Finite Group Databasebeta

← #23773962

Subgroups — #23773962

Order 10112.

412 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 129 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#19099118C211yesmaximal, characteristic, complemented
2#19099114C211yesmaximal, characteristic
3#19098959C211yesmaximal, characteristic, complemented
4#19098937C211yesmaximal, characteristic, complemented
5#19098910C211yesmaximal, characteristic, complemented
6#19098795C214yesmaximal, complemented
7#19098648C214yesmaximal, complemented
8C4×C8×D79C211yesmaximal, characteristic, complemented
9#487×C79C211yesmaximal, characteristic, complemented
10C2×#11929625—21no—
11C2×#11929611C2214yes—
12C2×C8×D79C2212yes—
13#14579161C2211yescharacteristic
14#14579158C2211yescharacteristic
15#14579152—21no—
16#14579150—21no—
17#14579141—21no—
18#14579137C2212yes—
19#14579136—21no—
20#14579136C2212yes—
21Q8×Dic79C2212yes—
22#14579126—21no—
23#14579123—21no—
24#14579123C2212yes—
25#14579119—21no—
26C42×D79C2211yescharacteristic
27#14579092C2214yes—
28#14579083C2214yes—
29C4×C79⋊C8C2211yescharacteristic
30C8×Dic79C2212yes—
31C4⋊Q8×C79C2211yescharacteristic
32C4⋊Q8×C79C2211yescharacteristic
33#103×C79C2214yes—
34C4×C8×C79C2211yescharacteristic
35#11929625—44no—
36C2×Dic158—21no—
37C2×D316—22no—
38C2×D316—21no—
39C2×D316—21no—
40C2×D316C2312yes—
41C2×C4×D79—22no—
42C2×C4×D79D411yescharacteristic
43C2×C4×D79D411yescharacteristic
44C2×C4×D79C2311yescharacteristic
45#11929611—28no—
46C2×C79⋊C8C2312yes—
47C8×D79—24no—
48C4⋊Dic79—22no—
49C4⋊Dic79—21no—
50C4⋊Dic79C2312yes—
51Dic79⋊C4—22no—
52(C2×D79)⋊C4—22no—
53(C2×D79)⋊C4—22no—
54(C2×D79)⋊C4—22no—
55C4×Dic79—22no—
56C4×Dic79D411yescharacteristic
57C4×Dic79D411yescharacteristic
58C4×Dic79C2311yescharacteristic
59C2×Q8×C79—21no—
60C2×Q8×C79C2312yes—
61C2×C8×C79C2312yes—
62C4⋊C4×C79—21no—
63C4⋊C4×C79—21no—
64C4⋊C4×C79—21no—
65C4⋊C4×C79C2312yes—
66C42×C79C2311yescharacteristic
67C22×D79—22no—
68C22×D79C2×D411yescharacteristic
69Q8×C79—24no—
70Q8×C79—42no—
71C2×C4×C79—22no—
72C2×C4×C79—22no—
73C2×C4×C79C2×D411yescharacteristic
74C2×C4×C79C2×D411yescharacteristic
75C2×C4×C79C2411yescharacteristic
76C2×Dic79—22no—
77C2×Dic79C2×D411yescharacteristic
78C2×Dic79C2×D411yescharacteristic
79C2×Dic79C2×D411yescharacteristic
80D316—24no—
81D316—44no—
82D316—42no—
83D316—42no—
84C4×D79—22no—
85C4×D79—22no—
86C4×D79—44no—
87C4×D79SD1614yescomplemented
88Dic158—42no—
89C8×C79—22no—
90C79⋊C8#4114yescomplemented
91C22×C79C22×D411yescharacteristic
92C2×D79—21no—
93C2×D79—21no—
94C2×D79—42no—
95C2×D79—42no—
96C2×D79—42no—
97C2×D79C2×SD1612yes—
98C4×C79—42no—
99C4×C79—42no—
100C4×C79C2×SD1612yes—
101C4×C79#13512yes—
102C4×C79C2×#4112yes—
103Dic79—21no—
104Dic79—21no—
105Dic79—42no—
106Dic79C2×SD1612yes—
107C2×C79#53211yescharacteristic
108C2×C79C22×SD1611yescharacteristic
109C2×C79C2×#13511yescharacteristic
110D79—22no—
111D79—82no—
112#3167—791nomaximal, Sylow
113C79#316711yescharacteristic, complemented, Sylow
114#533—791no—
115#532—791no—
116#498—791no—
117#492—791no—
118#487D7911yescharacteristic, complemented
119#486—791no—
120#465—794no—
121C4×SD16—794no—
122C2×C4×C8—791no—
123C2×#41—1581no—
124C2×SD16—794no—
125C22×C8—792no—
126C4⋊Q8—791no—
127C4⋊Q8C2×D7911yescharacteristic
128C4⋊Q8C2×D7911yescharacteristic
129#127—791no—
130#125—1581no—
131#124—1581no—
132C22⋊Q8—792no—
133C22⋊Q8—1581no—
134#121—792no—
135#121—1581no—
136C4×Q8—792no—
137C4×Q8—1581no—
138C4×D4—792no—
139C4×D4—1581no—
140#117—1581no—
141C2×C42—791no—
142#106—794no—
143#103C2×D7914yes—
144#102—794no—
145C4×C8—792no—
146C4×C8—791no—
147C4×C8C2×D7911yescharacteristic
148#41—3164no—
149C2×Q8—21no—
150C2×Q8—1581no—
151C2×Q8C22×D7912yes—
152C2×D4—792no—
153C2×D4—1582no—
154C2×D4—1581no—
155C2×D4—1581no—
156C22×C4—791no—
157C22×C4—791no—
158C22×C4—791no—
159C22×C4—1582no—
160SD16—1588no—
161C2×C8—792no—
162C2×C8—1584no—
163C2×C8C22×D7912yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—792no—
168C4⋊C4—1582no—
169C4⋊C4—1582no—
170C4⋊C4—1581no—
171C4⋊C4C22×D7912yes—
172C22⋊C4—1582no—
173C22⋊C4—1582no—
174C22⋊C4—1582no—
175C42—791no—
176C42—791no—
177C42—791no—
178C42—1582no—
179C42C22×D7911yescharacteristic
180C23—791no—
181C23—1582no—
182Q8—24no—
183Q8—42no—
184Q8—3162no—
185D4—3164no—
186D4—3162no—
187D4—3162no—
188D4—1584no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—3164no—
192C2×C4—791no—
193C2×C4—794no—
194C2×C4—791no—
195C2×C4—791no—
196C2×C4—1582no—
197C2×C4—1582no—
198C2×C4—1582no—
199C2×C4D4×D7911yescharacteristic
200C2×C4D4×D7911yescharacteristic
201C2×C4C23×D7911yescharacteristic
202C8—22no—
203C8—794no—
204C22—3162no—
205C22—3162no—
206C22—3162no—
207C22—792no—
208C22—1581no—
209C22—1581no—
210C22C2×D4×D7911yescharacteristic
211C4—42no—
212C4—42no—
213C4—3162no—
214C4—792no—
215C4—1581no—
216C4—1581no—
217C4SD16×D7912yes—
218C4#1457918412yes—
219C4#41×D7912yes—
220C2—6322no—
221C2—1582no—
222C2#1909911211yescharacteristic
223C2C2×SD16×D7911yescharacteristic
224C2C2×#1457918411yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#487×C79C2
socleC22×C79C22×D4
prime radical#19099114C2
hypercenter#487D79
hypocenterC79#3167
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #19099118C2semidirect
3. #19098959C2semidirect
4. #19098937C2semidirect
5. #19098910C2semidirect
6. #19098795C2semidirect
7. #19098648C2semidirect
8. C4×C8×D79C2semidirect
9. #487×C79C2semidirect
87. C4×D79SD16semidirect
90. C79⋊C8#41semidirect
113. C79#3167semidirect
118. #487D79semidirect