Finite Group Databasebeta

← #21434027

Subgroups — #21434027

Order 7552.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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#16837913C211yesmaximal, characteristic
2#16837743C214yesmaximal, complemented
3#16837726C214yesmaximal, complemented
4#16837442C212yesmaximal, complemented
5#16837401C212yesmaximal, complemented
6#16837366C211yesmaximal, characteristic, complemented
7C2×#117×C59C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9C2×#11745664C2212yes—
10#14273710—21no—
11#14273706C2212yes—
12#14273701C2212yes—
13#14273696—21no—
14C4×C22⋊D59—22no—
15#14273686C2211yescharacteristic
16#14273660C2214yescomplemented
17#14273658C2214yescomplemented
18#14273650C2214yescomplemented
19#14273647C2214yescomplemented
20C22⋊(C59⋊C8)C2214yes—
21C23×C4×C59C2211yescharacteristic
22#117×C59—22no—
23#117×C59C2214yes—
24C2×C4⋊C4×C59C2212yes—
25C2×C22⋊C4×C59—21no—
26C2×C42×C59—21no—
27C24×C59D411yescharacteristic
28C22×C4×C59—24no—
29C22×C4×C59—22no—
30C22×C4×C59D411yescharacteristic
31C22×C4×C59D412yes—
32C22×C4×C59C2312yes—
33C22×C4×C59C2311yescharacteristic
34C2×C22⋊D59—22no—
35C2×C22⋊D59—21no—
36#11745685—24no—
37C2×D236C2311yescharacteristic
38C2×C4×D59—21no—
39C2×Dic118C2311yescharacteristic
40C4⋊C4×C59—22no—
41C4⋊C4×C59C2314yes—
42C22⋊C4×C59—24no—
43C42×C59—24no—
44C22⋊Dic59—21no—
45C22⋊Dic59—22no—
46(C2×D59)⋊C4—22no—
47C4⋊Dic59C2312yes—
48Dic59⋊C4—22no—
49C4×Dic59—21no—
50#11745664—24no—
51C2×C59⋊C8C2314yes—
52C23×C59—22no—
53C23×C59—42no—
54C23×C59C2×D412yes—
55C23×C59C2×D411yescharacteristic
56C22×D59—21no—
57C2×C4×C59—22no—
58C2×C4×C59—24no—
59C2×C4×C59—24no—
60C2×C4×C59—24no—
61C2×C4×C59—44no—
62C2×C4×C59C2×D412yes—
63C2×C4×C59C2×D411yescharacteristic
64C2×C4×C59#4114yes—
65C2×C4×C59C2411yescharacteristic
66C22⋊D59—44no—
67C22⋊D59—42no—
68C2×Dic59—22no—
69C2×Dic59—21no—
70D236—22no—
71C4×D59—42no—
72Dic118—22no—
73C59⋊C8—24no—
74C22×C59—22no—
75C22×C59—22no—
76C22×C59—22no—
77C22×C59—22no—
78C22×C59—44no—
79C22×C59#12312yes—
80C22×C59C22×D411yescharacteristic
81C2×D59—41no—
82C2×D59—42no—
83C4×C59—22no—
84C4×C59—44no—
85C4×C59#12312yes—
86C4×C59C2×#4112yes—
87Dic59—41no—
88Dic59—42no—
89#3093—591nomaximal, Sylow
90C2×C59—22no—
91C2×C59—42no—
92C2×C59C2×#12311yescharacteristic
93C2×C59#57512yes—
94D59—81no—
95#525—591no—
96C2×#117D5911yescharacteristic, complemented
97#485—594no—
98#482—594no—
99#428—592no—
100#417—592no—
101#407—591no—
102C59#309311yescharacteristic, complemented, Sylow
103C2×#41—591no—
104C23×C4C2×D5911yescharacteristic
105C2×M16—592no—
106#123—1181no—
107C22⋊Q8—592no—
108#121—592no—
109#120—1181no—
110C4×D4—1182no—
111#117—22no—
112#117—591no—
113#117C2×D5914yes—
114C2×C4⋊C4C2×D5912yes—
115C2×C22⋊C4—21no—
116C2×C42—21no—
117#107—594no—
118#106—594no—
119#103—594no—
120#102—594no—
121C22⋊C8—594no—
122C24C22⋊D5911yescharacteristic
123#41—1184no—
124C2×Q8—591no—
125C2×D4—591no—
126C2×D4—1182no—
127C2×D4—1181no—
128C22×C4—24no—
129C22×C4—22no—
130C22×C4—1181no—
131C22×C4C22⋊D5911yescharacteristic
132C22×C4C22⋊D5912yes—
133C22×C4C22×D5912yes—
134C22×C4C22×D5911yescharacteristic
135M16—1184no—
136C2×C8—594no—
137C4⋊C4—22no—
138C4⋊C4—592no—
139C4⋊C4—1182no—
140C4⋊C4C22×D5914yes—
141C22⋊C4—24no—
142C22⋊C4—1181no—
143C22⋊C4—1182no—
144C22⋊C4—1182no—
145C42—24no—
146C42—1181no—
147C23—22no—
148C23—42no—
149C23—1181no—
150C23C2×C22⋊D5912yes—
151C23C2×C22⋊D5911yescharacteristic
152Q8—1182no—
153D4—1182no—
154D4—2364no—
155D4—2362no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—44no—
161C2×C4—1182no—
162C2×C4—1181no—
163C2×C4—2362no—
164C2×C4#1174568514yes—
165C2×C4C2×C22⋊D5912yes—
166C2×C4C2×C22⋊D5911yescharacteristic
167C2×C4C23×D5911yescharacteristic
168C8—1184no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—2361no—
175C22—2362no—
176C22#1427371012yes—
177C22C22×C22⋊D5911yescharacteristic
178C4—22no—
179C4—44no—
180C4—2361no—
181C4—2362no—
182C4#1427371012yes—
183C4C2×#1174568512yes—
184C2—22no—
185C2—42no—
186C2—4721no—
187C2C2×#1427371011yescharacteristic
188C2#1683820012yes—
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×#117×C59C2
socleC22×C59C22×D4
hypercenterC2×#117D59
hypocenterC59#3093
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #16837743C2semidirect
3. #16837726C2semidirect
4. #16837442C2semidirect
5. #16837401C2semidirect
6. #16837366C2semidirect
7. C2×#117×C59C2semidirect
16. #14273660C22semidirect
17. #14273658C22semidirect
18. #14273650C22semidirect
19. #14273647C22semidirect
96. C2×#117D59semidirect
102. C59#3093semidirect