Finite Group Databasebeta

← #23773577

Subgroups — #23773577

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#19099180C211yesmaximal, characteristic, complemented
2#19099038C211yesmaximal, characteristic, complemented
3#19098905C211yesmaximal, characteristic, complemented
4#19098884C211yesmaximal, characteristic, complemented
5#19098851C211yesmaximal, characteristic, complemented
6#19098841C211yesmaximal, characteristic, complemented
7#19098776C211yesmaximal, characteristic, complemented
8#19098776C211yesmaximal, characteristic, complemented
9#19098714C211yesmaximal, characteristic, complemented
10#19098675C211yesmaximal, characteristic, complemented
11#19098660C211yesmaximal, characteristic, complemented
12#19098654C211yesmaximal, characteristic, complemented
13D8×Dic79C211yesmaximal, characteristic, complemented
14#19098621C211yesmaximal, characteristic, complemented
15#447×C79C211yesmaximal, characteristic
16C2×#11929612C2211yescharacteristic
17C2×#11929612C2211yescharacteristic
18#14579160C2211yescharacteristic, complemented
19#14579154—21no—
20#14579148—21no—
21#14579148C2211yescharacteristic, complemented
22#14579142—21no—
23#14579140C2211yescharacteristic
24#14579138—21no—
25#14579126C2211yescharacteristic, complemented
26D4×Dic79—21no—
27D4×Dic79—21no—
28D4×Dic79C2211yescharacteristic
29D4×Dic79C2211yescharacteristic
30D4×Dic79C2211yescharacteristic
31D4×Dic79C2211yescharacteristic
32D4×Dic79C2211yescharacteristic, complemented
33#14579120C2211yescharacteristic
34#14579120C2211yescharacteristic
35C2×C22⋊Dic79—21no—
36C2×C22⋊Dic79—21no—
37#14579095C2211yescharacteristic, complemented
38#14579094C2211yescharacteristic, complemented
39#14579093C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42Dic79⋊C8C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579086C2211yescharacteristic, complemented
45#14579082C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic, complemented
48#14579082C2211yescharacteristic, complemented
49C22⋊(C79⋊C8)C2211yescharacteristic
50#14579071C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C22×D4×C79C2211yescharacteristic
53C2×D8×C79C2211yescharacteristic
54C2×D8×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic
59C2×Dic158—21no—
60C2×Dic158C2311yescharacteristic
61C22×Dic79—21no—
62C22×Dic79—21no—
63C22×Dic79—21no—
64C22×Dic79—21no—
65C22×Dic79—21no—
66#11929612—22no—
67#11929612—22no—
68C2×C79⋊C8C2311yescharacteristic
69C2×C79⋊C8C2311yescharacteristic
70C4⋊Dic79D411yescharacteristic
71C4⋊Dic79D411yescharacteristic
72C4⋊Dic79C2311yescharacteristic
73C4⋊Dic79C2311yescharacteristic
74C4⋊Dic79C2311yescharacteristic
75Dic79⋊C4—21no—
76Dic79⋊C4—21no—
77Dic79⋊C4—21no—
78C22⋊Dic79—21no—
79C22⋊Dic79—21no—
80C22⋊Dic79—21no—
81C22⋊Dic79—21no—
82C22⋊Dic79—21no—
83C22⋊Dic79—21no—
84C22⋊Dic79—21no—
85C22⋊Dic79—21no—
86C22⋊Dic79—21no—
87C22⋊Dic79D411yescharacteristic
88C22⋊Dic79D411yescharacteristic
89C4×Dic79—21no—
90C4×Dic79—21no—
91C4×Dic79C2311yescharacteristic
92C4×Dic79C2311yescharacteristic
93C24×C79—21no—
94C2×D4×C79—22no—
95C2×D4×C79—22no—
96C2×D4×C79—21no—
97C2×D4×C79—21no—
98C2×D4×C79C2311yescharacteristic
99C2×D4×C79C2311yescharacteristic
100C2×D4×C79C2311yescharacteristic
101C22×C4×C79C2311yescharacteristic
102D8×C79—22no—
103D8×C79—22no—
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C4⋊C4×C79C2311yescharacteristic
107C22⋊C4×C79—21no—
108C23×C79—24no—
109C23×C79—21no—
110C23×C79—21no—
111C23×C79—21no—
112C23×C79—81no—
113C23×C79—81no—
114C23×C79C2×D411yescharacteristic
115D4×C79—24no—
116D4×C79—21no—
117D4×C79—21no—
118D4×C79—21no—
119D4×C79—21no—
120D4×C79—81no—
121D4×C79#4112yes—
122D4×C79#4112yes—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2411yescharacteristic
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—81no—
133C2×Dic79—81no—
134C2×Dic79—81no—
135C2×Dic79—81no—
136C2×Dic79—81no—
137C2×Dic79C2×D411yescharacteristic
138C2×Dic79C2×D411yescharacteristic
139C2×Dic79C2×D411yescharacteristic
140C2×Dic79C2×D411yescharacteristic
141Dic158—21no—
142Dic158—21no—
143Dic158—81no—
144C8×C79—21no—
145C8×C79—21no—
146C79⋊C8—21no—
147C79⋊C8—21no—
148C22×C79—21no—
149C22×C79—22no—
150C22×C79—22no—
151C22×C79—21no—
152C22×C79—21no—
153C22×C79—41no—
154C22×C79—41no—
155C22×C79—41no—
156C22×C79—41no—
157C22×C79—41no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79—84no—
161C22×C79C22×D411yescharacteristic
162C4×C79—21no—
163C4×C79—41no—
164C4×C79C2×#4111yescharacteristic
165C4×C79C2×#4111yescharacteristic
166Dic79—21no—
167Dic79—21no—
168Dic79—21no—
169Dic79—21no—
170Dic79—41no—
171Dic79—41no—
172Dic79—41no—
173Dic79—41no—
174C2×C79—41no—
175C2×C79—42no—
176C2×C79—42no—
177C2×C79—81no—
178C2×C79#52511yescharacteristic
179C2×C79#57611yescharacteristic
180C2×C79#57711yescharacteristic
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#463—791no—
191#450—791no—
192#447D7911yescharacteristic
193#442—791no—
194#440—791no—
195C4×SD16—791no—
196C4×D8—791no—
197#433—791no—
198C22×D4C2×D7911yescharacteristic
199C2×SD16—791no—
200C2×SD16—791no—
201C2×D8C2×D7911yescharacteristic
202C2×D8C2×D7911yescharacteristic
203C4⋊Q8—791no—
204#126—1581no—
205#124—791no—
206#124—1581no—
207#123—1581no—
208C22⋊Q8—791no—
209C22⋊Q8—1581no—
210#121C2×D7911yescharacteristic
211C4×Q8—791no—
212C4×D4—791no—
213C4×D4—791no—
214C4×D4—791no—
215C4×D4—791no—
216C4×D4—791no—
217C4×D4—1581no—
218C4×D4—1581no—
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⋊C8—791no—
229#103—791no—
230#103—791no—
231#102—791no—
232#102—791no—
233#102—791no—
234#102—791no—
235#102C2×D7911yescharacteristic
236#102C2×D7911yescharacteristic
237C22⋊C8—791no—
238C22⋊C8C2×D7911yescharacteristic
239#97—791no—
240C4×C8—791no—
241C24—21no—
242C2×Q8—791no—
243C2×Q8—1581no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C22×D7911yescharacteristic
249C2×D4C22×D7911yescharacteristic
250C2×D4C22×D7911yescharacteristic
251C22×C4—1581no—
252C22×C4—1581no—
253C22×C4—1581no—
254C22×C4—1581no—
255C22×C4—1581no—
256C22×C4C22×D7911yescharacteristic
257SD16—1582no—
258SD16—1582no—
259D8—22no—
260D8—22no—
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—791no—
276C22⋊C4—791no—
277C22⋊C4—1581no—
278C22⋊C4—1581no—
279C22⋊C4—1581no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C42—791no—
287C42—791no—
288C42—1581no—
289C42—1581no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—81no—
295C23—81no—
296C23D4×D7911yescharacteristic
297Q8—6321no—
298Q8—1581no—
299Q8—1581no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—81no—
306D4#1192962312yes—
307D4#1192962312yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—791no—
312C2×C4—791no—
313C2×C4—791no—
314C2×C4—791no—
315C2×C4—6321no—
316C2×C4—6321no—
317C2×C4—6321no—
318C2×C4—6321no—
319C2×C4—6321no—
320C2×C4—1581no—
321C2×C4—1581no—
322C2×C4—1581no—
323C2×C4—1581no—
324C2×C4D4×D7911yescharacteristic
325C2×C4C23×D7911yescharacteristic
326C8—21no—
327C8—21no—
328C8—1581no—
329C8—1581no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—84no—
343C22C2×D4×D7911yescharacteristic
344C4—21no—
345C4—41no—
346C4—3161no—
347C4—3161no—
348C4—3161no—
349C4—3161no—
350C4—1581no—
351C4—1581no—
352C4—1581no—
353C4—1581no—
354C4C2×#1192962311yescharacteristic
355C4C2×#1192962311yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—81no—
360C2#1909906911yescharacteristic
361C2#1909936411yescharacteristic
362C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting, prime radical#447×C79C2
socleC22×C79C22×D4
hypercenter#447D79
hypocenterC79#3118
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #19099180C2semidirect
2. #19099038C2semidirect
3. #19098905C2semidirect
4. #19098884C2semidirect
5. #19098851C2semidirect
6. #19098841C2semidirect
7. #19098776C2semidirect
8. #19098776C2semidirect
9. #19098714C2semidirect
10. #19098675C2semidirect
11. #19098660C2semidirect
12. #19098654C2semidirect
13. D8×Dic79C2semidirect
14. #19098621C2semidirect
18. #14579160C22semidirect
21. #14579148C22semidirect
25. #14579126C22semidirect
32. D4×Dic79C22semidirect
37. #14579095C22semidirect
38. #14579094C22semidirect
39. #14579093C22semidirect
40. #14579092C22semidirect
41. Dic79⋊C8C22semidirect
42. Dic79⋊C8C22semidirect
43. #14579086C22semidirect
44. #14579086C22semidirect
47. #14579082C22semidirect
48. #14579082C22semidirect
50. #14579071C22semidirect
51. C8×Dic79C22semidirect
182. C79#3118semidirect