no—
307C2×C4—681no—
308C2×C4—681no—
309C2×C4—681no—
310C2×C4#1058755112yes—
311C2×C4#1058768012yes—
312C8—1362no—
313C8—1362no—
314C22—342no—
315C22—342no—
316C22—342no—
317C22—681no—
318C22—681no—
319C22—681no—
320C22—681no—
321C22#1176378411yescharacteristic
322C22C2×#1058755111yescharacteristic
323C22D17⋊#10111yescharacteristic
324C22#1176379911yescharacteristic
325C22#1176380011yescharacteristic
326C22#1176380611yescharacteristic
327C22#1176380611yescharacteristic
328C4—22no—
329C4—22no—
330C4—41no—
331C4—81no—
332C4—81no—
333C4—341no—
334C4—341no—
335C4—342no—
336C4—681no—
337C4—1361no—
338C4—1361no—
339C2—682no—
340C2#1454406411yescharacteristic
341C2#1454409811yescharacteristic
342C2#1454414211yescharacteristic
343C2#1454419911yescharacteristic
344C2#1454421011yescharacteristic
345C2#1454426711yescharacteristic
346C2#1454430611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×#125C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×#125#595
hypocenterC17#7731
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
3. #14543603C2semidirect
4. #14543603C2semidirect
226. C17#7731semidirect

Maximal subgroups

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

subgroupindex
#145446762
#145446392
#145436032
#145370892
#773117