Finite Group Databasebeta

← #21429838

Subgroups — #21429838

Order 7552.

632 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14273710C212yesmaximal, complemented
2C2×#14273701C211yesmaximal, characteristic
3#16837332C212yesmaximal, complemented
4#16837324C214yesmaximal, complemented
5#16837319C212yesmaximal, complemented
6#16837281C212yesmaximal, complemented
7#16837262C211yesmaximal, characteristic, complemented
8C22×C4⋊C4×C59C211yesmaximal, characteristic, complemented
9C22×D236C2211yescharacteristic
10C22×C22⋊D59C2212yes—
11#14273710—28no—
12#14273701—24no—
13C2×C4⋊Dic59C2211yescharacteristic
14C2×C4⋊Dic59C2212yes—
15C2×Dic59⋊C4C2214yes—
16C2×C22⋊Dic59C2212yes—
17C2×(C2×D59)⋊C4C2212yes—
18C2×(C2×D59)⋊C4C2214yes—
19C2×(C2×D59)⋊C4C2214yes—
20C59⋊#95C2212yes—
21C59⋊#95C2214yes—
22C23×C4×C59C2211yescharacteristic
23C23×C4×C59C2211yescharacteristic
24C23×C4×C59C2211yescharacteristic
25C2×C4⋊C4×C59—24no—
26C2×C4⋊C4×C59C2212yes—
27C2×C4⋊C4×C59C2212yes—
28C24×C59C2311yescharacteristic
29C23×D59C2312yes—
30C22×C4×C59—22no—
31C22×C4×C59—22no—
32C22×C4×C59—22no—
33C22×C4×C59—42no—
34C22×C4×C59—42no—
35C22×C4×C59D414yes—
36C22×C4×C59D414yescomplemented
37C22×C4×C59C2312yes—
38C22×C4×C59C2311yescharacteristic
39C22×C4×C59C2312yes—
40C22×C4×C59C2311yescharacteristic
41C2×C22⋊D59—24no—
42C2×C22⋊D59—24no—
43C2×C22⋊D59—24no—
44C22×Dic59C2314yes—
45C22×Dic59C2312yes—
46C2×D236—22no—
47C2×D236—42no—
48C4⋊C4×C59—24no—
49C4⋊C4×C59—24no—
50C22⋊Dic59—24no—
51(C2×D59)⋊C4—24no—
52(C2×D59)⋊C4—28no—
53(C2×D59)⋊C4—44no—
54C4⋊Dic59—22no—
55C4⋊Dic59—42no—
56Dic59⋊C4—28no—
57C23×C59—22no—
58C23×C59—22no—
59C23×C59C2×D412yes—
60C23×C59C2×D412yes—
61C23×C59#4112yes—
62C23×C59C2411yescharacteristic
63C22×D59—22no—
64C22×D59—22no—
65C22×D59—22no—
66C22×D59—24no—
67C22×D59—24no—
68C2×C4×C59—28no—
69C2×C4×C59—22no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—22no—
74C2×C4×C59—24no—
75C2×C4×C59—44no—
76C2×C4×C59—44no—
77C2×C4×C59C2×D414yes—
78C2×C4×C59C2×D412yes—
79C2×C4×C59C2×D412yes—
80C22⋊D59—48no—
81C2×Dic59—22no—
82C2×Dic59—24no—
83C2×Dic59—22no—
84C2×Dic59—22no—
85C2×Dic59—24no—
86C2×Dic59—24no—
87D236—44no—
88C22×C59—22no—
89C22×C59—22no—
90C22×C59—24no—
91C22×C59—24no—
92C22×C59#12114yes—
93C22×C59C22×D411yescharacteristic
94C22×C59C22×D411yescharacteristic
95C22×C59C2×#4111yescharacteristic
96C22×C59H(5,𝔽2)12yes—
97C22×C592−1+412yes—
98C2×D59—42no—
99C2×D59—42no—
100C2×D59—42no—
101C2×D59—44no—
102C2×D59—44no—
103C4×C59—24no—
104C4×C59—22no—
105C4×C59—22no—
106C4×C59—42no—
107Dic59—42no—
108Dic59—44no—
109#2618—591nomaximal, Sylow
110C2×C59—24no—
111C2×C59C2×#12111yescharacteristic
112C2×C59#53411yescharacteristic
113C2×C59#53611yescharacteristic
114C2×C59#53712yes—
115C2×C59#53912yes—
116D59—82no—
117C2×#123—592no—
118C2×#121—591no—
119C22×C4⋊C4D5911yescharacteristic, complemented
120#398—592no—
121#396—594no—
122#394—592no—
123#386—592no—
124#380—591no—
125C59#261811yescharacteristic, complemented, Sylow
126C22×D4—592no—
127C22×D4—591no—
128C23×C4C2×D5911yescharacteristic
129C23×C4C2×D5911yescharacteristic
130C23×C4C2×D5911yescharacteristic
131#123—1188no—
132#121—1184no—
133C2×C4⋊C4—24no—
134C2×C4⋊C4—591no—
135C2×C4⋊C4—594no—
136C2×C4⋊C4—592no—
137C2×C4⋊C4C2×D5912yes—
138C2×C4⋊C4C2×D5912yes—
139C2×C22⋊C4—592no—
140C2×C22⋊C4—592no—
141C2×C22⋊C4—594no—
142C2×C22⋊C4—594no—
143#95—592no—
144#95—594no—
145C24—592no—
146C24C22×D5911yescharacteristic
147C2×D4—1184no—
148C2×D4—1184no—
149C2×D4—1184no—
150C2×D4—1182no—
151C2×D4—2362no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—42no—
156C22×C4—42no—
157C22×C4—594no—
158C22×C4—592no—
159C22×C4D23614yescomplemented
160C22×C4C22⋊D5914yes—
161C22×C4C22×D5912yes—
162C22×C4C22×D5912yes—
163C22×C4C22×D5911yescharacteristic
164C22×C4C22×D5911yescharacteristic
165C4⋊C4—24no—
166C4⋊C4—24no—
167C4⋊C4—1188no—
168C4⋊C4—1182no—
169C4⋊C4—2362no—
170C22⋊C4—1184no—
171C22⋊C4—1188no—
172C22⋊C4—1184no—
173C22⋊C4—2364no—
174C23—22no—
175C23—22no—
176C23—1182no—
177C23—1182no—
178C23—1182no—
179C23—1184no—
180C23—1184no—
181C23C2×D23612yes—
182C23#1174568512yes—
183C23C2×C22⋊D5912yes—
184C23C23×D5911yescharacteristic
185D4—2364no—
186D4—2368no—
187C2×C4—28no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—24no—
194C2×C4—44no—
195C2×C4—44no—
196C2×C4—1182no—
197C2×C4—1184no—
198C2×C4—1182no—
199C2×C4—1182no—
200C2×C4—1184no—
201C2×C4—1184no—
202C2×C4C2×D23614yes—
203C2×C4C2×C22⋊D5912yes—
204C2×C4C2×C22⋊D5912yes—
205C22—22no—
206C22—22no—
207C22—24no—
208C22—24no—
209C22—2362no—
210C22—2362no—
211C22—2362no—
212C22—2364no—
213C22—2364no—
214C22#1427370114yes—
215C22C22×C22⋊D5911yescharacteristic
216C22C22×D23611yescharacteristic
217C22C2×#1174568511yescharacteristic
218C22#1427377212yes—
219C22#1427377512yes—
220C4—24no—
221C4—22no—
222C4—22no—
223C4—42no—
224C4—2362no—
225C4—2364no—
226C2—24no—
227C2—4722no—
228C2C2×#1427370111yescharacteristic
229C2#1683796111yescharacteristic
230C2#1683797611yescharacteristic
231C2#1683798312yes—
232C2#1683799912yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC22×C4⋊C4×C59C2
hypercenterC22×C4⋊C4D59
hypocenterC59#2618
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14273710C2semidirect
3. #16837332C2semidirect
4. #16837324C2semidirect
5. #16837319C2semidirect
6. #16837281C2semidirect
7. #16837262C2semidirect
8. C22×C4⋊C4×C59C2semidirect
36. C22×C4×C59D4semidirect
119. C22×C4⋊C4D59semidirect
125. C59#2618semidirect
159. C22×C4D236semidirect