Finite Group Databasebeta

← #21428366

Subgroups — #21428366

Order 7552.

672 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×(C2×D59)⋊C4C211yesmaximal, characteristic
2#16837337C212yesmaximal, complemented
3#16837328C212yesmaximal, complemented
4#16837293C214yesmaximal, complemented
5#16837274C212yesmaximal, complemented
6#16837265C211yesmaximal, characteristic, complemented
7#16837257C212yesmaximal
8C2×#117×C59C211yesmaximal, characteristic, complemented
9C24×D59C2211yescharacteristic
10C23×Dic59C2211yescharacteristic
11C2×Dic59⋊C4C2214yescomplemented
12C2×C22⋊Dic59C2212yes—
13C2×(C2×D59)⋊C4—24no—
14C2×(C2×D59)⋊C4C2214yes—
15C2×(C2×D59)⋊C4C2212yes—
16C2×(C2×D59)⋊C4C2212yes—
17C2×(C2×D59)⋊C4C2214yes—
18C59⋊#95C2212yescomplemented
19C59⋊#95C2212yescomplemented
20C59⋊#95C2214yescomplemented
21C23×C4×C59C2211yescharacteristic
22#117×C59—24no—
23C2×C4⋊C4×C59C2211yescharacteristic, complemented
24C2×C4⋊C4×C59C2211yescharacteristic, complemented
25C2×C22⋊C4×C59C2212yes—
26C2×C42×C59C2212yescomplemented
27C24×C59C2311yescharacteristic
28C23×D59—22no—
29C23×D59—24no—
30C23×D59—24no—
31C23×D59—42no—
32C23×D59C2312yes—
33C22×C4×C59—24no—
34C22×C4×C59D414yes—
35C22×C4×C59C2312yes—
36C22×C4×C59C2312yes—
37C22×C4×C59C2311yescharacteristic
38C22×C4×C59C2311yescharacteristic
39C22×Dic59—22no—
40C22×Dic59—42no—
41C22×Dic59C2314yes—
42C22×Dic59C2312yes—
43C4⋊C4×C59—22no—
44C4⋊C4×C59—22no—
45C22⋊C4×C59—24no—
46C42×C59—24no—
47C22⋊Dic59—24no—
48(C2×D59)⋊C4—28no—
49(C2×D59)⋊C4—24no—
50(C2×D59)⋊C4—24no—
51(C2×D59)⋊C4—44no—
52Dic59⋊C4—44no—
53C23×C59—22no—
54C23×C59—22no—
55C23×C59C2×D412yes—
56C23×C59#4114yes—
57C23×C59C2411yescharacteristic
58C22×D59—28no—
59C22×D59—22no—
60C22×D59—22no—
61C22×D59—24no—
62C22×D59—24no—
63C22×D59—416no—
64C22×D59—44no—
65C22×D59—44no—
66C22×D59#4114yes—
67C2×C4×C59—28no—
68C2×C4×C59—22no—
69C2×C4×C59—22no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—24no—
73C2×C4×C59—24no—
74C2×C4×C59C2×D412yes—
75C2×C4×C59C2×D412yes—
76C2×Dic59—22no—
77C2×Dic59—24no—
78C2×Dic59—24no—
79C2×Dic59—24no—
80C2×Dic59—24no—
81C2×Dic59—44no—
82C22×C59—22no—
83C22×C59—22no—
84C22×C59—28no—
85C22×C59#12314yes—
86C22×C59C22×D411yescharacteristic
87C22×C59C2×#4112yes—
88C22×C59C2×#4112yes—
89C22×C59H(5,𝔽2)12yes—
90C2×D59—24no—
91C2×D59—28no—
92C2×D59—416no—
93C2×D59—42no—
94C2×D59—42no—
95C2×D59—44no—
96C4×C59—22no—
97C4×C59—22no—
98C4×C59—42no—
99C4×C59—42no—
100Dic59—42no—
101Dic59—44no—
102#2482—591nomaximal, Sylow
103C2×C59—24no—
104C2×C59C2×#12311yescharacteristic
105C2×C59#52511yescharacteristic
106C2×C59#53511yescharacteristic
107C2×C59#55114yes—
108D59—44no—
109C2×#117D5911yescharacteristic, complemented
110C22×C22⋊C4—591no—
111#399—592no—
112#397—592no—
113#388—594no—
114#385—592no—
115#381—591no—
116#379—592no—
117C59#248211yescharacteristic, complemented, Sylow
118C25—591no—
119C23×C4—591no—
120C23×C4C2×D5911yescharacteristic
121#117—24no—
122C2×C4⋊C4—594no—
123C2×C4⋊C4C2×D5911yescharacteristic, complemented
124C2×C4⋊C4C2×D5911yescharacteristic, complemented
125C2×C22⋊C4—592no—
126C2×C22⋊C4—592no—
127C2×C22⋊C4—592no—
128C2×C22⋊C4—594no—
129C2×C22⋊C4—594no—
130C2×C22⋊C4—1184no—
131C2×C22⋊C4C2×D5912yes—
132C2×C42C2×D5912yescomplemented
133#95—592no—
134#95—592no—
135#95—594no—
136C24—592no—
137C24—1184no—
138C24—1182no—
139C24—1184no—
140C24—2362no—
141C24C22×D5911yescharacteristic
142C22×C4—24no—
143C22×C4—594no—
144C22×C4—592no—
145C22×C4—1182no—
146C22×C4—2362no—
147C22×C4C22⋊D5914yes—
148C22×C4C22×D5912yes—
149C22×C4C22×D5912yes—
150C22×C4C22×D5911yescharacteristic
151C22×C4C22×D5911yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—2364no—
155C22⋊C4—24no—
156C22⋊C4—1188no—
157C22⋊C4—1184no—
158C22⋊C4—1184no—
159C22⋊C4—1184no—
160C22⋊C4—2364no—
161C42—24no—
162C23—22no—
163C23—22no—
164C23—594no—
165C23—1188no—
166C23—1182no—
167C23—1182no—
168C23—1184no—
169C23—1184no—
170C23—23616no—
171C23—2364no—
172C23—2364no—
173C23#1174568514yes—
174C23C2×C22⋊D5912yes—
175C23C23×D5911yescharacteristic
176C2×C4—28no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—24no—
183C2×C4—1182no—
184C2×C4—1184no—
185C2×C4—1184no—
186C2×C4—1184no—
187C2×C4—1184no—
188C2×C4—2364no—
189C2×C4C2×C22⋊D5912yes—
190C2×C4C2×C22⋊D5912yes—
191C22—22no—
192C22—22no—
193C22—28no—
194C22—1184no—
195C22—1188no—
196C22—23616no—
197C22—2362no—
198C22—2362no—
199C22—2364no—
200C22#1427371014yes—
201C22C22×C22⋊D5911yescharacteristic
202C22#41×D5912yes—
203C22C2×#1174568512yes—
204C22#1427377312yes—
205C4—22no—
206C4—22no—
207C4—42no—
208C4—42no—
209C4—2362no—
210C4—2364no—
211C2—24no—
212C2—2364no—
213C2C2×#1427371011yescharacteristic
214C2#1683790911yescharacteristic
215C2#1683796611yescharacteristic
216C2#1683807614yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC2×#117×C59C2
hypercenterC2×#117D59
hypocenterC59#2482
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #16837337C2semidirect
3. #16837328C2semidirect
4. #16837293C2semidirect
5. #16837274C2semidirect
6. #16837265C2semidirect
8. C2×#117×C59C2semidirect
11. C2×Dic59⋊C4C22semidirect
18. C59⋊#95C22semidirect
19. C59⋊#95C22semidirect
20. C59⋊#95C22semidirect
23. C2×C4⋊C4×C59C22semidirect
24. C2×C4⋊C4×C59C22semidirect
26. C2×C42×C59C22semidirect
109. C2×#117D59semidirect
117. C59#2482semidirect
123. C2×C4⋊C4C2×D59semidirect
124. C2×C4⋊C4C2×D59semidirect
132. C2×C42C2×D59semidirect