Finite Group Databasebeta

← #23775359

Subgroups — #23775359

Order 10112.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099214C211yesmaximal, characteristic, complemented
2#19099204C211yesmaximal, characteristic, complemented
3#19098924C211yesmaximal, characteristic, complemented
4#19098883C211yesmaximal, characteristic, complemented
5#19098852C211yesmaximal, characteristic, complemented
6#19098817C211yesmaximal, characteristic, complemented
7#19098794C211yesmaximal, characteristic, complemented
8#19098781C211yesmaximal, characteristic, complemented
9#19098711C211yesmaximal, characteristic, complemented
10#19098699C211yesmaximal, characteristic, complemented
11#19098674C211yesmaximal, characteristic, complemented
12#19098631C211yesmaximal, characteristic, complemented
13#19098563C211yesmaximal, characteristic, complemented
14C2×#14579081C211yesmaximal, characteristic, complemented
15#483×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C2×#11929624—21no—
18C22×D316C2211yescharacteristic
19C2×#11929611C2211yescharacteristic, complemented
20C2×D632C2211yescharacteristic
21C2×D632C2211yescharacteristic
22C2×#11929607C2211yescharacteristic, complemented
23C22×C79⋊C8C2211yescharacteristic
24#14579160C2211yescharacteristic, complemented
25#14579150C2211yescharacteristic
26#14579146—21no—
27#14579146—21no—
28#14579144—21no—
29#14579139—21no—
30#14579136—21no—
31#14579136C2211yescharacteristic
32#14579136C2211yescharacteristic, complemented
33#14579135C2211yescharacteristic
34#14579131—21no—
35#14579123C2211yescharacteristic
36#14579123C2211yescharacteristic, complemented
37C4×C22⋊D79C2211yescharacteristic
38C4⋊C4×D79C2211yescharacteristic, complemented
39C22⋊C4×D79—21no—
40#14579092C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42#14579085C2211yescharacteristic, complemented
43#14579083C2211yescharacteristic
44#14579083C2211yescharacteristic
45#14579081C2211yescharacteristic
46#14579081C2211yescharacteristic
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic
49#14579081C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51#14579071C2211yescharacteristic, complemented
52C22⋊Q8×C79C2211yescharacteristic
53C2×C4⋊C4×C79C2211yescharacteristic
54#106×C79C2211yescharacteristic, complemented
55#106×C79C2211yescharacteristic, complemented
56#103×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58C22⋊C8×C79C2211yescharacteristic
59C23×D79—21no—
60#11929625—22no—
61#11929625—41no—
62#11929624—44no—
63C2×Dic158—21no—
64C2×D316—21no—
65C2×D316—21no—
66C2×D316—21no—
67C2×D316—22no—
68C2×D316—21no—
69C2×D316—41no—
70C2×D316C2311yescharacteristic
71C2×D316C2311yescharacteristic
72C2×D316C2311yescharacteristic
73C2×C22⋊D79—21no—
74C2×C22⋊D79D411yescharacteristic
75C2×C4×D79—21no—
76C2×C4×D79—21no—
77C2×C4×D79—21no—
78C2×C4×D79—21no—
79C2×C4×D79C2311yescharacteristic
80#11929611—41no—
81D632—22no—
82D632—41no—
83#11929607—41no—
84C2×C79⋊C8—41no—
85C2×C79⋊C8C2311yescharacteristic
86C2×C79⋊C8C2311yescharacteristic
87C4⋊Dic79C2311yescharacteristic
88Dic79⋊C4—21no—
89Dic79⋊C4—21no—
90Dic79⋊C4D411yescharacteristic
91C22⋊Dic79D411yescharacteristic
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4—21no—
98(C2×D79)⋊C4—21no—
99(C2×D79)⋊C4D411yescharacteristic
100C4×Dic79C2311yescharacteristic
101C2×Q8×C79C2311yescharacteristic
102C22×C4×C79—21no—
103C22×C4×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C4⋊C4×C79—21no—
107C4⋊C4×C79—21no—
108C4⋊C4×C79C2311yescharacteristic
109C4⋊C4×C79C2311yescharacteristic
110C4⋊C4×C79C2311yescharacteristic
111C22⋊C4×C79—21no—
112C23×C79C2×D411yescharacteristic
113C22×D79—21no—
114C22×D79—21no—
115C22×D79—21no—
116C22×D79—42no—
117C22×D79—42no—
118C22×D79—81no—
119C22×D79C2×D411yescharacteristic
120Q8×C79—21no—
121Q8×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—42no—
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2411yescharacteristic
131C22⋊D79—22no—
132C22⋊D79—42no—
133C2×Dic79—21no—
134C2×Dic79C2×D411yescharacteristic
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137D316—21no—
138D316—21no—
139D316—21no—
140D316—21no—
141D316—21no—
142D316—42no—
143D316—42no—
144D316—42no—
145D316—81no—
146D316#4112yescomplemented
147C4×D79—21no—
148C4×D79—21no—
149C4×D79—42no—
150C4×D79—42no—
151C4×D79—42no—
152C4×D79—81no—
153Dic158—42no—
154C8×C79—21no—
155C8×C79—21no—
156C79⋊C8—21no—
157C79⋊C8—21no—
158C22×C79—21no—
159C22×C79—21no—
160C22×C79AGL(1,ℤ/8)12yes—
161C22×C79C22×D411yescharacteristic
162C2×D79—22no—
163C2×D79—21no—
164C2×D79—21no—
165C2×D79—21no—
166C2×D79—41no—
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—41no—
172C2×D79—41no—
173C2×D79—41no—
174C2×D79—84no—
175C4×C79—21no—
176C4×C79—41no—
177C4×C79—41no—
178C4×C79—41no—
179C4×C79—41no—
180C4×C79C2×#4111yescharacteristic
181C4×C79H(5,𝔽2)11yescharacteristic
182Dic79—21no—
183Dic79—21no—
184Dic79—21no—
185Dic79—41no—
186C2×C79—22no—
187C2×C79#54611yescharacteristic
188C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C79#57711yescharacteristic
190D79—41no—
191D79—42no—
192D79—81no—
193D79—81no—
194#3306—791nomaximal, Sylow
195C79#330611yescharacteristic, complemented, Sylow
196#547—791no—
197#546—791no—
198#489—791no—
199#483D7911yescharacteristic, complemented
200#481—791no—
201#476—791no—
202#469—791no—
203#465—791no—
204#463—791no—
205#449—791no—
206#447—791no—
207#442—791no—
208#435—791no—
209#417—791no—
210C2×#102—791no—
211C2×#41—791no—
212C2×#41—1581no—
213C22×D4—791no—
214C2×SD16—791no—
215C2×D8—791no—
216C2×D8—791no—
217C2×M16—791no—
218C22×C8—791no—
219C4⋊Q8—791no—
220#124—791no—
221#123—1581no—
222#123—1581no—
223#123—1581no—
224C22⋊Q8—1581no—
225C22⋊Q8C2×D7911yescharacteristic
226#121—791no—
227#121—791no—
228#121—791no—
229#121—1581no—
230#120—1581no—
231C4×D4—791no—
232C4×D4—791no—
233C4×D4—791no—
234C2×C4⋊C4—791no—
235C2×C4⋊C4C2×D7911yescharacteristic
236C2×C22⋊C4—1581no—
237#106—791no—
238#106C2×D7911yescharacteristic, complemented
239#106C2×D7911yescharacteristic, complemented
240C4⋊C8—791no—
241#103—791no—
242#103C2×D7911yescharacteristic, complemented
243#103C2×D7911yescharacteristic, complemented
244#102—791no—
245#102—791no—
246#102—791no—
247#102—791no—
248#102—791no—
249#102—791no—
250#102—791no—
251C22⋊C8—791no—
252C22⋊C8C2×D7911yescharacteristic
253#97—791no—
254C24—1581no—
255#41—3164no—
256#41—3161no—
257#41—1582no—
258C2×Q8—1581no—
259C2×Q8C22×D7911yescharacteristic
260C2×D4—3161no—
261C2×D4—791no—
262C2×D4—791no—
263C2×D4—791no—
264C2×D4—791no—
265C2×D4—1581no—
266C2×D4—1581no—
267C2×D4—1582no—
268C2×D4—1581no—
269C2×D4—1581no—
270C2×D4—1581no—
271C22×C4—21no—
272C22×C4—791no—
273C22×C4—1581no—
274C22×C4—1581no—
275C22×C4—1581no—
276C22×C4—1581no—
277C22×C4C22×D7911yescharacteristic
278SD16—3161no—
279D8—3161no—
280D8—1582no—
281M16—3161no—
282C2×C8—3161no—
283C2×C8—791no—
284C2×C8—791no—
285C2×C8C22×D7911yescharacteristic
286C2×C8C22×D7911yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—791no—
290C4⋊C4—791no—
291C4⋊C4—1581no—
292C4⋊C4—1581no—
293C4⋊C4C22×D7911yescharacteristic
294C4⋊C4C22×D7911yescharacteristic
295C4⋊C4C22×D7911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—791no—
298C22⋊C4—791no—
299C22⋊C4—1581no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C22⋊C4—1581no—
305C22⋊C4—1581no—
306C42—791no—
307C23—3162no—
308C23—3162no—
309C23—791no—
310C23—6321no—
311C23—1581no—
312C23—1581no—
313C23—1581no—
314C23D4×D7911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—3162no—
318D4—3162no—
319D4—3162no—
320D4—3162no—
321D4—3162no—
322D4—792no—
323D4—6321no—
324D4—1582no—
325D4—1581no—
326D4—1581no—
327D4—1581no—
328D4—1581no—
329D4—1581no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—3162no—
338C2×C4—3162no—
339C2×C4—3162no—
340C2×C4—791no—
341C2×C4—791no—
342C2×C4—791no—
343C2×C4—6321no—
344C2×C4—1581no—
345C2×C4—1581no—
346C2×C4—1581no—
347C2×C4D4×D7911yescharacteristic
348C2×C4C23×D7911yescharacteristic
349C8—21no—
350C8—21no—
351C8—1581no—
352C8—1581no—
353C22—21no—
354C22—21no—
355C22—3161no—
356C22—3161no—
357C22—3161no—
358C22—3161no—
359C22—3161no—
360C22—3161no—
361C22—3161no—
362C22—3161no—
363C22—6324no—
364C22—1582no—
365C22—1581no—
366C22—1581no—
367C22—1581no—
368C22#1457918812yes—
369C22C2×D4×D7911yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—3161no—
376C4—1581no—
377C4—1581no—
378C4—1581no—
379C4#41×D7911yescharacteristic
380C4#1457920711yescharacteristic
381C2—22no—
382C2—3162no—
383C2—3161no—
384C2—6321no—
385C2—6321no—
386C2#1909920511yescharacteristic
387C2C2×#1457918811yescharacteristic
388C2#1909937211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#483×C79C2
socleC22×C79C22×D4
hypercenter#483D79
hypocenterC79#3306
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #19099214C2semidirect
2. #19099204C2semidirect
3. #19098924C2semidirect
4. #19098883C2semidirect
5. #19098852C2semidirect
6. #19098817C2semidirect
7. #19098794C2semidirect
8. #19098781C2semidirect
9. #19098711C2semidirect
10. #19098699C2semidirect
11. #19098674C2semidirect
12. #19098631C2semidirect
13. #19098563C2semidirect
14. C2×#14579081C2semidirect
15. #483×C79C2semidirect
19. C2×#11929611C22semidirect
22. C2×#11929607C22semidirect
24. #14579160C22semidirect
32. #14579136C22semidirect
36. #14579123C22semidirect
38. C4⋊C4×D79C22semidirect
40. #14579092C22semidirect
41. Dic79⋊C8C22semidirect
42. #14579085C22semidirect
49. #14579081C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. #14579071C22semidirect
54. #106×C79C22semidirect
55. #106×C79C22semidirect
56. #103×C79C22semidirect
57. #103×C79C22semidirect
146. D316#41semidirect
195. C79#3306semidirect
199. #483D79semidirect
238. #106C2×D79semidirect
239. #106C2×D79semidirect
242. #103C2×D79semidirect
243. #103C2×D79semidirect