Finite Group Databasebeta

← #21424504

Subgroups — #21424504

Order 7552.

578 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#14273695C211yesmaximal, characteristic
2C2×#14273642C211yesmaximal, characteristic, complemented
3#16837257C212yesmaximal, complemented
4#16837169C212yesmaximal, complemented
5C59×#518C211yesmaximal, characteristic, complemented
6C24×D59C2211yescharacteristic
7C22×C22⋊D59—21no—
8#14273695—22no—
9#14273695C414yescomplemented
10C2×C22⋊Dic59C2212yes—
11C2×C22⋊Dic59C2211yescharacteristic
12C2×(C2×D59)⋊C4—21no—
13C2×(C2×D59)⋊C4—24no—
14#14273642—22no—
15C22×D4×C59C2211yescharacteristic
16C4×D4×C59—24no—
17#117×C59—21no—
18C2×C22⋊C4×C59—21no—
19C2×C22⋊C4×C59C2212yes—
20C24×C59D411yescharacteristic
21C24×C59C2311yescharacteristic
22C23×D59—22no—
23C23×D59—21no—
24C23×D59—21no—
25C23×D59—22no—
26C23×D59—44no—
27C23×D59C2×C412yescomplemented
28C2×D4×C59—22no—
29C2×D4×C59—22no—
30C2×D4×C59C2×C412yes—
31C2×D4×C59D412yes—
32C22×C4×C59—22no—
33C22×C4×C59D411yescharacteristic
34C22×C4×C59D414yescomplemented
35C2×C22⋊D59—24no—
36C2×C22⋊D59—44no—
37C22×Dic59—21no—
38C22×Dic59—22no—
39C4⋊C4×C59—22no—
40C22⋊C4×C59—22no—
41C22⋊C4×C59—22no—
42C22⋊C4×C59—22no—
43C42×C59—22no—
44C22⋊Dic59—21no—
45C22⋊Dic59—22no—
46C22⋊Dic59—22no—
47C22⋊Dic59C2×C412yescomplemented
48(C2×D59)⋊C4—24no—
49(C2×D59)⋊C4—48no—
50C23×C59—21no—
51C23×C59—21no—
52C23×C59—42no—
53C23×C59—42no—
54C23×C59C22⋊C412yescomplemented
55C23×C59C22×C411yescharacteristic
56C23×C59C2×D411yescharacteristic
57C23×C59C2×D411yescharacteristic
58C23×C59C2×D412yes—
59C23×C59#4112yes—
60C22×D59—28no—
61C22×D59—24no—
62C22×D59—22no—
63C22×D59—24no—
64C22×D59—44no—
65C22×D59—44no—
66C22×D59—48no—
67C22×D59—44no—
68C22×D59—42no—
69C22×D59—41no—
70C22×D59—42no—
71C22×D59—41no—
72D4×C59—24no—
73D4×C59—24no—
74C2×C4×C59—21no—
75C2×C4×C59—21no—
76C2×C4×C59—24no—
77C2×C4×C59—44no—
78C2×C4×C59—82no—
79C2×C4×C59C22⋊C412yescomplemented
80C22⋊D59—48no—
81C2×Dic59—22no—
82C2×Dic59—42no—
83C2×Dic59—44no—
84C2×Dic59—42no—
85C22×C59—24no—
86C22×C59—22no—
87C22×C59—22no—
88C22×C59—41no—
89C22×C59—41no—
90C22×C59—42no—
91C22×C59—42no—
92C22×C59—42no—
93C22×C59—81no—
94C22×C59C2×C22⋊C411yescharacteristic
95C22×C59C4×D412yes—
96C22×C59#12011yescharacteristic
97C22×C59#12112yes—
98C22×C59#12311yescharacteristic
99C2×D59—24no—
100C2×D59—28no—
101C2×D59—42no—
102C2×D59—48no—
103C2×D59—44no—
104C2×D59—44no—
105C2×D59—42no—
106C2×D59—44no—
107C4×C59—22no—
108C4×C59—44no—
109Dic59—42no—
110Dic59—82no—
111#1889—591nomaximal, Sylow
112C2×C59—21no—
113C2×C59—22no—
114C2×C59—22no—
115C2×C59—21no—
116C2×C59—42no—
117C2×C59#38611yescharacteristic
118C2×C59B(4,𝔽2)12yes—
119D59—44no—
120C2×#120—591no—
121#518D5911yescharacteristic, complemented
122C2×#99—591no—
123#379—592no—
124#342—592no—
125C59#188911yescharacteristic, complemented, Sylow
126C25—591no—
127C22×D4—1181no—
128C22×D4C2×D5911yescharacteristic
129#120—594no—
130#120—1182no—
131C4×D4—24no—
132#117—21no—
133C2×C22⋊C4—21no—
134C2×C22⋊C4—591no—
135C2×C22⋊C4—592no—
136C2×C22⋊C4—1181no—
137C2×C22⋊C4—1184no—
138C2×C22⋊C4C2×D5912yes—
139#99—1182no—
140C24—592no—
141C24—1182no—
142C24—1181no—
143C24—1181no—
144C24—1182no—
145C24—2364no—
146C24C22⋊D5911yescharacteristic
147C24C22×D5911yescharacteristic
148C2×D4—22no—
149C2×D4—22no—
150C2×D4—1184no—
151C2×D4—2364no—
152C2×D4C4×D5912yes—
153C2×D4D23612yes—
154C22×C4—22no—
155C22×C4—1181no—
156C22×C4—1182no—
157C22×C4C22⋊D5911yescharacteristic
158C22×C4C22⋊D5914yescomplemented
159C4⋊C4—22no—
160C22⋊C4—22no—
161C22⋊C4—22no—
162C22⋊C4—22no—
163C22⋊C4—592no—
164C22⋊C4—1181no—
165C22⋊C4—1184no—
166C22⋊C4—1182no—
167C22⋊C4—1182no—
168C22⋊C4—2368no—
169C42—22no—
170C23—21no—
171C23—21no—
172C23—42no—
173C23—42no—
174C23—1188no—
175C23—1184no—
176C23—1182no—
177C23—1184no—
178C23—2364no—
179C23—2362no—
180C23—2364no—
181C23—2364no—
182C23—2368no—
183C23—2361no—
184C23—2362no—
185C23—2361no—
186C23(C2×D59)⋊C412yescomplemented
187C23C2×C4×D5911yescharacteristic
188C23C2×D23611yescharacteristic
189C23#1174568512yes—
190C23C2×C22⋊D5911yescharacteristic
191C23C2×C22⋊D5912yes—
192D4—24no—
193D4—24no—
194D4—2368no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—24no—
198C2×C4—44no—
199C2×C4—82no—
200C2×C4—1182no—
201C2×C4—2364no—
202C2×C4—2362no—
203C2×C4—2362no—
204C2×C4(C2×D59)⋊C412yescomplemented
205C22—24no—
206C22—22no—
207C22—22no—
208C22—41no—
209C22—41no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—81no—
214C22—1184no—
215C22—1188no—
216C22—2368no—
217C22—2362no—
218C22—2364no—
219C22—2364no—
220C22—2362no—
221C22—2364no—
222C22C2×(C2×D59)⋊C411yescharacteristic
223C22C4×C22⋊D5912yes—
224C22#1427369611yescharacteristic
225C22#1427370112yes—
226C22#1427371011yescharacteristic
227C4—22no—
228C4—44no—
229C4—4722no—
230C4—2362no—
231C2—22no—
232C2—21no—
233C2—21no—
234C2—22no—
235C2—42no—
236C2—2364no—
237C2#1683728111yescharacteristic
238C2#1683758912yes—
subgroupG/H
centerC22#14273696
commutatorC23×C59C22×C4
FrattiniC24C22×D59
FittingC59×#518C2
socleC22×C59#120
hypercenter#518D59
hypocenterC59#1889
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C24 ◁ #518

Complements

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

NH ≅ G/Ntype
2. C2×#14273642C2semidirect
3. #16837257C2semidirect
4. #16837169C2semidirect
5. C59×#518C2semidirect
9. #14273695C4semidirect
27. C23×D59C2×C4semidirect
34. C22×C4×C59D4semidirect
47. C22⋊Dic59C2×C4semidirect
54. C23×C59C22⋊C4semidirect
79. C2×C4×C59C22⋊C4semidirect
121. #518D59semidirect
125. C59#1889semidirect
158. C22×C4C22⋊D59semidirect
186. C23(C2×D59)⋊C4semidirect
204. C2×C4(C2×D59)⋊C4semidirect