Finite Group Databasebeta

← #23774212

Subgroups — #23774212

Order 10112.

466 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099070C211yesmaximal, characteristic, complemented
2#121×D79C211yesmaximal, characteristic, complemented
3#19098892C211yesmaximal, characteristic, complemented
4#19098888C211yesmaximal, characteristic, complemented
5#19098884C211yesmaximal, characteristic, complemented
6#19098875C211yesmaximal, characteristic, complemented
7#19098815C211yesmaximal, characteristic, complemented
8#19098813C211yesmaximal, characteristic, complemented
9#19098812C211yesmaximal, characteristic, complemented
10#19098806C211yesmaximal, characteristic, complemented
11#19098712C211yesmaximal, characteristic, complemented
12#19098708C211yesmaximal, characteristic, complemented
13#19098695C211yesmaximal, characteristic, complemented
14#19098525C211yesmaximal, characteristic, complemented
15#449×C79C211yesmaximal, characteristic, complemented
16C2×D4×D79—21no—
17C2×D4×D79C2211yescharacteristic
18C22×C4×D79C2211yescharacteristic
19C2×#11929611C2211yescharacteristic, complemented
20C2×#11929609C2211yescharacteristic, complemented
21C2×#11929607C2211yescharacteristic, complemented
22C2×#11929607C2211yescharacteristic, complemented
23#14579142—21no—
24#14579137C2211yescharacteristic
25#14579137C2211yescharacteristic, complemented
26#14579136C2211yescharacteristic
27#14579135C2211yescharacteristic
28#14579134—21no—
29#14579133—21no—
30#14579132C2211yescharacteristic
31#14579132C2211yescharacteristic
32#14579132C2211yescharacteristic, complemented
33#14579129—21no—
34C4×C22⋊D79—21no—
35C4×C22⋊D79—21no—
36#14579120C2211yescharacteristic, complemented
37C4⋊C4×D79C2211yescharacteristic
38C22⋊C4×D79—21no—
39#14579095C2211yescharacteristic, complemented
40#14579094C2211yescharacteristic, complemented
41#14579093C2211yescharacteristic, complemented
42#14579092C2211yescharacteristic, complemented
43#14579085C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic, complemented
46#14579082C2211yescharacteristic, complemented
47#14579082C2211yescharacteristic, complemented
48#14579082C2211yescharacteristic, complemented
49C22⋊(C79⋊C8)C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic
51(C2×D79)⋊C8C2211yescharacteristic
52C2×#41×C79C2211yescharacteristic, complemented
53C2×SD16×C79C2211yescharacteristic, complemented
54C2×D8×C79C2211yescharacteristic, complemented
55#121×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic, complemented
58C22⋊C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C23×D79D411yescharacteristic
61C2×D316—21no—
62C2×D316C2311yescharacteristic
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68D4×D79—41no—
69D4×D79—41no—
70D4×D79—44no—
71C22×Dic79D411yescharacteristic
72C2×C4×D79—21no—
73C2×C4×D79—41no—
74C2×C4×D79—41no—
75C2×C4×D79D411yescharacteristic
76C2×C4×D79D411yescharacteristic
77C2×C4×D79C2311yescharacteristic
78C2×C4×D79C2311yescharacteristic
79#11929611—41no—
80#11929609—41no—
81#11929607—41no—
82#11929607—41no—
83C2×C79⋊C8C2311yescharacteristic
84C2×C79⋊C8C2311yescharacteristic
85C4⋊Dic79C2311yescharacteristic
86C4⋊Dic79C2311yescharacteristic
87C4⋊Dic79C2311yescharacteristic
88Dic79⋊C4—21no—
89Dic79⋊C4—21no—
90Dic79⋊C4—21no—
91C22⋊Dic79—21no—
92C22⋊Dic79—21no—
93C22⋊Dic79—21no—
94C22⋊Dic79—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4—21no—
98(C2×D79)⋊C4—21no—
99C4×Dic79—21no—
100#41×C79—41no—
101#41×C79—41no—
102C2×Q8×C79C2311yescharacteristic
103C2×D4×C79—21no—
104C2×D4×C79—21no—
105C2×D4×C79C2311yescharacteristic
106C2×D4×C79C2311yescharacteristic
107C22×C4×C79—21no—
108C22×C4×C79C2311yescharacteristic
109SD16×C79—41no—
110D8×C79—41no—
111C2×C8×C79C2311yescharacteristic
112C2×C8×C79C2311yescharacteristic
113C4⋊C4×C79C2311yescharacteristic
114C22⋊C4×C79—21no—
115C23×C79—21no—
116C23×C79—21no—
117C23×C79C2×D411yescharacteristic
118C22×D79—22no—
119C22×D79—21no—
120C22×D79—41no—
121C22×D79—41no—
122C22×D79—42no—
123C22×D79—42no—
124C22×D79—42no—
125C22×D79C2×D411yescharacteristic
126C22×D79C2×D411yescharacteristic
127Q8×C79—21no—
128Q8×C79—21no—
129D4×C79—21no—
130D4×C79—21no—
131D4×C79—21no—
132D4×C79—21no—
133D4×C79—42no—
134D4×C79—42no—
135C2×C4×C79—21no—
136C2×C4×C79—21no—
137C2×C4×C79—21no—
138C2×C4×C79—21no—
139C2×C4×C79—42no—
140C2×C4×C79C2×D411yescharacteristic
141C2×C4×C79C2411yescharacteristic
142C22⋊D79—42no—
143C22⋊D79—42no—
144C22⋊D79—42no—
145C22⋊D79—42no—
146C22⋊D79—42no—
147C2×Dic79—21no—
148C2×Dic79—21no—
149C2×Dic79—21no—
150C2×Dic79—41no—
151C2×Dic79C2×D411yescharacteristic
152C2×Dic79C2×D411yescharacteristic
153D316—21no—
154D316—21no—
155D316—42no—
156C4×D79—21no—
157C4×D79—21no—
158C4×D79—21no—
159C4×D79—21no—
160C4×D79—41no—
161C4×D79—41no—
162C4×D79—42no—
163C8×C79—21no—
164C8×C79—21no—
165C79⋊C8—21no—
166C79⋊C8—21no—
167C22×C79—21no—
168C22×C79—21no—
169C22×C79—21no—
170C22×C79—41no—
171C22×C79—41no—
172C22×C79—41no—
173C22×C79—41no—
174C22×C79—41no—
175C22×C79—41no—
176C22×C79C22×D411yescharacteristic
177C2×D79—21no—
178C2×D79—21no—
179C2×D79—21no—
180C2×D79—21no—
181C2×D79—21no—
182C2×D79—44no—
183C2×D79—41no—
184C2×D79—41no—
185C2×D79—41no—
186C2×D79—84no—
187C2×D79AGL(1,ℤ/8)12yes—
188C4×C79—21no—
189C4×C79—41no—
190C4×C79—41no—
191C4×C79H(5,𝔽2)11yescharacteristic
192C4×C79H(5,𝔽2)11yescharacteristic
193Dic79—21no—
194Dic79—21no—
195Dic79—41no—
196Dic79—41no—
197Dic79—41no—
198C2×C79—41no—
199C2×C79—81no—
200C2×C79—81no—
201C2×C79#53411yescharacteristic
202C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
203C2×C79#57511yescharacteristic
204D79—22no—
205D79—41no—
206D79—81no—
207#3194—791nomaximal, Sylow
208C79#319411yescharacteristic, complemented, Sylow
209#525—791no—
210C2×#121—791no—
211#483—791no—
212#482—791no—
213#482—791no—
214#480—791no—
215#469—791no—
216#469—791no—
217#468—791no—
218#468—791no—
219#450—791no—
220#449—791no—
221#449D7911yescharacteristic, complemented
222#447—791no—
223#407—791no—
224C2×#41C2×D7911yescharacteristic, complemented
225C22×D4—791no—
226C22×D4—1581no—
227C23×C4—791no—
228C2×SD16—791no—
229C2×SD16C2×D7911yescharacteristic, complemented
230C2×D8—791no—
231C2×D8C2×D7911yescharacteristic, complemented
232C2×M16—791no—
233C2×M16—791no—
234#123—1581no—
235C22⋊Q8—791no—
236C22⋊Q8—791no—
237#121—791no—
238#121—791no—
239#121—791no—
240#121—791no—
241#121—791no—
242#121—1581no—
243#121—1581no—
244#121C2×D7911yescharacteristic
245#120—1581no—
246C4×D4—1581no—
247C4×D4—1581no—
248#117—791no—
249C2×C4⋊C4—791no—
250C2×C22⋊C4—1581no—
251#107—791no—
252#107—791no—
253#106—791no—
254#106—791no—
255#103—791no—
256#103C2×D7911yescharacteristic, complemented
257#102—791no—
258#102—791no—
259#102—791no—
260#102—791no—
261#102—791no—
262#102C2×D7911yescharacteristic, complemented
263C22⋊C8—791no—
264C22⋊C8—791no—
265C22⋊C8—791no—
266C22⋊C8C2×D7911yescharacteristic, complemented
267C24—791no—
268C24—1581no—
269#41—41no—
270#41—41no—
271C2×Q8C22×D7911yescharacteristic
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—3164no—
275C2×D4—3161no—
276C2×D4—3161no—
277C2×D4—791no—
278C2×D4—1581no—
279C2×D4—1581no—
280C2×D4—1581no—
281C2×D4—1581no—
282C2×D4—1581no—
283C2×D4—1581no—
284C2×D4C22×D7911yescharacteristic
285C2×D4C22×D7911yescharacteristic
286C22×C4—21no—
287C22×C4—3161no—
288C22×C4—3161no—
289C22×C4—791no—
290C22×C4—791no—
291C22×C4—791no—
292C22×C4—791no—
293C22×C4—791no—
294C22×C4—1581no—
295C22×C4C22×D7911yescharacteristic
296SD16—41no—
297SD16—3161no—
298D8—41no—
299D8—3161no—
300M16—3161no—
301M16—3161no—
302C2×C8—791no—
303C2×C8—791no—
304C2×C8C22×D7911yescharacteristic
305C2×C8C22×D7911yescharacteristic
306C4⋊C4—791no—
307C4⋊C4—791no—
308C4⋊C4—791no—
309C4⋊C4—1581no—
310C4⋊C4—1581no—
311C4⋊C4—1581no—
312C4⋊C4C22×D7911yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—1581no—
315C22⋊C4—1581no—
316C22⋊C4—1581no—
317C22⋊C4—1581no—
318C22⋊C4—1581no—
319C22⋊C4—1581no—
320C22⋊C4—1581no—
321C22⋊C4—1581no—
322C42—1581no—
323C23—21no—
324C23—21no—
325C23—3161no—
326C23—3161no—
327C23—3162no—
328C23—3162no—
329C23—3162no—
330C23—791no—
331C23—791no—
332C23—1582no—
333C23—1581no—
334C23D4×D7911yescharacteristic
335Q8—21no—
336Q8—21no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—3162no—
344D4—3162no—
345D4—3162no—
346D4—3162no—
347D4—3162no—
348D4—3162no—
349D4—1581no—
350D4—1581no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—3161no—
357C2×C4—3161no—
358C2×C4—3162no—
359C2×C4—3161no—
360C2×C4—791no—
361C2×C4—791no—
362C2×C4—1581no—
363C2×C4—1581no—
364C2×C4—1581no—
365C2×C4—1581no—
366C2×C4—1581no—
367C2×C4—1581no—
368C2×C4—1581no—
369C2×C4D4×D7911yescharacteristic
370C2×C4C23×D7911yescharacteristic
371C8—21no—
372C8—21no—
373C8—1581no—
374C8—1581no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—3164no—
385C22—3161no—
386C22—3161no—
387C22—3161no—
388C22—792no—
389C22—6324no—
390C22—1581no—
391C22—1581no—
392C22—1581no—
393C22—1581no—
394C22—1581no—
395C22C2×D4×D7911yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—3161no—
400C4—3161no—
401C4—3161no—
402C4—1581no—
403C4—1581no—
404C4#1457920611yescharacteristic
405C4#1457920611yescharacteristic
406C2—41no—
407C2—81no—
408C2—81no—
409C2—3161no—
410C2—6321no—
411C2—1582no—
412C2#1909912311yescharacteristic
413C2AGL(1,ℤ/8)×D7911yescharacteristic
414C2#1909936011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#449×C79C2
socleC22×C79C22×D4
hypercenter#449D79
hypocenterC79#3194
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #19099070C2semidirect
2. #121×D79C2semidirect
3. #19098892C2semidirect
4. #19098888C2semidirect
5. #19098884C2semidirect
6. #19098875C2semidirect
7. #19098815C2semidirect
8. #19098813C2semidirect
9. #19098812C2semidirect
10. #19098806C2semidirect
11. #19098712C2semidirect
12. #19098708C2semidirect
13. #19098695C2semidirect
14. #19098525C2semidirect
15. #449×C79C2semidirect
19. C2×#11929611C22semidirect
20. C2×#11929609C22semidirect
21. C2×#11929607C22semidirect
22. C2×#11929607C22semidirect
25. #14579137C22semidirect
32. #14579132C22semidirect
36. #14579120C22semidirect
39. #14579095C22semidirect
40. #14579094C22semidirect
41. #14579093C22semidirect
42. #14579092C22semidirect
43. #14579085C22semidirect
44. #14579083C22semidirect
45. #14579083C22semidirect
46. #14579082C22semidirect
47. #14579082C22semidirect
48. #14579082C22semidirect
49. C22⋊(C79⋊C8)C22semidirect
52. C2×#41×C79C22semidirect
53. C2×SD16×C79C22semidirect
54. C2×D8×C79C22semidirect
56. #103×C79C22semidirect
57. #102×C79C22semidirect
58. C22⋊C8×C79C22semidirect
208. C79#3194semidirect
221. #449D79semidirect
224. C2×#41C2×D79semidirect
229. C2×SD16C2×D79semidirect
231. C2×D8C2×D79semidirect
256. #103C2×D79semidirect
262. #102C2×D79semidirect
266. C22⋊C8C2×D79semidirect