Finite Group Databasebeta

← #21422610

Subgroups — #21422610

Order 7552.

346 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×D59C211yesmaximal, characteristic
2#16837364C211yesmaximal, characteristic, complemented
3#16837249C211yesmaximal, characteristic, complemented
4#16837137C211yesmaximal, characteristic, complemented
5#16837136C211yesmaximal, characteristic, complemented
6#16837135C211yesmaximal, characteristic, complemented
7C59×#327C211yesmaximal, characteristic, complemented
8C2×D4×D59—21no—
9C2×D4×D59C411yescharacteristic, complemented
10C22×C4×D59C2211yescharacteristic
11C2×#11745659—21no—
12#14273702C411yescharacteristic, complemented
13#14273701C2211yescharacteristic
14#14273700—21no—
15#14273699—21no—
16#14273698C411yescharacteristic, complemented
17C4⋊C4×D59C411yescharacteristic, complemented
18C2×(C2×D59)⋊C4—21no—
19C22⋊C4×D59—21no—
20C2×C4×Dic59—21no—
21C22⋊(C59⋊C8)C2211yescharacteristic, complemented
22(C2×D59)⋊C8—21no—
23C59⋊#95C2211yescharacteristic, complemented
24#121×C59C2211yescharacteristic
25C22⋊C8×C59C2211yescharacteristic, complemented
26#95×C59C2211yescharacteristic, complemented
27C23×D59—21no—
28C23×D59D411yescharacteristic
29C2×D4×C59—21no—
30C2×D4×C59C2×C411yescharacteristic
31C22×C4×C59—21no—
32C22×C4×C59C2311yescharacteristic
33C2×C22⋊D59—21no—
34C2×C22⋊D59—21no—
35C2×C22⋊D59—21no—
36C22×Dic59—21no—
37C22×Dic59D411yescharacteristic
38D4×D59—42no—
39D4×D59—42no—
40D4×D59—42no—
41C2×D236—21no—
42C2×D236C2×C411yescharacteristic
43C2×C4×D59—21no—
44C2×C4×D59—42no—
45C2×C4×D59C2×C411yescharacteristic
46C2×C4×D59C2×C411yescharacteristic
47C2×C4×D59D411yescharacteristic
48C2×C4×D59D411yescharacteristic
49C2×C8×C59—21no—
50C4⋊C4×C59C2×C411yescharacteristic
51C22⋊C4×C59—21no—
52C22⋊Dic59—21no—
53(C2×D59)⋊C4—24no—
54(C2×D59)⋊C4—21no—
55(C2×D59)⋊C4—21no—
56C4⋊Dic59C2×C411yescharacteristic
57Dic59⋊C4—21no—
58C4×Dic59—42no—
59C2×C59⋊C8—21no—
60#11745659—42no—
61C23×C59—21no—
62C23×C59C2×D411yescharacteristic
63C22×D59—21no—
64C22×D59—21no—
65C22×D59—22no—
66C22×D59—21no—
67C22×D59—41no—
68C22×D59—42no—
69C22×D59—42no—
70C22×D59—42no—
71C22×D59C22⋊C411yescharacteristic
72C22×D59C22⋊C411yescharacteristic
73D4×C59—41no—
74D4×C59—41no—
75D4×C59—41no—
76C2×C4×C59—22no—
77C2×C4×C59—21no—
78C2×C4×C59—41no—
79C2×C4×C59—41no—
80C2×C4×C59—41no—
81C2×C4×C59C22×C411yescharacteristic
82C2×C4×C59C2×D411yescharacteristic
83C22⋊D59—42no—
84C22⋊D59—41no—
85C22⋊D59—41no—
86C22⋊D59—42no—
87C2×Dic59—22no—
88C2×Dic59—22no—
89C2×Dic59—21no—
90C2×Dic59—41no—
91C2×Dic59—41no—
92C2×Dic59C22⋊C411yescharacteristic
93C2×Dic59C22⋊C411yescharacteristic
94D236—41no—
95D236—42no—
96C4×D59—22no—
97C4×D59—22no—
98C4×D59—41no—
99C4×D59—41no—
100C4×D59—42no—
101C8×C59—41no—
102C59⋊C8—41no—
103C22×C59—21no—
104C22×C59—21no—
105C22×C59—41no—
106C22×C59—41no—
107C22×C59—41no—
108C22×C59C2×C22⋊C411yescharacteristic
109C22×C59AGL(1,ℤ/8)11yescharacteristic
110C22×C59AGL(1,ℤ/8)11yescharacteristic
111C2×D59—21no—
112C2×D59—21no—
113C2×D59—21no—
114C2×D59—21no—
115C2×D59—21no—
116C2×D59—42no—
117C2×D59—42no—
118C2×D59—41no—
119C2×D59—41no—
120C2×D59—41no—
121C2×D59—84no—
122C2×D59#10412yes—
123C4×C59—21no—
124C4×C59—21no—
125C4×C59—42no—
126C4×C59—41no—
127Dic59—21no—
128Dic59—42no—
129Dic59—41no—
130Dic59#9912yes—
131#1507—591nomaximal, Sylow
132C2×C59—21no—
133C2×C59—21no—
134C2×C59—81no—
135C2×C59C2×#9911yescharacteristic
136C2×C59#41811yescharacteristic
137C2×C59C2×#10411yescharacteristic
138D59—22no—
139D59—41no—
140D59—81no—
141C2×#121—591no—
142#407—591no—
143C4×C22⋊C4—591no—
144#327—591no—
145#327—591no—
146#327—591no—
147#327D5911yescharacteristic, complemented
148C59#150711yescharacteristic, complemented, Sylow
149C22×D4—591no—
150C22×D4—1181no—
151C23×C4—591no—
152C2×M16—1181no—
153#121—591no—
154#121—591no—
155#121—591no—
156#121—1181no—
157#121—1181no—
158#121C2×D5911yescharacteristic
159C2×C4⋊C4—591no—
160C2×C22⋊C4—1181no—
161C2×C22⋊C4—1181no—
162C2×C42—1181no—
163C22⋊C8—591no—
164C22⋊C8—1181no—
165C22⋊C8C2×D5911yescharacteristic, complemented
166#95—591no—
167#95C2×D5911yescharacteristic, complemented
168C24—591no—
169C24—1181no—
170C2×D4—21no—
171C2×D4—591no—
172C2×D4—1181no—
173C2×D4—1181no—
174C2×D4—1181no—
175C2×D4—1181no—
176C2×D4—2362no—
177C2×D4—2362no—
178C2×D4—2362no—
179C2×D4C4×D5911yescharacteristic
180C22×C4—21no—
181C22×C4—591no—
182C22×C4—591no—
183C22×C4—591no—
184C22×C4—591no—
185C22×C4—591no—
186C22×C4—1181no—
187C22×C4—1181no—
188C22×C4—2362no—
189C22×C4C22×D5911yescharacteristic
190M16—2362no—
191C2×C8—21no—
192C2×C8—1181no—
193C4⋊C4—591no—
194C4⋊C4—1181no—
195C4⋊C4C4×D5911yescharacteristic
196C22⋊C4—21no—
197C22⋊C4—1181no—
198C22⋊C4—1184no—
199C22⋊C4—1181no—
200C22⋊C4—1181no—
201C42—2362no—
202C23—21no—
203C23—591no—
204C23—591no—
205C23—1182no—
206C23—1181no—
207C23—1181no—
208C23—1181no—
209C23—2361no—
210C23—2362no—
211C23—2362no—
212C23—2362no—
213C23D4×D5911yescharacteristic
214D4—41no—
215D4—41no—
216D4—41no—
217D4—2361no—
218D4—2362no—
219D4—2362no—
220D4—2362no—
221D4—2361no—
222D4—2361no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—591no—
229C2×C4—591no—
230C2×C4—1182no—
231C2×C4—1182no—
232C2×C4—1182no—
233C2×C4—1182no—
234C2×C4—1181no—
235C2×C4—2361no—
236C2×C4—2361no—
237C2×C4—2362no—
238C2×C4—2361no—
239C2×C4—2361no—
240C2×C4C2×C4×D5911yescharacteristic
241C2×C4D4×D5911yescharacteristic
242C8—41no—
243C8—2361no—
244C22—21no—
245C22—21no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—592no—
250C22—1181no—
251C22—1181no—
252C22—1181no—
253C22—1181no—
254C22—1181no—
255C22—4724no—
256C22—2362no—
257C22—2362no—
258C22—2361no—
259C22—2361no—
260C22—2361no—
261C22C22⋊C4×D5911yescharacteristic
262C22#1427375111yescharacteristic
263C22#1427375411yescharacteristic
264C4—21no—
265C4—21no—
266C4—42no—
267C4—41no—
268C4—592no—
269C4—1181no—
270C4—2362no—
271C4—2361no—
272C2—21no—
273C2—21no—
274C2—81no—
275C2—1182no—
276C2—4721no—
277C2—2361no—
278C2#99×D5911yescharacteristic
279C2#1683740511yescharacteristic
280C2#104×D5911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#327C2
socleC22×C59C2×C22⋊C4
hypercenter#327D59
hypocenterC59#1507
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #16837364C2semidirect
3. #16837249C2semidirect
4. #16837137C2semidirect
5. #16837136C2semidirect
6. #16837135C2semidirect
7. C59×#327C2semidirect
9. C2×D4×D59C4semidirect
12. #14273702C4semidirect
16. #14273698C4semidirect
17. C4⋊C4×D59C4semidirect
21. C22⋊(C59⋊C8)C22semidirect
23. C59⋊#95C22semidirect
25. C22⋊C8×C59C22semidirect
26. #95×C59C22semidirect
147. #327D59semidirect
148. C59#1507semidirect
165. C22⋊C8C2×D59semidirect
167. #95C2×D59semidirect