Finite Group Databasebeta

← #23775360

Subgroups — #23775360

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#19099216C211yesmaximal, characteristic, complemented
2#19099206C211yesmaximal, characteristic, complemented
3#19098892C211yesmaximal, characteristic, complemented
4#19098880C211yesmaximal, characteristic, complemented
5#19098850C211yesmaximal, characteristic, complemented
6#19098815C211yesmaximal, characteristic, complemented
7#19098795C211yesmaximal, characteristic, complemented
8#19098775C211yesmaximal, characteristic, complemented
9#19098711C211yesmaximal, characteristic, complemented
10#19098698C211yesmaximal, characteristic, complemented
11#19098676C211yesmaximal, characteristic, complemented
12#19098636C211yesmaximal, characteristic, complemented
13#19098563C211yesmaximal, characteristic, complemented
14#102×D79C211yesmaximal, characteristic, complemented
15#489×C79C211yesmaximal, characteristic, complemented
16C2×#11929625—21no—
17C2×#11929625C2211yescharacteristic
18C2×D4×D79C2211yescharacteristic
19C2×#11929611C2211yescharacteristic, complemented
20C2×D632C2211yescharacteristic
21C2×#11929609C2211yescharacteristic
22C2×#11929607C2211yescharacteristic, complemented
23C2×C8×D79C2211yescharacteristic
24#14579146—21no—
25#14579146—21no—
26#14579143—21no—
27#14579137—21no—
28#14579137C2211yescharacteristic
29#14579136C2211yescharacteristic
30#14579136C2211yescharacteristic, complemented
31#14579134—21no—
32#14579132C2211yescharacteristic
33#14579131—21no—
34C4×D316C2211yescharacteristic
35C4×D316C2211yescharacteristic
36C4×D316C2211yescharacteristic, complemented
37C4⋊C4×D79C2211yescharacteristic
38C4⋊C4×D79C2211yescharacteristic, complemented
39C22⋊C4×D79—21no—
40#14579093C2211yescharacteristic, complemented
41#14579092C2211yescharacteristic, complemented
42#14579092C2211yescharacteristic, complemented
43C4⋊(C79⋊C8)C2211yescharacteristic, complemented
44#14579085C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic
46#14579083C2211yescharacteristic, complemented
47#14579082C2211yescharacteristic
48#14579081C2211yescharacteristic
49#14579081C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51(C2×D79)⋊C8C2211yescharacteristic, complemented
52C4⋊Q8×C79C2211yescharacteristic, complemented
53#124×C79C2211yescharacteristic
54#103×C79C2211yescharacteristic, complemented
55#103×C79C2211yescharacteristic, complemented
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58#97×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929625—22no—
61#11929625—41no—
62#11929625—44no—
63C2×D316—21no—
64C2×D316—21no—
65C2×D316—21no—
66C2×D316D411yescharacteristic
67C2×D316C2311yescharacteristic
68C2×D316C2311yescharacteristic
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71D4×D79—22no—
72D4×D79—41no—
73C2×C4×D79—21no—
74C2×C4×D79—21no—
75C2×C4×D79—21no—
76C2×C4×D79—21no—
77C2×C4×D79—21no—
78C2×C4×D79C2311yescharacteristic
79C2×C4×D79C2311yescharacteristic
80#11929611—41no—
81D632—22no—
82#11929609—41no—
83#11929607—41no—
84C2×C79⋊C8C2311yescharacteristic
85C2×C79⋊C8C2311yescharacteristic
86C8×D79—41no—
87C4⋊Dic79D411yescharacteristic
88C4⋊Dic79C2311yescharacteristic
89C4⋊Dic79C2311yescharacteristic
90Dic79⋊C4—21no—
91Dic79⋊C4—21no—
92Dic79⋊C4—21no—
93C22⋊Dic79—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
100(C2×D79)⋊C4D411yescharacteristic
101C2×Q8×C79—21no—
102C2×Q8×C79C2311yescharacteristic
103C2×D4×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C4⋊C4×C79—21no—
107C4⋊C4×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C22⋊C4×C79—21no—
110C22⋊C4×C79—21no—
111C42×C79C2311yescharacteristic
112C23×C79—21no—
113C22×D79—21no—
114C22×D79—21no—
115C22×D79—42no—
116C22×D79—42no—
117C22×D79—81no—
118C22×D79C2×D411yescharacteristic
119C22×D79C2×D411yescharacteristic
120Q8×C79—21no—
121Q8×C79—21no—
122Q8×C79—42no—
123D4×C79—21no—
124D4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2411yescharacteristic
131C22⋊D79—42no—
132C22⋊D79—81no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137D316—22no—
138D316—21no—
139D316—21no—
140D316—21no—
141D316—42no—
142D316—42no—
143D316—42no—
144D316#4112yescomplemented
145C4×D79—21no—
146C4×D79—21no—
147C4×D79—21no—
148C4×D79—21no—
149C4×D79—42no—
150C4×D79—42no—
151C4×D79—42no—
152C4×D79—42no—
153C4×D79—81no—
154C8×C79—21no—
155C8×C79—21no—
156C79⋊C8—21no—
157C79⋊C8—21no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79C22×D411yescharacteristic
162C2×D79—21no—
163C2×D79—21no—
164C2×D79—22no—
165C2×D79—21no—
166C2×D79—21no—
167C2×D79—21no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—41no—
172C2×D79—41no—
173C2×D79—84no—
174C2×D79AGL(1,ℤ/8)12yes—
175C4×C79—21no—
176C4×C79—21no—
177C4×C79—41no—
178C4×C79—41no—
179C4×C79—41no—
180C4×C79C2×#4111yescharacteristic
181C4×C79H(5,𝔽2)11yescharacteristic
182Dic79—21no—
183Dic79—21no—
184Dic79—41no—
185Dic79—41no—
186C2×C79—81no—
187C2×C79#54611yescharacteristic
188C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C79#57711yescharacteristic
190D79—22no—
191D79—41no—
192D79—42no—
193D79—81no—
194#3306—791nomaximal, Sylow
195C79#330611yescharacteristic, complemented, Sylow
196#547—791no—
197#546—791no—
198#489D7911yescharacteristic, complemented
199#483—791no—
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⋊Q8C2×D7911yescharacteristic, complemented
220#124C2×D7911yescharacteristic
221#123—1581no—
222#123—1581no—
223#123—1581no—
224C22⋊Q8—791no—
225C22⋊Q8—1581no—
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⋊C4—791no—
236C2×C22⋊C4—1581no—
237#106—791no—
238#106—791no—
239#106—791no—
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#102C2×D7911yescharacteristic
250#102C2×D7911yescharacteristic
251C22⋊C8—791no—
252C22⋊C8—791no—
253#97C2×D7911yescharacteristic, complemented
254C24—1581no—
255#41—3164no—
256#41—3161no—
257#41—1582no—
258C2×Q8—21no—
259C2×Q8C22×D7911yescharacteristic
260C2×D4—3161no—
261C2×D4—791no—
262C2×D4—791no—
263C2×D4—791no—
264C2×D4—1581no—
265C2×D4—1581no—
266C2×D4—1581no—
267C2×D4—1581no—
268C2×D4—1582no—
269C2×D4—1581no—
270C2×D4C22×D7911yescharacteristic
271C22×C4—791no—
272C22×C4—791no—
273C22×C4—1581no—
274C22×C4—1581no—
275C22×C4—1581no—
276C22×C4—1581no—
277C22×C4—1581no—
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—791no—
289C4⋊C4—791no—
290C4⋊C4—791no—
291C4⋊C4—1581no—
292C4⋊C4—1581no—
293C4⋊C4—1581no—
294C4⋊C4C22×D7911yescharacteristic
295C4⋊C4C22×D7911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—791no—
299C22⋊C4—791no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C22⋊C4—1581no—
305C22⋊C4—1581no—
306C42C22×D7911yescharacteristic
307C23—21no—
308C23—3162no—
309C23—3162no—
310C23—791no—
311C23—791no—
312C23—6321no—
313C23—1581no—
314C23—1581no—
315Q8—21no—
316Q8—21no—
317Q8—42no—
318D4—21no—
319D4—21no—
320D4—3162no—
321D4—3162no—
322D4—3162no—
323D4—3162no—
324D4—792no—
325D4—6321no—
326D4—1582no—
327D4—1581no—
328D4—1581no—
329D4—1581no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—3162no—
334C2×C4—3162no—
335C2×C4—3162no—
336C2×C4—3162no—
337C2×C4—791no—
338C2×C4—791no—
339C2×C4—6321no—
340C2×C4—1581no—
341C2×C4—1581no—
342C2×C4—1581no—
343C2×C4—1581no—
344C2×C4—1581no—
345C2×C4—1581no—
346C2×C4D4×D7911yescharacteristic
347C2×C4D4×D7911yescharacteristic
348C2×C4C23×D7911yescharacteristic
349C8—21no—
350C8—21no—
351C8—1581no—
352C8—1581no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—3161no—
357C22—3161no—
358C22—3161no—
359C22—3161no—
360C22—3161no—
361C22—792no—
362C22—6324no—
363C22—1582no—
364C22—1581no—
365C22—1581no—
366C22—1581no—
367C22—1581no—
368C22—1581no—
369C22C2×D4×D7911yescharacteristic
370C4—21no—
371C4—21no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—3161no—
376C4—3161no—
377C4—1581no—
378C4—1581no—
379C4#41×D7911yescharacteristic
380C4#1457920711yescharacteristic
381C2—81no—
382C2—3162no—
383C2—3161no—
384C2—6321no—
385C2—1582no—
386C2#1909920611yescharacteristic
387C2AGL(1,ℤ/8)×D7911yescharacteristic
388C2#1909937211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#489×C79C2
socleC22×C79C22×D4
hypercenter#489D79
hypocenterC79#3306
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #19099216C2semidirect
2. #19099206C2semidirect
3. #19098892C2semidirect
4. #19098880C2semidirect
5. #19098850C2semidirect
6. #19098815C2semidirect
7. #19098795C2semidirect
8. #19098775C2semidirect
9. #19098711C2semidirect
10. #19098698C2semidirect
11. #19098676C2semidirect
12. #19098636C2semidirect
13. #19098563C2semidirect
14. #102×D79C2semidirect
15. #489×C79C2semidirect
19. C2×#11929611C22semidirect
22. C2×#11929607C22semidirect
30. #14579136C22semidirect
36. C4×D316C22semidirect
38. C4⋊C4×D79C22semidirect
40. #14579093C22semidirect
41. #14579092C22semidirect
42. #14579092C22semidirect
43. C4⋊(C79⋊C8)C22semidirect
44. #14579085C22semidirect
46. #14579083C22semidirect
51. (C2×D79)⋊C8C22semidirect
52. C4⋊Q8×C79C22semidirect
54. #103×C79C22semidirect
55. #103×C79C22semidirect
58. #97×C79C22semidirect
144. D316#41semidirect
195. C79#3306semidirect
198. #489D79semidirect
219. C4⋊Q8C2×D79semidirect
242. #103C2×D79semidirect
243. #103C2×D79semidirect
253. #97C2×D79semidirect