Finite Group Databasebeta

← #21426049

Subgroups — #21426049

Order 7552.

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

normal subgroups only

This group has 216 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#16838202C211yesmaximal, characteristic
2#16837845C212yesmaximal, complemented
3#16837660C211yesmaximal, characteristic, complemented
4#16837213C212yesmaximal, complemented
5C59×#349C211yesmaximal, characteristic, complemented
6C2×#11745685—21no—
7#14273760—22no—
8#14273755—22no—
9#14273749—21no—
10#14273749C2212yes—
11C2×Dic236C2211yescharacteristic, complemented
12#14273706—21no—
13Dic472—22no—
14#14273672—22no—
15#14273659C2211yescharacteristic, complemented
16#14273652—21no—
17C2×M16×C59C2211yescharacteristic
18M32×C59C2212yescomplemented
19C22×C4×C59D411yescharacteristic
20C2×C22⋊D59—41no—
21#11745685—22no—
22#11745685—22no—
23#11745685—41no—
24#11745685—41no—
25C2×D236—21no—
26C2×C4×D59—41no—
27C2×Dic118—21no—
28C2×Dic118—21no—
29M16×C59—22no—
30C2×C8×C59D411yescharacteristic
31C2×C8×C59C2311yescharacteristic
32C22⋊Dic59—41no—
33C4⋊Dic59—21no—
34Dic59⋊C4—41no—
35Dic236—21no—
36Dic236—22no—
37Dic236D412yes—
38D472—21no—
39D472D412yes—
40#11745660—22no—
41#11745660—22no—
42C16×C59—22no—
43C23×C59D811yescharacteristic
44C22×D59—41no—
45C2×C4×C59—21no—
46C2×C4×C59—21no—
47C2×C4×C59D811yescharacteristic
48C2×C4×C59C2×D411yescharacteristic
49C22⋊D59—42no—
50C22⋊D59—42no—
51C2×Dic59—41no—
52C2×Dic59—41no—
53C2×Dic59—41no—
54D236—22no—
55D236—41no—
56C4×D59—42no—
57C4×D59—42no—
58Dic118—22no—
59Dic118—41no—
60Dic118—41no—
61Dic118—41no—
62C8×C59—21no—
63C8×C59C2×D412yes—
64C22×C59—21no—
65C22×C59—41no—
66C22×C59C2×D811yescharacteristic
67C2×D59—42no—
68C2×D59—82no—
69C4×C59—21no—
70C4×C59#12011yescharacteristic
71C4×C59AGL(1,ℤ/8)11yescharacteristic
72Dic59—42no—
73Dic59—81no—
74Dic59—81no—
75#2191—591nomaximal, Sylow
76C2×C59—21no—
77C2×C59—41no—
78C2×C59#44711yescharacteristic
79D59—82no—
80#575—591no—
81#510—592no—
82#470—591no—
83#360—592no—
84#349D5911yescharacteristic, complemented
85C59#219111yescharacteristic, complemented, Sylow
86C2×#41—1181no—
87#137—1182no—
88AGL(1,ℤ/8)—1182no—
89#135—592no—
90#135—1181no—
91C2×Q16—591no—
92C2×M16C2×D5911yescharacteristic
93C22⋊Q8—1181no—
94Q32—1182no—
95SD32—1182no—
96M32C2×D5912yescomplemented
97#106—591no—
98#103—1181no—
99#41—1182no—
100#41—1182no—
101#41—2361no—
102#41—2361no—
103C2×Q8—1181no—
104C2×Q8—1181no—
105C2×D4—1181no—
106C2×D4—2361no—
107C22×C4—2361no—
108C22×C4D23611yescharacteristic
109Q16—592no—
110Q16—1181no—
111Q16—1182no—
112SD16—1182no—
113SD16—1182no—
114D8—592no—
115D8—1181no—
116M16—22no—
117C2×C8D23611yescharacteristic
118C2×C8C22×D5911yescharacteristic
119C4⋊C4—1181no—
120C4⋊C4—2361no—
121C22⋊C4—2361no—
122C16—22no—
123C23—2361no—
124C23D47211yescharacteristic
125Q8—1182no—
126Q8—2361no—
127Q8—2361no—
128Q8—2361no—
129D4—1182no—
130D4—2361no—
131D4—2362no—
132D4—2362no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—2362no—
136C2×C4—2361no—
137C2×C4—2361no—
138C2×C4—2361no—
139C2×C4—2362no—
140C2×C4D47211yescharacteristic
141C2×C4C2×D23611yescharacteristic
142C8—21no—
143C8D4×D5912yes—
144C22—21no—
145C22—41no—
146C22—4722no—
147C22—2362no—
148C22C2×D47211yescharacteristic
149C4—21no—
150C4—4721no—
151C4—4721no—
152C4—2362no—
153C4#1427369711yescharacteristic
154C4#1427375511yescharacteristic
155C2—21no—
156C2—41no—
157C2—4722no—
158C2#1683753811yescharacteristic
subgroupG/H
centerC2#16837538
commutatorC2×C8×C59C23
FrattiniC2×C8C22×D59
FittingC59×#349C2
socleC2×C59#447
hypercenter#349D59
hypocenterC59#2191
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
2. #16837845C2semidirect
3. #16837660C2semidirect
4. #16837213C2semidirect
5. C59×#349C2semidirect
11. C2×Dic236C22semidirect
15. #14273659C22semidirect
18. M32×C59C22semidirect
84. #349D59semidirect
85. C59#2191semidirect
96. M32C2×D59semidirect