Finite Group Databasebeta

← #21425760

Subgroups — #21425760

Order 7552.

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

normal subgroups only

This group has 258 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#16837951C211yesmaximal, characteristic
2#16837374C212yesmaximal, complemented
3#16837197C211yesmaximal, characteristic, complemented
4#16837194C212yesmaximal, complemented
5C59×#354C211yesmaximal, characteristic, complemented
6C2×#11745689C411yescharacteristic, complemented
7C2×#11745687C2211yescharacteristic
8#14273725C411yescharacteristic, complemented
9#14273723C2211yescharacteristic
10#14273715C411yescharacteristic, complemented
11#14273700—22no—
12(C22⋊D59)⋊C4—22no—
13#14273683—22no—
14C42×D59C411yescharacteristic, complemented
15#14273642C2212yes—
16#14273641—22no—
17#124×C59C2211yescharacteristic
18#99×C59C2212yes—
19C2×Q8×C59C2×C411yescharacteristic
20C2×D4×C59C2311yescharacteristic
21C2×C22⋊D59—22no—
22C2×C22⋊D59D412yes—
23C22×Dic59D412yes—
24#11745689—41no—
25#11745689—41no—
26#11745687—41no—
27#11745687—41no—
28C2×D236—21no—
29C2×D236C2×C411yescharacteristic
30C2×C4×D59—21no—
31C2×C4×D59—21no—
32C2×C4×D59C2×C411yescharacteristic
33C2×Dic118C2×C411yescharacteristic
34C22⋊C4×C59—22no—
35C22⋊C4×C59—22no—
36C42×C59C2×C411yescharacteristic
37C22⋊Dic59—22no—
38(C2×D59)⋊C4—22no—
39Dic59⋊C4—22no—
40Dic59⋊C4—42no—
41C4×Dic59—21no—
42C4×Dic59—42no—
43C4×Dic59C2×C411yescharacteristic
44C23×C59C2×D412yes—
45C22×D59—21no—
46C22×D59C22⋊C411yescharacteristic
47Q8×C59—41no—
48D4×C59—41no—
49C2×C4×C59—21no—
50C2×C4×C59—21no—
51C2×C4×C59—42no—
52C2×C4×C59C22×C411yescharacteristic
53C22⋊D59—42no—
54C22⋊D59—44no—
55C2×Dic59—21no—
56C2×Dic59—22no—
57C2×Dic59—22no—
58C2×Dic59—42no—
59C2×Dic59C22⋊C412yes—
60C2×Dic59C22⋊C411yescharacteristic
61D236—41no—
62D236—42no—
63C4×D59—21no—
64C4×D59—21no—
65C4×D59—42no—
66C4×D59—41no—
67C4×D59—41no—
68Dic118—41no—
69C22×C59—22no—
70C22×C59—42no—
71C22×C59C2×C22⋊C411yescharacteristic
72C2×D59—21no—
73C2×D59—41no—
74C2×D59—42no—
75C2×D59—41no—
76C4×C59—21no—
77C4×C59—41no—
78C4×C59—41no—
79C4×C59—82no—
80Dic59—22no—
81Dic59—22no—
82Dic59—82no—
83Dic59#9911yescharacteristic
84Dic59#9911yescharacteristic
85#2126—591nomaximal, Sylow
86C2×C59—21no—
87C2×C59—42no—
88C2×C59C2×#9911yescharacteristic
89D59—41no—
90D59—81no—
91#532—591no—
92#410—592no—
93#354—591no—
94#354D5911yescharacteristic, complemented
95#353—592no—
96C59#212611yescharacteristic, complemented, Sylow
97C2×#41—591no—
98C2×#41—591no—
99C4⋊Q8—591no—
100#127—591no—
101#124—591no—
102#124C2×D5911yescharacteristic
103#121—1182no—
104C4×D4—1182no—
105#117—1182no—
106C2×C42—591no—
107#99—592no—
108#99—1182no—
109#99C2×D5912yes—
110#41—2361no—
111#41—2361no—
112#41—2361no—
113#41—2361no—
114C2×Q8—591no—
115C2×Q8C4×D5911yescharacteristic
116C2×D4—592no—
117C2×D4—591no—
118C2×D4—1181no—
119C2×D4—1182no—
120C2×D4C22×D5911yescharacteristic
121C22×C4—592no—
122C22×C4—591no—
123C22×C4—1181no—
124C22×C4—1181no—
125C4⋊C4—1182no—
126C4⋊C4—2362no—
127C22⋊C4—22no—
128C22⋊C4—22no—
129C22⋊C4—1182no—
130C22⋊C4—1182no—
131C42—591no—
132C42—1181no—
133C42—2362no—
134C42C4×D5911yescharacteristic
135C23—591no—
136C23—1181no—
137C23D4×D5912yes—
138Q8—41no—
139Q8—2361no—
140D4—41no—
141D4—2361no—
142D4—2362no—
143D4—2362no—
144D4—2364no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—591no—
149C2×C4—592no—
150C2×C4—1181no—
151C2×C4—1181no—
152C2×C4—1182no—
153C2×C4—1182no—
154C2×C4—1181no—
155C2×C4—2361no—
156C2×C4—2361no—
157C2×C4—2362no—
158C2×C4—2362no—
159C2×C4C2×C4×D5911yescharacteristic
160C22—22no—
161C22—42no—
162C22—1181no—
163C22—2362no—
164C22—2361no—
165C22—2361no—
166C22C22⋊C4×D5911yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—82no—
171C4—591no—
172C4—591no—
173C4—1182no—
174C4—1182no—
175C4—4722no—
176C2—21no—
177C2—42no—
178C2—4721no—
179C2—2361no—
180C2#99×D5911yescharacteristic
subgroupG/H
centerC2#99×D59
commutatorC2×C4×C59C22×C4
FrattiniC2×D4C22×D59
FittingC59×#354C2
socleC2×C59C2×#99
hypercenter#354D59
hypocenterC59#2126
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #16837374C2semidirect
3. #16837197C2semidirect
4. #16837194C2semidirect
5. C59×#354C2semidirect
6. C2×#11745689C4semidirect
8. #14273725C4semidirect
10. #14273715C4semidirect
14. C42×D59C4semidirect
94. #354D59semidirect
96. C59#2126semidirect