Finite Group Databasebeta

← #23761936

Subgroups — #23761936

Order 10112.

222 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 69 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#19099097C211yesmaximal, characteristic
2#19098620C211yesmaximal, characteristic, complemented
3#19098299C212yesmaximal, complemented
4#19098296C212yesmaximal
5#382×C79C211yesmaximal, characteristic, complemented
6#14579155—21no—
7#14579153C411yescharacteristic, complemented
8#14579149C411yescharacteristic, complemented
9#14579144—21no—
10#14579140C2211yescharacteristic
11#14579135C2211yescharacteristic
12C4×Dic158C411yescharacteristic, complemented
13C4×D316C411yescharacteristic, complemented
14C4×C22⋊D79—21no—
15#14579118—21no—
16C4⋊(C79⋊C8)—21no—
17C22⋊(C79⋊C8)C2212yes—
18#14579072—21no—
19C2×C4⋊C4×C79—21no—
20C2×C42×C79C2211yescharacteristic
21#95×C79—21no—
22#95×C79C2212yes—
23C2×Dic158C2×C411yescharacteristic
24C2×D316C2×C411yescharacteristic
25C2×C22⋊D79—21no—
26C2×C4×D79—21no—
27C2×C79⋊C8—22no—
28C4⋊Dic79C2×C411yescharacteristic
29C4⋊Dic79C2×C411yescharacteristic
30Dic79⋊C4—21no—
31Dic79⋊C4—21no—
32Dic79⋊C4—21no—
33Dic79⋊C4—21no—
34C22⋊Dic79—21no—
35(C2×D79)⋊C4—21no—
36(C2×D79)⋊C4—21no—
37(C2×D79)⋊C4—21no—
38(C2×D79)⋊C4—21no—
39C4×Dic79—21no—
40C22×C4×C79—22no—
41C22×C4×C79D411yescharacteristic
42C22×C4×C79D411yescharacteristic
43C22×C4×C79C2311yescharacteristic
44C4⋊C4×C79—42no—
45C42×C79C2×C411yescharacteristic
46C42×C79C2×C411yescharacteristic
47C42×C79D411yescharacteristic
48C42×C79D411yescharacteristic
49C23×C79C2×D411yescharacteristic
50C22×D79—21no—
51C2×C4×C79—21no—
52C2×C4×C79—21no—
53C2×C4×C79—41no—
54C2×C4×C79—41no—
55C2×C4×C79—42no—
56C2×C4×C79—42no—
57C2×C4×C79—42no—
58C2×C4×C79C22⋊C411yescharacteristic
59C2×C4×C79C22⋊C411yescharacteristic
60C2×C4×C79C22⋊C411yescharacteristic
61C2×C4×C79C22⋊C411yescharacteristic
62C2×C4×C79C22×C411yescharacteristic
63C2×C4×C79C2×D411yescharacteristic
64C22⋊D79—41no—
65C22⋊D79—41no—
66C2×Dic79—21no—
67C2×Dic79—21no—
68C2×Dic79—21no—
69D316—41no—
70C4×D79—42no—
71Dic158—41no—
72C79⋊C8—42no—
73C22×C79—21no—
74C22×C79—21no—
75C22×C79C2×C22⋊C411yescharacteristic
76C22×C79AGL(1,ℤ/8)11yescharacteristic
77C22×C79#13711yescharacteristic
78C2×D79—41no—
79C2×D79—41no—
80C2×D79—41no—
81C4×C79—21no—
82C4×C79—21no—
83C4×C79—21no—
84C4×C79—21no—
85C4×C79—21no—
86C4×C79—21no—
87C4×C79—82no—
88Dic79—41no—
89Dic79—41no—
90Dic79—41no—
91C2×C79—21no—
92C2×C79—21no—
93C2×C79#41011yescharacteristic
94C2×C79#41711yescharacteristic
95C2×C79#42111yescharacteristic
96D79—81no—
97#1512—791nomaximal, Sylow
98C79#151211yescharacteristic, complemented, Sylow
99#529—791no—
100#432—791no—
101#382D7911yescharacteristic, complemented
102#328—792no—
103#327—792no—
104#126—1581no—
105#125—791no—
106#124—791no—
107#123—1581no—
108C22⋊Q8—791no—
109#121—791no—
110C4×Q8—791no—
111C4×D4—791no—
112C4×D4—1581no—
113#117—1581no—
114C2×C4⋊C4—21no—
115C2×C42C2×D7911yescharacteristic
116C4⋊C8—1581no—
117C22⋊C8—792no—
118#97—1581no—
119#95—21no—
120#95C2×D7912yes—
121C2×Q8—791no—
122C2×D4—791no—
123C2×D4—1581no—
124C22×C4—22no—
125C22×C4—1581no—
126C22×C4C22⋊D7911yescharacteristic
127C22×C4C22⋊D7911yescharacteristic
128C22×C4C22×D7911yescharacteristic
129C2×C8—1582no—
130C4⋊C4—42no—
131C4⋊C4—791no—
132C4⋊C4—791no—
133C4⋊C4—1581no—
134C4⋊C4—1581no—
135C4⋊C4—1581no—
136C4⋊C4—1581no—
137C22⋊C4—1581no—
138C22⋊C4—1581no—
139C22⋊C4—1581no—
140C22⋊C4—1581no—
141C22⋊C4—1581no—
142C42—1581no—
143C42C4×D7911yescharacteristic
144C42C4×D7911yescharacteristic
145C42D31611yescharacteristic
146C42D31611yescharacteristic
147C23—1581no—
148C23C2×C22⋊D7911yescharacteristic
149Q8—3161no—
150D4—3161no—
151D4—3161no—
152D4—3161no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—42no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—3162no—
161C2×C4—1581no—
162C2×C4—1581no—
163C2×C4—1581no—
164C2×C4(C2×D79)⋊C411yescharacteristic
165C2×C4(C2×D79)⋊C411yescharacteristic
166C2×C4(C2×D79)⋊C411yescharacteristic
167C2×C4(C2×D79)⋊C411yescharacteristic
168C2×C4C2×C4×D7911yescharacteristic
169C2×C4C2×D31611yescharacteristic
170C8—3162no—
171C22—21no—
172C22—21no—
173C22—3161no—
174C22—3161no—
175C22—3161no—
176C22C2×(C2×D79)⋊C411yescharacteristic
177C22#1457918711yescharacteristic
178C22#1457919211yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—82no—
186C4—3161no—
187C4—3161no—
188C4—3161no—
189C2—21no—
190C2—21no—
191C2—6321no—
192C2#1909853611yescharacteristic
193C2#1909856211yescharacteristic
194C2#1909858111yescharacteristic
subgroupG/H
centerC22C2×(C2×D79)⋊C4
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
Fitting#382×C79C2
socleC22×C79C2×C22⋊C4
prime radical#14579135C22
cosocleC22×C4×C79C23
hypercenter#382D79
hypocenterC79#1512
LCSG ▷ C2×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #19098620C2semidirect
3. #19098299C2semidirect
5. #382×C79C2semidirect
7. #14579153C4semidirect
8. #14579149C4semidirect
12. C4×Dic158C4semidirect
13. C4×D316C4semidirect
98. C79#1512semidirect
101. #382D79semidirect