Finite Group Databasebeta

← #19133619

Subgroups — #19133619

Order 5504.

236 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 53 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#14583525C211yesmaximal, characteristic
2#14583234C212yesmaximal, complemented
3#14582635C212yesmaximal, complemented
4#14582623C211yesmaximal, characteristic
5C43×#399C211yesmaximal, characteristic
6#13063304—21no—
7#13063304C2212yes—
8#13063302—22no—
9#13063302—22no—
10C2×C22⋊Dic43—21no—
11#13063258—22no—
12#13063248—22no—
13C22⋊(C43⋊C8)C2212yes—
14C2×C4⋊C4×C43—21no—
15C2×C4⋊C4×C43C2211yescharacteristic
16C2×C22⋊C4×C43—21no—
17C2×C22⋊C4×C43C2211yescharacteristic
18#95×C43C2211yescharacteristic
19C24×C43D411yescharacteristic
20C22×C4×C43—21no—
21C22×C4×C43—21no—
22C22×C4×C43D411yescharacteristic
23C22×C4×C43C2311yescharacteristic
24C22×Dic43—21no—
25C22×Dic43—21no—
26C2×Dic86—21no—
27C2×Dic86D412yes—
28C4⋊C4×C43—22no—
29C4⋊C4×C43—42no—
30C22⋊C4×C43—22no—
31C22⋊C4×C43—42no—
32C22⋊Dic43—22no—
33C22⋊Dic43—22no—
34C4⋊Dic43—21no—
35C4⋊Dic43D412yes—
36Dic43⋊C4—22no—
37Dic43⋊C4—22no—
38C2×C43⋊C8—22no—
39C23×C43—21no—
40C23×C43—21no—
41C23×C43—41no—
42C23×C43—41no—
43C23×C43Q1612yes—
44C23×C43C2×D411yescharacteristic
45C2×C4×C43—22no—
46C2×C4×C43—21no—
47C2×C4×C43—41no—
48C2×C4×C43—41no—
49C2×C4×C43—41no—
50C2×C4×C43—41no—
51C2×C4×C43—41no—
52C2×C4×C43—41no—
53C2×C4×C43—41no—
54C2×C4×C43C2×D412yes—
55C2×Dic43—22no—
56C2×Dic43—22no—
57C2×Dic43—81no—
58C2×Dic43—81no—
59Dic86—42no—
60Dic86—81no—
61C43⋊C8—42no—
62C22×C43—21no—
63C22×C43—21no—
64C22×C43—22no—
65C22×C43—42no—
66C22×C43—41no—
67C22×C43—41no—
68C22×C43—81no—
69C22×C43#12011yescharacteristic
70C22×C43C2×Q1611yescharacteristic
71C22×C43#13711yescharacteristic
72C4×C43—22no—
73C4×C43—42no—
74C4×C43—41no—
75C4×C43—81no—
76Dic43—42no—
77Dic43—42no—
78#1614—431nomaximal, Sylow
79C2×C43—21no—
80C2×C43—21no—
81C2×C43—42no—
82C2×C43#45111yescharacteristic
83C2×C43#45311yescharacteristic
84C2×C43#45811yescharacteristic
85#543—431no—
86#484—432no—
87#399D4311yescharacteristic
88#328—432no—
89#323—431no—
90C43#161411yescharacteristic, complemented, Sylow
91C22⋊Q8—432no—
92C22⋊Q8—862no—
93C22⋊Q8—862no—
94C22⋊Q8—861no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4C2×D4311yescharacteristic
97C2×C22⋊C4—21no—
98C2×C22⋊C4—861no—
99C2×C22⋊C4C2×D4311yescharacteristic
100#107—862no—
101#103—862no—
102C22⋊C8—432no—
103#95C2×D4311yescharacteristic
104C24C22⋊D4311yescharacteristic
105C2×Q8—432no—
106C2×Q8—861no—
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—861no—
110C22×C4—861no—
111C22×C4C22⋊D4311yescharacteristic
112C22×C4C22×D4311yescharacteristic
113C2×C8—862no—
114C4⋊C4—22no—
115C4⋊C4—42no—
116C4⋊C4—432no—
117C4⋊C4—862no—
118C4⋊C4—861no—
119C4⋊C4—862no—
120C22⋊C4—22no—
121C22⋊C4—42no—
122C22⋊C4—862no—
123C22⋊C4—862no—
124C23—21no—
125C23—21no—
126C23—41no—
127C23—41no—
128C23#1062188512yes—
129C23C2×C22⋊D4311yescharacteristic
130Q8—3441no—
131Q8—1722no—
132C2×C4—22no—
133C2×C4—21no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—862no—
142C2×C4—862no—
143C2×C4—3441no—
144C2×C4—3441no—
145C2×C4D4×D4312yes—
146C8—1722no—
147C22—21no—
148C22—21no—
149C22—22no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22—81no—
154C22#1306329311yescharacteristic
155C22C2×#1062188511yescharacteristic
156C22#1306335511yescharacteristic
157C4—22no—
158C4—42no—
159C4—41no—
160C4—81no—
161C4—1722no—
162C4—1722no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#1458305411yescharacteristic
167C2#1458306611yescharacteristic
168C2#1458308811yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#399C2
socleC22×C43#120
hypercenter#399D43
hypocenterC43#1614
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #399

Complements

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

NH ≅ G/Ntype
2. #14583234C2semidirect
3. #14582635C2semidirect
90. C43#1614semidirect