Finite Group Databasebeta

← #23775008

Subgroups — #23775008

Order 10112.

520 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579189C211yesmaximal, characteristic, complemented
2C2×#14579188C211yesmaximal, characteristic, complemented
3#19099210C211yesmaximal, characteristic, complemented
4#19099204C211yesmaximal, characteristic, complemented
5#19098944C211yesmaximal, characteristic, complemented
6#19098810C211yesmaximal, characteristic, complemented
7#19098781C211yesmaximal, characteristic, complemented
8#19098777C211yesmaximal, characteristic, complemented
9#19098728C211yesmaximal, characteristic, complemented
10#19098723C211yesmaximal, characteristic, complemented
11#19098698C211yesmaximal, characteristic, complemented
12#19098696C211yesmaximal, characteristic, complemented
13#19098645C211yesmaximal, characteristic, complemented
14#19098639C211yesmaximal, characteristic, complemented
15#468×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C2×#11929624C2211yescharacteristic
18C22×D316C2211yescharacteristic, complemented
19C2×D4×D79C2211yescharacteristic, complemented
20#14579189—24no—
21#14579188—24no—
22C2×#11929614C2211yescharacteristic, complemented
23C2×#11929613C2211yescharacteristic, complemented
24C2×#11929613C2211yescharacteristic, complemented
25C2×#11929611C2211yescharacteristic, complemented
26C2×D632C2211yescharacteristic
27C2×D632C2211yescharacteristic
28C2×#11929609C2211yescharacteristic
29C2×#11929609C2211yescharacteristic
30C2×#11929607C2211yescharacteristic, complemented
31#14579150C2211yescharacteristic, complemented
32#14579148C2211yescharacteristic, complemented
33#14579146—21no—
34#14579143—21no—
35#14579141C2211yescharacteristic, complemented
36#14579136—21no—
37#14579136C2211yescharacteristic
38#14579132—21no—
39#14579131—21no—
40#14579129—21no—
41#14579123C2211yescharacteristic, complemented
42#14579123C2211yescharacteristic, complemented
43C4×C22⋊D79C2211yescharacteristic
44C22⋊C4×D79—21no—
45C22⋊C4×D79—21no—
46Dic79⋊C8C2211yescharacteristic, complemented
47#14579084C2211yescharacteristic, complemented
48#14579081C2211yescharacteristic, complemented
49#14579081C2211yescharacteristic, complemented
50#14579081C2211yescharacteristic, complemented
51C22⋊(C79⋊C8)C2211yescharacteristic, complemented
52(C2×D79)⋊C8C2211yescharacteristic, complemented
53C8×Dic79C2211yescharacteristic, complemented
54C2×SD16×C79C2211yescharacteristic, complemented
55C2×M16×C79C2211yescharacteristic, complemented
56C22⋊Q8×C79C2211yescharacteristic, complemented
57#121×C79C2211yescharacteristic
58#107×C79C2211yescharacteristic, complemented
59#103×C79C2211yescharacteristic, complemented
60#102×C79C2211yescharacteristic, complemented
61C23×D79—21no—
62C23×D79—21no—
63#11929625—22no—
64#11929625—41no—
65#11929624—22no—
66#11929624—41no—
67C2×Dic158C2311yescharacteristic
68C2×D316—21no—
69C2×D316—21no—
70C2×D316—22no—
71C2×D316—21no—
72C2×D316—41no—
73C2×D316C2311yescharacteristic
74C2×D316C2311yescharacteristic
75C2×D316C2311yescharacteristic
76C2×C22⋊D79—21no—
77C2×C22⋊D79—21no—
78C2×C22⋊D79D411yescharacteristic
79D4×D79—22no—
80D4×D79—41no—
81C2×C4×D79—21no—
82C2×C4×D79—21no—
83C2×C4×D79—21no—
84C2×C4×D79—21no—
85C2×C4×D79C2311yescharacteristic
86#11929614—41no—
87#11929613—22no—
88#11929613—22no—
89#11929611—22no—
90D632—22no—
91D632D414yescomplemented
92#11929609—22no—
93#11929609—41no—
94#11929607—22no—
95C2×C79⋊C8C2311yescharacteristic
96C2×C79⋊C8C2311yescharacteristic
97C4⋊Dic79—21no—
98Dic79⋊C4D411yescharacteristic
99C22⋊Dic79—21no—
100C22⋊Dic79—21no—
101C22⋊Dic79D411yescharacteristic
102(C2×D79)⋊C4—21no—
103(C2×D79)⋊C4—21no—
104(C2×D79)⋊C4—21no—
105(C2×D79)⋊C4—21no—
106(C2×D79)⋊C4—21no—
107(C2×D79)⋊C4—21no—
108(C2×D79)⋊C4D411yescharacteristic
109C4×Dic79C2311yescharacteristic
110C2×Q8×C79C2311yescharacteristic
111C2×D4×C79—21no—
112C2×D4×C79C2311yescharacteristic
113C22×C4×C79C2311yescharacteristic
114SD16×C79—22no—
115M16×C79—22no—
116C2×C8×C79C2311yescharacteristic
117C2×C8×C79C2311yescharacteristic
118C4⋊C4×C79—21no—
119C4⋊C4×C79C2311yescharacteristic
120C4⋊C4×C79C2311yescharacteristic
121C22⋊C4×C79—21no—
122C22⋊C4×C79—21no—
123C23×C79—21no—
124C23×C79C2×D411yescharacteristic
125C22×D79—21no—
126C22×D79—21no—
127C22×D79—21no—
128C22×D79—42no—
129C22×D79—42no—
130C22×D79—42no—
131C22×D79—42no—
132C22×D79—81no—
133C22×D79—81no—
134C22×D79C2×D411yescharacteristic
135Q8×C79—21no—
136Q8×C79—21no—
137D4×C79—21no—
138D4×C79—21no—
139D4×C79—81no—
140C2×C4×C79—21no—
141C2×C4×C79—21no—
142C2×C4×C79—21no—
143C2×C4×C79—21no—
144C2×C4×C79—21no—
145C2×C4×C79C2×D411yescharacteristic
146C2×C4×C79C2411yescharacteristic
147C22⋊D79—41no—
148C22⋊D79—42no—
149C22⋊D79—42no—
150C2×Dic79—21no—
151C2×Dic79C2×D411yescharacteristic
152C2×Dic79C2×D411yescharacteristic
153C2×Dic79C2×D411yescharacteristic
154D316—21no—
155D316—21no—
156D316—21no—
157D316—21no—
158D316—42no—
159D316—42no—
160D316—81no—
161D316C2×D412yes—
162D316C2×D412yes—
163C4×D79—21no—
164C4×D79—21no—
165C4×D79—42no—
166C4×D79—42no—
167C4×D79—81no—
168C4×D79—81no—
169Dic158—21no—
170Dic158—21no—
171C8×C79—21no—
172C8×C79C2×D412yes—
173C79⋊C8—21no—
174C79⋊C8—21no—
175C22×C79—21no—
176C22×C79—21no—
177C22×C79—21no—
178C22×C79—41no—
179C22×C79—41no—
180C22×C79—41no—
181C22×C79C22×D411yescharacteristic
182C2×D79—22no—
183C2×D79—22no—
184C2×D79—21no—
185C2×D79—21no—
186C2×D79—21no—
187C2×D79—41no—
188C2×D79—41no—
189C2×D79—41no—
190C2×D79—41no—
191C2×D79—41no—
192C2×D79—41no—
193C2×D79—41no—
194C2×D79—84no—
195C2×D79—84no—
196C4×C79—21no—
197C4×C79—41no—
198C4×C79—41no—
199C4×C79—41no—
200C4×C79C22×D411yescharacteristic
201C4×C79H(5,𝔽2)11yescharacteristic
202Dic79—21no—
203Dic79—21no—
204Dic79—21no—
205Dic79—41no—
206C2×C79—41no—
207C2×C79—81no—
208C2×C79D4211yescharacteristic
209C2×C79#57511yescharacteristic
210C2×C79#57611yescharacteristic
211D79—41no—
212D79—42no—
213D79—42no—
214D79—81no—
215#3273—791nomaximal, Sylow
216C79#327311yescharacteristic, complemented, Sylow
217C2×AGL(1,ℤ/8)—791no—
218C2×AGL(1,ℤ/8)—791no—
219#546—791no—
220#546—791no—
221#495—791no—
222#468—791no—
223#468D7911yescharacteristic, complemented
224#463—791no—
225#463—791no—
226#452—791no—
227#452—791no—
228#447—791no—
229#447—791no—
230C4×D8—791no—
231#436—791no—
232C2×#41—791no—
233C2×#41—791no—
234C22×D4—791no—
235C22×D4—791no—
236AGL(1,ℤ/8)—1584no—
237AGL(1,ℤ/8)—1584no—
238C2×Q16—791no—
239C2×SD16—791no—
240C2×SD16—791no—
241C2×SD16—791no—
242C2×SD16C2×D7911yescharacteristic, complemented
243C2×D8—791no—
244C2×D8—791no—
245C2×D8—791no—
246C2×D8—791no—
247C2×M16—791no—
248C2×M16C2×D7911yescharacteristic, complemented
249#124—791no—
250#124—791no—
251#123—1581no—
252#123—1581no—
253C22⋊Q8—791no—
254C22⋊Q8C2×D7911yescharacteristic, complemented
255#121—791no—
256#121—1581no—
257#121—1581no—
258#121C2×D7911yescharacteristic
259#120—1581no—
260#120—1581no—
261C4×D4—791no—
262C4×D4—791no—
263C4×D4—791no—
264C2×C22⋊C4—1581no—
265C2×C22⋊C4—1581no—
266#107C2×D7911yescharacteristic, complemented
267C4⋊C8—791no—
268#103—791no—
269#103C2×D7911yescharacteristic, complemented
270#102—791no—
271#102—791no—
272#102—791no—
273#102C2×D7911yescharacteristic, complemented
274C22⋊C8—791no—
275C22⋊C8—791no—
276C4×C8—791no—
277C24—1581no—
278C24—1581no—
279#41—3161no—
280#41—3161no—
281#41—1582no—
282#41—1582no—
283C2×Q8—791no—
284C2×Q8C22×D7911yescharacteristic
285C2×D4—21no—
286C2×D4—3161no—
287C2×D4—3161no—
288C2×D4—791no—
289C2×D4—791no—
290C2×D4—791no—
291C2×D4—791no—
292C2×D4—1581no—
293C2×D4—1582no—
294C2×D4—1581no—
295C2×D4—1581no—
296C2×D4—1582no—
297C2×D4—1581no—
298C2×D4—1581no—
299C2×D4C22×D7911yescharacteristic
300C22×C4—791no—
301C22×C4—1581no—
302C22×C4—1581no—
303C22×C4—1581no—
304C22×C4—1581no—
305C22×C4C22×D7911yescharacteristic
306Q16—3161no—
307SD16—22no—
308SD16—1582no—
309SD16—1582no—
310SD16—1582no—
311D8—3161no—
312D8—794no—
313D8—1582no—
314D8—1582no—
315M16—22no—
316M16—1582no—
317C2×C8—791no—
318C2×C8—791no—
319C2×C8C22×D7911yescharacteristic
320C2×C8C22×D7911yescharacteristic
321C4⋊C4—21no—
322C4⋊C4—791no—
323C4⋊C4—1581no—
324C4⋊C4C22×D7911yescharacteristic
325C4⋊C4C22×D7911yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—791no—
329C22⋊C4—791no—
330C22⋊C4—1581no—
331C22⋊C4—1581no—
332C22⋊C4—1581no—
333C22⋊C4—1581no—
334C22⋊C4—1581no—
335C22⋊C4—1581no—
336C22⋊C4—1581no—
337C22⋊C4—1581no—
338C42—791no—
339C23—21no—
340C23—3162no—
341C23—3162no—
342C23—3162no—
343C23—3162no—
344C23—791no—
345C23—6321no—
346C23—6321no—
347C23—1581no—
348C23—1581no—
349C23—1581no—
350C23D4×D7911yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—1581no—
354Q8—1581no—
355D4—21no—
356D4—21no—
357D4—81no—
358D4—3162no—
359D4—3162no—
360D4—3162no—
361D4—3161no—
362D4—3162no—
363D4—792no—
364D4—792no—
365D4—6321no—
366D4—1581no—
367D4—1581no—
368D4—1581no—
369D4—1581no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—3162no—
376C2×C4—3162no—
377C2×C4—791no—
378C2×C4—791no—
379C2×C4—791no—
380C2×C4—6321no—
381C2×C4—6321no—
382C2×C4—1581no—
383C2×C4—1581no—
384C2×C4—1581no—
385C2×C4D4×D7911yescharacteristic
386C2×C4C23×D7911yescharacteristic
387C8—21no—
388C8—1581no—
389C8—1581no—
390C8D4×D7912yes—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—3161no—
398C22—3161no—
399C22—3161no—
400C22—3161no—
401C22—3161no—
402C22—3161no—
403C22—3161no—
404C22—6324no—
405C22—6324no—
406C22—1582no—
407C22—1582no—
408C22—1581no—
409C22—1581no—
410C22—1581no—
411C22C2×D4×D7911yescharacteristic
412C4—21no—
413C4—41no—
414C4—41no—
415C4—41no—
416C4—3161no—
417C4—1581no—
418C4—1581no—
419C4—1581no—
420C4C2×D4×D7911yescharacteristic
421C4#1457920711yescharacteristic
422C2—41no—
423C2—81no—
424C2—3162no—
425C2—3162no—
426C2—3161no—
427C2—6321no—
428C2#1909919711yescharacteristic
429C2#1909936211yescharacteristic
430C2#1909936711yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#468×C79C2
socleC22×C79C22×D4
hypercenter#468D79
hypocenterC79#3273
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#14579189C2semidirect
2. C2×#14579188C2semidirect
3. #19099210C2semidirect
4. #19099204C2semidirect
5. #19098944C2semidirect
6. #19098810C2semidirect
7. #19098781C2semidirect
8. #19098777C2semidirect
9. #19098728C2semidirect
10. #19098723C2semidirect
11. #19098698C2semidirect
12. #19098696C2semidirect
13. #19098645C2semidirect
14. #19098639C2semidirect
15. #468×C79C2semidirect
18. C22×D316C22semidirect
19. C2×D4×D79C22semidirect
22. C2×#11929614C22semidirect
23. C2×#11929613C22semidirect
24. C2×#11929613C22semidirect
25. C2×#11929611C22semidirect
30. C2×#11929607C22semidirect
31. #14579150C22semidirect
32. #14579148C22semidirect
35. #14579141C22semidirect
41. #14579123C22semidirect
42. #14579123C22semidirect
46. Dic79⋊C8C22semidirect
47. #14579084C22semidirect
48. #14579081C22semidirect
49. #14579081C22semidirect
50. #14579081C22semidirect
51. C22⋊(C79⋊C8)C22semidirect
52. (C2×D79)⋊C8C22semidirect
53. C8×Dic79C22semidirect
54. C2×SD16×C79C22semidirect
55. C2×M16×C79C22semidirect
56. C22⋊Q8×C79C22semidirect
58. #107×C79C22semidirect
59. #103×C79C22semidirect
60. #102×C79C22semidirect
91. D632D4semidirect
216. C79#3273semidirect
223. #468D79semidirect
242. C2×SD16C2×D79semidirect
248. C2×M16C2×D79semidirect
254. C22⋊Q8C2×D79semidirect
266. #107C2×D79semidirect
269. #103C2×D79semidirect
273. #102C2×D79semidirect