Finite Group Databasebeta

← #21429876

Subgroups — #21429876

Order 7552.

526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14273710C211yesmaximal, characteristic
2#16837340C212yesmaximal, complemented
3#16837337C212yesmaximal, complemented
4#16837333C212yesmaximal, complemented
5#16837328C212yesmaximal, complemented
6#16837281C212yesmaximal
7#16837275C212yesmaximal, complemented
8#16837265C211yesmaximal, characteristic, complemented
9C22×C4⋊C4×C59C211yesmaximal, characteristic, complemented
10C22×C22⋊D59C2211yescharacteristic
11#14273710—24no—
12C2×Dic59⋊C4C2211yescharacteristic
13C2×Dic59⋊C4C2211yescharacteristic
14C2×Dic59⋊C4C2214yes—
15C2×C22⋊Dic59C2211yescharacteristic
16C2×C22⋊Dic59C2212yes—
17C2×(C2×D59)⋊C4C2211yescharacteristic
18C2×(C2×D59)⋊C4C2211yescharacteristic
19C2×(C2×D59)⋊C4C2214yes—
20C59⋊#95C2212yes—
21C59⋊#95C2212yes—
22C59⋊#95C2214yes—
23C59⋊#95C2214yes—
24C23×C4×C59C2211yescharacteristic
25C23×C4×C59C2212yes—
26C2×C4⋊C4×C59—24no—
27C2×C4⋊C4×C59C2212yes—
28C2×C4⋊C4×C59C2212yes—
29C24×C59C2311yescharacteristic
30C23×D59C2311yescharacteristic
31C22×C4×C59—24no—
32C22×C4×C59—24no—
33C22×C4×C59—44no—
34C22×C4×C59D414yes—
35C22×C4×C59C2314yes—
36C22×C4×C59C2311yescharacteristic
37C22×C4×C59C2311yescharacteristic
38C2×C22⋊D59—22no—
39C2×C22⋊D59—24no—
40C22×Dic59C2311yescharacteristic
41C22×Dic59C2314yes—
42C22×Dic59C2311yescharacteristic
43C22×Dic59C2311yescharacteristic
44C4⋊C4×C59—24no—
45C4⋊C4×C59—24no—
46C22⋊Dic59—22no—
47C22⋊Dic59—24no—
48(C2×D59)⋊C4—22no—
49(C2×D59)⋊C4—22no—
50(C2×D59)⋊C4—44no—
51Dic59⋊C4—22no—
52Dic59⋊C4—22no—
53Dic59⋊C4—44no—
54C23×C59—22no—
55C23×C59—22no—
56C23×C59C2×D412yes—
57C23×C59#4114yes—
58C23×C59C2411yescharacteristic
59C22×D59—21no—
60C22×D59—22no—
61C22×D59—22no—
62C22×D59—22no—
63C2×C4×C59—28no—
64C2×C4×C59—22no—
65C2×C4×C59—22no—
66C2×C4×C59—24no—
67C2×C4×C59—24no—
68C2×C4×C59—24no—
69C2×C4×C59—48no—
70C2×C4×C59C2×D412yes—
71C2×C4×C59C2×D412yes—
72C22⋊D59—44no—
73C2×Dic59—21no—
74C2×Dic59—21no—
75C2×Dic59—21no—
76C2×Dic59—24no—
77C2×Dic59—22no—
78C2×Dic59—22no—
79C2×Dic59—24no—
80C2×Dic59—22no—
81C2×Dic59—24no—
82C22×C59—22no—
83C22×C59—22no—
84C22×C59—28no—
85C22×C59#12314yes—
86C22×C59C22×D411yescharacteristic
87C22×C59C2×#4112yes—
88C22×C59H(5,𝔽2)12yes—
89C22×C592−1+412yes—
90C2×D59—41no—
91C2×D59—41no—
92C2×D59—41no—
93C2×D59—44no—
94C4×C59—22no—
95C4×C59—22no—
96C4×C59—44no—
97Dic59—41no—
98Dic59—41no—
99Dic59—41no—
100Dic59—44no—
101#2623—591nomaximal, Sylow
102C2×C59—24no—
103C2×C59C2×#12311yescharacteristic
104C2×C59#53511yescharacteristic
105C2×C59#53611yescharacteristic
106C2×C59#53914yes—
107D59—81no—
108C2×#123—591no—
109C22×C4⋊C4D5911yescharacteristic, complemented
110#400—592no—
111#399—592no—
112#398—592no—
113#397—592no—
114#386—592no—
115#385—592no—
116#381—591no—
117C59#262311yescharacteristic, complemented, Sylow
118C22×D4—591no—
119C23×C4C2×D5911yescharacteristic
120C23×C4C2×D5912yes—
121#123—1184no—
122C2×C4⋊C4—24no—
123C2×C4⋊C4—591no—
124C2×C4⋊C4—591no—
125C2×C4⋊C4—594no—
126C2×C4⋊C4C2×D5912yes—
127C2×C4⋊C4C2×D5912yes—
128C2×C22⋊C4—591no—
129C2×C22⋊C4—592no—
130C2×C22⋊C4—591no—
131C2×C22⋊C4—591no—
132C2×C22⋊C4—594no—
133#95—592no—
134#95—592no—
135#95—594no—
136#95—594no—
137C24—591no—
138C24C22×D5911yescharacteristic
139C2×D4—1184no—
140C2×D4—1182no—
141C22×C4—24no—
142C22×C4—24no—
143C22×C4—44no—
144C22×C4—591no—
145C22×C4—594no—
146C22×C4—591no—
147C22×C4—591no—
148C22×C4C22⋊D5914yes—
149C22×C4C22×D5914yes—
150C22×C4C22×D5911yescharacteristic
151C22×C4C22×D5911yescharacteristic
152C4⋊C4—24no—
153C4⋊C4—24no—
154C4⋊C4—1182no—
155C4⋊C4—1182no—
156C4⋊C4—2364no—
157C22⋊C4—1184no—
158C22⋊C4—1182no—
159C22⋊C4—1182no—
160C22⋊C4—1182no—
161C22⋊C4—2364no—
162C23—22no—
163C23—22no—
164C23—1181no—
165C23—1182no—
166C23—1182no—
167C23—1182no—
168C23#1174568514yes—
169C23C2×C22⋊D5912yes—
170C23C23×D5911yescharacteristic
171D4—2364no—
172C2×C4—28no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—48no—
179C2×C4—1181no—
180C2×C4—1181no—
181C2×C4—1181no—
182C2×C4—1184no—
183C2×C4—1182no—
184C2×C4—1184no—
185C2×C4—1182no—
186C2×C4—1182no—
187C2×C4—1184no—
188C2×C4C2×C22⋊D5912yes—
189C2×C4C2×C22⋊D5912yes—
190C22—22no—
191C22—22no—
192C22—28no—
193C22—2361no—
194C22—2361no—
195C22—2361no—
196C22—2364no—
197C22#1427371014yes—
198C22C22×C22⋊D5911yescharacteristic
199C22C2×#1174568512yes—
200C22#1427377212yes—
201C22#1427377512yes—
202C4—22no—
203C4—22no—
204C4—44no—
205C4—2361no—
206C4—2361no—
207C4—2361no—
208C4—2364no—
209C2—24no—
210C2—4721no—
211C2C2×#1427371011yescharacteristic
212C2#1683796911yescharacteristic
213C2#1683797611yescharacteristic
214C2#1683799914yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC22×C4⋊C4×C59C2
hypercenterC22×C4⋊C4D59
hypocenterC59#2623
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #16837340C2semidirect
3. #16837337C2semidirect
4. #16837333C2semidirect
5. #16837328C2semidirect
7. #16837275C2semidirect
8. #16837265C2semidirect
9. C22×C4⋊C4×C59C2semidirect
109. C22×C4⋊C4D59semidirect
117. C59#2623semidirect