Finite Group Databasebeta

← #23774486

Subgroups — #23774486

Order 10112.

364 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 109 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#19099176C211yesmaximal, characteristic, complemented
2#19099133C211yesmaximal, characteristic
3#19098958C211yesmaximal, characteristic, complemented
4#19098943C211yesmaximal, characteristic, complemented
5#19098933C211yesmaximal, characteristic, complemented
6#19098784C212yesmaximal, complemented
7#19098772C212yesmaximal, complemented
8#19098726C212yesmaximal
9#19098720C212yesmaximal, complemented
10#19098622C211yesmaximal, characteristic, complemented
11#488×C79C211yesmaximal, characteristic, complemented
12C2×#11929623C2211yescharacteristic
13C2×Q8×D79C2211yescharacteristic
14C2×Dic316C2212yes—
15C2×Dic316C2212yes—
16C2×#11929614C2212yes—
17C2×#11929612C2212yes—
18#14579161C2211yescharacteristic
19#14579161C2211yescharacteristic
20#14579159C2211yescharacteristic
21#14579156—22no—
22#14579152—22no—
23#14579148C2211yescharacteristic
24#14579143—22no—
25#14579141C2212yes—
26#14579138—22no—
27#14579126C2212yes—
28#14579118C2211yescharacteristic
29Dic79⋊C8C2212yes—
30#14579084C2212yes—
31#14579084C2212yes—
32(C2×D79)⋊C8C2212yes—
33#14579072C2211yescharacteristic
34#125×C79C2211yescharacteristic
35#124×C79C2211yescharacteristic
36#103×C79C2212yes—
37#102×C79C2212yes—
38C4×C8×C79C2211yescharacteristic
39#11929623—42no—
40C2×Dic158—21no—
41C2×Dic158C2311yescharacteristic
42C2×Dic158C2311yescharacteristic
43C2×Dic158C2312yes—
44Q8×D79—42no—
45C2×C22⋊D79—21no—
46C22×Dic79—21no—
47C2×C4×D79—21no—
48C2×C4×D79C2311yescharacteristic
49Dic316—42no—
50Dic316—42no—
51#11929614—42no—
52#11929612—42no—
53C2×C79⋊C8C2312yes—
54C4⋊Dic79—22no—
55C4⋊Dic79—22no—
56C4⋊Dic79—22no—
57Dic79⋊C4—22no—
58Dic79⋊C4—22no—
59Dic79⋊C4D412yes—
60C22⋊Dic79—22no—
61(C2×D79)⋊C4—22no—
62(C2×D79)⋊C4D412yes—
63C4×Dic79—22no—
64C4×Dic79C2311yescharacteristic
65C2×Q8×C79C2311yescharacteristic
66C2×D4×C79C2311yescharacteristic
67C2×C8×C79C2312yes—
68C4⋊C4×C79—22no—
69C4⋊C4×C79C2312yes—
70C22⋊C4×C79—22no—
71C42×C79C2311yescharacteristic
72C23×C79—21no—
73C22×D79C2×D411yescharacteristic
74Q8×C79—22no—
75D4×C79—22no—
76C2×C4×C79—22no—
77C2×C4×C79—21no—
78C2×C4×C79C2×D412yes—
79C2×C4×C79C2411yescharacteristic
80C22⋊D79—42no—
81C2×Dic79—22no—
82C2×Dic79—21no—
83C2×Dic79—21no—
84C2×Dic79—42no—
85C2×Dic79C2×D412yes—
86C2×Dic79C2×D411yescharacteristic
87C4×D79—22no—
88C4×D79—42no—
89Dic158—22no—
90Dic158—22no—
91Dic158—22no—
92Dic158—22no—
93Dic158—42no—
94C8×C79—22no—
95C79⋊C8—22no—
96C22×C79—41no—
97C22×C79—42no—
98C22×C79C22×D411yescharacteristic
99C2×D79—21no—
100C2×D79—22no—
101C4×C79—22no—
102C4×C79—41no—
103C4×C79—42no—
104C4×C79H(5,𝔽2)12yes—
105Dic79—21no—
106Dic79—22no—
107Dic79—41no—
108Dic79—41no—
109Dic79—42no—
110C2×C79—81no—
111C2×C79#53511yescharacteristic
112C2×C79#57812yes—
113D79—41no—
114#3223—791nomaximal, Sylow
115C79#322311yescharacteristic, complemented, Sylow
116#541—791no—
117#536—791no—
118#497—791no—
119#494—791no—
120#491—791no—
121#488D7911yescharacteristic, complemented
122#464—792no—
123#462—792no—
124#452—792no—
125#451—792no—
126#433—791no—
127C2×#41—791no—
128C22×Q8—791no—
129C2×Q16—792no—
130C2×Q16—792no—
131C2×Q16—792no—
132C2×SD16—792no—
133C4⋊Q8—791no—
134C4⋊Q8—791no—
135C4⋊Q8—791no—
136#126—1582no—
137#125—1582no—
138#125C2×D7911yescharacteristic
139#124—791no—
140#124C2×D7911yescharacteristic
141#123—1582no—
142C22⋊Q8—792no—
143C22⋊Q8—1582no—
144C4×Q8—792no—
145#117—791no—
146C4⋊C8—792no—
147#103—792no—
148#103—792no—
149#103C2×D7912yes—
150#102C2×D7912yes—
151C22⋊C8—792no—
152#97—791no—
153C4×C8C2×D7911yescharacteristic
154#41—3162no—
155C2×Q8—3162no—
156C2×Q8—791no—
157C2×Q8—791no—
158C2×Q8—792no—
159C2×Q8—1581no—
160C2×Q8C22×D7911yescharacteristic
161C2×D4—1581no—
162C2×D4C22×D7911yescharacteristic
163C22×C4—791no—
164C22×C4—1581no—
165C22×C4—1581no—
166Q16—3162no—
167Q16—3162no—
168Q16—3162no—
169SD16—3162no—
170C2×C8—792no—
171C2×C8C22×D7912yes—
172C4⋊C4—22no—
173C4⋊C4—792no—
174C4⋊C4—1582no—
175C4⋊C4—1582no—
176C4⋊C4—1582no—
177C4⋊C4—1582no—
178C4⋊C4—1582no—
179C4⋊C4C22×D7912yes—
180C22⋊C4—22no—
181C22⋊C4—792no—
182C22⋊C4—1582no—
183C22⋊C4—1582no—
184C42—791no—
185C42—1582no—
186C42C22×D7911yescharacteristic
187C23—21no—
188C23—791no—
189Q8—22no—
190Q8—3162no—
191Q8—1582no—
192Q8—1582no—
193Q8—1582no—
194Q8—1582no—
195D4—22no—
196D4—3162no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—3162no—
200C2×C4—3162no—
201C2×C4—792no—
202C2×C4—791no—
203C2×C4—1582no—
204C2×C4—1581no—
205C2×C4—1581no—
206C2×C4—1582no—
207C2×C4D4×D7912yes—
208C2×C4C23×D7911yescharacteristic
209C8—22no—
210C8—1582no—
211C22—42no—
212C22—41no—
213C22—1582no—
214C22—1581no—
215C22C2×D4×D7911yescharacteristic
216C4—22no—
217C4—42no—
218C4—41no—
219C4—3161no—
220C4—3161no—
221C4—3162no—
222C4—1582no—
223C4—1581no—
224C4#1457920712yes—
225C2—81no—
226C2—3161no—
227C2#1909913111yescharacteristic
228C2#1909937712yes—
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#488×C79C2
socleC22×C79C22×D4
prime radicalC2×#11929623C22
hypercenter#488D79
hypocenterC79#3223
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #19099176C2semidirect
3. #19098958C2semidirect
4. #19098943C2semidirect
5. #19098933C2semidirect
6. #19098784C2semidirect
7. #19098772C2semidirect
9. #19098720C2semidirect
10. #19098622C2semidirect
11. #488×C79C2semidirect
115. C79#3223semidirect
121. #488D79semidirect