Finite Group Databasebeta

← #484×D79 #23773302

Subgroups — #484×D79 #23773302

Order 10112.

460 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 135 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
1C22⋊Q8×D79C211yesmaximal, characteristic
2C2×C4⋊C4×D79C211yesmaximal, characteristic
3#19098900C212yesmaximal, complemented
4#19098899C211yesmaximal, characteristic, complemented
5#19098898C211yesmaximal, characteristic, complemented
6#19098897C212yesmaximal, complemented
7#19098896C211yesmaximal, characteristic, complemented
8#107×D79C212yesmaximal, complemented
9#103×D79C212yesmaximal, complemented
10C22⋊C8×D79C211yesmaximal, characteristic
11#484×C79C211yesmaximal, characteristic, complemented
12C2×Q8×D79C2211yescharacteristic
13C22×C4×D79—21no—
14C22×C4×D79C2211yescharacteristic
15C2×C8×D79C2212yes—
16#14579141C2211yescharacteristic
17#14579140C2211yescharacteristic
18#14579139—21no—
19#14579138—21no—
20#14579137C2211yescharacteristic
21C2×C4⋊Dic79C2211yescharacteristic
22C2×Dic79⋊C4—21no—
23C4⋊C4×D79—21no—
24C4⋊C4×D79—21no—
25C4⋊C4×D79—21no—
26C4⋊C4×D79C2212yes—
27C4⋊C4×D79C2212yes—
28C4⋊C4×D79C2211yescharacteristic
29C22⋊C4×D79—21no—
30#14579095C2212yescomplemented
31#14579094C2212yescomplemented
32#14579094C2212yescomplemented
33#14579086C2212yescomplemented
34#14579085C2212yescomplemented
35#14579084C2212yescomplemented
36C22⋊(C79⋊C8)C2211yescharacteristic
37(C2×D79)⋊C8C2212yes—
38C22⋊Q8×C79C2211yescharacteristic
39C2×C4⋊C4×C79C2211yescharacteristic
40#107×C79C2212yescomplemented
41#103×C79C2212yescomplemented
42C22⋊C8×C79C2211yescharacteristic
43C23×D79D411yescharacteristic
44C2×Dic158—21no—
45C2×Dic158C2311yescharacteristic
46Q8×D79—24no—
47C22×Dic79—21no—
48C22×Dic79D411yescharacteristic
49C2×C4×D79—24no—
50C2×C4×D79—21no—
51C2×C4×D79—21no—
52C2×C4×D79—22no—
53C2×C4×D79—22no—
54C2×C4×D79—44no—
55C2×C4×D79D411yescharacteristic
56C2×C4×D79D411yescharacteristic
57C2×C4×D79C2311yescharacteristic
58C2×C4×D79C2311yescharacteristic
59C2×C79⋊C8C2312yes—
60C8×D79—24no—
61C4⋊Dic79—21no—
62C4⋊Dic79—21no—
63C4⋊Dic79C2312yes—
64C4⋊Dic79C2311yescharacteristic
65Dic79⋊C4—22no—
66Dic79⋊C4—22no—
67Dic79⋊C4—21no—
68Dic79⋊C4—21no—
69Dic79⋊C4—21no—
70C22⋊Dic79—21no—
71(C2×D79)⋊C4—21no—
72(C2×D79)⋊C4—21no—
73C2×Q8×C79C2311yescharacteristic
74C22×C4×C79—21no—
75C22×C4×C79C2311yescharacteristic
76C2×C8×C79C2312yes—
77C4⋊C4×C79—21no—
78C4⋊C4×C79—21no—
79C4⋊C4×C79C2312yes—
80C4⋊C4×C79C2311yescharacteristic
81C22⋊C4×C79—21no—
82C23×C79C2×D411yescharacteristic
83C22×D79—22no—
84C22×D79—22no—
85C22×D79Q1614yes—
86C22×D79C2×D411yescharacteristic
87C22×D79C2×D411yescharacteristic
88Q8×C79—22no—
89C2×C4×C79—22no—
90C2×C4×C79—21no—
91C2×C4×C79—21no—
92C2×C4×C79—22no—
93C2×C4×C79—42no—
94C2×C4×C79C2×D411yescharacteristic
95C2×C4×C79C2411yescharacteristic
96C2×Dic79—22no—
97C2×Dic79—21no—
98C2×Dic79—21no—
99C2×Dic79—22no—
100C2×Dic79—42no—
101C2×Dic79C2×D411yescharacteristic
102C2×Dic79C2×D411yescharacteristic
103C4×D79—22no—
104C4×D79—22no—
105C4×D79—22no—
106C4×D79—44no—
107C4×D79—42no—
108C4×D79—42no—
109C4×D79—44no—
110C4×D79#4114yes—
111Dic158—22no—
112Dic158—42no—
113C8×C79—22no—
114C79⋊C8—22no—
115C22×C79—21no—
116C22×C79—21no—
117C22×C79C2×Q1612yes—
118C22×C79C22×D411yescharacteristic
119C2×D79—21no—
120C2×D79—21no—
121C2×D79—28no—
122C2×D79#12312yes—
123C2×D79C2×Q1612yes—
124C2×D79C2×Q1612yes—
125C2×D79AGL(1,ℤ/8)12yes—
126C4×C79—21no—
127C4×C79—41no—
128C4×C79—42no—
129C4×C79—41no—
130C4×C79C2×#4112yes—
131Dic79—21no—
132Dic79—41no—
133Dic79—42no—
134Dic79—41no—
135Dic79#12312yes—
136C2×C79—22no—
137C2×C79C2×#12311yescharacteristic
138C2×C79C22×Q1611yescharacteristic
139C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
140D79—22no—
141D79#48414yesdirect product factor
142C2×#484—791nomaximal, Sylow
143C79C2×#48411yescharacteristic, complemented, Sylow
144C2×C22⋊Q8—791no—
145C22×C4⋊C4—791no—
146#484—791no—
147#484—791no—
148#484—792no—
149#484—792no—
150#484—791no—
151#484D7911yescharacteristic, direct product factor
152C2×#107—792no—
153C2×#103—792no—
154C2×C22⋊C8—791no—
155C22×Q8—791no—
156C23×C4—791no—
157C23×C4—1581no—
158C22×C8—792no—
159C22⋊Q8—791no—
160C22⋊Q8—791no—
161C22⋊Q8—791no—
162C22⋊Q8—1581no—
163C22⋊Q8—1581no—
164C22⋊Q8C2×D7911yescharacteristic
165C2×C4⋊C4—791no—
166C2×C4⋊C4—792no—
167C2×C4⋊C4—792no—
168C2×C4⋊C4—791no—
169C2×C4⋊C4—1581no—
170C2×C4⋊C4—1581no—
171C2×C4⋊C4—1581no—
172C2×C4⋊C4—1581no—
173C2×C4⋊C4C2×D7911yescharacteristic
174C2×C22⋊C4—1581no—
175#107—792no—
176#107—792no—
177#107—792no—
178#107C2×D7912yescomplemented
179#103—792no—
180#103—792no—
181#103—792no—
182#103C2×D7912yescomplemented
183C22⋊C8—791no—
184C22⋊C8—792no—
185C22⋊C8C2×D7911yescharacteristic
186C24—791no—
187C2×Q8—791no—
188C2×Q8—1581no—
189C2×Q8—1584no—
190C2×Q8C22×D7911yescharacteristic
191C22×C4—21no—
192C22×C4—3164no—
193C22×C4—791no—
194C22×C4—791no—
195C22×C4—791no—
196C22×C4—791no—
197C22×C4—791no—
198C22×C4—1581no—
199C22×C4—1581no—
200C22×C4—1582no—
201C22×C4—1582no—
202C22×C4—1584no—
203C22×C4—1581no—
204C22×C4C22×D7911yescharacteristic
205C2×C8—792no—
206C2×C8—1584no—
207C2×C8C22×D7912yes—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—792no—
211C4⋊C4—791no—
212C4⋊C4—1582no—
213C4⋊C4—1582no—
214C4⋊C4—1581no—
215C4⋊C4—1581no—
216C4⋊C4—1581no—
217C4⋊C4—1581no—
218C4⋊C4—1581no—
219C4⋊C4C22×D7912yes—
220C4⋊C4C22×D7911yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—1581no—
223C22⋊C4—1581no—
224C22⋊C4—1581no—
225C23—791no—
226C23—794no—
227C23—791no—
228C23—1582no—
229C23—1582no—
230C23D4×D7911yescharacteristic
231Q8—22no—
232Q8—3162no—
233Q8—1582no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—3164no—
240C2×C4—3162no—
241C2×C4—3162no—
242C2×C4—3164no—
243C2×C4—3162no—
244C2×C4—791no—
245C2×C4—794no—
246C2×C4—791no—
247C2×C4—1582no—
248C2×C4—1582no—
249C2×C4—1581no—
250C2×C4—1581no—
251C2×C4—1582no—
252C2×C4—1582no—
253C2×C4—1582no—
254C2×C4D4×D7911yescharacteristic
255C2×C4C23×D7911yescharacteristic
256C8—22no—
257C8—1582no—
258C22—21no—
259C22—21no—
260C22—792no—
261C22—792no—
262C22—792no—
263C22—792no—
264C22—1588no—
265C22—1581no—
266C22—1581no—
267C22Q16×D7912yes—
268C22C2×D4×D7911yescharacteristic
269C4—21no—
270C4—41no—
271C4—42no—
272C4—41no—
273C4—3161no—
274C4—3162no—
275C4—3161no—
276C4—792no—
277C4—1581no—
278C4#41×D7912yes—
279C2—22no—
280C2—794no—
281C2—1582no—
282C2#123×D7911yescharacteristic
283C2C2×Q16×D7911yescharacteristic
284C2AGL(1,ℤ/8)×D7911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#484×C79C2
socleC22×C79C22×D4
prime radicalC23×D79D4
hypercenter#484D79
hypocenterC79C2×#484
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #19098900C2semidirect
4. #19098899C2semidirect
5. #19098898C2semidirect
6. #19098897C2semidirect
7. #19098896C2semidirect
8. #107×D79C2semidirect
9. #103×D79C2semidirect
11. #484×C79C2semidirect
30. #14579095C22semidirect
31. #14579094C22semidirect
32. #14579094C22semidirect
33. #14579086C22semidirect
34. #14579085C22semidirect
35. #14579084C22semidirect
40. #107×C79C22semidirect
41. #103×C79C22semidirect
141. D79#484direct (N × H)
143. C79C2×#484semidirect
151. #484D79direct (N × H)
178. #107C2×D79semidirect
182. #103C2×D79semidirect