Finite Group Databasebeta

← #23764860

Subgroups — #23764860

Order 10112.

204 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 59 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#19098611C211yesmaximal, characteristic, complemented
2#19098568C211yesmaximal, characteristic
3#19098568C211yesmaximal, characteristic
4#19098335C211yesmaximal, characteristic, complemented
5#19098334C211yesmaximal, characteristic, complemented
6#19098320C211yesmaximal, characteristic, complemented
7C2×#100×C79C211yesmaximal, characteristic
8C2×#11929608C2211yescharacteristic
9C2×#11929608C2211yescharacteristic
10#14579120C2211yescharacteristic
11#14579120C2211yescharacteristic
12#14579096—22no—
13#14579082—22no—
14#14579082—22no—
15C22×D4×C79C2211yescharacteristic
16C2×M16×C79C2211yescharacteristic
17C2×M16×C79C2211yescharacteristic
18#100×C79—22no—
19#11929608—21no—
20#11929608—21no—
21#11929608—21no—
22#11929608—21no—
23C2×C79⋊C8—21no—
24C2×C79⋊C8D412yes—
25C4⋊Dic79—21no—
26C4⋊Dic79—21no—
27C22⋊Dic79—21no—
28C22⋊Dic79—21no—
29C4×Dic79—21no—
30C4×Dic79—21no—
31C24×C79—21no—
32C2×D4×C79—21no—
33C2×D4×C79—21no—
34C2×D4×C79—21no—
35C2×D4×C79—21no—
36C2×D4×C79—21no—
37C2×D4×C79D412yes—
38C22×C4×C79C2311yescharacteristic
39M16×C79—21no—
40M16×C79—21no—
41M16×C79—21no—
42M16×C79—21no—
43C2×C8×C79—21no—
44C2×C8×C79—21no—
45C23×C79—22no—
46C23×C79—41no—
47C23×C79—41no—
48C23×C79—82no—
49C23×C79#4111yescharacteristic
50D4×C79—22no—
51D4×C79—22no—
52D4×C79—41no—
53D4×C79—41no—
54C2×C4×C79C2×D411yescharacteristic
55C2×C4×C79C2×D411yescharacteristic
56C2×C4×C79#4111yescharacteristic
57C2×C4×C79#4111yescharacteristic
58C2×C4×C79#4111yescharacteristic
59C2×C4×C79#4111yescharacteristic
60C2×Dic79—41no—
61C2×Dic79—41no—
62C8×C79—41no—
63C8×C79—41no—
64C79⋊C8—22no—
65C79⋊C8—41no—
66C22×C79—41no—
67C22×C79—42no—
68C22×C79—82no—
69C22×C79—82no—
70C22×C79—82no—
71C22×C79#12311yescharacteristic
72C22×C79#12411yescharacteristic
73C22×C79#12611yescharacteristic
74C4×C79#12111yescharacteristic
75C4×C79#12311yescharacteristic
76C4×C79#12311yescharacteristic
77C4×C79#12611yescharacteristic
78Dic79—81no—
79Dic79—81no—
80C2×C79—21no—
81C2×C79—21no—
82C2×C79—21no—
83C2×C79—82no—
84C2×C79#39711yescharacteristic
85#2081—791nomaximal, Sylow
86C79#208111yescharacteristic, complemented, Sylow
87#430—791no—
88#418—791no—
89#418—791no—
90C2×#100D7911yescharacteristic
91#344—791no—
92#344—791no—
93H(3,ℤ/4)—791no—
94C22×D4C2×D7911yescharacteristic
95C2×M16—791no—
96C2×M16—791no—
97C2×M16C2×D7911yescharacteristic
98C2×M16C2×D7911yescharacteristic
99#117—791no—
100#117—791no—
101#108—1582no—
102#102—1582no—
103#102—1582no—
104#100—22no—
105C24—21no—
106C2×D4—21no—
107C2×D4—21no—
108C2×D4—21no—
109C2×D4—21no—
110C2×D4—21no—
111C2×D4C22⋊D7912yes—
112C22×C4C22×D7911yescharacteristic
113M16—21no—
114M16—21no—
115M16—21no—
116M16—21no—
117M16—1581no—
118M16—1581no—
119M16—1581no—
120M16—1581no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—792no—
124C2×C8—1581no—
125C4⋊C4—1581no—
126C4⋊C4—1581no—
127C22⋊C4—1581no—
128C22⋊C4—1581no—
129C42—1581no—
130C42—1581no—
131C23—22no—
132C23—41no—
133C23—41no—
134C23—82no—
135C23#1192962411yescharacteristic
136D4—22no—
137D4—22no—
138D4—41no—
139D4—41no—
140C2×C4—3161no—
141C2×C4—3161no—
142C2×C4D4×D7911yescharacteristic
143C2×C4C2×C22⋊D7911yescharacteristic
144C2×C4#1192962311yescharacteristic
145C2×C4#1192962311yescharacteristic
146C2×C4#1192962311yescharacteristic
147C2×C4#1192962411yescharacteristic
148C8—41no—
149C8—41no—
150C8—3161no—
151C8—1582no—
152C22—41no—
153C22—42no—
154C22—82no—
155C22—82no—
156C22—82no—
157C22#1457914411yescharacteristic
158C22#1457914711yescharacteristic
159C22#1457915411yescharacteristic
160C4—6321no—
161C4—6321no—
162C4#1457913311yescharacteristic
163C4#1457914211yescharacteristic
164C4#1457914311yescharacteristic
165C4#1457915411yescharacteristic
166C2—21no—
167C2—21no—
168C2—21no—
169C2—82no—
170C2#1909849111yescharacteristic
subgroupG/H
centerC2#19098491
commutator, cosocleC22×C4×C79C23
FrattiniC22×C4C22×D79
FittingC2×#100×C79C2
socleC2×C79#397
prime radicalC22×D4×C79C22
hypercenterC2×#100D79
hypocenterC79#2081
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. #19098611C2semidirect
4. #19098335C2semidirect
5. #19098334C2semidirect
6. #19098320C2semidirect
86. C79#2081semidirect