Finite Group Databasebeta

← #23773319

Subgroups — #23773319

Order 10112.

458 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 123 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#19099073C211yesmaximal, characteristic
2C2×C4⋊C4×D79C211yesmaximal, characteristic, complemented
3#19098900C212yesmaximal, complemented
4#19098894C211yesmaximal, characteristic, complemented
5#19098893C211yesmaximal, characteristic, complemented
6#19098880C212yesmaximal, complemented
7#19098874C211yesmaximal, characteristic, complemented
8#19098604C212yesmaximal, complemented
9#19098561C212yesmaximal, complemented
10#19098525C211yesmaximal, characteristic, complemented
11#480×C79C211yesmaximal, characteristic, complemented
12C2×#11929623C2211yescharacteristic
13C22×C4×D79—21no—
14C22×C4×D79C2211yescharacteristic
15C2×#11929607C2212yes—
16#14579143—21no—
17#14579141C2211yescharacteristic
18#14579140C2211yescharacteristic
19#14579132C2211yescharacteristic
20#14579129—21no—
21D4×Dic79—21no—
22(C22⋊D79)⋊C4—21no—
23#14579119C2211yescharacteristic
24C2×C4⋊Dic79C2211yescharacteristic
25C2×Dic79⋊C4—21no—
26C4⋊C4×D79—21no—
27C4⋊C4×D79—21no—
28C4⋊C4×D79C2212yes—
29C4⋊C4×D79C2212yes—
30#14579094C2212yescomplemented
31#14579093C2212yescomplemented
32#14579092C2212yescomplemented
33#14579086C2212yescomplemented
34#14579084C2212yescomplemented
35#14579082C2212yescomplemented
36C22⋊(C79⋊C8)C2211yescharacteristic
37(C2×D79)⋊C8C2212yes—
38#121×C79C2211yescharacteristic
39C2×C4⋊C4×C79C2211yescharacteristic
40#107×C79C2212yescomplemented
41#102×C79C2212yescomplemented
42C22⋊C8×C79C2211yescharacteristic
43C23×D79D411yescharacteristic
44#11929623—24no—
45C2×Dic158C2311yescharacteristic
46C2×C22⋊D79—21no—
47C2×C22⋊D79—21no—
48C22×Dic79—21no—
49C22×Dic79—21no—
50C22×Dic79D411yescharacteristic
51C2×C4×D79—24no—
52C2×C4×D79—22no—
53C2×C4×D79—22no—
54C2×C4×D79—44no—
55C2×C4×D79D411yescharacteristic
56C2×C4×D79D411yescharacteristic
57C2×C4×D79C2311yescharacteristic
58C2×C4×D79C2311yescharacteristic
59#11929607—24no—
60C2×C79⋊C8C2312yes—
61C4⋊Dic79—21no—
62C4⋊Dic79—21no—
63C4⋊Dic79C2312yes—
64C4⋊Dic79C2311yescharacteristic
65Dic79⋊C4—22no—
66Dic79⋊C4—22no—
67Dic79⋊C4—21no—
68C22⋊Dic79—21no—
69C22⋊Dic79—21no—
70(C2×D79)⋊C4—21no—
71(C2×D79)⋊C4—21no—
72C4×Dic79—21no—
73C2×D4×C79—21no—
74C2×D4×C79C2311yescharacteristic
75C22×C4×C79—21no—
76C22×C4×C79C2311yescharacteristic
77C2×C8×C79C2312yes—
78C4⋊C4×C79—21no—
79C4⋊C4×C79C2312yes—
80C4⋊C4×C79C2311yescharacteristic
81C22⋊C4×C79—21no—
82C23×C79—21no—
83C23×C79C2×D411yescharacteristic
84C22×D79—22no—
85C22×D79—22no—
86C22×D79—22no—
87C22×D79C2×D411yescharacteristic
88C22×D79C2×D411yescharacteristic
89D4×C79—22no—
90D4×C79—42no—
91C2×C4×C79—22no—
92C2×C4×C79—21no—
93C2×C4×C79—22no—
94C2×C4×C79—42no—
95C2×C4×C79C2×D411yescharacteristic
96C2×C4×C79C2411yescharacteristic
97C22⋊D79—42no—
98C22⋊D79—42no—
99C2×Dic79—22no—
100C2×Dic79—21no—
101C2×Dic79—21no—
102C2×Dic79—22no—
103C2×Dic79—42no—
104C2×Dic79—42no—
105C2×Dic79C2×D411yescharacteristic
106C2×Dic79C2×D411yescharacteristic
107C4×D79—22no—
108C4×D79—22no—
109C4×D79—22no—
110C4×D79—44no—
111C4×D79—44no—
112C4×D79#4114yes—
113Dic158—22no—
114C8×C79—22no—
115C79⋊C8—22no—
116C22×C79—21no—
117C22×C79—21no—
118C22×C79—41no—
119C22×C79—41no—
120C22×C79—41no—
121C22×C79AGL(1,ℤ/8)12yes—
122C22×C79C22×D411yescharacteristic
123C2×D79—28no—
124C2×D79—21no—
125C2×D79—21no—
126C2×D79—21no—
127C2×D79—21no—
128C2×D79#12312yes—
129C2×D79#13712yes—
130C4×C79—21no—
131C4×C79—42no—
132C4×C79—41no—
133C4×C79C2×#4112yes—
134Dic79—21no—
135Dic79—41no—
136Dic79—42no—
137Dic79—41no—
138Dic79#12312yes—
139C2×C79—22no—
140C2×C79—81no—
141C2×C79C2×#12311yescharacteristic
142C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
143C2×C79C2×#13711yescharacteristic
144D79—22no—
145D79—22no—
146#3092—791nomaximal, Sylow
147C79#309211yescharacteristic, complemented, Sylow
148#525—791no—
149C22×C4⋊C4—791no—
150#484—792no—
151#483—791no—
152#483—791no—
153#481—792no—
154#480—791no—
155#480D7911yescharacteristic, complemented
156#428—792no—
157#417—792no—
158#407—791no—
159C2×#41—791no—
160C23×C4—791no—
161C23×C4—1581no—
162C2×M16—792no—
163#123—1581no—
164C22⋊Q8—791no—
165C22⋊Q8—791no—
166#121—791no—
167#121C2×D7911yescharacteristic
168#120—1581no—
169C4×D4—1581no—
170C4×D4—1581no—
171#117—791no—
172C2×C4⋊C4—791no—
173C2×C4⋊C4—792no—
174C2×C4⋊C4—792no—
175C2×C4⋊C4—1581no—
176C2×C4⋊C4—1581no—
177C2×C4⋊C4—1581no—
178C2×C4⋊C4C2×D7911yescharacteristic
179#107—792no—
180#107C2×D7912yescomplemented
181#106—792no—
182#106—792no—
183#103—792no—
184#103—792no—
185#102—792no—
186#102C2×D7912yescomplemented
187C22⋊C8—791no—
188C22⋊C8—792no—
189C22⋊C8C2×D7911yescharacteristic
190C24—791no—
191#41—1584no—
192C2×Q8—791no—
193C2×D4—21no—
194C2×D4—1581no—
195C2×D4—1581no—
196C2×D4C22×D7911yescharacteristic
197C22×C4—21no—
198C22×C4—3164no—
199C22×C4—791no—
200C22×C4—791no—
201C22×C4—791no—
202C22×C4—791no—
203C22×C4—791no—
204C22×C4—1582no—
205C22×C4—1582no—
206C22×C4—1584no—
207C22×C4—1581no—
208C22×C4—1581no—
209C22×C4C22×D7911yescharacteristic
210M16—1584no—
211C2×C8—792no—
212C2×C8C22×D7912yes—
213C4⋊C4—21no—
214C4⋊C4—792no—
215C4⋊C4—791no—
216C4⋊C4—1582no—
217C4⋊C4—1582no—
218C4⋊C4—1581no—
219C4⋊C4—1581no—
220C4⋊C4—1581no—
221C4⋊C4C22×D7912yes—
222C4⋊C4C22×D7911yescharacteristic
223C22⋊C4—21no—
224C22⋊C4—1581no—
225C22⋊C4—1581no—
226C22⋊C4—1581no—
227C22⋊C4—1581no—
228C42—1581no—
229C23—21no—
230C23—791no—
231C23—791no—
232C23—1582no—
233C23—1582no—
234C23—1582no—
235C23D4×D7911yescharacteristic
236Q8—1582no—
237D4—22no—
238D4—42no—
239D4—3162no—
240D4—3162no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—42no—
245C2×C4—3164no—
246C2×C4—3164no—
247C2×C4—3162no—
248C2×C4—3162no—
249C2×C4—791no—
250C2×C4—794no—
251C2×C4—791no—
252C2×C4—1582no—
253C2×C4—1582no—
254C2×C4—1581no—
255C2×C4—1581no—
256C2×C4—1582no—
257C2×C4—1582no—
258C2×C4—1582no—
259C2×C4D4×D7911yescharacteristic
260C2×C4C23×D7911yescharacteristic
261C8—22no—
262C8—1582no—
263C22—21no—
264C22—21no—
265C22—41no—
266C22—41no—
267C22—41no—
268C22—792no—
269C22—792no—
270C22—1588no—
271C22—1581no—
272C22—1581no—
273C22—1581no—
274C22—1581no—
275C22#1457918512yes—
276C22C2×D4×D7911yescharacteristic
277C4—21no—
278C4—42no—
279C4—41no—
280C4—3161no—
281C4—3162no—
282C4—3161no—
283C4—792no—
284C4—1581no—
285C4#41×D7912yes—
286C2—22no—
287C2—81no—
288C2—1582no—
289C2—1582no—
290C2#123×D7911yescharacteristic
291C2C2×#1457918511yescharacteristic
292C2#137×D7911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#480×C79C2
socleC22×C79C22×D4
prime radical#19099073C2
hypercenter#480D79
hypocenterC79#3092
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D79C2semidirect
3. #19098900C2semidirect
4. #19098894C2semidirect
5. #19098893C2semidirect
6. #19098880C2semidirect
7. #19098874C2semidirect
8. #19098604C2semidirect
9. #19098561C2semidirect
10. #19098525C2semidirect
11. #480×C79C2semidirect
30. #14579094C22semidirect
31. #14579093C22semidirect
32. #14579092C22semidirect
33. #14579086C22semidirect
34. #14579084C22semidirect
35. #14579082C22semidirect
40. #107×C79C22semidirect
41. #102×C79C22semidirect
147. C79#3092semidirect
155. #480D79semidirect
180. #107C2×D79semidirect
186. #102C2×D79semidirect