Finite Group Databasebeta

← #21437162

Subgroups — #21437162

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#16838137C211yesmaximal, characteristic, complemented
2#16837794C211yesmaximal, characteristic, complemented
3#16837792C211yesmaximal, characteristic
4#16837784C211yesmaximal, characteristic, complemented
5#16837624C211yesmaximal, characteristic, complemented
6#16837621C211yesmaximal, characteristic, complemented
7#16837617C211yesmaximal, characteristic, complemented
8#16837614C211yesmaximal, characteristic, complemented
9#16837604C211yesmaximal, characteristic, complemented
10#16837602C211yesmaximal, characteristic, complemented
11#16837533C211yesmaximal, characteristic, complemented
12#16837512C211yesmaximal, characteristic, complemented
13#16837507C211yesmaximal, characteristic, complemented
14C4×#11745671C211yesmaximal, characteristic, complemented
15C59×#556C211yesmaximal, characteristic, complemented
16C2×#11745672C2211yescharacteristic
17C2×#11745672C2211yescharacteristic
18C2×#11745670C2211yescharacteristic
19C2×#11745671C2211yescharacteristic
20C2×#11745671C2211yescharacteristic
21C2×#11745671C2211yescharacteristic
22C2×#11745671C2211yescharacteristic
23C2×#11745669C2211yescharacteristic
24C2×#11745669C2211yescharacteristic
25#14273724C2211yescharacteristic
26#14273716—21no—
27#14273715C2211yescharacteristic
28#14273715C2211yescharacteristic
29#14273712—21no—
30#14273712—21no—
31C4×Dic118C2211yescharacteristic
32C4×D236C2211yescharacteristic
33C4×D236C2211yescharacteristic
34#14273689—21no—
35#14273658C2211yescharacteristic
36C4⋊(C59⋊C8)C2211yescharacteristic
37C4⋊(C59⋊C8)C2211yescharacteristic
38C4⋊(C59⋊C8)C2211yescharacteristic
39#14273651C2211yescharacteristic
40#14273651C2211yescharacteristic
41#14273650C2211yescharacteristic
42#14273648C2211yescharacteristic
43#14273647C2211yescharacteristic
44#14273647C2211yescharacteristic
45#14273638C2211yescharacteristic
46#14273638C2211yescharacteristic
47C4×C59⋊C8C2211yescharacteristic
48C4⋊Q8×C59C2211yescharacteristic
49#126×C59—21no—
50#126×C59—21no—
51#124×C59C2211yescharacteristic
52#124×C59C2211yescharacteristic
53C22⋊Q8×C59—21no—
54C4×Q8×C59C2211yescharacteristic
55C4×Q8×C59C2211yescharacteristic
56C4×Q8×C59C2211yescharacteristic
57C4×D4×C59C2211yescharacteristic
58#117×C59—21no—
59C2×Q8×C59D411yescharacteristic
60C2×Q8×C59C2311yescharacteristic
61C2×Q8×C59C2311yescharacteristic
62C2×D4×C59C2311yescharacteristic
63C22×C4×C59—21no—
64C2×D236—21no—
65C2×D236—21no—
66C2×D236C2311yescharacteristic
67C2×D236C2311yescharacteristic
68C2×C4×D59—21no—
69C2×C4×D59—21no—
70C2×Dic118C2311yescharacteristic
71C4⋊C4×C59—21no—
72C4⋊C4×C59—21no—
73C4⋊C4×C59—21no—
74C4⋊C4×C59—21no—
75C4⋊C4×C59D411yescharacteristic
76C4⋊C4×C59D411yescharacteristic
77C4⋊C4×C59D411yescharacteristic
78C4⋊C4×C59C2311yescharacteristic
79C22⋊C4×C59—21no—
80C22⋊C4×C59—21no—
81C22⋊C4×C59—21no—
82C22⋊C4×C59—21no—
83C22⋊C4×C59—21no—
84C42×C59—21no—
85C42×C59—21no—
86C42×C59C2311yescharacteristic
87C42×C59C2311yescharacteristic
88C42×C59C2311yescharacteristic
89#11745672—22no—
90#11745672—41no—
91#11745671—22no—
92#11745671—41no—
93#11745671—41no—
94#11745671—41no—
95#11745670—41no—
96#11745669—22no—
97#11745669—41no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104C4⋊Dic59C2311yescharacteristic
105Dic59⋊C4—21no—
106C4×Dic59—21no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C23×C59—21no—
112C22×D59—21no—
113C22×D59—21no—
114Q8×C59—21no—
115Q8×C59—21no—
116Q8×C59—21no—
117Q8×C59—21no—
118Q8×C59—41no—
119D4×C59—21no—
120D4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—42no—
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2×D411yescharacteristic
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2411yescharacteristic
132C2×Dic59—21no—
133C2×Dic59—21no—
134D236—21no—
135D236—21no—
136D236—21no—
137D236—21no—
138D236—42no—
139D236—81no—
140C4×D59—81no—
141C4×D59—81no—
142Dic118—21no—
143Dic118—21no—
144C59⋊C8—21no—
145C59⋊C8—21no—
146C59⋊C8—21no—
147C59⋊C8#4112yes—
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—21no—
161C4×C59—21no—
162C4×C59—21no—
163C4×C59—21no—
164C4×C59—41no—
165C4×C59—41no—
166C4×C59—41no—
167C4×C59C2×#4111yescharacteristic
168C4×C59H(5,𝔽2)11yescharacteristic
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#556D5911yescharacteristic, complemented
180#497—591no—
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×Q16—591no—
195C2×Q16—591no—
196C2×SD16—591no—
197C2×SD16—591no—
198C2×SD16—591no—
199C2×SD16—591no—
200C2×SD16—591no—
201C2×D8—591no—
202C2×D8—591no—
203C4⋊Q8C2×D5911yescharacteristic
204#127—591no—
205#126—21no—
206#126—21no—
207#124—591no—
208#124—591no—
209#124—1181no—
210#124C2×D5911yescharacteristic
211#124C2×D5911yescharacteristic
212#123—1181no—
213#123—1181no—
214C22⋊Q8—21no—
215C4×Q8—591no—
216C4×Q8C2×D5911yescharacteristic
217C4×Q8C2×D5911yescharacteristic
218C4×Q8C2×D5911yescharacteristic
219C4×D4—591no—
220C4×D4—591no—
221C4×D4—1181no—
222C4×D4C2×D5911yescharacteristic
223#117—21no—
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#97—591no—
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—21no—
247C22×C4—1181no—
248C22×C4—1181no—
249Q16—1182no—
250Q16—2361no—
251SD16—1182no—
252SD16—2361no—
253SD16—2361no—
254SD16—2361no—
255SD16—2361no—
256D8—1182no—
257D8—2361no—
258C2×C8—591no—
259C2×C8—591no—
260C2×C8—591no—
261C2×C8—591no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—591no—
267C4⋊C4—1181no—
268C4⋊C4C22⋊D5911yescharacteristic
269C4⋊C4C22⋊D5911yescharacteristic
270C4⋊C4C22⋊D5911yescharacteristic
271C4⋊C4C22×D5911yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—1181no—
278C22⋊C4—1181no—
279C22⋊C4—1181no—
280C22⋊C4—1181no—
281C22⋊C4—1181no—
282C22⋊C4—1181no—
283C42—21no—
284C42—21no—
285C42—1181no—
286C42C22×D5911yescharacteristic
287C42C22×D5911yescharacteristic
288C42C22×D5911yescharacteristic
289C23—21no—
290C23—1181no—
291C23—1181no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—41no—
297Q8—1181no—
298Q8—1181no—
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—42no—
311C2×C4—1181no—
312C2×C4—1181no—
313C2×C4—4721no—
314C2×C4—4721no—
315C2×C4C2×C22⋊D5911yescharacteristic
316C2×C4C2×C22⋊D5911yescharacteristic
317C2×C4C2×C22⋊D5911yescharacteristic
318C2×C4C2×C22⋊D5911yescharacteristic
319C2×C4C2×C22⋊D5911yescharacteristic
320C2×C4C2×C22⋊D5911yescharacteristic
321C2×C4C23×D5911yescharacteristic
322C8—592no—
323C8—1181no—
324C8—1181no—
325C8—1181no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—2361no—
330C22—2361no—
331C22—2361no—
332C22—2361no—
333C22—2361no—
334C22—2361no—
335C22C22×C22⋊D5911yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—2361no—
346C4—2361no—
347C4#41×D5911yescharacteristic
348C4#1427377311yescharacteristic
349C2—81no—
350C2—4721no—
351C2—4721no—
352C2#1683807111yescharacteristic
353C2#1683820011yescharacteristic
354C2#1683821011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#556C2
socleC22×C59C22×D4
hypercenter#556D59
hypocenterC59#3401
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. #16838137C2semidirect
2. #16837794C2semidirect
4. #16837784C2semidirect
5. #16837624C2semidirect
6. #16837621C2semidirect
7. #16837617C2semidirect
8. #16837614C2semidirect
9. #16837604C2semidirect
10. #16837602C2semidirect
11. #16837533C2semidirect
12. #16837512C2semidirect
13. #16837507C2semidirect
14. C4×#11745671C2semidirect
15. C59×#556C2semidirect
179. #556D59semidirect
193. C59#3401semidirect