Finite Group Databasebeta

← #21423656

Subgroups — #21423656

Order 7552.

176 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 49 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#16837748C211yesmaximal, characteristic, complemented
2#16837608C211yesmaximal, characteristic, complemented
3#16837594C211yesmaximal, characteristic
4#16837479C211yesmaximal, characteristic, complemented
5#16837152C211yesmaximal, characteristic, complemented
6#16837147C211yesmaximal, characteristic, complemented
7C59×#331C211yesmaximal, characteristic, complemented
8C2×#11745660—21no—
9C2×#11745669—21no—
10C2×#11745659—21no—
11#14273727C2211yescharacteristic
12C4×D236C2211yescharacteristic
13C4⋊(C59⋊C8)C2211yescharacteristic
14#14273652—21no—
15#14273648—21no—
16#14273648—21no—
17#14273648—21no—
18(C2×D59)⋊C8—21no—
19C4×C59⋊C8C2211yescharacteristic
20#127×C59C2211yescharacteristic
21C4⋊C8×C59C2211yescharacteristic
22C4⋊C8×C59C2211yescharacteristic
23C2×D4×C59—21no—
24C2×D4×C59—21no—
25C2×D4×C59—21no—
26C2×D236D411yescharacteristic
27C2×C4×D59—21no—
28C2×Dic118—21no—
29C2×C8×C59—21no—
30C2×C8×C59—21no—
31C42×C59C2311yescharacteristic
32#11745669—42no—
33(C2×D59)⋊C4—21no—
34C4⋊Dic59—21no—
35C4⋊Dic59—21no—
36C4⋊Dic59D411yescharacteristic
37C2×C59⋊C8—21no—
38C2×C59⋊C8D411yescharacteristic
39C2×C59⋊C8D411yescharacteristic
40#11745660—42no—
41#11745659—42no—
42C23×C59—41no—
43C22×D59—21no—
44D4×C59—41no—
45D4×C59—41no—
46D4×C59—41no—
47D4×C59—41no—
48D4×C59—81no—
49C2×C4×C59C2×D411yescharacteristic
50C2×C4×C59C2×D411yescharacteristic
51C2×C4×C59#4111yescharacteristic
52C2×Dic59—21no—
53C2×Dic59—41no—
54D236—21no—
55D236—21no—
56C4×D59—41no—
57C4×D59—41no—
58Dic118—41no—
59Dic118—41no—
60C8×C59—41no—
61C8×C59—41no—
62C59⋊C8—21no—
63C59⋊C8—21no—
64C59⋊C8—41no—
65C22×C59—81no—
66C22×C59—81no—
67C22×C59—81no—
68C22×C59#12111yescharacteristic
69C2×D59—41no—
70C2×D59—41no—
71C2×D59—41no—
72C4×C59—21no—
73C4×C59#13511yescharacteristic
74C4×C59AGL(1,ℤ/8)11yescharacteristic
75C4×C59AGL(1,ℤ/8)11yescharacteristic
76C4×C59AGL(1,ℤ/8)11yescharacteristic
77Dic59—41no—
78Dic59—81no—
79#1701—591nomaximal, Sylow
80C2×C59—161no—
81C2×C59#46311yescharacteristic
82C2×C59#46911yescharacteristic
83C2×C59#47111yescharacteristic
84D59—81no—
85#486—591no—
86#461—591no—
87#459—591no—
88#436—591no—
89#334—591no—
90#332—591no—
91#331D5911yescharacteristic, complemented
92C59#170111yescharacteristic, complemented, Sylow
93C2×SD16—1181no—
94C2×D8—1181no—
95C2×M16—1181no—
96C4⋊Q8—591no—
97#127C2×D5911yescharacteristic
98C4×D4—591no—
99C4⋊C8—591no—
100C4⋊C8C2×D5911yescharacteristic
101C4⋊C8C2×D5911yescharacteristic
102#103—1181no—
103#102—1181no—
104#102—1181no—
105#102—1181no—
106C22⋊C8—1181no—
107C4×C8—591no—
108C2×Q8—1181no—
109C2×D4—21no—
110C2×D4—21no—
111C2×D4—21no—
112C2×D4—591no—
113C22×C4—1181no—
114SD16—2362no—
115D8—2362no—
116M16—2362no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—591no—
120C2×C8—591no—
121C2×C8—1181no—
122C4⋊C4—591no—
123C4⋊C4—1181no—
124C4⋊C4—1181no—
125C22⋊C4—1181no—
126C42C22×D5911yescharacteristic
127C23—41no—
128C23—1181no—
129Q8—2361no—
130Q8—2361no—
131D4—41no—
132D4—41no—
133D4—41no—
134D4—41no—
135D4—81no—
136D4—1181no—
137D4—1181no—
138C2×C4—1181no—
139C2×C4—2361no—
140C2×C4—2361no—
141C2×C4—2361no—
142C2×C4#1174568511yescharacteristic
143C2×C4D4×D5911yescharacteristic
144C2×C4D4×D5911yescharacteristic
145C8—41no—
146C8—41no—
147C8—1181no—
148C8—1181no—
149C8—2361no—
150C22—81no—
151C22—81no—
152C22—81no—
153C22—2361no—
154C22—2361no—
155C22—2361no—
156C22#1427370011yescharacteristic
157C4—21no—
158C4—4721no—
159C4—2361no—
160C4#1427374811yescharacteristic
161C4#1427375111yescharacteristic
162C4#1427375111yescharacteristic
163C4#1427375411yescharacteristic
164C2—161no—
165C2—4721no—
166C2#1683761611yescharacteristic
167C2#1683765411yescharacteristic
168C2#1683766411yescharacteristic
subgroupG/H
centerC22#14273700
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×#331C2
socleC22×C59#121
hypercenter#331D59
hypocenterC59#1701
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #16837748C2semidirect
2. #16837608C2semidirect
4. #16837479C2semidirect
5. #16837152C2semidirect
6. #16837147C2semidirect
7. C59×#331C2semidirect
91. #331D59semidirect
92. C59#1701semidirect