Finite Group Databasebeta

← #21437157

Subgroups — #21437157

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#16838138C211yesmaximal, characteristic, complemented
2#16838121C211yesmaximal, characteristic, complemented
3#16837793C211yesmaximal, characteristic, complemented
4#16837785C211yesmaximal, characteristic, complemented
5#16837622C211yesmaximal, characteristic, complemented
6#16837621C211yesmaximal, characteristic, complemented
7#16837615C211yesmaximal, characteristic, complemented
8#16837615C211yesmaximal, characteristic, complemented
9#16837605C211yesmaximal, characteristic, complemented
10#16837599C211yesmaximal, characteristic, complemented
11#16837530C211yesmaximal, characteristic, complemented
12#16837514C211yesmaximal, characteristic, complemented
13#16837510C211yesmaximal, characteristic, complemented
14SD16×Dic59C211yesmaximal, characteristic, complemented
15C59×#496C211yesmaximal, characteristic
16C2×Dic236C2211yescharacteristic
17C2×#11745672C2211yescharacteristic
18C2×#11745670C2211yescharacteristic
19C2×#11745670C2211yescharacteristic
20C2×#11745670C2211yescharacteristic
21#14273725C2211yescharacteristic
22#14273720—21no—
23#14273720—21no—
24#14273714—21no—
25#14273714C2211yescharacteristic
26#14273714C2211yescharacteristic
27#14273714C2211yescharacteristic
28#14273708—21no—
29#14273708—21no—
30#14273704—21no—
31Q8×Dic59C2211yescharacteristic
32C4×Dic118C2211yescharacteristic
33C4×Dic118C2211yescharacteristic
34C4×Dic118C2211yescharacteristic
35D4×Dic59—21no—
36D4×Dic59C2211yescharacteristic
37D4×Dic59C2211yescharacteristic
38D4×Dic59C2211yescharacteristic
39#14273683—21no—
40#14273659C2211yescharacteristic
41C4⋊(C59⋊C8)C2211yescharacteristic
42Dic59⋊C8C2211yescharacteristic
43Dic59⋊C8C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273652C2211yescharacteristic
46#14273651C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273648C2211yescharacteristic
49#14273648C2211yescharacteristic
50#14273637C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52C2×SD16×C59C2211yescharacteristic
53C2×SD16×C59C2211yescharacteristic
54C2×D8×C59C2211yescharacteristic
55C2×D8×C59C2211yescharacteristic
56#127×C59C2211yescharacteristic
57#124×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic
59C2×Q8×C59C2311yescharacteristic
60C2×D4×C59—21no—
61C2×D4×C59—21no—
62C2×D4×C59C2311yescharacteristic
63C2×D4×C59C2311yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C22×Dic59—21no—
66C22×Dic59—21no—
67C22×Dic59—21no—
68C2×Dic118D411yescharacteristic
69C2×Dic118C2311yescharacteristic
70C2×Dic118C2311yescharacteristic
71SD16×C59—22no—
72SD16×C59—41no—
73D8×C59—22no—
74D8×C59—41no—
75C2×C8×C59C2311yescharacteristic
76C2×C8×C59C2311yescharacteristic
77C22⋊C4×C59—21no—
78C22⋊C4×C59—21no—
79C42×C59C2311yescharacteristic
80C22⋊Dic59—21no—
81C22⋊Dic59—21no—
82C22⋊Dic59—21no—
83C22⋊Dic59—21no—
84C22⋊Dic59—21no—
85C22⋊Dic59—21no—
86C22⋊Dic59—21no—
87C22⋊Dic59—21no—
88C22⋊Dic59—21no—
89#11745672—41no—
90#11745670—41no—
91#11745670—41no—
92#11745670—41no—
93C4⋊Dic59—21no—
94C4⋊Dic59D411yescharacteristic
95C4⋊Dic59C2311yescharacteristic
96C4⋊Dic59C2311yescharacteristic
97Dic59⋊C4—21no—
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4D411yescharacteristic
102Dic59⋊C4D411yescharacteristic
103C4×Dic59—21no—
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59C2311yescharacteristic
107C4×Dic59C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110Dic236—22no—
111C23×C59—21no—
112C23×C59—21no—
113C23×C59—21no—
114Q8×C59—21no—
115Q8×C59—21no—
116D4×C59—21no—
117D4×C59—21no—
118D4×C59—21no—
119D4×C59—21no—
120D4×C59—21no—
121D4×C59—21no—
122D4×C59—42no—
123D4×C59—81no—
124C2×C4×C59—21no—
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2411yescharacteristic
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—42no—
133C2×Dic59—81no—
134C2×Dic59—81no—
135C2×Dic59C2×D411yescharacteristic
136C2×Dic59C2×D411yescharacteristic
137C2×Dic59C2×D411yescharacteristic
138C2×Dic59C2×D411yescharacteristic
139Dic118—21no—
140Dic118—21no—
141Dic118—21no—
142Dic118—21no—
143Dic118—41no—
144C8×C59—21no—
145C8×C59#4112yes—
146C59⋊C8—21no—
147C59⋊C8—21no—
148C22×C59—41no—
149C22×C59—41no—
150C22×C59—41no—
151C22×C59—41no—
152C22×C59—41no—
153C22×C59—41no—
154C22×C59—41no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59C22×D411yescharacteristic
158C4×C59—21no—
159C4×C59—21no—
160C4×C59—41no—
161C4×C59C2×#4111yescharacteristic
162C4×C59H(5,𝔽2)11yescharacteristic
163Dic59—21no—
164Dic59—21no—
165Dic59—21no—
166Dic59—21no—
167Dic59—41no—
168Dic59—41no—
169Dic59—41no—
170Dic59—41no—
171#3401—591nomaximal, Sylow
172C2×C59—81no—
173C2×C59—81no—
174C2×C59—81no—
175C2×C59#55011yescharacteristic
176C2×C59#57511yescharacteristic
177C2×C59#57711yescharacteristic
178#559—591no—
179#556—591no—
180#497—591no—
181#496D5911yescharacteristic
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×Q16—591no—
195C2×Q16—591no—
196C2×SD16—591no—
197C2×SD16—591no—
198C2×SD16—591no—
199C2×SD16C2×D5911yescharacteristic
200C2×SD16C2×D5911yescharacteristic
201C2×D8C2×D5911yescharacteristic
202C2×D8C2×D5911yescharacteristic
203C4⋊Q8—591no—
204#127C2×D5911yescharacteristic
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×Q8—591no—
239C2×Q8—591no—
240C2×Q8C22×D5911yescharacteristic
241C2×D4—21no—
242C2×D4—21no—
243C2×D4C22×D5911yescharacteristic
244C2×D4C22×D5911yescharacteristic
245C2×D4C22×D5911yescharacteristic
246C22×C4—1181no—
247C22×C4—1181no—
248C22×C4—1181no—
249Q16—1182no—
250Q16—2361no—
251SD16—22no—
252SD16—41no—
253SD16—2361no—
254SD16—2361no—
255SD16—2361no—
256D8—22no—
257D8—41no—
258C2×C8—591no—
259C2×C8—591no—
260C2×C8C22×D5911yescharacteristic
261C2×C8C22×D5911yescharacteristic
262C4⋊C4—591no—
263C4⋊C4—591no—
264C4⋊C4—591no—
265C4⋊C4—591no—
266C4⋊C4—591no—
267C4⋊C4—1181no—
268C4⋊C4—1181no—
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—21no—
291C23—21no—
292Q8—21no—
293Q8—21no—
294Q8—1181no—
295Q8—1181no—
296Q8—1181no—
297Q8—1181no—
298Q8—2361no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—42no—
306D4—81no—
307C2×C4—21no—
308C2×C4—591no—
309C2×C4—591no—
310C2×C4—591no—
311C2×C4—591no—
312C2×C4—1181no—
313C2×C4—1181no—
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—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22C2×D4×D5911yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—1181no—
340C4—1181no—
341C4—1181no—
342C4—1181no—
343C4—2361no—
344C4—2361no—
345C4—2361no—
346C4—2361no—
347C4C2×#1174568711yescharacteristic
348C4#1427377211yescharacteristic
349C2—81no—
350C2—81no—
351C2—81no—
352C2#1683807211yescharacteristic
353C2#1683819811yescharacteristic
354C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#496C2
socleC22×C59C22×D4
hypercenter#496D59
hypocenterC59#3401
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #16838138C2semidirect
2. #16838121C2semidirect
3. #16837793C2semidirect
4. #16837785C2semidirect
5. #16837622C2semidirect
6. #16837621C2semidirect
7. #16837615C2semidirect
8. #16837615C2semidirect
9. #16837605C2semidirect
10. #16837599C2semidirect
11. #16837530C2semidirect
12. #16837514C2semidirect
13. #16837510C2semidirect
14. SD16×Dic59C2semidirect
193. C59#3401semidirect