Finite Group Databasebeta

← #21437161

Subgroups — #21437161

Order 7552.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838134C211yesmaximal, characteristic, complemented
2#16838126C211yesmaximal, characteristic, complemented
3#16837788C211yesmaximal, characteristic
4#16837787C211yesmaximal, characteristic, complemented
5#16837626C211yesmaximal, characteristic, complemented
6#16837626C211yesmaximal, characteristic, complemented
7#16837619C211yesmaximal, characteristic, complemented
8#16837614C211yesmaximal, characteristic, complemented
9#16837604C211yesmaximal, characteristic, complemented
10#16837600C211yesmaximal, characteristic, complemented
11#16837530C211yesmaximal, characteristic, complemented
12#16837515C211yesmaximal, characteristic, complemented
13#16837509C211yesmaximal, characteristic, complemented
14SD16×Dic59C211yesmaximal, characteristic, complemented
15C59×#497C211yesmaximal, characteristic, complemented
16C2×#11745671C2211yescharacteristic
17C2×#11745671C2211yescharacteristic
18C2×#11745671C2211yescharacteristic
19C2×D472C2211yescharacteristic
20C2×#11745669C2211yescharacteristic
21#14273723C2211yescharacteristic
22#14273722—21no—
23#14273722—21no—
24#14273716C2211yescharacteristic
25#14273716C2211yescharacteristic
26#14273716C2211yescharacteristic
27#14273713—21no—
28#14273711—21no—
29#14273709—21no—
30#14273707—21no—
31Q8×Dic59C2211yescharacteristic
32Q8×Dic59C2211yescharacteristic
33Q8×Dic59C2211yescharacteristic
34C4×Dic118C2211yescharacteristic
35C4×D236C2211yescharacteristic
36C4×D236C2211yescharacteristic
37D4×Dic59C2211yescharacteristic
38(C22⋊D59)⋊C4—21no—
39#14273685—21no—
40#14273659C2211yescharacteristic
41C4⋊(C59⋊C8)C2211yescharacteristic
42Dic59⋊C8C2211yescharacteristic
43Dic59⋊C8C2211yescharacteristic
44#14273651C2211yescharacteristic
45#14273651C2211yescharacteristic
46#14273651C2211yescharacteristic
47#14273649C2211yescharacteristic
48#14273649C2211yescharacteristic
49#14273648C2211yescharacteristic
50#14273637C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52C2×Q16×C59C2211yescharacteristic
53C2×Q16×C59C2211yescharacteristic
54C2×SD16×C59C2211yescharacteristic
55C2×SD16×C59C2211yescharacteristic
56C4⋊Q8×C59C2211yescharacteristic
57#124×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic
59C2×Q8×C59C2311yescharacteristic
60C2×Q8×C59C2311yescharacteristic
61C2×Q8×C59C2311yescharacteristic
62C2×D4×C59C2311yescharacteristic
63C2×C22⋊D59—21no—
64C2×C22⋊D59—21no—
65C22×Dic59—21no—
66C2×D236C2311yescharacteristic
67C2×D236C2311yescharacteristic
68C2×C4×D59—21no—
69C2×C4×D59—21no—
70C2×Dic118D411yescharacteristic
71Q16×C59—22no—
72Q16×C59—41no—
73SD16×C59—22no—
74SD16×C59—41no—
75C2×C8×C59C2311yescharacteristic
76C2×C8×C59C2311yescharacteristic
77C4⋊C4×C59—21no—
78C4⋊C4×C59—21no—
79C22⋊C4×C59—21no—
80C22⋊C4×C59—21no—
81C42×C59C2311yescharacteristic
82C22⋊Dic59—21no—
83#11745671—41no—
84#11745671—41no—
85#11745671—41no—
86#11745669—41no—
87(C2×D59)⋊C4—21no—
88(C2×D59)⋊C4—21no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95C4⋊Dic59—21no—
96C4⋊Dic59—21no—
97C4⋊Dic59—21no—
98C4⋊Dic59D411yescharacteristic
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101Dic59⋊C4D411yescharacteristic
102Dic59⋊C4D411yescharacteristic
103C4×Dic59—21no—
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59C2311yescharacteristic
107C4×Dic59C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110D472—22no—
111C23×C59—21no—
112C22×D59—21no—
113C22×D59—21no—
114Q8×C59—21no—
115Q8×C59—21no—
116Q8×C59—21no—
117Q8×C59—21no—
118Q8×C59—21no—
119Q8×C59—21no—
120D4×C59—21no—
121D4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2411yescharacteristic
128C22⋊D59—42no—
129C22⋊D59—81no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—81no—
133C2×Dic59C2×D411yescharacteristic
134C2×Dic59C2×D411yescharacteristic
135C2×Dic59C2×D411yescharacteristic
136C2×Dic59C2×D411yescharacteristic
137D236—21no—
138D236—21no—
139D236—21no—
140D236—21no—
141C4×D59—42no—
142C4×D59—81no—
143Dic118—41no—
144C8×C59—21no—
145C8×C59#4112yes—
146C59⋊C8—21no—
147C59⋊C8—21no—
148C22×C59—41no—
149C22×C59—41no—
150C22×C59—41no—
151C22×C59C22×D411yescharacteristic
152C2×D59—41no—
153C2×D59—41no—
154C2×D59—41no—
155C2×D59—41no—
156C2×D59—41no—
157C2×D59—41no—
158C4×C59—21no—
159C4×C59—21no—
160C4×C59—41no—
161C4×C59—41no—
162C4×C59—41no—
163C4×C59C2×#4111yescharacteristic
164C4×C59H(5,𝔽2)11yescharacteristic
165Dic59—21no—
166Dic59—21no—
167Dic59—21no—
168Dic59—21no—
169Dic59—41no—
170Dic59—41no—
171#3401—591nomaximal, Sylow
172C2×C59—81no—
173C2×C59#55011yescharacteristic
174C2×C59#57511yescharacteristic
175C2×C59#57711yescharacteristic
176D59—81no—
177D59—81no—
178#559—591no—
179#556—591no—
180#497D5911yescharacteristic, complemented
181#496—591no—
182#495—591no—
183#464—591no—
184#464—591no—
185#463—591no—
186#463—591no—
187#461—591no—
188#460—591no—
189#446—591no—
190#442—591no—
191#441—591no—
192C4×SD16—591no—
193C59#340111yescharacteristic, complemented, Sylow
194C2×Q16C2×D5911yescharacteristic
195C2×Q16C2×D5911yescharacteristic
196C2×SD16—591no—
197C2×SD16—591no—
198C2×SD16—591no—
199C2×SD16C2×D5911yescharacteristic
200C2×SD16C2×D5911yescharacteristic
201C2×D8—591no—
202C2×D8—591no—
203C4⋊Q8C2×D5911yescharacteristic
204#127—591no—
205#126—1181no—
206#126—1181no—
207#124—591no—
208#124—591no—
209#124—591no—
210#124—1181no—
211#124C2×D5911yescharacteristic
212#123—1181no—
213#123—1181no—
214C22⋊Q8—1181no—
215C4×Q8—591no—
216C4×Q8—591no—
217C4×Q8—591no—
218C4×Q8—591no—
219C4×D4—591no—
220C4×D4—591no—
221C4×D4—591no—
222C4×D4—1181no—
223#117—1181no—
224#106—591no—
225C4⋊C8—591no—
226C4⋊C8—591no—
227C4⋊C8—591no—
228#103—591no—
229#103—591no—
230#103—591no—
231#102—591no—
232#102—591no—
233#102—591no—
234#97—591no—
235#97C2×D5911yescharacteristic
236C4×C8—591no—
237C2×Q8—591no—
238C2×Q8C22×D5911yescharacteristic
239C2×Q8C22×D5911yescharacteristic
240C2×Q8C22×D5911yescharacteristic
241C2×D4—591no—
242C2×D4—591no—
243C2×D4—1181no—
244C2×D4—1181no—
245C2×D4C22×D5911yescharacteristic
246C22×C4—1181no—
247C22×C4—1181no—
248C22×C4—1181no—
249Q16—22no—
250Q16—41no—
251SD16—22no—
252SD16—41no—
253SD16—2361no—
254SD16—2361no—
255SD16—2361no—
256D8—1182no—
257D8—2361no—
258C2×C8—591no—
259C2×C8—591no—
260C2×C8C22×D5911yescharacteristic
261C2×C8C22×D5911yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—591no—
265C4⋊C4—591no—
266C4⋊C4—591no—
267C4⋊C4—591no—
268C4⋊C4—591no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4—1181no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—1181no—
275C22⋊C4—1181no—
276C22⋊C4—1181no—
277C22⋊C4—1181no—
278C22⋊C4—1181no—
279C22⋊C4—1181no—
280C22⋊C4—1181no—
281C22⋊C4—1181no—
282C22⋊C4—1181no—
283C42—591no—
284C42—591no—
285C42—1181no—
286C42—1181no—
287C42—1181no—
288C42C22×D5911yescharacteristic
289C23—21no—
290C23—1181no—
291C23—1181no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—2361no—
299D4—21no—
300D4—21no—
301D4—1181no—
302D4—1181no—
303D4—1181no—
304D4—1181no—
305D4—4721no—
306D4—2362no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—591no—
311C2×C4—591no—
312C2×C4—591no—
313C2×C4—591no—
314C2×C4—1181no—
315C2×C4—1181no—
316C2×C4—4721no—
317C2×C4—4721no—
318C2×C4—2362no—
319C2×C4D4×D5911yescharacteristic
320C2×C4D4×D5911yescharacteristic
321C2×C4C23×D5911yescharacteristic
322C8—21no—
323C8—1181no—
324C8—1181no—
325C8#1174568712yes—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—2361no—
330C22—2361no—
331C22—2361no—
332C22—2361no—
333C22—2361no—
334C22—2361no—
335C22C2×D4×D5911yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—1181no—
342C4—1181no—
343C4—1181no—
344C4—1181no—
345C4—2361no—
346C4—2361no—
347C4C2×#1174568711yescharacteristic
348C4#1427377211yescharacteristic
349C2—81no—
350C2—4721no—
351C2—4721no—
352C2#1683807211yescharacteristic
353C2#1683820111yescharacteristic
354C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#497C2
socleC22×C59C22×D4
hypercenter#497D59
hypocenterC59#3401
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #16838134C2semidirect
2. #16838126C2semidirect
4. #16837787C2semidirect
5. #16837626C2semidirect
6. #16837626C2semidirect
7. #16837619C2semidirect
8. #16837614C2semidirect
9. #16837604C2semidirect
10. #16837600C2semidirect
11. #16837530C2semidirect
12. #16837515C2semidirect
13. #16837509C2semidirect
14. SD16×Dic59C2semidirect
15. C59×#497C2semidirect
180. #497D59semidirect
193. C59#3401semidirect