Finite Group Databasebeta

← #481×D79 #23773296

Subgroups — #481×D79 #23773296

Order 10112.

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

normal subgroups only

This group has 512 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
1#121×D79C211yesmaximal, characteristic
2C2×C4⋊C4×D79C211yesmaximal, characteristic, complemented
3#19098883C212yesmaximal, complemented
4#19098882C211yesmaximal, characteristic, complemented
5#19098881C211yesmaximal, characteristic, complemented
6#19098880C212yesmaximal, complemented
7#19098879C211yesmaximal, characteristic, complemented
8#106×D79C212yesmaximal, complemented
9#102×D79C212yesmaximal, complemented
10C22⋊C8×D79C211yesmaximal, characteristic, complemented
11#481×C79C211yesmaximal, characteristic, complemented
12C2×D4×D79—21no—
13C2×D4×D79C2211yescharacteristic
14C22×C4×D79—21no—
15C22×C4×D79C2211yescharacteristic
16C2×C8×D79C2212yes—
17#14579136C2211yescharacteristic
18#14579135C2211yescharacteristic
19#14579134—21no—
20#14579133—21no—
21#14579132C2211yescharacteristic
22C2×C4⋊Dic79C2211yescharacteristic, complemented
23C2×Dic79⋊C4—21no—
24C4⋊C4×D79—21no—
25C4⋊C4×D79—21no—
26C4⋊C4×D79C2212yes—
27C4⋊C4×D79C2211yescharacteristic
28C4⋊C4×D79C2212yescomplemented
29C22⋊C4×D79—21no—
30#14579093C2212yescomplemented
31#14579092C2212yescomplemented
32#14579092C2212yescomplemented
33#14579083C2212yescomplemented
34#14579082C2212yescomplemented
35#14579081C2212yescomplemented
36C22⋊(C79⋊C8)C2211yescharacteristic, complemented
37(C2×D79)⋊C8C2212yescomplemented
38#121×C79C2211yescharacteristic
39C2×C4⋊C4×C79C2211yescharacteristic, complemented
40#106×C79C2212yescomplemented
41#102×C79C2212yescomplemented
42C22⋊C8×C79C2211yescharacteristic, complemented
43C23×D79—21no—
44C23×D79D411yescharacteristic
45C2×D316—21no—
46C2×D316C2311yescharacteristic
47C2×C22⋊D79—21no—
48C2×C22⋊D79—21no—
49C2×C22⋊D79—21no—
50D4×D79—24no—
51D4×D79—44no—
52C22×Dic79—21no—
53C22×Dic79D411yescharacteristic
54C2×C4×D79—24no—
55C2×C4×D79—21no—
56C2×C4×D79—22no—
57C2×C4×D79—22no—
58C2×C4×D79—44no—
59C2×C4×D79D411yescharacteristic
60C2×C4×D79D411yescharacteristic
61C2×C4×D79C2311yescharacteristic
62C2×C4×D79C2311yescharacteristic
63C2×C79⋊C8C2312yes—
64C8×D79—24no—
65C4⋊Dic79—21no—
66C4⋊Dic79C2312yes—
67C4⋊Dic79C2311yescharacteristic
68Dic79⋊C4—22no—
69Dic79⋊C4—22no—
70Dic79⋊C4—21no—
71C22⋊Dic79—21no—
72(C2×D79)⋊C4—21no—
73(C2×D79)⋊C4—21no—
74C2×D4×C79—21no—
75C2×D4×C79C2311yescharacteristic
76C22×C4×C79—21no—
77C22×C4×C79C2311yescharacteristic
78C2×C8×C79C2312yes—
79C4⋊C4×C79—21no—
80C4⋊C4×C79C2312yes—
81C4⋊C4×C79C2311yescharacteristic
82C22⋊C4×C79—21no—
83C23×C79—21no—
84C23×C79C2×D411yescharacteristic
85C22×D79—22no—
86C22×D79—22no—
87C22×D79—21no—
88C22×D79—42no—
89C22×D79—42no—
90C22×D79—42no—
91C22×D79SD1614yes—
92C22×D79C2×D411yescharacteristic
93C22×D79C2×D411yescharacteristic
94D4×C79—22no—
95D4×C79—42no—
96C2×C4×C79—22no—
97C2×C4×C79—21no—
98C2×C4×C79—22no—
99C2×C4×C79—42no—
100C2×C4×C79C2×D411yescharacteristic
101C2×C4×C79C2411yescharacteristic
102C22⋊D79—42no—
103C22⋊D79—42no—
104C22⋊D79—42no—
105C2×Dic79—22no—
106C2×Dic79—21no—
107C2×Dic79—22no—
108C2×Dic79—42no—
109C2×Dic79C2×D411yescharacteristic
110C2×Dic79C2×D411yescharacteristic
111D316—22no—
112D316—42no—
113C4×D79—22no—
114C4×D79—22no—
115C4×D79—22no—
116C4×D79—44no—
117C4×D79—42no—
118C4×D79—44no—
119C4×D79#4114yes—
120C8×C79—22no—
121C79⋊C8—22no—
122C22×C79—21no—
123C22×C79—21no—
124C22×C79—41no—
125C22×C79—41no—
126C22×C79—41no—
127C22×C79C2×SD1612yes—
128C22×C79C22×D411yescharacteristic
129C2×D79—21no—
130C2×D79—21no—
131C2×D79—28no—
132C2×D79—41no—
133C2×D79—41no—
134C2×D79—41no—
135C2×D79—84no—
136C2×D79#12312yes—
137C2×D79C2×SD1612yes—
138C2×D79C2×SD1612yes—
139C2×D79AGL(1,ℤ/8)12yes—
140C4×C79—21no—
141C4×C79—41no—
142C4×C79—42no—
143C4×C79C2×#4112yes—
144Dic79—21no—
145Dic79—41no—
146Dic79—42no—
147Dic79#12312yes—
148C2×C79—22no—
149C2×C79—81no—
150C2×C79C2×#12311yescharacteristic
151C2×C79C22×SD1611yescharacteristic
152C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
153D79—22no—
154D79—81no—
155D79#48114yesdirect product factor
156C2×#481—791nomaximal, Sylow
157C79C2×#48111yescharacteristic, complemented, Sylow
158C2×#121—791no—
159C22×C4⋊C4—791no—
160#481—791no—
161#481—791no—
162#481—792no—
163#481—792no—
164#481—791no—
165#481D7911yescharacteristic, direct product factor
166C2×#106—792no—
167C2×#102—792no—
168C2×C22⋊C8—791no—
169C22×D4—791no—
170C22×D4—1581no—
171C23×C4—791no—
172C23×C4—1581no—
173C22×C8—792no—
174#121—791no—
175#121—791no—
176#121—791no—
177#121—1581no—
178#121—1581no—
179#121C2×D7911yescharacteristic
180C2×C4⋊C4—791no—
181C2×C4⋊C4—792no—
182C2×C4⋊C4—792no—
183C2×C4⋊C4—791no—
184C2×C4⋊C4—1581no—
185C2×C4⋊C4—1581no—
186C2×C4⋊C4—1581no—
187C2×C4⋊C4C2×D7911yescharacteristic, complemented
188C2×C22⋊C4—1581no—
189#106—792no—
190#106—792no—
191#106—792no—
192#106C2×D7912yescomplemented
193#102—792no—
194#102—792no—
195#102—792no—
196#102C2×D7912yescomplemented
197C22⋊C8—791no—
198C22⋊C8—792no—
199C22⋊C8C2×D7911yescharacteristic, complemented
200C24—791no—
201C24—1581no—
202C2×D4—21no—
203C2×D4—3164no—
204C2×D4—791no—
205C2×D4—1581no—
206C2×D4—1584no—
207C2×D4—1581no—
208C2×D4—1581no—
209C2×D4—1581no—
210C2×D4C22×D7911yescharacteristic
211C22×C4—21no—
212C22×C4—3164no—
213C22×C4—791no—
214C22×C4—791no—
215C22×C4—791no—
216C22×C4—791no—
217C22×C4—791no—
218C22×C4—1581no—
219C22×C4—1582no—
220C22×C4—1582no—
221C22×C4—1584no—
222C22×C4—1581no—
223C22×C4C22×D7911yescharacteristic
224C2×C8—792no—
225C2×C8—1584no—
226C2×C8C22×D7912yes—
227C4⋊C4—21no—
228C4⋊C4—792no—
229C4⋊C4—791no—
230C4⋊C4—1582no—
231C4⋊C4—1582no—
232C4⋊C4—1581no—
233C4⋊C4—1581no—
234C4⋊C4C22×D7912yes—
235C4⋊C4C22×D7911yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—1581no—
238C22⋊C4—1581no—
239C22⋊C4—1581no—
240C23—21no—
241C23—3162no—
242C23—3162no—
243C23—3162no—
244C23—791no—
245C23—794no—
246C23—791no—
247C23—1582no—
248C23—1582no—
249C23—1581no—
250C23D4×D7911yescharacteristic
251D4—22no—
252D4—42no—
253D4—3162no—
254D4—3162no—
255D4—3162no—
256D4—3162no—
257D4—1582no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—3164no—
263C2×C4—3162no—
264C2×C4—3164no—
265C2×C4—3162no—
266C2×C4—791no—
267C2×C4—794no—
268C2×C4—791no—
269C2×C4—1582no—
270C2×C4—1582no—
271C2×C4—1581no—
272C2×C4—1582no—
273C2×C4—1582no—
274C2×C4—1582no—
275C2×C4D4×D7911yescharacteristic
276C2×C4C23×D7911yescharacteristic
277C8—22no—
278C8—1582no—
279C22—21no—
280C22—21no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—3161no—
285C22—3161no—
286C22—3161no—
287C22—792no—
288C22—792no—
289C22—792no—
290C22—792no—
291C22—6324no—
292C22—1588no—
293C22—1581no—
294C22—1581no—
295C22SD16×D7912yes—
296C22C2×D4×D7911yescharacteristic
297C4—21no—
298C4—41no—
299C4—42no—
300C4—3161no—
301C4—3162no—
302C4—792no—
303C4—1581no—
304C4#41×D7912yes—
305C2—22no—
306C2—81no—
307C2—794no—
308C2—6321no—
309C2—1582no—
310C2#123×D7911yescharacteristic
311C2C2×SD16×D7911yescharacteristic
312C2AGL(1,ℤ/8)×D7911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#481×C79C2
socleC22×C79C22×D4
prime radical#121×D79C2
hypercenter#481D79
hypocenterC79C2×#481
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D79C2semidirect
3. #19098883C2semidirect
4. #19098882C2semidirect
5. #19098881C2semidirect
6. #19098880C2semidirect
7. #19098879C2semidirect
8. #106×D79C2semidirect
9. #102×D79C2semidirect
10. C22⋊C8×D79C2semidirect
11. #481×C79C2semidirect
22. C2×C4⋊Dic79C22semidirect
28. C4⋊C4×D79C22semidirect
30. #14579093C22semidirect
31. #14579092C22semidirect
32. #14579092C22semidirect
33. #14579083C22semidirect
34. #14579082C22semidirect
35. #14579081C22semidirect
36. C22⋊(C79⋊C8)C22semidirect
37. (C2×D79)⋊C8C22semidirect
39. C2×C4⋊C4×C79C22semidirect
40. #106×C79C22semidirect
41. #102×C79C22semidirect
42. C22⋊C8×C79C22semidirect
155. D79#481direct (N × H)
157. C79C2×#481semidirect
165. #481D79direct (N × H)
187. C2×C4⋊C4C2×D79semidirect
192. #106C2×D79semidirect
196. #102C2×D79semidirect
199. C22⋊C8C2×D79semidirect