Finite Group Databasebeta

← #21435552

Subgroups — #21435552

Order 7552.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838023C211yesmaximal, characteristic, complemented
2#16837697C211yesmaximal, characteristic, complemented
3#16837694C211yesmaximal, characteristic, complemented
4#16837682C211yesmaximal, characteristic, complemented
5#16837679C211yesmaximal, characteristic, complemented
6#16837650C211yesmaximal, characteristic, complemented
7#16837646C211yesmaximal, characteristic, complemented
8#16837641C211yesmaximal, characteristic, complemented
9#16837636C211yesmaximal, characteristic
10#16837624C211yesmaximal, characteristic, complemented
11#16837621C211yesmaximal, characteristic, complemented
12#16837617C211yesmaximal, characteristic, complemented
13#16837614C211yesmaximal, characteristic, complemented
14#16837429C211yesmaximal, characteristic, complemented
15C59×#542C211yesmaximal, characteristic, complemented
16C2×#11745672C2211yescharacteristic
17C2×#11745670C2211yescharacteristic
18C2×#11745671C2211yescharacteristic
19C2×#11745669C2211yescharacteristic
20C2×#11745664C2211yescharacteristic
21C22×C59⋊C8C2211yescharacteristic
22#14273727C2211yescharacteristic
23#14273722—21no—
24#14273715C2211yescharacteristic
25#14273713—21no—
26#14273709—21no—
27#14273706C2211yescharacteristic
28#14273705—21no—
29#14273701C2211yescharacteristic
30C4×Dic118C2211yescharacteristic
31C4×D236C2211yescharacteristic
32#14273660C2211yescharacteristic
33#14273660C2211yescharacteristic
34#14273660C2211yescharacteristic
35#14273660C2211yescharacteristic
36C4⋊(C59⋊C8)C2211yescharacteristic
37C4⋊(C59⋊C8)C2211yescharacteristic
38C4⋊(C59⋊C8)C2211yescharacteristic
39C4⋊(C59⋊C8)C2211yescharacteristic
40#14273651C2211yescharacteristic
41#14273651C2211yescharacteristic
42#14273650C2211yescharacteristic
43#14273650C2211yescharacteristic
44#14273648C2211yescharacteristic
45#14273648C2211yescharacteristic
46#14273647C2211yescharacteristic
47#14273647C2211yescharacteristic
48C4⋊Q8×C59C2211yescharacteristic
49#126×C59—21no—
50#124×C59—21no—
51#124×C59C2211yescharacteristic
52#123×C59—21no—
53C22⋊Q8×C59—21no—
54C22⋊Q8×C59C2211yescharacteristic
55#121×C59C2211yescharacteristic
56C4×Q8×C59C2211yescharacteristic
57C4×D4×C59C2211yescharacteristic
58#117×C59C2211yescharacteristic
59C2×Q8×C59—21no—
60C2×Q8×C59C2311yescharacteristic
61C2×D4×C59—21no—
62C2×D4×C59C2311yescharacteristic
63C22×C4×C59—21no—
64C22×C4×C59C2311yescharacteristic
65C2×C22⋊D59—21no—
66C2×D236C2311yescharacteristic
67C2×C4×D59—21no—
68C2×Dic118—21no—
69C2×Dic118C2311yescharacteristic
70C4⋊C4×C59—21no—
71C4⋊C4×C59—21no—
72C4⋊C4×C59—21no—
73C4⋊C4×C59D411yescharacteristic
74C4⋊C4×C59D411yescharacteristic
75C4⋊C4×C59C2311yescharacteristic
76C4⋊C4×C59C2311yescharacteristic
77C22⋊C4×C59—21no—
78C22⋊C4×C59—21no—
79C22⋊C4×C59—21no—
80C22⋊C4×C59—21no—
81C22⋊C4×C59—21no—
82C22⋊C4×C59D411yescharacteristic
83C22⋊C4×C59D411yescharacteristic
84C42×C59—21no—
85C42×C59C2311yescharacteristic
86C42×C59C2311yescharacteristic
87C22⋊Dic59—21no—
88#11745672—41no—
89#11745671—41no—
90#11745670—41no—
91#11745669—41no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96C4⋊Dic59—21no—
97C4⋊Dic59C2311yescharacteristic
98C4⋊Dic59C2311yescharacteristic
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101C4×Dic59—21no—
102#11745664—41no—
103C2×C59⋊C8—41no—
104C2×C59⋊C8C2311yescharacteristic
105C2×C59⋊C8C2311yescharacteristic
106C2×C59⋊C8C2311yescharacteristic
107C2×C59⋊C8C2311yescharacteristic
108C23×C59—21no—
109C23×C59C2×D411yescharacteristic
110C22×D59—21no—
111Q8×C59—21no—
112Q8×C59—21no—
113Q8×C59—81no—
114D4×C59—21no—
115D4×C59—21no—
116D4×C59—81no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—81no—
123C2×C4×C59C2×D411yescharacteristic
124C2×C4×C59C2×D411yescharacteristic
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2×D411yescharacteristic
128C2×C4×C59C2411yescharacteristic
129C22⋊D59—81no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133D236—21no—
134D236—21no—
135C4×D59—81no—
136Dic118—21no—
137Dic118—21no—
138Dic118—81no—
139C59⋊C8—21no—
140C59⋊C8—21no—
141C59⋊C8—21no—
142C59⋊C8—21no—
143C22×C59—21no—
144C22×C59—21no—
145C22×C59—21no—
146C22×C59—41no—
147C22×C59—41no—
148C22×C59—41no—
149C22×C59C22×D411yescharacteristic
150C2×D59—41no—
151C2×D59—41no—
152C2×D59—41no—
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×C59H(5,𝔽2)11yescharacteristic
162C4×C592−1+411yescharacteristic
163Dic59—41no—
164Dic59—41no—
165Dic59—41no—
166#3262—591nomaximal, Sylow
167C2×C59—41no—
168C2×C59—81no—
169C2×C59#53711yescharacteristic
170C2×C59#57611yescharacteristic
171C2×C59#57811yescharacteristic
172D59—81no—
173#542—591no—
174#542D5911yescharacteristic, complemented
175#477—591no—
176#477—591no—
177#474—591no—
178#474—591no—
179#468—591no—
180#468—591no—
181#467—591no—
182#466—591no—
183#464—591no—
184#464—591no—
185#463—591no—
186#463—591no—
187#424—591no—
188C59#326211yescharacteristic, complemented, Sylow
189C2×Q16—591no—
190C2×SD16—591no—
191C2×SD16—591no—
192C2×D8—591no—
193C2×M16—591no—
194C22×C8—591no—
195C4⋊Q8—591no—
196C4⋊Q8C2×D5911yescharacteristic
197#126—21no—
198#126—1181no—
199#124—21no—
200#124—591no—
201#124—1181no—
202#124C2×D5911yescharacteristic
203#123—21no—
204#123—1181no—
205C22⋊Q8—21no—
206C22⋊Q8—591no—
207C22⋊Q8—1181no—
208C22⋊Q8C2×D5911yescharacteristic
209#121—591no—
210#121C2×D5911yescharacteristic
211C4×Q8—591no—
212C4×Q8C2×D5911yescharacteristic
213C4×D4—591no—
214C4×D4C2×D5911yescharacteristic
215#117C2×D5911yescharacteristic
216#107—591no—
217#107—591no—
218#107—591no—
219#107—591no—
220C4⋊C8—591no—
221C4⋊C8—591no—
222C4⋊C8—591no—
223C4⋊C8—591no—
224#103—591no—
225#103—591no—
226#103—591no—
227#103—591no—
228#102—591no—
229#102—591no—
230#102—591no—
231#102—591no—
232C2×Q8—21no—
233C2×Q8—591no—
234C2×Q8—1181no—
235C2×Q8C22×D5911yescharacteristic
236C2×D4—21no—
237C2×D4—591no—
238C2×D4—1181no—
239C2×D4C22×D5911yescharacteristic
240C22×C4—21no—
241C22×C4—1181no—
242C22×C4C22×D5911yescharacteristic
243Q16—2361no—
244SD16—2361no—
245SD16—2361no—
246D8—2361no—
247M16—2361no—
248C2×C8—591no—
249C2×C8—591no—
250C2×C8—591no—
251C2×C8—591no—
252C2×C8—2361no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—591no—
257C4⋊C4—591no—
258C4⋊C4—1181no—
259C4⋊C4—1181no—
260C4⋊C4—1181no—
261C4⋊C4C22⋊D5911yescharacteristic
262C4⋊C4C22⋊D5911yescharacteristic
263C4⋊C4C22×D5911yescharacteristic
264C4⋊C4C22×D5911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—1181no—
271C22⋊C4—1181no—
272C22⋊C4—1181no—
273C22⋊C4—1181no—
274C22⋊C4—1181no—
275C22⋊C4C22⋊D5911yescharacteristic
276C22⋊C4C22⋊D5911yescharacteristic
277C42—21no—
278C42—1181no—
279C42C22×D5911yescharacteristic
280C42C22×D5911yescharacteristic
281C23—21no—
282C23—1181no—
283C23C2×C22⋊D5911yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—1181no—
288Q8—1181no—
289Q8—4721no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—1181no—
294D4—1181no—
295D4—4721no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—81no—
302C2×C4—1181no—
303C2×C4—1181no—
304C2×C4—1181no—
305C2×C4—4721no—
306C2×C4C2×C22⋊D5911yescharacteristic
307C2×C4C2×C22⋊D5911yescharacteristic
308C2×C4C2×C22⋊D5911yescharacteristic
309C2×C4C2×C22⋊D5911yescharacteristic
310C2×C4C2×C22⋊D5911yescharacteristic
311C2×C4C23×D5911yescharacteristic
312C8—1181no—
313C8—1181no—
314C8—1181no—
315C8—1181no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—2361no—
323C22—2361no—
324C22—2361no—
325C22C22×C22⋊D5911yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—2361no—
335C4—2361no—
336C4—2361no—
337C4#1427377311yescharacteristic
338C4#1427377411yescharacteristic
339C2—41no—
340C2—81no—
341C2—4721no—
342C2#1683798011yescharacteristic
343C2#1683820511yescharacteristic
344C2#1683821711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#542C2
socleC22×C59C22×D4
hypercenter#542D59
hypocenterC59#3262
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #16838023C2semidirect
2. #16837697C2semidirect
3. #16837694C2semidirect
4. #16837682C2semidirect
5. #16837679C2semidirect
6. #16837650C2semidirect
7. #16837646C2semidirect
8. #16837641C2semidirect
10. #16837624C2semidirect
11. #16837621C2semidirect
12. #16837617C2semidirect
13. #16837614C2semidirect
14. #16837429C2semidirect
15. C59×#542C2semidirect
174. #542D59semidirect
188. C59#3262semidirect