Finite Group Databasebeta

← #24984454

Subgroups — #24984454

Order 11008.

186 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 25 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#19134209C211yesmaximal, characteristic
2#19132758C211yesmaximal, characteristic, complemented
3C43×#1408C211yesmaximal, characteristic, complemented
4#14583276C411yescharacteristic, complemented
5#14583275—21no—
6#14583275—21no—
7#14582692—21no—
8C8×C43⋊C8C411yescharacteristic, complemented
9C43×#493C2211yescharacteristic
10C43×#353—21no—
11C2×D344—41no—
12C2×#10621882—42no—
13C2×#10621882—42no—
14#13063322—21no—
15#13063240—41no—
16C4×C43⋊C8—21no—
17C2×D8×C43—41no—
18#127×C43D411yescharacteristic
19#127×C43D411yescharacteristic
20#99×C43—41no—
21C4×C8×C43C2×C411yescharacteristic
22C2×D4×C43—21no—
23C2×D4×C43—21no—
24C2×D4×C43—41no—
25C2×D4×C43—41no—
26C2×D172—41no—
27C2×D172—41no—
28C2×D172—41no—
29D8×C43—82no—
30C2×C8×C43—21no—
31C22⋊C4×C43—81no—
32C42×C43C22⋊C411yescharacteristic
33C22⋊Dic43—81no—
34#10621882—84no—
35#10621882—84no—
36C2×C43⋊C8—22no—
37D344—82no—
38C23×C43—41no—
39C23×C43—41no—
40C22×D43—81no—
41D4×C43—81no—
42D4×C43—81no—
43D4×C43—82no—
44D4×C43—82no—
45C2×C4×C43—21no—
46C2×C4×C43—161no—
47C2×C4×C43#9911yescharacteristic
48C2×Dic43—161no—
49D172—82no—
50D172—82no—
51D172—82no—
52C8×C43—22no—
53C43⋊C8—24no—
54#7529—431nomaximal, Sylow
55C22×C43—81no—
56C22×C43—81no—
57C22×C43—161no—
58C22×C43—161no—
59C22×C43#35311yescharacteristic
60C2×D43—161no—
61C2×D43—161no—
62C2×D43—161no—
63C4×C43—22no—
64C4×C43—21no—
65C4×C43—321no—
66Dic43—321no—
67#1712—431no—
68#1408—431no—
69#1408D4311yescharacteristic, complemented
70C2×C43—21no—
71C2×C43—161no—
72C2×C43—161no—
73C2×C43#140811yescharacteristic
74D43—321no—
75#493—431no—
76#493—861no—
77#493—861no—
78#493C2×D4311yescharacteristic
79#353—21no—
80#353—861no—
81C82—431no—
82C43#752911yescharacteristic, complemented, Sylow
83C2×D8—41no—
84C2×D8—1721no—
85C2×D8—1722no—
86C2×D8—1722no—
87#127—861no—
88#127D17211yescharacteristic
89#127C22⋊D4311yescharacteristic
90#99—41no—
91#99—1721no—
92C4×C8—861no—
93C4×C8C4×D4311yescharacteristic
94C2×D4—21no—
95C2×D4—21no—
96C2×D4—41no—
97C2×D4—41no—
98C2×D4—1721no—
99C2×D4—1721no—
100C2×D4—1721no—
101D8—82no—
102D8—3442no—
103D8—3444no—
104D8—3444no—
105C2×C8—21no—
106C2×C8—862no—
107C22⋊C4—81no—
108C22⋊C4—3441no—
109C42(C2×D43)⋊C411yescharacteristic
110C23—41no—
111C23—41no—
112C23—3441no—
113D4—81no—
114D4—81no—
115D4—82no—
116D4—82no—
117D4—3442no—
118D4—3442no—
119D4—3442no—
120C2×C4—21no—
121C2×C4—161no—
122C2×C4—6881no—
123C2×C4#1306323911yescharacteristic
124C8—22no—
125C8—864no—
126C22—81no—
127C22—81no—
128C22—161no—
129C22—161no—
130C22—6881no—
131C22—6881no—
132C22—6881no—
133C22#1458269111yescharacteristic
134C4—22no—
135C4—21no—
136C4—321no—
137C4—13761no—
138C2—21no—
139C2—161no—
140C2—161no—
141C2—13761no—
142C2#1913275711yescharacteristic
subgroupG/H
centerC2#19132757
commutatorC4×C8×C43C2×C4
Frattini#493C2×D43
FittingC43×#1408C2
socleC2×C43#1408
prime radical#19134209C2
cosocleC43×#493C22
hypercenter#1408D43
hypocenterC43#7529
LCSG ▷ C4×C8×C43 ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #493 ◁ #1408

Complements

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

NH ≅ G/Ntype
2. #19132758C2semidirect
3. C43×#1408C2semidirect
4. #14583276C4semidirect
8. C8×C43⋊C8C4semidirect
69. #1408D43semidirect
82. C43#7529semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191342092
#191327582
C43×#14082
#752943