Finite Group Databasebeta

← #21433677

Subgroups — #21433677

Order 7552.

520 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14273749C211yesmaximal, characteristic, complemented
2#16837913C212yesmaximal, complemented
3#16837643C212yesmaximal, complemented
4#16837638C212yesmaximal, complemented
5#16837631C214yesmaximal, complemented
6#16837440C211yesmaximal, characteristic, complemented
7#16837399C212yesmaximal, complemented
8C23×C8×C59C211yesmaximal, characteristic, complemented
9C2×#11745685C2212yes—
10#14273749—24no—
11C2×Dic236C2211yescharacteristic, complemented
12C2×#11745660C2212yescomplemented
13C2×D472C2211yescharacteristic, complemented
14#14273710—22no—
15#14273706C2214yes—
16#14273701C2214yes—
17#14273696—22no—
18C4×C22⋊D59—24no—
19#14273686C2212yes—
20#14273661C2212yescomplemented
21#14273659C2212yescomplemented
22#14273652C2214yescomplemented
23#14273649C2214yescomplemented
24C23×C4×C59C2211yescharacteristic
25C22×C8×C59—24no—
26C22×C8×C59C2212yes—
27C22×C8×C59C2211yescharacteristic
28C22×C8×C59C2212yes—
29C22×C8×C59C2211yescharacteristic
30C24×C59D411yescharacteristic
31C22×C4×C59—22no—
32C22×C4×C59—22no—
33C22×C4×C59D412yes—
34C22×C4×C59D411yescharacteristic
35C22×C4×C59C2312yes—
36C22×C4×C59C2311yescharacteristic
37C2×C22⋊D59—24no—
38C2×C22⋊D59—22no—
39#11745685—24no—
40#11745685—24no—
41C2×D236C2312yes—
42C2×C4×D59—22no—
43C2×Dic118C2312yes—
44C2×C8×C59—22no—
45C2×C8×C59—24no—
46C2×C8×C59—24no—
47C2×C8×C59D414yescomplemented
48C2×C8×C59C2312yes—
49C2×C8×C59C2311yescharacteristic
50C2×C8×C59C2311yescharacteristic
51C22⋊Dic59—22no—
52C22⋊Dic59—24no—
53(C2×D59)⋊C4—24no—
54C4⋊Dic59C2314yes—
55Dic59⋊C4—24no—
56C4×Dic59—22no—
57Dic236—22no—
58D472—22no—
59#11745660—24no—
60C23×C59—22no—
61C23×C59—24no—
62C23×C59C2×D411yescharacteristic
63C23×C59C2×D412yes—
64C22×D59—22no—
65C2×C4×C59—22no—
66C2×C4×C59—24no—
67C2×C4×C59—22no—
68C2×C4×C59—22no—
69C2×C4×C59C2×D412yes—
70C2×C4×C59C2×D411yescharacteristic
71C2×C4×C59C2×D412yes—
72C2×C4×C59#4112yes—
73C2×C4×C59C2411yescharacteristic
74C22⋊D59—44no—
75C22⋊D59—48no—
76C2×Dic59—24no—
77C2×Dic59—22no—
78D236—22no—
79D236—22no—
80C4×D59—44no—
81Dic118—22no—
82Dic118—22no—
83C8×C59—22no—
84C8×C59C2×D412yes—
85C8×C59C2×D412yes—
86C22×C59—28no—
87C22×C59—22no—
88C22×C59—22no—
89C22×C59—22no—
90C22×C59#12112yes—
91C22×C59#13514yescomplemented
92C22×C59C22×D411yescharacteristic
93C2×D59—42no—
94C2×D59—44no—
95C4×C59—22no—
96C4×C59#12112yes—
97C4×C59C22×D411yescharacteristic
98C4×C59C2×#4111yescharacteristic
99Dic59—42no—
100Dic59—44no—
101#3050—591nomaximal, Sylow
102C2×C59—22no—
103C2×C59—24no—
104C2×C59C2×#12111yescharacteristic
105C2×C59C2×#13512yes—
106D59—82no—
107C2×#135—591no—
108C23×C8D5911yescharacteristic, complemented
109#525—592no—
110#467—592no—
111#466—592no—
112#465—594no—
113#427—591no—
114#416—592no—
115C59#305011yescharacteristic, complemented, Sylow
116C2×#41—592no—
117C23×C4C2×D5911yescharacteristic
118#135—1184no—
119C2×Q16—591no—
120C2×SD16—592no—
121C2×D8—591no—
122C22×C8—24no—
123C22×C8C2×D5911yescharacteristic
124C22×C8C2×D5912yes—
125C22×C8C2×D5912yes—
126C22×C8C2×D5911yescharacteristic
127#123—1182no—
128C22⋊Q8—594no—
129#121—594no—
130#120—1182no—
131C4×D4—1184no—
132#117—592no—
133#107—592no—
134#106—592no—
135#103—594no—
136#102—594no—
137C24D23611yescharacteristic
138#41—1184no—
139#41—1184no—
140C2×Q8—592no—
141C2×D4—592no—
142C2×D4—1184no—
143C2×D4—1182no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—1182no—
147C22×C4D23611yescharacteristic
148C22×C4D23612yes—
149C22×C4C22×D5912yes—
150C22×C4C22×D5911yescharacteristic
151Q16—1182no—
152SD16—1184no—
153D8—1182no—
154C2×C8—22no—
155C2×C8—24no—
156C2×C8—24no—
157C2×C8C22⋊D5914yescomplemented
158C2×C8C22×D5912yes—
159C2×C8C22×D5911yescharacteristic
160C2×C8C22×D5911yescharacteristic
161C4⋊C4—594no—
162C4⋊C4—1184no—
163C22⋊C4—1182no—
164C22⋊C4—1184no—
165C22⋊C4—1184no—
166C42—1182no—
167C23—22no—
168C23—24no—
169C23—1182no—
170C23C2×D23611yescharacteristic
171C23C2×D23612yes—
172Q8—1182no—
173Q8—1182no—
174D4—1182no—
175D4—1182no—
176D4—2364no—
177D4—2368no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—1184no—
183C2×C4—1182no—
184C2×C4—2364no—
185C2×C4C2×D23612yes—
186C2×C4C2×D23611yescharacteristic
187C2×C4#1174568512yes—
188C2×C4C2×C22⋊D5912yes—
189C2×C4C23×D5911yescharacteristic
190C8—22no—
191C8C2×C22⋊D5912yes—
192C8C2×C22⋊D5912yes—
193C22—28no—
194C22—22no—
195C22—22no—
196C22—22no—
197C22—2362no—
198C22—2364no—
199C22#1427370112yes—
200C22#1427374914yescomplemented
201C22C22×D23611yescharacteristic
202C4—22no—
203C4—2362no—
204C4—2364no—
205C4#1427370112yes—
206C4C22×C22⋊D5911yescharacteristic
207C4C2×#1174568511yescharacteristic
208C2—22no—
209C2—24no—
210C2—4722no—
211C2C2×#1427370111yescharacteristic
212C2C2×#1427374912yes—
subgroupG/H
centerC2×C4C2×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC23×C8×C59C2
socleC22×C59C22×D4
hypercenterC23×C8D59
hypocenterC59#3050
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. C2×#14273749C2semidirect
2. #16837913C2semidirect
3. #16837643C2semidirect
4. #16837638C2semidirect
5. #16837631C2semidirect
6. #16837440C2semidirect
7. #16837399C2semidirect
8. C23×C8×C59C2semidirect
11. C2×Dic236C22semidirect
12. C2×#11745660C22semidirect
13. C2×D472C22semidirect
20. #14273661C22semidirect
21. #14273659C22semidirect
22. #14273652C22semidirect
23. #14273649C22semidirect
47. C2×C8×C59D4semidirect
91. C22×C59#135semidirect
108. C23×C8D59semidirect
115. C59#3050semidirect
157. C2×C8C22⋊D59semidirect
200. C22#14273749semidirect