Finite Group Databasebeta

← #23771689

Subgroups — #23771689

Order 10112.

1102 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C23×C4×D79C211yesmaximal, characteristic, complemented
2C2×#14579142C211yesmaximal, characteristic, complemented
3C2×#14579129C211yesmaximal, characteristic
4#19098439C214yesmaximal, complemented
5#19098434C214yesmaximal, complemented
6#19098426C211yesmaximal, characteristic, complemented
7#19098424C211yesmaximal, characteristic, complemented
8#19098418C211yesmaximal, characteristic, complemented
9C2×#123×C79C211yesmaximal, characteristic, complemented
10C24×D79C2211yescharacteristic
11C22×C22⋊D79C2212yes—
12C23×Dic79C2211yescharacteristic
13C22×C4×D79—24no—
14C22×C4×D79—24no—
15C22×C4×D79—24no—
16C22×C4×D79C2214yes—
17#14579142—24no—
18#14579129—24no—
19C2×Dic79⋊C4C2212yescomplemented
20C2×C22⋊Dic79C2211yescharacteristic
21C2×C22⋊Dic79C2211yescharacteristic
22C2×C22⋊Dic79C2212yescomplemented
23C2×(C2×D79)⋊C4C2214yes—
24C2×(C2×D79)⋊C4C2212yes—
25C79⋊#95C2214yescomplemented
26C79⋊#95C2214yescomplemented
27C22×D4×C79C2211yescharacteristic
28C23×C4×C79C2211yescharacteristic
29#123×C79—24no—
30C2×C4⋊C4×C79C2212yescomplemented
31C2×C22⋊C4×C79C2211yescharacteristic
32C2×C22⋊C4×C79C2212yescomplemented
33C23×D79—22no—
34C23×D79—22no—
35C23×D79—28no—
36C23×D79D414yes—
37C23×D79C2312yes—
38C2×C22⋊D79—24no—
39C2×C22⋊D79—28no—
40C22×Dic79—22no—
41C22×Dic79—22no—
42C22×Dic79D414yescomplemented
43C22×Dic79C2312yes—
44C22×Dic79C2312yes—
45C22×Dic79C2312yes—
46C2×C4×D79—232no—
47C2×C4×D79—28no—
48C2×C4×D79—28no—
49C2×C4×D79—28no—
50Dic79⋊C4—24no—
51C22⋊Dic79—24no—
52C22⋊Dic79—22no—
53C22⋊Dic79—22no—
54(C2×D79)⋊C4—24no—
55(C2×D79)⋊C4—28no—
56C24×C79C2311yescharacteristic
57C24×C79C2311yescharacteristic
58C2×D4×C79—22no—
59C2×D4×C79—22no—
60C2×D4×C79—22no—
61C22×C4×C79—22no—
62C22×C4×C79—22no—
63C22×C4×C79D414yescomplemented
64C22×C4×C79C2312yes—
65C22×C4×C79C2311yescharacteristic
66C22×C4×C79C2312yes—
67C4⋊C4×C79—24no—
68C22⋊C4×C79—22no—
69C22⋊C4×C79—24no—
70C23×C79—24no—
71C23×C79—21no—
72C23×C79—21no—
73C23×C79—21no—
74C23×C79—24no—
75C23×C79C2×D412yes—
76C23×C79C2×D412yes—
77C23×C79C2×D412yes—
78C23×C79C2411yescharacteristic
79C22×D79—216no—
80C22×D79—216no—
81C22×D79—28no—
82C22×D79—22no—
83C22×D79—22no—
84C22×D79—24no—
85C22×D79—216no—
86C22×D79C2×D414yes—
87C22×D79#4118yes—
88D4×C79—44no—
89C2×C4×C79—28no—
90C2×C4×C79—22no—
91C2×C4×C79—22no—
92C2×C4×C79—21no—
93C2×C4×C79—21no—
94C2×C4×C79—22no—
95C2×C4×C79—21no—
96C2×C4×C79—24no—
97C2×C4×C79C2×D414yes—
98C22⋊D79—48no—
99C2×Dic79—28no—
100C2×Dic79—22no—
101C2×Dic79—22no—
102C2×Dic79—22no—
103C2×Dic79—22no—
104C2×Dic79—24no—
105C2×Dic79—24no—
106C2×Dic79C2×D414yes—
107C4×D79—232no—
108C22×C79—24no—
109C22×C79—24no—
110C22×C79—24no—
111C22×C79—41no—
112C22×C79—42no—
113C22×C79—42no—
114C22×C79—42no—
115C22×C79#12014yes—
116C22×C79C22×D411yescharacteristic
117C22×C79C22×D411yescharacteristic
118C22×C79C22×D411yescharacteristic
119C22×C79C2×#4114yes—
120C2×D79—232no—
121C2×D79—24no—
122C2×D79—24no—
123C2×D79—28no—
124C2×D79—28no—
125C2×D79#12318yescomplemented
126C4×C79—24no—
127C4×C79—41no—
128C4×C79—42no—
129Dic79—24no—
130Dic79—42no—
131Dic79—42no—
132C2×C79—24no—
133C2×C79—81no—
134C2×C79C2×#12011yescharacteristic
135C2×C79C2×#12312yes—
136C2×C79#52512yes—
137C2×C79#52512yes—
138D79—28no—
139#2849—791nomaximal, Sylow
140C79#284911yescharacteristic, complemented, Sylow
141C24×C4—791no—
142C2×#123—791no—
143C2×#123D7911yescharacteristic, complemented
144C2×#120—791no—
145#386—794no—
146#385—794no—
147#381—791no—
148#381—791no—
149#379—791no—
150C25—791no—
151C22×D4—792no—
152C22×D4C2×D7911yescharacteristic
153C23×C4—791no—
154C23×C4—794no—
155C23×C4—1584no—
156C23×C4—1584no—
157C23×C4—1584no—
158C23×C4C2×D7911yescharacteristic
159#123—24no—
160#123—1584no—
161#120—1584no—
162C2×C4⋊C4—792no—
163C2×C4⋊C4C2×D7912yescomplemented
164C2×C22⋊C4—791no—
165C2×C22⋊C4—791no—
166C2×C22⋊C4—792no—
167C2×C22⋊C4—792no—
168C2×C22⋊C4—794no—
169C2×C22⋊C4C2×D7911yescharacteristic
170C2×C22⋊C4C2×D7912yescomplemented
171#95—794no—
172#95—794no—
173C24—792no—
174C24—794no—
175C24—1588no—
176C24—1582no—
177C24—1582no—
178C24C22×D7911yescharacteristic
179C24C22×D7911yescharacteristic
180C2×D4—22no—
181C2×D4—22no—
182C2×D4—22no—
183C2×D4—1584no—
184C2×D4—1588no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—794no—
188C22×C4—792no—
189C22×C4—792no—
190C22×C4—792no—
191C22×C4—1588no—
192C22×C4—1588no—
193C22×C4—15832no—
194C22×C4—1582no—
195C22×C4—1582no—
196C22×C4—1588no—
197C22×C4C22⋊D7914yescomplemented
198C22×C4C22×D7912yes—
199C22×C4C22×D7911yescharacteristic
200C22×C4C22×D7912yes—
201C4⋊C4—24no—
202C4⋊C4—1584no—
203C22⋊C4—22no—
204C22⋊C4—24no—
205C22⋊C4—1588no—
206C22⋊C4—1584no—
207C22⋊C4—1584no—
208C22⋊C4—1582no—
209C22⋊C4—1582no—
210C23—24no—
211C23—24no—
212C23—21no—
213C23—21no—
214C23—21no—
215C23—798no—
216C23—794no—
217C23—15816no—
218C23—15816no—
219C23—15816no—
220C23—1584no—
221C23—1588no—
222C23—1582no—
223C23—1582no—
224C23D4×D7912yes—
225C23D4×D7912yes—
226C23C2×C22⋊D7912yes—
227C23C23×D7911yescharacteristic
228D4—44no—
229D4—3168no—
230C2×C4—28no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—24no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—794no—
239C2×C4—15832no—
240C2×C4—1584no—
241C2×C4—1584no—
242C2×C4—1582no—
243C2×C4—1582no—
244C2×C4—1588no—
245C2×C4—1582no—
246C2×C4—1582no—
247C2×C4C2×C22⋊D7914yes—
248C22—24no—
249C22—24no—
250C22—24no—
251C22—41no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—798no—
256C22—15832no—
257C22—1584no—
258C22—1584no—
259C22—1588no—
260C22—1588no—
261C22#1457912914yes—
262C22C2×D4×D7911yescharacteristic
263C22C2×D4×D7911yescharacteristic
264C22C22×C22⋊D7911yescharacteristic
265C22#41×D7914yes—
266C4—24no—
267C4—41no—
268C4—42no—
269C4—3162no—
270C4—3162no—
271C4—1584no—
272C2—24no—
273C2—81no—
274C2—1588no—
275C2C2×#1457912911yescharacteristic
276C2#123×D7912yes—
277C2#1909907012yes—
278C2#1909907112yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
FittingC2×#123×C79C2
prime radicalC2×#14579129C2
hypercenterC2×#123D79
hypocenterC79#2849
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C23×C4×D79C2semidirect
2. C2×#14579142C2semidirect
4. #19098439C2semidirect
5. #19098434C2semidirect
6. #19098426C2semidirect
7. #19098424C2semidirect
8. #19098418C2semidirect
9. C2×#123×C79C2semidirect
19. C2×Dic79⋊C4C22semidirect
22. C2×C22⋊Dic79C22semidirect
25. C79⋊#95C22semidirect
26. C79⋊#95C22semidirect
30. C2×C4⋊C4×C79C22semidirect
32. C2×C22⋊C4×C79C22semidirect
42. C22×Dic79D4semidirect
63. C22×C4×C79D4semidirect
125. C2×D79#123semidirect
140. C79#2849semidirect
143. C2×#123D79semidirect
163. C2×C4⋊C4C2×D79semidirect
170. C2×C22⋊C4C2×D79semidirect
197. C22×C4C22⋊D79semidirect