Finite Group Databasebeta

← #23765374

Subgroups — #23765374

Order 10112.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#19099364C211yesmaximal, characteristic
2#19099006C211yesmaximal, characteristic, complemented
3C2×#14579105C211yesmaximal, characteristic, complemented
4#19098839C211yesmaximal, characteristic, complemented
5#19098369C211yesmaximal, characteristic, complemented
6#19098348C211yesmaximal, characteristic, complemented
7#361×C79C211yesmaximal, characteristic, complemented
8#14579206—21no—
9#14579194—21no—
10#14579187—21no—
11#14579185—22no—
12#14579183C2211yescharacteristic
13#14579180—21no—
14C2×Dic316C2211yescharacteristic, complemented
15D8×D79—21no—
16#14579167C2211yescharacteristic
17Dic632—21no—
18#14579106—21no—
19#14579105—22no—
20C2×C79⋊C16C2211yescharacteristic, complemented
21#14579079—21no—
22C2×D8×C79C2211yescharacteristic
23M32×C79C2211yescharacteristic, complemented
24#108×C79C2211yescharacteristic, complemented
25#11929624—21no—
26#11929624D411yescharacteristic
27#11929623—22no—
28#11929623—41no—
29C2×Dic158—21no—
30C2×C22⋊D79—42no—
31D4×D79—22no—
32D4×D79—41no—
33Dic316—21no—
34Dic316—21no—
35Dic316—41no—
36Dic316D411yescharacteristic
37#11929613—21no—
38#11929613—41no—
39#11929612—22no—
40D632D411yescharacteristic
41#11929609—22no—
42#11929608D411yescharacteristic
43#11929607—21no—
44C8×D79—21no—
45C79⋊C16—21no—
46C2×D4×C79—21no—
47D8×C79—21no—
48D8×C79D412yes—
49M16×C79—21no—
50C2×C8×C79C2311yescharacteristic
51C16×C79—21no—
52C23×C79—41no—
53C22×D79—42no—
54D4×C79—22no—
55D4×C79—41no—
56C2×C4×C79C2×D411yescharacteristic
57C22⋊D79—21no—
58C22⋊D79—42no—
59C22⋊D79—42no—
60C22⋊D79—41no—
61C2×Dic79—42no—
62C2×Dic79—41no—
63D316—21no—
64D316D811yescharacteristic
65C4×D79—21no—
66C4×D79—41no—
67Dic158—21no—
68Dic158—41no—
69Dic158—41no—
70Dic158D811yescharacteristic
71C8×C79—41no—
72C8×C79C2×D411yescharacteristic
73C8×C79C2×D411yescharacteristic
74C79⋊C8—21no—
75C22×C79—42no—
76C22×C79—161no—
77C22×C79AGL(1,ℤ/8)11yescharacteristic
78C2×D79—21no—
79C2×D79—41no—
80C2×D79—162no—
81C4×C79#12011yescharacteristic
82C4×C79C2×D811yescharacteristic
83Dic79—21no—
84Dic79—41no—
85Dic79—81no—
86C2×C79—21no—
87C2×C79—82no—
88C2×C79#44711yescharacteristic
89D79—41no—
90D79—81no—
91#2194—791nomaximal, Sylow
92C79#219411yescharacteristic, complemented, Sylow
93#576—791no—
94#510—791no—
95C2×SD32—791no—
96#473—791no—
97#361D7911yescharacteristic, complemented
98#359—791no—
99#350—791no—
100H(5,𝔽2)—1581no—
101#137—1581no—
102AGL(1,ℤ/8)—1581no—
103AGL(1,ℤ/8)—1582no—
104#135—791no—
105#135—1581no—
106C2×Q16—791no—
107C2×D8—1581no—
108C2×D8C2×D7911yescharacteristic
109#131—791no—
110Q32—1581no—
111SD32—1581no—
112SD32—1582no—
113M32C2×D7911yescharacteristic, complemented
114C2×C16—791no—
115#108C2×D7911yescharacteristic, complemented
116#101—1581no—
117#41—3161no—
118#41—791no—
119#41—1582no—
120#41—1581no—
121C2×Q8—1581no—
122C2×D4—21no—
123C2×D4—3161no—
124C2×D4—3162no—
125C2×D4—1582no—
126Q16—3161no—
127Q16—791no—
128Q16—1581no—
129Q16—1581no—
130SD16—3161no—
131SD16—1582no—
132SD16—1581no—
133D8—21no—
134D8—791no—
135D8—1582no—
136D8D31612yes—
137M16—21no—
138M16—791no—
139M16—1581no—
140C2×C8—1581no—
141C2×C8C22×D7911yescharacteristic
142C16—21no—
143C16—1581no—
144C23—41no—
145C23—3162no—
146Q8—3161no—
147Q8—3161no—
148Q8—791no—
149Q8—1581no—
150D4—22no—
151D4—41no—
152D4—3162no—
153D4—3161no—
154D4—3162no—
155D4—791no—
156D4—1581no—
157D4—1581no—
158C2×C4—3162no—
159C2×C4—3161no—
160C2×C4—3161no—
161C2×C4—1581no—
162C2×C4D4×D7911yescharacteristic
163C8—41no—
164C8—1581no—
165C8D4×D7911yescharacteristic
166C8C2×D31611yescharacteristic
167C22—42no—
168C22—161no—
169C22—3161no—
170C22—1581no—
171C22—12642no—
172C22#1457918811yescharacteristic
173C4—3161no—
174C4—6321no—
175C4—1581no—
176C4#1457913111yescharacteristic
177C4D8×D7911yescharacteristic
178C2—21no—
179C2—82no—
180C2—3161no—
181C2—6321no—
182C2#1909869811yescharacteristic
subgroupG/H
centerC2#19098698
commutator, cosocleC2×C8×C79C23
FrattiniC2×C8C22×D79
Fitting#361×C79C2
socleC2×C79#447
prime radical#19099364C2
hypercenter#361D79
hypocenterC79#2194
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
2. #19099006C2semidirect
3. C2×#14579105C2semidirect
4. #19098839C2semidirect
5. #19098369C2semidirect
6. #19098348C2semidirect
7. #361×C79C2semidirect
14. C2×Dic316C22semidirect
20. C2×C79⋊C16C22semidirect
23. M32×C79C22semidirect
24. #108×C79C22semidirect
92. C79#2194semidirect
97. #361D79semidirect
113. M32C2×D79semidirect
115. #108C2×D79semidirect