Finite Group Databasebeta

← #21437171

Subgroups — #21437171

Order 7552.

356 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838125C211yesmaximal, characteristic, complemented
2#16837797C211yesmaximal, characteristic, complemented
3#16837794C211yesmaximal, characteristic, complemented
4#16837784C211yesmaximal, characteristic
5#16837624C211yesmaximal, characteristic, complemented
6#16837621C211yesmaximal, characteristic, complemented
7#16837617C211yesmaximal, characteristic
8#16837614C211yesmaximal, characteristic
9#16837612C211yesmaximal, characteristic, complemented
10#16837609C211yesmaximal, characteristic, complemented
11#16837533C211yesmaximal, characteristic, complemented
12#16837502C211yesmaximal, characteristic, complemented
13#16837500C211yesmaximal, characteristic, complemented
14C4×#11745672C211yesmaximal, characteristic, complemented
15C59×#556C211yesmaximal, characteristic, complemented
16C2×#11745672C2211yescharacteristic
17C2×#11745672C2211yescharacteristic
18C2×#11745672C2211yescharacteristic
19C2×#11745672C2211yescharacteristic
20C2×#11745670C2211yescharacteristic
21C2×#11745670C2211yescharacteristic
22C2×#11745671C2211yescharacteristic
23C2×#11745671C2211yescharacteristic
24C2×#11745669C2211yescharacteristic
25#14273727C2211yescharacteristic
26#14273722—21no—
27#14273722—21no—
28#14273715C2211yescharacteristic
29#14273715C2211yescharacteristic
30#14273703—21no—
31C4×Dic118C2211yescharacteristic
32C4×Dic118C2211yescharacteristic
33C4×D236C2211yescharacteristic
34#14273685—21no—
35#14273660C2211yescharacteristic
36C4⋊(C59⋊C8)C2211yescharacteristic
37C4⋊(C59⋊C8)C2211yescharacteristic
38C4⋊(C59⋊C8)C2211yescharacteristic
39#14273651C2211yescharacteristic
40#14273651C2211yescharacteristic
41#14273650C2211yescharacteristic
42#14273650C2211yescharacteristic
43#14273648C2211yescharacteristic
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×D236C2311yescharacteristic
65C2×C4×D59—21no—
66C2×Dic118C2311yescharacteristic
67C2×Dic118C2311yescharacteristic
68C4⋊C4×C59—21no—
69C4⋊C4×C59—21no—
70C4⋊C4×C59—21no—
71C4⋊C4×C59—21no—
72C4⋊C4×C59D411yescharacteristic
73C4⋊C4×C59D411yescharacteristic
74C4⋊C4×C59D411yescharacteristic
75C4⋊C4×C59C2311yescharacteristic
76C22⋊C4×C59—21no—
77C22⋊C4×C59—21no—
78C22⋊C4×C59—21no—
79C22⋊C4×C59—21no—
80C22⋊C4×C59—21no—
81C42×C59—21no—
82C42×C59—21no—
83C42×C59C2311yescharacteristic
84C42×C59C2311yescharacteristic
85C42×C59C2311yescharacteristic
86#11745672—22no—
87#11745672—41no—
88#11745672—41no—
89#11745672—41no—
90#11745671—22no—
91#11745671—41no—
92#11745670—22no—
93#11745670—41no—
94#11745669—41no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100C4⋊Dic59—21no—
101C4⋊Dic59—21no—
102C4⋊Dic59C2311yescharacteristic
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105C4×Dic59—21no—
106C4×Dic59—21no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C23×C59—21no—
112C22×D59—21no—
113Q8×C59—21no—
114Q8×C59—21no—
115Q8×C59—21no—
116Q8×C59—21no—
117Q8×C59—41no—
118D4×C59—21no—
119D4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—42no—
124C2×C4×C59C2×D411yescharacteristic
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2×D411yescharacteristic
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2411yescharacteristic
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134D236—21no—
135D236—21no—
136C4×D59—42no—
137Dic118—21no—
138Dic118—21no—
139Dic118—21no—
140Dic118—21no—
141C59⋊C8—21no—
142C59⋊C8—21no—
143C59⋊C8—21no—
144C59⋊C8#4112yes—
145C22×C59—41no—
146C22×C59—41no—
147C22×C59—41no—
148C22×C59C22×D411yescharacteristic
149C2×D59—41no—
150C2×D59—41no—
151C2×D59—41no—
152C4×C59—21no—
153C4×C59—21no—
154C4×C59—21no—
155C4×C59—21no—
156C4×C59—21no—
157C4×C59—21no—
158C4×C59—41no—
159C4×C59—41no—
160C4×C59—41no—
161C4×C59C2×#4111yescharacteristic
162C4×C59H(5,𝔽2)11yescharacteristic
163Dic59—41no—
164Dic59—41no—
165Dic59—41no—
166#3402—591nomaximal, Sylow
167C2×C59—81no—
168C2×C59#55011yescharacteristic
169C2×C59#57511yescharacteristic
170C2×C59#57811yescharacteristic
171D59—81no—
172#556—591no—
173#556D5911yescharacteristic, complemented
174#497—591no—
175#497—591no—
176#495—591no—
177#464—591no—
178#464—591no—
179#463—591no—
180#463—591no—
181#462—591no—
182#462—591no—
183#446—591no—
184#440—591no—
185#440—591no—
186C4×Q16—591no—
187C59#340211yescharacteristic, complemented, Sylow
188C2×Q16—591no—
189C2×Q16—591no—
190C2×Q16—591no—
191C2×Q16—591no—
192C2×SD16—591no—
193C2×SD16—591no—
194C2×SD16—591no—
195C2×SD16—591no—
196C2×D8—591no—
197C4⋊Q8—591no—
198C4⋊Q8C2×D5911yescharacteristic
199#126—21no—
200#126—21no—
201#126—1181no—
202#126—1181no—
203#124—591no—
204#124—591no—
205#124C2×D5911yescharacteristic
206#124C2×D5911yescharacteristic
207C22⋊Q8—21no—
208C22⋊Q8—1181no—
209C4×Q8—591no—
210C4×Q8—591no—
211C4×Q8C2×D5911yescharacteristic
212C4×Q8C2×D5911yescharacteristic
213C4×Q8C2×D5911yescharacteristic
214C4×D4—591no—
215C4×D4C2×D5911yescharacteristic
216#117—21no—
217#117—1181no—
218#107—591no—
219C4⋊C8—591no—
220C4⋊C8—591no—
221C4⋊C8—591no—
222#103—591no—
223#103—591no—
224#103—591no—
225#103—591no—
226#102—591no—
227#102—591no—
228#97—591no—
229#97—591no—
230C4×C8—591no—
231C2×Q8—591no—
232C2×Q8—591no—
233C2×Q8C22⋊D5911yescharacteristic
234C2×Q8C22×D5911yescharacteristic
235C2×Q8C22×D5911yescharacteristic
236C2×D4—591no—
237C2×D4C22×D5911yescharacteristic
238C22×C4—21no—
239C22×C4—1181no—
240Q16—1182no—
241Q16—2361no—
242Q16—2361no—
243Q16—2361no—
244SD16—1182no—
245SD16—1182no—
246SD16—2361no—
247SD16—2361no—
248D8—2361no—
249C2×C8—591no—
250C2×C8—591no—
251C2×C8—591no—
252C2×C8—591no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—591no—
258C4⋊C4—1181no—
259C4⋊C4—1181no—
260C4⋊C4—1181no—
261C4⋊C4—1181no—
262C4⋊C4C22⋊D5911yescharacteristic
263C4⋊C4C22⋊D5911yescharacteristic
264C4⋊C4C22⋊D5911yescharacteristic
265C4⋊C4C22×D5911yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—1181no—
272C22⋊C4—1181no—
273C22⋊C4—1181no—
274C22⋊C4—1181no—
275C22⋊C4—1181no—
276C42—21no—
277C42—21no—
278C42—1181no—
279C42—1181no—
280C42C22×D5911yescharacteristic
281C42C22×D5911yescharacteristic
282C42C22×D5911yescharacteristic
283C23—21no—
284C23—1181no—
285Q8—21no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—41no—
290Q8—1181no—
291Q8—1181no—
292Q8—1181no—
293Q8—1181no—
294D4—21no—
295D4—21no—
296D4—1181no—
297D4—1181no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—1181no—
303C2×C4—1181no—
304C2×C4—1181no—
305C2×C4—2362no—
306C2×C4C2×C22⋊D5911yescharacteristic
307C2×C4C2×C22⋊D5911yescharacteristic
308C2×C4C2×C22⋊D5911yescharacteristic
309C2×C4C2×C22⋊D5911yescharacteristic
310C2×C4C2×C22⋊D5911yescharacteristic
311C2×C4C2×C22⋊D5911yescharacteristic
312C2×C4C23×D5911yescharacteristic
313C8—592no—
314C8—1181no—
315C8—1181no—
316C8—1181no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—2361no—
321C22—2361no—
322C22—2361no—
323C22C22×C22⋊D5911yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—2361no—
334C4—2361no—
335C4—2361no—
336C4#41×D5911yescharacteristic
337C4#1427377311yescharacteristic
338C2—81no—
339C2—4721no—
340C2#1683807111yescharacteristic
341C2#1683820011yescharacteristic
342C2#1683821711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#556C2
socleC22×C59C22×D4
hypercenter#556D59
hypocenterC59#3402
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. #16838125C2semidirect
2. #16837797C2semidirect
3. #16837794C2semidirect
5. #16837624C2semidirect
6. #16837621C2semidirect
9. #16837612C2semidirect
10. #16837609C2semidirect
11. #16837533C2semidirect
12. #16837502C2semidirect
13. #16837500C2semidirect
14. C4×#11745672C2semidirect
15. C59×#556C2semidirect
173. #556D59semidirect
187. C59#3402semidirect