Finite Group Databasebeta

← #21426050

Subgroups — #21426050

Order 7552.

220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 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#16838204C211yesmaximal, characteristic, complemented
2C2×#14273668C211yesmaximal, characteristic, complemented
3#16837669C211yesmaximal, characteristic, complemented
4#16837216C211yesmaximal, characteristic, complemented
5#16837209C211yesmaximal, characteristic, complemented
6#16837187C211yesmaximal, characteristic, complemented
7C59×#509C211yesmaximal, characteristic, complemented
8#14273773—21no—
9#14273754—22no—
10#14273753—21no—
11#14273752—21no—
12#14273750—21no—
13C2×D472C2211yescharacteristic
14D8×D59—21no—
15#14273733C2211yescharacteristic
16#14273668—22no—
17C2×C59⋊C16C2211yescharacteristic, complemented
18#14273663C2211yescharacteristic, complemented
19#14273644—21no—
20#135×C59C2211yescharacteristic
21C2×D8×C59C2211yescharacteristic, complemented
22SD32×C59—21no—
23D16×C59—21no—
24M32×C59C2211yescharacteristic, complemented
25#41×C59—21no—
26C2×D4×C59—21no—
27#11745689—22no—
28D4×D59—22no—
29D4×D59—42no—
30#11745685—41no—
31#11745685D411yescharacteristic
32C2×D236—21no—
33C2×D236—41no—
34Q16×C59D411yescharacteristic
35SD16×C59—21no—
36D8×C59—21no—
37D8×C59—21no—
38D8×C59D411yescharacteristic
39C2×C8×C59C2311yescharacteristic
40#11745671—22no—
41#11745670—41no—
42#11745669—22no—
43#11745669—41no—
44#11745664—21no—
45#11745664D411yescharacteristic
46D472—21no—
47D472D412yes—
48#11745659—21no—
49C8×D59—21no—
50C16×C59—21no—
51C59⋊C16—21no—
52C23×C59—41no—
53C22×D59—42no—
54C22×D59—41no—
55Q8×C59—21no—
56D4×C59—21no—
57D4×C59—41no—
58D4×C59—41no—
59D4×C59—41no—
60C2×C4×C59—41no—
61C2×C4×C59C2×D411yescharacteristic
62C22⋊D59—21no—
63C22⋊D59—42no—
64D236—22no—
65D236—42no—
66D236—41no—
67D236D811yescharacteristic
68C4×D59—21no—
69C4×D59—42no—
70Dic118D811yescharacteristic
71C8×C59C2×D411yescharacteristic
72C8×C59C2×D411yescharacteristic
73C59⋊C8—21no—
74C59⋊C8—41no—
75C22×C59—41no—
76C22×C59—81no—
77C22×C59—161no—
78C22×C59AGL(1,ℤ/8)11yescharacteristic
79C2×D59—21no—
80C2×D59—42no—
81C2×D59—162no—
82C2×D59—161no—
83C4×C59—41no—
84C4×C59#12011yescharacteristic
85C4×C59C2×D811yescharacteristic
86Dic59—21no—
87#2192—591nomaximal, Sylow
88C2×C59—21no—
89C2×C59—81no—
90C2×C59—161no—
91C2×C59#44711yescharacteristic
92D59—41no—
93D59—82no—
94#576—591no—
95#509D5911yescharacteristic, complemented
96C2×D16—591no—
97#472—591no—
98#361—591no—
99#359—591no—
100#350—591no—
101C59#219211yescharacteristic, complemented, Sylow
102H(5,𝔽2)—1181no—
103AGL(1,ℤ/8)—1181no—
104AGL(1,ℤ/8)—1182no—
105AGL(1,ℤ/8)—1181no—
106#135—1181no—
107#135C2×D5911yescharacteristic
108C2×D8—591no—
109C2×D8—1181no—
110C2×D8C2×D5911yescharacteristic, complemented
111#131—591no—
112SD32—21no—
113D16—21no—
114D16—1182no—
115M32C2×D5911yescharacteristic, complemented
116C2×C16—591no—
117#108—591no—
118#100—1181no—
119#41—21no—
120#41—591no—
121#41—1182no—
122#41—2361no—
123C2×D4—21no—
124C2×D4—1182no—
125C2×D4—1181no—
126C2×D4—2361no—
127C2×D4—2362no—
128Q16C22⋊D5911yescharacteristic
129SD16—21no—
130SD16—1182no—
131SD16—2361no—
132D8—21no—
133D8—21no—
134D8—592no—
135D8—1182no—
136D8—1181no—
137D8—2361no—
138D8C22⋊D5911yescharacteristic
139M16—591no—
140M16—1181no—
141M16—1181no—
142C2×C8—1181no—
143C2×C8C22×D5911yescharacteristic
144C16—21no—
145C16—1181no—
146C23—41no—
147C23—2362no—
148C23—2361no—
149Q8—21no—
150Q8—591no—
151D4—21no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—591no—
156D4—1181no—
157D4—1182no—
158D4—2362no—
159D4—2362no—
160D4—2361no—
161C2×C4—41no—
162C2×C4—1181no—
163C2×C4—2362no—
164C2×C4D4×D5911yescharacteristic
165C8—1181no—
166C8—2361no—
167C8D4×D5911yescharacteristic
168C8C2×C22⋊D5911yescharacteristic
169C22—41no—
170C22—81no—
171C22—161no—
172C22—1181no—
173C22—9441no—
174C22—9442no—
175C22—2362no—
176C22#1427375111yescharacteristic
177C4—41no—
178C4—1181no—
179C4#1427369511yescharacteristic
180C4D8×D5911yescharacteristic
181C2—21no—
182C2—81no—
183C2—161no—
184C2—4722no—
185C2—2361no—
186C2#1683753411yescharacteristic
subgroupG/H
centerC2#16837534
commutatorC2×C8×C59C23
FrattiniC2×C8C22×D59
FittingC59×#509C2
socleC2×C59#447
hypercenter#509D59
hypocenterC59#2192
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #16838204C2semidirect
2. C2×#14273668C2semidirect
3. #16837669C2semidirect
4. #16837216C2semidirect
5. #16837209C2semidirect
6. #16837187C2semidirect
7. C59×#509C2semidirect
17. C2×C59⋊C16C22semidirect
18. #14273663C22semidirect
21. C2×D8×C59C22semidirect
24. M32×C59C22semidirect
95. #509D59semidirect
101. C59#2192semidirect
110. C2×D8C2×D59semidirect
115. M32C2×D59semidirect