Finite Group Databasebeta

← #21436988

Subgroups — #21436988

Order 7552.

324 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 133 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#16838130C212yesmaximal
2#16837807C211yesmaximal, characteristic
3#16837804C212yesmaximal
4#16837710C214yesmaximal
5#16837688C212yesmaximal
6C4×Dic236C212yesmaximal
7C4×Dic236C211yesmaximal, characteristic
8C8×Q8×C59C211yesmaximal, characteristic
9C2×Dic236C2211yescharacteristic
10#14273727C2212yes—
11#14273725—22no—
12#14273719C2214yes—
13#14273717—24no—
14C4×Dic118C2212yes—
15C4×Dic118C2214yes—
16#14273692—22no—
17#14273661C2212yes—
18#14273661C2211yescharacteristic
19#14273661C2212yes—
20#14273659C2214yes—
21#14273652C2214yes—
22#14273652C2212yes—
23C4×Q8×C59C2211yescharacteristic
24C4⋊C8×C59C2211yescharacteristic
25C4⋊C8×C59C2212yes—
26C4×C8×C59C2212yes—
27C4×C8×C59C2211yescharacteristic
28C2×Q8×C59D411yescharacteristic
29C2×Dic118—22no—
30C2×Dic118C2312yes—
31C2×C8×C59C2312yes—
32C2×C8×C59C2311yescharacteristic
33C2×C8×C59C2311yescharacteristic
34C4⋊C4×C59D411yescharacteristic
35C4⋊C4×C59D412yes—
36C42×C59C2312yes—
37C42×C59C2311yescharacteristic
38C4⋊Dic59—22no—
39C4⋊Dic59C2312yes—
40C4⋊Dic59C2314yes—
41Dic59⋊C4—24no—
42Dic59⋊C4—22no—
43Dic59⋊C4—24no—
44Dic59⋊C4—24no—
45C4×Dic59—24no—
46C4×Dic59—22no—
47Dic236Q814yescomplemented
48Q8×C59—22no—
49C2×C4×C59C2×D412yes—
50C2×C4×C59C2×D412yes—
51C2×C4×C59C2×D411yescharacteristic
52C2×C4×C59C2×D411yescharacteristic
53C2×C4×C59C2411yescharacteristic
54C2×Dic59—22no—
55C2×Dic59—22no—
56C2×Dic59—24no—
57Dic118—22no—
58Dic118—44no—
59Dic118C2×Q814yes—
60C8×C59—22no—
61C8×C59—21no—
62C8×C59C2×Q812yes—
63C22×C59C22×D411yescharacteristic
64C4×C59—22no—
65C4×C59—22no—
66C4×C59—21no—
67C4×C59#13512yes—
68C4×C59C22×Q811yescharacteristic
69C4×C592−1+411yescharacteristic
70Dic59—24no—
71Dic59—44no—
72Dic59—42no—
73#3383—591nomaximal, Sylow
74C2×C59D4×Q811yescharacteristic
75C2×C59C2×#13511yescharacteristic
76C2×C59#57811yescharacteristic
77#557—592no—
78#500—591no—
79#499—592no—
80#479—594no—
81#475—592no—
82C8×Q8D5911yescharacteristic
83C4×Q16—592no—
84C4×Q16—591no—
85C59#338311yescharacteristic, complemented, Sylow
86C2×Q16—591no—
87C4⋊Q8—592no—
88C4⋊Q8—1182no—
89#125—594no—
90#125—1184no—
91C4×Q8—592no—
92C4×Q8—594no—
93C4×Q8—1182no—
94C4×Q8C2×D5911yescharacteristic
95#107—591no—
96#107—592no—
97#107—592no—
98#106—594no—
99C4⋊C8C2×D5911yescharacteristic
100C4⋊C8C2×D5912yes—
101#103—594no—
102#103—592no—
103C4×C8C2×D5912yes—
104C4×C8C2×D5911yescharacteristic
105C2×Q8—592no—
106C2×Q8—1182no—
107C2×Q8D23611yescharacteristic
108Q16—594no—
109C2×C8C22×D5912yes—
110C2×C8C22×D5911yescharacteristic
111C2×C8C22×D5911yescharacteristic
112C4⋊C4—592no—
113C4⋊C4—594no—
114C4⋊C4—1182no—
115C4⋊C4—1184no—
116C4⋊C4—1184no—
117C4⋊C4—1184no—
118C4⋊C4—1182no—
119C4⋊C4D23611yescharacteristic
120C4⋊C4D23612yes—
121C42—1184no—
122C42—1182no—
123C42C22×D5912yes—
124C42C22×D5911yescharacteristic
125Q8—22no—
126Q8—594no—
127Q8—1182no—
128Q8—2364no—
129C2×C4—1182no—
130C2×C4—1182no—
131C2×C4—1184no—
132C2×C4C2×D23612yes—
133C2×C4C2×D23611yescharacteristic
134C2×C4C2×D23612yes—
135C2×C4C2×D23611yescharacteristic
136C2×C4C23×D5911yescharacteristic
137C8—22no—
138C8—21no—
139C8Q8×D5912yes—
140C22C22×D23611yescharacteristic
141C4—22no—
142C4—22no—
143C4—21no—
144C4—1184no—
145C4—2364no—
146C4—2362no—
147C4#1427374912yes—
148C4C2×Q8×D5911yescharacteristic
149C4#1427377411yescharacteristic
150C2Q8×D23611yescharacteristic
151C2C2×#1427374911yescharacteristic
152C2#1683821911yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC8×Q8×C59C2
socleC22×C59C22×D4
hypercenterC8×Q8D59
hypocenterC59#3383
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8

Complements

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

NH ≅ G/Ntype
47. Dic236Q8semidirect
85. C59#3383semidirect