Finite Group Databasebeta

← #23774891

Subgroups — #23774891

Order 10112.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579187C211yesmaximal, characteristic, complemented
2C22×#11929612C211yesmaximal, characteristic, complemented
3#19099222C211yesmaximal, characteristic, complemented
4#19098950C211yesmaximal, characteristic, complemented
5#19098807C211yesmaximal, characteristic, complemented
6#19098797C211yesmaximal, characteristic, complemented
7#19098778C211yesmaximal, characteristic, complemented
8#19098760C211yesmaximal, characteristic, complemented
9#19098714C211yesmaximal, characteristic, complemented
10#19098706C211yesmaximal, characteristic, complemented
11#19098701C211yesmaximal, characteristic, complemented
12#19098697C211yesmaximal, characteristic, complemented
13#19098663C211yesmaximal, characteristic, complemented
14#19098635C211yesmaximal, characteristic, complemented
15D42×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic, complemented
17C22×Dic158C2211yescharacteristic, complemented
18#14579187—24no—
19C2×#11929612—24no—
20C2×#11929612C2211yescharacteristic
21C2×#11929612C2211yescharacteristic
22C2×#11929612C2211yescharacteristic, complemented
23C2×#11929612C2211yescharacteristic, complemented
24C2×#11929612C2211yescharacteristic, complemented
25C2×#11929612C2211yescharacteristic, complemented
26C2×#11929609C2211yescharacteristic
27C2×#11929609C2211yescharacteristic, complemented
28C2×#11929609C2211yescharacteristic, complemented
29C2×#11929608C2211yescharacteristic, complemented
30C22×C79⋊C8C2211yescharacteristic, complemented
31#14579149C2211yescharacteristic, complemented
32#14579147—21no—
33#14579140C2211yescharacteristic, complemented
34#14579139—21no—
35#14579135C2211yescharacteristic, complemented
36#14579133—21no—
37C4×Dic158C2211yescharacteristic, complemented
38(C22⋊D79)⋊C4—21no—
39#14579094C2211yescharacteristic, complemented
40C4⋊(C79⋊C8)C2211yescharacteristic, complemented
41#14579084C2211yescharacteristic, complemented
42#14579084C2211yescharacteristic, complemented
43#14579082C2211yescharacteristic
44#14579082C2211yescharacteristic, complemented
45#14579082C2211yescharacteristic, complemented
46#14579081C2211yescharacteristic, complemented
47C22⋊(C79⋊C8)C2211yescharacteristic, complemented
48C22⋊(C79⋊C8)C2211yescharacteristic, complemented
49#14579072C2211yescharacteristic, complemented
50C22×D4×C79—21no—
51C22×D4×C79C2211yescharacteristic
52C22×D4×C79C2211yescharacteristic
53#127×C79C2211yescharacteristic
54#121×C79—21no—
55#121×C79C2211yescharacteristic
56#121×C79C2211yescharacteristic
57#120×C79—21no—
58#120×C79—21no—
59C4×D4×C79C2211yescharacteristic
60C4×D4×C79C2211yescharacteristic
61#11929624—22no—
62#11929624—41no—
63C2×Dic158—22no—
64C2×Dic158—21no—
65C2×Dic158—41no—
66C2×Dic158C2311yescharacteristic
67C2×Dic158C2311yescharacteristic
68C2×D316C2311yescharacteristic
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71C22×Dic79—21no—
72C2×C4×D79—21no—
73#11929612—22no—
74#11929612—22no—
75#11929612—22no—
76#11929612—22no—
77#11929612—41no—
78#11929612D414yescomplemented
79#11929609—22no—
80#11929609—22no—
81#11929609—41no—
82#11929608—22no—
83C2×C79⋊C8—22no—
84C2×C79⋊C8C2311yescharacteristic
85C2×C79⋊C8C2311yescharacteristic
86C2×C79⋊C8C2311yescharacteristic
87C2×C79⋊C8C2311yescharacteristic
88C4⋊Dic79C2311yescharacteristic
89Dic79⋊C4—21no—
90Dic79⋊C4—21no—
91C22⋊Dic79—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95C4×Dic79—21no—
96C24×C79—21no—
97C24×C79—21no—
98C2×D4×C79—22no—
99C2×D4×C79—22no—
100C2×D4×C79—21no—
101C2×D4×C79—21no—
102C2×D4×C79—21no—
103C2×D4×C79—21no—
104C2×D4×C79—21no—
105C2×D4×C79—21no—
106C2×D4×C79—41no—
107C2×D4×C79—41no—
108C2×D4×C79—44no—
109C2×D4×C79D411yescharacteristic
110C2×D4×C79C2311yescharacteristic
111C2×D4×C79C2311yescharacteristic
112C2×D4×C79C2311yescharacteristic
113C22×C4×C79—21no—
114C22×C4×C79C2311yescharacteristic
115C22×C4×C79C2311yescharacteristic
116C4⋊C4×C79D411yescharacteristic
117C4⋊C4×C79C2311yescharacteristic
118C22⋊C4×C79—21no—
119C22⋊C4×C79—21no—
120C22⋊C4×C79—21no—
121C22⋊C4×C79D411yescharacteristic
122C22⋊C4×C79D411yescharacteristic
123C42×C79C2311yescharacteristic
124C23×C79—21no—
125C23×C79—21no—
126C23×C79—21no—
127C23×C79—42no—
128C23×C79—42no—
129C23×C79—42no—
130C23×C79—42no—
131C23×C79—81no—
132C23×C79—81no—
133C23×C79C2×D411yescharacteristic
134C23×C79C2×D411yescharacteristic
135C22×D79—21no—
136D4×C79—22no—
137D4×C79—21no—
138D4×C79—21no—
139D4×C79—21no—
140D4×C79—21no—
141D4×C79—21no—
142D4×C79—42no—
143D4×C79—42no—
144D4×C79—42no—
145D4×C79—42no—
146D4×C79—42no—
147D4×C79—81no—
148D4×C79C2×D412yes—
149C2×C4×C79—21no—
150C2×C4×C79—21no—
151C2×C4×C79—21no—
152C2×C4×C79—21no—
153C2×C4×C79—21no—
154C2×C4×C79—42no—
155C2×C4×C79C2×D411yescharacteristic
156C2×C4×C79C2×D411yescharacteristic
157C2×C4×C79C2×D411yescharacteristic
158C2×C4×C79C2×D411yescharacteristic
159C2×C4×C79C2411yescharacteristic
160C22⋊D79—42no—
161C22⋊D79—42no—
162C2×Dic79—21no—
163C2×Dic79—21no—
164C2×Dic79—21no—
165C2×Dic79—42no—
166D316—21no—
167D316—21no—
168C4×D79—42no—
169Dic158—21no—
170Dic158—21no—
171Dic158—21no—
172Dic158—42no—
173Dic158C2×D412yescomplemented
174C79⋊C8—21no—
175C79⋊C8—21no—
176C79⋊C8—21no—
177C79⋊C8C2×D412yescomplemented
178C22×C79—21no—
179C22×C79—21no—
180C22×C79—21no—
181C22×C79—22no—
182C22×C79—21no—
183C22×C79—21no—
184C22×C79—41no—
185C22×C79—41no—
186C22×C79—41no—
187C22×C79—41no—
188C22×C79—41no—
189C22×C79—41no—
190C22×C79—41no—
191C22×C79—41no—
192C22×C79—84no—
193C22×C79—84no—
194C22×C79AGL(1,ℤ/8)12yescomplemented
195C22×C79C22×D411yescharacteristic
196C2×D79—41no—
197C2×D79—41no—
198C2×D79—41no—
199C4×C79—21no—
200C4×C79—21no—
201C4×C79—21no—
202C4×C79—21no—
203C4×C79—41no—
204C4×C79C22×D411yescharacteristic
205C4×C79H(5,𝔽2)11yescharacteristic
206Dic79—22no—
207Dic79—41no—
208Dic79—41no—
209C2×C79—22no—
210C2×C79—41no—
211C2×C79—42no—
212C2×C79—81no—
213C2×C79—81no—
214C2×C79D4211yescharacteristic
215C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
216C2×C79#57711yescharacteristic
217D79—81no—
218#3265—791nomaximal, Sylow
219C79#326511yescharacteristic, complemented, Sylow
220C2×AGL(1,ℤ/8)—791no—
221C22×SD16—791no—
222#548—791no—
223D42D7911yescharacteristic, complemented
224#496—791no—
225#468—791no—
226#466—791no—
227#463—791no—
228#460—791no—
229#450—791no—
230#449—791no—
231#448—791no—
232#447—791no—
233#440—791no—
234#435—791no—
235C2×#41—791no—
236C22×Q8—791no—
237C22×D4—21no—
238C22×D4C2×D7911yescharacteristic
239C22×D4C2×D7911yescharacteristic
240AGL(1,ℤ/8)—1584no—
241C2×SD16—791no—
242C2×SD16—791no—
243C2×SD16—791no—
244C2×SD16—791no—
245C2×SD16—791no—
246C2×SD16—791no—
247C2×SD16—1584no—
248C2×D8—791no—
249C2×D8—791no—
250C2×D8—791no—
251C2×M16—791no—
252C22×C8—791no—
253#127C2×D7911yescharacteristic
254#124—791no—
255#124—1581no—
256C22⋊Q8—791no—
257C22⋊Q8—1581no—
258#121—21no—
259#121—791no—
260#121—1581no—
261#121C2×D7911yescharacteristic
262#121C2×D7911yescharacteristic
263#120—21no—
264#120—21no—
265C4×Q8—791no—
266C4×D4—1581no—
267C4×D4C2×D7911yescharacteristic
268C4×D4C2×D7911yescharacteristic
269#107—791no—
270C4⋊C8—791no—
271#103—791no—
272#103—791no—
273#102—791no—
274#102—791no—
275#102—791no—
276#102—791no—
277C22⋊C8—791no—
278C22⋊C8—791no—
279#97—791no—
280C24—21no—
281C24—21no—
282#41—3161no—
283#41—1582no—
284C2×Q8—3161no—
285C2×Q8—791no—
286C2×Q8—791no—
287C2×Q8—1582no—
288C2×Q8—1581no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—44no—
300C2×D4—791no—
301C2×D4—1581no—
302C2×D4—1581no—
303C2×D4C22⋊D7911yescharacteristic
304C2×D4C22×D7911yescharacteristic
305C2×D4C22×D7911yescharacteristic
306C2×D4C22×D7911yescharacteristic
307C22×C4—21no—
308C22×C4—1581no—
309C22×C4—1581no—
310C22×C4C22×D7911yescharacteristic
311C22×C4C22×D7911yescharacteristic
312SD16—3161no—
313SD16—794no—
314SD16—1582no—
315SD16—1582no—
316SD16—1582no—
317SD16—1582no—
318D8—3161no—
319D8—1582no—
320D8—1582no—
321M16—1582no—
322C2×C8—791no—
323C2×C8—791no—
324C2×C8—791no—
325C2×C8—791no—
326C2×C8—1582no—
327C4⋊C4—791no—
328C4⋊C4—1581no—
329C4⋊C4—1581no—
330C4⋊C4C22⋊D7911yescharacteristic
331C4⋊C4C22×D7911yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—1581no—
336C22⋊C4—1581no—
337C22⋊C4—1581no—
338C22⋊C4—1581no—
339C22⋊C4C22⋊D7911yescharacteristic
340C22⋊C4C22⋊D7911yescharacteristic
341C42—1581no—
342C42C22×D7911yescharacteristic
343C23—21no—
344C23—21no—
345C23—21no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—81no—
351C23—81no—
352C23—1581no—
353C23C2×C22⋊D7911yescharacteristic
354C23C2×C22⋊D7911yescharacteristic
355Q8—3162no—
356Q8—792no—
357Q8—1581no—
358Q8—1581no—
359Q8—1581no—
360D4—22no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—21no—
366D4—42no—
367D4—42no—
368D4—42no—
369D4—42no—
370D4—42no—
371D4—81no—
372D4—3162no—
373D4—3162no—
374D4—1581no—
375D4—1581no—
376D4D4×D7912yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—3162no—
384C2×C4—3162no—
385C2×C4—1581no—
386C2×C4—1581no—
387C2×C4—1581no—
388C2×C4C2×C22⋊D7911yescharacteristic
389C2×C4C2×C22⋊D7911yescharacteristic
390C2×C4C2×C22⋊D7911yescharacteristic
391C2×C4C2×C22⋊D7911yescharacteristic
392C2×C4C23×D7911yescharacteristic
393C8—792no—
394C8—1581no—
395C8—1581no—
396C8—1581no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—22no—
401C22—21no—
402C22—21no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—84no—
412C22—84no—
413C22—3161no—
414C22—3161no—
415C22—3161no—
416C22#1457918712yescomplemented
417C22C22×C22⋊D7911yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—41no—
423C4—3161no—
424C4—3161no—
425C4—1582no—
426C4C2×D4×D7911yescharacteristic
427C4#1457920611yescharacteristic
428C2—22no—
429C2—41no—
430C2—42no—
431C2—81no—
432C2—81no—
433C2—6321no—
434C2D4×C22⋊D7911yescharacteristic
435C2C2×#1457918711yescharacteristic
436C2#1909937411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingD42×C79C2
socleC22×C79C22×D4
hypercenterD42D79
hypocenterC79#3265
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#14579187C2semidirect
2. C22×#11929612C2semidirect
3. #19099222C2semidirect
4. #19098950C2semidirect
5. #19098807C2semidirect
6. #19098797C2semidirect
7. #19098778C2semidirect
8. #19098760C2semidirect
9. #19098714C2semidirect
10. #19098706C2semidirect
11. #19098701C2semidirect
12. #19098697C2semidirect
13. #19098663C2semidirect
14. #19098635C2semidirect
15. D42×C79C2semidirect
16. C2×#11929624C22semidirect
17. C22×Dic158C22semidirect
22. C2×#11929612C22semidirect
23. C2×#11929612C22semidirect
24. C2×#11929612C22semidirect
25. C2×#11929612C22semidirect
27. C2×#11929609C22semidirect
28. C2×#11929609C22semidirect
29. C2×#11929608C22semidirect
30. C22×C79⋊C8C22semidirect
31. #14579149C22semidirect
33. #14579140C22semidirect
35. #14579135C22semidirect
37. C4×Dic158C22semidirect
39. #14579094C22semidirect
40. C4⋊(C79⋊C8)C22semidirect
41. #14579084C22semidirect
42. #14579084C22semidirect
44. #14579082C22semidirect
45. #14579082C22semidirect
46. #14579081C22semidirect
47. C22⋊(C79⋊C8)C22semidirect
48. C22⋊(C79⋊C8)C22semidirect
49. #14579072C22semidirect
78. #11929612D4semidirect
173. Dic158C2×D4semidirect
177. C79⋊C8C2×D4semidirect
194. C22×C79AGL(1,ℤ/8)semidirect
219. C79#3265semidirect
223. D42D79semidirect
416. C22#14579187semidirect