Finite Group Databasebeta

← #21423391

Subgroups — #21423391

Order 7552.

230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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#16838150C211yesmaximal, characteristic, complemented
2#16837791C212yesmaximal, complemented
3#16837768C211yesmaximal, characteristic, complemented
4#16837141C212yesmaximal, complemented
5C59×#330C211yesmaximal, characteristic, complemented
6C2×#11745660—22no—
7C2×D472—22no—
8#14273724C2211yescharacteristic
9#14273715C2212yes—
10#14273712—22no—
11#14273705—22no—
12#14273702—22no—
13#14273647—22no—
14#14273638C2211yescharacteristic
15#125×C59C2211yescharacteristic
16#97×C59C2212yes—
17C2×D236—21no—
18C2×D236—22no—
19C2×D236—22no—
20C2×D236D412yes—
21C2×C4×D59—22no—
22C2×Dic118D412yes—
23C2×C8×C59—22no—
24C4⋊C4×C59—22no—
25C4⋊C4×C59D412yes—
26C42×C59C2311yescharacteristic
27(C2×D59)⋊C4—22no—
28(C2×D59)⋊C4—22no—
29(C2×D59)⋊C4—22no—
30Dic59⋊C4—22no—
31C2×C59⋊C8—21no—
32D472—44no—
33#11745660—44no—
34C22×D59—22no—
35C22×D59—41no—
36C2×C4×C59—22no—
37C2×C4×C59C2×D411yescharacteristic
38C2×C4×C59C2×D412yes—
39C2×Dic59—22no—
40D236—42no—
41D236—42no—
42D236—42no—
43D236—42no—
44D236—82no—
45C4×D59—82no—
46Dic118—42no—
47C8×C59—24no—
48C59⋊C8—41no—
49C22×C59#12011yescharacteristic
50C2×D59—42no—
51C2×D59—42no—
52C2×D59—42no—
53C2×D59—82no—
54C2×D59—81no—
55C4×C59—22no—
56C4×C59—21no—
57C4×C59—42no—
58Dic59—42no—
59#1656—591nomaximal, Sylow
60C2×C59#45312yes—
61C2×C59#45411yescharacteristic
62D59—82no—
63D59—161no—
64#562—591no—
65#496—592no—
66#490—591no—
67#330D5911yescharacteristic, complemented
68#329—592no—
69C59#165611yescharacteristic, complemented, Sylow
70C2×SD16—1182no—
71C2×D8—1182no—
72#127—591no—
73#125C2×D5911yescharacteristic
74#124—592no—
75#123—1182no—
76C22⋊Q8—1182no—
77#121—1182no—
78#102—1182no—
79#97—591no—
80#97C2×D5912yes—
81C2×Q8—592no—
82C2×D4—592no—
83C2×D4—1182no—
84C2×D4—1181no—
85C2×D4—1182no—
86C22×C4—1182no—
87SD16—2364no—
88D8—2364no—
89C2×C8—22no—
90C2×C8—1181no—
91C4⋊C4—22no—
92C4⋊C4—1182no—
93C4⋊C4D23612yes—
94C22⋊C4—1182no—
95C22⋊C4—1182no—
96C22⋊C4—1182no—
97C42C22×D5911yescharacteristic
98C23—1182no—
99C23—2361no—
100Q8—2362no—
101D4—4722no—
102D4—2362no—
103D4—2362no—
104D4—2362no—
105D4—2362no—
106C2×C4—22no—
107C2×C4—1182no—
108C2×C4—4722no—
109C2×C4C2×D23611yescharacteristic
110C2×C4D4×D5912yes—
111C8—24no—
112C8—2361no—
113C22—4722no—
114C22—4721no—
115C22—2362no—
116C22—2362no—
117C22—2362no—
118C22#1427369711yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—2362no—
123C2—9441no—
124C2—4722no—
125C2#1683757112yes—
126C2#1683757711yescharacteristic
subgroupG/H
centerC22#14273697
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×#330C2
socleC22×C59#120
hypercenter#330D59
hypocenterC59#1656
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #16838150C2semidirect
2. #16837791C2semidirect
3. #16837768C2semidirect
4. #16837141C2semidirect
5. C59×#330C2semidirect
67. #330D59semidirect
69. C59#1656semidirect