Finite Group Databasebeta

← #23775018

Subgroups — #23775018

Order 10112.

556 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579187C211yesmaximal, characteristic, complemented
2C2×#14579185C211yesmaximal, characteristic, complemented
3#19099231C211yesmaximal, characteristic, complemented
4D4×C22⋊D79C211yesmaximal, characteristic, complemented
5#19098938C211yesmaximal, characteristic, complemented
6#19098815C211yesmaximal, characteristic, complemented
7#19098814C211yesmaximal, characteristic, complemented
8#19098762C211yesmaximal, characteristic, complemented
9#19098756C211yesmaximal, characteristic, complemented
10#19098710C211yesmaximal, characteristic, complemented
11#19098705C211yesmaximal, characteristic, complemented
12#19098698C211yesmaximal, characteristic, complemented
13#19098654C211yesmaximal, characteristic, complemented
14#19098638C211yesmaximal, characteristic, complemented
15#447×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic, complemented
17C2×#11929623C2211yescharacteristic, complemented
18C22×C22⋊D79—21no—
19C2×D4×D79C2211yescharacteristic
20#14579187—24no—
21#14579185—24no—
22C2×#11929613C2211yescharacteristic, complemented
23C2×#11929612C2211yescharacteristic
24C2×#11929612C2211yescharacteristic, complemented
25C2×D632C2211yescharacteristic, complemented
26C2×#11929609C2211yescharacteristic
27C2×#11929609C2211yescharacteristic, complemented
28C2×#11929609C2211yescharacteristic, complemented
29C2×#11929608C2211yescharacteristic, complemented
30C2×#11929607C2211yescharacteristic, complemented
31#14579157—21no—
32#14579157C2211yescharacteristic
33#14579157C2211yescharacteristic, complemented
34#14579136C2211yescharacteristic, complemented
35#14579135C2211yescharacteristic
36#14579134—21no—
37#14579133—21no—
38#14579133—21no—
39#14579132C2211yescharacteristic
40#14579130—21no—
41#14579129—21no—
42#14579126C2211yescharacteristic, complemented
43D4×Dic79C2211yescharacteristic
44C4×C22⋊D79C2211yescharacteristic
45(C22⋊D79)⋊C4—21no—
46#14579092C2211yescharacteristic, complemented
47Dic79⋊C8C2211yescharacteristic, complemented
48#14579086C2211yescharacteristic, complemented
49#14579083C2211yescharacteristic, complemented
50#14579082C2211yescharacteristic, complemented
51#14579081C2211yescharacteristic, complemented
52(C2×D79)⋊C8C2211yescharacteristic, complemented
53C8×Dic79C2211yescharacteristic, complemented
54C22×D4×C79C2211yescharacteristic
55C2×D8×C79C2211yescharacteristic
56C2×D8×C79C2211yescharacteristic, complemented
57#121×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic
59#102×C79C2211yescharacteristic, complemented
60C22⋊C8×C79C2211yescharacteristic, complemented
61C23×D79—21no—
62#11929624—22no—
63#11929624—41no—
64#11929623—22no—
65#11929623—41no—
66C2×Dic158C2311yescharacteristic
67C2×D316—21no—
68C2×D316C2311yescharacteristic
69C2×D316C2311yescharacteristic
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72C2×C22⋊D79—21no—
73C2×C22⋊D79—21no—
74C2×C22⋊D79—21no—
75C2×C22⋊D79—21no—
76C2×C22⋊D79—21no—
77C2×C22⋊D79—21no—
78C2×C22⋊D79—21no—
79C2×C22⋊D79—44no—
80C2×C22⋊D79D411yescharacteristic
81D4×D79—22no—
82D4×D79—41no—
83C22×Dic79—21no—
84C22×Dic79—21no—
85C2×C4×D79—21no—
86C2×C4×D79C2311yescharacteristic
87#11929613—22no—
88#11929612—22no—
89#11929612D414yescomplemented
90D632—41no—
91#11929609—22no—
92#11929609—22no—
93#11929609—22no—
94#11929608—22no—
95#11929607—22no—
96C2×C79⋊C8C2311yescharacteristic
97C2×C79⋊C8C2311yescharacteristic
98C4⋊Dic79C2311yescharacteristic
99Dic79⋊C4—21no—
100Dic79⋊C4D411yescharacteristic
101C22⋊Dic79—21no—
102C22⋊Dic79—21no—
103C22⋊Dic79D411yescharacteristic
104(C2×D79)⋊C4—21no—
105(C2×D79)⋊C4—21no—
106(C2×D79)⋊C4D411yescharacteristic
107C4×Dic79—21no—
108C4×Dic79C2311yescharacteristic
109C24×C79—21no—
110C2×D4×C79—22no—
111C2×D4×C79—21no—
112C2×D4×C79—21no—
113C2×D4×C79—41no—
114C2×D4×C79C2311yescharacteristic
115C2×D4×C79C2311yescharacteristic
116C2×D4×C79C2311yescharacteristic
117C22×C4×C79C2311yescharacteristic
118D8×C79—22no—
119D8×C79—41no—
120C2×C8×C79C2311yescharacteristic
121C2×C8×C79C2311yescharacteristic
122C4⋊C4×C79C2311yescharacteristic
123C22⋊C4×C79—21no—
124C23×C79—21no—
125C23×C79—21no—
126C23×C79—21no—
127C23×C79—42no—
128C23×C79—42no—
129C23×C79—81no—
130C23×C79C2×D411yescharacteristic
131C22×D79—21no—
132C22×D79—21no—
133C22×D79—42no—
134C22×D79—42no—
135C22×D79—81no—
136C22×D79C2×D411yescharacteristic
137D4×C79—21no—
138D4×C79—21no—
139D4×C79—21no—
140D4×C79—21no—
141D4×C79—21no—
142D4×C79—42no—
143D4×C79—81no—
144D4×C79C2×D412yes—
145C2×C4×C79—21no—
146C2×C4×C79—21no—
147C2×C4×C79—21no—
148C2×C4×C79C2×D411yescharacteristic
149C2×C4×C79C2411yescharacteristic
150C22⋊D79—22no—
151C22⋊D79—42no—
152C22⋊D79—42no—
153C22⋊D79—42no—
154C22⋊D79—42no—
155C22⋊D79—42no—
156C22⋊D79—42no—
157C22⋊D79—42no—
158C22⋊D79—81no—
159C22⋊D79—81no—
160C2×Dic79—21no—
161C2×Dic79—21no—
162C2×Dic79—42no—
163C2×Dic79—42no—
164C2×Dic79C2×D411yescharacteristic
165C2×Dic79C2×D411yescharacteristic
166C2×Dic79C2×D411yescharacteristic
167D316—21no—
168D316—21no—
169D316—21no—
170D316—21no—
171D316—81no—
172C4×D79—21no—
173C4×D79—21no—
174C4×D79—42no—
175Dic158—21no—
176Dic158C2×D412yescomplemented
177C8×C79—21no—
178C8×C79—21no—
179C79⋊C8—21no—
180C79⋊C8C2×D412yescomplemented
181C22×C79—21no—
182C22×C79—22no—
183C22×C79—21no—
184C22×C79—21no—
185C22×C79—41no—
186C22×C79—41no—
187C22×C79—41no—
188C22×C79—41no—
189C22×C79—41no—
190C22×C79—41no—
191C22×C79—41no—
192C22×C79—41no—
193C22×C79—84no—
194C22×C79C22×D411yescharacteristic
195C2×D79—21no—
196C2×D79—21no—
197C2×D79—21no—
198C2×D79—41no—
199C2×D79—41no—
200C2×D79—41no—
201C2×D79—41no—
202C2×D79—41no—
203C2×D79—41no—
204C2×D79—84no—
205C4×C79—21no—
206C4×C79—41no—
207C4×C79C22×D411yescharacteristic
208C4×C79H(5,𝔽2)11yescharacteristic
209Dic79—22no—
210Dic79—21no—
211Dic79—21no—
212Dic79—41no—
213Dic79AGL(1,ℤ/8)12yescomplemented
214C2×C79—42no—
215C2×C79—41no—
216C2×C79—81no—
217C2×C79—81no—
218C2×C79D4211yescharacteristic
219C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
220C2×C79#57611yescharacteristic
221D79—41no—
222D79—81no—
223D79—81no—
224#3274—791nomaximal, Sylow
225C79#327411yescharacteristic, complemented, Sylow
226C2×AGL(1,ℤ/8)—791no—
227C2×AGL(1,ℤ/8)—791no—
228#550—791no—
229D42—791no—
230#493—791no—
231#469—791no—
232#469—791no—
233#460—791no—
234#459—791no—
235#449—791no—
236#449—791no—
237#447—791no—
238#447D7911yescharacteristic, complemented
239C4×SD16—791no—
240#436—791no—
241C2×#41—791no—
242C2×#41—791no—
243C22×D4—791no—
244C22×D4—1581no—
245C22×D4C2×D7911yescharacteristic
246AGL(1,ℤ/8)—1584no—
247AGL(1,ℤ/8)—1584no—
248C2×SD16—791no—
249C2×SD16—791no—
250C2×SD16—791no—
251C2×D8—791no—
252C2×D8—791no—
253C2×D8—791no—
254C2×D8—791no—
255C2×D8C2×D7911yescharacteristic
256C2×D8C2×D7911yescharacteristic, complemented
257C2×M16—791no—
258C2×M16—791no—
259#127—791no—
260#127—791no—
261#127—1581no—
262#121—791no—
263#121—791no—
264#121—791no—
265#121—1581no—
266#121—1581no—
267#121—1581no—
268#121C2×D7911yescharacteristic, complemented
269#120—1581no—
270#120—1581no—
271C4×Q8—791no—
272C4×D4—791no—
273C4×D4—791no—
274C4×D4—1581no—
275#106—791no—
276C4⋊C8—791no—
277#103—791no—
278#102—791no—
279#102—791no—
280#102—791no—
281#102C2×D7911yescharacteristic
282#102C2×D7911yescharacteristic, complemented
283C22⋊C8—791no—
284C22⋊C8C2×D7911yescharacteristic, complemented
285C4×C8—791no—
286C24—21no—
287C24—1581no—
288#41—3161no—
289#41—3161no—
290#41—1582no—
291#41—1582no—
292C2×Q8—791no—
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4—3164no—
298C2×D4—3161no—
299C2×D4—791no—
300C2×D4—791no—
301C2×D4—791no—
302C2×D4—1581no—
303C2×D4—1581no—
304C2×D4—1581no—
305C2×D4—1581no—
306C2×D4—1581no—
307C2×D4—1581no—
308C2×D4—1581no—
309C2×D4—1581no—
310C2×D4—1581no—
311C2×D4—1581no—
312C2×D4—1582no—
313C2×D4C22×D7911yescharacteristic
314C2×D4C22×D7911yescharacteristic
315C2×D4C22×D7911yescharacteristic
316C22×C4—791no—
317C22×C4—1581no—
318C22×C4—1581no—
319C22×C4—1581no—
320C22×C4C22×D7911yescharacteristic
321SD16—794no—
322SD16—1582no—
323SD16—1582no—
324D8—22no—
325D8—41no—
326D8—3161no—
327D8—1582no—
328D8—1582no—
329D8—1582no—
330M16—1582no—
331M16—1582no—
332C2×C8—791no—
333C2×C8—791no—
334C2×C8C22×D7911yescharacteristic
335C2×C8C22×D7911yescharacteristic
336C4⋊C4—791no—
337C4⋊C4—791no—
338C4⋊C4—1581no—
339C4⋊C4C22×D7911yescharacteristic
340C22⋊C4—21no—
341C22⋊C4—791no—
342C22⋊C4—791no—
343C22⋊C4—1581no—
344C22⋊C4—1581no—
345C22⋊C4—1581no—
346C22⋊C4—1581no—
347C42—791no—
348C42—1581no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—42no—
353C23—42no—
354C23—81no—
355C23—3162no—
356C23—3162no—
357C23—791no—
358C23—6321no—
359C23—1581no—
360C23—1581no—
361C23D4×D7911yescharacteristic
362Q8—792no—
363Q8—1581no—
364D4—21no—
365D4—21no—
366D4—21no—
367D4—21no—
368D4—21no—
369D4—42no—
370D4—81no—
371D4—3162no—
372D4—3162no—
373D4—3162no—
374D4—3162no—
375D4—3162no—
376D4—3162no—
377D4—3162no—
378D4—6321no—
379D4—6321no—
380D4—6321no—
381D4—1582no—
382D4—1581no—
383D4—1581no—
384D4—1581no—
385D4—1581no—
386D4D4×D7912yes—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—3162no—
391C2×C4—3162no—
392C2×C4—3162no—
393C2×C4—791no—
394C2×C4—791no—
395C2×C4—791no—
396C2×C4—1581no—
397C2×C4—1581no—
398C2×C4—1581no—
399C2×C4—1581no—
400C2×C4D4×D7911yescharacteristic
401C2×C4C23×D7911yescharacteristic
402C8—21no—
403C8—21no—
404C8—792no—
405C8—1581no—
406C22—21no—
407C22—22no—
408C22—21no—
409C22—21no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—84no—
419C22—3161no—
420C22—3161no—
421C22—3161no—
422C22—3161no—
423C22—3161no—
424C22—3161no—
425C22—6324no—
426C22—1581no—
427C22—1581no—
428C22—1581no—
429C22C2×D4×D7911yescharacteristic
430C4—21no—
431C4—41no—
432C4—3161no—
433C4—792no—
434C4—1581no—
435C4—1582no—
436C4—1581no—
437C4C2×D4×D7911yescharacteristic
438C4#1457920611yescharacteristic
439C2—41no—
440C2—42no—
441C2—81no—
442C2—81no—
443C2—3161no—
444C2—6321no—
445C2—6321no—
446C2#1909919511yescharacteristic
447C2AGL(1,ℤ/8)×D7911yescharacteristic
448C2#1909936411yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#447×C79C2
socleC22×C79C22×D4
hypercenter#447D79
hypocenterC79#3274
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#14579187C2semidirect
2. C2×#14579185C2semidirect
3. #19099231C2semidirect
4. D4×C22⋊D79C2semidirect
5. #19098938C2semidirect
6. #19098815C2semidirect
7. #19098814C2semidirect
8. #19098762C2semidirect
9. #19098756C2semidirect
10. #19098710C2semidirect
11. #19098705C2semidirect
12. #19098698C2semidirect
13. #19098654C2semidirect
14. #19098638C2semidirect
15. #447×C79C2semidirect
16. C2×#11929624C22semidirect
17. C2×#11929623C22semidirect
22. C2×#11929613C22semidirect
24. C2×#11929612C22semidirect
25. C2×D632C22semidirect
27. C2×#11929609C22semidirect
28. C2×#11929609C22semidirect
29. C2×#11929608C22semidirect
30. C2×#11929607C22semidirect
33. #14579157C22semidirect
34. #14579136C22semidirect
42. #14579126C22semidirect
46. #14579092C22semidirect
47. Dic79⋊C8C22semidirect
48. #14579086C22semidirect
49. #14579083C22semidirect
50. #14579082C22semidirect
51. #14579081C22semidirect
52. (C2×D79)⋊C8C22semidirect
53. C8×Dic79C22semidirect
56. C2×D8×C79C22semidirect
57. #121×C79C22semidirect
59. #102×C79C22semidirect
60. C22⋊C8×C79C22semidirect
89. #11929612D4semidirect
176. Dic158C2×D4semidirect
180. C79⋊C8C2×D4semidirect
213. Dic79AGL(1,ℤ/8)semidirect
225. C79#3274semidirect
238. #447D79semidirect
256. C2×D8C2×D79semidirect
268. #121C2×D79semidirect
282. #102C2×D79semidirect
284. C22⋊C8C2×D79semidirect