Finite Group Databasebeta

← #21424878

Subgroups — #21424878

Order 7552.

196 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#14273662C211yesmaximal, characteristic
2#16837445C211yesmaximal, characteristic
3C2×#14273660C211yesmaximal, characteristic
4#16837358C211yesmaximal, characteristic
5#16837171C211yesmaximal, characteristic
6#16837170C211yesmaximal, characteristic
7C59×#428C211yesmaximal, characteristic
8C2×#11745664C2211yescharacteristic
9C2×#11745664C2211yescharacteristic
10C22×C59⋊C8C2211yescharacteristic
11C2×C4⋊Dic59C2211yescharacteristic
12#14273662C414yescomplemented
13#14273660—21no—
14#14273660—21no—
15#14273660—21no—
16#14273658—21no—
17#14273638—21no—
18C4×C59⋊C8—21no—
19C2×M16×C59C2211yescharacteristic
20#117×C59C2211yescharacteristic
21C2×C4⋊C4×C59C2211yescharacteristic
22#107×C59—21no—
23#106×C59—21no—
24C22×C4×C59—21no—
25C22×C4×C59C2311yescharacteristic
26C22×Dic59—21no—
27M16×C59—21no—
28M16×C59C2×C412yes—
29C2×C8×C59—21no—
30C4⋊C4×C59—21no—
31C4⋊C4×C59—21no—
32C4⋊C4×C59D411yescharacteristic
33C4⋊C4×C59D411yescharacteristic
34C22⋊C4×C59—21no—
35C42×C59—21no—
36C4⋊Dic59—21no—
37C4⋊Dic59—21no—
38#11745664—21no—
39#11745664—21no—
40#11745664C2×C412yes—
41#11745664Q812yes—
42C2×C59⋊C8—21no—
43C2×C59⋊C8—21no—
44C2×C59⋊C8C2×C412yes—
45C2×C59⋊C8D411yescharacteristic
46C2×C59⋊C8D411yescharacteristic
47C2×C59⋊C8Q812yes—
48C23×C59#4111yescharacteristic
49C2×C4×C59—21no—
50C2×C4×C59—21no—
51C2×C4×C59—41no—
52C2×C4×C59—81no—
53C2×C4×C59C22×C411yescharacteristic
54C2×C4×C59C2×D411yescharacteristic
55C2×C4×C59C2×D411yescharacteristic
56C2×C4×C59C2×Q811yescharacteristic
57C2×C4×C59C2×Q811yescharacteristic
58C2×C4×C59#4111yescharacteristic
59C2×Dic59—41no—
60C2×Dic59—81no—
61C8×C59—22no—
62C59⋊C8—22no—
63C59⋊C8—22no—
64C59⋊C8C4⋊C412yes—
65C59⋊C8C4⋊C412yes—
66C22×C59—21no—
67C22×C59—21no—
68C22×C59C4×Q811yescharacteristic
69C22×C59#12111yescharacteristic
70C22×C59#12511yescharacteristic
71C4×C59—41no—
72C4×C59—41no—
73C4×C59—81no—
74C4×C59C2×C4⋊C411yescharacteristic
75C4×C59C4×D411yescharacteristic
76C4×C59C22⋊Q811yescharacteristic
77C4×C59C4⋊Q811yescharacteristic
78Dic59—81no—
79#1952—591nomaximal, Sylow
80C2×C59—21no—
81C2×C59—21no—
82C2×C59#38911yescharacteristic
83C2×C59#47211yescharacteristic
84C2×C59#47311yescharacteristic
85C2×#108—591no—
86#428—591no—
87#428D5911yescharacteristic
88C2×#107—591no—
89#405—591no—
90#343—591no—
91#343—591no—
92C59#195211yescharacteristic, complemented, Sylow
93C2×M16—591no—
94C2×M16—591no—
95C2×M16C2×D5911yescharacteristic
96C22×C8—591no—
97#117C2×D5911yescharacteristic
98C2×C4⋊C4—591no—
99C2×C4⋊C4C2×D5911yescharacteristic
100#108—594no—
101#107—21no—
102#107—1181no—
103#107—1181no—
104#107—1181no—
105#106—21no—
106#106—1181no—
107#97—1181no—
108C4×C8—1181no—
109C22×C4—21no—
110C22×C4—1181no—
111C22×C4C22×D5911yescharacteristic
112M16—21no—
113M16—592no—
114M16—592no—
115M16—1181no—
116M16—1181no—
117M16C4×D5912yes—
118C2×C8—21no—
119C2×C8—592no—
120C2×C8—591no—
121C2×C8—591no—
122C2×C8—592no—
123C2×C8—1181no—
124C2×C8—1181no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—1181no—
128C4⋊C4—1181no—
129C4⋊C4C22⋊D5911yescharacteristic
130C4⋊C4C22⋊D5911yescharacteristic
131C22⋊C4—21no—
132C42—21no—
133C23#1174568711yescharacteristic
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—81no—
138C2×C4—4721no—
139C2×C4—2361no—
140C2×C4C2×C4×D5911yescharacteristic
141C2×C4#1174568511yescharacteristic
142C2×C4D4×D5911yescharacteristic
143C2×C4Q8×D5911yescharacteristic
144C2×C4Q8×D5911yescharacteristic
145C2×C4C2×C22⋊D5911yescharacteristic
146C8—22no—
147C8—592no—
148C8—592no—
149C8—1182no—
150C8—1182no—
151C22—21no—
152C22—21no—
153C22#1427369211yescharacteristic
154C22#1427369911yescharacteristic
155C22#1427371711yescharacteristic
156C4—41no—
157C4—41no—
158C4—81no—
159C4—4721no—
160C4C4⋊C4×D5911yescharacteristic
161C4C4×C22⋊D5911yescharacteristic
162C4#1427370511yescharacteristic
163C4#1427372511yescharacteristic
164C2—21no—
165C2—21no—
166C2#1683729711yescharacteristic
167C2#1683767011yescharacteristic
168C2#1683767511yescharacteristic
subgroupG/H
centerC22#14273699
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#428C2
socleC22×C59#121
hypercenter#428D59
hypocenterC59#1952
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
12. #14273662C4semidirect
92. C59#1952semidirect