Finite Group Databasebeta

← #23762938

Subgroups — #23762938

Order 10112.

156 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 51 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#19098909C211yesmaximal, characteristic
2#19098858C211yesmaximal, characteristic, complemented
3#19098694C211yesmaximal, characteristic, complemented
4#19098315C211yesmaximal, characteristic, complemented
5#19098311C211yesmaximal, characteristic, complemented
6#19098307C211yesmaximal, characteristic
7#460×C79C211yesmaximal, characteristic
8#14579161C2211yescharacteristic
9#14579094—21no—
10C4⋊(C79⋊C8)—21no—
11C4⋊(C79⋊C8)C2211yescharacteristic
12C4⋊(C79⋊C8)C2211yescharacteristic
13#14579085—21no—
14#14579082—21no—
15#14579082—21no—
16#14579072—21no—
17C4×C79⋊C8C2211yescharacteristic
18C2×SD16×C79—21no—
19#127×C79C2211yescharacteristic
20C4×Q8×C79C2211yescharacteristic
21C4⋊C8×C79C2211yescharacteristic
22#102×C79—21no—
23C2×Dic158—21no—
24C2×C79⋊C8—21no—
25C2×C79⋊C8—21no—
26C2×C79⋊C8D411yescharacteristic
27C2×C79⋊C8D411yescharacteristic
28C4⋊Dic79—21no—
29C4⋊Dic79—21no—
30C2×Q8×C79D411yescharacteristic
31C2×D4×C79—21no—
32C2×D4×C79—21no—
33C2×D4×C79—21no—
34SD16×C79—42no—
35C2×C8×C79—21no—
36C4⋊C4×C79—21no—
37C4⋊C4×C79D411yescharacteristic
38C42×C79—21no—
39C42×C79C2311yescharacteristic
40C23×C79—41no—
41Q8×C79—21no—
42Q8×C79—21no—
43D4×C79—41no—
44D4×C79—41no—
45D4×C79—41no—
46D4×C79—41no—
47D4×C79—81no—
48C2×C4×C79—21no—
49C2×C4×C79—21no—
50C2×C4×C79C2×D411yescharacteristic
51C2×C4×C79C2×D411yescharacteristic
52C2×C4×C79#4111yescharacteristic
53C2×Dic79—41no—
54Dic158—81no—
55C8×C79—41no—
56C79⋊C8—21no—
57C79⋊C8—21no—
58C79⋊C8—41no—
59C79⋊C8—41no—
60C22×C79—81no—
61C22×C79—81no—
62C22×C79—81no—
63C22×C79#12111yescharacteristic
64C4×C79—21no—
65C4×C79—41no—
66C4×C79—41no—
67C4×C79#13511yescharacteristic
68C4×C79AGL(1,ℤ/8)11yescharacteristic
69C4×C79#13711yescharacteristic
70C4×C79#13711yescharacteristic
71Dic79—81no—
72C2×C79—161no—
73C2×C79#46411yescharacteristic
74C2×C79#46811yescharacteristic
75C2×C79#47211yescharacteristic
76#1698—791nomaximal, Sylow
77C79#169811yescharacteristic, complemented, Sylow
78#486—791no—
79#477—791no—
80#460D7911yescharacteristic
81#446—791no—
82#335—791no—
83#333—791no—
84#331—791no—
85C2×SD16—21no—
86C4⋊Q8—791no—
87#127C2×D7911yescharacteristic
88C4×Q8C2×D7911yescharacteristic
89#107—1581no—
90C4⋊C8—791no—
91C4⋊C8—791no—
92C4⋊C8—1581no—
93C4⋊C8C2×D7911yescharacteristic
94#103—1581no—
95#102—21no—
96#102—1581no—
97#102—1581no—
98#97—1581no—
99C4×C8—791no—
100C2×Q8—1581no—
101C2×Q8C22⋊D7911yescharacteristic
102C2×D4—21no—
103C2×D4—21no—
104C2×D4—21no—
105SD16—42no—
106C2×C8—21no—
107C2×C8—791no—
108C2×C8—791no—
109C2×C8—1581no—
110C2×C8—1581no—
111C4⋊C4—21no—
112C4⋊C4—1581no—
113C4⋊C4—1581no—
114C4⋊C4C22⋊D7911yescharacteristic
115C42—21no—
116C42C22×D7911yescharacteristic
117C23—41no—
118Q8—21no—
119Q8—21no—
120Q8—6321no—
121D4—41no—
122D4—41no—
123D4—41no—
124D4—41no—
125D4—81no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—3161no—
129C2×C4D4×D7911yescharacteristic
130C2×C4C2×C22⋊D7911yescharacteristic
131C2×C4#1192962311yescharacteristic
132C8—41no—
133C8—3161no—
134C8—3161no—
135C8—1581no—
136C8—1581no—
137C22—81no—
138C22—81no—
139C22—81no—
140C22#1457913311yescharacteristic
141C4—21no—
142C4—41no—
143C4—41no—
144C4—6321no—
145C4#1457918211yescharacteristic
146C4#1457918711yescharacteristic
147C4#1457919011yescharacteristic
148C4#1457919111yescharacteristic
149C2—161no—
150C2#1909878311yescharacteristic
151C2#1909880711yescharacteristic
152C2#1909883111yescharacteristic
subgroupG/H
centerC22#14579133
commutator, cosocleC42×C79C23
FrattiniC42C22×D79
Fitting#460×C79C2
socleC22×C79#121
prime radical#127×C79C22
hypercenter#460D79
hypocenterC79#1698
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #19098858C2semidirect
3. #19098694C2semidirect
4. #19098315C2semidirect
5. #19098311C2semidirect
77. C79#1698semidirect