Finite Group Databasebeta

← #23775560

Subgroups — #23775560

Order 10112.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099277C211yesmaximal, characteristic, complemented
2#19099201C211yesmaximal, characteristic, complemented
3#19098924C211yesmaximal, characteristic, complemented
4#19098902C211yesmaximal, characteristic, complemented
5#19098888C211yesmaximal, characteristic, complemented
6#19098841C211yesmaximal, characteristic, complemented
7#19098806C211yesmaximal, characteristic, complemented
8#19098797C211yesmaximal, characteristic, complemented
9#19098780C211yesmaximal, characteristic, complemented
10#19098695C211yesmaximal, characteristic, complemented
11#19098675C211yesmaximal, characteristic, complemented
12#19098631C211yesmaximal, characteristic, complemented
13#19098566C211yesmaximal, characteristic, complemented
14#19098559C211yesmaximal, characteristic, complemented
15#449×C79C211yesmaximal, characteristic, complemented
16C2×D4×D79C2211yescharacteristic
17C2×#11929609C2211yescharacteristic
18C2×#11929607C2211yescharacteristic
19C22×C79⋊C8C2211yescharacteristic, complemented
20#14579160C2211yescharacteristic, complemented
21#14579150C2211yescharacteristic
22#14579148—21no—
23#14579147—21no—
24#14579144—21no—
25#14579137C2211yescharacteristic
26#14579135C2211yescharacteristic
27#14579133—21no—
28#14579133—21no—
29#14579132C2211yescharacteristic
30#14579129—21no—
31D4×Dic79C2211yescharacteristic
32D4×Dic79C2211yescharacteristic, complemented
33C4×C22⋊D79C2211yescharacteristic
34#14579120C2211yescharacteristic, complemented
35#14579119C2211yescharacteristic
36#14579117—21no—
37C2×(C2×D79)⋊C4—21no—
38#14579095C2211yescharacteristic, complemented
39#14579094C2211yescharacteristic, complemented
40#14579093C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42#14579085C2211yescharacteristic, complemented
43#14579085C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic
45#14579083C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic, complemented
49#14579081C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51#14579071C2211yescharacteristic, complemented
52C2×#41×C79C2211yescharacteristic
53C2×SD16×C79C2211yescharacteristic, complemented
54C2×D8×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic, complemented
56#103×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C2×Dic158—21no—
61C2×D316C2311yescharacteristic
62C2×C22⋊D79—21no—
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65C2×C22⋊D79D411yescharacteristic
66D4×D79—22no—
67D4×D79—41no—
68C22×Dic79—21no—
69C22×Dic79—21no—
70C2×C4×D79C2311yescharacteristic
71#11929609—41no—
72#11929607—41no—
73C2×C79⋊C8—41no—
74C2×C79⋊C8C2311yescharacteristic
75C2×C79⋊C8C2311yescharacteristic
76C4⋊Dic79C2311yescharacteristic
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81Dic79⋊C4D411yescharacteristic
82C22⋊Dic79—21no—
83C22⋊Dic79—21no—
84C22⋊Dic79—21no—
85C22⋊Dic79—21no—
86C22⋊Dic79D411yescharacteristic
87(C2×D79)⋊C4—21no—
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4D411yescharacteristic
93C4×Dic79—21no—
94C4×Dic79—21no—
95C4×Dic79C2311yescharacteristic
96#41×C79—22no—
97#41×C79—41no—
98C2×Q8×C79C2311yescharacteristic
99C2×D4×C79—21no—
100C2×D4×C79—21no—
101C2×D4×C79C2311yescharacteristic
102C2×D4×C79C2311yescharacteristic
103C22×C4×C79—21no—
104C22×C4×C79C2311yescharacteristic
105SD16×C79—41no—
106D8×C79—22no—
107C2×C8×C79C2311yescharacteristic
108C2×C8×C79C2311yescharacteristic
109C4⋊C4×C79C2311yescharacteristic
110C22⋊C4×C79—21no—
111C23×C79—21no—
112C23×C79—21no—
113C23×C79C2×D411yescharacteristic
114C22×D79—21no—
115C22×D79—42no—
116C22×D79—42no—
117C22×D79—81no—
118C22×D79C2×D411yescharacteristic
119Q8×C79—21no—
120Q8×C79—21no—
121D4×C79—21no—
122D4×C79—21no—
123D4×C79—21no—
124D4×C79—42no—
125D4×C79—81no—
126D4×C79#4112yes—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—42no—
132C2×C4×C79C2×D411yescharacteristic
133C2×C4×C79C2411yescharacteristic
134C22⋊D79—41no—
135C22⋊D79—42no—
136C22⋊D79—81no—
137C22⋊D79—81no—
138C2×Dic79—21no—
139C2×Dic79—21no—
140C2×Dic79—21no—
141C2×Dic79—42no—
142C2×Dic79—81no—
143C2×Dic79C2×D411yescharacteristic
144C2×Dic79C2×D411yescharacteristic
145C2×Dic79C2×D411yescharacteristic
146D316—21no—
147D316—21no—
148C4×D79—21no—
149C4×D79—21no—
150Dic158—81no—
151C8×C79—21no—
152C8×C79—21no—
153C79⋊C8—21no—
154C79⋊C8—21no—
155C22×C79—22no—
156C22×C79—21no—
157C22×C79—21no—
158C22×C79—21no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79C22×D411yescharacteristic
165C2×D79—21no—
166C2×D79—21no—
167C2×D79—21no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—84no—
172C4×C79—21no—
173C4×C79—41no—
174C4×C79—41no—
175C4×C79C2×#4111yescharacteristic
176C4×C79H(5,𝔽2)11yescharacteristic
177Dic79—21no—
178Dic79—21no—
179Dic79—21no—
180Dic79—41no—
181Dic79—41no—
182Dic79—41no—
183C2×C79—42no—
184C2×C79—41no—
185C2×C79—81no—
186C2×C79#54611yescharacteristic
187C2×C79#57511yescharacteristic
188C2×C79#57611yescharacteristic
189D79—41no—
190D79—81no—
191#3319—791nomaximal, Sylow
192C79#331911yescharacteristic, complemented, Sylow
193#555—791no—
194#546—791no—
195#489—791no—
196#485—791no—
197#482—791no—
198#474—791no—
199#468—791no—
200#466—791no—
201#463—791no—
202#449D7911yescharacteristic, complemented
203#447—791no—
204#442—791no—
205#435—791no—
206#418—791no—
207#416—791no—
208C2×#41C2×D7911yescharacteristic
209C22×D4—791no—
210C2×SD16C2×D7911yescharacteristic, complemented
211C2×D8—791no—
212C2×D8C2×D7911yescharacteristic
213C2×M16—791no—
214C22×C8—791no—
215C4⋊Q8—791no—
216#124—791no—
217#124—1581no—
218#124—1581no—
219#123—1581no—
220C22⋊Q8—791no—
221#121—791no—
222#121—791no—
223#121—1581no—
224#121—1581no—
225#121C2×D7911yescharacteristic, complemented
226#120—1581no—
227C4×D4—791no—
228C4×D4—791no—
229C4×D4—791no—
230#117—791no—
231#117—791no—
232#117—1581no—
233C2×C22⋊C4—1581no—
234#107—791no—
235#107—791no—
236#106—791no—
237C4⋊C8—791no—
238#103—791no—
239#103—791no—
240#103C2×D7911yescharacteristic, complemented
241#102—791no—
242#102—791no—
243#102—791no—
244#102—791no—
245#102—791no—
246#102—791no—
247#102C2×D7911yescharacteristic
248C22⋊C8—791no—
249C22⋊C8C2×D7911yescharacteristic, complemented
250#97—791no—
251C24—1581no—
252#41—22no—
253#41—41no—
254C2×Q8—1581no—
255C2×Q8C22×D7911yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—3161no—
259C2×D4—791no—
260C2×D4—791no—
261C2×D4—1581no—
262C2×D4—1582no—
263C2×D4—1581no—
264C2×D4—1581no—
265C2×D4C22×D7911yescharacteristic
266C2×D4C22×D7911yescharacteristic
267C22×C4—21no—
268C22×C4—791no—
269C22×C4—1581no—
270C22×C4—1581no—
271C22×C4C22×D7911yescharacteristic
272SD16—41no—
273D8—22no—
274D8—3161no—
275M16—3161no—
276C2×C8—3161no—
277C2×C8—791no—
278C2×C8—791no—
279C2×C8C22×D7911yescharacteristic
280C2×C8C22×D7911yescharacteristic
281C4⋊C4—791no—
282C4⋊C4—791no—
283C4⋊C4—791no—
284C4⋊C4—791no—
285C4⋊C4—1581no—
286C4⋊C4—1581no—
287C4⋊C4C22×D7911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—791no—
290C22⋊C4—791no—
291C22⋊C4—1581no—
292C22⋊C4—1581no—
293C22⋊C4—1581no—
294C22⋊C4—1581no—
295C22⋊C4—1581no—
296C22⋊C4—1581no—
297C22⋊C4—1581no—
298C22⋊C4—1581no—
299C22⋊C4—1581no—
300C42—791no—
301C42—1581no—
302C42—1581no—
303C23—21no—
304C23—21no—
305C23—3162no—
306C23—3162no—
307C23—791no—
308C23—6321no—
309C23—1581no—
310C23D4×D7911yescharacteristic
311Q8—21no—
312Q8—21no—
313Q8—6321no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—42no—
318D4—81no—
319D4—3162no—
320D4—3161no—
321D4—6321no—
322D4—6321no—
323D4—1581no—
324D4—1581no—
325D4#1192962312yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—3162no—
332C2×C4—791no—
333C2×C4—791no—
334C2×C4—791no—
335C2×C4—6321no—
336C2×C4—1581no—
337C2×C4—1581no—
338C2×C4—1581no—
339C2×C4—1581no—
340C2×C4—1581no—
341C2×C4D4×D7911yescharacteristic
342C2×C4C23×D7911yescharacteristic
343C8—21no—
344C8—21no—
345C8—1581no—
346C8—1581no—
347C22—21no—
348C22—22no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—3161no—
357C22—3161no—
358C22—3161no—
359C22—6324no—
360C22—1581no—
361C22—1581no—
362C22—1581no—
363C22C2×D4×D7911yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—3161no—
368C4—3161no—
369C4—3161no—
370C4—1581no—
371C4—1581no—
372C4—1581no—
373C4C2×#1192962311yescharacteristic
374C4#1457920611yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—3161no—
379C2—6321no—
380C2#1909920011yescharacteristic
381C2#1909936011yescharacteristic
382C2#1909936711yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#449×C79C2
socleC22×C79C22×D4
hypercenter#449D79
hypocenterC79#3319
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. #19099277C2semidirect
2. #19099201C2semidirect
3. #19098924C2semidirect
4. #19098902C2semidirect
5. #19098888C2semidirect
6. #19098841C2semidirect
7. #19098806C2semidirect
8. #19098797C2semidirect
9. #19098780C2semidirect
10. #19098695C2semidirect
11. #19098675C2semidirect
12. #19098631C2semidirect
13. #19098566C2semidirect
14. #19098559C2semidirect
15. #449×C79C2semidirect
19. C22×C79⋊C8C22semidirect
20. #14579160C22semidirect
32. D4×Dic79C22semidirect
34. #14579120C22semidirect
38. #14579095C22semidirect
39. #14579094C22semidirect
40. #14579093C22semidirect
41. Dic79⋊C8C22semidirect
42. #14579085C22semidirect
43. #14579085C22semidirect
48. #14579082C22semidirect
51. #14579071C22semidirect
53. C2×SD16×C79C22semidirect
55. #121×C79C22semidirect
56. #103×C79C22semidirect
58. C22⋊C8×C79C22semidirect
192. C79#3319semidirect
202. #449D79semidirect
210. C2×SD16C2×D79semidirect
225. #121C2×D79semidirect
240. #103C2×D79semidirect
249. C22⋊C8C2×D79semidirect