Finite Group Databasebeta

← #23773489

Subgroups — #23773489

Order 10112.

488 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099110C211yesmaximal, characteristic, complemented
2C4×D4×D79C211yesmaximal, characteristic, complemented
3#19098883C211yesmaximal, characteristic, complemented
4#19098880C211yesmaximal, characteristic, complemented
5#19098852C211yesmaximal, characteristic, complemented
6#19098851C211yesmaximal, characteristic, complemented
7#19098757C211yesmaximal, characteristic, complemented
8#19098756C211yesmaximal, characteristic, complemented
9#19098698C211yesmaximal, characteristic, complemented
10#19098695C211yesmaximal, characteristic, complemented
11#19098676C211yesmaximal, characteristic, complemented
12#19098673C211yesmaximal, characteristic, complemented
13#19098673C211yesmaximal, characteristic, complemented
14#19098618C211yesmaximal, characteristic, complemented
15#442×C79C211yesmaximal, characteristic, complemented
16C2×#11929624—21no—
17C2×D4×D79C2211yescharacteristic
18C22×C4×D79—21no—
19C2×D632C2211yescharacteristic
20C2×#11929609C2211yescharacteristic
21C2×#11929609C2211yescharacteristic
22#14579160C2211yescharacteristic, complemented
23#14579157C2211yescharacteristic, complemented
24#14579147—21no—
25#14579136C2211yescharacteristic
26#14579134—21no—
27#14579132C2211yescharacteristic
28C4×D316C2211yescharacteristic
29C4×D316C2211yescharacteristic, complemented
30D4×Dic79C2211yescharacteristic
31#14579123C2211yescharacteristic
32C4×C22⋊D79—21no—
33C4×C22⋊D79—21no—
34(C22⋊D79)⋊C4—21no—
35C4⋊C4×D79C2211yescharacteristic
36C22⋊C4×D79—21no—
37C42×D79C2211yescharacteristic
38#14579093C2211yescharacteristic, complemented
39#14579092C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42Dic79⋊C8C2211yescharacteristic, complemented
43#14579083C2211yescharacteristic
44#14579083C2211yescharacteristic, complemented
45#14579082C2211yescharacteristic
46#14579082C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic, complemented
49(C2×D79)⋊C8C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51#14579072C2211yescharacteristic, complemented
52C2×D8×C79C2211yescharacteristic
53C4×D4×C79C2211yescharacteristic
54C4×D4×C79C2211yescharacteristic, complemented
55#106×C79C2211yescharacteristic, complemented
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic, complemented
58#97×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929624—44no—
61C2×Dic158—21no—
62C2×D316—21no—
63C2×D316C2311yescharacteristic
64C2×D316C2311yescharacteristic
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69D4×D79—22no—
70D4×D79—22no—
71C22×Dic79—21no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74C2×C4×D79—21no—
75C2×C4×D79—21no—
76C2×C4×D79—44no—
77C2×C4×D79D411yescharacteristic
78C2×C4×D79D411yescharacteristic
79C2×C4×D79C2311yescharacteristic
80D632—22no—
81#11929609—22no—
82#11929609—22no—
83C2×C79⋊C8C2311yescharacteristic
84C2×C79⋊C8C2311yescharacteristic
85C4⋊Dic79C2311yescharacteristic
86C4⋊Dic79C2311yescharacteristic
87Dic79⋊C4—21no—
88Dic79⋊C4—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95C4×Dic79D411yescharacteristic
96C4×Dic79D411yescharacteristic
97C4×Dic79C2311yescharacteristic
98C2×D4×C79C2311yescharacteristic
99C2×D4×C79C2311yescharacteristic
100C22×C4×C79—21no—
101C22×C4×C79—21no—
102D8×C79—22no—
103C2×C8×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C4⋊C4×C79C2311yescharacteristic
106C4⋊C4×C79C2311yescharacteristic
107C22⋊C4×C79—21no—
108C22⋊C4×C79—21no—
109C42×C79C2311yescharacteristic
110C23×C79—21no—
111C23×C79—21no—
112C22×D79—24no—
113C22×D79—21no—
114C22×D79—21no—
115C22×D79—42no—
116C22×D79—42no—
117C22×D79C2×D411yescharacteristic
118D4×C79—21no—
119D4×C79—21no—
120D4×C79—21no—
121D4×C79#4112yescomplemented
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—42no—
125C2×C4×C79—42no—
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2411yescharacteristic
129C22⋊D79—24no—
130C22⋊D79—42no—
131C22⋊D79—42no—
132C22⋊D79—42no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—42no—
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138C2×Dic79C2×D411yescharacteristic
139D316—21no—
140D316—21no—
141D316—21no—
142D316—42no—
143D316#4112yescomplemented
144C4×D79—22no—
145C4×D79—21no—
146C4×D79—21no—
147C4×D79—22no—
148C4×D79—42no—
149C4×D79—42no—
150C4×D79—42no—
151C4×D79—42no—
152Dic158—42no—
153C8×C79—21no—
154C8×C79—21no—
155C79⋊C8—21no—
156C79⋊C8—21no—
157C22×C79—22no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79C22×D411yescharacteristic
164C2×D79—21no—
165C2×D79—21no—
166C2×D79—22no—
167C2×D79—48no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—41no—
172C2×D79—41no—
173C2×D79AGL(1,ℤ/8)12yes—
174C4×C79—21no—
175C4×C79—21no—
176C4×C79—41no—
177C4×C79—41no—
178C4×C79C2×#4111yescharacteristic
179C4×C79C2×#4111yescharacteristic
180Dic79—21no—
181Dic79—21no—
182Dic79—41no—
183Dic79—41no—
184Dic79AGL(1,ℤ/8)12yes—
185C2×C79—42no—
186C2×C79—81no—
187C2×C79#52511yescharacteristic
188C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
190D79—22no—
191D79—42no—
192D79—81no—
193#3109—791nomaximal, Sylow
194C79#310911yescharacteristic, complemented, Sylow
195#532—791no—
196C2×C4×D4—791no—
197#481—791no—
198#481—791no—
199#476—791no—
200#476—791no—
201#459—791no—
202#459—791no—
203#447—791no—
204#447—791no—
205#442—791no—
206#442—791no—
207#442—791no—
208#442D7911yescharacteristic, complemented
209#432—791no—
210C2×#41—1581no—
211C22×D4—791no—
212C23×C4—1581no—
213C2×D8—791no—
214C2×D8—791no—
215C2×D8—791no—
216C2×D8C2×D7911yescharacteristic
217C4⋊Q8—791no—
218#127—791no—
219#124—1581no—
220#121—791no—
221#121—791no—
222#121—1581no—
223C4×D4—791no—
224C4×D4—791no—
225C4×D4—791no—
226C4×D4—791no—
227C4×D4—1581no—
228C4×D4—1581no—
229C4×D4—1581no—
230C4×D4C2×D7911yescharacteristic
231C4×D4C2×D7911yescharacteristic, complemented
232C2×C4⋊C4—791no—
233C2×C22⋊C4—1581no—
234C2×C42—791no—
235#106—791no—
236#106—791no—
237#106—791no—
238#106C2×D7911yescharacteristic, complemented
239C4⋊C8—791no—
240C4⋊C8—791no—
241#102—791no—
242#102—791no—
243#102—791no—
244#102—791no—
245#102—791no—
246#102—791no—
247#102C2×D7911yescharacteristic
248#102C2×D7911yescharacteristic, complemented
249C22⋊C8—791no—
250C22⋊C8—791no—
251#97—791no—
252#97C2×D7911yescharacteristic, complemented
253C24—1581no—
254#41—3164no—
255C2×Q8—1581no—
256C2×D4—791no—
257C2×D4—791no—
258C2×D4—1581no—
259C2×D4—1581no—
260C2×D4—1581no—
261C2×D4—1581no—
262C2×D4—1582no—
263C2×D4—1581no—
264C2×D4—1582no—
265C2×D4C22×D7911yescharacteristic
266C2×D4C22×D7911yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—3164no—
270C22×C4—791no—
271C22×C4—791no—
272C22×C4—791no—
273C22×C4—1581no—
274C22×C4—1581no—
275C22×C4—1581no—
276C22×C4—1581no—
277C22×C4—1581no—
278D8—22no—
279D8—1582no—
280D8—1582no—
281D8—1582no—
282C2×C8—791no—
283C2×C8—791no—
284C2×C8C22×D7911yescharacteristic
285C2×C8C22×D7911yescharacteristic
286C4⋊C4—791no—
287C4⋊C4—791no—
288C4⋊C4—1581no—
289C4⋊C4—1581no—
290C4⋊C4C22×D7911yescharacteristic
291C4⋊C4C22×D7911yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—1581no—
295C22⋊C4—1581no—
296C22⋊C4—1581no—
297C22⋊C4—1581no—
298C22⋊C4—1581no—
299C22⋊C4—1581no—
300C42—791no—
301C42—791no—
302C42—791no—
303C42C22×D7911yescharacteristic
304C23—21no—
305C23—21no—
306C23—3162no—
307C23—3162no—
308C23—791no—
309C23—1584no—
310C23—1581no—
311C23—1581no—
312Q8—3162no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—3162no—
317D4—3162no—
318D4—3162no—
319D4—3162no—
320D4—792no—
321D4—1584no—
322D4—1581no—
323D4—1581no—
324D4—1581no—
325D4#1192962412yescomplemented
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—3162no—
331C2×C4—3162no—
332C2×C4—3162no—
333C2×C4—3162no—
334C2×C4—3162no—
335C2×C4—791no—
336C2×C4—791no—
337C2×C4—791no—
338C2×C4—1582no—
339C2×C4—1582no—
340C2×C4—1581no—
341C2×C4—1581no—
342C2×C4—1581no—
343C2×C4—1581no—
344C2×C4D4×D7911yescharacteristic
345C2×C4D4×D7911yescharacteristic
346C2×C4C23×D7911yescharacteristic
347C8—21no—
348C8—21no—
349C8—1581no—
350C8—1581no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—3168no—
358C22—3161no—
359C22—3161no—
360C22—3161no—
361C22—3161no—
362C22—3161no—
363C22—792no—
364C22—1582no—
365C22—1581no—
366C22—1581no—
367C22C2×D4×D7911yescharacteristic
368C4—21no—
369C4—21no—
370C4—41no—
371C4—41no—
372C4—3161no—
373C4—3161no—
374C4—792no—
375C4—1581no—
376C4—1581no—
377C4#41×D7911yescharacteristic
378C4C2×#1192962411yescharacteristic
379C2—42no—
380C2—81no—
381C2—3162no—
382C2—6321no—
383C2—1582no—
384C2#1909907211yescharacteristic
385C2AGL(1,ℤ/8)×D7911yescharacteristic
386C2AGL(1,ℤ/8)×D7911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#442×C79C2
socleC22×C79C22×D4
hypercenter#442D79
hypocenterC79#3109
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #19099110C2semidirect
2. C4×D4×D79C2semidirect
3. #19098883C2semidirect
4. #19098880C2semidirect
5. #19098852C2semidirect
6. #19098851C2semidirect
7. #19098757C2semidirect
8. #19098756C2semidirect
9. #19098698C2semidirect
10. #19098695C2semidirect
11. #19098676C2semidirect
12. #19098673C2semidirect
13. #19098673C2semidirect
14. #19098618C2semidirect
15. #442×C79C2semidirect
22. #14579160C22semidirect
23. #14579157C22semidirect
29. C4×D316C22semidirect
38. #14579093C22semidirect
39. #14579092C22semidirect
40. #14579092C22semidirect
41. Dic79⋊C8C22semidirect
42. Dic79⋊C8C22semidirect
44. #14579083C22semidirect
46. #14579082C22semidirect
48. #14579081C22semidirect
51. #14579072C22semidirect
54. C4×D4×C79C22semidirect
55. #106×C79C22semidirect
57. #102×C79C22semidirect
58. #97×C79C22semidirect
121. D4×C79#41semidirect
143. D316#41semidirect
194. C79#3109semidirect
208. #442D79semidirect
231. C4×D4C2×D79semidirect
238. #106C2×D79semidirect
248. #102C2×D79semidirect
252. #97C2×D79semidirect
325. D4#11929624semidirect