Finite Group Databasebeta

← #21424084

Subgroups — #21424084

Order 7552.

380 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 113 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×#14273642C212yesmaximal
2#16837262C212yesmaximal, complemented
3#16837169C212yesmaximal, complemented
4C2×C4×D4×C59C211yesmaximal, characteristic
5C2×C4⋊Dic59—22no—
6C2×C22⋊Dic59C2214yes—
7#14273642—24no—
8C59⋊#95—22no—
9C22×D4×C59C2211yescharacteristic
10C23×C4×C59C411yescharacteristic, complemented
11C23×C4×C59C2211yescharacteristic
12C4×D4×C59—22no—
13C4×D4×C59—22no—
14C2×C4⋊C4×C59C411yescharacteristic, complemented
15C2×C22⋊C4×C59C411yescharacteristic, complemented
16C2×C22⋊C4×C59C2211yescharacteristic
17C2×C42×C59C411yescharacteristic, complemented
18C24×C59C2×C411yescharacteristic
19C24×C59C2311yescharacteristic
20C2×D4×C59—22no—
21C2×D4×C59—22no—
22C2×D4×C59D412yes—
23C2×D4×C59Q812yes—
24C22×C4×C59—21no—
25C22×C4×C59—21no—
26C22×C4×C59—42no—
27C22×C4×C59—42no—
28C22×C4×C59C2×C411yescharacteristic
29C22×C4×C59C2×C411yescharacteristic
30C22×C4×C59C2×C411yescharacteristic
31C22×C4×C59C2×C411yescharacteristic
32C22×C4×C59C2×C411yescharacteristic
33C22×C4×C59D412yes—
34C22×C4×C59D412yes—
35C22×Dic59—24no—
36C4⋊C4×C59—22no—
37C22⋊C4×C59—22no—
38C22⋊C4×C59—22no—
39C42×C59—21no—
40C42×C59—21no—
41C22⋊Dic59—24no—
42C22⋊Dic59—24no—
43C4⋊Dic59—44no—
44C23×C59—21no—
45C23×C59—21no—
46C23×C59—41no—
47C23×C59—41no—
48C23×C59—41no—
49C23×C59—41no—
50C23×C59C4⋊C412yescomplemented
51C23×C59C22×C411yescharacteristic
52C23×C59C2×D411yescharacteristic
53C23×C59C2×D412yes—
54C23×C59C2×Q811yescharacteristic
55C23×C59#4112yes—
56D4×C59—24no—
57D4×C59—24no—
58C2×C4×C59—21no—
59C2×C4×C59—21no—
60C2×C4×C59—24no—
61C2×C4×C59—22no—
62C2×C4×C59—21no—
63C2×C4×C59—21no—
64C2×C4×C59—41no—
65C2×C4×C59—42no—
66C2×C4×C59—42no—
67C2×C4×C59—42no—
68C2×C4×C59—41no—
69C2×C4×C59—41no—
70C2×C4×C59C22⋊C411yescharacteristic
71C2×C4×C59C22⋊C412yes—
72C2×C4×C59C22⋊C411yescharacteristic
73C2×C4×C59C4⋊C412yescomplemented
74C2×Dic59—44no—
75C2×Dic59—44no—
76C2×Dic59—44no—
77C22×C59—22no—
78C22×C59—21no—
79C22×C59—22no—
80C22×C59—21no—
81C22×C59—22no—
82C22×C59—41no—
83C22×C59—41no—
84C22×C59—42no—
85C22×C59—42no—
86C22×C59—42no—
87C22×C59—41no—
88C22×C59—41no—
89C22×C59C2×C22⋊C411yescharacteristic
90C22×C59C2×C4⋊C411yescharacteristic
91C22×C59#11711yescharacteristic
92C22×C59#12112yes—
93C22×C59C22⋊Q812yes—
94C4×C59—22no—
95C4×C59—21no—
96C4×C59—22no—
97C4×C59—41no—
98C4×C59—41no—
99C4×C59#9912yescomplemented
100Dic59—84no—
101#1799—591nomaximal, Sylow
102C2×C59—22no—
103C2×C59—21no—
104C2×C59—21no—
105C2×C59—22no—
106C2×C59—42no—
107C2×C59#38011yescharacteristic
108C2×C59C2×#9911yescharacteristic
109C2×C59#41011yescharacteristic
110C2×C4×D4D5911yescharacteristic
111C2×#99—592no—
112#380—592no—
113#342—592no—
114C59#179911yescharacteristic, complemented, Sylow
115C22×D4C2×D5911yescharacteristic
116C23×C4Dic5911yescharacteristic, complemented
117C23×C4C2×D5911yescharacteristic
118C4×D4—22no—
119C4×D4—22no—
120C2×C4⋊C4—1182no—
121C2×C4⋊C4Dic5911yescharacteristic, complemented
122C2×C22⋊C4—594no—
123C2×C22⋊C4Dic5911yescharacteristic, complemented
124C2×C22⋊C4C2×D5911yescharacteristic
125C2×C42Dic5911yescharacteristic, complemented
126#99—1184no—
127#95—1182no—
128C24C2×Dic5911yescharacteristic
129C24C22×D5911yescharacteristic
130C2×D4—22no—
131C2×D4—22no—
132C2×D4Dic11812yes—
133C2×D4D23612yes—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—42no—
137C22×C4—42no—
138C22×C4—1184no—
139C22×C4C2×Dic5911yescharacteristic
140C22×C4C2×Dic5911yescharacteristic
141C22×C4C2×Dic5911yescharacteristic
142C22×C4C2×Dic5911yescharacteristic
143C22×C4C2×Dic5911yescharacteristic
144C22×C4C22⋊D5912yes—
145C22×C4C22⋊D5912yes—
146C4⋊C4—22no—
147C4⋊C4—2364no—
148C22⋊C4—22no—
149C22⋊C4—22no—
150C22⋊C4—1184no—
151C22⋊C4—1184no—
152C42—21no—
153C42—21no—
154C23—21no—
155C23—21no—
156C23—41no—
157C23—41no—
158C23—41no—
159C23—41no—
160C23C4⋊Dic5912yescomplemented
161C23C2×Dic11811yescharacteristic
162C23C2×D23611yescharacteristic
163C23#1174568512yes—
164C23C22×Dic5911yescharacteristic
165C23C2×C22⋊D5912yes—
166D4—24no—
167D4—24no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—24no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—2364no—
181C2×C4—2364no—
182C2×C4—2364no—
183C2×C4C4⋊Dic5912yescomplemented
184C2×C4C22⋊Dic5911yescharacteristic
185C2×C4C22⋊Dic5912yes—
186C2×C4C22⋊Dic5911yescharacteristic
187C22—21no—
188C22—22no—
189C22—21no—
190C22—22no—
191C22—22no—
192C22—41no—
193C22—41no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22—41no—
198C22—41no—
199C22C2×C22⋊Dic5911yescharacteristic
200C22C2×C4⋊Dic5911yescharacteristic
201C22#1427368611yescharacteristic
202C22#1427370112yes—
203C22#1427370612yes—
204C4—22no—
205C4—21no—
206C4—22no—
207C4—41no—
208C4—41no—
209C4—4724no—
210C4#1427364212yescomplemented
211C2—22no—
212C2—21no—
213C2—21no—
214C2—22no—
215C2—42no—
216C2#1683726211yescharacteristic
217C2C2×#1427364211yescharacteristic
218C2#1683737611yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic59
commutatorC23×C59C22×C4
FrattiniC24C22×D59
FittingC2×C4×D4×C59C2
socleC22×C59C2×C22⋊C4
hypercenterC2×C4×D4D59
hypocenterC59#1799
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. #16837262C2semidirect
3. #16837169C2semidirect
10. C23×C4×C59C4semidirect
14. C2×C4⋊C4×C59C4semidirect
15. C2×C22⋊C4×C59C4semidirect
17. C2×C42×C59C4semidirect
50. C23×C59C4⋊C4semidirect
73. C2×C4×C59C4⋊C4semidirect
99. C4×C59#99semidirect
114. C59#1799semidirect
116. C23×C4Dic59semidirect
121. C2×C4⋊C4Dic59semidirect
123. C2×C22⋊C4Dic59semidirect
125. C2×C42Dic59semidirect
160. C23C4⋊Dic59semidirect
183. C2×C4C4⋊Dic59semidirect
210. C4#14273642semidirect