Finite Group Databasebeta

← #21424694

Subgroups — #21424694

Order 7552.

186 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 75 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#16837440C211yesmaximal, characteristic
2#16837430C211yesmaximal, characteristic
3#16837360C211yesmaximal, characteristic
4#16837163C211yesmaximal, characteristic
5#16837163C211yesmaximal, characteristic
6#16837156C211yesmaximal, characteristic
7C59×#341C211yesmaximal, characteristic
8C22×C59⋊C8C2211yescharacteristic
9#14273686C2211yescharacteristic
10#14273686C2211yescharacteristic
11C2×C4×Dic59C2211yescharacteristic
12#14273661C411yescharacteristic, complemented
13#14273661C411yescharacteristic, complemented
14#14273659C411yescharacteristic, complemented
15#14273659C411yescharacteristic, complemented
16Dic59⋊C8—21no—
17Dic59⋊C8—21no—
18#14273637—21no—
19C8×Dic59—21no—
20C2×M16×C59C2211yescharacteristic
21C2×M16×C59C2211yescharacteristic
22C22×C8×C59C2211yescharacteristic
23C22×C4×C59C2311yescharacteristic
24C22×Dic59—21no—
25M16×C59—21no—
26M16×C59—21no—
27M16×C59—21no—
28M16×C59Q812yes—
29C2×C8×C59—21no—
30C2×C8×C59—21no—
31C2×C8×C59—21no—
32C2×C8×C59—21no—
33C2×C8×C59C2×C411yescharacteristic
34C2×C8×C59C2×C411yescharacteristic
35C22⋊Dic59—21no—
36C22⋊Dic59—21no—
37C4⋊Dic59C2×C411yescharacteristic
38C4⋊Dic59C2×C411yescharacteristic
39C4⋊Dic59C2×C411yescharacteristic
40C4⋊Dic59C2×C411yescharacteristic
41C4×Dic59—21no—
42C4×Dic59—21no—
43C4×Dic59—21no—
44C4×Dic59—21no—
45C2×C59⋊C8—21no—
46C2×C59⋊C8—21no—
47C2×C59⋊C8D411yescharacteristic
48C2×C59⋊C8D411yescharacteristic
49C23×C59#4111yescharacteristic
50C2×C4×C59C22×C411yescharacteristic
51C2×C4×C59C2×D411yescharacteristic
52C2×C4×C59C2×Q811yescharacteristic
53C2×C4×C59#4111yescharacteristic
54C2×C4×C59#4111yescharacteristic
55C2×C4×C59#4111yescharacteristic
56C2×Dic59—22no—
57C2×Dic59—21no—
58C2×Dic59—21no—
59C2×Dic59—21no—
60C2×Dic59—21no—
61C2×Dic59—41no—
62C2×Dic59—41no—
63C8×C59—21no—
64C8×C59—21no—
65C8×C59—22no—
66C8×C59—41no—
67C59⋊C8—21no—
68C59⋊C8—21no—
69C22×C59—21no—
70C22×C59—21no—
71C22×C59C4×D411yescharacteristic
72C22×C59#12511yescharacteristic
73C22×C59#12611yescharacteristic
74C4×C59#11711yescharacteristic
75C4×C59C4×Q811yescharacteristic
76C4×C59C22⋊Q811yescharacteristic
77C4×C59#12311yescharacteristic
78Dic59—42no—
79Dic59—41no—
80Dic59—41no—
81Dic59—41no—
82Dic59—41no—
83#1922—591nomaximal, Sylow
84C2×C59—21no—
85C2×C59—21no—
86C2×C59#38711yescharacteristic
87C2×C59#44311yescharacteristic
88C2×C59#44411yescharacteristic
89#427—591no—
90#424—591no—
91#405—591no—
92#341D5911yescharacteristic
93#339—591no—
94#339—591no—
95#336—591no—
96C59#192211yescharacteristic, complemented, Sylow
97C2×M16C2×D5911yescharacteristic
98C2×M16C2×D5911yescharacteristic
99C22×C8—591no—
100C22×C8C2×D5911yescharacteristic
101#117—591no—
102#117—591no—
103C2×C42—591no—
104#107—591no—
105#107—591no—
106#106—591no—
107#106—591no—
108C4⋊C8—1181no—
109C4⋊C8—1181no—
110#97—1181no—
111C4×C8—1181no—
112C22×C4—1181no—
113C22×C4C22×D5911yescharacteristic
114M16—21no—
115M16—21no—
116M16—21no—
117M16Dic11812yes—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—591no—
123C2×C8—591no—
124C2×C8—1181no—
125C2×C8—1181no—
126C2×C8C4×D5911yescharacteristic
127C2×C8C4×D5911yescharacteristic
128C4⋊C4—591no—
129C4⋊C4—591no—
130C4⋊C4—591no—
131C4⋊C4—591no—
132C22⋊C4—1181no—
133C22⋊C4—1181no—
134C42—1181no—
135C42—1181no—
136C42—1181no—
137C42—1181no—
138C23#1174568911yescharacteristic
139C2×C4—1182no—
140C2×C4—1181no—
141C2×C4—1181no—
142C2×C4—1181no—
143C2×C4—1181no—
144C2×C4—2361no—
145C2×C4—2361no—
146C2×C4C2×Dic11811yescharacteristic
147C2×C4C2×C4×D5911yescharacteristic
148C2×C4#1174568511yescharacteristic
149C2×C4D4×D5911yescharacteristic
150C2×C4#1174568711yescharacteristic
151C2×C4#1174568711yescharacteristic
152C8—21no—
153C8—21no—
154C8—22no—
155C8—41no—
156C8—1181no—
157C8—1181no—
158C22—21no—
159C22—21no—
160C22#1427368911yescharacteristic
161C22#1427371811yescharacteristic
162C22#1427372211yescharacteristic
163C4—2362no—
164C4—2361no—
165C4—2361no—
166C4—2361no—
167C4—2361no—
168C4#1427368311yescharacteristic
169C4C4×Dic11811yescharacteristic
170C4#1427370411yescharacteristic
171C4#1427370911yescharacteristic
172C2—21no—
173C2—21no—
174C2#1683728511yescharacteristic
175C2#1683751811yescharacteristic
176C2#1683752311yescharacteristic
subgroupG/H
centerC2×C4D4×D59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#341C2
socleC22×C59C4×D4
hypercenter#341D59
hypocenterC59#1922
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #341

Complements

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

NH ≅ G/Ntype
12. #14273661C4semidirect
13. #14273661C4semidirect
14. #14273659C4semidirect
15. #14273659C4semidirect
96. C59#1922semidirect