Finite Group Databasebeta

← #21423293

Subgroups — #21423293

Order 7552.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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#16838072C211yesmaximal, characteristic
2#16837684C211yesmaximal, characteristic, complemented
3#16837604C211yesmaximal, characteristic, complemented
4#16837146C211yesmaximal, characteristic, complemented
5#16837134C211yesmaximal, characteristic, complemented
6#16837131C211yesmaximal, characteristic, complemented
7C59×#486C211yesmaximal, characteristic, complemented
8C2×#11745687—21no—
9C2×#11745671—21no—
10#14273723—21no—
11#14273699—22no—
12#14273698—21no—
13C4×Dic118C2211yescharacteristic
14C4×D236C2211yescharacteristic
15D4×Dic59—21no—
16#14273658—21no—
17C4⋊(C59⋊C8)C2211yescharacteristic
18C4⋊(C59⋊C8)C2211yescharacteristic
19#14273651—21no—
20#14273650—21no—
21C4⋊Q8×C59C2211yescharacteristic
22#127×C59C2211yescharacteristic
23#102×C59—22no—
24C4×C8×C59C2211yescharacteristic
25C2×Q8×C59—21no—
26C2×D4×C59—21no—
27C2×D4×C59—21no—
28C2×D4×C59D412yes—
29C2×C22⋊D59—22no—
30C2×C22⋊D59—22no—
31C22×Dic59—22no—
32#11745687—42no—
33#11745687—42no—
34C2×D236D411yescharacteristic
35C2×C4×D59—21no—
36C2×Dic118D411yescharacteristic
37C2×C8×C59—21no—
38C4⋊C4×C59—21no—
39C4⋊C4×C59—21no—
40C42×C59C2311yescharacteristic
41C22⋊Dic59—22no—
42#11745671—42no—
43(C2×D59)⋊C4—21no—
44C4⋊Dic59D411yescharacteristic
45C4⋊Dic59D411yescharacteristic
46Dic59⋊C4—21no—
47C4×Dic59—21no—
48C2×C59⋊C8—21no—
49C2×C59⋊C8—21no—
50C23×C59—22no—
51C22×D59—21no—
52Q8×C59—41no—
53Q8×C59—41no—
54D4×C59—42no—
55D4×C59—41no—
56D4×C59—41no—
57D4×C59—41no—
58D4×C59—41no—
59C2×C4×C59—41no—
60C2×C4×C59C2×D411yescharacteristic
61C2×C4×C59C2×D411yescharacteristic
62C2×C4×C59C2×D411yescharacteristic
63C22⋊D59—44no—
64C22⋊D59—82no—
65C2×Dic59—21no—
66C2×Dic59—21no—
67C2×Dic59—21no—
68C2×Dic59—44no—
69D236—21no—
70D236—21no—
71C4×D59—41no—
72C4×D59—41no—
73Dic118—21no—
74Dic118SD1612yescomplemented
75C8×C59—41no—
76C59⋊C8—41no—
77C59⋊C8—41no—
78C22×C59—42no—
79C22×C59—42no—
80C22×C59—42no—
81C22×C59#12011yescharacteristic
82C2×D59—41no—
83C2×D59—41no—
84C2×D59—41no—
85C4×C59—21no—
86C4×C59—81no—
87C4×C59C2×SD1611yescharacteristic
88C4×C59#13511yescharacteristic
89C4×C59AGL(1,ℤ/8)11yescharacteristic
90C4×C59AGL(1,ℤ/8)11yescharacteristic
91Dic59—22no—
92Dic59—41no—
93Dic59—41no—
94#1642—591nomaximal, Sylow
95C2×C59—82no—
96C2×C59#44911yescharacteristic
97C2×C59#45011yescharacteristic
98C2×C59#45511yescharacteristic
99D59—81no—
100#550—591no—
101#486D5911yescharacteristic, complemented
102#475—591no—
103#461—591no—
104#331—591no—
105Q8⋊C8—591no—
106D4⋊C8—591no—
107C59#164211yescharacteristic, complemented, Sylow
108C2×#41—1181no—
109C2×SD16—1181no—
110C4⋊Q8C2×D5911yescharacteristic
111#127—1181no—
112#127C2×D5911yescharacteristic
113#121—1181no—
114#121—1182no—
115C4×Q8—591no—
116C4×D4—591no—
117C4×D4—1181no—
118#106—1181no—
119C4⋊C8—591no—
120C4⋊C8—591no—
121#103—1181no—
122#103—1181no—
123#102—22no—
124C4×C8C2×D5911yescharacteristic
125#41—2362no—
126#41—2362no—
127C2×Q8—21no—
128C2×Q8—591no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—591no—
132C2×D4—1182no—
133C2×D4—1182no—
134C2×D4C22⋊D5912yes—
135C22×C4—1182no—
136C22×C4—1181no—
137SD16—2362no—
138C2×C8—21no—
139C2×C8—1181no—
140C2×C8—1181no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—591no—
144C4⋊C4—591no—
145C4⋊C4—1181no—
146C22⋊C4—1182no—
147C22⋊C4—1181no—
148C42—1181no—
149C42C22×D5911yescharacteristic
150C23—22no—
151C23—1181no—
152Q8—41no—
153Q8—41no—
154Q8—592no—
155Q8—1181no—
156D4—42no—
157D4—41no—
158D4—41no—
159D4—41no—
160D4—41no—
161D4—1181no—
162D4—1181no—
163D4—4722no—
164D4—2364no—
165C2×C4—41no—
166C2×C4—1181no—
167C2×C4—1181no—
168C2×C4—1181no—
169C2×C4—2364no—
170C2×C4—2361no—
171C2×C4—2361no—
172C2×C4D4×D5911yescharacteristic
173C2×C4D4×D5911yescharacteristic
174C2×C4C2×C22⋊D5911yescharacteristic
175C8—41no—
176C8—2361no—
177C8—2361no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—2361no—
182C22—2361no—
183C22—2361no—
184C22#1427369511yescharacteristic
185C4—21no—
186C4—81no—
187C4—1182no—
188C4—2361no—
189C4—2361no—
190C4SD16×D5911yescharacteristic
191C4#1427374611yescharacteristic
192C4#1427375111yescharacteristic
193C4#1427375411yescharacteristic
194C2—82no—
195C2—4721no—
196C2#1683754411yescharacteristic
197C2#1683755111yescharacteristic
198C2#1683757911yescharacteristic
subgroupG/H
centerC22#14273695
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×#486C2
socleC22×C59#120
hypercenter#486D59
hypocenterC59#1642
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #16837684C2semidirect
3. #16837604C2semidirect
4. #16837146C2semidirect
5. #16837134C2semidirect
6. #16837131C2semidirect
7. C59×#486C2semidirect
74. Dic118SD16semidirect
101. #486D59semidirect
107. C59#1642semidirect