Finite Group Databasebeta

← #23775167

Subgroups — #23775167

Order 10112.

464 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099375C211yesmaximal, characteristic, complemented
2#19099370C211yesmaximal, characteristic, complemented
3#19099368C211yesmaximal, characteristic, complemented
4#19099365C211yesmaximal, characteristic, complemented
5#19098952C211yesmaximal, characteristic, complemented
6#19098834C211yesmaximal, characteristic, complemented
7#19098833C211yesmaximal, characteristic, complemented
8#19098827C211yesmaximal, characteristic, complemented
9#19098826C211yesmaximal, characteristic, complemented
10#19098742C211yesmaximal, characteristic, complemented
11#19098737C211yesmaximal, characteristic, complemented
12#19098732C211yesmaximal, characteristic, complemented
13#19098732C211yesmaximal, characteristic, complemented
14#19098686C211yesmaximal, characteristic, complemented
15#444×C79C211yesmaximal, characteristic, complemented
16#14579208C2211yescharacteristic, complemented
17#14579207C2211yescharacteristic
18#14579207C2211yescharacteristic, complemented
19#14579207C2211yescharacteristic, complemented
20#14579194—21no—
21#14579194C2211yescharacteristic, complemented
22#14579193—21no—
23#14579191C2211yescharacteristic, complemented
24#14579189—21no—
25#14579189—21no—
26#14579189—21no—
27#14579189C2211yescharacteristic
28#14579189C2211yescharacteristic, complemented
29#14579189C2211yescharacteristic, complemented
30#14579188—21no—
31#14579188—21no—
32#14579186C2211yescharacteristic
33#14579186C2211yescharacteristic, complemented
34#14579186C2211yescharacteristic, complemented
35#14579185—21no—
36#14579184—21no—
37#14579183—21no—
38#14579183—21no—
39#14579183C2211yescharacteristic
40#14579182—21no—
41C2×#11929613—21no—
42C2×#11929613C2211yescharacteristic, complemented
43C2×#11929613C2211yescharacteristic, complemented
44SD16×D79—21no—
45C2×D632—21no—
46C2×D632C2211yescharacteristic, complemented
47C2×D632C2211yescharacteristic, complemented
48D8×D79—21no—
49#14579167C2211yescharacteristic, complemented
50#14579167C2211yescharacteristic, complemented
51#14579158C2211yescharacteristic, complemented
52#14579149C2211yescharacteristic, complemented
53#14579097C2211yescharacteristic, complemented
54#14579089C2211yescharacteristic, complemented
55#14579089C2211yescharacteristic, complemented
56#14579079C2211yescharacteristic, complemented
57#14579077C2211yescharacteristic, complemented
58#14579077C2211yescharacteristic, complemented
59#14579077C2211yescharacteristic, complemented
60#135×C79C2211yescharacteristic
61#131×C79C2211yescharacteristic, complemented
62#131×C79C2211yescharacteristic, complemented
63#108×C79C2211yescharacteristic, complemented
64#104×C79C2211yescharacteristic, complemented
65#104×C79C2211yescharacteristic, complemented
66#97×C79C2211yescharacteristic, complemented
67#11929625—21no—
68#11929625—21no—
69#11929625—21no—
70#11929624—21no—
71#11929624—21no—
72#11929624—21no—
73#11929624—21no—
74#11929624C2311yescharacteristic
75#11929624C2311yescharacteristic
76#11929623—21no—
77#11929623—41no—
78C2×Dic158—21no—
79C2×Dic158C2311yescharacteristic
80Q8×D79—21no—
81C2×D316—21no—
82C2×D316—21no—
83C2×D316—21no—
84C2×D316—41no—
85C2×D316C2311yescharacteristic
86C2×D316C2311yescharacteristic
87C2×D316C2311yescharacteristic
88D4×D79—21no—
89D4×D79—21no—
90D4×D79—21no—
91D4×D79—41no—
92D4×D79—41no—
93D4×D79—41no—
94Dic316—21no—
95Dic316D411yescharacteristic, complemented
96#11929614—21no—
97#11929613—21no—
98#11929613—21no—
99#11929613—21no—
100#11929613—21no—
101#11929613—21no—
102#11929613—21no—
103#11929613—21no—
104#11929613—21no—
105#11929613D411yescharacteristic, complemented
106#11929613D411yescharacteristic, complemented
107#11929612—21no—
108#11929611—21no—
109#11929611—21no—
110#11929611—21no—
111D632—21no—
112D632—21no—
113D632—21no—
114D632—21no—
115D632—21no—
116D632—21no—
117D632—21no—
118D632D411yescharacteristic, complemented
119#11929609—21no—
120#11929609—21no—
121#11929609—21no—
122#11929608C2311yescharacteristic
123#11929608C2311yescharacteristic
124#11929607—21no—
125#11929607—21no—
126C8×D79—21no—
127C8×D79—21no—
128(C2×D79)⋊C4—41no—
129#41×C79C2311yescharacteristic
130#41×C79C2311yescharacteristic
131Q16×C79D411yescharacteristic, complemented
132SD16×C79D411yescharacteristic, complemented
133SD16×C79D411yescharacteristic, complemented
134D8×C79D411yescharacteristic, complemented
135M16×C79—21no—
136M16×C79—21no—
137M16×C79C2311yescharacteristic
138M16×C79C2311yescharacteristic
139C2×C8×C79—21no—
140C2×C8×C79—21no—
141C2×C8×C79C2311yescharacteristic
142C2×C8×C79C2311yescharacteristic
143C42×C79C2311yescharacteristic
144C22×D79—21no—
145C22×D79—21no—
146C22×D79—21no—
147C22×D79—41no—
148C22×D79—41no—
149C22×D79—41no—
150Q8×C79C2×D411yescharacteristic
151Q8×C79C2×D411yescharacteristic
152D4×C79—21no—
153D4×C79—21no—
154D4×C79C2×D411yescharacteristic
155D4×C79C2×D411yescharacteristic
156C2×C4×C79—21no—
157C2×C4×C79—21no—
158C2×C4×C79—21no—
159C2×C4×C79C2411yescharacteristic
160C22⋊D79—21no—
161C22⋊D79—21no—
162C22⋊D79—41no—
163C22⋊D79—41no—
164C22⋊D79—41no—
165C22⋊D79—41no—
166C2×Dic79—21no—
167C2×Dic79—41no—
168D316—21no—
169D316—21no—
170D316—21no—
171D316—21no—
172D316—21no—
173D316—21no—
174D316—41no—
175D316—41no—
176D316—41no—
177D316—82no—
178D316C2×D411yescharacteristic
179D316C2×D411yescharacteristic
180C4×D79—21no—
181C4×D79—21no—
182C4×D79—41no—
183C4×D79—41no—
184C4×D79—41no—
185C4×D79—41no—
186Dic158—21no—
187Dic158—21no—
188Dic158—41no—
189Dic158C2×D411yescharacteristic
190Dic158C2×D411yescharacteristic
191C8×C79—21no—
192C8×C79—21no—
193C8×C79C2×D411yescharacteristic
194C8×C79C2×D411yescharacteristic
195C8×C79C2×D411yescharacteristic
196C8×C79C2×D411yescharacteristic
197C79⋊C8—21no—
198C79⋊C8—21no—
199C22×C79—21no—
200C22×C79—21no—
201C22×C79H(5,𝔽2)11yescharacteristic
202C2×D79—21no—
203C2×D79—21no—
204C2×D79—41no—
205C2×D79—41no—
206C2×D79—41no—
207C2×D79—81no—
208C2×D79—81no—
209C2×D79—81no—
210C2×D79—161no—
211C2×D79—161no—
212C2×D79—161no—
213C4×C79—21no—
214C4×C79—21no—
215C4×C79—41no—
216C4×C79C22×D411yescharacteristic
217C4×C79C22×D411yescharacteristic
218Dic79—21no—
219Dic79—21no—
220Dic79—41no—
221C2×C79—21no—
222C2×C79—41no—
223C2×C79—41no—
224C2×C79D4211yescharacteristic
225D79—41no—
226D79—41no—
227D79—81no—
228D79—81no—
229D79—81no—
230#3288—791nomaximal, Sylow
231C79#328811yescharacteristic, complemented, Sylow
232#577—791no—
233#577—791no—
234#576—791no—
235#576—791no—
236#496—791no—
237#472—791no—
238#472—791no—
239#471—791no—
240#471—791no—
241#455—791no—
242#454—791no—
243#453—791no—
244#453—791no—
245#444—791no—
246#444D7911yescharacteristic, complemented
2472−1+4—791no—
248H(5,𝔽2)—791no—
249H(5,𝔽2)—791no—
250H(5,𝔽2)—791no—
251#137—791no—
252#137—791no—
253#137—1581no—
254#137—1581no—
255AGL(1,ℤ/8)—791no—
256AGL(1,ℤ/8)—791no—
257AGL(1,ℤ/8)—791no—
258AGL(1,ℤ/8)—791no—
259AGL(1,ℤ/8)—791no—
260AGL(1,ℤ/8)—791no—
261AGL(1,ℤ/8)—1581no—
262AGL(1,ℤ/8)—1581no—
263AGL(1,ℤ/8)—1581no—
264AGL(1,ℤ/8)—1581no—
265AGL(1,ℤ/8)—1581no—
266AGL(1,ℤ/8)—1581no—
267#135—791no—
268#135—1581no—
269#135—1581no—
270#135—1581no—
271#135—1581no—
272#135C2×D7911yescharacteristic
273C2×SD16—791no—
274C2×SD16—791no—
275C2×SD16—1581no—
276C2×SD16—1581no—
277C2×D8—791no—
278C2×D8—791no—
279C2×D8—1581no—
280C2×D8—1581no—
281#131—791no—
282#131—791no—
283#131C2×D7911yescharacteristic, complemented
284#131C2×D7911yescharacteristic, complemented
285#127—791no—
286#124—791no—
287#108—791no—
288#108C2×D7911yescharacteristic, complemented
289#104—791no—
290#104—791no—
291#104C2×D7911yescharacteristic, complemented
292#104C2×D7911yescharacteristic, complemented
293#101—791no—
294#100—791no—
295#100—791no—
296#100—791no—
297#97C2×D7911yescharacteristic, complemented
298#41—3161no—
299#41—791no—
300#41—791no—
301#41—1581no—
302#41—1581no—
303#41—1581no—
304#41—1581no—
305#41—1581no—
306#41—1581no—
307#41—1581no—
308#41—1581no—
309#41C22×D7911yescharacteristic
310#41C22×D7911yescharacteristic
311C2×Q8—791no—
312C2×Q8—1581no—
313C2×Q8—1581no—
314C2×D4—3161no—
315C2×D4—3161no—
316C2×D4—3161no—
317C2×D4—3161no—
318C2×D4—791no—
319C2×D4—791no—
320C2×D4—791no—
321C2×D4—1581no—
322C2×D4—1581no—
323C2×D4—1581no—
324C2×D4—1581no—
325C2×D4—1581no—
326C2×D4—1581no—
327Q16—791no—
328Q16—1581no—
329Q16—1581no—
330Q16D31611yescharacteristic, complemented
331SD16—791no—
332SD16—791no—
333SD16—1581no—
334SD16—1581no—
335SD16—1581no—
336SD16—1581no—
337SD16—1581no—
338SD16—1581no—
339SD16—1581no—
340SD16—1581no—
341SD16—1581no—
342SD16—1581no—
343SD16—1581no—
344SD16—1581no—
345SD16D31611yescharacteristic, complemented
346SD16D31611yescharacteristic, complemented
347D8—791no—
348D8—1581no—
349D8—1581no—
350D8—1581no—
351D8—1581no—
352D8—1581no—
353D8—1581no—
354D8—1581no—
355D8—1581no—
356D8—1581no—
357D8—1581no—
358D8D31611yescharacteristic, complemented
359M16—21no—
360M16—21no—
361M16—791no—
362M16—791no—
363M16—1581no—
364M16—1581no—
365M16C22×D7911yescharacteristic
366M16C22×D7911yescharacteristic
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—1581no—
370C2×C8—1581no—
371C2×C8C22×D7911yescharacteristic
372C2×C8C22×D7911yescharacteristic
373C22⋊C4—3161no—
374C42C22×D7911yescharacteristic
375C23—3161no—
376C23—3161no—
377C23—3161no—
378C23—1581no—
379C23—1581no—
380C23—1581no—
381Q8—3161no—
382Q8—791no—
383Q8—791no—
384Q8—1581no—
385Q8—1581no—
386Q8C2×D31611yescharacteristic
387Q8C2×D31611yescharacteristic
388D4—21no—
389D4—21no—
390D4—3161no—
391D4—3161no—
392D4—3161no—
393D4—3161no—
394D4—3161no—
395D4—3161no—
396D4—3161no—
397D4—791no—
398D4—791no—
399D4—6322no—
400D4—1581no—
401D4—1581no—
402D4—1581no—
403D4—1581no—
404D4—1581no—
405D4—1581no—
406D4—1581no—
407D4—1581no—
408D4C2×D31611yescharacteristic
409D4C2×D31611yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—3161no—
414C2×C4—3161no—
415C2×C4—3161no—
416C2×C4—3161no—
417C2×C4—3161no—
418C2×C4—1581no—
419C2×C4—1581no—
420C2×C4—1581no—
421C2×C4C23×D7911yescharacteristic
422C8—21no—
423C8—21no—
424C8—1581no—
425C8—1581no—
426C8D4×D7911yescharacteristic
427C8D4×D7911yescharacteristic
428C8C2×D31611yescharacteristic
429C8C2×D31611yescharacteristic
430C22—21no—
431C22—21no—
432C22—3161no—
433C22—3161no—
434C22—3161no—
435C22—6321no—
436C22—6321no—
437C22—6321no—
438C22—1581no—
439C22—1581no—
440C22—12641no—
441C22—12641no—
442C22—12641no—
443C22#1457920711yescharacteristic
444C4—21no—
445C4—21no—
446C4—41no—
447C4—3161no—
448C4—1581no—
449C4—1581no—
450C4C2×D4×D7911yescharacteristic
451C4C22×D31611yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—3161no—
456C2—3161no—
457C2—6321no—
458C2—6321no—
459C2—6321no—
460C2D4×D31611yescharacteristic
subgroupG/H
centerC2D4×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#444×C79C2
socleC2×C79D42
hypercenter#444D79
hypocenterC79#3288
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2 ◁ C2×C4 ◁ #444

Complements

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

NH ≅ G/Ntype
1. #19099375C2semidirect
2. #19099370C2semidirect
3. #19099368C2semidirect
4. #19099365C2semidirect
5. #19098952C2semidirect
6. #19098834C2semidirect
7. #19098833C2semidirect
8. #19098827C2semidirect
9. #19098826C2semidirect
10. #19098742C2semidirect
11. #19098737C2semidirect
12. #19098732C2semidirect
13. #19098732C2semidirect
14. #19098686C2semidirect
15. #444×C79C2semidirect
16. #14579208C22semidirect
18. #14579207C22semidirect
19. #14579207C22semidirect
21. #14579194C22semidirect
23. #14579191C22semidirect
28. #14579189C22semidirect
29. #14579189C22semidirect
33. #14579186C22semidirect
34. #14579186C22semidirect
42. C2×#11929613C22semidirect
43. C2×#11929613C22semidirect
46. C2×D632C22semidirect
47. C2×D632C22semidirect
49. #14579167C22semidirect
50. #14579167C22semidirect
51. #14579158C22semidirect
52. #14579149C22semidirect
53. #14579097C22semidirect
54. #14579089C22semidirect
55. #14579089C22semidirect
56. #14579079C22semidirect
57. #14579077C22semidirect
58. #14579077C22semidirect
59. #14579077C22semidirect
61. #131×C79C22semidirect
62. #131×C79C22semidirect
63. #108×C79C22semidirect
64. #104×C79C22semidirect
65. #104×C79C22semidirect
66. #97×C79C22semidirect
95. Dic316D4semidirect
105. #11929613D4semidirect
106. #11929613D4semidirect
118. D632D4semidirect
131. Q16×C79D4semidirect
132. SD16×C79D4semidirect
133. SD16×C79D4semidirect
134. D8×C79D4semidirect
231. C79#3288semidirect
246. #444D79semidirect
283. #131C2×D79semidirect
284. #131C2×D79semidirect
288. #108C2×D79semidirect
291. #104C2×D79semidirect
292. #104C2×D79semidirect
297. #97C2×D79semidirect
330. Q16D316semidirect
345. SD16D316semidirect
346. SD16D316semidirect
358. D8D316semidirect