Finite Group Databasebeta

← #21424638

Subgroups — #21424638

Order 7552.

380 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 89 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#16837961C211yesmaximal, characteristic
2C2×#14273642C211yesmaximal, characteristic, complemented
3C2×#14273641C212yesmaximal, complemented
4#16837168C212yesmaximal, complemented
5C59×#518C211yesmaximal, characteristic, complemented
6C22×C22⋊D59C2211yescharacteristic
7#14273710—21no—
8#14273708C412yescomplemented
9#14273699—22no—
10#14273696—21no—
11#14273695C412yescomplemented
12C2×C22⋊Dic59C2212yes—
13C2×C22⋊Dic59C2211yescharacteristic
14#14273642—22no—
15#14273641—24no—
16C22×D4×C59C2211yescharacteristic
17C4×D4×C59—24no—
18#117×C59—21no—
19C2×C22⋊C4×C59—21no—
20C2×C22⋊C4×C59C2212yes—
21C24×C59D411yescharacteristic
22C24×C59C2311yescharacteristic
23C23×D59C2×C411yescharacteristic, complemented
24C2×D4×C59—22no—
25C2×D4×C59—22no—
26C2×D4×C59C2×C412yes—
27C2×D4×C59D412yes—
28C22×C4×C59—22no—
29C22×C4×C59—22no—
30C22×C4×C59D411yescharacteristic
31C2×C22⋊D59—22no—
32C2×C22⋊D59—21no—
33C2×C22⋊D59—21no—
34C2×C22⋊D59—22no—
35C2×C22⋊D59—22no—
36C22×Dic59—21no—
37C22×Dic59—22no—
38C22×Dic59C2×C411yescharacteristic, complemented
39C4⋊C4×C59—22no—
40C22⋊C4×C59—22no—
41C22⋊C4×C59—22no—
42C22⋊C4×C59D414yescomplemented
43C42×C59—22no—
44C22⋊Dic59—22no—
45C22⋊Dic59—21no—
46C22⋊Dic59—22no—
47C22⋊Dic59—22no—
48C22⋊Dic59C2×C412yescomplemented
49(C2×D59)⋊C4—22no—
50Dic59⋊C4—22no—
51C23×C59—21no—
52C23×C59—21no—
53C23×C59—81no—
54C23×C59—81no—
55C23×C59C22⋊C412yes—
56C23×C59C22×C411yescharacteristic
57C23×C59C2×D411yescharacteristic
58C23×C59C2×D411yescharacteristic
59C23×C59C2×D412yes—
60C23×C59#4112yes—
61C22×D59—21no—
62C22×D59—22no—
63C22×D59—81no—
64D4×C59—24no—
65D4×C59—24no—
66C2×C4×C59—21no—
67C2×C4×C59—21no—
68C2×C4×C59—24no—
69C2×C4×C59—82no—
70C2×C4×C59—82no—
71C2×C4×C59C22⋊C412yes—
72C22⋊D59—41no—
73C22⋊D59—42no—
74C22⋊D59—41no—
75C22⋊D59—82no—
76C2×Dic59—21no—
77C2×Dic59—22no—
78C2×Dic59—22no—
79C2×Dic59—42no—
80C2×Dic59—81no—
81C2×Dic59—82no—
82C22×C59—22no—
83C22×C59—41no—
84C22×C59—42no—
85C22×C59—42no—
86C22×C59—41no—
87C22×C59—41no—
88C22×C59—42no—
89C22×C59—42no—
90C22×C59—81no—
91C22×C59C2×C22⋊C411yescharacteristic
92C22×C59C4×D412yes—
93C22×C59#12011yescharacteristic
94C22×C59#12112yes—
95C22×C59#12311yescharacteristic
96C2×D59—42no—
97C2×D59—41no—
98C2×D59—82no—
99C4×C59—22no—
100C4×C59—44no—
101Dic59—42no—
102Dic59—41no—
103Dic59—82no—
104#1913—591nomaximal, Sylow
105C2×C59—21no—
106C2×C59—22no—
107C2×C59—21no—
108C2×C59—22no—
109C2×C59—21no—
110C2×C59—42no—
111C2×C59#38611yescharacteristic
112D59—81no—
113#534—591no—
114#518D5911yescharacteristic, complemented
115C2×#99—591no—
116C2×#99—592no—
117#342—592no—
118C59#191311yescharacteristic, complemented, Sylow
119C22×D4—591no—
120C22×D4C2×D5911yescharacteristic
121#123—592no—
122#123—1181no—
123#121—1182no—
124#120—592no—
125#120—1181no—
126C4×D4—24no—
127#117—21no—
128C2×C22⋊C4—21no—
129C2×C22⋊C4—591no—
130C2×C22⋊C4—592no—
131C2×C22⋊C4C2×D5912yes—
132#99—1182no—
133#99—1184no—
134C24—591no—
135C24C22⋊D5911yescharacteristic
136C24C22×D5911yescharacteristic
137C2×D4—22no—
138C2×D4—22no—
139C2×D4—1182no—
140C2×D4—1181no—
141C2×D4—1182no—
142C2×D4—1182no—
143C2×D4—1181no—
144C2×D4C4×D5912yes—
145C2×D4D23612yes—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—591no—
149C22×C4—1181no—
150C22×C4—1182no—
151C22×C4C22⋊D5911yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—1182no—
154C22⋊C4—22no—
155C22⋊C4—22no—
156C22⋊C4—592no—
157C22⋊C4—1182no—
158C22⋊C4—1181no—
159C22⋊C4—1182no—
160C22⋊C4—1182no—
161C22⋊C4—1182no—
162C22⋊C4C22⋊D5914yescomplemented
163C42—22no—
164C23—21no—
165C23—21no—
166C23—81no—
167C23—81no—
168C23—1182no—
169C23—1181no—
170C23—4721no—
171C23(C2×D59)⋊C412yes—
172C23C2×C4×D5911yescharacteristic
173C23C2×D23611yescharacteristic
174C23#1174568512yes—
175C23C2×C22⋊D5911yescharacteristic
176C23C2×C22⋊D5912yes—
177D4—24no—
178D4—24no—
179D4—4722no—
180D4—2361no—
181D4—2362no—
182D4—2361no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—24no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—1182no—
189C2×C4—1181no—
190C2×C4—1182no—
191C2×C4—4722no—
192C2×C4—4721no—
193C2×C4—2362no—
194C2×C4(C2×D59)⋊C412yes—
195C22—22no—
196C22—42no—
197C22—41no—
198C22—42no—
199C22—41no—
200C22—41no—
201C22—42no—
202C22—42no—
203C22—81no—
204C22—4722no—
205C22—2362no—
206C22—2361no—
207C22C2×(C2×D59)⋊C411yescharacteristic
208C22C4×C22⋊D5912yes—
209C22#1427369611yescharacteristic
210C22#1427370112yes—
211C22#1427371011yescharacteristic
212C4—22no—
213C4—44no—
214C4—4722no—
215C4—2362no—
216C4—2361no—
217C2—21no—
218C2—22no—
219C2—21no—
220C2—21no—
221C2—22no—
222C2—42no—
223C2—4721no—
224C2#1683728111yescharacteristic
subgroupG/H
centerC2#16837281
commutatorC23×C59C22×C4
FrattiniC24C22×D59
FittingC59×#518C2
socleC2×C59#386
hypercenter#518D59
hypocenterC59#1913
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C24 ◁ #518

Complements

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

NH ≅ G/Ntype
2. C2×#14273642C2semidirect
3. C2×#14273641C2semidirect
4. #16837168C2semidirect
5. C59×#518C2semidirect
8. #14273708C4semidirect
11. #14273695C4semidirect
23. C23×D59C2×C4semidirect
38. C22×Dic59C2×C4semidirect
42. C22⋊C4×C59D4semidirect
48. C22⋊Dic59C2×C4semidirect
114. #518D59semidirect
118. C59#1913semidirect
162. C22⋊C4C22⋊D59semidirect