Finite Group Databasebeta

← #23765052

Subgroups — #23765052

Order 10112.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#19099135C211yesmaximal, characteristic
2#19098544C211yesmaximal, characteristic
3#19098535C211yesmaximal, characteristic
4#19098354C211yesmaximal, characteristic, complemented
5#19098353C211yesmaximal, characteristic, complemented
6#19098352C211yesmaximal, characteristic, complemented
7#352×C79C211yesmaximal, characteristic, complemented
8C2×#11929623C2211yescharacteristic
9C22×Dic158C411yescharacteristic, complemented
10M16×D79—21no—
11#14579160—21no—
12#14579147—21no—
13#14579145C411yescharacteristic, complemented
14#14579144C411yescharacteristic, complemented
15#14579142C2211yescharacteristic
16#14579139—21no—
17#14579138—21no—
18#14579117—21no—
19#14579117C411yescharacteristic, complemented
20#14579079—21no—
21#14579078C2211yescharacteristic
22#14579076C2211yescharacteristic
23#14579075—21no—
24#123×C79C2211yescharacteristic
25#100×C79C2211yescharacteristic
26#99×C79C2211yescharacteristic
27#11929623—41no—
28#11929623—41no—
29C2×Dic158—21no—
30C2×Dic158—21no—
31C2×Dic158—41no—
32C2×Dic158—41no—
33C2×Dic158D411yescharacteristic
34C2×C22⋊D79C2×C411yescharacteristic
35C2×C22⋊D79D411yescharacteristic
36C22×Dic79C2×C411yescharacteristic
37C22×Dic79C2×C411yescharacteristic
38C22×Dic79D411yescharacteristic
39C2×C4×D79D411yescharacteristic
40#11929608—21no—
41#11929607—41no—
42C8×D79—41no—
43C4⋊Dic79—21no—
44Dic79⋊C4—21no—
45Dic79⋊C4—21no—
46Dic79⋊C4—21no—
47Dic79⋊C4—41no—
48C22⋊Dic79—21no—
49C22⋊Dic79—21no—
50C22⋊Dic79C2×C411yescharacteristic
51(C2×D79)⋊C4—21no—
52(C2×D79)⋊C4—21no—
53C4×Dic79—21no—
54C4×Dic79—41no—
55C2×D4×C79C2311yescharacteristic
56C22×C4×C79C2×C411yescharacteristic
57M16×C79—21no—
58C4⋊C4×C79—21no—
59C22⋊C4×C79—21no—
60C22⋊C4×C79—21no—
61C22⋊C4×C79C2×C411yescharacteristic
62C23×C79C22×C411yescharacteristic
63C23×C79C2×D411yescharacteristic
64C22×D79C22⋊C411yescharacteristic
65D4×C79—41no—
66C2×C4×C79—21no—
67C2×C4×C79—21no—
68C2×C4×C79—41no—
69C2×C4×C79—41no—
70C2×C4×C79C2×D411yescharacteristic
71C22⋊D79—41no—
72C22⋊D79—41no—
73C2×Dic79—21no—
74C2×Dic79—21no—
75C2×Dic79—21no—
76C2×Dic79—21no—
77C2×Dic79—21no—
78C2×Dic79—21no—
79C2×Dic79—41no—
80C2×Dic79—41no—
81C2×Dic79C22⋊C411yescharacteristic
82C2×Dic79C22⋊C411yescharacteristic
83C2×Dic79C22⋊C411yescharacteristic
84C4×D79—21no—
85C4×D79—21no—
86Dic158—41no—
87Dic158—42no—
88Dic158—41no—
89Dic158—41no—
90C8×C79—41no—
91C79⋊C8—41no—
92C22×C79—21no—
93C22×C79—21no—
94C22×C79—41no—
95C22×C79—41no—
96C22×C79C2×C22⋊C411yescharacteristic
97C2×D79—21no—
98C2×D79—41no—
99C4×C79—21no—
100C4×C79—41no—
101C4×C79—41no—
102C4×C79—81no—
103Dic79—21no—
104Dic79—21no—
105Dic79—41no—
106Dic79—41no—
107Dic79—81no—
108Dic79#9911yescharacteristic
109Dic79#9911yescharacteristic
110C2×C79—21no—
111C2×C79—41no—
112C2×C79—41no—
113C2×C79C2×#9911yescharacteristic
114D79—41no—
115#2123—791nomaximal, Sylow
116C79#212311yescharacteristic, complemented, Sylow
117#536—791no—
118#413—791no—
119#410—791no—
120#352—791no—
121#352—791no—
122#352—791no—
123#352D7911yescharacteristic, complemented
124C2×#41—791no—
125C22×Q8—791no—
126C2×M16—1581no—
127C4⋊Q8—1581no—
128#124—1581no—
129#123—791no—
130#123—791no—
131#123—791no—
132#123C2×D7911yescharacteristic
133C22⋊Q8—1581no—
134C22⋊Q8—1581no—
135#117—791no—
136#117—1581no—
137#101—1581no—
138#100—791no—
139#100C2×D7911yescharacteristic
140#99—791no—
141#99—1581no—
142#99C2×D7911yescharacteristic
143#41—3161no—
144#41—3161no—
145C2×Q8—3161no—
146C2×Q8—3161no—
147C2×Q8—791no—
148C2×Q8—1581no—
149C2×Q8—1581no—
150C2×D4—791no—
151C2×D4—791no—
152C2×D4C22×D7911yescharacteristic
153C22×C4—791no—
154C22×C4—791no—
155C22×C4—791no—
156C22×C4—791no—
157C22×C4C4×D7911yescharacteristic
158M16—21no—
159M16—3161no—
160M16—1581no—
161C2×C8—3161no—
162C4⋊C4—21no—
163C4⋊C4—3161no—
164C4⋊C4—1581no—
165C4⋊C4—1581no—
166C4⋊C4—1581no—
167C4⋊C4—1581no—
168C22⋊C4—21no—
169C22⋊C4—21no—
170C22⋊C4—791no—
171C22⋊C4—1581no—
172C22⋊C4—1581no—
173C22⋊C4—1581no—
174C22⋊C4—1581no—
175C22⋊C4C4×D7911yescharacteristic
176C42—3161no—
177C42—1581no—
178C23—791no—
179C23C2×C4×D7911yescharacteristic
180C23D4×D7911yescharacteristic
181Q8—3161no—
182Q8—3161no—
183Q8—3161no—
184Q8—3162no—
185D4—41no—
186D4—3161no—
187D4—3161no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—3161no—
193C2×C4—3161no—
194C2×C4—791no—
195C2×C4—791no—
196C2×C4—791no—
197C2×C4—1581no—
198C2×C4—1581no—
199C2×C4—1581no—
200C2×C4—1581no—
201C2×C4—1581no—
202C2×C4—1581no—
203C2×C4—1581no—
204C2×C4—1581no—
205C2×C4D4×D7911yescharacteristic
206C8—41no—
207C8—3161no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—3161no—
213C22—1581no—
214C22C22⋊C4×D7911yescharacteristic
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—3161no—
220C4—3161no—
221C4—791no—
222C4—791no—
223C4—6321no—
224C4—1581no—
225C4—1581no—
226C2—21no—
227C2—41no—
228C2—41no—
229C2—3161no—
230C2#99×D7911yescharacteristic
subgroupG/H
centerC2#99×D79
commutatorC23×C79C22×C4
FrattiniC2×D4C22×D79
Fitting#352×C79C2
socleC2×C79C2×#99
prime radicalC2×#11929623C22
cosocleC2×D4×C79C23
hypercenter#352D79
hypocenterC79#2123
LCSG ▷ C23×C79 ▷ C22×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
4. #19098354C2semidirect
5. #19098353C2semidirect
6. #19098352C2semidirect
7. #352×C79C2semidirect
9. C22×Dic158C4semidirect
13. #14579145C4semidirect
14. #14579144C4semidirect
19. #14579117C4semidirect
116. C79#2123semidirect
123. #352D79semidirect