Finite Group Databasebeta

← #21436269

Subgroups — #21436269

Order 7552.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838098C211yesmaximal, characteristic
2D4×Dic118C211yesmaximal, characteristic, complemented
3#16837771C211yesmaximal, characteristic, complemented
4#16837744C211yesmaximal, characteristic, complemented
5#16837738C211yesmaximal, characteristic, complemented
6#16837710C211yesmaximal, characteristic, complemented
7#16837648C211yesmaximal, characteristic, complemented
8#16837631C211yesmaximal, characteristic, complemented
9#16837608C211yesmaximal, characteristic, complemented
10#16837543C211yesmaximal, characteristic, complemented
11#16837543C211yesmaximal, characteristic, complemented
12#16837504C211yesmaximal, characteristic, complemented
13#16837412C211yesmaximal, characteristic, complemented
14C2×#14273652C211yesmaximal, characteristic, complemented
15C59×#435C211yesmaximal, characteristic, complemented
16C22×Dic118C2211yescharacteristic
17C22×Dic118C2211yescharacteristic
18C2×#11745660C2211yescharacteristic
19C2×#11745660C2211yescharacteristic
20C2×#11745660C2211yescharacteristic
21#14273727C2211yescharacteristic
22#14273726—21no—
23#14273722—21no—
24#14273719C2211yescharacteristic
25#14273709—21no—
26#14273706C2211yescharacteristic
27#14273706C2211yescharacteristic
28#14273704—21no—
29#14273704—21no—
30#14273701C2211yescharacteristic
31#14273701C2211yescharacteristic
32#14273699—21no—
33C4×Dic118C2211yescharacteristic
34C4×D236C2211yescharacteristic
35D4×Dic59—21no—
36(C22⋊D59)⋊C4—21no—
37#14273686C2211yescharacteristic
38C2×C4⋊Dic59C2211yescharacteristic
39#14273661C2211yescharacteristic
40#14273661C2211yescharacteristic
41#14273659C2211yescharacteristic
42#14273652C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273652C2211yescharacteristic
46#14273652C2211yescharacteristic
47#14273652C2211yescharacteristic
48#14273652C2211yescharacteristic
49#14273652C2211yescharacteristic
50#14273652C2211yescharacteristic
51#14273649C2211yescharacteristic
52C2×M16×C59C2211yescharacteristic
53C22×C8×C59C2211yescharacteristic
54C4×D4×C59C2211yescharacteristic
55C4⋊C8×C59C2211yescharacteristic
56C22⋊C8×C59C2211yescharacteristic
57C22⋊C8×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic
59C2×D4×C59D411yescharacteristic
60C22×C4×C59C2311yescharacteristic
61C22×C4×C59C2311yescharacteristic
62C2×C22⋊D59—21no—
63C2×C22⋊D59—21no—
64C22×Dic59—21no—
65C22×Dic59—21no—
66C22×Dic59—21no—
67C2×D236C2311yescharacteristic
68C2×C4×D59—21no—
69C2×Dic118—22no—
70C2×Dic118—22no—
71C2×Dic118—21no—
72C2×Dic118—21no—
73C2×Dic118—41no—
74C2×Dic118—41no—
75C2×Dic118C2311yescharacteristic
76C2×Dic118C2311yescharacteristic
77C2×Dic118C2311yescharacteristic
78M16×C59—41no—
79C2×C8×C59—41no—
80C2×C8×C59C2311yescharacteristic
81C2×C8×C59C2311yescharacteristic
82C2×C8×C59C2311yescharacteristic
83C2×C8×C59C2311yescharacteristic
84C4⋊C4×C59D411yescharacteristic
85C22⋊C4×C59D411yescharacteristic
86C22⋊C4×C59D411yescharacteristic
87C42×C59C2311yescharacteristic
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90C22⋊Dic59—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94C4⋊Dic59—21no—
95C4⋊Dic59—21no—
96C4⋊Dic59—21no—
97C4⋊Dic59C2311yescharacteristic
98C4⋊Dic59C2311yescharacteristic
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106C4×Dic59—21no—
107C4×Dic59—21no—
108#11745660—22no—
109#11745660—41no—
110#11745660—41no—
111C23×C59C2×D411yescharacteristic
112C23×C59C2×D411yescharacteristic
113C22×D59—21no—
114D4×C59—22no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59C2×D411yescharacteristic
120C2×C4×C59C2×D411yescharacteristic
121C2×C4×C59C2×D411yescharacteristic
122C2×C4×C59C2×D411yescharacteristic
123C2×C4×C59C2411yescharacteristic
124C22⋊D59—42no—
125C22⋊D59—81no—
126C2×Dic59—21no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59—42no—
134C2×Dic59—42no—
135C2×Dic59—81no—
136D236—21no—
137D236—21no—
138C4×D59—81no—
139Dic118—21no—
140Dic118—21no—
141Dic118—21no—
142Dic118—21no—
143Dic118—21no—
144Dic118—42no—
145Dic118—42no—
146Dic118#4112yes—
147C8×C59—21no—
148C8×C59—21no—
149C8×C59—21no—
150C8×C59—21no—
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59#13712yes—
157C22×C59C22×D411yescharacteristic
158C2×D59—41no—
159C2×D59—41no—
160C2×D59—41no—
161C4×C59—21no—
162C4×C59—21no—
163C4×C59—21no—
164C4×C59—21no—
165C4×C59C2×#4111yescharacteristic
166C4×C59H(5,𝔽2)11yescharacteristic
167Dic59—22no—
168Dic59—41no—
169Dic59—41no—
170Dic59—41no—
171Dic59—41no—
172Dic59—41no—
173Dic59—41no—
174#3320—591nomaximal, Sylow
175C2×C59—22no—
176C2×C59—41no—
177C2×C59#54611yescharacteristic
178C2×C59C2×#13711yescharacteristic
179C2×C59#57711yescharacteristic
180D59—81no—
181#553—591no—
182D4×Q8—591no—
183#491—591no—
184#485—591no—
185#484—591no—
186#479—591no—
187#468—591no—
188#465—591no—
189#461—591no—
190#448—591no—
191#448—591no—
192#440—591no—
193#435D5911yescharacteristic, complemented
194#419—591no—
195C2×#103—591no—
196C59#332011yescharacteristic, complemented, Sylow
197C22×Q8—591no—
198C22×Q8—591no—
199C2×SD16—591no—
200C2×SD16—591no—
201C2×SD16—591no—
202C2×M16C2×D5911yescharacteristic
203C22×C8C2×D5911yescharacteristic
204C4⋊Q8—591no—
205C4⋊Q8—1181no—
206#126—1181no—
207#125—591no—
208#123—1181no—
209C22⋊Q8—591no—
210C22⋊Q8—591no—
211C22⋊Q8—1181no—
212C22⋊Q8—1181no—
213#121—591no—
214#121—591no—
215#121—1181no—
216C4×Q8—591no—
217C4×D4—591no—
218C4×D4—1181no—
219C4×D4—1181no—
220C4×D4C2×D5911yescharacteristic
221#117—591no—
222C2×C4⋊C4—591no—
223#107—591no—
224#107—591no—
225#106—591no—
226C4⋊C8C2×D5911yescharacteristic
227#103—591no—
228#103—591no—
229#103—591no—
230#103—591no—
231#103—591no—
232#103—591no—
233#103—591no—
234#103—591no—
235#103—591no—
236#102—591no—
237C22⋊C8C2×D5911yescharacteristic
238C22⋊C8C2×D5911yescharacteristic
239#97C2×D5911yescharacteristic
240C2×Q8—591no—
241C2×Q8—591no—
242C2×Q8—591no—
243C2×Q8—1182no—
244C2×Q8—1182no—
245C2×Q8—1181no—
246C2×Q8—1181no—
247C2×Q8—2361no—
248C2×Q8—2361no—
249C2×D4—591no—
250C2×D4—1181no—
251C2×D4—1181no—
252C2×D4D23611yescharacteristic
253C22×C4—1181no—
254C22×C4—1181no—
255C22×C4—1181no—
256C22×C4—1181no—
257C22×C4C22×D5911yescharacteristic
258C22×C4C22×D5911yescharacteristic
259SD16—1182no—
260SD16—2361no—
261SD16—2361no—
262M16—41no—
263C2×C8—41no—
264C2×C8C22×D5911yescharacteristic
265C2×C8C22×D5911yescharacteristic
266C2×C8C22×D5911yescharacteristic
267C2×C8C22×D5911yescharacteristic
268C4⋊C4—591no—
269C4⋊C4—591no—
270C4⋊C4—591no—
271C4⋊C4—591no—
272C4⋊C4—1181no—
273C4⋊C4—1181no—
274C4⋊C4—1181no—
275C4⋊C4—1181no—
276C4⋊C4—1181no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4—1181no—
280C4⋊C4D23611yescharacteristic
281C22⋊C4—1181no—
282C22⋊C4—1181no—
283C22⋊C4—1181no—
284C22⋊C4—1181no—
285C22⋊C4—1181no—
286C22⋊C4—1181no—
287C22⋊C4D23611yescharacteristic
288C22⋊C4D23611yescharacteristic
289C42—1181no—
290C42—1181no—
291C42C22×D5911yescharacteristic
292C23—1181no—
293C23C2×D23611yescharacteristic
294C23C2×D23611yescharacteristic
295Q8—592no—
296Q8—1181no—
297Q8—1181no—
298Q8—1181no—
299Q8—1181no—
300Q8—1181no—
301Q8—2362no—
302Q8—2362no—
303D4—22no—
304D4—1181no—
305D4—1181no—
306D4—4721no—
307D4—2362no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—1181no—
313C2×C4—1181no—
314C2×C4—1181no—
315C2×C4—1181no—
316C2×C4—1181no—
317C2×C4—1181no—
318C2×C4—1181no—
319C2×C4—4721no—
320C2×C4—4721no—
321C2×C4—2362no—
322C2×C4—2362no—
323C2×C4C2×D23611yescharacteristic
324C2×C4C2×D23611yescharacteristic
325C2×C4C2×D23611yescharacteristic
326C2×C4C2×D23611yescharacteristic
327C2×C4C23×D5911yescharacteristic
328C8—21no—
329C8—21no—
330C8—21no—
331C8—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—2361no—
338C22—2361no—
339C22—2361no—
340C22#1427376012yes—
341C22C22×D23611yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—1182no—
347C4—2361no—
348C4—2361no—
349C4—2361no—
350C4—2361no—
351C4—2361no—
352C4—2361no—
353C4#41×D5911yescharacteristic
354C4#1427377211yescharacteristic
355C2—22no—
356C2—41no—
357C2—4721no—
358C2#1683804711yescharacteristic
359C2C2×#1427376011yescharacteristic
360C2#1683821411yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#435C2
socleC22×C59C22×D4
hypercenter#435D59
hypocenterC59#3320
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. D4×Dic118C2semidirect
3. #16837771C2semidirect
4. #16837744C2semidirect
5. #16837738C2semidirect
6. #16837710C2semidirect
7. #16837648C2semidirect
8. #16837631C2semidirect
9. #16837608C2semidirect
10. #16837543C2semidirect
11. #16837543C2semidirect
12. #16837504C2semidirect
13. #16837412C2semidirect
14. C2×#14273652C2semidirect
15. C59×#435C2semidirect
193. #435D59semidirect
196. C59#3320semidirect