Finite Group Databasebeta

← #21423039

Subgroups — #21423039

Order 7552.

320 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 49 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#16837989C211yesmaximal, characteristic, complemented
2#16837553C211yesmaximal, characteristic, complemented
3#16837310C211yesmaximal, characteristic, complemented
4#16837140C211yesmaximal, characteristic, complemented
5#16837136C211yesmaximal, characteristic, complemented
6#16837125C211yesmaximal, characteristic, complemented
7C59×#447C211yesmaximal, characteristic, complemented
8C22×C22⋊D59—21no—
9C2×#11745670—21no—
10#14273722—21no—
11#14273713—21no—
12#14273711—21no—
13#14273706C2211yescharacteristic
14#14273699—21no—
15#14273695—21no—
16D4×Dic59—21no—
17C2×C22⋊Dic59—21no—
18C2×(C2×D59)⋊C4C2211yescharacteristic
19#14273648—21no—
20C22⋊(C59⋊C8)C2211yescharacteristic
21C59⋊#95C2211yescharacteristic
22C22×D4×C59C2211yescharacteristic
23C2×D8×C59—21no—
24#121×C59C2211yescharacteristic
25#102×C59—21no—
26C22⋊C8×C59C2211yescharacteristic
27C24×C59—21no—
28C23×D59D411yescharacteristic
29C2×D4×C59—21no—
30C2×D4×C59—21no—
31C2×D4×C59—21no—
32C2×D4×C59—42no—
33C2×D4×C59D411yescharacteristic, complemented
34C22×C4×C59C2311yescharacteristic
35C2×C22⋊D59—21no—
36C2×C22⋊D59—21no—
37C2×C22⋊D59—42no—
38C2×C22⋊D59—42no—
39C2×C22⋊D59—42no—
40C22×Dic59—21no—
41C22×Dic59—21no—
42C22×Dic59D411yescharacteristic
43C2×Dic118D411yescharacteristic, complemented
44D8×C59—42no—
45C2×C8×C59—21no—
46C4⋊C4×C59D411yescharacteristic, complemented
47C22⋊C4×C59—21no—
48C22⋊Dic59—21no—
49C22⋊Dic59—21no—
50C22⋊Dic59—42no—
51#11745670—42no—
52(C2×D59)⋊C4—21no—
53(C2×D59)⋊C4—21no—
54(C2×D59)⋊C4—21no—
55(C2×D59)⋊C4—21no—
56C4⋊Dic59—21no—
57C4⋊Dic59D411yescharacteristic, complemented
58Dic59⋊C4—21no—
59C4×Dic59—21no—
60C2×C59⋊C8—21no—
61C23×C59—22no—
62C23×C59—21no—
63C23×C59—41no—
64C23×C59—41no—
65C23×C59—41no—
66C23×C59—41no—
67C23×C59—41no—
68C23×C59—41no—
69C23×C59C2×D411yescharacteristic
70C22×D59—21no—
71C22×D59—21no—
72C22×D59—21no—
73C22×D59—41no—
74C22×D59—41no—
75D4×C59—22no—
76D4×C59—22no—
77D4×C59—41no—
78D4×C59—41no—
79D4×C59—41no—
80D4×C59—41no—
81D4×C59—41no—
82C2×C4×C59—21no—
83C2×C4×C59—41no—
84C2×C4×C59C2×D411yescharacteristic
85C2×C4×C59C2×D411yescharacteristic
86C22⋊D59—48no—
87C22⋊D59—81no—
88C22⋊D59—81no—
89C2×Dic59—22no—
90C2×Dic59—21no—
91C2×Dic59—21no—
92C2×Dic59—21no—
93C2×Dic59—41no—
94C2×Dic59—41no—
95C2×Dic59—41no—
96C2×Dic59—81no—
97Dic118—41no—
98C8×C59—41no—
99C59⋊C8—41no—
100C22×C59—21no—
101C22×C59—21no—
102C22×C59—42no—
103C22×C59—42no—
104C22×C59—41no—
105C22×C59—41no—
106C22×C59—41no—
107C22×C59—42no—
108C22×C59—81no—
109C22×C59—81no—
110C22×C59—81no—
111C22×C59—81no—
112C22×C59#12011yescharacteristic
113C22×C59#13511yescharacteristic
114C22×C59AGL(1,ℤ/8)11yescharacteristic
115C2×D59—42no—
116C2×D59—41no—
117C2×D59—41no—
118C2×D59—41no—
119C2×D59—81no—
120C4×C59—21no—
121C4×C59—21no—
122C4×C59—41no—
123Dic59—42no—
124Dic59—41no—
125Dic59—41no—
126Dic59—41no—
127#1600—591nomaximal, Sylow
128C2×C59—21no—
129C2×C59—21no—
130C2×C59—81no—
131C2×C59—82no—
132C2×C59#44911yescharacteristic
133C2×C59#45311yescharacteristic
134C2×C59B(4,𝔽2)11yescharacteristic
135D59—81no—
136#538—591no—
137#450—591no—
138#447D5911yescharacteristic, complemented
139#392—591no—
140#328—591no—
141#327—591no—
142#323—591no—
143C59#160011yescharacteristic, complemented, Sylow
144C22×D4—1181no—
145C22×D4C2×D5911yescharacteristic
146C2×SD16—1181no—
147C2×D8—21no—
148#126—1181no—
149#124—1181no—
150#123—1181no—
151C22⋊Q8—591no—
152#121—1181no—
153#121C2×D5911yescharacteristic
154#120—1181no—
155C4×D4—1181no—
156C2×C22⋊C4—591no—
157C2×C22⋊C4—1181no—
158#102—21no—
159#102—1181no—
160C22⋊C8—591no—
161C22⋊C8C2×D5911yescharacteristic
162#95—591no—
163C24—21no—
164C24—591no—
165C2×Q8—591no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—42no—
170C2×D4—1181no—
171C2×D4—1181no—
172C2×D4—2362no—
173C2×D4—2362no—
174C2×D4—2362no—
175C2×D4C22⋊D5911yescharacteristic, complemented
176C22×C4—591no—
177C22×C4—1181no—
178C22×C4—1181no—
179C22×C4C22×D5911yescharacteristic
180SD16—2362no—
181D8—42no—
182C2×C8—21no—
183C2×C8—1181no—
184C4⋊C4—591no—
185C4⋊C4—1181no—
186C4⋊C4—1181no—
187C4⋊C4C22⋊D5911yescharacteristic, complemented
188C22⋊C4—21no—
189C22⋊C4—1181no—
190C22⋊C4—1181no—
191C22⋊C4—1181no—
192C22⋊C4—1181no—
193C22⋊C4—1181no—
194C22⋊C4—1181no—
195C22⋊C4—2362no—
196C42—1181no—
197C23—22no—
198C23—21no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23—41no—
203C23—41no—
204C23—41no—
205C23—1181no—
206C23—1181no—
207C23—1181no—
208C23—2361no—
209C23—2361no—
210C23D4×D5911yescharacteristic
211Q8—2361no—
212D4—22no—
213D4—22no—
214D4—41no—
215D4—41no—
216D4—41no—
217D4—41no—
218D4—41no—
219D4—4721no—
220D4—4721no—
221D4—2368no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—1182no—
225C2×C4—1181no—
226C2×C4—1181no—
227C2×C4—1181no—
228C2×C4—4721no—
229C2×C4—2361no—
230C2×C4—2361no—
231C2×C4—2361no—
232C2×C4D4×D5911yescharacteristic
233C2×C4C2×C22⋊D5911yescharacteristic
234C8—41no—
235C8—2361no—
236C22—21no—
237C22—21no—
238C22—42no—
239C22—42no—
240C22—41no—
241C22—41no—
242C22—42no—
243C22—41no—
244C22—81no—
245C22—81no—
246C22—81no—
247C22—81no—
248C22—4721no—
249C22—2362no—
250C22—2361no—
251C22—2361no—
252C22—2361no—
253C22#1427369511yescharacteristic
254C22#1427374611yescharacteristic
255C22#1427375111yescharacteristic
256C4—21no—
257C4—21no—
258C4—41no—
259C4—2362no—
260C4—2361no—
261C4—2361no—
262C4—2361no—
263C2—21no—
264C2—21no—
265C2—82no—
266C2—81no—
267C2—4721no—
268C2#1683754411yescharacteristic
269C2#1683756811yescharacteristic
270C2#1683758811yescharacteristic
subgroupG/H
centerC22#14273695
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#447C2
socleC22×C59#120
hypercenter#447D59
hypocenterC59#1600
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #16837989C2semidirect
2. #16837553C2semidirect
3. #16837310C2semidirect
4. #16837140C2semidirect
5. #16837136C2semidirect
6. #16837125C2semidirect
7. C59×#447C2semidirect
33. C2×D4×C59D4semidirect
43. C2×Dic118D4semidirect
46. C4⋊C4×C59D4semidirect
57. C4⋊Dic59D4semidirect
138. #447D59semidirect
143. C59#1600semidirect
175. C2×D4C22⋊D59semidirect
187. C4⋊C4C22⋊D59semidirect