Finite Group Databasebeta

← #21423318

Subgroups — #21423318

Order 7552.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#16838132C211yesmaximal, characteristic
2#16837752C211yesmaximal, characteristic
3#16837688C211yesmaximal, characteristic
4#16837613C211yesmaximal, characteristic
5#16837132C211yesmaximal, characteristic
6#16837132C211yesmaximal, characteristic
7C59×#333C211yesmaximal, characteristic
8C2×Dic236—21no—
9#14273727C2211yescharacteristic
10#14273726—21no—
11#14273726—21no—
12#14273725—22no—
13C4×Dic118C2211yescharacteristic
14C4×Dic118C2211yescharacteristic
15#14273692—21no—
16#14273692—21no—
17#14273659—21no—
18#14273652—21no—
19#14273652—21no—
20#14273651—22no—
21C4×C59⋊C8C2211yescharacteristic
22C4⋊Q8×C59C2211yescharacteristic
23C4⋊C8×C59C2211yescharacteristic
24C4⋊C8×C59C2211yescharacteristic
25C2×Q8×C59D412yes—
26C2×Dic118—21no—
27C2×Dic118—22no—
28C2×Dic118D411yescharacteristic
29C2×Dic118D411yescharacteristic
30C2×C8×C59—21no—
31C2×C8×C59—21no—
32C4⋊C4×C59—21no—
33C4⋊C4×C59—21no—
34C42×C59C2311yescharacteristic
35C4⋊Dic59—21no—
36C4⋊Dic59—21no—
37C4⋊Dic59D411yescharacteristic
38C4⋊Dic59D411yescharacteristic
39Dic59⋊C4—22no—
40Dic59⋊C4—22no—
41Dic59⋊C4—21no—
42Dic59⋊C4—21no—
43C4×Dic59—22no—
44C4×Dic59—21no—
45C4×Dic59—21no—
46C2×C59⋊C8—21no—
47Dic236—42no—
48Q8×C59—42no—
49C2×C4×C59—22no—
50C2×C4×C59C2×D411yescharacteristic
51C2×C4×C59C2×D411yescharacteristic
52C2×C4×C59C2×D411yescharacteristic
53C2×Dic59—21no—
54C2×Dic59—21no—
55C2×Dic59—21no—
56C2×Dic59—21no—
57C2×Dic59—41no—
58Dic118—21no—
59Dic118—21no—
60Dic118—41no—
61Dic118—41no—
62Dic118—82no—
63Dic118SD1612yes—
64Dic118Q1612yescomplemented
65C8×C59—41no—
66C8×C59—41no—
67C59⋊C8—41no—
68C22×C59#12011yescharacteristic
69C4×C59—21no—
70C4×C59—42no—
71C4×C59C2×SD1611yescharacteristic
72C4×C59C2×Q1611yescharacteristic
73C4×C59#13711yescharacteristic
74C4×C59#13711yescharacteristic
75Dic59—22no—
76Dic59—22no—
77Dic59—41no—
78Dic59—41no—
79Dic59—81no—
80#1645—591nomaximal, Sylow
81C2×C59#44811yescharacteristic
82C2×C59#45111yescharacteristic
83C2×C59#45511yescharacteristic
84Q82—591no—
85#487—591no—
86#475—591no—
87#462—591no—
88#333D5911yescharacteristic
89Q8⋊C8—591no—
90Q8⋊C8—591no—
91C59#164511yescharacteristic, complemented, Sylow
92C2×Q16—1181no—
93C4⋊Q8—591no—
94C4⋊Q8—1181no—
95C4⋊Q8—1181no—
96C4⋊Q8—1182no—
97C4⋊Q8C2×D5911yescharacteristic
98C4×Q8—591no—
99C4×Q8—591no—
100C4×Q8—1181no—
101C4×Q8—1181no—
102#106—1181no—
103C4⋊C8C2×D5911yescharacteristic
104C4⋊C8C2×D5911yescharacteristic
105#103—1181no—
106#103—1181no—
107#103—1182no—
108C4×C8—591no—
109C2×Q8—591no—
110C2×Q8—591no—
111C2×Q8—1182no—
112C2×Q8—1181no—
113C2×Q8D23612yes—
114Q16—2362no—
115C2×C8—21no—
116C2×C8—21no—
117C2×C8—1181no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—591no—
121C4⋊C4—591no—
122C4⋊C4—1182no—
123C4⋊C4—1182no—
124C4⋊C4—1181no—
125C4⋊C4—1181no—
126C4⋊C4—1181no—
127C4⋊C4—1181no—
128C42—1182no—
129C42—1181no—
130C42—1181no—
131C42C22×D5911yescharacteristic
132Q8—42no—
133Q8—592no—
134Q8—592no—
135Q8—1181no—
136Q8—1181no—
137Q8—4722no—
138Q8—2361no—
139Q8—2361no—
140C2×C4—22no—
141C2×C4—1181no—
142C2×C4—1181no—
143C2×C4—1181no—
144C2×C4—1181no—
145C2×C4—2361no—
146C2×C4C2×D23611yescharacteristic
147C2×C4D4×D5911yescharacteristic
148C2×C4D4×D5911yescharacteristic
149C8—41no—
150C8—41no—
151C8—2361no—
152C22#1427369711yescharacteristic
153C4—21no—
154C4—42no—
155C4—1182no—
156C4—1182no—
157C4—4721no—
158C4—2361no—
159C4—2361no—
160C4SD16×D5911yescharacteristic
161C4Q16×D5911yescharacteristic
162C4#1427375611yescharacteristic
163C4#1427375911yescharacteristic
164C2#1683754211yescharacteristic
165C2#1683755911yescharacteristic
166C2#1683758211yescharacteristic
subgroupG/H
centerC22#14273697
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×#333C2
socleC22×C59#120
hypercenter#333D59
hypocenterC59#1645
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
64. Dic118Q16semidirect
91. C59#1645semidirect