Finite Group Databasebeta

← #21425762

Subgroups — #21425762

Order 7552.

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

normal subgroups only

This group has 286 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#99×D59C212yesmaximal, complemented
3#16837196C212yesmaximal, complemented
4#16837195C211yesmaximal, characteristic, complemented
5C59×#353C211yesmaximal, characteristic, complemented
6C2×#11745687C411yescharacteristic, complemented
7C2×D4×D59C2211yescharacteristic
8#14273723C411yescharacteristic, complemented
9#14273715C411yescharacteristic, complemented
10#14273714C2211yescharacteristic
11#14273699—22no—
12#14273695—22no—
13#14273684C411yescharacteristic, complemented
14C22⋊C4×D59—22no—
15#14273642C2212yes—
16#14273641—22no—
17#127×C59C2211yescharacteristic
18#99×C59C2212yes—
19C23×D59D412yes—
20C2×D4×C59—22no—
21C2×D4×C59C2×C411yescharacteristic, complemented
22C2×D4×C59C2311yescharacteristic
23C2×C22⋊D59—21no—
24C2×C22⋊D59—22no—
25C2×C22⋊D59D412yes—
26C22×Dic59—21no—
27#11745687—42no—
28D4×D59—42no—
29C2×D236C2×C411yescharacteristic
30C2×C4×D59—42no—
31C2×C4×D59C2×C411yescharacteristic
32C2×Dic118C2×C411yescharacteristic, complemented
33C22⋊C4×C59—22no—
34C42×C59C2×C411yescharacteristic, complemented
35C22⋊Dic59—22no—
36C22⋊Dic59—22no—
37(C2×D59)⋊C4—21no—
38(C2×D59)⋊C4—22no—
39(C2×D59)⋊C4—42no—
40Dic59⋊C4—21no—
41C4×Dic59C2×C411yescharacteristic, complemented
42C23×C59—21no—
43C23×C59C2×D412yes—
44C22×D59—22no—
45C22×D59—22no—
46C22×D59—82no—
47C22×D59C22⋊C412yes—
48C22×D59C22⋊C411yescharacteristic
49D4×C59—41no—
50D4×C59—41no—
51D4×C59—82no—
52C2×C4×C59—21no—
53C2×C4×C59—42no—
54C2×C4×C59C22×C411yescharacteristic
55C22⋊D59—42no—
56C22⋊D59—42no—
57C22⋊D59—82no—
58C2×Dic59—21no—
59C2×Dic59—21no—
60C2×Dic59—42no—
61C2×Dic59—42no—
62C2×Dic59C22⋊C411yescharacteristic
63D236—41no—
64C4×D59—22no—
65C4×D59—84no—
66Dic118—41no—
67C22×C59—22no—
68C22×C59—42no—
69C22×C59—42no—
70C22×C59—41no—
71C22×C59C2×C22⋊C411yescharacteristic
72C2×D59—22no—
73C2×D59—41no—
74C2×D59—44no—
75C2×D59—42no—
76C2×D59—82no—
77C2×D59#9912yes—
78C4×C59—21no—
79C4×C59—41no—
80C4×C59—82no—
81Dic59—21no—
82Dic59—41no—
83Dic59—41no—
84Dic59—82no—
85#2127—591nomaximal, Sylow
86C2×C59—21no—
87C2×C59—42no—
88C2×C59—81no—
89C2×C59C2×#9911yescharacteristic
90D59—22no—
91D59—42no—
92#535—591no—
93C2×#99—592no—
94#354—592no—
95#353—591no—
96#353D5911yescharacteristic, complemented
97C59#212711yescharacteristic, complemented, Sylow
98C2×#41—591no—
99C22×D4—591no—
100#127—591no—
101#127C2×D5911yescharacteristic
102#124—591no—
103#124—591no—
104#121—1182no—
105#120—1182no—
106#117—591no—
107C2×C22⋊C4—1182no—
108#99—592no—
109#99—1182no—
110#99C2×D5912yes—
111C24—592no—
112#41—2362no—
113C2×Q8—591no—
114C2×D4—22no—
115C2×D4—592no—
116C2×D4—591no—
117C2×D4—1182no—
118C2×D4—1181no—
119C2×D4—2362no—
120C2×D4C4×D5911yescharacteristic, complemented
121C2×D4C22×D5911yescharacteristic
122C22×C4—591no—
123C22×C4—1181no—
124C22×C4—2362no—
125C4⋊C4—1181no—
126C22⋊C4—22no—
127C22⋊C4—1181no—
128C22⋊C4—1182no—
129C22⋊C4—1182no—
130C22⋊C4—1182no—
131C22⋊C4—2362no—
132C42—591no—
133C42C4×D5911yescharacteristic, complemented
134C23—21no—
135C23—591no—
136C23—592no—
137C23—1182no—
138C23—1182no—
139C23—4722no—
140C23D4×D5912yes—
141Q8—2361no—
142D4—41no—
143D4—41no—
144D4—82no—
145D4—4722no—
146D4—2361no—
147D4—2362no—
148D4—2362no—
149C2×C4—21no—
150C2×C4—42no—
151C2×C4—591no—
152C2×C4—1182no—
153C2×C4—1181no—
154C2×C4—1181no—
155C2×C4—4724no—
156C2×C4—2362no—
157C2×C4—2362no—
158C2×C4C2×C4×D5911yescharacteristic
159C22—22no—
160C22—42no—
161C22—42no—
162C22—41no—
163C22—592no—
164C22—1182no—
165C22—4722no—
166C22—2361no—
167C22—2362no—
168C22—2364no—
169C22C22⋊C4×D5911yescharacteristic
170C4—21no—
171C4—41no—
172C4—82no—
173C4—1181no—
174C4—4722no—
175C4—2361no—
176C4—2361no—
177C2—21no—
178C2—42no—
179C2—81no—
180C2—1182no—
181C2—2362no—
182C2#99×D5911yescharacteristic
subgroupG/H
centerC2#99×D59
commutatorC2×C4×C59C22×C4
FrattiniC2×D4C22×D59
FittingC59×#353C2
socleC2×C59C2×#99
hypercenter#353D59
hypocenterC59#2127
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. #99×D59C2semidirect
3. #16837196C2semidirect
4. #16837195C2semidirect
5. C59×#353C2semidirect
6. C2×#11745687C4semidirect
8. #14273723C4semidirect
9. #14273715C4semidirect
13. #14273684C4semidirect
21. C2×D4×C59C2×C4semidirect
32. C2×Dic118C2×C4semidirect
34. C42×C59C2×C4semidirect
41. C4×Dic59C2×C4semidirect
96. #353D59semidirect
97. C59#2127semidirect
120. C2×D4C4×D59semidirect
133. C42C4×D59semidirect