Finite Group Databasebeta

← #23773583

Subgroups — #23773583

Order 10112.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099182C211yesmaximal, characteristic, complemented
2#19099035C211yesmaximal, characteristic, complemented
3#19098902C211yesmaximal, characteristic, complemented
4#19098886C211yesmaximal, characteristic, complemented
5#19098854C211yesmaximal, characteristic, complemented
6#19098843C211yesmaximal, characteristic, complemented
7#19098775C211yesmaximal, characteristic, complemented
8#19098712C211yesmaximal, characteristic, complemented
9#19098695C211yesmaximal, characteristic
10#19098675C211yesmaximal, characteristic, complemented
11#19098666C211yesmaximal, characteristic, complemented
12SD16×Dic79C211yesmaximal, characteristic, complemented
13#19098643C211yesmaximal, characteristic, complemented
14#19098623C211yesmaximal, characteristic, complemented
15#463×C79C211yesmaximal, characteristic, complemented
16C2×D4×D79C2211yescharacteristic
17C2×#11929611C2211yescharacteristic
18C2×#11929609C2211yescharacteristic
19#14579161C2211yescharacteristic, complemented
20#14579154—21no—
21#14579147—21no—
22#14579145—21no—
23#14579138—21no—
24#14579137C2211yescharacteristic
25#14579132C2211yescharacteristic
26Q8×Dic79C2211yescharacteristic, complemented
27C4×D316C2211yescharacteristic
28D4×Dic79C2211yescharacteristic
29D4×Dic79C2211yescharacteristic, complemented
30#14579123C2211yescharacteristic
31C4×C22⋊D79—21no—
32(C22⋊D79)⋊C4—21no—
33#14579119C2211yescharacteristic
34#14579118C2211yescharacteristic
35C2×(C2×D79)⋊C4—21no—
36C22⋊C4×D79—21no—
37#14579094C2211yescharacteristic, complemented
38#14579094C2211yescharacteristic, complemented
39#14579093C2211yescharacteristic, complemented
40#14579093C2211yescharacteristic, complemented
41C4⋊(C79⋊C8)C2211yescharacteristic, complemented
42#14579085C2211yescharacteristic, complemented
43#14579083C2211yescharacteristic
44#14579083C2211yescharacteristic
45#14579082C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic, complemented
48(C2×D79)⋊C8C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50#14579071C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C2×SD16×C79C2211yescharacteristic
53C2×D8×C79C2211yescharacteristic
54#124×C79C2211yescharacteristic, complemented
55C4×D4×C79C2211yescharacteristic
56C4⋊C8×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C2×Dic158—21no—
61C2×D316C2311yescharacteristic
62C2×C22⋊D79—21no—
63C2×C22⋊D79—21no—
64D4×D79—22no—
65D4×D79—22no—
66C22×Dic79—21no—
67C22×Dic79—21no—
68C2×C4×D79—21no—
69C2×C4×D79—21no—
70C2×C4×D79C2311yescharacteristic
71#11929611—22no—
72#11929609—22no—
73C2×C79⋊C8C2311yescharacteristic
74C2×C79⋊C8C2311yescharacteristic
75C4⋊Dic79—21no—
76C4⋊Dic79—21no—
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79C4⋊Dic79C2311yescharacteristic
80Dic79⋊C4—21no—
81Dic79⋊C4D411yescharacteristic
82Dic79⋊C4D411yescharacteristic
83C22⋊Dic79—21no—
84C22⋊Dic79—21no—
85C22⋊Dic79—21no—
86(C2×D79)⋊C4—21no—
87(C2×D79)⋊C4—21no—
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4D411yescharacteristic
91(C2×D79)⋊C4D411yescharacteristic
92C4×Dic79—21no—
93C4×Dic79—21no—
94C4×Dic79C2311yescharacteristic
95C2×Q8×C79C2311yescharacteristic
96C2×D4×C79C2311yescharacteristic
97C2×D4×C79C2311yescharacteristic
98C22×C4×C79—21no—
99SD16×C79—22no—
100D8×C79—22no—
101C2×C8×C79C2311yescharacteristic
102C2×C8×C79C2311yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C22⋊C4×C79—21no—
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C42×C79C2311yescharacteristic
108C23×C79—21no—
109C23×C79—21no—
110C22×D79—21no—
111C22×D79—24no—
112C22×D79—81no—
113C22×D79—81no—
114C22×D79C2×D411yescharacteristic
115Q8×C79—21no—
116Q8×C79—21no—
117D4×C79—21no—
118D4×C79—21no—
119D4×C79—21no—
120D4×C79#4112yes—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—81no—
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2411yescharacteristic
127C22⋊D79—24no—
128C22⋊D79—81no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—81no—
133C2×Dic79—81no—
134C2×Dic79C2×D411yescharacteristic
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137D316—21no—
138D316#4112yes—
139C4×D79—21no—
140C4×D79—21no—
141C4×D79—81no—
142C4×D79—81no—
143Dic158—81no—
144C8×C79—21no—
145C8×C79—21no—
146C79⋊C8—21no—
147C79⋊C8—21no—
148C22×C79—22no—
149C22×C79—41no—
150C22×C79—41no—
151C22×C79—41no—
152C22×C79—41no—
153C22×C79—41no—
154C22×C79C22×D411yescharacteristic
155C2×D79—22no—
156C2×D79—21no—
157C2×D79—21no—
158C2×D79—21no—
159C2×D79—41no—
160C2×D79—41no—
161C2×D79—84no—
162C4×C79—21no—
163C4×C79—21no—
164C4×C79—41no—
165C4×C79—41no—
166C4×C79C2×#4111yescharacteristic
167C4×C79C2×#4111yescharacteristic
168Dic79—21no—
169Dic79—21no—
170Dic79—21no—
171Dic79—41no—
172Dic79—41no—
173Dic79—41no—
174C2×C79—42no—
175C2×C79—81no—
176C2×C79#52511yescharacteristic
177C2×C79#57611yescharacteristic
178C2×C79#57711yescharacteristic
179D79—41no—
180D79—42no—
181#3118—791nomaximal, Sylow
182C79#311811yescharacteristic, complemented, Sylow
183#542—791no—
184#518—791no—
185#485—791no—
186#482—791no—
187#476—791no—
188#474—791no—
189#463—791no—
190#463D7911yescharacteristic, complemented
191#450—791no—
192#447—791no—
193#442—791no—
194#440—791no—
195C4×SD16—791no—
196C4×D8—791no—
197#433—791no—
198C22×D4—791no—
199C2×SD16—791no—
200C2×SD16C2×D7911yescharacteristic
201C2×D8—791no—
202C2×D8C2×D7911yescharacteristic
203C4⋊Q8—791no—
204#126—1581no—
205#124—1581no—
206#124C2×D7911yescharacteristic, complemented
207#123—1581no—
208C22⋊Q8—791no—
209C22⋊Q8—1581no—
210#121—791no—
211C4×Q8—791no—
212C4×D4—791no—
213C4×D4—791no—
214C4×D4—791no—
215C4×D4—791no—
216C4×D4—1581no—
217C4×D4—1581no—
218C4×D4C2×D7911yescharacteristic
219#117—791no—
220#117—791no—
221C2×C22⋊C4—1581no—
222C2×C22⋊C4—1581no—
223#107—791no—
224#107—791no—
225#106—791no—
226#106—791no—
227C4⋊C8—791no—
228C4⋊C8C2×D7911yescharacteristic, complemented
229#103—791no—
230#103C2×D7911yescharacteristic, complemented
231#102—791no—
232#102—791no—
233#102—791no—
234#102—791no—
235#102—791no—
236#102C2×D7911yescharacteristic, complemented
237C22⋊C8—791no—
238C22⋊C8—791no—
239#97—791no—
240C4×C8—791no—
241C24—1581no—
242C2×Q8—1581no—
243C2×Q8C22×D7911yescharacteristic
244C2×D4—791no—
245C2×D4—1581no—
246C2×D4—1582no—
247C2×D4—1581no—
248C2×D4—1582no—
249C2×D4C22×D7911yescharacteristic
250C2×D4C22×D7911yescharacteristic
251C22×C4—21no—
252C22×C4—791no—
253C22×C4—1581no—
254C22×C4—1581no—
255C22×C4—1581no—
256C22×C4—1581no—
257SD16—22no—
258SD16—1582no—
259D8—22no—
260D8—1582no—
261C2×C8—791no—
262C2×C8—791no—
263C2×C8C22×D7911yescharacteristic
264C2×C8C22×D7911yescharacteristic
265C4⋊C4—791no—
266C4⋊C4—791no—
267C4⋊C4—791no—
268C4⋊C4—791no—
269C4⋊C4—791no—
270C4⋊C4—1581no—
271C4⋊C4—1581no—
272C4⋊C4—1581no—
273C4⋊C4C22×D7911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—791no—
278C22⋊C4—791no—
279C22⋊C4—1581no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C42—791no—
287C42—1581no—
288C42—1581no—
289C42C22×D7911yescharacteristic
290C23—21no—
291C23—21no—
292C23—791no—
293C23—6321no—
294C23—6321no—
295C23—1584no—
296C23—1581no—
297Q8—21no—
298Q8—21no—
299Q8—6321no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—792no—
304D4—6321no—
305D4—1584no—
306D4—1581no—
307D4#1192962312yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—791no—
312C2×C4—791no—
313C2×C4—791no—
314C2×C4—6321no—
315C2×C4—6321no—
316C2×C4—6321no—
317C2×C4—6321no—
318C2×C4—1581no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4—1581no—
322C2×C4—1581no—
323C2×C4D4×D7911yescharacteristic
324C2×C4D4×D7911yescharacteristic
325C2×C4C23×D7911yescharacteristic
326C8—21no—
327C8—21no—
328C8—1581no—
329C8—1581no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—3161no—
337C22—3161no—
338C22—6324no—
339C22—1581no—
340C22—1582no—
341C22—1581no—
342C22—1581no—
343C22C2×D4×D7911yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—3161no—
349C4—3161no—
350C4—3161no—
351C4—1581no—
352C4—1581no—
353C4—1581no—
354C4#41×D7911yescharacteristic
355C4C2×#1192962311yescharacteristic
356C2—42no—
357C2—81no—
358C2—3162no—
359C2—3161no—
360C2#1909907311yescharacteristic
361C2#1909936711yescharacteristic
362C2#1909937011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#463×C79C2
socleC22×C79C22×D4
prime radical#19098695C2
hypercenter#463D79
hypocenterC79#3118
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #19099182C2semidirect
2. #19099035C2semidirect
3. #19098902C2semidirect
4. #19098886C2semidirect
5. #19098854C2semidirect
6. #19098843C2semidirect
7. #19098775C2semidirect
8. #19098712C2semidirect
10. #19098675C2semidirect
11. #19098666C2semidirect
12. SD16×Dic79C2semidirect
13. #19098643C2semidirect
14. #19098623C2semidirect
15. #463×C79C2semidirect
19. #14579161C22semidirect
26. Q8×Dic79C22semidirect
29. D4×Dic79C22semidirect
37. #14579094C22semidirect
38. #14579094C22semidirect
39. #14579093C22semidirect
40. #14579093C22semidirect
41. C4⋊(C79⋊C8)C22semidirect
42. #14579085C22semidirect
47. #14579082C22semidirect
50. #14579071C22semidirect
51. C8×Dic79C22semidirect
54. #124×C79C22semidirect
56. C4⋊C8×C79C22semidirect
57. #103×C79C22semidirect
58. #102×C79C22semidirect
182. C79#3118semidirect
190. #463D79semidirect
206. #124C2×D79semidirect
228. C4⋊C8C2×D79semidirect
230. #103C2×D79semidirect
236. #102C2×D79semidirect