Finite Group Databasebeta

← #21425766

Subgroups — #21425766

Order 7552.

270 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 55 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#16837965C211yesmaximal, characteristic
2#16837374C212yesmaximal, complemented
3#16837195C211yesmaximal, characteristic, complemented
4#16837194C212yesmaximal, complemented
5C59×#353C211yesmaximal, characteristic, complemented
6C2×#11745687C2211yescharacteristic
7C2×D4×D59C411yescharacteristic, complemented
8#14273723C2211yescharacteristic
9#14273715C411yescharacteristic, complemented
10#14273714C411yescharacteristic, complemented
11#14273699—22no—
12#14273695—22no—
13#14273684C411yescharacteristic, complemented
14#14273683—22no—
15#14273642C2212yescomplemented
16#14273641—22no—
17#127×C59C2211yescharacteristic
18#99×C59C2212yescomplemented
19C23×D59—21no—
20C2×D4×C59—22no—
21C2×D4×C59C2×C411yescharacteristic
22C2×D4×C59C2311yescharacteristic
23C2×C22⋊D59—22no—
24C2×C22⋊D59—21no—
25C2×C22⋊D59D412yes—
26C22×Dic59D412yes—
27#11745687—42no—
28D4×D59—42no—
29C2×D236C2×C411yescharacteristic
30C2×C4×D59C2×C411yescharacteristic
31C2×Dic118C2×C411yescharacteristic
32C22⋊C4×C59—22no—
33C42×C59C2×C411yescharacteristic
34C22⋊Dic59—22no—
35C22⋊Dic59—22no—
36(C2×D59)⋊C4—21no—
37(C2×D59)⋊C4—22no—
38Dic59⋊C4—21no—
39Dic59⋊C4—42no—
40C4×Dic59—42no—
41C4×Dic59C2×C411yescharacteristic
42C23×C59—21no—
43C23×C59C2×D412yes—
44C22×D59—21no—
45C22×D59—42no—
46C22×D59—82no—
47C22×D59C22⋊C411yescharacteristic
48D4×C59—41no—
49D4×C59—41no—
50D4×C59—82no—
51C2×C4×C59—21no—
52C2×C4×C59—42no—
53C2×C4×C59C22×C411yescharacteristic
54C22⋊D59—42no—
55C22⋊D59—42no—
56C22⋊D59—82no—
57C2×Dic59—22no—
58C2×Dic59—22no—
59C2×Dic59—21no—
60C2×Dic59—42no—
61C2×Dic59C22⋊C412yes—
62C2×Dic59C22⋊C411yescharacteristic
63D236—41no—
64C4×D59—22no—
65Dic118—41no—
66C22×C59—22no—
67C22×C59—42no—
68C22×C59—42no—
69C22×C59—41no—
70C22×C59C2×C22⋊C411yescharacteristic
71C2×D59—21no—
72C2×D59—41no—
73C2×D59—42no—
74C2×D59—41no—
75C2×D59—84no—
76C4×C59—21no—
77C4×C59—41no—
78C4×C59—82no—
79Dic59—22no—
80Dic59—41no—
81Dic59—82no—
82Dic59#9912yes—
83#2128—591nomaximal, Sylow
84C2×C59—21no—
85C2×C59—42no—
86C2×C59—81no—
87C2×C59C2×#9911yescharacteristic
88D59—41no—
89D59—81no—
90#535—591no—
91#410—592no—
92#353—591no—
93#353—592no—
94#353D5911yescharacteristic, complemented
95C59#212811yescharacteristic, complemented, Sylow
96C2×#41—591no—
97C22×D4—591no—
98#127—591no—
99#127C2×D5911yescharacteristic
100#124—591no—
101#124—591no—
102#121—1182no—
103#120—1182no—
104#117—591no—
105#117—1182no—
106#99—592no—
107#99—1182no—
108#99C2×D5912yescomplemented
109C24—1181no—
110#41—2362no—
111C2×Q8—591no—
112C2×D4—22no—
113C2×D4—592no—
114C2×D4—591no—
115C2×D4—1181no—
116C2×D4—1182no—
117C2×D4—2362no—
118C2×D4C4×D5911yescharacteristic
119C2×D4C22×D5911yescharacteristic
120C22×C4—592no—
121C22×C4—591no—
122C4⋊C4—1181no—
123C4⋊C4—2362no—
124C22⋊C4—22no—
125C22⋊C4—1182no—
126C22⋊C4—1181no—
127C22⋊C4—1182no—
128C22⋊C4—1182no—
129C42—591no—
130C42—2362no—
131C42C4×D5911yescharacteristic
132C23—21no—
133C23—591no—
134C23—1181no—
135C23—4722no—
136C23—2362no—
137C23D4×D5912yes—
138Q8—2361no—
139D4—41no—
140D4—41no—
141D4—82no—
142D4—4722no—
143D4—2361no—
144D4—2362no—
145D4—2362no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—591no—
149C2×C4—592no—
150C2×C4—1182no—
151C2×C4—1182no—
152C2×C4—1182no—
153C2×C4—1181no—
154C2×C4—2362no—
155C2×C4C2×C4×D5911yescharacteristic
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—1181no—
161C22—4724no—
162C22—2362no—
163C22—2361no—
164C22—2361no—
165C22C22⋊C4×D5911yescharacteristic
166C4—21no—
167C4—41no—
168C4—82no—
169C4—592no—
170C4—1182no—
171C4—4722no—
172C4—2361no—
173C2—21no—
174C2—42no—
175C2—81no—
176C2—4721no—
177C2—2361no—
178C2#99×D5911yescharacteristic
subgroupG/H
centerC2#99×D59
commutatorC2×C4×C59C22×C4
FrattiniC2×D4C22×D59
FittingC59×#353C2
socleC2×C59C2×#99
hypercenter#353D59
hypocenterC59#2128
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #16837374C2semidirect
3. #16837195C2semidirect
4. #16837194C2semidirect
5. C59×#353C2semidirect
7. C2×D4×D59C4semidirect
9. #14273715C4semidirect
10. #14273714C4semidirect
13. #14273684C4semidirect
15. #14273642C22semidirect
18. #99×C59C22semidirect
94. #353D59semidirect
95. C59#2128semidirect
108. #99C2×D59semidirect